AASHTO LRFD BRIDGE
DESIGN SPECIFICATIONS
Customary U.S. Units Sixth Edition 2012
ISBN: 978-1-56051-555-5
Publication Code: LRFDUS-6-I1
© 2013 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2013
Revision
444 North Capitol Street, NW, Suite 249
Washington, DC 20001
202-624-5800 phone/202-624-5806 fax
www.transportation.org
© 2013 by the American Association of State Highway and Transportation Officials. All rights reserved. Duplication is
a violation of applicable law.
ISBN: 978-1-56051-555-5
Publication Code: LRFDUS-6-I1
© 2013 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2013
Revision
American Association of State Highway and Transportation Officials
444 North Capitol Street, NW Suite 249
Washington, DC 20001
202-624-5800 phone/202-624-5806 fax
www.transportation.org
© 2012 by the American Association of State Highway and Transportation Officials. All rights reserved. Duplication is a
violation of applicable law.
ISBN: 978-1-56051-523-4
Pub Code: LRFDUS-6
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
PREFACE AND
ABBREVIATED TABLE OF CONTENTS
The AASHTO LRFD Bridge Design Specifications, Sixth Edition contains the following 15 sections and
an index:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Introduction
General Design and Location Features
Loads and Load Factors
Structural Analysis and Evaluation
Concrete Structures
Steel Structures
Aluminum Structures
Wood Structures
Decks and Deck Systems
Foundations
Abutments, Piers, and Walls
Buried Structures and Tunnel Liners
Railings
Joints and Bearings
Design of Sound Barriers
Index
Detailed Tables of Contents precede each section. The last article of each section is a list of references displayed
alphabetically by author.
Figures, tables, and equations are denoted by their home article number and an extension, for example 1.2.3.4.5-1
wherever they are cited. In early editions, when they were referenced in their home article or its commentary, these objects
were identified only by the extension. For example, in Article 1.2.3.4.5, Eq. 1.2.3.4.5-2 would simply have been called
“Eq. 2.” The same convention applies to figures and tables. Starting with this edition, these objects are identified by their
whole nomenclature throughout the text, even within their home articles. This change was to increase the speed and
accuracy of electronic production (i.e., CDs and downloadable files) with regard to linking citations to objects.
Please note that the AASHTO materials standards (starting with M or T) cited throughout the LRFD Specifications
can be found in Standard Specifications for Transportation Materials and Methods of Sampling and Testing, adopted by
the AASHTO Highway Subcommittee on Materials. The individual standards are also available as downloads on the
AASHTO Bookstore, https://bookstore.transportation.org. Unless otherwise indicated, these citations refer to the current
edition. ASTM materials specifications are also cited and have been updated to reflect ASTM’s revised coding system,
e.g., spaces removed between the letter and number.
ix
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 1: INTRODUCTION
TABLE OF CONTENTS
1
1.1—SCOPE OF THE SPECIFICATIONS .................................................................................................................. 1-1
1.2—DEFINITIONS ..................................................................................................................................................... 1-2
1.3—DESIGN PHILOSOPHY ..................................................................................................................................... 1-3
1.3.1—General ....................................................................................................................................................... 1-3
1.3.2—Limit States ................................................................................................................................................ 1-3
1.3.2.1—General............................................................................................................................................. 1-3
1.3.2.2—Service Limit State........................................................................................................................... 1-4
1.3.2.3—Fatigue and Fracture Limit State ...................................................................................................... 1-4
1.3.2.4—Strength Limit State ......................................................................................................................... 1-4
1.3.2.5—Extreme Event Limit States ............................................................................................................. 1-5
1.3.3—Ductility ..................................................................................................................................................... 1-5
1.3.4—Redundancy ............................................................................................................................................... 1-6
1.3.5—Operational Importance.............................................................................................................................. 1-7
1.4—REFERENCES..................................................................................................................................................... 1-7
1-i
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 1
INTRODUCTION
1
1.1—SCOPE OF THE SPECIFICATIONS
C1.1
The provisions of these Specifications are intended for
the design, evaluation, and rehabilitation of both fixed and
movable highway bridges. Mechanical, electrical, and
special vehicular and pedestrian safety aspects of movable
bridges, however, are not covered. Provisions are not
included for bridges used solely for railway, rail-transit, or
public utilities. For bridges not fully covered herein, the
provisions of these Specifications may be applied, as
augmented with additional design criteria where required.
These Specifications are not intended to supplant
proper training or the exercise of judgment by the
Designer, and state only the minimum requirements
necessary to provide for public safety. The Owner or the
Designer may require the sophistication of design or the
quality of materials and construction to be higher than the
minimum requirements.
The concepts of safety through redundancy and
ductility and of protection against scour and collision are
emphasized.
The design provisions of these Specifications employ
the Load and Resistance Factor Design (LRFD)
methodology. The factors have been developed from the
theory of reliability based on current statistical knowledge
of loads and structural performance.
Methods of analysis other than those included in
previous Specifications and the modeling techniques
inherent in them are included, and their use is encouraged.
Seismic design shall be in accordance with either the
provisions in these Specifications or those given in the
AASHTO Guide Specifications for LRFD Seismic Bridge
Design.
The commentary is not intended to provide a complete
historical background concerning the development of these
or previous Specifications, nor is it intended to provide a
detailed summary of the studies and research data
reviewed in formulating the provisions of the
Specifications. However, references to some of the
research data are provided for those who wish to study the
background material in depth.
The commentary directs attention to other documents
that provide suggestions for carrying out the requirements
and intent of these Specifications. However, those
documents and this commentary are not intended to be a
part of these Specifications.
Construction specifications consistent with these
design specifications are the AASHTO LRFD Bridge
Construction Specifications. Unless otherwise specified,
the Materials Specifications referenced herein are the
AASHTO Standard Specifications for Transportation
Materials and Methods of Sampling and Testing.
The term “notional” is often used in these
Specifications to indicate an idealization of a physical
phenomenon, as in “notional load” or “notional
resistance.” Use of this term strengthens the separation of
an engineer's “notion” or perception of the physical world
in the context of design from the physical reality itself.
The term “shall” denotes a requirement for
compliance with these Specifications.
The term “should” indicates a strong preference for a
given criterion.
The term “may” indicates a criterion that is usable, but
other local and suitably documented, verified, and
approved criterion may also be used in a manner consistent
with the LRFD approach to bridge design.
1-1
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
1-2
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
1.2—DEFINITIONS
Bridge—Any structure having an opening not less than 20.0 ft that forms part of a highway or that is located over or under
a highway.
Collapse—A major change in the geometry of the bridge rendering it unfit for use.
Component—Either a discrete element of the bridge or a combination of elements requiring individual design
consideration.
Design—Proportioning and detailing the components and connections of a bridge.
Design Life—Period of time on which the statistical derivation of transient loads is based: 75 yr for these Specifications.
Ductility—Property of a component or connection that allows inelastic response.
Engineer—Person responsible for the design of the bridge and/or review of design-related field submittals such as erection
plans.
Evaluation—Determination of load-carrying capacity of an existing bridge.
Extreme Event Limit States—Limit states relating to events such as earthquakes, ice load, and vehicle and vessel collision,
with return periods in excess of the design life of the bridge.
Factored Load—The nominal loads multiplied by the appropriate load factors specified for the load combination under
consideration.
Factored Resistance—The nominal resistance multiplied by a resistance factor.
Fixed Bridge—A bridge with a fixed vehicular or navigational clearance.
Force Effect—A deformation, stress, or stress resultant (i.e., axial force, shear force, torsional, or flexural moment) caused
by applied loads, imposed deformations, or volumetric changes.
Limit State—A condition beyond which the bridge or component ceases to satisfy the provisions for which it was designed.
Load and Resistance Factor Design (LRFD)—A reliability-based design methodology in which force effects caused by
factored loads are not permitted to exceed the factored resistance of the components.
Load Factor—A statistically-based multiplier applied to force effects accounting primarily for the variability of loads, the
lack of accuracy in analysis, and the probability of simultaneous occurrence of different loads, but also related to the
statistics of the resistance through the calibration process.
Load Modifier—A factor accounting for ductility, redundancy, and the operational classification of the bridge.
Model—An idealization of a structure for the purpose of analysis.
Movable Bridge—A bridge with a variable vehicular or navigational clearance.
Multiple-Load-Path Structure—A structure capable of supporting the specified loads following loss of a main loadcarrying component or connection.
Nominal Resistance—Resistance of a component or connection to force effects, as indicated by the dimensions specified in
the contract documents and by permissible stresses, deformations, or specified strength of materials.
Owner—Person or agency having jurisdiction over the bridge.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
SECTION 1: INTRODUCTION
1-3
Regular Service—Condition excluding the presence of special permit vehicles, wind exceeding 55 mph, and extreme
events, including scour.
Rehabilitation—A process in which the resistance of the bridge is either restored or increased.
Resistance Factor—A statistically-based multiplier applied to nominal resistance accounting primarily for variability of
material properties, structural dimensions and workmanship, and uncertainty in the prediction of resistance, but also
related to the statistics of the loads through the calibration process.
Service Life—The period of time that the bridge is expected to be in operation.
Service Limit States—Limit states relating to stress, deformation, and cracking under regular operating conditions.
Strength Limit States—Limit states relating to strength and stability during the design life.
1.3—DESIGN PHILOSOPHY
1.3.1—General
C1.3.1
Bridges shall be designed for specified limit states to
achieve the objectives of constructibility, safety, and
serviceability, with due regard to issues of inspectability,
economy, and aesthetics, as specified in Article 2.5.
Regardless of the type of analysis used, Eq. 1.3.2.1-1
shall be satisfied for all specified force effects and
combinations thereof.
The limit states specified herein are intended to
provide for a buildable, serviceable bridge, capable of
safely carrying design loads for a specified lifetime.
The resistance of components and connections is
determined, in many cases, on the basis of inelastic
behavior, although the force effects are determined by
using elastic analysis. This inconsistency is common to
most current bridge specifications as a result of incomplete
knowledge of inelastic structural action.
1.3.2—Limit States
1.3.2.1—General
C1.3.2.1
Each component and connection shall satisfy
Eq. 1.3.2.1-1 for each limit state, unless otherwise
specified. For service and extreme event limit states,
resistance factors shall be taken as 1.0, except for bolts, for
which the provisions of Article 6.5.5 shall apply, and for
concrete columns in Seismic Zones 2, 3, and 4, for which
the provisions of Articles 5.10.11.3 and 5.10.11.4.1b shall
apply. All limit states shall be considered of equal
importance.
ηi γ i Qi ≤ φRn = Rr
(1.3.2.1-1)
in which:
For loads for which a maximum value of γi is appropriate:
ηi = ηD ηR ηI ≥ 0.95
(1.3.2.1-2)
For loads for which a minimum value of γi is appropriate:
ηi =
1
≤ 1.0
η D ηR ηI
Eq. 1.3.2.1-1 is the basis of LRFD methodology.
Assigning resistance factor φ = 1.0 to all nonstrength
limit states is a default, and may be over-ridden by
provisions in other Sections.
Ductility, redundancy, and operational classification
are considered in the load modifier η. Whereas the first
two directly relate to physical strength, the last concerns
the consequences of the bridge being out of service. The
grouping of these aspects on the load side of
Eq. 1.3.2.1-1 is, therefore, arbitrary. However, it
constitutes a first effort at codification. In the absence of
more precise information, each effect, except that for
fatigue and fracture, is estimated as ±5 percent,
accumulated geometrically, a clearly subjective
approach. With time, improved quantification of
ductility, redundancy, and operational classification, and
their interaction with system reliability, may be attained,
possibly leading to a rearrangement of Eq. 1.3.2.1-1, in
which these effects may appear on either side of the
equation or on both sides.
(1.3.2.1-3)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
1-4
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
where:
γi
=
load factor: a statistically based multiplier applied
to force effects
φ
=
resistance factor: a statistically based multiplier
applied to nominal resistance, as specified in
Sections 5, 6, 7, 8, 10, 11, and 12
ηi
=
load modifier: a factor relating to ductility,
redundancy, and operational classification
ηD =
a factor relating to ductility, as specified in
Article 1.3.3
ηR =
a factor relating to redundancy as specified in
Article 1.3.4
ηI
a factor relating to operational classification as
specified in Article 1.3.5
=
Qi =
force effect
Rn =
nominal resistance
Rr =
factored resistance: φRn
1.3.2.2—Service Limit State
The service limit state shall be taken as restrictions on
stress, deformation, and crack width under regular service
conditions.
1.3.2.3—Fatigue and Fracture Limit State
The fatigue limit state shall be taken as restrictions on
stress range as a result of a single design truck occurring at
the number of expected stress range cycles.
The fracture limit state shall be taken as a set of
material toughness requirements of the AASHTO
Materials Specifications.
1.3.2.4—Strength Limit State
Strength limit state shall be taken to ensure that
strength and stability, both local and global, are provided
to resist the specified statistically significant load
combinations that a bridge is expected to experience in its
design life.
The influence of η on the girder reliability index, β,
can be estimated by observing its effect on the minimum
values of β calculated in a database of girder-type bridges.
Cellular structures and foundations were not a part of the
database; only individual member reliability was
considered. For discussion purposes, the girder bridge data
used in the calibration of these Specifications was
modified by multiplying the total factored loads by
η = 0.95, 1.0, 1.05, and 1.10. The resulting minimum
values of β for 95 combinations of span, spacing, and type
of construction were determined to be approximately 3.0,
3.5, 3.8, and 4.0, respectively. In other words, using
η > 1.0 relates to a β higher than 3.5.
A further approximate representation of the effect of η
values can be obtained by considering the percent of
random normal data less than or equal to the mean value
plus λ σ, where λ is a multiplier, and σ is the standard
deviation of the data. If λ is taken as 3.0, 3.5, 3.8, and 4.0,
the percent of values less than or equal to the mean value
plus λ σ would be about 99.865 percent, 99.977 percent,
99.993 percent, and 99.997 percent, respectively.
The Strength I Limit State in the AASHTO LRFD
Design Specifications has been calibrated for a target
reliability index of 3.5 with a corresponding probability of
exceedance of 2.0E-04 during the 75-yr design life of the
bridge. This 75-yr reliability is equivalent to an annual
probability of exceedance of 2.7E-06 with a corresponding
annual target reliability index of 4.6. Similar calibration
efforts for the Service Limit States are underway. Return
periods for extreme events are often based on annual
probability of exceedance and caution must be used when
comparing reliability indices of various limit states.
C1.3.2.2
The service limit state provides certain experiencerelated provisions that cannot always be derived solely
from strength or statistical considerations.
C1.3.2.3
The fatigue limit state is intended to limit crack
growth under repetitive loads to prevent fracture during the
design life of the bridge.
C1.3.2.4
The strength limit state considers stability or yielding
of each structural element. If the resistance of any element,
including splices and connections, is exceeded, it is
assumed that the bridge resistance has been exceeded. In
fact, in multigirder cross-sections there is significant
elastic reserve capacity in almost all such bridges beyond
such a load level. The live load cannot be positioned to
maximize the force effects on all parts of the cross-section
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2012
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SECTION 1: INTRODUCTION
1-5
simultaneously. Thus, the flexural resistance of the bridge
cross-section typically exceeds the resistance required for
the total live load that can be applied in the number of
lanes available. Extensive distress and structural damage
may occur under strength limit state, but overall structural
integrity is expected to be maintained.
C1.3.2.5
1.3.2.5—Extreme Event Limit States
The extreme event limit state shall be taken to ensure
the structural survival of a bridge during a major
earthquake or flood, or when collided by a vessel, vehicle,
or ice flow, possibly under scoured conditions.
Extreme event limit states are considered to be unique
occurrences whose return period may be significantly
greater than the design life of the bridge.
1.3.3—Ductility
C1.3.3
The structural system of a bridge shall be proportioned
and detailed to ensure the development of significant and
visible inelastic deformations at the strength and extreme
event limit states before failure.
Energy-dissipating devices may be substituted for
conventional ductile earthquake resisting systems and the
associated methodology addressed in these Specifications
or in the AASHTO Guide Specifications for Seismic Design
of Bridges.
For the strength limit state:
The response of structural components or connections
beyond the elastic limit can be characterized by either
brittle or ductile behavior. Brittle behavior is undesirable
because it implies the sudden loss of load-carrying
capacity immediately when the elastic limit is exceeded.
Ductile behavior is characterized by significant inelastic
deformations before any loss of load-carrying capacity
occurs. Ductile behavior provides warning of structural
failure by large inelastic deformations. Under repeated
seismic loading, large reversed cycles of inelastic
deformation dissipate energy and have a beneficial effect
on structural survival.
If, by means of confinement or other measures, a
structural component or connection made of brittle
materials can sustain inelastic deformations without
significant loss of load-carrying capacity, this component
can be considered ductile. Such ductile performance shall
be verified by testing.
In order to achieve adequate inelastic behavior the
system should have a sufficient number of ductile
members and either:
ηD ≥
1.05 for nonductile components and connections
=
1.00 for conventional designs and details
complying with these Specifications
≥
0.95 for components and connections for which
additional ductility-enhancing measures have
been specified beyond those required by these
Specifications
For all other limit states:
ηD =
1.00
•
Joints and connections that are also ductile and can
provide energy dissipation without loss of capacity;
or
•
Joints and connections that have sufficient excess
strength so as to assure that the inelastic response
occurs at the locations designed to provide ductile,
energy absorbing response.
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All rights reserved. Duplication is a violation of applicable law.
2012
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1-6
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Statically ductile, but dynamically nonductile response
characteristics should be avoided. Examples of this
behavior are shear and bond failures in concrete members
and loss of composite action in flexural components.
Past experience indicates that typical components
designed in accordance with these provisions generally
exhibit adequate ductility. Connection and joints require
special attention to detailing and the provision of load
paths.
The Owner may specify a minimum ductility factor as
an assurance that ductile failure modes will be obtained.
The factor may be defined as:
μ=
Δu
Δy
(C1.3.3-1)
where:
Δu =
deformation at ultimate
Δy =
deformation at the elastic limit
The ductility capacity of structural components or
connections may either be established by full- or largescale testing or with analytical models based on
documented material behavior. The ductility capacity for a
structural system may be determined by integrating local
deformations over the entire structural system.
The special requirements for energy dissipating
devices are imposed because of the rigorous demands
placed on these components.
1.3.4—Redundancy
C1.3.4
Multiple-load-path and continuous structures should
be used unless there are compelling reasons not to use
them.
For the strength limit state:
For each load combination and limit state under
consideration, member redundancy classification
(redundant or nonredundant) should be based upon the
member contribution to the bridge safety. Several
redundancy measures have been proposed (Frangopol and
Nakib, 1991).
Single-cell boxes and single-column bents may be
considered nonredundant at the Owner’s discretion. For
prestressed concrete boxes, the number of tendons in each
web should be taken into consideration. For steel crosssections and fracture-critical considerations, see Section 6.
The Manual for Bridge Evaluation (2008) defines
bridge redundancy as “the capability of a bridge structural
system to carry loads after damage to or the failure of one
or more of its members.” System factors are provided for
post-tensioned segmental concrete box girder bridges in
Appendix E of the Guide Manual.
System reliability encompasses redundancy by
considering the system of interconnected components and
members. Rupture or yielding of an individual component
may or may not mean collapse or failure of the whole
structure or system (Nowak, 2000). Reliability indices for
ηR ≥
1.05 for nonredundant members
=
1.00 for conventional levels of redundancy,
foundation elements where φ already accounts for
redundancy as specified in Article 10.5
≥
0.95 for exceptional levels of redundancy beyond
girder continuity and a torsionally-closed crosssection
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2012
Edition
SECTION 1: INTRODUCTION
1-7
entire systems are a subject of ongoing research and are
anticipated to encompass ductility, redundancy, and
member correlation.
For all other limit states:
ηR =
1.00
1.3.5—Operational Importance
C1.3.5
This Article shall apply to the strength and extreme
event limit states only.
The Owner may declare a bridge or any structural
component and connection thereof to be of operational
priority.
Such classification should be done by personnel
responsible for the affected transportation network and
knowledgeable of its operational needs. The definition of
operational priority may differ from Owner to Owner and
network to network. Guidelines for classifying critical or
essential bridges are as follows:
For the strength limit state:
ηI
≥
1.05 for critical or essential bridges
=
1.00 for typical bridges
≥
0.95 for relatively less important bridges.
•
Bridges that are required to be open to all traffic once
inspected after the design event and are usable by
emergency vehicles and for security, defense,
economic, or secondary life safety purposes
immediately after the design event.
•
Bridges that should, as a minimum, be open to
emergency vehicles and for security, defense, or
economic purposes after the design event, and open to
all traffic within days after that event.
Owner-classified bridges may use a value for η < 1.0
based on ADTT, span length, available detour length, or
other rationale to use less stringent criteria.
For all other limit states:
ηI
=
1.00
1.4—REFERENCES
AASHTO. 2010. AASHTO LRFD Bridge Construction Specifications, Third Edition with Interims, LRFDCONS-3-M.
American Association of State Highway and Transportation Officials, Washington, DC.
AASHTO. 2011. AASHTO Guide Specifications for LRFD Seismic Bridge Design, Second Edition, LRFDSEIS-2.
American Association of State Highway and Transportation Officials, Washington, DC.
AASHTO. 2011. The Manual for Bridge Evaluation, Second Edition with Interim, MBE-2-M. American Association of
State Highway and Transportation Officials, Washington, DC.
AASHTO. 2011. Standard Specifications for Transportation Materials and Methods of Sampling and Testing,
31th Edition, HM-31. American Association of State Highway and Transportation Officials, Washington, DC.
Frangopol, D. M., and R. Nakib. 1991. “Redundancy in Highway Bridges.” Engineering Journal, American Institute of
Steel Construction, Chicago, IL, Vol. 28, No. 1, pp. 45–50.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
1-8
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Mertz, D. 2009. “Quantification of Structural Safety of Highway Bridges” (white paper), Annual Probability of Failure.
Internal communication.
Nowak, A., and K. R. Collins. 2000. Reliability of Structures. McGraw–Hill Companies, Inc., New York, NY.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 2: GENERAL DESIGN AND LOCATION FEATURES
TABLE OF CONTENTS
2
2.1—SCOPE ................................................................................................................................................................. 2-1
2.2—DEFINITIONS ..................................................................................................................................................... 2-1
2.3—LOCATION FEATURES .................................................................................................................................... 2-3
2.3.1—Route Location ........................................................................................................................................... 2-3
2.3.1.1—General............................................................................................................................................. 2-3
2.3.1.2—Waterway and Floodplain Crossings ............................................................................................... 2-3
2.3.2—Bridge Site Arrangement ........................................................................................................................... 2-4
2.3.2.1—General............................................................................................................................................. 2-4
2.3.2.2—Traffic Safety ................................................................................................................................... 2-4
2.3.2.2.1—Protection of Structures ......................................................................................................... 2-4
2.3.2.2.2—Protection of Users ................................................................................................................ 2-5
2.3.2.2.3—Geometric Standards .............................................................................................................. 2-5
2.3.2.2.4—Road Surfaces ........................................................................................................................ 2-5
2.3.2.2.5—Vessel Collisions ................................................................................................................... 2-5
2.3.3—Clearances .................................................................................................................................................. 2-6
2.3.3.1—Navigational ..................................................................................................................................... 2-6
2.3.3.2—Highway Vertical ............................................................................................................................. 2-6
2.3.3.3—Highway Horizontal ......................................................................................................................... 2-6
2.3.3.4—Railroad Overpass ............................................................................................................................ 2-6
2.3.4—Environment ............................................................................................................................................... 2-7
2.4—FOUNDATION INVESTIGATION .................................................................................................................... 2-7
2.4.1—General ....................................................................................................................................................... 2-7
2.4.2—Topographic Studies .................................................................................................................................. 2-7
2.5—DESIGN OBJECTIVES....................................................................................................................................... 2-7
2.5.1—Safety ......................................................................................................................................................... 2-7
2.5.2—Serviceability ............................................................................................................................................. 2-8
2.5.2.1—Durability ......................................................................................................................................... 2-8
2.5.2.1.1—Materials ................................................................................................................................ 2-8
2.5.2.1.2—Self-Protecting Measures ....................................................................................................... 2-8
2.5.2.2—Inspectability.................................................................................................................................... 2-9
2.5.2.3—Maintainability ................................................................................................................................. 2-9
2.5.2.4—Rideability........................................................................................................................................ 2-9
2.5.2.5—Utilities ............................................................................................................................................ 2-9
2.5.2.6—Deformations ................................................................................................................................. 2-10
2.5.2.6.1—General ................................................................................................................................ 2-10
2.5.2.6.2—Criteria for Deflection.......................................................................................................... 2-11
2.5.2.6.3—Optional Criteria for Span-to-Depth Ratios ......................................................................... 2-13
2.5.2.7—Consideration of Future Widening ................................................................................................. 2-14
2.5.2.7.1—Exterior Beams on Multibeam Bridges ................................................................................ 2-14
2-i
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
2-ii
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
2.5.2.7.2—Substructure ......................................................................................................................... 2-14
2.5.3—Constructibility .........................................................................................................................................2-14
2.5.4—Economy .................................................................................................................................................. 2-15
2.5.4.1—General ...........................................................................................................................................2-15
2.5.4.2—Alternative Plans ............................................................................................................................ 2-15
2.5.5—Bridge Aesthetics .....................................................................................................................................2-16
2.6—HYDROLOGY AND HYDRAULICS ............................................................................................................... 2-17
2.6.1—General ..................................................................................................................................................... 2-17
2.6.2—Site Data ................................................................................................................................................... 2-18
2.6.3—Hydrologic Analysis .................................................................................................................................2-18
2.6.4—Hydraulic Analysis ...................................................................................................................................2-19
2.6.4.1—General ...........................................................................................................................................2-19
2.6.4.2—Stream Stability .............................................................................................................................. 2-19
2.6.4.3—Bridge Waterway ........................................................................................................................... 2-20
2.6.4.4—Bridge Foundations ........................................................................................................................ 2-20
2.6.4.4.1—General.................................................................................................................................2-20
2.6.4.4.2—Bridge Scour ........................................................................................................................ 2-21
2.6.4.5—Roadway Approaches to Bridge .....................................................................................................2-23
2.6.5—Culvert Location, Length, and Waterway Area ........................................................................................ 2-23
2.6.6—Roadway Drainage ...................................................................................................................................2-24
2.6.6.1—General ...........................................................................................................................................2-24
2.6.6.2—Design Storm..................................................................................................................................2-24
2.6.6.3—Type, Size, and Number of Drains .................................................................................................2-24
2.6.6.4—Discharge from Deck Drains ..........................................................................................................2-25
2.6.6.5—Drainage of Structures.................................................................................................................... 2-25
2.7—BRIDGE SECURITY ........................................................................................................................................2-25
2.7.1—General ..................................................................................................................................................... 2-25
2.7.2—Design Demand ........................................................................................................................................2-26
2.8—REFERENCES ................................................................................................................................................... 2-26
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
SECTION 2
GENERAL DESIGN AND LOCATION FEATURES
2.1—SCOPE
C2.1
Minimum requirements are provided for clearances,
environmental protection, aesthetics, geological studies,
economy, rideability, durability, constructibility,
inspectability, and maintainability. Minimum requirements
for traffic safety are referenced.
Minimum requirements for drainage facilities and selfprotecting measures against water, ice, and water-borne
salts are included.
In recognition that many bridge failures have been
caused by scour, hydrology and hydraulics are covered in
detail.
2
2.2—DEFINITIONS
This Section is intended to provide the Designer with
sufficient information to determine the configuration and
overall dimensions of a bridge.
Aggradation—A general and progressive buildup or raising of the longitudinal profile of the channel bed as a result of
sediment deposition.
Check Flood for Bridge Scour—Check flood for scour. The flood resulting from storm, storm surge, and/or tide having a
flow rate in excess of the design flood for scour, but in no case a flood with a recurrence interval exceeding the typically
used 500 yr. The check flood for bridge scour is used in the investigation and assessment of a bridge foundation to
determine whether the foundation can withstand that flow and its associated scour and remain stable with no reserve. See
also superflood.
Clear Zone—An unobstructed, relatively flat area beyond the edge of the traveled way for the recovery of errant vehicles.
The traveled way does not include shoulders or auxiliary lanes.
Clearance—An unobstructed horizontal or vertical space.
Degradation—A general and progressive lowering of the longitudinal profile of the channel bed as a result of long-term
erosion.
Design Discharge—Maximum flow of water a bridge is expected to accommodate without exceeding the adopted design
constraints.
Design Flood for Bridge Scour—The flood flow equal to or less than the 100-yr flood that creates the deepest scour at
bridge foundations. The highway or bridge may be inundated at the stage of the design flood for bridge scour. The worstcase scour condition may occur for the overtopping flood as a result of the potential for pressure flow.
Design Flood for Waterway Opening—The peak discharge, volume, stage, or wave crest elevation and its associated
probability of exceedence that are selected for the design of a highway or bridge over a watercourse or floodplain. By
definition, the highway or bridge will not be inundated at the stage of the design flood for the waterway opening.
Detention Basin—A storm water management facility that impounds runoff and temporarily discharges it through a
hydraulic outlet structure to a downstream conveyance system.
Drip Groove—Linear depression in the bottom of components to cause water flowing on the surface to drop.
Five-Hundred-Year Flood—The flood due to storm and/or tide having a 0.2 percent chance of being equaled or exceeded
in any given year.
General or Contraction Scour—Scour in a channel or on a floodplain that is not localized at a pier or other obstruction to
flow. In a channel, general/contraction scour usually affects all or most of the channel width and is typically caused by a
contraction of the flow.
Hydraulics—The science concerned with the behavior and flow of liquids, especially in pipes and channels.
2-1
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2012
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2-2
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Hydrology—The science concerned with the occurrence, distribution, and circulation of water on the earth, including
precipitation, runoff, and groundwater.
Local Scour—Scour in a channel or on a floodplain that is localized at a pier, abutment, or other obstruction to flow.
Mixed Population Flood—Flood flows derived from two or more causative factors, e.g., a spring tide driven by hurricanegenerated onshore winds or rainfall on a snowpack.
One-Hundred-Year Flood—The flood due to storm and/or tide having a 1 percent chance of being equaled or exceeded in
any given year.
Overtopping Flood—The flood flow that, if exceeded, results in flow over a highway or bridge, over a watershed divide, or
through structures provided for emergency relief. The worst-case scour condition may be caused by the overtopping flood.
Relief Bridge—An opening in an embankment on a floodplain to permit passage of overbank flow.
River Training Structure—Any configuration constructed in a stream or placed on, adjacent to, or in the vicinity of a
streambank to deflect current, induce sediment deposition, induce scour, or in some other way alter the flow and sediment
regimens of the stream.
Scupper—A device to drain water through the deck.
Sidewalk Width—Unobstructed space for exclusive pedestrian use between barriers or between a curb and a barrier.
Spring Tide—A tide of increased range that occurs about every two weeks when the moon is full or new.
Stable Channel—A condition that exists when a stream has a bed slope and cross-section that allows its channel to
transport the water and sediment delivered from the upstream watershed without significant degradation, aggradation, or
bank erosion.
Stream Geomorphology—The study of a stream and its floodplain with regard to its land forms, the general configuration
of its surface, and the changes that take place due to erosion and the buildup of erosional debris.
Superelevation—A tilting of the roadway surface to partially counterbalance the centrifugal forces on vehicles on
horizontal curves.
Superflood—Any flood or tidal flow with a flow rate greater than that of the 100-yr flood but not greater than a 500-yr
flood.
Tide—The periodic rise and fall of the earth s ocean that results from the effect of the moon and sun acting on a rotating
earth.
Watershed—An area confined by drainage divides, and often having only one outlet for discharge; the total drainage area
contributing runoff to a single point.
Waterway—Any stream, river, pond, lake, or ocean.
Waterway Opening—Width or area of bridge opening at a specified stage, and measured normal to principal direction of
flow.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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SECTION 2: GENERAL DESIGN AND LOCATION FEATURES
2-3
2.3—LOCATION FEATURES
2.3.1—Route Location
2.3.1.1—General
The choice of location of bridges shall be supported by
analyses of alternatives with consideration given to
economic, engineering, social, and environmental concerns
as well as costs of maintenance and inspection associated
with the structures and with the relative importance of the
above-noted concerns.
Attention, commensurate with the risk involved, shall
be directed toward providing for favorable bridge locations
that:
Fit the conditions created by the obstacle being
crossed;
Facilitate practical cost effective design, construction,
operation, inspection and maintenance;
Provide for the desired level of traffic service and
safety; and
Minimize adverse highway impacts.
2.3.1.2—Waterway and Floodplain Crossings
Waterway crossings shall be located with regard to
initial capital costs of construction and the optimization of
total costs, including river channel training works and the
maintenance measures necessary to reduce erosion. Studies
of alternative crossing locations should include assessments
of:
The hydrologic and hydraulic characteristics of the
waterway and its floodplain, including channel
stability, flood history, and, in estuarine crossings,
tidal ranges and cycles;
The effect of the proposed bridge on flood flow
patterns and the resulting scour potential at bridge
foundations;
The potential for creating new or augmenting existing
flood hazards; and
C2.3.1.2
Detailed guidance on procedures for evaluating the
location of bridges and their approaches on floodplains is
contained in Federal Regulations and the Planning and
Location Chapter of the AASHTO Model Drainage Manual
(see Commentary on Article 2.6.1). Engineers with
knowledge and experience in applying the guidance and
procedures in the AASHTO Model Drainage Manual
should be involved in location decisions. It is generally safer
and more cost effective to avoid hydraulic problems through
the selection of favorable crossing locations than to attempt
to minimize the problems at a later time in the project
development process through design measures.
Experience at existing bridges should be part of the
calibration or verification of hydraulic models, if possible.
Evaluation of the performance of existing bridges during
past floods is often helpful in selecting the type, size, and
location of new bridges.
Environmental impacts on the waterway and its
floodplain.
Bridges and their approaches on floodplains should be
located and designed with regard to the goals and
objectives of floodplain management, including:
Prevention of uneconomic, hazardous, or incompatible
use and development of floodplains;
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2012
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2-4
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Avoidance of significant transverse and longitudinal
encroachments, where practicable;
Minimization of adverse highway impacts and
mitigation of unavoidable impacts, where practicable;
Consistency with the intent of the standards and
criteria of the National Flood Insurance Program,
where applicable;
Long-term aggradation or degradation; and
Commitments
approvals.
made
to
obtain
environmental
2.3.2—Bridge Site Arrangement
2.3.2.1—General
C2.3.2.1
The location and the alignment of the bridge should be
selected to satisfy both on-bridge and under-bridge traffic
requirements. Consideration should be given to possible
future variations in alignment or width of the waterway,
highway, or railway spanned by the bridge.
Where appropriate, consideration should be given to
future addition of mass-transit facilities or bridge widening.
Although the location of a bridge structure over a
waterway is usually determined by other considerations than
the hazards of vessel collision, the following preferences
should be considered where possible and practical:
Locating the bridge away from bends in the navigation
channel. The distance to the bridge should be such that
vessels can line up before passing the bridge, usually
eight times the length of the vessel. This distance
should be increased further where high currents and
winds are prevalent at the site.
Crossing the navigation channel near right angles and
symmetrically with respect to the navigation channel.
Providing an adequate distance from locations with
congested navigation, vessel berthing maneuvers or
other navigation problems.
Locating the bridge where the waterway is shallow or
narrow and the bridge piers could be located out of
vessel reach.
2.3.2.2—Traffic Safety
2.3.2.2.1—Protection of Structures
C2.3.2.2.1
Consideration shall be given to safe passage of
vehicles on or under a bridge. The hazard to errant vehicles
within the clear zone should be minimized by locating
obstacles at a safe distance from the travel lanes.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 2: GENERAL DESIGN AND LOCATION FEATURES
Pier columns or walls for grade separation structures
should be located in conformance with the clear zone concept
as contained in Chapter 3 of the AASHTO Roadside Design
Guide, 1996. Where the practical limits of structure costs,
type of structure, volume and design speed of through traffic,
span arrangement, skew, and terrain make conformance with
the AASHTO Roadside Design Guide impractical, the pier
or wall should be protected by the use of guardrail or other
barrier devices. The guardrail or other device should, if
practical, be independently supported, with its roadway face
at least 2.0 ft. from the face of pier or abutment, unless a
rigid barrier is provided.
The face of the guardrail or other device should be at
least 2.0 ft. outside the normal shoulder line.
2.3.2.2.2—Protection of Users
Railings shall be provided along the edges of structures
conforming to the requirements of Section 13.
All protective structures shall have adequate surface
features and transitions to safely redirect errant traffic.
In the case of movable bridges, warning signs, lights,
signal bells, gates, barriers, and other safety devices shall
be provided for the protection of pedestrian, cyclists, and
vehicular traffic. These shall be designed to operate before
the opening of the movable span and to remain operational
until the span has been completely closed. The devices
shall conform to the requirements for ―Traffic Control at
Movable Bridges,‖ in the Manual on Uniform Traffic
Control Devices or as shown on plans.
Where specified by the Owner, sidewalks shall be
protected by barriers.
2-5
The intent of providing structurally independent
barriers is to prevent transmission of force effects from the
barrier to the structure to be protected.
C2.3.2.2.2
Protective structures include those that provide a safe
and controlled separation of traffic on multimodal facilities
using the same right-of-way.
Special conditions, such as curved alignment, impeded
visibility, etc., may justify barrier protection, even with low
design velocities.
2.3.2.2.3—Geometric Standards
Requirements of the AASHTO publication A Policy on
Geometric Design of Highways and Streets shall either be
satisfied or exceptions thereto shall be justified and
documented. Width of shoulders and geometry of traffic
barriers shall meet the specifications of the Owner.
2.3.2.2.4—Road Surfaces
Road surfaces on a bridge shall be given antiskid
characteristics, crown, drainage, and superelevation in
accordance with A Policy on Geometric Design of
Highways and Streets or local requirements.
2.3.2.2.5—Vessel Collisions
Bridge structures shall either be protected against
vessel collision forces by fenders, dikes, or dolphins as
specified in Article 3.14.15, or shall be designed to
withstand collision force effects as specified in
Article 3.14.14.
C2.3.2.2.5
The need for dolphin and fender systems can be
eliminated at some bridges by judicious placement of bridge
piers. Guidance on use of dolphin and fender systems is
included in the AASHTO Highway Drainage Guidelines,
Volume 7; Hydraulic Analyses for the Location and Design of
Bridges; and the AASHTO Guide Specification and
Commentary for Vessel Collision Design of Highway Bridges.
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2012
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2-6
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
2.3.3—Clearances
2.3.3.1—Navigational
Permits for construction of a bridge over navigable
waterways shall be obtained from the U.S. Coast Guard
and/or other agencies having jurisdiction. Navigational
clearances, both vertical and horizontal, shall be
established in cooperation with the U.S. Coast Guard.
2.3.3.2—Highway Vertical
The vertical clearance of highway structures shall be in
conformance with the AASHTO publication A Policy on
Geometric Design of Highways and Streets for the
Functional Classification of the Highway or exceptions
thereto shall be justified. Possible reduction of vertical
clearance, due to settlement of an overpass structure, shall
be investigated. If the expected settlement exceeds 1.0 in.,
it shall be added to the specified clearance.
The vertical clearance to sign supports and pedestrian
overpasses should be 1.0 ft. greater than the highway
structure clearance, and the vertical clearance from the
roadway to the overhead cross bracing of through-truss
structures should not be less than 17.5 ft.
2.3.3.3—Highway Horizontal
The bridge width shall not be less than that of the
approach roadway section, including shoulders or curbs,
gutters, and sidewalks.
Horizontal clearance under a bridge should meet the
requirements of Article 2.3.2.2.1.
No object on or under a bridge, other than a barrier,
should be located closer than 4.0 ft. to the edge of a
designated traffic lane. The inside face of a barrier should
not be closer than 2.0 ft. to either the face of the object or
the edge of a designated traffic lane.
2.3.3.4—Railroad Overpass
Structures designed to pass over a railroad shall be in
accordance with standards established and used by the
affected railroad in its normal practice. These overpass
structures shall comply with applicable federal, state,
county, and municipal laws.
Regulations, codes, and standards should, as a
minimum, meet the specifications and design standards of
the American Railway Engineering and Maintenance of
Way Association (AREMA), the Association of American
Railroads, and AASHTO.
C2.3.3.1
Where bridge permits are required, early coordination
should be initiated with the U.S. Coast Guard to evaluate the
needs of navigation and the corresponding location and
design requirements for the bridge.
Procedures for addressing navigational requirements for
bridges, including coordination with the Coast Guard, are
set forth in the Code of Federal Regulations, 23 CFR,
Part 650, Subpart H, ―Navigational Clearances for Bridges,‖
and 33 U.S.C. 401, 491, 511, et seq.
C2.3.3.2
The specified minimum clearance should include 6.0 in.
for possible future overlays. If overlays are not
contemplated by the Owner, this requirement may be
nullified.
Sign supports, pedestrian bridges, and overhead cross
bracings require the higher clearance because of their lesser
resistance to impact.
C2.3.3.3
The usable width of the shoulders should generally be
taken as the paved width.
The specified minimum distances between the edge of
the traffic lane and fixed object are intended to prevent
collision with slightly errant vehicles and those carrying
wide loads.
C2.3.3.4
Attention is particularly called to the following chapters
in the Manual for Railway Engineering (AREMA, 2003):
Chapter 7—Timber Structures,
Chapter 8—Concrete Structures and Foundations,
Chapter 9—Highway-Railroad Crossings,
Chapter 15— Steel Structures, and
Chapter 18—Clearances.
The provisions of the individual railroads and the
AREMA Manual should be used to determine:
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 2: GENERAL DESIGN AND LOCATION FEATURES
2-7
Clearances,
Loadings,
Pier protection,
Waterproofing, and
Blast protection.
2.3.4—Environment
C2.3.4
The impact of a bridge and its approaches on local
communities, historic sites, wetlands, and other
aesthetically, environmentally, and ecologically sensitive
areas shall be considered. Compliance with state water
laws; federal and state regulations concerning
encroachment on floodplains, fish, and wildlife habitats;
and the provisions of the National Flood Insurance
Program shall be assured. Stream geomorphology,
consequences of riverbed scour, removal of embankment
stabilizing vegetation, and, where appropriate, impacts to
estuarine tidal dynamics shall be considered.
Stream, i.e., fluvial, geomorphology is a study of the
structure and formation of the earth s features that result
from the forces of water. For purposes of this Section, this
involves evaluating the streams, potential for aggradation,
degradation, or lateral migration.
2.4—FOUNDATION INVESTIGATION
2.4.1—General
A subsurface investigation, including borings and soil
tests, shall be conducted in accordance with the provisions
of Article 10.4 to provide pertinent and sufficient
information for the design of substructure units. The type
and cost of foundations should be considered in the
economic and aesthetic studies for location and bridge
alternate selection.
2.4.2—Topographic Studies
Current topography of the bridge site shall be
established via contour maps and photographs. Such
studies shall include the history of the site in terms of
movement of earth masses, soil and rock erosion, and
meandering of waterways.
2.5—DESIGN OBJECTIVES
2.5.1—Safety
C2.5.1
The primary responsibility of the Engineer shall be
providing for the safety of the public.
Minimum requirements to ensure the structural safety of
bridges as conveyances are included in these Specifications.
The philosophy of achieving adequate structural safety is
outlined in Article 1.3. It is recommended that an approved
QC/QA review and checking process be utilized to ensure
that the design work meets these Specifications.
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All rights reserved. Duplication is a violation of applicable law.
2012
Edition
2-8
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
2.5.2—Serviceability
2.5.2.1—Durability
2.5.2.1.1—Materials
C2.5.2.1.1
The contract documents shall call for quality materials
and for the application of high standards of fabrication and
erection.
Structural steel shall be self-protecting, or have longlife coating systems or cathodic protection.
Reinforcing bars and prestressing strands in concrete
components, which may be expected to be exposed to
airborne or waterborne salts, shall be protected by an
appropriate combination of epoxy and/or galvanized
coating, concrete cover, density, or chemical composition
of concrete, including air-entrainment and a nonporous
painting of the concrete surface or cathodic protection.
Prestress strands in cable ducts shall be grouted or
otherwise protected against corrosion.
Attachments and fasteners used in wood construction
shall be of stainless steel, malleable iron, aluminum, or
steel that is galvanized, cadmium-plated, or otherwise
coated. Wood components shall be treated with
preservatives.
Aluminum products shall be electrically insulated from
steel and concrete components.
Protection shall be provided to materials susceptible to
damage from solar radiation and/or air pollution.
Consideration shall be given to the durability of
materials in direct contact with soil and/or water.
2.5.2.1.2—Self-Protecting Measures
Continuous drip grooves shall be provided along the
underside of a concrete deck at a distance not exceeding
10.0 in. from the fascia edges. Where the deck is
interrupted by a sealed deck joint, all surfaces of piers and
abutments, other than bearing seats, shall have a minimum
slope of 5 percent toward their edges. For open deck joints,
this minimum slope shall be increased to 15 percent. In the
case of open deck joints, the bearings shall be protected
against contact with salt and debris.
Wearing surfaces shall be interrupted at the deck joints
and shall be provided with a smooth transition to the deck
joint device.
Steel formwork shall be protected against corrosion in
accordance with the specifications of the Owner.
The intent of this Article is to recognize the significance
of corrosion and deterioration of structural materials to the
long-term performance of a bridge. Other provisions
regarding durability can be found in Article 5.12.
Other than the deterioration of the concrete deck itself,
the single most prevalent bridge maintenance problem is the
disintegration of beam ends, bearings, pedestals, piers, and
abutments due to percolation of waterborne road salts
through the deck joints. Experience appears to indicate that
a structurally continuous deck provides the best protection
for components below the deck. The potential consequences
of the use of road salts on structures with unfilled steel
decks and unprestressed wood decks should be taken into
account.
These Specifications permit the use of discontinuous
decks in the absence of substantial use of road salts.
Transverse saw-cut relief joints in cast-in-place concrete
decks have been found to be of no practical value where
composite action is present. Economy, due to structural
continuity and the absence of expansion joints, will usually
favor the application of continuous decks, regardless of
location.
Stringers made simply supported by sliding joints, with
or without slotted bolt holes, tend to ―freeze‖ due to the
accumulation of corrosion products and cause maintenance
problems. Because of the general availability of computers,
analysis of continuous decks is no longer a problem.
Experience indicates that, from the perspective of
durability, all joints should be considered subject to some
degree of movement and leakage.
C2.5.2.1.2
Ponding of water has often been observed on the seats
of abutments, probably as a result of construction tolerances
and/or tilting. The 15 percent slope specified in conjunction
with open joints is intended to enable rains to wash away
debris and salt.
In the past, for many smaller bridges, no expansion
device was provided at the ―fixed joint,‖ and the wearing
surface was simply run over the joint to give a continuous
riding surface. As the rotation center of the superstructure is
always below the surface, the ―fixed joint‖ actually moves
due to load and environmental effects, causing the wearing
surface to crack, leak, and disintegrate.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
SECTION 2: GENERAL DESIGN AND LOCATION FEATURES
2.5.2.2—Inspectability
Inspection ladders, walkways, catwalks, covered
access holes, and provision for lighting, if necessary, shall
be provided where other means of inspection are not
practical.
Where practical, access to permit manual or visual
inspection, including adequate headroom in box sections,
shall be provided to the inside of cellular components and
to interface areas, where relative movement may occur.
2.5.2.3—Maintainability
Structural systems whose maintenance is expected to
be difficult should be avoided. Where the climatic and/or
traffic environment is such that a bridge deck may need to
be replaced before the required service life, provisions shall
be shown on the contract documents for:
a contemporary or future protective overlay,
a future deck replacement, or
supplemental structural resistance.
2-9
C2.5.2.2
The Guide Specifications for Design and Construction
of Segmental Concrete Bridges requires external access
hatches with a minimum size of 2.5 ft. 4.0 ft., larger
openings at interior diaphragms, and venting by drains or
screened vents at intervals of no more than 50.0 ft. These
recommendations should be used in bridges designed under
these Specifications.
C2.5.2.3
Maintenance of traffic during replacement should be
provided either by partial width staging of replacement or
by the utilization of an adjacent parallel structure.
Measures for increasing the durability of concrete and
wood decks include epoxy coating of reinforcing bars, posttensioning ducts, and prestressing strands in the deck.
Microsilica and/or calcium nitrite additives in the deck
concrete, waterproofing membranes, and overlays may be
used to protect black steel. See Article 5.14.2.3.10e for
additional requirements regarding overlays.
Areas around bearing seats and under deck joints
should be designed to facilitate jacking, cleaning, repair,
and replacement of bearings and joints.
Jacking points shall be indicated on the plans, and the
structure shall be designed for jacking forces specified in
Article 3.4.3. Inaccessible cavities and corners should be
avoided. Cavities that may invite human or animal
inhabitants shall either be avoided or made secure.
2.5.2.4—Rideability
The deck of the bridge shall be designed to permit the
smooth movement of traffic. On paved roads, a structural
transition slab should be located between the approach
roadway and the abutment of the bridge. Construction
tolerances, with regard to the profile of the finished deck,
shall be indicated on the plans or in the specifications or
special provisions.
The number of deck joints shall be kept to a practical
minimum. Edges of joints in concrete decks exposed to
traffic should be protected from abrasion and spalling. The
plans for prefabricated joints shall specify that the joint
assembly be erected as a unit.
Where concrete decks without an initial overlay are
used, consideration should be given to providing an
additional thickness of 0.5 in. to permit correction of the
deck profile by grinding, and to compensate for thickness
loss due to abrasion.
2.5.2.5—Utilities
Where required, provisions shall be made to support
and maintain the conveyance for utilities.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
2-10
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
2.5.2.6—Deformations
2.5.2.6.1—General
C2.5.2.6.1
Bridges should be designed to avoid undesirable
structural or psychological effects due to their
deformations. While deflection and depth limitations are
made optional, except for orthotropic plate decks, any large
deviation from past successful practice regarding
slenderness and deflections should be cause for review of
the design to determine that it will perform adequately.
If dynamic analysis is used, it shall comply with the
principles and requirements of Article 4.7.
Service load deformations may cause deterioration of
wearing surfaces and local cracking in concrete slabs and in
metal bridges that could impair serviceability and durability,
even if self-limiting and not a potential source of collapse.
As early as 1905, attempts were made to avoid these
effects by limiting the depth-to-span ratios of trusses and
girders, and starting in the 1930s, live load deflection limits
were prescribed for the same purpose. In a study of
deflection limitations of bridges (ASCE, 1958), an ASCE
committee found numerous shortcomings in these traditional
approaches and noted, for example:
The limited survey conducted by the Committee
revealed no evidence of serious structural damage
that could be attributed to excessive deflection.
The few examples of damaged stringer connections
or cracked concrete floors could probably be
corrected more effectively by changes in design
than by more restrictive limitations on deflection.
On the other hand, both the historical study and the
results from the survey indicate clearly that
unfavorable psychological reaction to bridge
deflection is probably the most frequent and
important source of concern regarding the
flexibility of bridges. However, those
characteristics of bridge vibration which are
considered objectionable by pedestrians or
passengers in vehicles cannot yet be defined.
For straight skewed steel girder bridges and
horizontally curved steel girder bridges with or without
skewed supports, the following additional investigations
shall be considered:
Elastic vertical, lateral, and rotational deflections due
to applicable load combinations shall be considered to
ensure satisfactory service performance of bearings,
joints, integral abutments, and piers.
Since publication of the study, there has been extensive
research on human response to motion. It is now generally
agreed that the primary factor affecting human sensitivity is
acceleration, rather than deflection, velocity, or the rate of
change of acceleration for bridge structures, but the problem
is a difficult subjective one. Thus, there are as yet no simple
definitive guidelines for the limits of tolerable static
deflection or dynamic motion. Among current
specifications, the Ontario Highway Bridge Design Code of
1991 contains the most comprehensive provisions regarding
vibrations tolerable to humans.
Horizontally curved steel bridges are subjected to
torsion resulting in larger lateral deflections and twisting
than tangent bridges. Therefore, rotations due to dead load
and thermal forces tend to have a larger effect on the
performance of bearings and expansion joints of curved
bridges.
Bearing rotations during construction may exceed the
dead load rotations computed for the completed bridge, in
particular at skewed supports. Identification of this
temporary situation may be critical to ensure the bridge can
be built without damaging the bearings or expansion
devices.
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2012
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SECTION 2: GENERAL DESIGN AND LOCATION FEATURES
2-11
Computed girder rotations at bearings should be
accumulated over the Engineer’s assumed construction
sequence. Computed rotations at bearings shall not
exceed the specified rotational capacity of the bearings
for the accumulated factored loads corresponding to
the stage investigated.
Camber diagrams shall satisfy the provisions of
Article 6.7.2 and may reflect the computed
accumulated deflections due to the Engineer’s
assumed construction sequence.
2.5.2.6.2—Criteria for Deflection
The criteria in this Section shall be considered
optional, except for the following:
The provisions for orthotropic decks shall be
considered mandatory.
The provisions in Article 12.14.5.9 for precast
reinforced concrete three-sided structures shall be
considered mandatory.
Metal grid decks and other lightweight metal and
concrete bridge decks shall be subject to the
serviceability provisions of Article 9.5.2.
In applying these criteria, the vehicular load shall
include the dynamic load allowance.
If an Owner chooses to invoke deflection control, the
following principles may be applied:
When investigating the maximum absolute deflection
for straight girder systems, all design lanes should be
loaded, and all supporting components should be
assumed to deflect equally;
For curved steel box and I-girder systems, the
deflection of each girder should be determined
individually based on its response as part of a
system;
C2.5.2.6.2
These provisions permit, but do not encourage, the use
of past practice for deflection control. Designers were
permitted to exceed these limits at their discretion in the
past. Calculated deflections of structures have often been
found to be difficult to verify in the field due to numerous
sources of stiffness not accounted for in calculations.
Despite this, many Owners and designers have found
comfort in the past requirements to limit the overall stiffness
of bridges. The desire for continued availability of some
guidance in this area, often stated during the development of
these Specifications, has resulted in the retention of optional
criteria, except for orthotropic decks, for which the criteria
are required. Deflection criteria are also mandatory for
lightweight decks comprised of metal and concrete, such as
filled and partially filled grid decks, and unfilled grid decks
composite with reinforced concrete slabs, as provided in
Article 9.5.2.
Additional guidance regarding deflection of steel
bridges can be found in Wright and Walker (1971).
Additional considerations and recommendations for
deflection in timber bridge components are discussed in
more detail in Chapters 7, 8, and 9 in Ritter (1990).
For a straight multibeam bridge, this is equivalent to
saying that the distribution factor for deflection is equal to
the number of lanes divided by the number of beams.
For curved steel girder systems, the deflection limit is
applied to each individual girder because the curvature causes
each girder to deflect differently than the adjacent girder so
that an average deflection has little meaning. For curved steel
girder systems, the span used to compute the deflection limit
should be taken as the arc girder length between bearings.
For composite design, the stiffness of the design crosssection used for the determination of deflection should
include the entire width of the roadway and the
structurally continuous portions of the railings,
sidewalks, and median barriers;
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2012
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2-12
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
For straight girder systems, the composite bending
stiffness of an individual girder may be taken as the
stiffness determined as specified above, divided by the
number of girders;
When investigating maximum relative displacements,
the number and position of loaded lanes should be
selected to provide the worst differential effect;
The live load portion of Load Combination Service I
of Table 3.4.1-1 should be used, including the dynamic
load allowance, IM;
The live load shall be taken from Article 3.6.1.3.2;
The provisions of Article 3.6.1.1.2 should apply; and
For skewed bridges, a right cross-section may be used,
and for curved and curved skewed bridges, a radial
cross-section may be used.
In the absence of other criteria, the following
deflection limits may be considered for steel, aluminum,
and/or concrete vehicular bridges:
Vehicular load, general ............................. Span/800,
Vehicular and pedestrian loads ............... Span/1000,
Vehicular load on cantilever arms .............................
Span/300, and
Vehicular and pedestrian loads on cantilever arms
Span/375.
For steel I-shaped beams and girders, and for steel box and
tub girders, the provisions of Articles 6.10.4.2 and 6.11.4,
respectively, regarding the control of permanent deflections
through flange stress controls, shall apply. For pedestrian
bridges, i.e., bridges whose primary function is to carry
pedestrians, bicyclists, equestrians, and light maintenance
vehicles, the provisions of Section 5 of AASHTO’s LRFD
Guide Specifications for the Design of Pedestrian Bridges
shall apply.
In the absence of other criteria, the following
deflection limits may be considered for wood construction:
Vehicular and pedestrian loads .......... Span/425, and
Vehicular load on wood planks and panels (extreme
relative deflection between adjacent edges) . 0.10 in.
The following provisions shall apply to orthotropic
plate decks:
Vehicular load on deck plate ..................... Span/300,
Vehicular load on ribs of orthotropic metal decks
Span/1000, and
From a structural viewpoint, large deflections in wood
components cause fasteners to loosen and brittle materials,
such as asphalt pavement, to crack and break. In addition,
members that sag below a level plane present a poor
appearance and can give the public a perception of
structural inadequacy. Deflections from moving vehicle
loads also produce vertical movement and vibrations that
annoy motorists and alarm pedestrians (Ritter, 1990).
Excessive deformation can cause premature
deterioration of the wearing surface and affect the
performance of fasteners, but limits on the latter have not
yet been established.
The intent of the relative deflection criterion is to
protect the wearing surface from debonding and fracturing
due to excessive flexing of the deck.
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SECTION 2: GENERAL DESIGN AND LOCATION FEATURES
2-13
Vehicular load on ribs of orthotropic metal decks
(extreme relative deflection between adjacent ribs)
0.10 in.
The 0.10-in. relative deflection limitation is tentative.
2.5.2.6.3—Optional Criteria for Span-to-Depth
Ratios
C2.5.2.6.3
Unless otherwise specified herein, if an Owner chooses
to invoke controls on span-to-depth ratios, the limits in
Table 2.5.2.6.3-1, in which S is the slab span length and L
is the span length, both in ft., may be considered in the
absence of other criteria. Where used, the limits in Table
2.5.2.6.3-1 shall be taken to apply to overall depth unless
noted.
For curved steel girder systems, the span-to-depth
ratio, Las/D, of each steel girder should not exceed 25 when
the specified minimum yield strength of the girder in
regions of positive flexure is 50.0 ksi or less, and:
When the specified minimum yield strength of the
girder is 70.0 ksi or less in regions of negative flexure,
or
When hybrid sections satisfying the provisions of
Article 6.10.1.3 are used in regions of negative
flexure.
For all other curved steel girder systems, Las/D of each steel
girder should not exceed the following:
Las
50
≤ 25
D
Fyt
(2.5.2.6.3-1)
Traditional minimum depths for constant depth
superstructures, contained in previous editions of the
AASHTO Standard Specifications for Highway Bridges, are
given in Table 2.5.2.6.3-1 with some modifications.
A larger preferred minimum girder depth is specified
for curved steel girders to reflect the fact that the outermost
curved girder receives a disproportionate share of the load
and needs to be stiffer. In curved skewed bridges, crossframe forces are directly related to the relative girder
deflections. Increasing the depth and stiffness of all the
girders in a curved skewed bridge leads to smaller relative
differences in the deflections and smaller cross-frame
forces. Deeper girders also result in reduced out-of-plane
rotations, which may make the bridge easier to erect.
An increase in the preferred minimum girder depth for
curved steel girders not satisfying the conditions specified
herein is recommended according to Eq. 2.5.2.6.3-1. In such
cases, the girders will tend to be significantly more flexible
and less steel causes increased deflections without an
increase in the girder depth.
A shallower curved girder might be used if the Engineer
evaluates effects such as cross-frame forces and bridge
deformations, including girder rotations, and finds the
bridge forces and geometric changes within acceptable
ranges. For curved composite girders, the recommended
ratios apply to the steel girder portion of the composite
section.
where:
Fyt =
specified minimum yield strength of the
compression flange (ksi)
D
depth of steel girder (ft.)
=
Las =
an arc girder length defined as follows (ft.):
arc span for simple spans;
0.9 times the arc span for continuous end-spans;
0.8 times the arc span for continuous interior spans.
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2012
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2-14
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 2.5.2.6.3-1—Traditional Minimum Depths for Constant Depth Superstructures
Minimum Depth (Including Deck)
Material
Reinforced
Concrete
Prestressed
Concrete
Steel
Superstructure
Type
Slabs with main reinforcement
parallel to traffic
T-Beams
Box Beams
Pedestrian Structure
Beams
Slabs
CIP Box Beams
Precast I-Beams
Pedestrian Structure Beams
Adjacent Box Beams
Overall Depth of Composite I-Beam
Depth of I-Beam Portion of
Composite I-Beam
Trusses
When variable depth members are used, values may be
adjusted to account for changes in relative stiffness of
positive and negative moment sections
Simple Spans
Continuous Spans
S +10
1.2 S + 10
≥ 0.54 ft.
30
30
0.070L
0.065L
0.060L
0.055L
0.035L
0.033L
0.030L ≥ 6.5 in.
0.045L
0.045L
0.033L
0.030L
0.040L
0.033L
0.027L ≥ 6.5 in.
0.040L
0.040L
0.030L
0.025L
0.032L
0.027L
0.100L
0.100L
2.5.2.7—Consideration of Future Widening
2.5.2.7.1—Exterior Beams on Multibeam Bridges
Unless future widening is virtually inconceivable, the
load carrying capacity of exterior beams shall not be less
than the load carrying capacity of an interior beam.
C2.5.2.7.1
This provision applies to any longitudinal flexural
members traditionally considered to be stringers, beams, or
girders.
2.5.2.7.2—Substructure
When future widening can be anticipated, consideration
should be given to designing the substructure for the
widened condition.
2.5.3—Constructibility
C2.5.3
Constructability issues should include, but not be
limited to, consideration of deflection, strength of steel and
concrete, and stability during critical stages of construction.
An example of a particular sequence of construction
would be where the designer requires a steel girder to be
supported while the concrete deck is cast, so that the girder
and the deck will act compositely for dead load as well as
live load.
An example of a complex bridge might be a cablestayed bridge that has limitations on what it will carry,
especially in terms of construction equipment, while it is
under construction. If these limitations are not evident to an
experienced contractor, the contractor may be required to
do more prebid analysis than is reasonable. Given the usual
constraints of time and budget for bidding, this may not be
feasible for the contractor to do.
Bridges should be designed in a manner such that
fabrication and erection can be performed without undue
difficulty or distress and that locked-in construction force
effects are within tolerable limits.
When the designer has assumed a particular sequence
of construction in order to induce certain stresses under
dead load, that sequence shall be defined in the contract
documents.
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SECTION 2: GENERAL DESIGN AND LOCATION FEATURES
Where there are, or are likely to be, constraints
imposed on the method of construction, by environmental
considerations or for other reasons, attention shall be drawn
to those constraints in the contract documents.
Where the bridge is of unusual complexity, such that it
would be unreasonable to expect an experienced contractor
to predict and estimate a suitable method of construction
while bidding the project, at least one feasible construction
method shall be indicated in the contract documents.
If the design requires some strengthening and/or
temporary bracing or support during erection by the
selected method, indication of the need thereof shall be
indicated in the contract documents.
Details that require welding in restricted areas or
placement of concrete through congested reinforcing should
be avoided.
Climatic and hydraulic conditions that may affect the
construction of the bridge shall be considered.
2-15
This Article does not require the designer to educate a
contractor on how to construct a bridge; it is expected that
the contractor will have the necessary expertise. Nor is it
intended to restrict a contractor from using innovation to
gain an edge over the competitors.
All other factors being equal, designs that are selfsupporting or use standardized falsework systems are
normally preferred to those requiring unique and complex
falsework.
Temporary falsework within the clear zone should be
adequately protected from traffic.
2.5.4—Economy
2.5.4.1—General
C2.5.4.1
Structural types, span lengths, and materials shall be
selected with due consideration of projected cost. The cost
of future expenditures during the projected service life of
the bridge should be considered. Regional factors, such as
availability of material, fabrication, location, shipping, and
erection constraints, shall be considered.
If data for the trends in labor and material cost
fluctuation are available, the effect of such trends should be
projected to the time the bridge will likely be constructed.
Cost comparisons of structural alternatives should be
based on long-range considerations, including inspection,
maintenance, repair, and/or replacement. Lowest first cost
does not necessarily lead to lowest total cost.
2.5.4.2—Alternative Plans
In instances where economic studies do not indicate a
clear choice, the Owner may require that alternative
contract plans be prepared and bid competitively. Designs
for alternative plans shall be of equal safety, serviceability,
and aesthetic value.
Movable bridges over navigable waterways should be
avoided to the extent feasible. Where movable bridges are
proposed, at least one fixed bridge alternative should be
included in the economic comparisons.
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2012
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2-16
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
2.5.5—Bridge Aesthetics
C2.5.5
Bridges should complement their surroundings, be
graceful in form, and present an appearance of adequate
strength.
Significant improvements in appearance can often be
made with small changes in shape or position of structural
members at negligible cost. For prominent bridges,
however, additional cost to achieve improved appearance is
often justified, considering that the bridge will likely be a
feature of the landscape for 75 or more years.
Comprehensive guidelines for the appearance of
bridges are beyond the scope of these Specifications.
Engineers may resort to such documents as the
Transportation Research Board s Bridge Aesthetics Around
the World (1991) for guidance.
The most admired modern structures are those that rely
for their good appearance on the forms of the structural
component themselves:
Engineers should seek more pleasant appearance by
improving the shapes and relationships of the structural
component themselves. The application of extraordinary
and nonstructural embellishment should be avoided.
The following guidelines should be considered:
Alternative bridge designs without piers or with few
piers should be studied during the site selection and
location stage and refined during the preliminary
design stage.
Pier form should be consistent in shape and detail with
the superstructure.
Abrupt changes in the form of components and
structural type should be avoided. Where the interface
of different structural types cannot be avoided, a
smooth transition in appearance from one type to
another should be attained.
Attention to details, such as deck drain downspouts,
should not be overlooked.
If the use of a through structure is dictated by
performance and/or economic considerations, the
structural system should be selected to provide an open
and uncluttered appearance.
The use of the bridge as a support for message or
directional signing or lighting should be avoided
wherever possible.
Transverse web stiffeners, other than those located at
bearing points, should not be visible in elevation.
For spanning deep ravines, arch-type structures should
be preferred.
Components are shaped to respond to the structural
function. They are thick where the stresses are greatest
and thin where the stresses are smaller.
The function of each part and how the function is
performed is visible.
Components are slender and widely spaced, preserving
views through the structure.
The bridge is seen as a single whole, with all members
consistent and contributing to that whole; for example,
all elements should come from the same family of
shapes, such as shapes with rounded edges.
The bridge fulfills its function with a minimum of
material and minimum number of elements.
The size of each member compared with the others is
clearly related to the overall structural concept and the
job the component does, and
The bridge as a whole has a clear and logical
relationship to its surroundings.
Several procedures have been proposed to integrate
aesthetic thinking into the design process (Gottemoeller,
1991).
Because the major structural components are the
largest parts of a bridge and are seen first, they determine
the appearance of a bridge. Consequently, engineers should
seek excellent appearance in bridge parts in the following
order of importance:
Horizontal and vertical alignment and position in the
environment;
Superstructure type, i.e., arch, girder, etc.;
Pier placement;
Abutment placement and height;
Superstructure shape, i.e., haunched, tapered, depth;
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SECTION 2: GENERAL DESIGN AND LOCATION FEATURES
2-17
Pier shape;
Abutment shape;
Parapet and railing details;
Surface colors and textures; and
Ornament.
The Designer should determine the likely position of
the majority of viewers of the bridge, then use that
information as a guide in judging the importance of various
elements in the appearance of the structure.
Perspective drawings of photographs taken from the
important viewpoints can be used to analyze the appearance
of proposed structures. Models are also useful.
The appearance of standard details should be reviewed
to make sure they fit the bridge s design concept.
2.6—HYDROLOGY AND HYDRAULICS
2.6.1—General
C2.6.1
Hydrologic and hydraulic studies and assessments of
bridge sites for stream crossings shall be completed as part
of the preliminary plan development. The detail of these
studies should be commensurate with the importance of and
risks associated with the structure.
Temporary structures for the Contractor s use or for
accommodating traffic during construction shall be
designed with regard to the safety of the traveling public
and the adjacent property owners, as well as minimization
of impact on floodplain natural resources. The Owner may
permit revised design requirements consistent with the
intended service period for, and flood hazard posed by, the
temporary structure. Contract documents for temporary
structures shall delineate the respective responsibilities and
risks to be assumed by the highway agency and the
Contractor.
Evaluation of bridge design alternatives shall consider
stream stability, backwater, flow distribution, stream
velocities, scour potential, flood hazards, tidal dynamics
where appropriate and consistency with established criteria
for the National Flood Insurance Program.
The provisions in this Article incorporate improved
practices and procedures for the hydraulic design of
bridges. Detailed guidance for applying these practices and
procedures are contained in the AASHTO Model Drainage
Manual. This document contains guidance and references
on design procedures and computer software for hydrologic
and hydraulic design. It also incorporates guidance and
references from the AASHTO Drainage Guidelines, which
is a companion document to the AASHTO Model Drainage
Manual.
Information on the National Flood Insurance Program
is contained in 42 USC 4001-4128, The National Flood
Insurance Act (see also 44 CFR 59 through 77) and 23 CFR
650, Subpart A, Location and Hydraulic Design of
Encroachment on Floodplains.
Hydrologic, hydraulic, scour, and stream stability
studies are concerned with the prediction of flood flows and
frequencies and with the complex physical processes
involving the actions and interactions of water and soil
during the occurrence of predicted flood flows. These
studies should be performed by the Engineer with the
knowledge and experience to make practical judgments
regarding the scope of the studies to be performed and the
significance of the results obtained. The design of bridge
foundations is best accomplished by an interdisciplinary
team of structural, hydraulic, and geotechnical engineers.
The AASHTO Model Drainage Manual also contains
guidance and references on:
Design methods for evaluating the accuracy of
hydraulic studies, including elements of a data
collection plan;
Guidance on estimating flood flow peaks and volumes,
including requirements for the design of Interstate
highways as per 23 CFR 650, Subpart A,
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2-18
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
―Encroachments;‖
Procedures or references for analysis of tidal
waterways, regulated streams, and urban watersheds;
Evaluation of stream stability;
Use of recommended design procedures and software
for sizing bridge waterways;
Location and design of bridges to resist damage from
scour and hydraulic loads created by stream current,
ice, and debris;
Calculation of magnitude of contraction scour, local
scour, and countermeasures thereto;
Design of relief bridges, road overtopping, guide
banks, and other river training works; and
Procedures for hydraulic design of bridge-size culverts.
2.6.2—Site Data
C2.6.2
A site-specific data collection plan shall include
consideration of:
The assessment of hydraulics necessarily involves
many assumptions. Key among these assumptions are the
roughness coefficients and projection of long-term flow
magnitudes, e.g., the 500-yr flood or other superfloods. The
runoff from a given storm can be expected to change with
the seasons, immediate past weather conditions, and longterm natural and man-made changes in surface conditions.
The ability to statistically project long recurrence interval
floods is a function of the adequacy of the database of past
floods, and such projections often change as a result of new
experience.
The above factors make the check flood investigation
of scour an important, but highly variable, safety criterion
that may be expected to be difficult to reproduce, unless all
of the Designer s original assumptions are used in a postdesign scour investigation. Obviously, those original
assumptions must be reasonable given the data, conditions,
and projections available at the time of the original design.
Collection of aerial and/or ground survey data for
appropriate distances upstream and downstream from
the bridge for the main stream channel and its
floodplain;
Estimation of roughness elements for the stream and
the floodplain within the reach of the stream under
study;
Sampling of streambed material to a depth sufficient to
ascertain material characteristics for scour analysis;
Subsurface borings;
Factors affecting water stages, including high water
from streams, reservoirs, detention basins, tides, and
flood control structures and operating procedures;
Existing studies and reports, including those conducted
in accordance with the provisions of the National Flood
Insurance Program or other flood control programs;
Available historical information on the behavior of the
stream and the performance of the structure during past
floods, including observed scour, bank erosion, and
structural damage due to debris or ice flows; and
Possible geomorphic changes in channel flow.
2.6.3—Hydrologic Analysis
C2.6.3
The Owner shall determine the extent of hydrologic
studies on the basis of the functional highway classification,
the applicable federal and state requirements, and the flood
hazards at the site.
The following flood flows should be investigated, as
appropriate, in the hydrologic studies:
The return period of tidal flows should be correlated to
the hurricane or storm tide elevations of water as reported
in studies by FEMA or other agencies.
Particular attention should be given to selecting design
and checking flood discharges for mixed population flood
events. For example, flow in an estuary may consist of both
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SECTION 2: GENERAL DESIGN AND LOCATION FEATURES
For assessing flood hazards and meeting floodplain
management requirements—the 100-yr flood;
For assessing risks to highway users and damage to the
bridge and its roadway approaches—the overtopping
flood and/or the design flood for bridge scour;
For assessing catastrophic flood damage at high risk
sites—a check flood of a magnitude selected by the
Owner, as appropriate for the site conditions and the
perceived risk;
For investigating the adequacy of bridge foundations to
resist scour—the check flood for bridge scour;
2-19
tidal flow and runoff from the upland watershed.
If mixed population flows are dependent on the
occurrence of a major meteorological event, such as a
hurricane, the relative timing of the individual peak flow
events needs to be evaluated and considered in selecting the
design discharge. This is likely to be the case for flows in
an estuary.
If the events tend to be independent, as might be the
case for floods in a mountainous region caused by rainfall
runoff or snow melt, the Designer should evaluate both
events independently and then consider the probability of
their occurrence at the same time.
To satisfy agency design policies and criteria—design
floods for waterway opening and bridge scour for the
various functional classes of highways;
To calibrate water surface profiles and to evaluate the
performance of existing structures—historical floods,
and
To evaluate environmental conditions—low or base
flow information, and in estuarine crossings, the spring
and tide range.
Investigation of the effect of sea level rise on tidal
ranges should be specified for structures spanning
marine/estuarine resources.
2.6.4—Hydraulic Analysis
2.6.4.1—General
The Engineer shall utilize analytical models and
techniques that have been approved by the Owner and that
are consistent with the required level of analysis.
2.6.4.2—Stream Stability
Studies shall be carried out to evaluate the stability of
the waterway and to assess the impact of construction on the
waterway. The following items shall be considered:
Whether the stream reach is degrading, aggrading, or in
equilibrium;
For stream crossing near confluences, the effect of the
main stream and the tributary on the flood stages,
velocities, flow distribution, vertical, and lateral
movements of the stream, and the effect of the
foregoing conditions on the hydraulic design of the
bridge;
Location of favorable stream crossing, taking into
account whether the stream is straight, meandering,
braided, or transitional, or control devices to protect
the bridge from existing or anticipated future stream
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Edition
2-20
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
conditions;
The effect of any proposed channel changes;
The effect of aggregate mining or other operations in
the channel;
Potential changes in the rates or volumes of runoff due
to land use changes;
The effect of natural geomorphic stream pattern
changes on the proposed structure; and
The effect of geomorphic changes on existing
structures in the vicinity of, and caused by, the
proposed structure.
For unstable streams or flow conditions, special studies
shall be carried out to assess the probable future changes to
the plan form and profile of the stream and to determine
countermeasures to be incorporated in the design, or at a
future time, for the safety of the bridge and approach
roadways.
2.6.4.3—Bridge Waterway
C2.6.4.3
The design process for sizing the bridge waterway shall
include:
Trial combinations should take the following into
account:
The evaluation of flood flow patterns in the main
channel and floodplain for existing conditions, and
Increases in flood water surface elevations caused by
the bridge,
The evaluation of trial combinations of highway
profiles, alignments, and bridge lengths for consistency
with design objectives.
Changes in flood flow patterns and velocities in the
channel and on the floodplain,
Where use is made of existing flood studies, their
accuracy shall be determined.
Location of hydraulic controls affecting flow through
the structure or long-term stream stability,
Clearances between the flood water elevations and low
sections of the superstructure to allow passage of ice
and debris,
Need for protection of bridge foundations and stream
channel bed and banks, and
Evaluation of capital costs and flood hazards
associated with the candidate bridge alternatives
through risk assessment or risk analysis procedures.
2.6.4.4—Bridge Foundations
2.6.4.4.1—General
C2.6.4.4.1
The structural, hydraulic, and geotechnical aspects of
foundation design shall be coordinated and differences
resolved prior to approval of preliminary plans.
To reduce the vulnerability of the bridge to damage
from scour and hydraulic loads, consideration should be
given to the following general design concepts:
Set deck elevations as high as practical for the given
site conditions to minimize inundation by floods.
Where bridges are subject to inundation, provide for
overtopping of roadway approach sections, and
streamline the superstructure to minimize the area
subject to hydraulic loads and the collection of ice,
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 2: GENERAL DESIGN AND LOCATION FEATURES
2-21
debris, and drifts.
Utilize relief bridges, guide banks, dikes, and other
river training devices to reduce the turbulence and
hydraulic forces acting at the bridge abutments.
Utilize
continuous
span
designs.
Anchor
superstructures to their substructures where subject to
the effects of hydraulic loads, buoyancy, ice, or debris
impacts or accumulations. Provide for venting and
draining of the superstructure.
Where practical, limit the number of piers in the
channel, streamline pier shapes, and align piers with
the direction of flood flows. Avoid pier types that
collect ice and debris. Locate piers beyond the
immediate vicinity of stream banks.
Locate abutments back from the channel banks where
significant problems with ice/debris buildup, scour, or
channel stability are anticipated, or where special
environmental or regulatory needs must be met, e.g.,
spanning wetlands.
Design piers on floodplains as river piers. Locate their
foundations at the appropriate depth if there is a
likelihood that the stream channel will shift during the
life of the structure or that channel cutoffs are likely to
occur.
Where practical, use debris racks or ice booms to stop
debris and ice before it reaches the bridge. Where
significant ice or debris buildup is unavoidable, its
effects should be accounted for in determining scour
depths and hydraulic loads.
2.6.4.4.2—Bridge Scour
As required by Article 3.7.5, scour at bridge
foundations is investigated for two conditions:
For the design flood for scour, the streambed material
in the scour prism above the total scour line shall be
assumed to have been removed for design conditions.
The design flood storm surge, tide, or mixed
population flood shall be the more severe of the 100-yr
events or from an overtopping flood of lesser
recurrence interval.
For the check flood for scour, the stability of bridge
foundation shall be investigated for scour conditions
resulting from a designated flood storm surge, tide, or
mixed population flood not to exceed the 500-yr event
or from an overtopping flood of lesser recurrence
interval. Excess reserve beyond that required for
stability under this condition is not necessary. The
extreme event limit state shall apply.
If the site conditions, due to ice or debris jams, and low
tail water conditions near stream confluences dictate the use
C2.6.4.4.2
A majority of bridge failures in the United States and
elsewhere are the result of scour.
The added cost of making a bridge less vulnerable to
damage from scour is small in comparison to the total cost
of a bridge failure.
The design flood for scour shall be determined on the
basis of the Engineer s judgment of the hydrologic and
hydraulic flow conditions at the site. The recommended
procedure is to evaluate scour due to the specified flood
flows and to design the foundation for the event expected to
cause the deepest total scour.
The recommended procedure for determining the total
scour depth at bridge foundations is as follows:
Estimate the long-term channel profile aggradation or
degradation over the service life of the bridge;
Estimate the long-term channel plan form changes over
the service life of the bridge;
As a design check, adjust the existing channel and
floodplain cross-sections upstream and downstream of
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2012
Edition
2-22
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
of a more severe flood event for either the design or check
flood for scour, the Engineer may use such flood event.
Spread footings on soil or erodible rock shall be
located so that the bottom of footing is below scour depths
determined for the check flood for scour. Spread footings
on scour-resistant rock shall be designed and constructed to
maintain the integrity of the supporting rock.
Deep foundations with footings shall be designed to
place the top of the footing below the estimated contraction
scour depth where practical to minimize obstruction to
flood flows and resulting local scour. Even lower elevations
should be considered for pile-supported footings where the
piles could be damaged by erosion and corrosion from
exposure to stream currents. Where conditions dictate a
need to construct the top of a footing to an elevation above
the streambed, attention shall be given to the scour potential
of the design.
When fendering or other pier protection systems are
used, their effect on pier scour and collection of debris shall
be taken into consideration in the design.
bridge as necessary to reflect anticipated changes in the
channel profile and plan form;
Determine the combination of existing or likely future
conditions and flood events that might be expected to
result in the deepest scour for design conditions;
Determine water surface profiles for a stream reach
that extends both upstream and downstream of the
bridge site for the various combinations of conditions
and events under consideration;
Determine the magnitude of contraction scour and local
scour at piers and abutments; and
Evaluate the results of the scour analysis, taking into
account the variables in the methods used, the available
information on the behavior of the watercourse, and the
performance of existing structures during past floods.
Also consider present and anticipated future flow
patterns in the channel and its floodplain. Visualize the
effect of the bridge on these flow patterns and the
effect of the flow on the bridge. Modify the bridge
design where necessary to satisfy concerns raised by
the scour analysis and the evaluation of the channel
plan form.
Foundation designs should be based on the total scour
depths estimated by the above procedure, taking into
account appropriate geotechnical safety factors. Where
necessary, bridge modifications may include:
Relocation or redesign of piers or abutments to avoid
areas of deep scour or overlapping scour holes from
adjacent foundation elements,
Addition of guide banks, dikes, or other river training
works to provide for smoother flow transitions or to
control lateral movement of the channel,
Enlargement of the waterway area, or
Relocation of the crossing to avoid an undesirable
location.
The stability of abutments in areas of turbulent flow
shall be thoroughly investigated. Exposed embankment
slopes should be protected with appropriate scour
countermeasures.
Foundations should be designed to withstand the
conditions of scour for the design flood and the check
flood. In general, this will result in deep foundations. The
design of the foundations of existing bridges that are being
rehabilitated should consider underpinning if scour
indicates the need. Riprap and other scour countermeasures
may be appropriate if underpinning is not cost effective.
Available technology has not developed sufficiently to
provide reliable scour estimates for some conditions, such
as bridge abutments located in areas of turbulence due to
converging or diverging flows.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 2: GENERAL DESIGN AND LOCATION FEATURES
2.6.4.5—Roadway Approaches to Bridge
The design of the bridge shall be coordinated with the
design of the roadway approaches to the bridge on the
floodplain so that the entire flood flow pattern is developed
and analyzed as a single, interrelated entity. Where roadway
approaches on the floodplain obstruct overbank flow, the
highway segment within the floodplain limits shall be
designed to minimize flood hazards.
Where diversion of flow to another watershed occurs as
a result of backwater and obstruction of flood flows, an
evaluation of the design shall be carried out to ensure
compliance with legal requirements in regard to flood
hazards in the other watershed.
2-23
C2.6.4.5
Highway embankments on floodplains serve to redirect
overbank flow, causing it to flow generally parallel to the
embankment and return to the main channel at the bridge.
For such cases, the highway designs shall include
countermeasures where necessary to limit damage to
highway fills and bridge abutments. Such countermeasures
may include:
Relief bridges,
Retarding the velocity of the overbank flow by
promoting growth of trees and shrubs on the floodplain
and highway embankment within the highway right-ofway or constructing small dikes along the highway
embankment,
Protecting fill slopes subject to erosive velocities by
use of riprap or other erosion protection materials on
highway fills and spill-through abutments, and
Use of guide banks where overbank flow is large to
protect abutments of main channel and relief bridges
from turbulence and resulting scour.
Although overtopping may result in failure of the
embankment, this consequence is preferred to failure of the
bridge. The low point of the overtopping section should not
be located immediately adjacent to the bridge, because its
failure at this location could cause damage to the bridge
abutment. If the low point of the overtopping section must
be located close to the abutment, due to geometric
constraints, the scouring effect of the overtopping flow
should be considered in the design of the abutment. Design
studies for overtopping should also include evaluation of
any flood hazards created by changes to existing flood flow
patterns or by flow concentrations in the vicinity of
developed properties.
2.6.5—Culvert Location, Length, and Waterway Area
C2.6.5
In addition to the provisions of Articles 2.6.3 and 2.6.4,
the following conditions should be considered:
The discussion of site investigations and hydrologic
and hydraulic analyses for bridges is generally applicable to
large culvert installations classified as bridges.
The use of safety grates on culvert ends to protect
vehicles that run off the road is generally discouraged for
large culverts, including those classified as bridges, because
of the potential for clogging and subsequent unexpected
increase in the flood hazard to the roadway and adjacent
properties. Preferred methods of providing for traffic safety
include the installation of barriers or the extension of the
culvert ends to increase the vehicle recovery zone at the
site.
Passage of fish and wildlife,
Effect of high outlet velocities and flow concentrations
on the culvert outlet, the downstream channel, and
adjacent property,
Buoyancy effects at culvert inlets,
Traffic safety, and
The effects of high tail water conditions as may be
caused by downstream controls or storm tides.
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All rights reserved. Duplication is a violation of applicable law.
2012
Edition
2-24
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
2.6.6—Roadway Drainage
2.6.6.1—General
C2.6.6.1
The bridge deck and its highway approaches shall be
designed to provide safe and efficient conveyance of
surface runoff from the traveled way in a manner that
minimizes damage to the bridge and maximizes the safety
of passing vehicles. Transverse drainage of the deck,
including roadway, bicycle paths, and pedestrian walkways,
shall be achieved by providing a cross slope or
superelevation sufficient for positive drainage. For wide
bridges with more than three lanes in each direction, special
design of bridge deck drainage and/or special rough road
surfaces may be needed to reduce the potential for
hydroplaning. Water flowing downgrade in the roadway
gutter section shall be intercepted and not permitted to run
onto the bridge. Drains at bridge ends shall have sufficient
capacity to carry all contributing runoff.
In those unique environmentally sensitive instances
where it is not possible to discharge into the underlying
watercourse, consideration should be given to conveying
the water in a longitudinal storm drain affixed to the
underside of the bridge and discharging it into appropriate
facilities on natural ground at bridge end.
Where feasible, bridge decks should be watertight and
all of the deck drainage should be carried to the ends of the
bridge.
A longitudinal gradient on bridges should be
maintained. Zero gradients and sag vertical curves should
be avoided. Design of the bridge deck and the approach
roadway drainage systems should be coordinated.
Under certain conditions, open bridge railings may be
desirable for maximum discharge of surface runoff from
bridge decks.
The ―Storm Drainage‖ chapter of the AASHTO Model
Drainage Manual contains guidance on recommended
values for cross slopes.
2.6.6.2—Design Storm
The design storm for bridge deck drainage shall not be
less than the storm used for design of the pavement
drainage system of the adjacent roadway, unless otherwise
specified by the Owner.
2.6.6.3—Type, Size, and Number of Drains
The number of deck drains should be kept to a
minimum consistent with hydraulic requirements.
In the absence of other applicable guidance, for bridges
where the highway design speed is less than 45 mph, the
size and number of deck drains should be such that the
spread of deck drainage does not encroach on more than
one-half the width of any designated traffic lane. For
bridges where the highway design speed is not less than
45 mph, the spread of deck drainage should not encroach on
any portion of the designated traffic lanes. Gutter flow
should be intercepted at cross slope transitions to prevent
flow across the bridge deck.
Scuppers or inlets of a deck drain shall be hydraulically
efficient and accessible for cleaning.
C2.6.6.3
For further guidance or design criteria on bridge deck
drainage, see the ―Storm Drainage‖ chapter of the
AASHTO Model Drainage Manual, Policy on Geometric
Design of Highways and Streets, and AASHTO/FHWA
Research Report RD-87-014, Bridge Deck Drainage
Guidelines.
The minimum internal dimension of a downspout
should not normally be less than 6.0 in., but not less than
8.0 in. where ice accretion on the bridge deck is expected.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 2: GENERAL DESIGN AND LOCATION FEATURES
2.6.6.4—Discharge from Deck Drains
Deck drains shall be designed and located such that
surface water from the bridge deck or road surface is
directed away from the bridge superstructure elements and
the substructure.
If the Owner has no specific requirements for
controlling the effluent from drains and pipes, consideration
should be given to:
2-25
C2.6.6.4
Consideration should be given to the effect of drainage
systems on bridge aesthetics.
A minimum 4.0-in. projection below the lowest
adjacent superstructure component,
Location of pipe outlets such that a 45º cone of splash
will not touch structural components,
Use of free drops or slots in parapets wherever
practical and permissible,
Use of bends not greater than 45º, and
Use of cleanouts.
Runoff from bridge decks and deck drains shall be
disposed of in a manner consistent with environmental and
safety requirements.
2.6.6.5—Drainage of Structures
Cavities in structures where there is a likelihood for
entrapment of water shall be drained at their lowest point.
Decks and wearing surfaces shall be designed to prevent the
ponding of water, especially at deck joints. For bridge
decks with nonintegral wearing surfaces or stay-in-place
forms, consideration shall be given to the evacuation of
water that may accumulate at the interface.
For bridges where free drops are not feasible, attention
should be given to the design of the outlet piping system to:
Minimize clogging and other maintenance problems
and
Minimize the intrusive effect of the piping on the
bridge symmetry and appearance.
Free drops should be avoided where runoff creates
problems with traffic, rail, or shipping lanes. Riprap or
pavement should be provided under the free drops to
prevent erosion.
C2.6.6.5
Weep holes in concrete decks and drain holes in stayin-place forms can be used to permit the egress of water.
2.7—BRIDGE SECURITY
2.7.1—General
C2.7.1
An assessment of the priority of a bridge should be
conducted during the planning of new bridges and/or during
rehabilitation of existing bridges. This should take into
account the social/economic impact of the loss of the
bridge, the availability of alternate routes, and the effect of
closing the bridge on the security/defense of the region.
For bridges deemed critical or essential, a formal
vulnerability study should be conducted, and measures to
mitigate the vulnerabilities should be considered for
incorporation into the design.
At the time of this writing, there are no uniform
procedures for assessing the priority of a bridge to the
social/economic and defense/security of a region. Work is
being done to produce a uniform procedure to prioritize
bridges for security.
In the absence of uniform procedures, some states have
developed procedures that incorporate their own security
prioritization methods which, while similar, differ in details.
In addition, procedures to assess bridge priority were
developed by departments of transportation in some states
to assist in prioritizing seismic rehabilitation. The
procedures established for assessing bridge priority may
also be used in conjunction with security considerations.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
2-26
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Guidance on security strategies and risk reduction may
be found in the following documents: Science Applications
International Corporation (2002), The Blue Ribbon Panel
on Bridge and Tunnel Security (2003), Winget (2003),
Jenkins (2001), Abramson (1999), and Williamson (2006).
2.7.2—Design Demand
C2.7.2
Bridge Owners should establish criteria for the size and
location of the threats to be considered in the analysis of
bridges for security. These criteria should take into account
the type, geometry, and priority of the structure being
considered. The criteria should also consider multi-tier
threat sizes and define the associated level of structural
performance for each tier.
It is not possible to protect a bridge from every
conceivable threat. The most likely threat scenarios should
be determined based on the bridge structural system and
geometry and the identified vulnerabilities. The most likely
attack scenarios will minimize the attacker’s required time
on target, possess simplicity in planning and execution, and
have a high probability of achieving maximum damage.
The level of acceptable damage should be
proportionate to the size of the attack. For example, linear
behavior and/or local damage should be expected under a
small-size attack, while significant permanent deformations
and significant damage and/or partial failure of some
components should be acceptable under larger size attacks.
The level of threat and the operational classification of
the bridge should be taken into account when determining
the level of analysis to be used in determining the demands.
Approximate methods may be used for low-force,
low-importance bridges, while more sophisticated analyses
should be used for high-force threats to priority bridges.
Design demands should be determined from analysis of
a given size design threat, taking into account the
associated performance levels. Given the demands, a design
strategy should be developed and approved by the Bridge
Owner.
2.8—REFERENCES
AASHTO. 2009. Guide Specification and Commentary for Vessel Collision Design of Highway Bridges, Second Edition
with Interim Revisions, GVCB-2-M. American Association State Highway and Transportation Officials, Washington, DC.
AASHTO. 2005. Model Drainage Manual, Third Edition, MDM-3. American Association of State Highway and
Transportation Officials, Washington, DC.
AASHTO. 2011. Roadside Design Guide, RSDG-4. American Association of State Highway and Transportation Officials,
Washington, DC.
AASHTO and FHWA. 1987. Bridge Deck Drainage Guidelines, Research Report RD-87-014. American Association of
State Highway and Transportation Officials/Federal Highway Administration, Washington, DC.
Abramson, H. N., et al. 1999. Improving Surface Transportation Security: A Research and Development Strategy.
Committee on R & D Strategies to Improve Surface Transportation Security, National Research Council, National
Academy Press, Washington, DC.
AREMA. 2003. Manual for Railway Engineering. American Railway Engineers Association, Washington, DC.
ASCE. 1958. “Deflection Limitations of Bridges: Progress Report of the Committee on Deflection Limitations of Bridges
of the Structural Division.” Journal of the Structural Division, American Society of Civil Engineers, New York, NY,
Vol. 84, No. ST 3, May 1958.
The Blue Ribbon Panel on Bridge and Tunnel Security. 2003. Recommendations for Bridge and Tunnel Security. Special
report prepared for FHWA and AASHTO, Washington, DC.
FHWA. 1991. “Evaluating Scour at Bridges,” FHWA-1P-90-017. Hydraulic Engineering Circular 18. Federal Highway
Administration, U.S. Department of Transportation, Washington, DC.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 2: GENERAL DESIGN AND LOCATION FEATURES
2-27
FHWA. 1991. “Stream Stability at Highway Structures,” FHWA-1P-90-014. Hydraulic Engineering Circular 20. Federal
Highway Administration, U.S. Department of Transportation, Washington, DC.
Gottemoeller, F. 1991. “Aesthetics and Engineers: Providing for Aesthetic Quality in Bridge Design.” Bridge Aesthetics
Around the World, Transportation Research Board, National Research Council, Washington, DC, pp. 80–88.
Highway Engineering Division. 1991. Ontario Highway Bridge Design Code, Highway Engineering Division, Ministry of
Transportation and Communications, Toronto, Canada.
Jenkins, B. M. 2001. Protecting Public Surface Transportation Against Terrorism and Serious Crime: An Executive
Overview. MTI Report 01-14. Mineta Transportation Institute, San Jose, CA. Available at
http://transweb.sjsu.edu/mtiportal/research/publications/summary/0114.html.
Location and Hydraulic Design of Encroachment on Floodplains, U.S. Code, 23 CFR 650, Subpart A, U.S. Government
Printing Office, Washington, DC.
National Flood Insurance Act, U.S. Code, Title 42, Secs. 4001–28, U.S. Government Printing Office, Washington, DC.
NRC. 1991. Bridge Aesthetics around the World, Transportation Research Board, National Research Council,
Washington, DC.
Ritter, M. A. 1990. Timber Bridges, Design, Construction, Inspection, and Maintenance, EM7700-B. Forest Service, U.S.
Department of Agriculture, Washington, DC.
Science Applications International Corporation (SAIC), Transportation Policy and Analysis Center. 2002. A Guide to
Highway Vulnerability Assessment for Critical Asset Identification and Protection. Report prepared for The American
Association of State Highway and Transportation Officials’ Security Task Force, Washington, DC. Available at
http://security.transportation.org/sites/security/docs/guide-VA_FinalReport.pdf.
Williamson, E. B., D. G. Winget, J. C. Gannon, and K. A. Marchand. 2006. Design of Critical Bridges for Security Against
Terrorist Attacks: Phase II. Pooled Fund Project TPF-5(056) Final Report. University of Texas, Austin, TX.
Winget, D. G., and E. B. Williamson. 2003. Design of Critical Bridges for Security Against Terrorist Attacks. TXDOT
Project No. 0-4569, Phase 1 Report. University of Texas, Austin, TX.
Wright, R. N., and W. H. Walker. 1971. “Criteria for the Deflection of Steel Bridges,” AISI Bulletin, No. 19, November
1971, Washington, DC.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 3: LOADS AND LOAD FACTORS
TABLE OF CONTENTS
3
3.1—SCOPE ................................................................................................................................................................. 3-1
3.2—DEFINITIONS ..................................................................................................................................................... 3-1
3.3—NOTATION ......................................................................................................................................................... 3-3
3.3.1—General ....................................................................................................................................................... 3-3
3.3.2—Load and Load Designation ....................................................................................................................... 3-7
3.4—LOAD FACTORS AND COMBINATIONS ....................................................................................................... 3-8
3.4.1—Load Factors and Load Combinations ....................................................................................................... 3-8
3.4.2—Load Factors for Construction Loads ....................................................................................................... 3-15
3.4.2.1—Evaluation at the Strength Limit State ........................................................................................... 3-15
3.4.2.2—Evaluation of Deflection at the Service Limit State ....................................................................... 3-15
3.4.3—Load Factors for Jacking and Post-Tensioning Forces............................................................................. 3-16
3.4.3.1—Jacking Forces ............................................................................................................................... 3-16
3.4.3.2—Force for Post-Tensioning Anchorage Zones................................................................................. 3-16
3.4.4—Load Factors for Orthotropic Decks......................................................................................................... 3-16
3.5—PERMANENT LOADS ..................................................................................................................................... 3-16
3.5.1—Dead Loads: DC, DW, and EV ................................................................................................................. 3-16
3.5.2—Earth Loads: EH, ES, and DD .................................................................................................................. 3-17
3.6—LIVE LOADS .................................................................................................................................................... 3-17
3.6.1—Gravity Loads: LL and PL ........................................................................................................................ 3-17
3.6.1.1—Vehicular Live Load ...................................................................................................................... 3-17
3.6.1.1.1—Number of Design Lanes ..................................................................................................... 3-17
3.6.1.1.2—Multiple Presence of Live Load ........................................................................................... 3-18
3.6.1.2—Design Vehicular Live Load .......................................................................................................... 3-19
3.6.1.2.1—General ................................................................................................................................ 3-19
3.6.1.2.2—Design Truck ....................................................................................................................... 3-23
3.6.1.2.3—Design Tandem .................................................................................................................... 3-24
3.6.1.2.4—Design Lane Load ................................................................................................................ 3-24
3.6.1.2.5—Tire Contact Area ................................................................................................................ 3-24
3.6.1.2.6—Distribution of Wheel Loads through Earth Fills ................................................................. 3-25
3.6.1.3—Application of Design Vehicular Live Loads ................................................................................ 3-25
3.6.1.3.1—General ................................................................................................................................ 3-25
3.6.1.3.2—Loading for Optional Live Load Deflection Evaluation ...................................................... 3-26
3.6.1.3.3—Design Loads for Decks, Deck Systems, and the Top Slabs of Box Culverts ..................... 3-27
3.6.1.3.4—Deck Overhang Load ........................................................................................................... 3-28
3.6.1.4—Fatigue Load .................................................................................................................................. 3-28
3.6.1.4.1—Magnitude and Configuration .............................................................................................. 3-28
3.6.1.4.2—Frequency ............................................................................................................................ 3-28
3.6.1.4.3—Load Distribution for Fatigue .............................................................................................. 3-29
3.6.1.4.3a—Refined Methods ......................................................................................................... 3-29
3.6.1.4.3b—Approximate Methods ................................................................................................ 3-29
3-i
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
3.6.1.5—Rail Transit Load ...........................................................................................................................3-30
3.6.1.6—Pedestrian Loads ............................................................................................................................3-30
3.6.1.7—Loads on Railings...........................................................................................................................3-30
3.6.2—Dynamic Load Allowance: IM ................................................................................................................. 3-30
3.6.2.1—General ...........................................................................................................................................3-30
3.6.2.2—Buried Components ........................................................................................................................3-31
3.6.2.3—Wood Components .........................................................................................................................3-32
3.6.3—Centrifugal Forces: CE ............................................................................................................................. 3-32
3.6.4—Braking Force: BR .................................................................................................................................... 3-32
3.6.5—Vehicular Collision Force: CT ................................................................................................................. 3-35
3.6.5.1—Protection of Structures ..................................................................................................................3-35
3.6.5.2—Vehicle Collision with Barriers ......................................................................................................3-36
3.7—WATER LOADS: WA ........................................................................................................................................ 3-37
3.7.1—Static Pressure .......................................................................................................................................... 3-37
3.7.2—Buoyancy ................................................................................................................................................. 3-37
3.7.3—Stream Pressure ........................................................................................................................................ 3-37
3.7.3.1—Longitudinal ...................................................................................................................................3-37
3.7.3.2—Lateral ............................................................................................................................................3-38
3.7.4—Wave Load ............................................................................................................................................... 3-39
3.7.5—Change in Foundations Due to Limit State for Scour ............................................................................... 3-39
3.8—WIND LOAD: WL AND WS .............................................................................................................................. 3-39
3.8.1—Horizontal Wind Pressure ........................................................................................................................ 3-39
3.8.1.1—General ...........................................................................................................................................3-39
3.8.1.2—Wind Pressure on Structures: WS ...................................................................................................3-41
3.8.1.2.1—General ................................................................................................................................. 3-41
3.8.1.2.2—Loads from Superstructures ................................................................................................. 3-41
3.8.1.2.3—Forces Applied Directly to the Substructure ........................................................................ 3-42
3.8.1.3—Wind Pressure on Vehicles: WL .....................................................................................................3-42
3.8.2—Vertical Wind Pressure............................................................................................................................. 3-43
3.8.3—Aeroelastic Instability .............................................................................................................................. 3-43
3.8.3.1—General ...........................................................................................................................................3-43
3.8.3.2—Aeroelastic Phenomena ..................................................................................................................3-44
3.8.3.3—Control of Dynamic Responses ......................................................................................................3-44
3.8.3.4—Wind Tunnel Tests .........................................................................................................................3-44
3.9—ICE LOADS: IC ................................................................................................................................................. 3-44
3.9.1—General ..................................................................................................................................................... 3-44
3.9.2—Dynamic Ice Forces on Piers .................................................................................................................... 3-46
3.9.2.1—Effective Ice Strength .....................................................................................................................3-46
3.9.2.2—Crushing and Flexing .....................................................................................................................3-47
3.9.2.3—Small Streams.................................................................................................................................3-48
3.9.2.4—Combination of Longitudinal and Transverse Forces ....................................................................3-49
3.9.2.4.1—Piers Parallel to Flow ........................................................................................................... 3-49
3.9.2.4.2—Piers Skewed to Flow ........................................................................................................... 3-49
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
TABLE OF CONTENTS
3-iii
3.9.2.5—Slender and Flexible Piers ............................................................................................................. 3-50
3.9.3—Static Ice Loads on Piers .......................................................................................................................... 3-50
3.9.4—Hanging Dams and Ice Jams .................................................................................................................... 3-50
3.9.5—Vertical Forces Due to Ice Adhesion ....................................................................................................... 3-50
3.9.6—Ice Accretion and Snow Loads on Superstructures .................................................................................. 3-51
3.10—EARTHQUAKE EFFECTS: EQ ...................................................................................................................... 3-52
3.10.1—General ................................................................................................................................................... 3-52
3.10.2—Seismic Hazard ...................................................................................................................................... 3-54
3.10.2.1—General Procedure........................................................................................................................ 3-54
3.10.2.2—Site Specific Procedure ................................................................................................................ 3-83
3.10.3—Site Effects ............................................................................................................................................. 3-84
3.10.3.1—Site Class Definitions................................................................................................................... 3-84
3.10.3.2—Site Factors .................................................................................................................................. 3-88
3.10.4—Seismic Hazard Characterization ........................................................................................................... 3-89
3.10.4.1—Design Response Spectrum.......................................................................................................... 3-89
3.10.4.2—Elastic Seismic Response Coefficient .......................................................................................... 3-90
3.10.5—Operational Classification ...................................................................................................................... 3-90
3.10.6—Seismic Performance Zones ................................................................................................................... 3-91
3.10.7—Response Modification Factors .............................................................................................................. 3-91
3.10.7.1—General......................................................................................................................................... 3-91
3.10.7.2—Application .................................................................................................................................. 3-92
3.10.8—Combination of Seismic Force Effects ................................................................................................... 3-92
3.10.9—Calculation of Design Forces ................................................................................................................. 3-93
3.10.9.1—General......................................................................................................................................... 3-93
3.10.9.2—Seismic Zone 1............................................................................................................................. 3-93
3.10.9.3—Seismic Zone 2............................................................................................................................. 3-93
3.10.9.4—Seismic Zones 3 and 4 ................................................................................................................. 3-94
3.10.9.4.1—General .............................................................................................................................. 3-94
3.10.9.4.2—Modified Design Forces..................................................................................................... 3-94
3.10.9.4.3—Inelastic Hinging Forces .................................................................................................... 3-94
3.10.9.4.3a—General...................................................................................................................... 3-94
3.10.9.4.3b—Single Columns and Piers ......................................................................................... 3-95
3.10.9.4.3c—Piers with Two or More Columns ............................................................................. 3-96
3.10.9.4.3d— Column and Pile Bent Design Forces ...................................................................... 3-97
3.10.9.4.3e—Pier Design Forces .................................................................................................... 3-97
3.10.9.4.3f—Foundation Design Forces ......................................................................................... 3-97
3.10.9.5—Longitudinal Restrainers .............................................................................................................. 3-98
3.10.9.6—Hold-Down Devices .................................................................................................................... 3-98
3.10.10—Requirements for Temporary Bridges and Stage Construction ............................................................ 3-98
3.11—EARTH PRESSURE: EH, ES, LS, AND DD .................................................................................................... 3-99
3.11.1—General ................................................................................................................................................... 3-99
3.11.2—Compaction .......................................................................................................................................... 3-100
3.11.3—Presence of Water ................................................................................................................................ 3-100
3.11.4—Effect of Earthquake ............................................................................................................................ 3-101
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
3-iv
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
3.11.5—Earth Pressure: EH ............................................................................................................................... 3-101
3.11.5.1—Lateral Earth Pressure ................................................................................................................3-101
3.11.5.2—At-Rest Lateral Earth Pressure Coefficient, ko ...........................................................................3-102
3.11.5.3—Active Lateral Earth Pressure Coefficient, ka .............................................................................3-103
3.11.5.4—Passive Lateral Earth Pressure Coefficient, kp............................................................................3-105
3.11.5.5—Equivalent-Fluid Method of Estimating Rankine Lateral Earth Pressures .................................3-107
3.11.5.6—Lateral Earth Pressures for Nongravity Cantilevered Walls .......................................................3-109
3.11.5.7—Apparent Earth Pressure (AEP) for Anchored Walls .................................................................3-113
3.11.5.7.1—Cohesionless Soils ........................................................................................................... 3-113
3.11.5.7.2—Cohesive Soils .................................................................................................................. 3-114
3.11.5.7.2a—Stiff to Hard ............................................................................................................ 3-115
3.11.5.7.2b—Soft to Medium Stiff ............................................................................................... 3-115
3.11.5.8—Lateral Earth Pressures for Mechanically Stabilized Earth Walls ..............................................3-116
3.11.5.8.1—General ............................................................................................................................. 3-116
3.11.5.8.2—Internal Stability............................................................................................................... 3-118
3.11.5.9—Lateral Earth Pressures for Prefabricated Modular Walls ..........................................................3-118
3.11.6—Surcharge Loads: ES and LS ................................................................................................................ 3-123
3.11.6.1—Uniform Surcharge Loads (ES) ..................................................................................................3-123
3.11.6.2—Point, Line, and Strip Loads (ES): Walls Restrained from Movement .......................................3-124
3.11.6.3—Strip Loads (ES): Flexible Walls ................................................................................................3-127
3.11.6.4—Live Load Surcharge (LS) ..........................................................................................................3-129
3.11.6.5—Reduction of Surcharge ..............................................................................................................3-130
3.11.7—Reduction Due to Earth Pressure .......................................................................................................... 3-131
3.11.8—Downdrag ............................................................................................................................................. 3-131
3.12—FORCE EFFECTS DUE TO SUPERIMPOSED DEFORMATIONS: TU, TG, SH, CR, SE, PS ..................... 3-133
3.12.1—General ................................................................................................................................................. 3-133
3.12.2—Uniform Temperature ........................................................................................................................... 3-133
3.12.2.1—Temperature Range for Procedure A ..........................................................................................3-133
3.12.2.2—Temperature Range for Procedure B ..........................................................................................3-134
3.12.2.3—Design Thermal Movements ......................................................................................................3-136
3.12.3—Temperature Gradient........................................................................................................................... 3-136
3.12.4—Differential Shrinkage .......................................................................................................................... 3-137
3.12.5—Creep .................................................................................................................................................... 3-137
3.12.6—Settlement ............................................................................................................................................. 3-138
3.12.7—Secondary Forces from Post-Tensioning, PS ....................................................................................... 3-138
3.13—FRICTION FORCES: FR ............................................................................................................................... 3-138
3.14—VESSEL COLLISION: CV............................................................................................................................. 3-138
3.14.1—General ................................................................................................................................................. 3-138
3.14.2—Owner’s Responsibility ........................................................................................................................ 3-140
3.14.3—Operational Classification .................................................................................................................... 3-140
3.14.4—Design Vessel ....................................................................................................................................... 3-140
3.14.5—Annual Frequency of Collapse ............................................................................................................. 3-141
3.14.5.1—Vessel Frequency Distribution ...................................................................................................3-142
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2012
Edition
TABLE OF CONTENTS
3-v
3.14.5.2—Probability of Aberrancy............................................................................................................ 3-143
3.14.5.2.1—General ............................................................................................................................ 3-143
3.14.5.2.2—Statistical Method ............................................................................................................ 3-143
3.14.5.2.3—Approximate Method ....................................................................................................... 3-143
3.14.5.3—Geometric Probability ................................................................................................................ 3-146
3.14.5.4—Probability of Collapse .............................................................................................................. 3-147
3.14.5.5 Protection Factor ........................................................................................................................... 3-147
3.14.6—Design Collision Velocity .................................................................................................................... 3-150
3.14.7—Vessel Collision Energy ....................................................................................................................... 3-150
3.14.8—Ship Collision Force on Pier ................................................................................................................ 3-151
3.14.9—Ship Bow Damage Length ................................................................................................................... 3-153
3.14.10—Ship Collision Force on Superstructure.............................................................................................. 3-153
3.14.10.1—Collision with Bow .................................................................................................................. 3-153
3.14.10.2—Collision with Deck House ...................................................................................................... 3-153
3.14.10.3—Collision with Mast .................................................................................................................. 3-154
3.14.11—Barge Collision Force on Pier ............................................................................................................ 3-154
3.14.12—Barge Bow Damage Length ............................................................................................................... 3-155
3.14.13—Damage at the Extreme Limit State ................................................................................................... 3-155
3.14.14—Application of Impact Force .............................................................................................................. 3-156
3.14.14.1—Substructure Design ................................................................................................................. 3-156
3.14.14.2—Superstructure Design .............................................................................................................. 3-157
3.14.15—Protection of Substructures ................................................................................................................ 3-157
3.14.16—Security Considerations ..................................................................................................................... 3-158
3.15—BLAST LOADING ........................................................................................................................................ 3-159
3.15.1—Introduction .......................................................................................................................................... 3-159
3.16—REFERENCES............................................................................................................................................... 3-159
APPENDIX A3—SEISMIC DESIGN FLOWCHARTS ........................................................................................... 3-167
APPENDIX B3—OVERSTRENGTH RESISTANCE ............................................................................................. 3-169
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 3:
LOADS AND LOAD FACTORS
3
3.1—SCOPE
C3.1
This Section specifies minimum requirements for
loads and forces, the limits of their application, load
factors, and load combinations used for the design of new
bridges. The load provisions may also be applied to the
structural evaluation of existing bridges.
Where multiple performance levels are provided, the
selection of the design performance level is the
responsibility of the Owner.
A minimum load factor is specified for force effects
that may develop during construction. Additional
requirements for construction of segmental concrete
bridges are specified in Article 5.14.2.
This Section includes, in addition to traditional loads,
the force effects due to collisions, earthquakes, and
settlement and distortion of the structure.
Vehicle and vessel collisions, earthquakes, and
aeroelastic instability develop force effects that are
dependent upon structural response. Therefore, such force
effects cannot be determined without analysis and/or
testing.
With the exception of segmental concrete bridges,
construction loads are not provided, but the Designer
should obtain pertinent information from prospective
contractors.
3.2—DEFINITIONS
Active Earth Pressure—Lateral pressure resulting from the retention of the earth by a structure or component that is
tending to move away from the soil mass.
Active Earth Wedge—Wedge of earth with a tendency to become mobile if not retained by a structure or component.
Aeroelastic Vibration—Periodic, elastic response of a structure to wind.
Apparent Earth Pressure—Lateral pressure distribution for anchored walls constructed from the top down.
Axle Unit—Single axle or tandem axle.
Berm—An earthwork used to redirect or slow down impinging vehicles or vessels and to stabilize fill, embankment, or soft
ground and cut slopes.
Centrifugal Force—A lateral force resulting from a change in the direction of a vehicle’s movement.
Damper—A device that transfers and reduces forces between superstructure elements and/or superstructure and
substructure elements, while permitting thermal movements. The device provides damping by dissipating energy under
seismic, braking or other dynamic loads.
Deep Draft Waterways—A navigable waterway used by merchant ships with loaded drafts of 14–60+ ft.
Design Lane—A notional traffic lane positioned transversely on the roadway.
Design Thermal Movement Range—The structure movement range resulting from the difference between the maximum
design temperature and minimum design temperature as defined in Article 3.12.
Design Water Depth—Depth of water at mean high water.
Distortion—Change in structural geometry.
Dolphin—Protective object that may have its own fender system and that is usually circular in plan and structurally
independent from the bridge.
Dynamic Load Allowance—An increase in the applied static force effects to account for the dynamic interaction between
the bridge and moving vehicles.
Equivalent Fluid—A notional substance whose density is such that it would exert the same pressure as the soil it is seen to
replace for computational purposes.
3-1
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
3-2
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Exposed—A condition in which a portion of a bridge’s substructure or superstructure is subject to physical contact by any
portion of a colliding vessel’s bow, deck house, or mast.
Extreme—A maximum or a minimum.
Fender—Protection hardware attached to the structural component to be protected or used to delineate channels or to
redirect aberrant vessels.
Frazil Ice—Ice resulting from turbulent water flow.
Global—Pertinent to the entire superstructure or to the whole bridge.
Influence Surface—A continuous or discretized function over a bridge deck whose value at a point, multiplied by a load
acting normal to the deck at that point, yields the force effect being sought.
Knot—A velocity of 1.1508 mph.
Lane—The area of deck receiving one vehicle or one uniform load line.
Lever Rule—The statical summation of moments about one point to calculate the reaction at a second point.
Liquefaction—The loss of shear strength in a saturated soil due to excess hydrostatic pressure. In saturated, cohesionless
soils, such a strength loss can result from loads that are applied instantaneously or cyclically, particularly in loose fine to
medium sands that are uniformly graded.
Load—The effect of acceleration, including that due to gravity, imposed deformation, or volumetric change.
Local—Pertinent to a component or subassembly of components.
Mode of Vibration—A shape of dynamic deformation associated with a frequency of vibration.
Navigable Waterway—A waterway, determined by the U.S. Coast Guard as being suitable for interstate or foreign
commerce, as described in 33CFR205-25.
Nominal Load—An arbitrarily selected design load level.
Normally Consolidated Soil—A soil for which the current effective overburden pressure is the same as the maximum
pressure that has been experienced.
Overconsolidated Soil—A soil that has been under greater overburden pressure than currently exists.
Overall Stability—Stability of the entire retaining wall or abutment structure and is determined by evaluating potential slip
surfaces located outside of the whole structure.
Overconsolidation Ratio—Ratio of the maximum preconsolidation pressure to the overburden pressure.
Passive Earth Pressure—Lateral pressure resulting from the earth’s resistance to the lateral movement of a structure or
component into the soil mass.
Permanent Loads—Loads and forces that are, or are assumed to be, either constant upon completion of construction or
varying only over a long time interval.
Permit Vehicle—Any vehicle whose right to travel is administratively restricted in any way due to its weight or size.
Reliability Index—A quantitative assessment of safety expressed as the ratio of the difference between the mean resistance
and mean force effect to the combined standard deviation of resistance and force effect.
Restrainers—A system of high-strength cables or rods that transfers forces between superstructure elements and/or
superstructure and substructure elements under seismic or other dynamic loads after an initial slack is taken up, while
permitting thermal movements.
Roadway Width—Clear space between barriers and/or curbs.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 3: LOADS AND LOAD FACTORS
3-3
Setting Temperature—A structure’s average temperature, which is used to determine the dimensions of a structure when a
component is added or set in place.
Shallow Draft Waterways—A navigable waterway used primarily by barge vessels with loaded drafts of less than 9–10 ft.
Shock Transmission Unit (STU)—A device that provides a temporary rigid link between superstructure elements and/or
superstructure and substructure elements under seismic, braking or other dynamic loads, while permitting thermal
movements.
Structurally Continuous Barrier—A barrier, or any part thereof, that is interrupted only at deck joints.
Substructure—Structural parts of the bridge that support the horizontal span.
Superstructure—Structural parts of the bridge that provide the horizontal span.
Surcharge—A load used to model the weight of earth fill or other loads applied to the top of the retained material.
Tandem—Two closely spaced axles, usually connected to the same under-carriage, by which the equalization of load
between the axles is enhanced.
Transient Loads—Loads and forces that can vary over a short time interval relative to the lifetime of the structure.
Tonne—2.205 kip.
Wall Friction Angle—An angle whose arctangent represents the apparent friction between a wall and a soil mass.
Wheel—Single or dual tire at one end of an axle.
Wheel Line—A transverse or longitudinal grouping of wheels.
3.3—NOTATION
2013 Revision
3.3.1—General
A
AEP
AF
a
=
=
=
=
aB
as
AS
Β
B′
Be
BM
Bp
BR
b
bf
C
=
=
=
=
=
=
=
=
=
=
=
=
Ca
CD
CH
CL
Cn
Csm
=
=
=
=
=
=
plan area of ice floe (ft2); depth of temperature gradient (in.) (C3.9.2.3) (3.12.3)
apparent earth pressure for anchored walls (ksf) (3.4.1)
annual frequency of bridge element collapse (number/yr.) (C3.14.4)
length of uniform deceleration at braking (ft); truncated distance (ft); average bow damage length (ft)
(C3.6.4) (C3.9.5) (C3.14.9)
bow damage length of standard hopper barge (ft) (3.14.11)
bow damage length of ship (ft) (3.14.9)
peak seismic ground acceleration coefficient modified by short-period site factor (3.10.4.2)
notional slope of backfill (degrees) (3.11.5.8.1)
equivalent footing width (ft) (3.11.6.3)
width of excavation (ft) (3.11.5.7.2b)
beam (width) for barge, barge tows, and ship vessels (ft) (C3.14.5.1)
width of bridge pier (ft) (3.14.5.3)
vehicular braking force; base rate of vessel aberrancy (3.3.2) (3.14.5.2.3)
braking force coefficient; width of a discrete vertical wall element (ft) (C3.6.4) (3.11.5.6)
width of applied load or footing (ft) (3.11.6.3)
coefficient to compute centrifugal forces; constant for terrain conditions in relation to wind approach (3.6.3)
(C3.8.1.1)
coefficient for force due to crushing of ice (3.9.2.2)
drag coefficient (s2 lbs./ft4) (3.7.3.1)
hydrodynamic mass coefficient (3.14.7)
lateral drag coefficient (C3.7.3.1)
coefficient for nose inclination to compute Fb (3.9.2.2)
elastic seismic response coefficient for the mth mode of vibration (3.10.4.2)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
3-4
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
c
cf
D
=
=
=
DB
DE
Do
=
=
=
DWT
D1
d
=
=
=
dc
ds
E
EB
e′
F
=
=
=
=
=
=
Fa
Fb
Fc
Fpga
FSBH
Ft
Fv
=
=
=
=
=
=
=
F1
F2
f
=
=
=
f′ c
g
H
=
=
=
HL
Hp
Hs
H1
Hn+1
h
heq
IM
KE
K1
k
ka
ko
kp
ks
L
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
ℓ
LOA
m
N
N
=
=
=
=
=
soil cohesion (ksf) (3.11.5.4)
distance from back of a wall face to the front of an applied load or footing (ft) (3.11.6.3)
depth of embedment for a permanent nongravity cantilever wall with discrete vertical wall elements (ft)
(3.11.5.6)
bow depth (ft) (C3.14.5.1)
minimum depth of earth cover (ft) (3.6.2.2)
calculated embedment depth to provide equilibrium for nongravity cantilevered with continuous vertical
elements by the simplified method (ft) (3.11.5.6)
size of vessel based on deadweight tonnage (tonne) (C3.14.1)
effective width of applied load at any depth (ft) (3.11.6.3)
depth of potential base failure surface below base of excavation (ft); horizontal distance from the back of a
wall face to the centerline of an applied load (ft) (3.11.5.7.2b) (3.11.6.3)
total thickness of cohesive soil layers in the top 100 ft (3.10.3.1)
total thickness of cohesionless soil layers in the top 100 ft (3.10.3.1)
Young’s modulus (ksf) (C3.9.5)
deformation energy (kip-ft) (C3.14.11)
eccentricity of load on footing (ft) (3.11.6.3)
longitudinal force on pier due to ice floe (kip); force required to fail an ice sheet (kip/ft); force at base of
nongravity cantilevered wall required to provide force equilibrium (kip/ft) (3.9.2.2) (C3.9.5) (3.11.5.6)
site factor for short-period range of acceleration response spectrum (3.10.3.2)
horizontal force due to failure of ice flow due to bending (kip) (3.9.2.2)
horizontal force due to crushing of ice (kip) (3.9.2.2)
site factor at zero-period on acceleration response spectrum (3.10.3.2)
factor of safety against basal heave (C3.11.5.6)
transverse force on pier due to ice flow (kip) (3.9.2.4.1)
vertical ice force due to adhesion (kip); site factor for long-period range of acceleration response spectrum
(3.9.5) (3.10.3.2)
lateral force due to earth pressure (kip/ft) (3.11.6.3)
lateral force due to traffic surcharge (kip/ft) (3.11.6.3)
constant applied in calculating the coefficient C used to compute centrifugal forces, taken equal to 4/3 for
load combinations other than fatigue and 1.0 for fatigue (3.6.3)
specified compressive strength of concrete for use in design (ksi) (3.5.1)
gravitational acceleration (ft/s2) (3.6.3)
ultimate bridge element strength (kip); final height of retaining wall (ft); total excavation depth (ft);
resistance of bridge component to a horizontal force (kip) (C3.11.1) (3.11.5.7.1) (3.14.5.4)
depth of barge head-block on its bow (ft) (3.14.14.1)
ultimate bridge pier resistance (kip) (3.14.5.4)
ultimate bridge superstructure resistance (kip) (3.14.5.4)
distance from ground surface to uppermost ground anchor (ft) (3.11.5.7.1)
distance from base of excavation to lowermost ground anchor (ft) (3.11.5.7.1)
notional height of earth pressure diagram (ft) (3.11.5.7)
equivalent height of soil for vehicular load (ft) (3.11.6.4)
dynamic load allowance (C3.6.1.2.5)
design impact energy of vessel collision (kip-ft) (3.14.7)
ice force reduction factor for small streams (C3.9.2.3)
coefficient of lateral earth pressure; number of cohesive soil layers in the top 100 ft (3.11.6.2) (3.10.3.1)
coefficient of active lateral earth pressure (3.11.5.1)
coefficient of at rest lateral earth pressure (3.11.5.1)
coefficient of passive lateral earth pressure (3.11.5.1)
coefficient of earth pressure due to surcharge (3.11.6.1)
perimeter of pier (ft); length of soil reinforcing elements in an MSE wall (ft); length of footing (ft);
expansion length (in.) (3.9.5) (3.11.5.8) (3.11.6.3) (3.12.2.3)
characteristic length (ft); center-to-center spacing of vertical wall elements (ft) (C3.9.5) (3.11.5.6)
length overall of ship or barge tow including the tug or tow boat (ft) (3.14.5)
multiple presence factor; number of cohesionless soil layers in the top 100 ft (3.6.1.1.2) (3.10.3.1)
number of one-way passages of vessels navigating through the bridge (number/yr.) (3.14.5)
average Standard Penetration Test (SPT) blow count (blows/ft) (ASTM D1586) for the upper 100 ft of the
soil profile (3.10.3.1)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 3: LOADS AND LOAD FACTORS
N ch
=
Nchi
Ni
=
=
Ns
OCR
P
=
=
=
PA
Pa
PB
=
=
=
PB
PBH
PC
PD
PDH
PG
PGA
PH
Ph
PI
PMT
Pp
PS
Pv
=
=
=
=
=
=
=
=
=
=
=
=
=
=
P′v
p
=
=
pa
pp
Q
Qi
q
qs
R
=
=
=
=
=
=
=
RB
RBH
RC
RD
RDH
RXC
r
SDS
=
=
=
=
=
=
=
=
SD1
=
Sf
Sm
SS
=
=
=
3-5
average Standard Penetration Test (SPT) blow count (blows/ft) (ASTM D1586) for cohesive soil layers in the
upper 100 ft of the soil profile and su for cohesive soil layers (PI > 20) in the top 100 ft ( su method) (3.10.3.1)
blowcount for a cohesionless soil layer (not to exceed 100 blows/ft in the above expression) (3.10.3.1)
Standard Penetration Test blow count of a layer (not to exceed 100 blows/ft in the above expression). Note
that when using Method B, N values are for cohesionless soils and cohesive soil and rock layers within the
upper 100 ft Where refusal is met for a rock layer, Ni should be taken as 100 blows/ft (3.10.3.1)
stability number (3.11.5.6)
overconsolidation ratio (3.11.5.2)
maximum vertical force for single ice wedge (kip); load resulting from vessel impact (kip); concentrated
wheel load (kip); live load intensity; point load (kip) (C3.9.5) (3.14.5.4) (C3.6.1.2.5) (C3.11.6.2) (3.11.6.1)
probability of vessel aberrancy (3.14.5)
force resultant per unit width of wall (kip/ft) (3.11.5.8.1)
barge collision impact force for head-on collision between barge bow and a rigid object (kip); base wind
pressure corresponding to a wind speed of 100 mph (ksf) (3.14.11) (3.8.1.2)
average equivalent static barge impact force resulting from Meir-Dornberg Study (kip) (C3.14.11)
ship collision impact force between ship bow and a rigid superstructure (kip) (3.14.10.1)
probability of bridge collapse (3.14.5)
design wind pressure (ksf) (3.8.1.2.1)
ship collision impact force between ship deck house and a rigid superstructure (kip) (3.14.5.4)
geometric probability of vessel collision with bridge pier/span (3.14.5)
peak seismic ground acceleration coefficient on rock (Site Class B) (3.10.2.1) (3.10.4.2)
lateral force due to superstructure or other concentrated lateral loads (kip/ft) (3.11.6.3)
horizontal component of resultant earth pressure on wall (kip/ft) (3.11.5.5)
plasticity index (ASTM D4318) (3.10.3.1)
ship collision impact force between ship mast and a rigid superstructure (kip) (3.14.5.4)
passive earth pressure (kip/ft) (3.11.5.4)
ship collision impact force for head-on collision between ship bow and a rigid object (kip) (3.14.5.4)
vertical component of resultant earth pressure on wall (kip/ft); load per linear foot of strip footing (kip/ft)
(3.11.5.5) (3.11.6.3)
load on isolated rectangular footing or point load (kip) (3.11.6.3)
effective ice crushing strength (ksf); stream pressure (ksf); basic earth pressure (psf); fraction of truck traffic
in a single lane; load intensity (ksf) (3.9.2.2) (3.7.3.1) (3.11.5.1) (3.6.1.4.2) (3.11.6.1)
apparent earth pressure (ksf); maximum ordinate of pressure diagram (ksf) (3.11.5.3) (3.11.5.7.1)
passive earth pressure (ksf) (3.11.5.4)
total factored load; load intensity for infinitely long line loading (kip/ft) (3.4.1) (3.11.6.2)
force effects (3.4.1)
surcharge pressure (ksf) (3.11.6.3)
uniform surcharge pressure (ksf) (3.11.6.1)
radius of curvature (ft); radius of circular pier (ft); seismic response modification factor; reduction factor of
lateral passive earth pressure; radial distance from point of load application to a point on the wall (ft);
reaction force to be resisted by subgrade below base of excavation (kip/ft) (3.6.3) (3.9.5) (3.10.7.1) (3.11.5.4)
(3.11.6.1) (3.11.5.7.1)
PA correction factor for bridge location (3.14.5.2.3)
ratio of exposed superstructure depth to the total ship bow depth (3.14.10.1)
PA correction factor for currents parallel to vessel transit path (3.14.5.2.3)
PA correction factor for vessel traffic density (3.14.5.2.3)
reduction factor for ship deck house collision force (3.14.10.2)
PA correction factor for cross-currents acting perpendicular to vessel transit path (3.14.5.2.3)
radius of pier nose (ft) (C3.9.2.3)
horizontal response spectral acceleration coefficient at 0.2-s period modified by short-period site factor
(3.10.4.2)
horizontal response spectral acceleration coefficient at 1.0-s period modified by long-period site factor
(3.10.4.2)
freezing index (C3.9.2.2)
shear strength of rock mass (ksf) (3.11.5.6)
horizontal response spectral acceleration coefficient at 0.2-s period on rock (Site Class B) (3.10.2.1)
(3.10.4.2)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
3-6
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Su
Sub
Sv
su
=
=
=
=
sui
S1
=
=
T
=
TF
=
Thi
=
Tm
=
Tmax
=
TMaxDesign=
TMinDesign =
TS
=
T0
t
V
VB
VC
VDZ
VMIN
=
=
=
=
=
=
=
VT
VXC
V0
=
=
=
V30
v
vs
W
w
=
=
=
=
=
X
=
Xc
XL
X1
X2
Z
=
=
=
=
=
Z0
Z2
z
α
=
=
=
=
β
=
undrained shear strength of cohesive soil (ksf) (3.11.5.6)
undrained strength of soil below excavation base (ksf) (3.11.5.7.2b)
vertical spacing of reinforcements (ft) (3.11.5.8.1)
average undrained shear strength in ksf (ASTM D2166 or ASTM D2850) for the upper 100 ft of the soil
profile (3.10.3.1)
undrained shear strength for a cohesive soil layer (not to exceed 5.0 ksf in the above expression) (3.10.3.1)
horizontal response spectral acceleration coefficient at 1.0-s period on rock (Site Class B) (3.10.2.1)
(3.10.4.2)
mean daily air temperature (°F) (C3.9.2.2)
period of fundamental mode of vibration of bridge (s) (3.10.2.2)
horizontal load in anchor i (kip/ft) (3.11.5.7.1)
period of vibration for mth mode (s) (3.10.4.2)
applied load to reinforcement in a mechanically stabilized earth wall (kip/ft) (3.11.5.8.2)
maximum design temperature used for thermal movement effects (°F) (3.12.2.1) (3.12.2.2) (3.12.2.3)
minimum design temperature used for thermal movement effects (°F) (3.12.2.1) (3.12.2.2) (3.12.2.3)
corner period at which acceleration response spectrum changes from being independent of period to being
inversely proportional to period (s) (3.10.4.2)
reference period used to define shape of acceleration response spectrum (s) (3.10.4.2)
thickness of ice (ft); thickness of deck (in.) (3.9.2.2) (3.12.3)
design velocity of water (ft/s); design impact speed of vessel (ft/s) (3.7.3.1) (3.14.6)
base wind velocity taken as 100 mph (3.8.1.1)
waterway current component acting parallel to the vessel transit path (knots) (3.14.5.2.3)
design wind velocity at design Elevation Z (mph) (3.8.1.1)
minimum design impact velocity taken not less than the yearly mean current velocity for the bridge location
(ft/s) (3.14.6)
vessel transit speed in the navigable channel (ft/s) (3.14.6)
waterway current component acting perpendicular to the vessel transit path (knots) (3.14.5.2.3)
friction velocity, a meteorological wind characteristic for various upwind surface characteristics (mph)
(3.8.1.1)
wind speed at 30.0 ft above low ground or water level (mph) (3.8.1.1)
highway design speed (ft/s) (3.6.3)
average shear wave velocity for the upper 100 ft of the soil profile (3.10.3.1)
displacement weight of vessel (tonne) (C3.14.5.1)
width of clear roadway (ft); width of clear pedestrian and/or bicycle bridge (ft); width of pier at level of ice
action (ft); specific weight of water (kcf); moisture content (ASTM D2216) (3.6.1.1.1) (3.6.1.6) (3.9.2.2)
(C3.7.3.1) (3.10.3.1)
horizontal distance from back of wall to point of load application (ft); distance to bridge element from the
centerline of vessel transit path (ft) (3.11.6.2) (3.14.6)
distance to edge of channel from centerline of vessel transit path (ft) (3.14.6)
distance from centerline of vessel transit path equal to 3 × LOA (ft) (3.14.6)
distance from the back of the wall to the start of the line load (ft) (3.11.6.2)
length of the line load (ft) (3.11.6.2)
structure height above low ground or water level > 30.0 ft (ft); depth below surface of soil (ft); depth from
the ground surface to a point on the wall under consideration (ft); vertical distance from point of load
application to the elevation of a point on the wall under consideration (ft) (3.8.1.1) (3.11.6.3) (3.11.6.2)
friction length of upstream fetch, a meteorological wind characteristic (ft) (3.8.1.1)
depth where effective width intersects back of wall face (ft) (3.11.6.3)
depth below surface of backfill (ft) (3.11.5.1)
constant for terrain conditions in relation to wind approach; coefficient for local ice condition; inclination of
pier nose with respect to a vertical axis (degrees); inclination of back of wall with respect to a vertical axis
(degrees); angle between foundation wall and a line connecting the point on the wall under consideration and
a point on the bottom corner of the footing nearest to the wall (rad); coefficient of thermal expansion
(in./in./°F) (C3.8.1.1) (C3.9.2.2) (3.9.2.2) (C3.11.5.3) (3.11.6.2) (3.12.2.3)
safety index; nose angle in a horizontal plane used to calculate transverse ice forces (degrees); slope of
backfill surface behind retaining wall; {+ for slope up from wall; − for slope down from wall} (degrees)
(C3.4.1) (3.9.2.4.1) (3.11.5.3)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 3: LOADS AND LOAD FACTORS
β′
=
γ
=
γs
γ′s
γEQ
γeq
γi
γp
γSE
γTG
Δ
=
=
=
=
=
=
=
=
=
Δp
Δph
=
=
ΔT
ΔσH
Δσv
δ
=
=
=
=
ηi
θ
=
=
θf
σ
σT
ν
φ
φf
φ′f
φr
φ′s
=
=
=
=
=
=
=
=
=
3-7
slope of ground surface in front of wall {+ for slope up from wall; − for slope down from wall} (degrees)
(3.11.5.6)
load factors; unit weight of materials (kcf); unit weight of water (kcf); unit weight of soil (kcf) (C3.4.1)
(3.5.1) (C3.9.5) (3.11.5.1)
unit weight of soil (kcf) (3.11.5.1)
effective soil unit weight (kcf) (3.11.5.6)
load factor for live load applied simultaneously with seismic loads (3.4.1)
equivalent-fluid unit weight of soil (kcf) (3.11.5.5)
load factor (3.4.1)
load factor for permanent loading (3.4.1)
load factor for settlement (3.4.1)
load factor for temperature gradient (3.4.1)
movement of top of wall required to reach minimum active or maximum passive pressure by tilting or lateral
translation (ft) (C3.11.1) (3.11.5.5)
constant horizontal earth pressure due to uniform surcharge (ksf) (3.11.6.1)
constant horizontal pressure distribution on wall resulting from various types of surcharge loading (ksf)
(3.11.6.2)
design thermal movement range (in.) (3.12.2.3)
horizontal stress due to surcharge load (ksf) (3.11.6.3)
vertical stress due to surcharge load (ksf) (3.11.6.3)
angle of truncated ice wedge (degrees); friction angle between fill and wall (degrees); angle between
foundation wall and a line connecting the point on the wall under consideration and a point on the bottom
corner of the footing furthest from the wall (rad) (C3.9.5) (3.11.5.3) (3.11.6.2)
load modifier specified in Article 1.3.2; wall face batter (3.4.1) (3.11.5.9)
angle of back of wall to the horizontal (degrees); angle of channel turn or bend (degrees); angle between
direction of stream flow and the longitudinal axis of pier (degrees) (3.11.5.3) (3.14.5.2.3) (3.7.3.2)
friction angle between ice floe and pier (degrees) (3.9.2.4.1)
standard deviation of normal distribution (3.14.5.3)
tensile strength of ice (ksf) (C3.9.5)
Poisson’s Ratio (dim.) (3.11.6.2)
resistance factors (C3.4.1)
angle of internal friction (degrees) (3.11.5.4)
effective angle of internal friction (degrees) (3.11.5.2)
internal friction angle of reinforced fill (degrees) (3.11.6.3)
angle of internal friction of retained soil (degrees) (3.11.5.6)
3.3.2—Load and Load Designation
The following permanent and transient loads and
forces shall be considered:
•
Permanent Loads
CR =
DD =
DC =
DW =
EH =
EL =
ES =
EV =
force effects due to creep
downdrag force
dead load of structural components and
nonstructural attachments
dead load of wearing surfaces and utilities
horizontal earth pressure load
miscellaneous locked-in force effects resulting
from the construction process, including jacking
apart of cantilevers in segmental construction
earth surcharge load
vertical pressure from dead load of earth fill
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
3-8
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
PS =
SH =
secondary forces from post-tensioning
force effects due to shrinkage
•
Transient Loads
BL
BR
CE
CT
CV
EQ
FR
IC
IM
LL
LS
PL
SE
TG
TU
WA
WL
WS
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
blast loading
vehicular braking force
vehicular centrifugal force
vehicular collision force
vessel collision force
earthquake load
friction load
ice load
vehicular dynamic load allowance
vehicular live load
live load surcharge
pedestrian live load
force effect due to settlement
force effect due to temperature gradient
force effect due to uniform temperature
water load and stream pressure
wind on live load
wind load on structure
3.4—LOAD FACTORS AND COMBINATIONS
3.4.1—Load Factors and Load Combinations
2013 Revision
The total factored force effect shall be taken as:
Q = ηi γ i Qi
where:
ηi =
Qi =
γi =
(3.4.1-1)
C3.4.1
The background for the load factors specified herein,
and the resistance factors specified in other Sections of
these Specifications is developed in Nowak (1992).
load modifier specified in Article 1.3.2
force effects from loads specified herein
load factors specified in Tables 3.4.1-1 and
3.4.1-2
Components and connections of a bridge shall satisfy
Eq. 1.3.2.1-1 for the applicable combinations of factored
extreme force effects as specified at each of the following
limit states:
•
Strength I—Basic load combination relating to the
normal vehicular use of the bridge without wind.
•
Strength II—Load combination relating to the use of
the bridge by Owner-specified special design vehicles,
evaluation permit vehicles, or both without wind.
•
Strength III—Load combination relating to the bridge
exposed to wind velocity exceeding 55 mph.
The permit vehicle should not be assumed to be the
only vehicle on the bridge unless so assured by traffic
control. See Article 4.6.2.2.5 regarding other traffic on the
bridge simultaneously.
Vehicles become unstable at higher wind velocities.
Therefore, high winds prevent the presence of significant
live load on the bridge.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 3: LOADS AND LOAD FACTORS
•
Strength IV—Load combination relating to very high
dead load to live load force effect ratios.
•
Strength V—Load combination relating to normal
vehicular use of the bridge with wind of 55 mph
velocity.
•
Extreme Event I—Load combination including
earthquake. The load factor for live load γEQ, shall be
determined on a project-specific basis.
•
Extreme Event II—Load combination relating to ice
load, collision by vessels and vehicles, check floods,
and certain hydraulic events with a reduced live load
other than that which is part of the vehicular collision
load, CT. The cases of check floods shall not be
combined with BL, CV, CT, or IC.
3-9
The standard calibration process for the strength limit
state consists of trying out various combinations of load
and resistance factors on a number of bridges and their
components. Combinations that yield a safety index close
to the target value of β = 3.5 are retained for potential
application. From these are selected constant load factors γ
and corresponding resistance factors φ for each type of
structural component reflecting its use.
This calibration process had been carried out for a large
number of bridges with spans not exceeding 200 ft These
calculations were for completed bridges. For the primary
components of large bridges, the ratio of dead and live load
force effects is rather high, and could result in a set of
resistance factors different from those found acceptable for
small- and medium-span bridges. It is believed to be more
practical to investigate one additional load case than to
require the use of two sets of resistance factors with the load
factors provided in Strength Load Combination I, depending
on other permanent loads present. Spot checks had been
made on a few bridges with up to 600-ft spans, and it
appears that Strength Load Combination IV will govern
where the dead load to live load force effect ratio exceeds
about 7.0. This load combination can control during
investigation of construction stages.
Past editions of the Standard Specifications used
γEQ = 0.0. This issue is not resolved. The possibility of
partial live load, i.e., γEQ < 1.0, with earthquakes should be
considered. Application of Turkstra’s rule for combining
uncorrelated loads indicates that γEQ = 0.50 is reasonable
for a wide range of values of average daily truck traffic
(ADTT).
The following applies to both Extreme Event I and II:
•
The recurrence interval of extreme events is thought
to exceed the design life.
•
Although these limit states include water loads, WA,
the effects due to WA are considerably less significant
than the effects on the structure stability due to scour.
Therefore, unless specific site conditions dictate
otherwise, local pier scour and contraction scour
depths should not be combined with BL, EQ, CT, CV,
or IC. However, the effects due to degradation of the
channel should be considered. Alternatively, one-half
of the total scour may be considered in combination
with BL, EQ, CT, CV, or IC.
•
The joint probability of these events is extremely low,
and, therefore, the events are specified to be applied
separately. Under these extreme conditions, the
structure may undergo considerable inelastic
deformation by which locked-in force effects due to
TU, TG, CR, SH, and SE are expected to be relieved.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
3-10
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
•
Service I—Load combination relating to the normal
operational use of the bridge with a 55 mph wind and
all loads taken at their nominal values. Also related to
deflection control in buried metal structures, tunnel
liner plate, and thermoplastic pipe, to control crack
width in reinforced concrete structures, and for
transverse analysis relating to tension in concrete
segmental girders. This load combination should also
be used for the investigation of slope stability.
•
Service II—Load combination intended to control
yielding of steel structures and slip of slip-critical
connections due to vehicular live load.
•
Service III—Load combination for longitudinal
analysis relating to tension in prestressed concrete
superstructures with the objective of crack control and
to principal tension in the webs of segmental concrete
girders.
•
Service IV—Load combination relating only to
tension in prestressed concrete columns with the
objective of crack control.
•
Fatigue I—Fatigue and fracture load combination
related to infinite load-induced fatigue life.
The 0.50 live load factor signifies a low probability of
the concurrence of the maximum vehicular live load (other
than CT) and the extreme events.
Compression in prestressed concrete components and
tension in prestressed bent caps are investigated using this
load combination. Service III is used to investigate tensile
stresses in prestressed concrete components.
This load combination corresponds to the overload
provision for steel structures in past editions of the
AASHTO Specifications, and it is applicable only to steel
structures. From the point of view of load level, this
combination is approximately halfway between that used
for Service I and Strength I Limit States.
The live load specified in these specifications reflects,
among other things, current exclusion weight limits
mandated by various jurisdictions. Vehicles permitted
under these limits have been in service for many years
prior to 1993. For longitudinal loading, there is no
nationwide physical evidence that these vehicles have
caused cracking in existing prestressed concrete
components. The statistical significance of the 0.80 factor
on live load is that the event is expected to occur about
once a year for bridges with two traffic lanes, less often for
bridges with more than two traffic lanes, and about once a
day for bridges with a single traffic lane. Service I should
be used for checking tension related to transverse analysis
of concrete segmental girders.
The principal tensile stress check is introduced in
order to verify the adequacy of webs of segmental concrete
girder bridges for longitudinal shear and torsion.
The 0.70 factor on wind represents an 84 mph wind.
This should result in zero tension in prestressed concrete
columns for ten-year mean reoccurrence winds. The
prestressed concrete columns must still meet strength
requirements as set forth in Load Combination Strength III
in Article 3.4.1.
It is not recommended that thermal gradient be
combined with high wind forces. Superstructure expansion
forces are included.
The load factor for the Fatigue I load combination,
applied to a single design truck having the axle spacing
specified in Article 3.6.1.4.1, reflects load levels found to
be representative of the maximum stress range of the truck
population for infinite fatigue life design. The factor was
chosen on the assumption that the maximum stress range
in the random variable spectrum is twice the effective
stress range caused by Fatigue II load combination.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 3: LOADS AND LOAD FACTORS
•
Fatigue II—Fatigue and fracture load combination
related to finite load-induced fatigue life.
The load factors for various loads comprising a design
load combination shall be taken as specified in
Table 3.4.1-1. All relevant subsets of the load
combinations shall be investigated. For each load
combination, every load that is indicated to be taken into
account and that is germane to the component being
designed, including all significant effects due to distortion,
shall be multiplied by the appropriate load factor and
multiple presence factor specified in Article 3.6.1.1.2, if
applicable. The products shall be summed as specified in
Eq. 1.3.2.1-1 and multiplied by the load modifiers
specified in Article 1.3.2.
The factors shall be selected to produce the total
extreme factored force effect. For each load combination,
both positive and negative extremes shall be investigated.
In load combinations where one force effect decreases
another effect, the minimum value shall be applied to the
load reducing the force effect. For permanent force effects,
the load factor that produces the more critical combination
shall be selected from Table 3.4.1-2. Where the permanent
load increases the stability or load-carrying capacity of a
component or bridge, the minimum value of the load factor
for that permanent load shall also be investigated.
3-11
The load factor for the Fatigue II load combination,
applied to a single design truck, reflects a load level found
to be representative of the effective stress range of the
truck population with respect to a small number of stress
range cycles and to their cumulative effects in steel
elements, components, and connections for finite fatigue
life design.
This Article reinforces the traditional method of
selecting load combinations to obtain realistic extreme
effects and is intended to clarify the issue of the variability
of permanent loads and their effects. As has always been
the case, the Owner or Designer may determine that not all
of the loads in a given load combination apply to the
situation under investigation.
It is recognized herein that the actual magnitude of
permanent loads may also be less than the nominal value.
This becomes important where the permanent load reduces
the effects of transient loads.
It has been observed that permanent loads are more
likely to be greater than the nominal value than to be less
than this value.
The earth load factor for thermoplastic culverts is set
to 1.3; however, to preserve the overall safety at the same
levels as historical specifications, an earth-load-installation
factor is introduced later in these Specifications as part of
the implementation of NCHRP Report 631. This factor
may be adjusted based on field control of construction
practices.
In the application of permanent loads, force effects for
each of the specified six load types should be computed
separately. It is unnecessary to assume that one type of
load varies by span, length, or component within a bridge.
For example, when investigating uplift at a bearing in a
continuous beam, it would not be appropriate to use the
maximum load factor for permanent loads in spans that
produce a negative reaction and the minimum load factor
in spans that produce a positive reaction. Consider the
investigation of uplift. Uplift, which was treated as a
separate load case in past editions of the AASHTO
Standard Specifications, now becomes a strength load
combination. Where a permanent load produces uplift, that
load would be multiplied by the maximum load factor,
regardless of the span in which it is located. If another
permanent load reduces the uplift, it would be multiplied
by the minimum load factor, regardless of the span in
which it is located. For example, at Strength I Limit State
where the permanent load reaction is positive and live load
can cause a negative reaction, the load combination would
be 0.9DC + 0.65DW + 1.75(LL + IM). If both reactions
were negative, the load combination would be 1.25DC +
1.50DW + 1.75(LL + IM). For each force effect, both
extreme combinations may need to be investigated by
applying either the high or the low load factor as
appropriate. The algebraic sums of these products are the
total force effects for which the bridge and its components
should be designed.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
3-12
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The larger of the two values provided for load factor of
TU shall be used for deformations and the smaller values for
all other effects. For simplified analysis of concrete
substructures in the strength limit state, a value of 0.50 for
γTU may be used when calculating force effects, but shall be
taken in conjunction with the gross moment of inertia in the
columns or piers. When a refined analysis is completed for
concrete substructures in the strength limit state, a value of
1.0 for γTU shall be used in conjunction with a partially
cracked moment of inertia determined by analysis. For
concrete substructures in the strength limit state, the value of
0.50 for γPS, γCR, and γSH may similarly be used when
calculating force effects in non-segmental structures, but
shall be taken in conjunction with the gross moment of
inertia in the columns or piers. For steel substructures, a
value of 1.0 for γTU, γPS, γCR, and γSH shall be used.
The evaluation of overall stability of retained fills, as
well as earth slopes with or without a shallow or deep
foundation unit should be investigated at the service limit
state based on the Service I Load Combination and an
appropriate resistance factor as specified in Article 11.5.6
and Article 11.6.2.3.
For structural plate box structures complying with the
provisions of Article 12.9, the live load factor for the
vehicular live loads LL and IM shall be taken as 2.0.
The load factor for temperature gradient, γTG, should
be considered on a project-specific basis. In lieu of projectspecific information to the contrary, γTG may be taken as:
•
0.0 at the strength and extreme event limit states,
•
1.0 at the service limit state when live load is not
considered, and
•
0.50 at the service limit state when live load is
considered.
PS, CR, SH, TU, and TG are superimposed
deformations as defined in Article 3.12. Load factors for
TU, and TG are as shown in Table 3.4.1-1. Load factors
for PS, CR, and SH are as shown in Table 3.4.1-3. For
prestressed members in typical bridge types, secondary
prestressing, creep and shrinkage are generally designed
for in the service limit state. In concrete segmental
structures, CR and SH are factored by γP for DC because
analysis for time-dependent effects in segmental bridges is
nonlinear. Abutments, piers, columns, and bent caps are to
be considered as substructure components.
The calculation of displacements for TU utilizes a
factor greater than 1.0 to avoid undersizing joints,
expansion devices, and bearings.
Applying these criteria for the evaluation of the
sliding resistance of walls:
•
The vertical earth load on the rear of a cantilevered
retaining wall would be multiplied by γpmin (1.00) and
the weight of the structure would be multiplied by
γpmin (0.90) because these forces result in an increase
in the contact stress (and shear strength) at the base of
the wall and foundation.
•
The horizontal earth load on a cantilevered retaining
wall would be multiplied by γpmax (1.50) for an active
earth pressure distribution because the force results in
a more critical sliding force at the base of the wall.
Similarly, the values of γpmax for structure weight (1.25),
vertical earth load (1.35) and horizontal active earth pressure
(1.50) would represent the critical load combination for an
evaluation of foundation bearing resistance.
Water load and friction are included in all strength
load combinations at their respective nominal values.
For creep and shrinkage, the specified nominal values
should be used. For friction, settlement, and water loads,
both minimum and maximum values need to be
investigated to produce extreme load combinations.
The load factor for temperature gradient should be
determined on the basis of the:
•
Type of structure, and
•
Limit state being investigated.
Open girder construction and multiple steel box
girders have traditionally, but perhaps not necessarily
correctly, been designed without consideration of
temperature gradient, i.e., γTG = 0.0.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
SECTION 3: LOADS AND LOAD FACTORS
3-13
The load factor for settlement, γSE, should be
considered on a project-specific basis. In lieu of projectspecific information to the contrary, γSE, may be taken as
1.0. Load combinations which include settlement shall also
be applied without settlement.
For segmentally constructed bridges, the following
combination shall be investigated at the service limit state:
DC + DW + EH + EV + ES + WA + CR + SH + TG + EL + PS
(3.4.1-2)
Table 3.4.1-1—Load Combinations and Load Factors
Use One of These at a Time
DC
DD
DW
EH
EV
ES
EL
PS
CR
SH
Ȗp
LL
IM
CE
BR
PL
LS
1.75
WA
1.00
WS
—
WL
—
FR
1.00
TU
0.50/1.20
TG
ȖTG
SE
ȖSE
EQ
—
BL
—
IC
—
CT
—
CV
—
Ȗp
Ȗp
1.35
—
1.00
1.00
—
—
1.00
1.00
0.50/1.20
0.50/1.20
ȖTG
ȖTG
ȖSE
ȖSE
—
—
—
—
—
—
—
—
—
—
Strength IV
Strength V
Ȗp
Ȗp
—
1.35
1.00
1.00
—
1.0
1.00
1.00
0.50/1.20
0.50/1.20
—
ȖTG
—
ȖSE
—
—
—
—
—
—
—
—
—
—
Extreme
Event I
Extreme
Event II
Service I
Ȗp
ȖEQ
1.00
—
1.4
0
—
0.4
0
—
—
1.00
—
—
—
1.00
—
—
—
—
Ȗp
0.50
1.00
—
—
1.00
—
—
—
—
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.0
1.00
1.00/1.20
ȖTG
ȖSE
—
—
—
—
—
Service II
Service III
Service IV
1.00
1.00
1.00
1.30
0.80
—
1.00
1.00
1.00
—
—
—
1.00
1.00
1.00
1.00/1.20
1.00/1.20
1.00/1.20
—
ȖTG
—
—
ȖSE
1.0
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
1.50
—
0.3
0
—
—
0.7
0
—
—
—
—
—
—
—
—
—
—
—
—
0.75
—
—
—
—
—
—
—
—
—
—
—
—
Load
Combination
Limit State
Strength I
(unless noted)
Strength II
Strength III
Fatigue I—
LL, IM & CE
only
Fatigue II—
LL, IM & CE
only
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2012
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
3-14
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 3.4.1-2—Load Factors for Permanent Loads, Ȗp
Load Factor
Maximum
Minimum
Type of Load, Foundation Type, and
Method Used to Calculate Downdrag
DC: Component and Attachments
DC: Strength IV only
DD: Downdrag
Piles, α Tomlinson Method
Piles, λ Method
Drilled shafts, O’Neill and Reese (1999) Method
DW: Wearing Surfaces and Utilities
EH: Horizontal Earth Pressure
• Active
• At-Rest
• AEP for anchored walls
EL: Locked-in Construction Stresses
EV: Vertical Earth Pressure
• Overall Stability
• Retaining Walls and Abutments
• Rigid Buried Structure
• Rigid Frames
• Flexible Buried Structures
o Metal Box Culverts and Structural Plate Culverts with Deep Corrugations
o Thermoplastic culverts
o All others
ES: Earth Surcharge
1.25
1.50
1.4
1.05
1.25
1.50
0.90
0.90
0.25
0.30
0.35
0.65
1.50
1.35
1.35
1.00
0.90
0.90
N/A
1.00
1.00
1.35
1.30
1.35
N/A
1.00
0.90
0.90
1.5
1.3
1.95
0.9
0.9
0.9
1.50
0.75
Table 3.4.1-3—Load Factors for Permanent Loads Due to Superimposed Deformations, Ȗp
PS
1.0
CR, SH
See γP for DC, Table 3.4.1-2
1.0
1.0
Substructures supporting non-segmental Superstructures
• using Ig
• using Ieffectuve
0.5
1.0
0.5
1.0
Steel Substructures
1.0
1.0
Bridge Component
Superstructures—Segmental
Concrete Substructures supporting Segmental
Superstructures (see 3.12.4, 3.12.5)
Concrete Superstructures—non-segmental
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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SECTION 3: LOADS AND LOAD FACTORS
Where prestressed components are used in
conjunction with steel girders, the force effects from the
following sources shall be considered as construction
loads, EL:
•
In conjunction with longitudinal prestressing of a
precast deck prior to making the deck sections
composite with the girders, the friction between the
precast deck sections and the steel girders.
•
When longitudinal post-tensioning is performed after
the deck becomes composite with the girders, the
additional forces induced in the steel girders and shear
connectors.
•
The effects of differential creep and shrinkage of the
concrete.
•
The Poisson effect.
The load factor for live load in Extreme Event Load
Combination I, γEQ, shall be determined on a projectspecific basis.
Engineering judgment shall be exercised when
applying blast loadings and when combining them with
other loads.
3-15
The most common applications of prestressed
concrete in steel girder bridges are transverse posttensioning of the deck and integral pier caps in which the
tendons penetrate the girder webs. When a composite deck
is prestressed longitudinally, the shear connectors transfer
force to the steel. The effect of shrinkage and long-term
creep around the shear connectors should be evaluated to
ensure that the composite girder is able to recognize the
prestressing over the life of the bridge. The contribution of
long-term deformations in closure pours between precast
deck panels which have been aged to reduce shrinkage and
creep may need evaluation.
The Poisson effect recognizes the bulging of concrete
when subjected to prestressing. When used in pier caps,
post-tensioning causes a transverse Poisson tensile stress
resulting in a longitudinal stress in the steel girders.
A load factor for passive lateral earth pressure is not
given in Table 3.4.1-2 because, strictly speaking, passive
lateral earth pressure is a resistance and not a load. For
discussion of the selection of a passive lateral earth
pressure resistance factor see Article 10.5.5.2.2.
Blast loads are considered an Extreme Event case of
loading. However, not enough information exists at the
time of this writing to determine what other loads should
be combined with blast loads and the appropriate load
factors.
3.4.2—Load Factors for Construction Loads
3.4.2.1—Evaluation at the Strength Limit State
All appropriate strength load combinations in
Table 3.4.1-1, modified as specified herein, shall be
investigated.
When investigating Strength Load Combinations I, III,
and V during construction, load factors for the weight of
the structure and appurtenances, DC and DW, shall not be
taken to be less than 1.25.
Unless otherwise specified by the Owner, the load
factor for construction loads and for any associated
dynamic effects shall not be less than 1.5 in Strength Load
Combination I. The load factor for wind in Strength Load
Combination III shall not be less than 1.25.
C3.4.2.1
The load factors presented here should not relieve the
contractor of responsibility for safety and damage control
during construction.
Construction loads are permanent loads and other
loads that act on the structure only during construction.
Construction loads include the weight of equipment such
as deck finishing machines or loads applied to the structure
through falsework or other temporary supports. Often the
construction loads are not accurately known at design
time; however, the magnitude and location of these loads
considered in the design should be noted on the contract
documents.
3.4.2.2—Evaluation of Deflection at the Service
Limit State
In the absence of special provisions to the contrary,
where evaluation of construction deflections are required by
the contract documents, Load Combination Service I shall
apply. Construction dead loads shall be considered as part of
the permanent load and construction transient loads
considered part of the live load. The associated permitted
deflections shall be included in the contract documents.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
3-16
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
3.4.3—Load Factors for Jacking and Post-Tensioning
Forces
3.4.3.1—Jacking Forces
Unless otherwise specified by the Owner, the design
forces for jacking in service shall not be less than 1.3 times
the permanent load reaction at the bearing, adjacent to the
point of jacking.
Where the bridge will not be closed to traffic during
the jacking operation, the jacking load shall also contain a
live load reaction consistent with the maintenance of
traffic plan, multiplied by the load factor for live load.
3.4.3.2—Force for Post-Tensioning Anchorage
Zones
The design force for post-tensioning anchorage zones
shall be taken as 1.2 times the maximum jacking force.
3.4.4—Load Factors for Orthotropic Decks
C3.4.4
The Fatigue I live load factor (γLL) shall be multiplied
by an additional factor of 1.5 when evaluating fatigue at
the welded rib-to-floorbeam cut-out detail and the rib-todeck weld.
Evaluation of the maximum stress range in the rib-todeck weld as well as in the vicinity of the cut-out for this
type of detail has demonstrated that the use of a 1.5 load
factor for LL is unconservative. For the rib-to-deck weld and
when a cut-out is used to relive the secondary stresses
imparted by the rotation of the rib relative to the floorbeam,
the appropriate γLL should be increased to 2.25 (Connor,
2002). The increased Fatigue I load factor is based on stress
range spectra monitoring of orthotropic decks. Studies
indicate that the ratio of maximum stress range to effective
stress range is increased as compared to standard bridge
girders. This is due to a number of factors such as occasional
heavy wheels and reduced local load distribution that occurs
in deck elements. These Specifications produce a ratio that is
consistent with the original findings of NCHRP Report 299
(Moses et al., 1987).
3.5—PERMANENT LOADS
3.5.1—Dead Loads: DC, DW, and EV
Dead load shall include the weight of all components
of the structure, appurtenances and utilities attached
thereto, earth cover, wearing surface, future overlays, and
planned widenings.
In the absence of more precise information, the unit
weights, specified in Table 3.5.1-1, may be used for dead
loads.
C3.5.1
Table 3.5.1-1 provides traditional unit weights. The
unit weight of granular materials depends upon the degree
of compaction and water content. The unit weight of
concrete is primarily affected by the unit weight of the
aggregate, which varies by geographical location and
increases with concrete compressive strength. The unit
weight of reinforced concrete is generally taken as
0.005 kcf greater than the unit weight of plain concrete.
The values provided for wood include the weight of
mandatory preservatives. The weight of transit rails, etc., is
to be used only for preliminary design.
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2012
Edition
SECTION 3: LOADS AND LOAD FACTORS
3-17
Table 3.5.1-1—Unit Weights
Unit Weight
(kcf)
0.175
0.140
0.450
0.060
0.120
0.110
0.120
0.145
0.140 + 0.001 f′c
0.100
0.100
0.140
0.490
0.170
0.060
0.050
0.0624
0.0640
Weight per Unit Length (klf)
0.200
Material
Aluminum Alloys
Bituminous Wearing Surfaces
Cast Iron
Cinder Filling
Compacted Sand, Silt, or Clay
Concrete
Lightweight
Sand-Lightweight
Normal Weight with f′c ≤ 5.0 ksi
Normal Weight with 5.0 < f′c ≤ 15.0 ksi
Loose Sand, Silt, or Gravel
Soft Clay
Rolled Gravel, Macadam, or Ballast
Steel
Stone Masonry
Wood
Hard
Soft
Water
Fresh
Salt
Item
Transit Rails, Ties, and Fastening per Track
3.5.2—Earth Loads: EH, ES, and DD
Earth pressure, earth surcharge, and downdrag loads
shall be as specified in Article 3.11.
3.6—LIVE LOADS
3.6.1—Gravity Loads: LL and PL
3.6.1.1—Vehicular Live Load
3.6.1.1.1—Number of Design Lanes
2013 Revision
Generally, the number of design lanes should be
determined by taking the integer part of the ratio w/12.0,
where w is the clear roadway width in ft between curbs
and/or barriers. Possible future changes in the physical or
functional clear roadway width of the bridge should be
considered.
In cases where the traffic lanes are less than 12.0 ft
wide, the number of design lanes shall be equal to the
number of traffic lanes, and the width of the design lane
shall be taken as the width of the traffic lane.
Roadway widths from 20.0 to 24.0 ft shall have two
design lanes, each equal to one-half the roadway width.
C3.6.1.1.1
It is not the intention of this Article to promote bridges
with narrow traffic lanes. Wherever possible, bridges
should be built to accommodate the standard design lane
and appropriate shoulders.
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2012
Edition
3-18
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
3.6.1.1.2—Multiple Presence of Live Load
The provisions of this Article shall not be applied to
the fatigue limit state for which one design truck is used,
regardless of the number of design lanes. Where
the single-lane approximate distribution factors in
Articles 4.6.2.2 and 4.6.2.3 are used, other than the lever
rule and statical method, the force effects shall be divided
by 1.20.
Unless specified otherwise herein, the extreme live
load force effect shall be determined by considering each
possible combination of number of loaded lanes multiplied
by a corresponding multiple presence factor to account for
the probability of simultaneous lane occupation by the full
HL93 design live load. In lieu of site specific data, the
values in Table 3.6.1.1.2-1:
•
Shall be used when investigating the effect of one lane
loaded,
•
May be used when investigating the effect of three or
more lanes loaded.
For the purpose of determining the number of lanes when
the loading condition includes the pedestrian loads
specified in Article 3.6.1.6 combined with one or more
lanes of the vehicular live load, the pedestrian loads may
be taken to be one loaded lane.
The factors specified in Table 3.6.1.1.2-1 shall not be
applied in conjunction with approximate load distribution
factors specified in Articles 4.6.2.2 and 4.6.2.3, except
where the lever rule is used or where special requirements
for exterior beams in beam-slab bridges, specified in
Article 4.6.2.2.2d, are used.
Table 3.6.1.1.2-1—Multiple Presence Factors, m
Number of Loaded Lanes
1
2
3
>3
Multiple Presence
Factors, m
1.20
1.00
0.85
0.65
C3.6.1.1.2
The multiple presence factors have been included in
the approximate equations for distribution factors in
Articles 4.6.2.2 and 4.6.2.3, both for single and multiple
lanes loaded. The equations are based on evaluation of
several combinations of loaded lanes with their appropriate
multiple presence factors and are intended to account for
the worst case scenario. Where use of the lever rule is
specified in Article 4.6.2.2 and 4.6.2.3, the Engineer must
determine the number and location of vehicles and lanes,
and, therefore, must include the multiple presence. Stated
another way, if a sketch is required to determine load
distribution, the Engineer is responsible for including
multiple presence factors and selecting the worst design
case. The factor 1.20 from Table 3.6.1.1.2-1 has already
been included in the approximate equations and should be
removed for the purpose of fatigue investigations.
The entry greater than 1.0 in Table 3.6.1.1.2-1 results
from statistical calibration of these Specifications on the
basis of pairs of vehicles instead of a single vehicle.
Therefore, when a single vehicle is on the bridge, it can be
heavier than each one of a pair of vehicles and still have
the same probability of occurrence.
The consideration of pedestrian loads counting as a
“loaded lane” for the purpose of determining a multiple
presence factor (m) is based on the assumption that
simultaneous occupancy by a dense loading of people
combined with a 75-yr design live load is remote. For the
purpose of this provision, it has been assumed that if a
bridge is used as a viewing stand for eight hours each year
for a total time of about one month, the appropriate live
load to combine with it would have a one-month
recurrence interval. This is reasonably approximated by
use of the multiple presence factors, even though they are
originally developed for vehicular live load.
Thus, if a component supported a sidewalk and one
lane, it would be investigated for the vehicular live load
alone with m = 1.20, and for the pedestrian loads combined
with the vehicular live load with m = 1.0. If a component
supported a sidewalk and two lanes of vehicular live load,
it would be investigated for:
•
One lane of vehicular live load, m = 1.20;
•
The greater of the more significant lanes of vehicular
live load and the pedestrian loads or two lanes of
vehicular live load, m = 1.0, applied to the governing
case; and
•
Two lanes of vehicular live load and the pedestrian
loads, m = 0.85.
The multiple presence factor of 1.20 for a single lane
does not apply to the pedestrian loads. Therefore, the case
of the pedestrian loads without the vehicular live load is a
subset of the second bulleted item.
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2012
Edition
SECTION 3: LOADS AND LOAD FACTORS
3-19
The multiple presence factors in Table 3.6.1.1.2-1
were developed on the basis of an ADTT of 5,000 trucks
in one direction. The force effect resulting from the
appropriate number of lanes may be reduced for sites with
lower ADTT as follows:
•
If 100 ≤ ADTT ≤ 1,000, 95 percent of the specified
force effect may be used; and
•
If ADTT < 100, 90 percent of the specified force effect
may be used.
This adjustment is based on the reduced probability of
attaining the design event during a 75-year design life with
reduced truck volume.
3.6.1.2—Design Vehicular Live Load
3.6.1.2.1—General
C3.6.1.2.1
Vehicular live loading on the roadways of bridges or
incidental structures, designated HL-93, shall consist of a
combination of the:
•
Design truck or design tandem, and
•
Design lane load.
Except as modified in Article 3.6.1.3.1, each design
lane under consideration shall be occupied by either the
design truck or tandem, coincident with the lane load,
where applicable. The loads shall be assumed to occupy
10.0 ft transversely within a design lane.
Consideration should be given to site-specific
modifications to the design truck, design tandem, and/or
the design lane load under the following conditions:
•
The legal load of a given jurisdiction is significantly
greater than typical;
•
The roadway is expected to carry unusually high
percentages of truck traffic;
•
Flow control, such as a stop sign, traffic signal, or toll
booth, causes trucks to collect on certain areas of a
bridge or to not be interrupted by light traffic; or
•
Special industrial loads are common due to the
location of the bridge.
See also discussion in Article C3.6.1.3.1.
The live load model, consisting of either a truck or
tandem coincident with a uniformly distributed load, was
developed as a notional representation of shear and
moment produced by a group of vehicles routinely
permitted on highways of various states under
“grandfather” exclusions to weight laws. The vehicles
considered to be representative of these exclusions were
based on a study conducted by the Transportation
Research Board (Cohen, 1990). The load model is called
“notional” because it is not intended to represent any
particular truck.
In the initial development of the notional live load
model, no attempt was made to relate to escorted permit
loads, illegal overloads, or short duration special permits.
The moment and shear effects were subsequently
compared to the results of truck weight studies (Csagoly
and Knobel, 1981; Nowak, 1992), selected WIM data, and
the 1991 OHBDC live load model. These subsequent
comparisons showed that the notional load could be scaled
by appropriate load factors to be representative of these
other load spectra.
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2012
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3-20
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The
following
nomenclature
applies
to
Figures C3.6.1.2.1-1 through C3.6.1.2.1-6, which show
results of live load studies involving two equal continuous
spans or simple spans:
M POS 0.4L =
positive moment at 4/10 point
in either span
M NEG 0.4L =
negative moment at 4/10 point
in either span
M SUPPORT=
moment at interior support
Vab
=
shear adjacent to either exterior
support
Vba
=
shear adjacent to interior
support
Mss
=
midspan moment in a simply
supported span
The “span” is the length of the simple-span or of one
of each of the two continuous spans. The comparison is in
the form of ratios of the load effects produced in either
simple-span or two-span continuous girders. A ratio
greater than 1.0 indicates that one or more of the exclusion
vehicles produces a larger load effect than the HS20
loading. The figures indicate the degree by which the
exclusion loads deviate from the HS loading of
designation, e.g., HS25.
Figures C3.6.1.2.1-1 and C3.6.1.2.1-2 show moment
and shear comparisons between the envelope of effects
caused by 22 truck configurations chosen to be
representative of the exclusion vehicles and the HS20
loading, either the HS20 truck or the lane load, or the
interstate load consisting of two 24.0-kip axles 4.0 ft apart,
as used in previous editions of the AASHTO Standard
Specifications. The largest and smallest of the 22
configurations can be found in Kulicki and Mertz (1991).
In the case of negative moment at an interior support, the
results presented are based on two identical exclusion
vehicles in tandem and separated by at least 50.0 ft.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
SECTION 3: LOADS AND LOAD FACTORS
3-21
Figure C3.6.1.2.1-1—Moment Ratios: Exclusion Vehicles
to HS20 (truck or lane) or Two 24.0-kip Axles at 4.0 ft
Figure C3.6.1.2.1-2—Shear Ratios: Exclusion Vehicles to
HS20 (truck or lane) or Two 24.0-kip Axles at 4.0 ft
Figures C3.6.1.2.1-3 and C3.6.1.2.1-4 show
comparisons between the force effects produced by a
single exclusion truck per lane and the notional load
model, except for negative moment, where the tandem
exclusion vehicles were used. In the case of negative
moment at a support, the provisions of Article 3.6.1.3.1
requiring investigation of 90 percent of the effect of two
design trucks, plus 90 percent of the design lane load, has
been included in Figures C3.6.1.2.1-3 and C3.6.1.2.1-5.
Compared with Figures C3.6.1.2.1-1 and C3.6.1.2.1-2, the
range of ratios can be seen as more closely grouped:
•
Over the span range,
•
Both for shear and moment, and
•
Both for simple-span and continuous spans.
The implication of close grouping is that the notional
load model with a single-load factor has general
applicability.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
3-22
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure C3.6.1.2.1-3—Moment Ratios: Exclusion Vehicles
to Notional Model
Figure C3.6.1.2.1-4—Shear Ratios: Exclusion Vehicles to
Notional Model
Figures C3.6.1.2.1-5 and C3.6.1.2.1-6 show the ratios
of force effects produced by the notional load model and
the greatest of the HS20 truck or lane loading, or Alternate
Military Loading.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 3: LOADS AND LOAD FACTORS
3-23
Figure C3.6.1.2.1-5—Moment Ratios: Notional Model to
HS20 (truck or lane) or Two 24.0-kip Axles at 4.0 ft
Figure C3.6.1.2.1-6—Shear Ratios: Notional Model to
HS20 (truck and lane) or Two 24.0-kip Axles at 4.0 ft
In reviewing Figures C3.6.1.2.1-5 and C3.6.1.2.1-6, it
should be noted that the total design force effect is also a
function of load factor, load modifier, load distribution,
and dynamic load allowance.
3.6.1.2.2—Design Truck
The weights and spacings of axles and wheels for the
design truck shall be as specified in Figure 3.6.1.2.2-1. A
dynamic load allowance shall be considered as specified in
Article 3.6.2.
Except as specified in Articles 3.6.1.3.1 and 3.6.1.4.1,
the spacing between the two 32.0-kip axles shall be varied
between 14.0 ft and 30.0 ft to produce extreme force
effects.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
3-24
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure 3.6.1.2.2-1—Characteristics of the Design Truck
3.6.1.2.3—Design Tandem
The design tandem shall consist of a pair of 25.0-kip
axles spaced 4.0 ft apart. The transverse spacing of wheels
shall be taken as 6.0 ft. A dynamic load allowance shall be
considered as specified in Article 3.6.2.
3.6.1.2.4—Design Lane Load
The design lane load shall consist of a load of 0.64 klf
uniformly distributed in the longitudinal direction.
Transversely, the design lane load shall be assumed to be
uniformly distributed over a 10.0-ft width. The force
effects from the design lane load shall not be subject to a
dynamic load allowance.
3.6.1.2.5—Tire Contact Area
The tire contact area of a wheel consisting of one or
two tires shall be assumed to be a single rectangle, whose
width is 20.0 in. and whose length is 10.0 in.
The tire pressure shall be assumed to be uniformly
distributed over the contact area. The tire pressure shall be
assumed to be distributed as follows:
•
On continuous surfaces, uniformly over the specified
contact area, and
•
On interrupted surfaces, uniformly over the actual
contact area within the footprint with the pressure
increased in the ratio of the specified to actual contact
areas.
For the design of orthotropic decks and wearing
surfaces on orthotropic decks, the front wheels shall be
assumed to be a single rectangle whose width and length
are both 10.0 in. as specified in Article 3.6.1.4.1.
C3.6.1.2.5
The area load applies only to the design truck and
tandem. For other design vehicles, the tire contact area
should be determined by the engineer.
As a guideline for other truck loads, the tire area in
in.2 may be calculated from the following dimensions:
Tire width = P/0.8
Tire length = 6.4γ(1 + IM/100)
where:
γ =
IM =
P =
load factor
dynamic load allowance percent
design wheel load (kip)
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All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 3: LOADS AND LOAD FACTORS
3.6.1.2.6—Distribution of Wheel Loads through
Earth Fills
2013 Revision
Where the depth of fill is less than 2.0 ft, live loads
shall be distributed to the top slabs of culverts as specified
in Article 4.6.2.10.
In lieu of a more precise analysis, or the use of other
acceptable approximate methods of load distribution
permitted in Section 12, where the depth of fill is 2.0 ft or
greater, wheel loads may be considered to be uniformly
distributed over a rectangular area with sides equal to the
dimension of the tire contact area, as specified in
Article 3.6.1.2.5, and increased by either 1.15 times the
depth of the fill in select granular backfill, or the depth of
the fill in all other cases. The provisions of
Articles 3.6.1.1.2 and 3.6.1.3 shall apply.
Where such areas from several wheels overlap, the
total load shall be uniformly distributed over the area.
For single-span culverts, the effects of live load may
be neglected where the depth of fill is more than 8.0 ft and
exceeds the span length; for multiple span culverts, the
effects may be neglected where the depth of fill exceeds
the distance between faces of end walls.
Where the live load and impact moment in concrete
slabs, based on the distribution of the wheel load through
earth fills, exceeds the live load and impact moment
calculated according to Article 4.6.2.10, the latter moment
shall be used.
3-25
C3.6.1.2.6
Elastic solutions for pressures produced within an
infinite half-space by loads on the ground surface can be
found in Poulos and Davis (1974), NAVFAC DM-7.1
(1982), and soil mechanics textbooks.
This approximation is similar to the 60-degree rule
found in many texts on soil mechanics. The dimensions of
the tire contact area are determined at the surface based on
the dynamic load allowance of 33 percent at depth = 0.
They are projected through the soil as specified. The
pressure intensity on the surface is based on the wheel load
without dynamic load allowance. A dynamic load
allowance is added to the pressure on the projected area.
The dynamic load allowance also varies with depth as
specified in Article 3.6.2.2. The design lane load is applied
where appropriate and multiple presence factors apply.
This provision applies to relieving slabs below grade
and to top slabs of box culverts.
Traditionally, the effect of fills less than 2.0 ft deep on
live load has been ignored. Research (McGrath, et al.
2004) has shown that in design of box sections allowing
distribution of live load through fill in the direction parallel
to the span provides a more accurate design model to
predict moment, thrust, and shear forces. Provisions in
Article 4.6.2.10 provide a means to address the effect of
shallow fills.
3.6.1.3—Application of Design Vehicular Live
Loads
3.6.1.3.1—General
C3.6.1.3.1
Unless otherwise specified, the extreme force effect
shall be taken as the larger of the following:
•
The effect of the design tandem combined with the
effect of the design lane load, or
•
The effect of one design truck with the variable axle
spacing specified in Article 3.6.1.2.2, combined with
the effect of the design lane load, and
The effects of an axle sequence and the lane load are
superposed in order to obtain extreme values. This is a
deviation from the traditional AASHTO approach, in
which either the truck or the lane load, with an additional
concentrated load, provided for extreme effects.
The lane load is not interrupted to provide space for
the axle sequences of the design tandem or the design
truck; interruption is needed only for patch loading
patterns to produce extreme force effects.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
3-26
•
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
For negative moment between points of contraflexure
under a uniform load on all spans, and reaction at
interior piers only, 90 percent of the effect of two design
trucks spaced a minimum of 50.0 ft between the lead
axle of one truck and the rear axle of the other truck,
combined with 90 percent of the effect of the design
lane load. The distance between the 32.0-kip axles of
each truck shall be taken as 14.0 ft. The two design
trucks shall be placed in adjacent spans to produce
maximum force effects.
Axles that do not contribute to the extreme force
effect under consideration shall be neglected.
Both the design lanes and the 10.0-ft loaded width in
each lane shall be positioned to produce extreme force
effects. The design truck or tandem shall be positioned
transversely such that the center of any wheel load is not
closer than:
•
For the design of the deck overhang—1.0 ft from the
face of the curb or railing, and
•
For the design of all other components—2.0 ft from
the edge of the design lane.
The notional design loads were based on the
information described in Article C3.6.1.2.1, which
contained data on “low boy” type vehicles weighing up to
about 110 kip. Where multiple lanes of heavier versions of
this type of vehicle are considered probable, consideration
should be given to investigating negative moment and
reactions at interior supports for pairs of the design tandem
spaced from 26.0 ft to 40.0 ft apart, combined with the
design lane load specified in Article 3.6.1.2.4. The design
tandems should be placed in adjacent spans to produce
maximum force effect. One hundred percent of the
combined effect of the design tandems and the design lane
load should be used. This is consistent with
Article 3.6.1.2.1 and should not be considered a
replacement for the Strength II Load Combination.
Only those areas or parts of areas that contribute to the
same extreme being sought should be loaded. The loaded
length should be determined by the points where the
influence surface meets the centerline of the design lane.
Where a sidewalk is not separated from the roadway
by a crashworthy traffic barrier, consideration should be
given to the possibility that vehicles can mount the
sidewalk.
Unless otherwise specified, the lengths of design
lanes, or parts thereof, that contribute to the extreme force
effect under consideration, shall be loaded with the design
lane load.
3.6.1.3.2—Loading for Optional Live Load
Deflection Evaluation
If the Owner invokes the optional live load deflection
criteria specified in Article 2.5.2.6.2, the deflection should
be taken as the larger of:
•
That resulting from the design truck alone, or
•
That resulting from 25 percent of the design truck
taken together with the design lane load.
C3.6.1.3.2
As indicated in C2.5.2.6.1, live load deflection is a
service issue, not a strength issue. Experience with bridges
designed under previous editions of the AASHTO
Standard Specifications indicated no adverse effects of live
load deflection per se. Therefore, there appears to be little
reason to require that the past criteria be compared to a
deflection based upon the heavier live load required by
these Specifications.
The provisions of this Article are intended to produce
apparent live load deflections similar to those used in the
past. The current design truck is identical to the HS20
truck of past Standard Specifications. For the span lengths
where the design lane load controls, the design lane load
together with 25 percent of the design truck, i.e., three
concentrated loads totaling 18.0 kip, is similar to the past
lane load with its single concentrated load of 18.0 kip.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 3: LOADS AND LOAD FACTORS
3.6.1.3.3—Design Loads for Decks, Deck Systems,
and the Top Slabs of Box Culverts
The provisions of this Article shall not apply to decks
designed under the provisions of Article 9.7.2, “Empirical
Design.”
Where the approximate strip method is used to
analyze decks and top slabs of culverts, force effects shall
be determined on the following basis:
•
Where the slab spans primarily in the transverse
direction, only the axles of the design truck of Article
3.6.1.2.2 or design tandem of Article 3.6.1.2.3 shall be
applied to the deck slab or the top slab of box
culverts.
•
Where the slab spans primarily in the longitudinal
direction:
o
3-27
C3.6.1.3.3
This Article clarifies the selection of wheel loads to be
used in the design of bridge decks, slab bridges, and top
slabs of box culverts.
The design load is always an axle load; single wheel
loads should not be considered.
The design truck and tandem without the lane load
and with a multiple presence factor of 1.2 results in
factored force effects that are similar to the factored force
effects using earlier specifications for typical span ranges
of box culverts.
Individual Owners may choose to develop other axle
weights and configurations to capture the load effects of
the actual loads in their jurisdiction based upon local legalload and permitting policies. Triple axle configurations of
single unit vehicles have been observed to have load
effects in excess of the HL-93 tandem axle load.
For top slabs of box culverts of all spans and
for all other cases, including slab-type
bridges where the span does not exceed
15.0 ft, only the axle loads of the design
truck or design tandem of Articles 3.6.1.2.2
and 3.6.1.2.3, respectively, shall be applied.
o For all other cases, including slab-type
bridges (excluding top slabs of box culverts)
where the span exceeds 15.0 ft, all of the
load specified in Article 3.6.1.2 shall be
applied.
Where the refined methods are used to analyze decks,
force effects shall be determined on the following basis:
•
•
Where the slab spans primarily in the transverse
direction, only the axles of the design truck of
Article 3.6.1.2.2 or design tandem of
Article 3.6.1.2.3 shall be applied to the deck slab.
Where the slab spans primarily in the longitudinal
direction (including slab-type bridges), all of the loads
specified in Article 3.6.1.2 shall be applied.
Wheel loads shall be assumed to be equal within an
axle unit, and amplification of the wheel loads due to
centrifugal and braking forces need not be considered for
the design of decks.
It is theoretically possible that an extreme force effect
could result from a 32.0-kip axle in one lane and a 50.0-kip
tandem in a second lane, but such sophistication is not
warranted in practical design.
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2012
Edition
3-28
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
3.6.1.3.4—Deck Overhang Load
C3.6.1.3.4
For the design of deck overhangs with a cantilever,
not exceeding 6.0 ft from the centerline of the exterior
girder to the face of a structurally continuous concrete
railing, the outside row of wheel loads may be replaced
with a uniformly distributed line load of 1.0 klf intensity,
located 1.0 ft from the face of the railing.
Horizontal loads on the overhang resulting from
vehicle collision with barriers shall be in accordance with
the provisions of Section 13.
Structurally continuous barriers have been observed to
be effective in distributing wheel loads in the overhang.
Implicit in this provision is the assumption that the
25.0-kip half weight of a design tandem is distributed over
a longitudinal length of 25.0 ft, and that there is a cross
beam or other appropriate component at the end of the
bridge supporting the barrier which is designed for the half
tandem weight. This provision does not apply if the barrier
is not structurally continuous.
3.6.1.4—Fatigue Load
3.6.1.4.1—Magnitude and Configuration
The fatigue load shall be one design truck or axles
thereof specified in Article 3.6.1.2.2, but with a constant
spacing of 30.0 ft between the 32.0-kip axles.
The dynamic load allowance specified in Article 3.6.2
shall be applied to the fatigue load.
For the design of orthotropic decks and wearing
surfaces on orthotropic decks, the loading pattern as shown
in Figure 3.6.1.4.1-1 shall be used.
2’–0”
C3.6.1.4.1
For orthotropic steel decks, the governing 16.0-kip
wheel loads should be modeled in more detail as two
closely spaced 8.0-kip wheels 4.0 ft apart to more
accurately reflect a modern tractor-trailer with tandem rear
axles. Further, these wheel loads should be distributed over
the specified contact area (20.0 in. wide × 10.0 in. long for
rear axles and 10.0 in. square for front axles), which better
approximates actual pressures applied from a dual tire unit
(Kulicki and Mertz, 2006; Nowak, 2008). Note that the
smaller 10.0 in. × 10.0 in. front wheels can be the
controlling load for fatigue design of many orthotropic
deck details.
This loading should be positioned both longitudinally
and transversely on the bridge deck, ignoring the striped
lanes, to create the worst stress or deflection, as applicable.
C
L 1st Rear Axle
Group (32 kip)
C
L 2nd Rear Axle
Group (32 kip)
2’–0”
2’–0”
C
L Steering
Axle (8 kip)
2’–0”
3’–0”
3’–0”
6’–0”
C
L Wheel Patch
C
L Truck
10” × 10” Front
Axle Patch (TYP)
20” × 10” Patch (TYP)
30’–0”
14’–0”
Figure 3.6.1.4.1-1—Refined Design Truck Footprint for Fatigue Design
3.6.1.4.2—Frequency
The frequency of the fatigue load shall be taken as the
single-lane average daily truck traffic (ADTTSL). This
frequency shall be applied to all components of the bridge,
even to those located under lanes that carry a lesser
number of trucks.
In the absence of better information, the single-lane
average daily truck traffic shall be taken as:
C3.6.1.4.2
Since the fatigue and fracture limit state is defined in
terms of accumulated stress-range cycles, specification of
load alone is not adequate. Load should be specified along
with the frequency of load occurrence.
For the purposes of this Article, a truck is defined as
any vehicle with more than either two axles or four
wheels.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 3: LOADS AND LOAD FACTORS
3-29
(3.6.1.4.2-1)
ADTTSL = p × ADTT
where:
ADTT
=
ADTTSL =
p
=
the number of trucks per day in one direction
averaged over the design life
the number of trucks per day in a single-lane
averaged over the design life
fraction of traffic in a single lane, taken as
specified in Table 3.6.1.4.2-1
Table 3.6.1.4.2-1—Fraction of Truck Traffic in a Single
Lane, p
Number of Lanes Available to Trucks
1
2
3 or more
p
1.00
0.85
0.80
The single-lane ADTT is that for the traffic lane in
which the majority of the truck traffic crosses the bridge.
On a typical bridge with no nearby entrance/exit ramps,
the shoulder lane carries most of the truck traffic. The
frequency of the fatigue load for a single lane is assumed
to apply to all lanes since future traffic patterns on the
bridge are uncertain.
Consultation with traffic engineers regarding any
directionality of truck traffic may lead to the conclusion
that one direction carries more than one-half of the
bidirectional ADTT. If such data is not available from
traffic engineers, designing for 55 percent of the
bidirectional ADTT is suggested.
The value of ADTTSL is best determined in consultation
with traffic engineers. However, traffic growth data is usually
not predicted for the design life of the bridge, taken as 75 yr
in these Specifications unless specified otherwise by the
Owner. Techniques exist to extrapolate available data such as
curve fitting growth rate vs. time and using extreme value
distributions, but some judgment is required. Research has
shown that the average daily traffic (ADT), including all
vehicles, i.e., cars and trucks, is physically limited to about
20,000 vehicles per lane per day under normal conditions.
This limiting value of traffic should be considered when
estimating the ADTT. The ADTT can be determined by
multiplying the ADT by the fraction of trucks in the traffic. In
lieu of site-specific fraction of truck traffic data, the values of
Table C3.6.1.4.2-1 may be applied for routine bridges.
Table C3.6.1.4.2-1—Fraction of Trucks in Traffic
Class of Highway
Rural Interstate
Urban Interstate
Other Rural
Other Urban
Fraction of Trucks in Traffic
0.20
0.15
0.15
0.10
3.6.1.4.3—Load Distribution for Fatigue
3.6.1.4.3a—Refined Methods
Where the bridge is analyzed by any refined method,
as specified in Article 4.6.3, a single design truck shall be
positioned transversely and longitudinally to maximize
stress range at the detail under consideration, regardless of
the position of traffic or design lanes on the deck.
C3.6.1.4.3a
If it were assured that the traffic lanes would remain as
they are indicated at the opening of the bridge throughout its
entire service life, it would be more appropriate to place the
truck at the center of the traffic lane that produces maximum
stress range in the detail under consideration. But because
future traffic patterns on the bridge are uncertain and in the
interest of minimizing the number of calculations required of
the Designer, the position of the truck is made independent of
the location of both the traffic lanes and the design lanes.
3.6.1.4.3b—Approximate Methods
Where the bridge is analyzed by approximate load
distribution, as specified in Article 4.6.2, the distribution
factor for one traffic lane shall be used.
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All rights reserved. Duplication is a violation of applicable law.
2012
Edition
3-30
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
3.6.1.5—Rail Transit Load
Where a bridge also carries rail-transit vehicles, the
Owner shall specify the transit load characteristics and the
expected interaction between transit and highway traffic.
C3.6.1.5
If rail transit is designed to occupy an exclusive lane,
transit loads should be included in the design, but the
bridge should not have less strength than if it had been
designed as a highway bridge of the same width.
If the rail transit is supposed to mix with regular highway
traffic, the Owner should specify or approve an appropriate
combination of transit and highway loads for the design.
Transit load characteristics may include:
•
Loads,
•
Load distribution,
•
Load frequency,
•
Dynamic allowance, and
•
Dimensional requirements.
3.6.1.6—Pedestrian Loads
A pedestrian load of 0.075 ksf shall be applied to all
sidewalks wider than 2.0 ft and considered simultaneously
with the vehicular design live load in the vehicle lane. Where
vehicles can mount the sidewalk, sidewalk pedestrian load
shall not be considered concurrently. If a sidewalk may be
removed in the future, the vehicular live loads shall be applied
at 1 ft from edge-of-deck for design of the overhang, and 2 ft
from edge-of-deck for design of all other components. The
pedestrian load shall not be considered to act concurrently
with vehicles. The dynamic load allowance need not be
considered for vehicles.
Bridges intended for only pedestrian, equestrian, light
maintenance vehicle, and/or bicycle traffic should be
designed in accordance with AASHTO’s LRFD Guide
Specifications for the Design of Pedestrian Bridges.
C3.6.1.6
See the provisions of Article C3.6.1.1.2 for applying
the pedestrian loads in combination with the vehicular live
load.
3.6.1.7—Loads on Railings
Loads on railings shall be taken as specified in
Section 13.
3.6.2—Dynamic Load Allowance: IM
C3.6.2.1
3.6.2.1—General
Unless otherwise permitted in Articles 3.6.2.2 and
3.6.2.3, the static effects of the design truck or tandem,
other than centrifugal and braking forces, shall be
increased by the percentage specified in Table 3.6.2.1-1
for dynamic load allowance.
The factor to be applied to the static load shall be
taken as: (1 + IM/100).
The dynamic load allowance shall not be applied to
pedestrian loads or to the design lane load.
Page (1976) contains the basis for some of these
provisions.
The dynamic load allowance (IM) in Table 3.6.2.1-1
is an increment to be applied to the static wheel load to
account for wheel load impact from moving vehicles.
Dynamic effects due to moving vehicles may be
attributed to two sources:
•
Hammering effect is the dynamic response of the wheel
assembly to riding surface discontinuities, such as deck
joints, cracks, potholes, and delaminations, and
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 3: LOADS AND LOAD FACTORS
3-31
•
Table 3.6.2.1-1—Dynamic Load Allowance, IM
Component
Deck Joints—All Limit States
All Other Components:
IM
75%
•
Fatigue and Fracture Limit State
15%
•
All Other Limit States
33%
The application of dynamic load allowance for buried
components, covered in Section 12, shall be as specified in
Article 3.6.2.2.
Dynamic load allowance need not be applied to:
•
Retaining walls not subject to vertical reactions from
the superstructure, and
•
Foundation components that are entirely below
ground level.
The dynamic load allowance may be reduced for
components, other than joints, if justified by sufficient
evidence, in accordance with the provisions of
Article 4.7.2.1.
Dynamic response of the bridge as a whole to passing
vehicles, which may be due to long undulations in the
roadway pavement, such as those caused by
settlement of fill, or to resonant excitation as a result
of similar frequencies of vibration between bridge and
vehicle.
Field tests indicate that in the majority of highway
bridges, the dynamic component of the response does not
exceed 25 percent of the static response to vehicles. This is
the basis for dynamic load allowance with the exception of
deck joints. However, the specified live load combination
of the design truck and lane load, represents a group of
exclusion vehicles that are at least 4/3 of those caused by
the design truck alone on short- and medium-span bridges.
The specified value of 33 percent in Table 3.6.2.1-1 is the
product of 4/3 and the basic 25 percent.
Generally speaking, the dynamic amplification of
trucks follows the following general trends:
•
As the weight of the vehicle goes up, the apparent
amplification goes down.
•
Multiple vehicles produce a lower dynamic
amplification than a single vehicle.
•
More axles result in a lower dynamic amplification.
For heavy permit vehicles which have many axles
compared to the design truck, a reduction in the dynamic
load allowance may be warranted. A study of dynamic
effects presented in a report by the Calibration Task Group
(Nowak 1992) contains details regarding the relationship
between dynamic load allowance and vehicle
configuration.
This Article recognizes the damping effect of soil
when in contact with some buried structural components,
such as footings. To qualify for relief from impact, the
entire component must be buried. For the purpose of this
Article, a retaining type component is considered to be
buried to the top of the fill.
3.6.2.2—Buried Components
The dynamic load allowance for culverts and other
buried structures covered by Section 12, in percent, shall
be taken as:
IM = 33(1.0 − 0.125 DE ) ≥ 0%
(3.6.2.2-1)
where:
DE =
the minimum depth of earth cover above the
structure (ft)
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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3-32
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
C3.6.2.3
3.6.2.3—Wood Components
Dynamic load allowance need not be applied to wood
components.
Wood structures are known to experience reduced
dynamic wheel load effects due to internal friction
between the components and the damping characteristics
of wood. Additionally, wood is stronger for short duration
loads, as compared to longer duration loads. This increase
in strength is greater than the increase in force effects
resulting from the dynamic load allowance.
3.6.3—Centrifugal Forces: CE
C3.6.3
For the purpose of computing the radial force or the
overturning effect on wheel loads, the centrifugal effect on
live load shall be taken as the product of the axle weights
of the design truck or tandem and the factor C, taken as:
Centrifugal force is not required to be applied to the
design lane load, as the spacing of vehicles at high speed is
assumed to be large, resulting in a low density of vehicles
following and/or preceding the design truck. For all other
consideration of live load other than for fatigue, the design
lane load is still considered even though the centrifugal
effect is not applied to it.
The specified live load combination of the design
truck and lane load, however, represents a group of
exclusion vehicles that produce force effects of at least 4/3
of those caused by the design truck alone on short- and
medium-span bridges. This ratio is indicated in Eq. 3.6.3-1
for the service and strength limit states. For the fatigue and
fracture limit state, the factor 1.0 is consistent with
cumulative damage analysis. The provision is not
technically perfect, yet it reasonably models the
representative exclusion vehicle traveling at design speed
with large headways to other vehicles. The approximation
attributed to this convenient representation is acceptable in
the framework of the uncertainty of centrifugal force from
random traffic patterns.
1.0 ft/s = 0.682 mph
Centrifugal force also causes an overturning effect on
the wheel loads because the radial force is applied 6.0 ft
above the top of the deck. Thus, centrifugal force tends to
cause an increase in the vertical wheel loads toward the
outside of the bridge and an unloading of the wheel loads
toward the inside of the bridge. Superelevation helps to
balance the overturning effect due to the centrifugal force
and this beneficial effect may be considered. The effects
due to vehicle cases with centrifugal force effects included
should be compared to the effects due to vehicle cases with
no centrifugal force, and the worst case selected.
C= f
2
v
gR
(3.6.3-1)
where:
v
f
=
=
g
R
=
=
highway design speed (ft/s)
4/3 for load combinations other than fatigue and
1.0 for fatigue
gravitational acceleration: 32.2 (ft/s2)
radius of curvature of traffic lane (ft)
Highway design speed shall not be taken to be less
than the value specified in the current edition of the
AASHTO publication, A Policy of Geometric Design of
Highways and Streets.
The multiple presence factors specified in
Article 3.6.1.1.2 shall apply.
Centrifugal forces shall be applied horizontally at a
distance 6.0 ft above the roadway surface. A load path to
carry the radial force to the substructure shall be provided.
The effect of superelevation in reducing the
overturning effect of centrifugal force on vertical wheel
loads may be considered.
3.6.4—Braking Force: BR
The braking force shall be taken as the greater of:
•
25 percent of the axle weights of the design truck or
design tandem or,
•
Five percent of the design truck plus lane load or
five percent of the design tandem plus lane load
C3.6.4
Based on energy principles, and assuming uniform
deceleration, the braking force determined as a fraction of
vehicle weight is:
2
b=
v
2 ga
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(C3.6.4-1)
2012
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SECTION 3: LOADS AND LOAD FACTORS
This braking force shall be placed in all design lanes which
are considered to be loaded in accordance with
Article 3.6.1.1.1 and which are carrying traffic headed in
the same direction. These forces shall be assumed to act
horizontally at a distance of 6.0 ft above the roadway
surface in either longitudinal direction to cause extreme
force effects. All design lanes shall be simultaneously
loaded for bridges likely to become one-directional in the
future.
The multiple presence factors specified in
Article 3.6.1.1.2 shall apply.
3-33
where a is the length of uniform deceleration and b is the
fraction. Calculations using a braking length of 400 ft and
a speed of 55 mph yield b = 0.25 for a horizontal force that
will act for a period of about 10 s. The factor b applies to
all lanes in one direction because all vehicles may have
reacted within this time frame.
For short- and medium-span bridges, the specified
braking force can be significantly larger than was required
in the Standard Specifications. The braking force specified
in the Standard Specifications dates back to at least the
early 1940’s without any significant changes to address the
improved braking capacity of modern trucks. A review of
other bridge design codes in Canada and Europe showed
that the braking force required by the Standard
Specification is much lower than that specified in other
design codes for most typical bridges. One such
comparison is shown in Figure C3.6.4-1.
Figure C3.6.4-1—Comparison of Braking Force Models
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure C3.6.4-1 (continued)—Comparison of Braking
Force Models
where:
OHBDC =
LFD
=
LRFD
=
LRFD′ =
CHBDC =
factored braking force as specified in the 3rd
edition of the Ontario Highway Bridge
Design Code
factored braking force as specified in the
AASHTO Standard Specifications (Load
Factor)
factored braking force as specified in
previous
versions
of
the
LRFD
Specifications (up to 2001 Interim edition)
factored braking force as specified in
Article 3.6.4
factored braking force as specified in the
Canadian Highway Bridge Design Code
The sloping portion of the curves represents the braking
force that includes a portion of the lane load. This
represents the possibility of having multiple lanes of
vehicles contributing to the same braking event on a long
bridge. Although the probability of such an event is likely
to be small, the inclusion of a portion of the lane load gives
such an event consideration for bridges with heavy truck
traffic and is consistent with other design codes.
Because the LRFD braking force is significantly
higher than that required in the Standard Specifications,
this issue becomes important in rehabilitation projects
designed under previous versions of the design code. In
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2012
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SECTION 3: LOADS AND LOAD FACTORS
3-35
cases where substructures are found to be inadequate to
resist the increased longitudinal forces, consideration
should be given to design and detailing strategies which
distribute the braking force to additional substructure units
during a braking event.
3.6.5—Vehicular Collision Force: CT
3.6.5.1—Protection of Structures
Unless the Owner determines that site conditions
indicate otherwise, abutments and piers located within a
distance of 30.0 ft to the edge of roadway shall be
investigated for collision. Collision shall be addressed by
either providing structural resistance or by redirecting
or absorbing the collision load. The provisions of
Article 2.3.2.2.1 shall apply as appropriate.
Where the design choice is to provide structural
resistance, the pier or abutment shall be designed for an
equivalent static force of 600 kip, which is assumed to act
in a direction of zero to 15 degrees with the edge of the
pavement in a horizontal plane, at a distance of 5.0 ft
above ground.
Where the design choice is to redirect or absorb the
collision load, protection shall consist of one of the
following:
•
An embankment;
•
A structurally independent, crashworthy groundmounted 54.0-in. high barrier, located within 10.0 ft
from the component being protected; or
•
A 42.0-in. high barrier located at more than 10.0 ft
from the component being protected.
Such barrier shall be structurally and geometrically
capable of surviving the crash test for Test Level 5, as
specified in Section 13.
C3.6.5.1
Where an Owner chooses to make an assessment of
site conditions for the purpose of implementing this
provision, input from highway or safety engineers and
structural engineers should be part of that assessment.
The equivalent static force of 600 kip is based on the
information from full-scale crash tests of rigid columns
impacted by 80.0-kip tractor trailers at 50 mph. For
individual column shafts, the 600-kip load should be
considered a point load. Field observations indicate shear
failures are the primary mode of failure for individual
columns and columns that are 30.0 in. in diameter and
smaller are the most vulnerable. For wall piers, the load
may be considered to be a point load or may be distributed
over and area deemed suitable for the size of the structure
and the anticipated impacting vehicle, but not greater than
5.0 ft wide by 2.0 ft high. These dimensions were
determined by considering the size of a truck frame.
Requirements for train collision load found in
previous editions have been removed. Designers are
encouraged to consult the AREMA Manual for Railway
Engineering or local railroad company guidelines for train
collision requirements.
For the purpose of this Article, a barrier may be
considered structurally independent if it does not transmit
loads to the bridge.
Full-scale crash tests have shown that some vehicles
have a greater tendency to lean over or partially cross over
a 42.0-in. high barrier than a 54.0-in. high barrier. This
behavior would allow a significant collision of the vehicle
with the component being protected if the component is
located within a few ft of the barrier. If the component is
more than about 10.0 ft behind the barrier, the difference
between the two barrier heights is no longer important.
One way to determine whether site conditions qualify
for exemption from protection is to evaluate the annual
frequency of impact from heavy vehicles. With the
approval of the Owner, the annual frequency for a bridge
pier to be hit by a heavy vehicle, AFHPB, can be calculated
by:
AFHBP = 2(ADTT) (PHBP)365
(C3.6.5.1-1)
where:
ADTT =
PHBP
=
the number of trucks per day in one
direction
the annual probability for a bridge pier to be
hit by a heavy vehicle
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table C3.6.1.4.2-1 may be used to determine ADTT
from available ADT data.
PHBP = 3.457 x 10–9 for undivided roadways in tangent and
horizontally curved sections
1.090 x 10–9 for divided roadways in tangent sections
2.184 x 10–9 for divided roadways in horizontally curved
sections
Design for vehicular collision force is not required if
AFHBP is less than 0.0001 for critical or essential bridges or
0.001 for typical bridges.
The determination of the annual frequency for a
bridge pier to be hit by a heavy vehicle, AFHPB, is derived
from limited statistical studies performed by the Texas
Transportation Institute. Due to limited data, no distinction
has been made between tangent sections and horizontally
curved sections for undivided roadways. The target values
for AFHBP mirror those for vessel collision force found in
Article 3.14.5.
Table C3.6.5.1-1 provides typical resulting values for
AFHBP.
Table C3.6.5.1-1—Typical Values of AFHBP
Undivided
ADT
(Both Directions)
1000
2000
3000
4000
6000
8000
12000
14000
16000
18000
20000
22000
24000
26000
28000
ADTT*
(One Way)
50
100
150
200
300
400
600
700
800
900
1000
1100
1200
1300
1400
*Assumes ten percent of ADT is truck traffic.
Divided
Curved
Divided
Tangent
PHBP=3.457E-09
PHBP=2.184E-09
PHBP=1.09E-09
AFHPB = 2 × ADTT × 365 × PHBP
0.0001
0.0001
0.0000
0.0003
0.0002
0.0001
0.0004
0.0002
0.0001
0.0005
0.0003
0.0002
0.0008
0.0005
0.0002
0.0010
0.0006
0.0003
0.0015
0.0010
0.0005
0.0018
0.0011
0.0006
0.0020
0.0013
0.0006
0.0023
0.0014
0.0007
0.0025
0.0016
0.0008
0.0028
0.0018
0.0009
0.0030
0.0019
0.0010
0.0033
0.0021
0.0010
0.0035
0.0022
0.0011
3.6.5.2—Vehicle Collision with Barriers
The provisions of Section 13 shall apply.
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SECTION 3: LOADS AND LOAD FACTORS
3-37
3.7—WATER LOADS: WA
3.7.1—Static Pressure
Static pressure of water shall be assumed to act
perpendicular to the surface that is retaining the water.
Pressure shall be calculated as the product of height of
water above the point of consideration and the specific
weight of water.
Design water levels for various limit states shall be as
specified and/or approved by the Owner.
3.7.2—Buoyancy
C3.7.2
Buoyancy shall be considered to be an uplift force,
taken as the sum of the vertical components of static
pressures, as specified in Article 3.7.1, acting on all
components below design water level.
For substructures with cavities in which the presence
or absence of water cannot be ascertained, the condition
producing the least favorable force effect should be
chosen.
3.7.3—Stream Pressure
3.7.3.1—Longitudinal
C3.7.3.1
The pressure of flowing water acting in the
longitudinal direction of substructures shall be taken as:
p=
CDV 2
1, 000
(3.7.3.1-1)
p = CD
where:
p =
CD =
V
=
For the purpose of this Article, the longitudinal
direction refers to the major axis of a substructure unit.
The theoretically correct expression for Eq. 3.7.3.1-1
is:
pressure of flowing water (ksf)
drag coefficient for piers as specified in
Table 3.7.3.1-1
design velocity of water for the design flood in
strength and service limit states and for the check
flood in the extreme event limit state (ft/s)
Table 3.7.3.1-1—Drag Coefficient
Type
Semicircular-nosed pier
Square-ended pier
Debris lodged against the pier
Wedged-nosed pier with nose angle 90 degrees
or less
w 2
V
2g
(C3.7.3.1-1)
where:
w = specific weight of water (kcf)
V = velocity of water (ft/s)
g = gravitational acceleration constant—32.2 (ft/s2)
As a convenience, Eq. 3.7.3.1-1 recognizes that
w/2g ~ 1/1,000, but the dimensional consistency is lost in
the simplification.
CD
0.7
1.4
1.4
0.8
The longitudinal drag force shall be taken as the
product of longitudinal stream pressure and the projected
surface exposed thereto.
The drag coefficient, CD, and the lateral drag
coefficient, CL, given in Tables 3.7.3.1-1 and 3.7.3.2-1,
were adopted from the Ontario Highway Bridge Design
Code (1991). The more favorable drag coefficients
measured by some researchers for wedge-type pier nose
angles of less than 90 degrees are not given here because
such pier noses are more prone to catching debris.
Floating logs, roots, and other debris may accumulate
at piers and, by blocking parts of the waterway, increase
stream pressure load on the pier. Such accumulation is a
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
function of the availability of such debris and level of
maintenance efforts by which it is removed. It may be
accounted for by the judicious increase in both the exposed
surface and the velocity of water.
The draft New Zealand Highway Bridge Design
Specification contains the following provision, which may
be used as guidance in the absence of site-specific criteria:
Where a significant amount of driftwood is carried,
water pressure shall also be allowed for on a
driftwood raft lodged against the pier. The size of the
raft is a matter of judgment, but as a guide,
Dimension A in Figure C3.7.3.1-1 should be half the
water depth, but not greater than 10.0 ft. Dimension B
should be half the sum of adjacent span lengths, but
no greater than 45.0 ft. Pressure shall be calculated
using Eq. 3.7.3.1-1, with CD = 0.5. (Distances have
been changed from SI.)
Figure C3.7.3.1-1—Debris Raft for Pier Design
3.7.3.2—Lateral
C3.7.3.2
The lateral, uniformly distributed pressure on a
substructure due to water flowing at an angle, θ, to the
longitudinal axis of the pier shall be taken as:
p=
CLV 2
1000
The discussion of Eq. 3.7.3.1-1 also applies to
Eq. 3.7.3.2-1.
(3.7.3.2-1)
where:
p =
CL =
lateral pressure (ksf)
lateral
drag
coefficient
Table 3.7.3.2-1
specified
in
Figure 3.7.3.2-1—Plan View of Pier Showing Stream Flow
Pressure
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SECTION 3: LOADS AND LOAD FACTORS
3-39
Table 3.7.3.2-1—Lateral Drag Coefficient
Angle, θ, between direction of flow and
longitudinal axis of the pier
0 degrees
5 degrees
10 degrees
20 degrees
≥30 degrees
CL
0.0
0.5
0.7
0.9
1.0
The lateral drag force shall be taken as the product of
the lateral stream pressure and the surface exposed thereto.
3.7.4—Wave Load
C3.7.4
Wave action on bridge structures shall be considered
for exposed structures where the development of
significant wave forces may occur.
Loads due to wave action on bridge structures shall be
determined using accepted engineering practice methods.
Site-specific conditions should be considered. The latest
edition of the Shore Protection Manual, published by the
Coastal Engineering Research Center, Department of the
Army, is recommended for the computation of wave
forces.
3.7.5—Change in Foundations Due to Limit State for
Scour
C3.7.5
The provisions of Article 2.6.4.4 shall apply.
The consequences of changes in foundation conditions
resulting from the design flood for scour shall be
considered at strength and service limit states. The
consequences of changes in foundation conditions due to
scour resulting from the check flood for bridge scour and
from hurricanes shall be considered at the extreme event
limit states.
Statistically speaking, scour is the most common
reason for the failure of highway bridges in the United
States.
Provisions concerning the effects of scour are given in
Section 2. Scour per se is not a force effect, but by
changing the conditions of the substructure it may
significantly alter the consequences of force effects acting
on structures.
3.8—WIND LOAD: WL AND WS
3.8.1—Horizontal Wind Pressure
C3.8.1.1
3.8.1.1—General
Pressures specified herein shall be assumed to be
caused by a base design wind velocity, VB, of 100 mph.
Wind load shall be assumed to be uniformly
distributed on the area exposed to the wind. The exposed
area shall be the sum of areas of all components, including
floor system, railing, and sound barriers, as seen in
elevation taken perpendicular to the assumed wind
direction. This direction shall be varied to determine the
extreme force effect in the structure or in its components.
Areas that do not contribute to the extreme force effect
under consideration may be neglected in the analysis.
For bridges or parts of bridges and sound barriers
more than 30.0 ft above low ground or water level, the
design wind velocity, VDZ, should be adjusted according to:
Base design wind velocity varies significantly due to
local conditions. For small and/or low structures, wind
usually does not govern. For large and/or tall bridges and
sound barriers, however, the local conditions should be
investigated.
Pressures on windward and leeward sides are to be
taken simultaneously in the assumed direction of wind.
Typically, a bridge structure should be examined
separately under wind pressures from two or more
different directions in order to ascertain those windward,
leeward, and side pressures producing the most critical
loads on the structure.
Eq. 3.8.1.1-1 is based on boundary layer theory
combined with empirical observations and represents the
most recent approach to defining wind speeds for various
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
V Z
VDZ = 2.5V0 30 ln
VB Z0
(3.8.1.1-1)
where:
VDZ =
V30 =
VB =
Z
=
V0 =
Z0 =
design wind velocity at design elevation, Z (mph)
wind velocity at 30.0 ft above low ground or
above design water level (mph)
base wind velocity of 100 mph at 30.0 ft height,
yielding design pressures specified in
Articles 3.8.1.2.1 and 3.8.1.2.2
height of structure at which wind loads are being
calculated as measured from low ground, or from
water level, > 30.0 ft
friction velocity, a meteorological wind
characteristic
taken,
as
specified
in
Table 3.8.1.1-1, for various upwind surface
characteristics (mph)
friction length of upstream fetch, a
meteorological wind characteristic taken as
specified in Table 3.8.1.1-1 (ft)
conditions as used in meteorology. In the past, an
exponential equation was sometimes used to relate wind
speed to heights above 30.0 ft. This formulation was based
solely on empirical observations and had no theoretical
basis.
Z
VDZ = CV30
30
α
(C3.8.1.1-1)
The purpose of the term C and exponent α was to adjust
the equation for various upstream surface conditions,
similar to the use of Table 3.8.1.1-1. Further information
can be found in Liu (1991) and Simiu (1973, 1976).
The following descriptions for the terms “open
country,” “suburban,” and “city” in Table 3.8.1.1-1 are
paraphrased from ASCE-7-93:
•
Open Country—Open terrain with scattered
obstructions having heights generally less than 30.0 ft.
This category includes flat open country and
grasslands.
•
Suburban—Urban and suburban areas, wooded areas,
or other terrain with numerous closely spaced
obstructions having the size of single-family or larger
dwellings. Use of this category shall be limited to
those areas for which representative terrain prevails in
the upwind direction at least 1,500 ft.
•
City—Large city centers with at least 50 percent of
the buildings having a height in excess of 70.0 ft. Use
of this category shall be limited to those areas for
which representative terrain prevails in the upwind
direction at least one-half mile. Possible channeling
effects of increased velocity pressures due to the
bridge or structure’s location in the wake of adjacent
structures shall be taken into account.
Table 3.8.1.1-1—Values of V0 and Z0 for Various Upstream
Surface Conditions
Condition
V0 (mph)
Z0 (ft)
Open Country
8.20
0.23
Suburban
10.90
3.28
City
12.00
8.20
Except for sound barriers, V30 may be established
from:
•
Fastest-mile-of-wind charts available in ASCE 7-88
for various recurrence intervals,
•
Site-specific wind surveys, and
•
In the absence of better criterion, the assumption that
V30 = VB = 100 mph.
For sound barriers, V30 shall be taken as specified in
Article 15.8.2.
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SECTION 3: LOADS AND LOAD FACTORS
3-41
3.8.1.2—Wind Pressure on Structures: WS
3.8.1.2.1—General
C3.8.1.2.1
If justified by local conditions, a different base design
wind velocity may be selected for load combinations not
involving wind on live load. The direction of the design
wind shall be assumed to be horizontal, unless otherwise
specified in Article 3.8.3. In the absence of more precise
data, design wind pressure, in ksf, may be determined as:
2
V
V 2
PD = PB DZ = PB DZ
10, 000
VB
PB =
(3.8.1.2.1-1)
base wind pressure specified in Table 3.8.1.2.1-1
(ksf)
The wind force on the structure shall be calculated by
multiplying the design wind pressure, PD, calculated using
Eq. 3.8.1.2.1-1, by the exposed area, including the area of
sound barriers, if existing, regardless of the design wind
pressure used in designing the sound barriers themselves.
Table 3.8.1.2.1-1—Base Pressures, PB, Corresponding to
VB = 100 mph
Superstructure
Component
Trusses, Columns,
and Arches
Beams
Large Flat Surfaces
Windward
Load, ksf
0.050
Leeward
Load, ksf
0.025
0.050
0.040
NA
NA
The stagnation pressure associated with a wind
velocity of 100 mph is 0.0256 ksf, which is significantly
less than the values specified in Table 3.8.1.2.1-1. The
difference reflects the effect of gusting combined with
some tradition of long-time usage.
The pressures specified in klf or ksf should be
chosen to produce the greater net wind load on the
structure.
Wind tunnel tests may be used to provide more
precise estimates of wind pressures. Such testing should
be considered where wind is a major design load.
Due to the lack of information on the wind force on
sound barriers, the wind pressure specified in Article
15.8.2 for the design of sound barriers is based on
producing similar wind pressures to those used for the
design of sound barriers (AASHTO, 1989). Such values
of wind pressures proved to produce safe designs in the
past.
The term “columns” in Table 3.8.1.2.1-1 refers to
columns in superstructures such as spandrel columns in
arches.
The total wind loading shall not be taken less than
0.30 klf in the plane of a windward chord and 0.15 klf in
the plane of a leeward chord on truss and arch components,
and not less than 0.30 klf on beam or girder spans.
3.8.1.2.2—Loads from Superstructures
Except where specified herein, where the wind is not
taken as normal to the structure, the base wind pressures,
PB, for various angles of wind direction may be taken as
specified in Table 3.8.1.2.2-1 and shall be applied to the
centroid of a single plane of exposed area. The skew angle
shall be taken as measured from a perpendicular to the
longitudinal axis. The wind direction for design shall be
that which produces the extreme force effect on the
component under investigation. The transverse and
longitudinal pressures shall be applied simultaneously.
C3.8.1.2.2
For trusses, columns, and arches, the base wind
pressures specified in Table 3.8.1.2.2-1 are the sum of
the pressures applied to both the windward and leeward
areas.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 3.8.1.2.2-1—Base Wind Pressures, PB, for Various Angles of Attack and VB = 100 mph
Trusses,
Columns and Arches
Lateral Load
Longitudinal Load
(ksf)
(ksf)
0.075
0.000
0.070
0.012
0.065
0.028
0.047
0.041
0.024
0.050
Skew Angle of Wind
(degrees)
0
15
30
45
60
Lateral Load
(ksf)
0.050
0.044
0.041
0.033
0.017
Girders
Longitudinal Load
(ksf)
0.000
0.006
0.012
0.016
0.019
For the usual girder and slab bridges having an
individual span length of not more than 125 ft and a
maximum height of 30.0 ft above low ground or water
level the following wind loading may be used:
•
0.05 ksf, transverse
•
0.012 ksf, longitudinal
Both forces shall be applied simultaneously. These
forces shall not be used in determining the forces on
sound barriers.
Wind pressure on sound barriers should be
determined using the provisions of Article 15.8.2.
3.8.1.2.3—Forces Applied Directly to the
Substructure
The transverse and longitudinal forces to be applied
directly to the substructure shall be calculated from an
assumed base wind pressure of 0.040 ksf. For wind
directions taken skewed to the substructure, this force
shall be resolved into components perpendicular to the
end and front elevations of the substructure. The
component perpendicular to the end elevation shall act
on the exposed substructure area as seen in end
elevation, and the component perpendicular to the front
elevation shall act on the exposed areas and shall be
applied simultaneously with the wind loads from the
superstructure.
3.8.1.3—Wind Pressure on Vehicles: WL
When vehicles are present, the design wind
pressure shall be applied to both structure and vehicles.
Wind pressure on vehicles shall be represented by an
interruptible, moving force of 0.10 klf acting normal to,
and 6.0 ft above, the roadway and shall be transmitted
to the structure.
Except where specified herein, when wind on
vehicles is not taken as normal to the structure, the
components of normal and parallel force applied to the
live load may be taken as specified in Table 3.8.1.3-1
with the skew angle taken as referenced normal to the
surface.
C3.8.1.3
Based on practical experience, maximum live loads
are not expected to be present on the bridge when the
wind velocity exceeds 55 mph. The load factor
corresponding to the treatment of wind on structure only
in Load Combination Strength III would be (55/100)2
(1.4) = 0.42, which has been rounded to 0.40 in the
Strength V Load Combination. This load factor
corresponds to 0.3 in Service I.
The 0.10 klf wind load is based on a long row of
randomly sequenced passenger cars, commercial vans,
and trucks exposed to the 55 mph design wind. This
horizontal live load, similar to the design lane load,
should be applied only to the tributary areas producing a
force effect of the same kind.
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SECTION 3: LOADS AND LOAD FACTORS
3-43
Table 3.8.1.3-1—Wind Components on Live Load
Skew Angle
(degrees)
0
15
30
45
60
Normal
Component
(klf)
0.100
0.088
0.082
0.066
0.034
Parallel
Component
(klf)
0.000
0.012
0.024
0.032
0.038
For the usual girder and slab bridges having an
individual span length of not more than 125 ft and a
maximum height of 30.0 ft above low ground or water
level, the following wind loading may be used:
•
0.10 klf, transverse
•
0.04 klf, longitudinal
Both forces shall be applied simultaneously.
3.8.2—Vertical Wind Pressure
C3.8.2
Unless otherwise determined in Article 3.8.3, a
vertical upward wind force of 0.020 ksf times the width
of the deck, including parapets and sidewalks, shall be
considered to be a longitudinal line load. This force
shall be applied only for the Strength III and Service IV
limit states which do not involve wind on live load, and
only when the direction of wind is taken to be
perpendicular to the longitudinal axis of the bridge. This
lineal force shall be applied at the windward quarterpoint of the deck width in conjunction with the
horizontal wind loads specified in Article 3.8.1.
The intent of this Article is to account for the effect
resulting from interruption of the horizontal flow of air
by the superstructure. This load is to be applied even to
discontinuous bridge decks, such as grid decks. This
load may govern where overturning of the bridge is
investigated.
3.8.3—Aeroelastic Instability
3.8.3.1—General
C3.8.3.1
Aeroelastic force effects shall be taken into account
in the design of bridges and structural components apt
to be wind-sensitive. For the purpose of this Article, all
bridges with a span to depth ratio, and structural
components thereof with a length to width ratio,
exceeding 30.0 shall be deemed to be wind-sensitive.
The vibration of cables due to the interaction of
wind and rain shall also be considered.
Because of the complexity of analyses often
necessary for an in-depth evaluation of structural
aeroelasticity, this Article is intentionally kept to a
simple statement. Many bridges, decks, or individual
structural components have been shown to be
aeroelastically insensitive if the specified ratios are
under 30.0, a somewhat arbitrary value helpful only in
identifying likely wind-sensitive cases.
Flexible bridges, such as cable-supported or very
long spans of any type, may require special studies
based on wind tunnel information. In general,
appropriate wind tunnel tests involve simulation of the
wind environment local to the bridge site. Details of this
are part of the existing wind tunnel state of the art and
are beyond the scope of this commentary.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
3.8.3.2—Aeroelastic Phenomena
The aeroelastic phenomena of vortex excitation,
galloping, flutter, and divergence shall be considered
where applicable.
3.8.3.3—Control of Dynamic Responses
Bridges and structural components thereof,
including cables, shall be designed to be free of fatigue
damage due to vortex-induced or galloping oscillations.
Bridges shall be designed to be free of divergence and
catastrophic flutter up to 1.2 times the design wind
velocity applicable at bridge deck height.
3.8.3.4—Wind Tunnel Tests
Representative wind tunnel tests may be used to
satisfy the requirements of Articles 3.8.3.2 and 3.8.3.3.
C3.8.3.2
Excitation due to vortex shedding is the escape of
wind-induced vortices behind the member, which tend
to excite the component at its fundamental natural
frequency in harmonic motion. It is important to keep
stresses due to vortex-induced oscillations below the
“infinite life” fatigue stress. Methods exist for
estimating such stress amplitudes, but they are outside
the scope of this commentary.
Tubular components can be protected against
vortex-induced oscillation by adding bracing, strakes, or
tuned mass dampers or by attaching horizontal flat
plates parallel to the tube axis above and/or below the
central third of their span. Such aerodynamic damper
plates should lie about one-third tube diameter above or
below the tube to allow free passage of wind. The width
of the plates may be the diameter of the tube.
Galloping is a high-amplitude oscillation associated
with ice-laden cables or long, flexible members having
aerodynamically unsymmetrical cross-sections. Cablestays, having circular sections, will not gallop unless
their circumferences are deformed by ice, dropping
water, or accumulated debris.
Flexible bridge decks, as in very long spans and
some pedestrian bridges, may be prone to wind-induced
flutter, a wind-excited oscillation of destructive
amplitudes, or, on some occasions, divergence, an
irreversible twist under high wind. Analysis methods,
including wind tunnel studies leading to adjustments of
the deck form, are available for prevention of both
flutter and divergence.
C3.8.3.3
Cables in stayed-girder bridges have been
successfully stabilized against excessive dynamic
responses by attaching automotive dampers to the
bridge at deck level or by cross-tying multiple cablestays.
C3.8.3.4
Wind tunnel testing of bridges and other civil
engineering structures is a highly developed technology,
which may be used to study the wind response
characteristics of a structural model or to verify the
results of analysis (Simiu, 1976).
3.9—ICE LOADS: IC
3.9.1—General
C3.9.1
This Article refers only to freshwater ice in rivers
and lakes; ice loads in seawater should be determined
by suitable specialists using site-specific information.
Most of the information for ice loads was taken
from Montgomery et al. (1984), which provided
background for the clauses on ice loads for Canadian
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SECTION 3: LOADS AND LOAD FACTORS
Ice forces on piers shall be determined with regard
to site conditions and expected modes of ice action as
follows:
3-45
•
Dynamic pressure due to moving sheets or floes of
ice being carried by stream flow, wind, or currents;
•
Static pressure due to thermal movements of ice
sheets;
•
Pressure resulting from hanging dams or jams of
ice; and
Standards Association (1988). A useful additional
source has been Neill (1981).
It is convenient to classify ice forces on piers as
dynamic forces and static forces.
Dynamic forces occur when a moving ice floe
strikes a bridge pier. The forces imposed by the ice floe
on a pier are dependent on the size of the floe, the
strength and thickness of the ice, and the geometry of
the pier.
The following types of ice failure have been
observed (Montgomery et al., 1984):
•
Static uplift or vertical load resulting from adhering
ice in waters of fluctuating level.
•
The expected thickness of ice, the direction of its
movement, and the height of its action shall be
determined by field investigations, review of public
records, aerial surveys, or other suitable means.
Crushing, where the ice fails by local crushing
across the width of a pier. The crushed ice is
continually cleared from a zone around the pier as
the floe moves past.
•
Bending, where a vertical reaction component acts
on the ice floe impinging on a pier with an inclined
nose. This reaction causes the floe to rise up the
pier nose, as flexural cracks form.
•
Splitting, where a comparatively small floe strikes
a pier and is split into smaller parts by stress cracks
propagating from the pier.
•
Impact, where a small floe is brought to a halt by
impinging on the nose of the pier before it has
crushed over the full width of the pier, bent or split.
•
Buckling, where compressive forces cause a large
floe to fail by buckling in front of the nose of a
very wide pier.
For bridge piers of usual proportions on larger
bodies of water, crushing and bending failures usually
control the magnitude of the design dynamic ice force.
On smaller streams, which cannot carry large ice floes,
impact failure can be the controlling mode.
In all three cases, it is essential to recognize the
effects of resonance between the pier and the ice forces.
Montgomery et al. (1980) have shown that for a
massive pier with a damping coefficient of 20 percent of
critical, the maximum dynamic effect is approximately
equal to the greatest force, but for lesser damping values
there is a considerable amplification.
Montgomery and Lipsett (1980) measured damping
of a massive pier at 19 percent of critical, but it is
expected that slender piers and individual piles may
have damping values of five percent or less.
In the discussion of impact-type ice failure above, the
indication is that the floe is “small.” Small is extremely
difficult to define and is site-specific. Floes up to 75.0 ft
long have been observed to fail by splitting when driven
by water velocities of 10.0 ft/s (Haynes, 1996).
Static forces may be caused by the thermal
expansion of ice in which a pier is embedded or by
irregular growth of the ice field. This has typically been
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3-46
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
observed downstream of a dam, or hydroelectric plant
or other channel where ice predominantly forms only on
one side of the river or pier.
Ice jams can arch between bridge piers. The breakup ice jam is a more or less cohesionless accumulation
of ice fragments (Montgomery et al., 1984).
Hanging dams are created when frazil ice passes
under the surface layer of ice and accumulates under the
surface ice at the bridge site. The frazil ice comes
typically from rapids or waterfalls upstream. The
hanging dam can cause a backup of water, which exerts
pressure on the pier and can cause scour around or
under piers as water flows at an increased velocity.
3.9.2—Dynamic Ice Forces on Piers
3.9.2.1—Effective Ice Strength
In the absence of more precise information, the
following values may be used for effective ice crushing
strength:
•
8.0 ksf, where breakup occurs at melting
temperatures and the ice structure is substantially
disintegrated;
•
16.0 ksf, where breakup occurs at melting
temperatures and the ice structure is somewhat
disintegrated;
•
24.0 ksf, where breakup or major ice movement
occurs at melting temperatures, but the ice moves
in large pieces and is internally sound; and
•
32.0 ksf, where breakup or major ice movement
occurs when the ice temperature, averaged over its
depth, is measurably below the melting point.
C3.9.2.1
It should be noted that the effective ice strengths
given herein are for the purpose of entering into a
formula to arrive at forces on piers. Different formulas
might require different effective ice strengths to arrive
at the same result.
As a guide, the 8.0 ksf strength is appropriate for
piers where long experience indicates that ice forces are
minimal, but some allowance is required for ice effects;
the 32.0 ksf strength is considered to be a reasonable
upper limit based on the observed history of bridges that
have survived ice conditions (Neill, 1981). Effective ice
strengths of up to 57.6 ksf have been used in the design
of some bridges in Alaska (Haynes, 1996).
The effective ice strength depends mostly on the
temperature and grain size of the ice (Montgomery et
al., 1984). For example, laboratory measured
compressive strengths at 32°F vary from about 60.0 ksf
for grain sizes of 0.04 in. to 27.0 ksf for grain sizes of
0.2 in., and at 23°F ice strengths are approximately
double the values given. Thus, the effective ice
strengths given herein are not necessarily representative
of laboratory tests or actual ice strengths, and, in fact,
are on the order of one-half of observed values (Neill,
1981).
The compressive strength of the ice depends upon
temperature, but the tensile strength is not sensitive to
temperature. Because much ice failure is the result of
splitting or tensile failure in bending, and because grain
sizes, cracks, and other imperfections vary in the field,
only crude approximations of ice strengths can be made.
Thus, temperature is not a consideration for setting
effective ice strengths in these Specifications.
Some of the most severe ice runs in the United
States occur during a rapid January thaw, when the air
temperature is about 50°F, but the average ice
temperature can still be below 32°F because of an
insulating snow cover (Haynes, 1996).
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SECTION 3: LOADS AND LOAD FACTORS
3-47
3.9.2.2—Crushing and Flexing
C3.9.2.2
The horizontal force, F, resulting from the pressure
of moving ice shall be taken as:
•
If
F
=
•
If
F
=
w
≤ 6.0 , then:
t
lesser of either Fc or, when ice failure by
flexure is considered applicable as described
herein, Fb, and
w
> 6.0 , then:
t
Fc
in which:
Fc = Ca ptw
(3.9.2.2-1)
Fb = Cn pt 2
(3.9.2.2-2)
Ca = (5 t / w + 1) 0.5
(3.9.2.2-3)
0.5
tan(α − 15 )
(3.9.2.2-4)
Cn =
where:
t
α
p
=
=
=
w =
Fc =
Fb =
Ca =
Cn =
thickness of ice (ft)
inclination of the nose to the vertical (degrees)
effective ice crushing strength as specified in
Article 3.9.2.1 (ksf)
pier width at level of ice action (ft)
horizontal ice force caused by ice floes that fail
by crushing over the full width of the pier (kip)
horizontal ice force caused by ice floes that
fail by flexure as they ride up the inclined pier
nose (kip)
coefficient accounting for the effect of the pier
width/ice thickness ratio where the floe fails
by crushing
coefficient accounting for the inclination of the
pier nose with respect to a vertical
where α ≤ 15 degrees, ice failure by flexure shall not be
considered to be a possible ice failure mode for the
purpose of calculating the horizontal force, F, in which
case F shall be taken as Fc.
The expression of Fc is based on field measurements
of forces on two bridge piers in Alberta (Lipsett and
Gerard, 1980). See also Huiskamp (1983), with a Ca
proposed by Afanas'ev et al. (1971), and verified by Neill
(1976).
The expression for Fb is taken from Lipsett and
Gerard (1980).
w/t = 6.0 is a rough estimate of the upper limit of w/t
at which ice that has failed by bending will be washed
around the pier.
It is assumed that the force on the pier is governed by
the crushing or bending strength of the ice, and thus there
is not a term in Eqs. 3.9.2.2-1 or 3.9.2.2-2 relating to
velocity of the ice. The interaction between an ice floe
and a pier depends on the size and strength of the floe and
how squarely it strikes the pier. It has been reported that
an ice floe 200 ft in size will usually fail by crushing if it
hits a pier squarely. If a floe 100 ft in size does not hit the
pier squarely, it will usually impact the pier and rotate
around the pier and pass downstream with only little local
crushing.
Although no account is taken of the shape of the nose
of the pier, laboratory tests at the U.S. Army Corps of
Engineers’ Cold Regions Research and Engineering
Laboratory (CRREL) have shown the bullet-shaped pier
nose can reduce ice forces the most compared to other
types of geometry. Pointed angular noses, as shown in
Figure C3.9.2.4.1-1, have been found to cause lateral
vibrations of the pier without reducing the streamwise
force. CRREL has measured lateral or torsional vibrations
on the pointed nose Yukon River Bridge piers. The longterm ramifications of these vibrations are not known at
this time (Haynes, 1996).
Ice thickness is the greatest unknown in the
determination of ice forces on piers. Equations can be used
for estimating ice thickness. The design should be based
on the extreme, not average, ice thickness. The elevation
on the pier where the design force shall be applied is
important for calculating the overturning moments.
Because ice stage increases during an ice run, relying on
local knowledge of the maximum stage is vital to proper
design (Haynes, 1995). For the purpose of design, the
preferred method to establish the thickness of ice, t, is to
base it on measurements of maximum thicknesses, taken
over a period of several years, at the potential bridge sites.
Where observations over a long period of time are
not available, an empirical method based on Neill (1981)
is suggested as follows:
t = 0.083α S f
(C3.9.2.2-1)
where:
α
=
coefficient for local conditions, normally less
than 1.0
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Sf
=
T
=
freezing index, being the algebraic sum,
Σ(32 – T), summed from the date of freeze-up
to the date of interest, in degree days
mean daily air temperature (degrees F)
Assuming that temperature records are available,
the maximum recorded value of Sf can be determined.
One possible method of determining α is by simple
calibration in which, through the course of a single
winter, the ice thickness can be measured at various
times and plotted against S f .
As a guide, Neill (1981) indicates the following
values for α:
windy lakes without snow .......................................0.8
average lake with snow ....................................0.5–0.7
average river with snow....................................0.4–0.5
sheltered small river with snow ........................0.2–0.4
Due to its good insulating characteristics, snow has a
significant effect on ice growth. Williams (1963) has
shown that a snow cover greater than 6.0 in. in thickness
has the effect of reducing α by as much as 50 percent.
Neill does not define “average,” and it has been noted
by Gerard and Stanely (1992) that deep snow can produce
snow-ice, thus offsetting the benefits of snow insulation.
Large lakes take longer to cool down, which leads
to a later freeze-up date. This results in fewer degreedays of freezing and, hence, smaller ice thicknesses.
The remaining decision is to establish the
appropriate elevation of the ice force to be applied to
the pier. The elevation required is that at break-up, not
at the mean winter level. Neill (1981) suggests several
methods of determining ice elevations, but the most
common method in general use is probably to rely on
local knowledge and examination of the river banks to
determine the extent of damage by ice, such as the
marking or removal of trees.
C3.9.2.3
3.9.2.3—Small Streams
On small streams not conducive to the formation of
large ice floes, consideration may be given to reducing
the forces Fb and Fc, determined in accordance with
Article 3.9.2.2, but under no circumstances shall the
forces be reduced by more than 50 percent.
CAN/CSA-S6-88 has an expression for ice forces
in small streams, for which a theory is given by
Montgomery et al. (1984). It is considered insufficiently
verified to be included herein.
On small streams, with a width of less than 300 ft at
the mean water level, dynamic ice forces, as determined
in Article 3.9.2.2, may be reduced in accordance with
Table C3.9.2.3-1. Another important factor that
determines the ice floe size are the type of features in
the river upstream of the site. Islands, dams, and bridge
piers can break ice into small floes.
where:
A
r
=
=
plan area of the largest ice floe in (ft2)
radius of pier nose (ft)
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SECTION 3: LOADS AND LOAD FACTORS
3-49
Table C3.9.2.3-1—Reduction Factor K1 for Small
Streams
A/r2
1000
500
200
100
50
Reduction Factor, K1
1.0
0.9
0.7
0.6
0.5
The rationale for the reduction factor, K1, is that the
bridge may be struck only by small ice floes with
insufficient momentum to cause failure of the floe.
3.9.2.4—Combination of Longitudinal and
Transverse Forces
C3.9.2.4.1
3.9.2.4.1—Piers Parallel to Flow
The force F, determined as specified in
Articles 3.9.2.2 and 3.9.2.3, shall be taken to act along
the longitudinal axis of the pier if the ice movement has
only one direction and the pier is approximately aligned
with that direction. In this case, two design cases shall
be investigated as follows:
•
A longitudinal force equal to F shall be combined
with a transverse force of 0.15F, or
•
A longitudinal force of 0.5F shall be combined
with a transverse force of Ft.
It would be unrealistic to expect the ice force to be
exactly parallel to the pier, so a minimum lateral
component of 15 percent of the longitudinal force is
specified.
The expression for Ft comes from Montgomery et
al. (1984), and is explained in Figure C3.9.2.4.1-1 taken
from the same source.
The transverse force, Ft, shall be taken as:
Ft =
F
2 tan(β / 2 + θ f )
(3.9.2.4.1-1)
where:
β
=
θf
=
nose angle in a horizontal plane for a round
nose taken as 100 (degrees)
friction angle between ice and pier nose
(degrees)
Both the longitudinal and transverse forces shall be
assumed to act at the pier nose.
Figure C3.9.2.4.1-1—Transverse Ice Force Where a
Floe Fails over a Portion of a Pier
3.9.2.4.2—Piers Skewed to Flow
Where the longitudinal axis of a pier is not parallel to
the principal direction of ice action, or where the direction
of ice action may shift, the total force on the pier shall be
determined on the basis of the projected pier width and
resolved into components. Under such conditions, forces
transverse to the longitudinal axis of the pier shall be
taken to be at least 20 percent of the total force.
C3.9.2.4.2
The provisions for piers skewed to flow are taken
from CAN/CSA-S6-88 (1988).
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
3.9.2.5—Slender and Flexible Piers
C3.9.2.5
Slender and flexible piers shall not be used in
regions where ice forces are significant, unless advice
on ice/structure interaction has been obtained from an
ice specialist. This provision also applies to slender and
flexible components of piers, including piles that come
into contact with water-borne ice.
It has been shown by Montgomery et al. (1980) and
others that flexible piers and pier components may
experience considerable amplification of the ice forces
as a result of resonant ice/structure interaction at low
levels of structural damping. In this case, the provisions
of Article 3.9.5 may be inadequate for vertical forces on
piers.
3.9.3—Static Ice Loads on Piers
C3.9.3
Ice pressures on piers frozen into ice sheets shall be
investigated where the ice sheets are subject to
significant thermal movements relative to the pier where
the growth of shore ice is on one side only or in other
situations that may produce substantial unbalanced
forces on the pier.
Little guidance is available for predicting static ice
loads on piers. Under normal circumstances, the effects of
static ice forces on piers may be strain-limited, but expert
advice should be sought if there is reason for concern.
Static ice forces due to thermal expansion of ice are
discussed in Haynes (1995). Ice force can be reduced by
several mitigating factors that usually apply. For example,
ice does not act simultaneously over the full length of the
pier. Thermal stresses relax in time and prevent high
stresses over the full ice thickness. A snow cover on the
ice insulates the ice and reduces the thermal stresses, and
ice usually acts simultaneously on both sides of the pier
surrounded by the ice so that the resultant force is
considerably less than the larger directional force, i.e.,
force on one side of the pier. Article C3.9.1 contains
additional discussion.
3.9.4—Hanging Dams and Ice Jams
C3.9.4
The frazil accumulation in a hanging dam may be
taken to exert a pressure of 0.2 to 2.0 ksf as it moves by
the pier. An ice jam may be taken to exert a pressure of
0.02 to 0.20 ksf.
The theory behind the ice pressures given for hanging
dams can be found in Montgomery et al. (1984). The wide
spread of pressures quoted reflects both the variability of
the ice and the lack of firm information on the subject.
3.9.5—Vertical Forces Due to Ice Adhesion
C3.9.5
The vertical force, in kips, on a bridge pier due to
rapid water level fluctuation shall be taken as:
Eq. 3.9.5-1 was derived by considering the failure
of a semi-infinite, wedge-shaped ice sheet on an elastic
foundation under vertical load applied at its apex. For a
single ice wedge, the maximum vertical force, P, can be
evaluated from the expression (Nevel, 1972).
For a circular pier:
0.03R
Fv = 80.0t 2 0.35 + 0.75
t
(3.9.5-1)
0.03R
Fv = 0.2t1.25 L + 80.0t 2 0.35 + 0.75
t
where:
=
3
a
a
1.05 + 2 + 0.5
in which:
For an oblong pier:
t
δ
tan σT t 2
2
P=
3
ice thickness (ft)
(3.9.5-2)
(C3.9.5-1)
0.25
Et 3
=
12 γ
= 21.0t 0.75
(C3.9.5-2)
where:
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SECTION 3: LOADS AND LOAD FACTORS
R
=
L
=
radius of circular pier (ft); or radius of half
circles at ends of an oblong pier (ft); or radius
of a circle that circumscribes each end of an
oblong pier of which the ends are not circular
in plan at water level (ft)
perimeter of pier, excluding half circles at ends
of oblong pier (ft)
3-51
σT
t
δ
a
=
=
=
=
ℓ
=
E
γ
=
=
tensile strength of ice (ksf)
maximum thickness of ice (ft)
angle of the truncated wedge (degrees)
truncated distance, which is assumed to be
equal to the radius of a circular pier (ft)
characteristic length calculated from the
expression (ft)
Young’s modulus for ice (ksf)
unit weight of water (kcf)
To obtain Eq. 3.9.5-1, the vertical force is summed
for four wedges, each with a truncated angle of
90 degrees. It is assumed that the tensile strength of ice
is 0.84 times an effective crushing strength of 23 ksf
and that the ratio of the truncated distance to the
characteristic length, a/ ℓ, is less than 0.6.
Eq. 3.9.5-2 is the sum of two expressions:
•
Eq. 3.9.5-1, which accounts for the vertical ice
forces acting on the half circles at the ends of an
oblong pier, and
•
An expression that calculates the vertical ice forces
on the straight walls of the pier.
The expression for calculating the vertical ice forces
on the long straight walls of the pier was derived by
considering a semi-infinite, rectangular ice sheet on an
elastic foundation under a uniformly distributed edge
load. The force required to fail the ice sheet, F, can be
expressed as F = 0.236 σT t2/ ℓ (Montgomery et al., 1984).
Eqs. 3.9.5-1 and 3.9.5-2 are based on the
conservative assumption that ice adheres around the full
perimeter of the pier cross-section. They neglect creep
and are, therefore, conservative for water level
fluctuations occurring over more than a few minutes.
However, they are also based on the nonconservative
assumption that failure occurs on the formation of the
first crack.
Some issues surrounding ice forces have been
reported in Zabilansky (1996).
3.9.6—Ice Accretion and Snow Loads on
Superstructures
C3.9.6
Generally snow loads, other than those caused by
an avalanche, need not be considered. However,
Owners in areas where unique accumulations of snow
and/or ice are possible should specify appropriate loads
for that condition.
Loads due to icing of the superstructure by freezing
rain shall be specified if local conditions so warrant.
The following discussion of snow loads is taken
from Ritter (1990).
Snow loads should be considered where a bridge is
located in an area of potentially heavy snowfall. This
can occur at high elevations in mountainous areas with
large seasonal accumulations. Snow loads are normally
negligible in areas of the United States that are below
2,000 ft elevation and east of longitude 105°W, or
below 1,000 ft elevation and west of longitude 105°W.
In other areas of the country, snow loads as large as
0.7 ksf may be encountered in mountainous locations.
The effects of snow are assumed to be offset by an
accompanying decrease in vehicle live load. This
assumption is valid for most structures, but is not
realistic in areas where snowfall is significant. When
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3-52
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
prolonged winter closure of a road makes snow removal
impossible, the magnitude of snow loads may exceed
those from vehicular live loads. Loads also may be
notable where plowed snow is stockpiled or otherwise
allowed to accumulate. The applicability and magnitude
of snow loads are left to the Designer’s judgment.
Snow loads vary from year to year and depend on
the depth and density of snowpack. The depth used for
design should be based on a mean recurrence interval or
the maximum recorded depth. Density is based on the
degree of compaction. The lightest accumulation is
produced by fresh snow falling at cold temperatures.
Density increases when the snowpack is subjected to
freeze-thaw cycles or rain. Probable densities for
several snowpack conditions are indicated in
Table C3.9.6-1, ASCE (1980).
Table C3.9.6-1—Snow Density
Condition of Snowpack
Freshly Fallen
Accumulated
Compacted
Rain or Snow
Probable Density (kcf)
0.006
0.019
0.031
0.031
Estimated snow load can be determined from
historical records or other reliable data. General
information on ground snow loads is available from the
National Weather Service, from state and local agencies,
and ASCE (1988). Snow loads in mountain areas are
subject to extreme variations. The extent of these loads
should be determined on the basis of local experience or
records, instead of on generalized information.
The effect of snow loads on a bridge structure is
influenced by the pattern of snow accumulation.
Windblown snow drifts may produce unbalanced loads
considerably greater than those produced from
uniformly distributed loads. Drifting is influenced by
the terrain, structure shape, and other features that cause
changes in the general wind flow. Bridge components,
such as railings, can serve to contain drifting snow and
cause large accumulations to develop.
3.10—EARTHQUAKE EFFECTS: EQ
3.10.1—General
C3.10.1
Bridges shall be designed to have a low probability
of collapse but may suffer significant damage and
disruption to service when subject to earthquake ground
motions that have a seven percent probability of
exceedance in 75 yr. Partial or complete replacement
may be required. Higher levels of performance may be
used with the authorization of the Bridge Owner.
Earthquake loads shall be taken to be horizontal
force effects determined in accordance with the
The design earthquake motions and forces specified
in these provisions are based on a low probability of
their being exceeded during the normal life expectancy
of a bridge. Bridges that are designed and detailed in
accordance with these provisions may suffer damage,
but should have low probability of collapse due to
seismically induced ground shaking.
The principles used for the development of these
Specifications are:
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SECTION 3: LOADS AND LOAD FACTORS
provisions of Article 4.7.4 on the basis of the elastic
response coefficient, Csm, specified in Article 3.10.4,
and the equivalent weight of the superstructure, and
adjusted by the response modification factor, R,
specified in Article 3.10.7.1.
The provisions herein shall apply to bridges of
conventional construction. The Owner shall specify
and/or
approve
appropriate
provisions
for
nonconventional construction. Unless otherwise
specified by the Owner, these provisions need not be
applied to completely buried structures.
Seismic effects for box culverts and buried
structures need not be considered, except where they
cross active faults.
The potential for soil liquefaction and slope
movements shall be considered.
3-53
•
Small to moderate earthquakes should be resisted
within the elastic range of the structural
components without significant damage;
•
Realistic seismic ground motion intensities and
forces should be used in the design procedures; and
•
Exposure to shaking from large earthquakes should
not cause collapse of all or part of the bridge.
Where possible, damage that does occur should be
readily detectable and accessible for inspection and
repair.
Bridge Owners may choose to mandate higher levels
of performance for special bridges.
Earthquake loads are given by the product of the
elastic seismic response coefficient Csm and the
equivalent weight of the superstructure. The equivalent
weight is a function of the actual weight and bridge
configuration and is automatically included in both the
single-mode and multimode methods of analysis
specified in Article 4.7.4. Design and detailing
provisions for bridges to minimize their susceptibility to
damage from earthquakes are contained in Sections 3, 4,
5, 6, 7, 10, and 11. A flow chart summarizing these
provisions is presented in Appendix A3.
Conventional bridges include those with slab, beam,
box girder, or truss superstructures, and single- or
multiple-column piers, wall-type piers, or pile-bent
substructures. In addition, conventional bridges are
founded on shallow or piled footings, or shafts.
Substructures for conventional bridges are also listed in
Table 3.10.7.1-1. Nonconventional bridges include bridges
with cable-stayed/cable-suspended superstructures, bridges
with truss towers or hollow piers for substructures, and
arch bridges.
These Specifications are considered to be forcebased wherein a bridge is designed to have adequate
strength (capacity) to resist earthquake forces (demands).
In recent years, there has been a trend away from forcebased procedures to those that are displacement-based,
wherein a bridge is designed to have adequate
displacement capacity to accommodate earthquake
demands. Displacement-based procedures are believed to
more reliably identify the limit states that cause damage
leading to collapse, and in some cases produce more
efficient designs against collapse. It is recommended that
the displacement capacity of bridges designed in
accordance with these Specifications, be checked using a
displacement-based procedure, particularly those bridges
in high seismic zones. The AASHTO Guide Specifications
for LRFD Seismic Design (AASHTO, 2009), are
displacement-based.
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
TABLE OF CONTENTS
4 Eq
4.1—SCOPE ................................................................................................................................................................. 4-1
4.2—DEFINITIONS..................................................................................................................................................... 4-2
4.3—NOTATION ......................................................................................................................................................... 4-6
4.4—ACCEPTABLE METHODS OF STRUCTURAL ANALYSIS .......................................................................... 4-9
4.5—MATHEMATICAL MODELING ..................................................................................................................... 4-10
4.5.1—General ..................................................................................................................................................... 4-10
4.5.2—Structural Material Behavior.................................................................................................................... 4-11
4.5.2.1—Elastic Versus Inelastic Behavior .................................................................................................. 4-11
4.5.2.2—Elastic Behavior ............................................................................................................................. 4-11
4.5.2.3—Inelastic Behavior .......................................................................................................................... 4-11
4.5.3—Geometry ................................................................................................................................................. 4-12
4.5.3.1—Small Deflection Theory................................................................................................................ 4-12
4.5.3.2—Large Deflection Theory................................................................................................................ 4-12
4.5.3.2.1—General ................................................................................................................................ 4-12
4.5.3.2.2—Approximate Methods ......................................................................................................... 4-13
4.5.3.2.2a—General ....................................................................................................................... 4-13
4.5.3.2.2b—Moment Magnification—Beam Columns .................................................................. 4-14
4.5.3.2.2c—Moment Magnification—Arches ................................................................................ 4-15
4.5.3.2.3—Refined Methods ................................................................................................................. 4-16
4.5.4—Modeling Boundary Conditions ............................................................................................................... 4-16
4.5.5—Equivalent Members ................................................................................................................................ 4-16
4.6—STATIC ANALYSIS ......................................................................................................................................... 4-17
4.6.1—Influence of Plan Geometry ..................................................................................................................... 4-17
4.6.1.1—Plan Aspect Ratio .......................................................................................................................... 4-17
4.6.1.2—Structures Curved in Plan .............................................................................................................. 4-17
4.6.1.2.1—General ................................................................................................................................ 4-17
4.6.1.2.2—Single-Girder Torsionally Stiff Superstructures .................................................................. 4-18
4.6.1.2.3—Concrete Box Girder Bridges .............................................................................................. 4-18
4.6.1.2.4—Steel Multiple-Beam Superstructures .................................................................................. 4-20
4.6.1.2.4a—General ....................................................................................................................... 4-20
4.6.1.2.4b—I-Girders ..................................................................................................................... 4-20
4.6.1.2.4c—Closed Box and Tub Girders ...................................................................................... 4-21
4.6.2—Approximate Methods of Analysis .......................................................................................................... 4-22
4.6.2.1—Decks ............................................................................................................................................. 4-22
4.6.2.1.1—General ................................................................................................................................ 4-22
4.6.2.1.2—Applicability ........................................................................................................................ 4-22
4.6.2.1.3—Width of Equivalent Interior Strips ..................................................................................... 4-23
4.6.2.1.4—Width of Equivalent Strips at Edges of Slabs ...................................................................... 4-25
4.6.2.1.4a—General ....................................................................................................................... 4-25
4.6.2.1.4b—Longitudinal Edges ..................................................................................................... 4-25
4.6.2.1.4c—Transverse Edges ........................................................................................................ 4-25
4-i
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4-ii
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
4.6.2.1.5—Distribution of Wheel Loads ................................................................................................ 4-26
4.6.2.1.6—Calculation of Force Effects ................................................................................................ 4-26
4.6.2.1.7—Cross-Sectional Frame Action ............................................................................................. 4-27
4.6.2.1.8—Live Load Force Effects for Fully and Partially Filled Grids and for Unfilled
Grid Decks Composite with Reinforced Concrete Slabs ....................................................................... 4-27
4.6.2.1.9—Inelastic Analysis ................................................................................................................. 4-29
4.6.2.2—Beam-Slab Bridges ........................................................................................................................4-29
4.6.2.2.1—Application .......................................................................................................................... 4-29
4.6.2.2.2—Distribution Factor Method for Moment and Shear ............................................................. 4-35
4.6.2.2.2a—Interior Beams with Wood Decks ...............................................................................4-35
4.6.2.2.2b—Interior Beams with Concrete Decks ..........................................................................4-35
4.6.2.2.2c—Interior Beams with Corrugated Steel Decks ..............................................................4-38
4.6.2.2.2d—Exterior Beams ...........................................................................................................4-39
4.6.2.2.2e—Skewed Bridges ..........................................................................................................4-40
4.6.2.2.2f—Flexural Moments and Shear in Transverse Floorbeams.............................................4-41
4.6.2.2.3—Distribution Factor Method for Shear .................................................................................. 4-42
4.6.2.2.3a—Interior Beams .............................................................................................................4-42
4.6.2.2.3b—Exterior Beams ...........................................................................................................4-44
4.6.2.2.3c—Skewed Bridges ..........................................................................................................4-46
4.6.2.2.4—Curved Steel Bridges ........................................................................................................... 4-46
4.6.2.2.5—Special Loads with Other Traffic ......................................................................................... 4-47
4.6.2.3—Equivalent Strip Widths for Slab-Type Bridges.............................................................................4-48
4.6.2.4—Truss and Arch Bridges..................................................................................................................4-49
4.6.2.5—Effective Length Factor, K .............................................................................................................4-49
4.6.2.6—Effective Flange Width ..................................................................................................................4-54
4.6.2.6.1—General ................................................................................................................................. 4-54
4.6.2.6.2—Segmental Concrete Box Beams and Single-Cell, Cast-in-Place Box Beams ..................... 4-55
4.6.2.6.3—Cast-in-Place Multicell Superstructures............................................................................... 4-59
4.6.2.6.4—Orthotropic Steel Decks ....................................................................................................... 4-59
4.6.2.6.5—Transverse Floorbeams and Integral Bent Caps................................................................... 4-61
4.6.2.7—Lateral Wind Load Distribution in Multibeam Bridges .................................................................4-62
4.6.2.7.1—I-Sections ............................................................................................................................. 4-62
4.6.2.7.2—Box Sections ........................................................................................................................ 4-63
4.6.2.7.3—Construction ......................................................................................................................... 4-63
4.6.2.8—Seismic Lateral Load Distribution .................................................................................................4-63
4.6.2.8.1—Applicability ........................................................................................................................ 4-63
4.6.2.8.2—Design Criteria ..................................................................................................................... 4-64
4.6.2.8.3—Load Distribution ................................................................................................................. 4-64
4.6.2.9—Analysis of Segmental Concrete Bridges .......................................................................................4-65
4.6.2.9.1—General ................................................................................................................................. 4-65
4.6.2.9.2—Strut-and-Tie Models ........................................................................................................... 4-65
4.6.2.9.3—Effective Flange Width ........................................................................................................ 4-65
4.6.2.9.4—Transverse Analysis ............................................................................................................. 4-66
4.6.2.9.5—Longitudinal Analysis .......................................................................................................... 4-66
4.6.2.9.5a—General ........................................................................................................................4-66
4.6.2.9.5b—Erection Analysis ........................................................................................................4-66
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TABLE OF CONTENTS
4-iii
4.6.2.9.5c—Analysis of the Final Structural System...................................................................... 4-66
4.6.2.10—Equivalent Strip Widths for Box Culverts ................................................................................... 4-67
4.6.2.10.1—General .............................................................................................................................. 4-67
4.6.2.10.2—Case 1: Traffic Travels Parallel to Span ............................................................................ 4-67
4.6.2.10.3—Case 2: Traffic Travels Perpendicular to Span .................................................................. 4-67
4.6.2.10.4—Precast Box Culverts ........................................................................................................ 4-68
4.6.3—Refined Methods of Analysis................................................................................................................... 4-68
4.6.3.1—General .......................................................................................................................................... 4-68
4.6.3.2—Decks ............................................................................................................................................. 4-69
4.6.3.2.1—General ................................................................................................................................ 4-69
4.6.3.2.2—Isotropic Plate Model........................................................................................................... 4-69
4.6.3.2.3—Orthotropic Plate Model ...................................................................................................... 4-70
4.6.3.2.4—Refined Orthotropic Deck Model ........................................................................................ 4-70
4.6.3.3—Beam-Slab Bridges ........................................................................................................................ 4-70
4.6.3.3.1—General ................................................................................................................................ 4-70
4.6.3.3.2—Curved Steel Bridges ........................................................................................................... 4-71
4.6.3.4—Cellular and Box Bridges............................................................................................................... 4-72
4.6.3.5—Truss Bridges ................................................................................................................................. 4-72
4.6.3.6—Arch Bridges .................................................................................................................................. 4-73
4.6.3.7—Cable-Stayed Bridges .................................................................................................................... 4-73
4.6.3.8—Suspension Bridges........................................................................................................................ 4-74
4.6.4—Redistribution of Negative Moments in Continuous Beam Bridges ........................................................ 4-74
4.6.4.1—General .......................................................................................................................................... 4-74
4.6.4.2—Refined Method ............................................................................................................................. 4-75
4.6.4.3—Approximate Procedure ................................................................................................................. 4-75
4.6.5—Stability .................................................................................................................................................... 4-75
4.6.6—Analysis for Temperature Gradient.......................................................................................................... 4-75
4.7—DYNAMIC ANALYSIS .................................................................................................................................... 4-77
4.7.1—Basic Requirements of Structural Dynamics ........................................................................................... 4-77
4.7.1.1—General .......................................................................................................................................... 4-77
4.7.1.2—Distribution of Masses ................................................................................................................... 4-77
4.7.1.3—Stiffness ......................................................................................................................................... 4-78
4.7.1.4—Damping ........................................................................................................................................ 4-78
4.7.1.5—Natural Frequencies ....................................................................................................................... 4-78
4.7.2—Elastic Dynamic Responses ..................................................................................................................... 4-79
4.7.2.1—Vehicle-Induced Vibration ............................................................................................................ 4-79
4.7.2.2—Wind-Induced Vibration ................................................................................................................ 4-79
4.7.2.2.1—Wind Velocities ................................................................................................................... 4-79
4.7.2.2.2—Dynamic Effects .................................................................................................................. 4-79
4.7.2.2.3—Design Considerations ......................................................................................................... 4-79
4.7.3—Inelastic Dynamic Responses .................................................................................................................. 4-80
4.7.3.1—General .......................................................................................................................................... 4-80
4.7.3.2—Plastic Hinges and Yield Lines ...................................................................................................... 4-80
4.7.4—Analysis for Earthquake Loads ................................................................................................................ 4-80
4.7.4.1—General .......................................................................................................................................... 4-80
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4-iv
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
4.7.4.2—Single-Span Bridges.......................................................................................................................4-80
4.7.4.3—Multispan Bridges ..........................................................................................................................4-81
4.7.4.3.1—Selection of Method ............................................................................................................. 4-81
4.7.4.3.2—Single-Mode Methods of Analysis ...................................................................................... 4-82
4.7.4.3.2a—General ........................................................................................................................4-82
4.7.4.3.2b—Single-Mode Spectral Method ....................................................................................4-82
4.7.4.3.2c—Uniform Load Method ................................................................................................4-83
4.7.4.3.3—Multimode Spectral Method ................................................................................................ 4-85
4.7.4.3.4—Time-History Method .......................................................................................................... 4-85
4.7.4.3.4a—General ........................................................................................................................4-85
4.7.4.3.4b—Acceleration Time Histories .......................................................................................4-85
4.7.4.4—Minimum Support Length Requirements .......................................................................................4-88
4.7.4.5 P-∆ Requirements .............................................................................................................................4-89
4.7.5—Analysis for Collision Loads .................................................................................................................... 4-90
4.7.6—Analysis of Blast Effects .......................................................................................................................... 4-90
4.8—ANALYSIS BY PHYSICAL MODELS ............................................................................................................4-90
4.8.1—Scale Model Testing................................................................................................................................. 4-90
4.8.2—Bridge Testing .......................................................................................................................................... 4-90
4.9—REFERENCES ...................................................................................................................................................4-91
APPENDIX A4—DECK SLAB DESIGN TABLE ....................................................................................................4-97
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SECTION 4
STRUCTURAL ANALYSIS AND EVALUATION
4.1—SCOPE
C4.1
This section describes methods of analysis suitable
for the design and evaluation of bridges and is limited to
the modeling of structures and the determination of
force effects.
Other methods of analysis that are based on
documented material characteristics and that satisfy
equilibrium and compatibility may also be used.
In general, bridge structures are to be analyzed
elastically. However, this section permits the inelastic
analysis or redistribution of force effects in some
continuous beam superstructures. It specifies inelastic
analysis for compressive members behaving inelastically
and as an alternative for extreme event limit states.
This section identifies and promotes the application
of methods of structural analysis that are suitable for
bridges. The selected method of analysis may vary from
the approximate to the very sophisticated, depending on
the size, complexity, and priority of the structure. The
primary objective in the use of more sophisticated
methods of analysis is to obtain a better understanding
of structural behavior. Such improved understanding
may often, but not always, lead to the potential for
saving material.
The outlined methods of analysis, which are
suitable for the determination of deformations and force
effects in bridge structures, have been successfully
demonstrated, and most have been used for years.
Although many methods will require a computer for
practical implementation, simpler methods that are
amenable to hand calculation and/or to the use of
existing computer programs based on line-structure
analysis have also been provided. Comparison with hand
calculations should always be encouraged and basic
equilibrium checks should be standard practice.
With rapidly improving computing technology, the
more refined and complex methods of analysis are
expected to become commonplace. Hence, this section
addresses the assumptions and limitations of such
methods. It is important that the user understand the
method employed and its associated limitations.
In general, the suggested methods of analysis are
based on linear material models. This does not mean that
cross-sectional resistance is limited to the linear range.
This presents an obvious inconsistency in that the
analysis is based on material linearity and the resistance
model may be based on inelastic behavior for the
strength limit states. This same inconsistency existed,
however, in the load factor design method of previous
editions of the AASHTO Standard Specifications, and is
present in design codes of other nations using a factored
design approach.
The loads and load factors, defined in Section 3,
and the resistance factors specified throughout these
Specifications were developed using probabilistic
principles combined with analyses based on linear
material models. Hence, analysis methods based on
material nonlinearities to obtain force effects that are
more realistic at the strength limit states and subsequent
economics that may be derived are permitted only where
explicitly outlined herein.
Some nonlinear behavioral effects are addressed in
both the analysis and resistance sections. For example,
long column behavior may be modeled via geometric
nonlinear methods and may also be modeled using
approximate formulae in Sections 5, 6, 7, and 8. Either
method may be used, but the more refined formulations
are recommended.
4-1
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4-2
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
4.2—DEFINITIONS
Accepted Method of Analysis—A method of analysis that requires no further verification and that has become a
regular part of structural engineering practice.
Arc Span—Distance between centers of adjacent bearings, or other points of support, measured horizontally along the
centerline of a horizontally curved member.
Aspect Ratio—Ratio of the length to the width of a rectangle.
Boundary Conditions—Structural restraint characteristics regarding the support for and/or the continuity between
structural models.
Bounding—Taking two or more extreme values of parameters to envelop the response with a view to obtaining a
conservative design.
Central Angle—The angle included between two points along the centerline of a curved bridge measured from the
center of the curve as shown in Figure 4.6.1.2.3-1.
Classical Deformation Method—A method of analysis in which the structure is subdivided into components whose
stiffness can be independently calculated. Equilibrium and compatibility among the components is restored by
determining the deformations at the interfaces.
Classical Force Method—A method of analysis in which the structure is subdivided into statically determinate
components. Compatibility among the components is restored by determining the interface forces.
Closed-Box Section—A cross-section composed of two vertical or inclined webs which has at least one completely
enclosed cell. A closed-section member is effective in resisting applied torsion by developing shear flow in the webs
and flanges.
Closed-Form Solution—One or more equations, including those based on convergent series, that permit calculation of
force effects by the direct introduction of loads and structural parameters.
Compatibility—The geometrical equality of movement at the interface of joined components.
Component—A structural unit requiring separate design consideration; synonymous with member.
Condensation— Relating the variables to be eliminated from the analysis to those being kept to reduce the number of
equations to be solved.
Core Width—The width of the superstructure of monolithic construction minus the deck overhangs.
Cross-Section Distortion—Change in shape of the cross-section profile due to torsional loading.
Curved Girder—An I-, closed-box, or tub girder that is curved in a horizontal plane.
Damper—A device that transfers and reduces forces between superstructure elements and/or superstructure and
substructure elements, while permitting thermal movements. The device provides damping by dissipating energy
under seismic, braking, or other dynamic loads.
Deck—A component, with or without wearing surface, directly supporting wheel loads.
Deck System—A superstructure in which the deck is integral with its supporting components or in which the effects or
deformation of supporting components on the behavior of the deck is significant.
Deformation—A change in structural geometry due to force effects, including axial displacement, shear displacement,
and rotations.
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-3
Degree-of-Freedom—One of a number of translations or rotations required to define the movement of a node. The
displaced shape of components and/or the entire structure may be defined by a number of degrees-of-freedom.
Design—Proportioning and detailing the components and connections of a bridge to satisfy the requirements of these
Specifications.
Dynamic Degree-of-Freedom—A degree-of-freedom with which mass or mass effects have been associated.
Elastic—A structural material behavior in which the ratio of stress to strain is constant, the material returns to its
original unloaded state upon load removal.
Element—A part of a component or member consisting of one material.
End Zone—Region of structures where normal beam theory does not apply due to structural discontinuity and/or
distribution of concentrated loads.
Equilibrium—A state where the sum of forces and moments about any point in space is 0.0.
Equivalent Beam—A single straight or curved beam resisting both flexural and torsional effects.
Equivalent Strip—An artificial linear element, isolated from a deck for the purpose of analysis, in which extreme
force effects calculated for a line of wheel loads, transverse or longitudinal, will approximate those actually taking
place in the deck.
Finite Difference Method—A method of analysis in which the governing differential equation is satisfied at discrete
points on the structure.
Finite Element Method—A method of analysis in which a structure is discretized into elements connected at nodes,
the shape of the element displacement field is assumed, partial or complete compatibility is maintained among the
element interfaces, and nodal displacements are determined by using energy variational principles or equilibrium
methods.
Finite Strip Method—A method of analysis in which the structure is discretized into parallel strips. The shape of the
strip displacement field is assumed and partial compatibility is maintained among the element interfaces. Model
displacement parameters are determined by using energy variational principles or equilibrium methods.
First-Order Analysis—Analysis in which equilibrium conditions are formulated on the undeformed structure; that is,
the effect of deflections is not considered in writing equations of equilibrium.
Flange Lateral Bending—Bending of a flange about an axis perpendicular to the flange plane due to lateral loads
applied to the flange and/or nonuniform torsion in the member.
Flange Lateral Bending Stress—The normal stress caused by flange lateral bending.
Folded Plate Method—A method of analysis in which the structure is subdivided into plate components, and both
equilibrium and compatibility requirements are satisfied at the component interfaces.
Footprint—The specified contact area between wheel and roadway surface.
Force Effect—A deformation, stress, or stress resultant, i.e., axial force, shear force, flexural, or torsional moment,
caused by applied loads, imposed deformations, or volumetric changes.
Foundation—A supporting element that derives its resistance by transferring its load to the soil or rock supporting the
bridge.
Frame Action—Transverse continuity between the deck and the webs of cellular cross-section or between the deck
and primary components in large bridges.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
4-4
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Frame Action for Wind—Transverse flexure of the beam web and that of framed stiffeners, if present, by which lateral
wind load is partially or completely transmitted to the deck.
Girder Radius—The radius of the circumferential centerline of a segment of a curved girder.
Global Analysis—Analysis of a structure as a whole.
Governing Position—The location and orientation of transient load to cause extreme force effects.
Grillage Analogy Method—A method of analysis in which all or part of the superstructure is discretized into
orthotropic components that represent the characteristics of the structure.
Inelastic—Any structural behavior in which the ratio of stress and strain is not constant, and part of the deformation
remains after load removal.
Lane Live Load—The combination of tandem axle and uniformly distributed loads or the combination of the design
truck and design uniformly distributed load.
Large Deflection Theory—Any method of analysis in which the effects of deformation upon force effects is taken into
account.
Lever Rule—The statical summation of moments about one point to calculate the reaction at a second point.
Linear Response—Structural behavior in which deflections are directly proportional to loads.
Local Analysis—An in-depth study of strains and stresses in or among components using force effects obtained from a
more global analysis.
Local Structural Stress—The stress at a welded detail including all stress raising effects of a structural detail but
excluding all stress concentrations due to the local weld profile itself.
Member—Same as Component.
Method of Analysis—A mathematical process by which structural deformations, forces, and stresses are determined.
Model—A mathematical or physical idealization of a structure or component used for analysis.
Monolithic Construction—Single cell steel and/or concrete box bridges, solid or cellular cast-in-place concrete deck
systems, and decks consisting of precast, solid, or cellular longitudinal elements effectively tied together by transverse
post-tensioning.
M/R Method—An approximate method for the analysis of curved box girders in which the curved girder is treated as
an equivalent straight girder to calculate flexural effects and as a corresponding straight conjugate beam to calculate
the concomitant St. Venant torsional moments due to curvature.
Negative Moment—Moment producing tension at the top of a flexural element.
Node—A point where finite elements or grid components meet; in conjunction with finite differences, a point where
the governing differential equations are satisfied.
Nonlinear Response—Structural behavior in which the deflections are not directly proportional to the loads due to
stresses in the inelastic range, or deflections causing significant changes in force effects, or by a combination thereof.
Nonuniform Torsion—An internal resisting torsion in thin-walled sections, also known as warping torsion, producing
shear stress and normal stresses, and under which cross-sections do not remain plane. Members resist the externally
applied torsion by warping torsion and St. Venant torsion. Each of these components of internal resisting torsion
varies along the member length, although the externally applied concentrated torque may be uniform along the
member between two adjacent points of torsional restraint. Warping torsion is dominant over St. Venant torsion in
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-5
members having open cross-sections, whereas St. Venant torsion is dominant over warping torsion in members having
closed cross-sections.
Open Section—A cross-section which has no enclosed cell. An open-section member resists torsion primarily by
nonuniform torsion, which causes normal stresses at the flange tips.
Orthotropic—Perpendicular to each other, having physical properties that differ in two or more orthogonal directions.
Panel Point—The point where centerlines of members meet, usually in trusses, arches, cable-stayed, and suspension
bridges.
Pin Connection—A connection among members by a notionally frictionless pin at a point.
Pinned End—A boundary condition permitting free rotation but not translation in the plane of action.
Point of Contraflexure—The point where the sense of the flexural moment changes; synonymous with point of
inflection.
Positive Moment—Moment producing tension at the bottom of a flexural element.
Primary Member—A member designed to carry the loads applied to the structure as determined from an analysis.
Rating Vehicle—A sequence of axles used as a common basis for expressing bridge resistance.
Refined Methods of Analysis— Methods of structural analysis that consider the entire superstructure as an integral unit
and provide the required deflections and actions.
Restrainers—A system of high-strength cables or rods that transfers forces between superstructure elements and/or
superstructure and substructure elements under seismic or other dynamic loads after an initial slack is taken up, while
permitting thermal movements.
Rigidity—Force effect caused by a corresponding unit deformation per unit length of a component.
Secondary Member—A member in which stress is not normally evaluated in the analysis.
Second-Order Analysis—Analysis in which equilibrium conditions are formulated on the deformed structure; that is,
in which the deflected position of the structure is used in writing the equations of equilibrium.
Series or Harmonic Method—A method of analysis in which the load model is subdivided into suitable parts,
allowing each part to correspond to one term of a convergent infinite series by which structural deformations are
described.
Shear Flow—Shear force per unit width acting parallel to the edge of a plate element.
Shear Lag—Nonlinear distribution of normal stress across a component due to shear distortions.
Shock Transmission Unit (STU)—A device that provides a temporary rigid link between superstructure elements
and/or superstructure and substructure elements under seismic, braking, or other dynamic loads, while permitting
thermal movements.
Skew Angle—Angle between the centerline of a support and a line normal to the roadway centerline.
Small Deflection Theory—A basis for methods of analysis where the effects of deformation upon force effects in the
structure is neglected.
Spacing of Beams—The center-to-center distance between lines of support.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
4-6
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Spine Beam Model—An analytical model of a bridge in which the superstructure is represented by a single beam
element or a series of straight, chorded beam elements located along the centerline of the bridge.
Spread Beams—Beams not in physical contact, carrying a cast-in-place concrete deck.
Stiffness—Force effect resulting from a unit deformation.
Strain—Elongation per unit length.
Stress Range—The algebraic difference between extreme stresses.
St. Venant Torsion—That portion of the internal resisting torsion in a member producing only pure shear stresses on a
cross-section; also referred to as pure torsion or uniform torsion.
Submodel—A constituent part of the global structural model.
Superimposed Deformation—Effect of settlement, creep, and change in temperature and/or moisture content.
Superposition—The situation where the force effect due to one loading can be added to the force effect due to another
loading. Use of superposition is only valid when the stress-strain relationship is linearly elastic and the small
deflection theory is used.
Tandem—Two closely spaced and mechanically interconnected axles of equal weight.
Through-Thickness Stress—Bending stress in a web or box flange induced by distortion of the cross-section.
Torsional Shear Stress—Shear stress induced by St. Venant torsion.
Tub Section—An open-topped section which is composed of a bottom flange, two inclined or vertical webs, and top
flanges.
Uncracked Section—A section in which the concrete is assumed to be fully effective in tension and compression.
V-Load Method—An approximate method for the analysis of curved I-girder bridges in which the curved girders are
represented by equivalent straight girders and the effects of curvature are represented by vertical and lateral forces
applied at cross-frame locations. Lateral flange bending at brace points due to curvature is estimated.
Warping Stress—Normal stress induced in the cross-section by warping torsion and/or by distortion of the cross-section.
Wheel Load—One-half of a specified design axle load.
Yield Line—A plastic hinge line.
Yield Line Method—A method of analysis in which a number of possible yield line patterns are examined in order to
determine load-carrying capacity.
4.3—NOTATION
A
Ab
Ac
Ao
As
a
=
=
=
=
=
=
B
b
=
=
2013 Revision
area of a stringer, beam, or component (in.2) (4.6.2.2.1)
cross-sectional area of barrier (in.2) (C4.6.2.6.1)
cross-section area—transformed for steel beams (in.2) (C4.6.6)
area enclosed by centerlines of elements (in.2) (C4.6.2.2.1)
total area of stiffeners (in.2) (4.6.2.6.4)
length of transition region for effective flange width of a concrete box beam (in.); longitudinal stiffener,
spacing, or rib width in an orthotropic steel deck (in.) (4.6.2.6.2) (4.6.2.6.4)
spacing of transverse beams (in.) (4.6.2.6.4)
tire length (in.); width of a beam (in.); width of plate element (in.); flange width each side of the web
(in.) (4.6.2.1.8) (4.6.2.2.1) (C4.6.2.2.1) (4.6.2.6.2)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
be
=
bm
=
bn
bo
bs
=
=
=
C
Cm
Csm
c1
D
=
=
=
=
=
Dx
Dy
d
de
=
=
=
=
do
E
=
=
EB
Ec
ED
Eg
EMOD
Espan
e
=
=
=
=
=
=
=
eg
fc
f2b
f2s
G
Ga
Gb
GD
Gp
g
gm
g1
H
=
=
=
=
=
=
=
=
=
=
=
=
=
H, H1, H2=
h
=
I
=
=
Ic
Ig
IM
Ip
Is
J
K
=
=
=
=
=
=
Kg
=
4-7
effective flange width corresponding to the particular position of the section of interest in the span as
specified in Figure 4.6.2.6.2-1 (in.) (4.6.2.6.2)
effective flange width for interior portions of a span as determined from Figure 4.6.2.6.2-2; a special
case of be (in.) (4.6.2.6.2)
effective flange width for normal forces acting at anchorage zones (in.) (4.6.2.6.2)
width of web projected to midplane of deck (in.) (4.6.2.6.2)
effective flange width at interior support or for cantilever arm as determined from Figure 4.6.2.6.2-2; a
special case of be (in.) (4.6.2.6.2)
continuity factor; stiffness parameter (4.6.2.1.8) (4.6.2.2.1)
moment gradient coefficient (4.5.3.2.2b)
the dimensionless elastic seismic response coefficient (C4.7.4.3.2b)
parameter for skewed supports (4.6.2.2.2e)
web depth of a horizontally curved girder (ft); Dx/Dy; width of distribution per lane (ft) (C4.6.1.2.4b)
(4.6.2.1.8) (4.6.2.2.1)
flexural rigidity in direction of main bars (kip- ft2/ft) (4.6.2.1.8)
flexural rigidity perpendicular to the main bars (kip-ft2/ft) (4.6.2.1.8)
depth of a beam or stringer (in.); depth of member (ft) (4.6.2.2.1) (C4.6.2.7.1)
horizontal distance from the centerline of the exterior web of exterior beam at the deck level to the interior
edge of curb or traffic barrier (ft) (4.6.2.2.1)
depth of superstructure (in.) (4.6.2.6.2)
modulus of elasticity (ksi); equivalent width (in.); equivalent distribution width perpendicular to span
(in.) (4.5.3.2.2b) (4.6.2.3) (4.6.2.10.2)
modulus of elasticity of beam material (ksi) (4.6.2.2.1)
modulus of elasticity of column (ksi) (C4.6.2.5)
modulus of elasticity of deck material (ksi) (4.6.2.2.1)
modulus of elasticity of beam or other restraining member (ksi) (C4.6.2.5)
cable modulus of elasticity, modified for nonlinear effects (ksi) (4.6.3.7)
equivalent distribution length parallel to span (in.) (4.6.2.10.2)
correction factor for distribution; eccentricity of a lane from the center of gravity of the pattern of girders
(ft); rib spacing in orthotropic steel deck (in.) (4.6.2.2.1) (C4.6.2.2.2d) (4.6.2.6.4)
distance between the centers of gravity of the beam and deck (in.) (4.6.2.2.1)
factored stress, corrected to account for second-order effects (ksi) (4.5.3.2.2b)
stress corresponding to M2b (ksi) (4.5.3.2.2b)
stress corresponding to M2s (ksi) (4.5.3.2.2b)
final force effect applied to a girder (kip or kip-ft); shear modulus (ksi) (4.6.2.2.4) (C4.6.3.3)
ratio of stiffness of column to stiffness of members resisting column bending at “a” end (C4.6.2.5)
ratio of stiffness of column to stiffness of members resisting column bending at “b” end (C4.6.2.5)
force effect due to design loads (kip or kip-ft) (4.6.2.2.4)
force effect due to overload truck (kip or kip-ft) (4.6.2.2.4)
distribution factor; acceleration of gravity (ft/sec.2) (4.6.2.2.1) (C4.7.4.3.2)
multiple lane live load distribution factor (4.6.2.2.4)
single lane live load distribution factor (4.6.2.2.4)
depth of fill from top of culvert to top of pavement (in.); average height of substructure supporting the
seat under consideration (ft) (4.6.2.10.2) (4.7.4.4)
horizontal component of cable force (kip) (4.6.3.7)
depth of deck (in.) (4.6.2.1.3)
moment of inertia (in.4) (4.5.3.2.2b)
moment of inertia of column (in.4); inertia of cross-section—transformed for steel beams (in.4)
(C4.6.2.5) (C4.6.6)
moment of inertia of member acting to restrain column bending (in.4) (C4.6.2.5)
dynamic load allowance (C4.7.2.1)
polar moment of inertia (in.4) (4.6.2.2.1)
inertia of equivalent strip (in.4) (4.6.2.1.5)
St. Venant torsional inertia (in.4) (4.6.2.2.1)
effective length factor for columns and arch ribs; constant for different types of construction; effective
length factor for columns in the plane of bending (4.5.3.2.2b) (4.6.2.2.1) (4.6.2.5)
longitudinal stiffness parameter (in.4) (4.6.2.2.1)
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
4-8
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
k
ks
L
=
=
=
Las
Lb
Lc
Lg
LLDF
LT
L1
=
=
=
=
=
=
=
L2
li
ℓ
ℓu
=
=
=
=
M
=
Mc
=
Mlat
MM
Mn
Mw
M1b
=
=
=
=
=
M2b
=
M2s
=
N
=
Nb
Nc
NL
n
P
PD
Pe
Pu
Pw
p
pe
=
=
=
=
=
=
=
=
=
=
=
pe(x)
=
po
R
=
=
Rd
r
S
=
=
=
Sb
SM
s
T
=
=
=
=
factor used in calculation of distribution factor for multibeam bridges (4.6.2.2.1)
strip stiffness factor (kip/in.) (4.6.2.1.5)
span length of deck (ft); span length (ft); span length of beam (ft); length of bridge deck (ft) (4.6.2.1.3)
(4.6.2.1.8) (4.6.2.2.1) (4.7.4.4)
effective arc span of a horizontally curved girder (ft) (4.6.1.2.4b)
spacing of brace points (ft) (C4.6.2.7.1)
unbraced length of column (in.) (C4.6.2.5)
unsupported length of beam or other restraining member (in.) (C4.6.2.5)
factor for distribution of live load with depth of fill, 1.15 or 1.00, as specified in Article 3.6.1.2.6 (4.6.2.10.2)
length of tire contact area parallel to span, as specified in Article 3.6.1.2.5 (in.) (4.6.2.10.2)
modified span length taken to be equal to the lesser of the actual span or 60.0 (ft); distance between
points of inflection of the transverse beam (in.) (4.6.2.3) (4.6.2.6.4)
distances between points of inflection of the transverse beam (in.) (4.6.2.6.4)
a notional span length (ft) (4.6.2.6.2)
unbraced length of a horizontally curved girder (ft) (C4.6.1.2.4b)
unsupported length of a compression member (in.); one-half of the length of the arch rib (ft) (4.5.3.2.2b)
(4.5.3.2.2c)
major-axis bending moment in a horizontally curved girder (kip-ft); moment due to live load in filled or
partially filled grid deck (kip-in./ft) (C4.6.1.2.4b) (4.6.2.1.8)
factored moment, corrected to account for second-order effects (kip-ft); moment required to restrain
uplift caused by thermal effects (kip-in.) (4.5.3.2.2b) (C4.6.6)
flange lateral bending moment due to curvature (kip-ft) (C4.6.1.2.4b)
multimode elastic method (4.7.4.3.1)
nominal flexural strength (4.7.4.5)
maximum lateral moment in the flange due to the factored wind loading (kip-ft) (C4.6.2.7.1)
smaller end moment on compression member due to gravity loads that result in no appreciable sidesway;
positive if member is bent in single curvature, negative if bent in double curvature (kip-in.) (4.5.3.2.2b)
moment on compression member due to factored gravity loads that result in no appreciable sidesway
calculated by conventional first-order elastic frame analysis; always positive (kip-ft) (4.5.3.2.2b)
moment on compression member due to factored lateral or gravity loads that result in sidesway, Δ,
greater than ℓu /1500, calculated by conventional first-order elastic frame analysis; always positive
(kip-ft) (4.5.3.2.2b)
constant for determining the lateral flange bending moment in I-girder flanges due to curvature, taken as
10 or 12 in past practice; axial force (kip); minimum support length (in.) (C4.6.1.2.4b) (C4.6.6) (4.7.4.4)
number of beams, stringers, or girders (4.6.2.2.1)
number of cells in a concrete box girder (4.6.2.2.1)
number of design lanes (4.6.2.2.1)
modular ratio between beam and deck (4.6.2.2.1)
axle load (kip) (4.6.2.1.3)
design horizontal wind pressure (ksf) (C4.6.2.7.1)
Euler buckling load (kip) (4.5.3.2.2b)
factored axial load (kip) (4.5.3.2.2b) (4.7.4.5)
lateral wind force applied to the brace point (kips) (C4.6.2.7.1)
tire pressure (ksi) (4.6.2.1.8)
equivalent uniform static seismic loading per unit length of bridge that is applied to represent the
primary mode of vibration (kip/ft) (C4.7.4.3.2c)
the intensity of the equivalent static seismic loading that is applied to represent the primary mode of
vibration (kip/ft) (C4.7.4.3.2b)
a uniform load arbitrarily set equal to 1.0 (kip/ft) (C4.7.4.3.2b)
girder radius (ft); load distribution to exterior beam in terms of lanes; radius of curvature; R-factor for
calculation of seismic design forces due to inelastic action (C4.6.1.2.4b) (C4.6.2.2.2d) (C4.6.6) (4.7.4.5)
Rd-factor for calculation of seismic displacements due to inelastic action (4.7.4.5)
reduction factor for longitudinal force effect in skewed bridges (4.6.2.3)
spacing of supporting components (ft); spacing of beams or webs (ft); clear span (ft); skew of support
measured from line normal to span (degrees) (4.6.2.1.3) (4.6.2.2.1) (4.6.2.10.2) (4.7.4.4)
spacing of grid bars (in.) (4.6.2.1.3)
single-mode elastic method (4.7.4.3.1)
length of a side element (in.) (C4.6.2.2.1)
period of fundamental mode of vibration (sec.) (4.7.4.5)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
TG
TH
Tm
TS
Tu
TUG
t
=
=
=
=
=
=
=
tg
=
to
ts
VLD
=
=
=
VLL
VLU
vs(x)
vs,MAX
W
=
=
=
=
=
We
W1
=
=
w
w(x)
=
=
wp
X
Xext
x
Z
=
=
=
=
=
z
α
=
=
β
γ
Δ
=
=
=
Δe
Δw
δb
δs
εu
ηi
=
=
=
=
=
=
θ
μ
σE
φ
φK
=
=
=
=
=
4-9
temperature gradient (Δ°F) (C4.6.6)
time history method (4.7.4.3.1)
period of mth mode of vibration (sec.) (C4.7.4.3.2b)
reference period used to define shape of seismic response spectrum (sec.) (4.7.4.5)
uniform specified temperature (°F) (C4.6.6)
temperature averaged across the cross-section (°F) (C4.6.6)
thickness of plate-like element (in.); thickness of flange plate in orthotropic steel deck (in.) (C4.6.2.2.1)
(4.6.2.6.4)
depth of steel grid or corrugated steel plank including integral concrete overlay or structural concrete
component, less a provision for grinding, grooving, or wear (in.) (4.6.2.2.1)
depth of structural overlay (in.) (4.6.2.2.1)
depth of concrete slab (in.) (4.6.2.2.1)
maximum vertical shear at 3d or L/4 due to wheel loads distributed laterally as specified herein (kips)
(4.6.2.2.2a)
distributed live load vertical shear (kips) (4.6.2.2.2a)
maximum vertical shear at 3d or L/4 due to undistributed wheel loads (kips) (4.6.2.2.2a)
deformation corresponding to po (ft) (C4.7.4.3.2b)
maximum value of vs(x) (ft) (C4.7.4.3.2c)
edge-to-edge width of bridge (ft); factored wind force per unit length (kip/ft); total weight of cable (kip);
total weight of bridge (kip) (4.6.2.2.1) (C4.6.2.7.1) (4.6.3.7) (C4.7.4.3.2c)
half the web spacing, plus the total overhang (ft) (4.6.2.2.1)
modified edge-to-edge width of bridge taken to be equal to the lesser of the actual width or 60.0 for
multilane loading, or 30.0 for single-lane loading (ft) (4.6.2.3)
width of clear roadway (ft); width of element in cross-section (in.) (4.6.2.2.2b) (C4.6.6)
nominal, unfactored dead load of the bridge superstructure and tributary substructure (kip/ft)
(C4.7.4.3.2) (4.7.4.3.2c)
plank width (in.) (4.6.2.1.3)
distance from load to point of support (ft) (4.6.2.1.3)
horizontal distance from the center of gravity of the pattern of girders to the exterior girder (ft) (C4.6.2.2.2d)
horizontal distance from the center of gravity of the pattern of girders to each girder (ft) (C4.6.2.2.2d)
a factor taken as 1.20 where the lever rule was not utilized, and 1.0 where the lever rule was used for a
single lane live load distribution factor (4.6.2.2.4)
vertical distance from center of gravity of cross-section (in.) (C4.6.6)
angle between cable and horizontal (degrees); coefficient of thermal expansion (in./in./°F); generalized
flexibility (4.6.3.7) (C4.6.6) (C4.7.4.3.2b)
generalized participation (C4.7.4.3.2b)
load factor; generalized mass (C4.6.2.7.1) (C4.7.4.3.2b)
displacement of point of contraflexure in column or pier relative to point of fixity for the foundation (in.)
(4.7.4.5)
displacement calculated from elastic seismic analysis (in.) (4.7.4.5)
overhang width extension (in.) (C4.6.2.6.1)
moment or stress magnifier for braced mode deflection (4.5.3.2.2b)
moment or stress magnifier for unbraced mode deflection (4.5.3.2.2b)
uniform axial strain due to axial thermal expansion (in./in.) (C4.6.6)
load modifier relating to ductility, redundancy, and operational importance as specified in Article 1.3.2.1
(C4.2.6.7.1)
skew angle (degrees) (4.6.2.2.1)
Poisson’s ratio (4.6.2.2.1)
internal stress due to thermal effects (ksi) (C4.6.6)
rotation per unit length; flexural resistance factor (C4.6.6) (4.7.4.5)
stiffness reduction factor = 0.75 for concrete members and 1.0 for steel and aluminum members
(4.5.3.2.2b)
4.4—ACCEPTABLE METHODS OF
STRUCTURAL ANALYSIS
C4.4
Any method of analysis that satisfies the
requirements of equilibrium and compatibility and
Many computer programs are available for bridge
analysis. Various methods of analysis, ranging from
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
4-10
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
utilizes stress-strain relationships for the proposed
materials may be used, including, but not limited to:
simple formulae to detailed finite element procedures,
are implemented in such programs. Many computer
programs have specific engineering assumptions
embedded in their code, which may or may not be
applicable to each specific case.
When using a computer program, the Designer
should clearly understand the basic assumptions of the
program and the methodology that is implemented.
A computer program is only a tool, and the user is
responsible for the generated results. Accordingly, all
output should be verified to the extent possible.
Computer programs should be verified against the
results of:
•
Classical force and displacement methods,
•
Finite difference method,
•
Finite element method,
•
Folded plate method,
•
Finite strip method,
•
Grillage analogy method,
•
Series or other harmonic methods,
•
Universally accepted closed-form solutions,
•
Methods based on the formation of plastic hinges,
and
•
Other previously verified computer programs, or
•
Yield line method.
•
Physical testing.
The Designer shall be responsible for the
implementation of computer programs used to facilitate
structural analysis and for the interpretation and use of
results.
The name, version, and release date of software
used should be indicated in the contract documents.
The purpose of identifying software is to establish
code compliance and to provide a means of locating
bridges designed with software that may later be found
deficient.
4.5—MATHEMATICAL MODELING
4.5.1—General
C4.5.1
Mathematical models shall include loads, geometry,
and material behavior of the structure, and, where
appropriate, response characteristics of the foundation.
The choice of model shall be based on the limit states
investigated, the force effect being quantified, and the
accuracy required.
Unless otherwise permitted, consideration of
continuous composite barriers shall be limited to service
and fatigue limit states and to structural evaluation.
The stiffness of structurally discontinuous railings,
curbs, elevated medians, and barriers shall not be
considered in structural analysis.
Service and fatigue limit states should be analyzed
as fully elastic, as should strength limit states, except in
case of certain continuous girders where inelastic
analysis is specifically permitted, inelastic redistribution
of negative bending moment and stability investigation.
The extreme event limit states may require collapse
investigation based entirely on inelastic modeling.
Very flexible bridges, e.g., suspension and cablestayed bridges, should be analyzed using nonlinear
elastic methods, such as the large deflection theory.
The need for sophisticated modeling of foundations
is a function of the sensitivity of the structure to
foundation movements.
In some cases, the foundation model may be as
simple as unyielding supports. In other cases, an
estimate of settlement may be acceptable. Where the
structural response is particularly sensitive to the
boundary conditions, such as in a fixed-end arch or in
computing natural frequencies, rigorous modeling of the
foundation should be made to account for the conditions
present. In lieu of rigorous modeling, the boundary
conditions may be varied to extreme bounds, such as
fixed or free of restraint, and envelopes of force effects
considered.
Where lift-off restraints are provided in the contract
documents, the construction stage at which the restraints
are to be installed should be clearly indicated. The
For the purpose of this section, an appropriate
representation of the soil and/or rock that supports the
bridge shall be included in the mathematical model of
the foundation.
In the case of seismic design, gross soil movement
and liquefaction should also be considered.
If lift-off is indicated at a bearing, the analysis shall
recognize the vertical freedom of the girder at that
bearing.
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-11
analysis should recognize the vertical freedom of the
girder consistent with the construction sequence shown
in the contract documents.
4.5.2—Structural Material Behavior
4.5.2.1—Elastic Versus Inelastic Behavior
For the purpose of analysis, structural materials
shall be considered to behave linearly up to an elastic
limit and inelastically thereafter.
Actions at the extreme event limit state may be
accommodated in both the inelastic and elastic ranges.
4.5.2.2—Elastic Behavior
Elastic material properties and characteristics shall
be in accordance with the provisions of Sections 5, 6, 7,
and 8. Changes in these values due to maturity of
concrete and environmental effects should be included
in the model, where appropriate.
The stiffness properties of concrete and composite
members shall be based upon cracked and/or uncracked
sections consistent with the anticipated behavior.
Stiffness characteristics of beam-slab-type bridges may
be based on full participation of concrete decks.
4.5.2.3—Inelastic Behavior
Sections of components that may undergo inelastic
deformation shall be shown to be ductile or made ductile
by confinement or other means. Where inelastic analysis
is used, a preferred design failure mechanism and its
attendant hinge locations shall be determined. It shall be
ascertained in the analysis that shear, buckling, and bond
failures in the structural components do not precede the
formation of a flexural inelastic mechanism. Unintended
overstrength of a component in which hinging is
expected should be considered. Deterioration of
geometrical integrity of the structure due to large
deformations shall be taken into account.
The inelastic model shall be based either upon the
results of physical tests or upon a representation of loaddeformation behavior that is validated by tests. Where
inelastic behavior is expected to be achieved by
confinement, test specimens shall include the elements
that provide such confinement. Where extreme force
effects are anticipated to be repetitive, the tests shall
reflect their cyclic nature.
Except where noted, stresses and deformations shall
be based on a linear distribution of strains in the crosssection of prismatic components. Shear deformation of
deep components shall be considered. Limits on concrete
strain, as specified in Section 5, shall not be exceeded.
The inelastic behavior of compressive components
shall be taken into account, wherever applicable.
C4.5.2.2
Tests indicate that in the elastic range of structural
behavior, cracking of concrete seems to have little effect
on the global behavior of bridge structures. This effect
can, therefore, be safely neglected by modeling the
concrete as uncracked for the purposes of structural
analysis (King et al., 1975; Yen et al., 1995).
C4.5.2.3
Where technically possible, the preferred failure
mechanism should be based on a response that has
generally been observed to provide for large
deformations as a means of warning of structural
distress.
The selected mechanism should be used to estimate
the extreme force effect that can be applied adjacent to a
hinge.
Unintended overstrength of a component may result
in an adverse formation of a plastic hinge at an
undesirable location, forming a different mechanism.
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4-12
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
4.5.3—Geometry
4.5.3.1—Small Deflection Theory
If the deformation of the structure does not result in
a significant change in force effects due to an increase in
the eccentricity of compressive or tensile forces, such
secondary force effects may be ignored.
C4.5.3.1
Small deflection theory is usually adequate for the
analysis of beam-type bridges. Bridges that resist loads
primarily through a couple whose tensile and compressive
forces remain in essentially fixed positions relative to each
other while the bridge deflects, such as in trusses and tied
arches, are generally insensitive to deformations. Columns
and structures in which the flexural moments are increased
or decreased by deflection tend to be sensitive to deflection
considerations. Such structures include suspension bridges,
very flexible cable-stayed bridges, and some arches other
than tied arches and frames.
In many cases, the degree of sensitivity can be
assessed and evaluated by a single-step approximate
method, such as the moment magnification factor
method. In the remaining cases, a complete second-order
analysis may be necessary.
The past traditional boundary between small- and
large-deflection theory becomes less distinct as bridges
and bridge components become more flexible due to
advances in material technology, the change from
mandatory to optional deflection limits, and the trend
toward more accurate, optimized design. The Engineer
needs to consider these aspects in the choice of an
analysis method.
Small-deflection elastic behavior permits the use of
the principle of superposition and efficient analytical
solutions. These assumptions are typically used in
bridge analysis for this reason. The behavior of the
members assumed in these provisions is generally
consistent with this type of analysis.
Superposition does not apply for the analysis of
construction processes that include changes in the
stiffness of the structure.
Moments from noncomposite and composite
analyses may not be added for the purpose of computing
stresses. The addition of stresses and deflections due to
noncomposite and composite actions computed from
separate analyses is appropriate.
4.5.3.2—Large Deflection Theory
4.5.3.2.1—General
C4.5.3.2.1
If the deformation of the structure results in a
significant change in force effects, the effects of
deformation shall be considered in the equations of
equilibrium.
The effect of deformation and out-of-straightness of
components shall be included in stability analyses and
large deflection analyses.
For slender concrete compressive components,
those time- and stress-dependent material characteristics
that cause significant changes in structural geometry
shall be considered in the analysis.
A properly formulated large deflection analysis is
one that provides all the force effects necessary for the
design. Further application of moment magnification
factors is neither required nor appropriate. The presence
of compressive axial forces amplifies both out-ofstraightness of a component and the deformation due to
nontangential loads acting thereon, thereby increasing
the eccentricity of the axial force with respect to the
centerline of the component. The synergistic effect of
this interaction is the apparent softening of the
component, i.e., a loss of stiffness. This is commonly
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
The interaction effects of tensile and compressive
axial forces in adjacent components should be
considered in the analysis of frames and trusses.
Only factored loads shall be used and no
superposition of force effects shall be applied in the
nonlinear range. The order of load application in
nonlinear analysis shall be consistent with that on the
actual bridge.
4-13
referred to as a second-order effect. The converse is true
for tension. As axial compressive stress becomes a
higher percentage of the so called Euler buckling stress,
this effect becomes increasingly more significant.
The second-order effect arises from the translation
of applied load creating increased eccentricity. It is
considered as geometric nonlinearity and is typically
addressed by iteratively solving the equilibrium
equations or by using geometric stiffness terms in the
elastic range (Przemieniecki, 1968). The analyst should
be aware of the characteristics of the elements
employed, the assumptions upon which they are based,
and the numerical procedures used in the computer code.
Discussions on the subject are given by White and
Hajjar (1991) and Galambos (1998). Both references are
related to metal structures, but the theory and
applications are generally usable. Both contain
numerous additional references that summarize the
state-of-the-art in this area.
Because large deflection analysis is inherently
nonlinear, the loads are not proportional to the
displacements, and superposition cannot be used. This
includes force effects due to changes in time-dependent
properties, such as creep and shrinkage of concrete.
Therefore, the order of load application can be important
and traditional approaches, such as influence functions,
are not directly applicable. The loads should be applied
in the order experienced by the structure, i.e., dead load
stages followed by live load stages, etc. If the structure
undergoes nonlinear deformation, the loads should be
applied incrementally with consideration for the changes
in stiffness after each increment.
In conducting nonlinear analysis, it is prudent to
perform a linear analysis for a baseline and to use the
procedures employed on the problem at hand on a
simple structure that can be analyzed by hand, such as a
cantilever beam. This permits the analyst to observe
behavior and develop insight into behavior that is not
easily gained from more complex models.
4.5.3.2.2—Approximate Methods
4.5.3.2.2a—General
Where permitted in Sections 5, 6, and 7, the effects
of deflection on force effects on beam-columns and
arches which meet the provisions of these Specifications
may be approximated by the single-step adjustment
method known as moment magnification.
C4.5.3.2.2a
The moment magnification procedure outlined
herein is one of several variations of the approximate
process and was selected as a compromise between
accuracy and ease of use. It is believed to be
conservative. An alternative procedure thought to be
more accurate than the one specified herein may be
found in AISC (1993). This alternative procedure will
require supplementary calculations not commonly
made in bridge design using modern computational
methods.
In some cases, the magnitude of movement implied
by the moment magnification process cannot be
physically attained. For example, the actual movement
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4-14
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
of a pier may be limited to the distance between the end
of longitudinal beams and the backwall of the abutment.
In cases where movement is limited, the moment
magnification factors of elements so limited may be
reduced accordingly.
4.5.3.2.2b—Moment Magnification—Beam
Columns
C4.5.3.2.2b
The factored moments or stresses may be increased
to reflect effects of deformations as follows:
M c = δb M 2b + δ s M 2s
(4.5.3.2.2b-1)
f c = δb f 2b + δ s f 2s
(4.5.3.2.2b-2)
in which:
Cm
δb =
≥ 1.0
P
1− u
φ K Pe
(4.5.3.2.2b-3)
δs =
1
ΣPu
1−
φ K ΣPe
(4.5.3.2.2b-4)
where:
M2b =
M2s =
f2b
f2s
Pu
φK
=
=
=
=
Pe =
moment on compression member due to
factored gravity loads that result in no
appreciable
sidesway
calculated
by
conventional first-order elastic frame analysis;
always positive (kip-ft)
moment on compression member due to
factored lateral or gravity loads that result in
sidesway, Δ, greater than ℓu/1500, calculated by
conventional first-order elastic frame analysis;
always positive (kip-ft)
stress corresponding to M2b (ksi)
stress corresponding to M2s (ksi)
factored axial load (kip)
stiffness reduction factor; 0.75 for concrete
members and 1.0 for steel and aluminum
members
Euler buckling load (kip)
For steel/concrete composite columns, the Euler
buckling load, Pe, shall be determined as specified in
Article 6.9.5.1. For all other cases, Pe shall be taken as:
Pe =
π2 EI
(K u ) 2
(4.5.3.2.2b-5)
where:
E
I
=
=
modulus of elasticity (ksi)
moment of inertia about
consideration (in.4)
axis
under
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
K
=
ℓu =
4-15
effective length factor in the plane of bending
as specified in Article 4.6.2.5. For calculation
of δb, Pe shall be based on the K-factor for
braced frames; for calculation of δs, Pe shall be
based on the K-factor for unbraced frames
unsupported length of a compression member
(in.)
For concrete compression members, the provisions
of Article 5.7.4.3 also apply.
For members braced against sidesway, δs shall be
taken as 1.0 unless analysis indicates that a lower value
may be used. For members not braced against sidesway,
δb shall be determined as for a braced member and δs for
an unbraced member.
For members braced against sidesway and without
transverse loads between supports, Cm may be taken as:
Cm = 0.6 + 0.4
M 1b
M 2b
(4.5.3.2.2b-6)
The previous limit Cm ≥ 0.4 has been shown to be
unnecessary in AISC (1994), Chapter C, of commentary.
where:
M1b =
M2b =
smaller end moment
larger end moment
The ratio M1b/M2b is considered positive if the
component is bent in single curvature and negative if it
is bent in double curvature.
For all other cases, Cm shall be taken as 1.0.
In structures that are not braced against sidesway,
the flexural members and foundation units framing into
the compression member shall be designed for the sum
of end moments of the compression member at the joint.
Where compression members are subject to flexure
about both principal axes, the moment about each axis
shall be magnified by δ, determined from the
corresponding conditions of restraint about that axis.
Where a group of compression members on one
level comprise a bent, or where they are connected
integrally to the same superstructure, and collectively
resist the sidesway of the structure, the value of δs shall
be computed for the member group with ΣPu and ΣPe
equal to the summations for all columns in the group.
4.5.3.2.2c—Moment Magnification—Arches
Live load and impact moments from a small
deflection analysis shall be increased by the moment
as
specified
in
magnification
factor,
δb,
Article 4.5.3.2.2b, with the following definitions:
ℓu =
K =
Cm =
one-half of the length of the arch rib (ft)
effective
length
factor
specified
Table 4.5.3.2.2c-1
1.0
in
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 4.5.3.2.2c-1—K Values for Effective Length of Arch
Ribs
Rise to Span
Ratio
0.1–0.2
0.2–0.3
0.3–0.4
3-Hinged
Arch
1.16
1.13
1.16
2-Hinged
Arch
1.04
1.10
1.16
Fixed
Arch
0.70
0.70
0.72
4.5.3.2.3—Refined Methods
C4.5.3.2.3
Refined methods of analysis shall be based upon the
concept of forces satisfying equilibrium in a deformed
position.
Flexural equilibrium in a deformed position may be
iteratively satisfied by solving a set of simultaneous
equations, or by evaluating a closed-form solution
formulated using the displaced shape.
4.5.4—Modeling Boundary Conditions
C4.5.4
Boundary conditions shall represent actual
characteristics of support and continuity.
Foundation conditions shall be modeled in such a
manner as to represent the soil properties underlying the
bridge, the soil-pile interaction, and the elastic properties
of piles.
If the accurate assessment of boundary conditions
cannot be made, their effects may be bounded.
4.5.5—Equivalent Members
C4.5.5
Nonprismatic components may be modeled by
discretizing the components into a number of frame
elements with stiffness properties representative of the
actual structure at the location of the element.
Components or groups of components of bridges with
or without variable cross-sections may be modeled as a
single equivalent component provided that it represents all
the stiffness properties of the components or group of
components. The equivalent stiffness properties may be
obtained by closed-form solutions, numerical integration,
submodel analysis, and series and parallel analogies.
Standard frame elements in available analysis
programs may be used. The number of elements
required to model the nonprismatic variation is
dependent on the type of behavior being modeled, e.g.,
static, dynamic, or stability analysis. Typically, eight
elements per span will give sufficient accuracy for
actions in a beam loaded statically with cross-sectional
properties that vary smoothly. Fewer elements are
required to model for deflection and frequency
analyses.
Alternatively, elements may be used that are based
on the assumed tapers and cross-sections. Karabalis
(1983) provides a comprehensive examination of this
issue. Explicit forms of stiffness coefficients are given
for linearly tapered rectangular, flanged, and box
sections. Aristizabal (1987) presents similar equations
in a simple format that can be readily implemented into
stiffness-based computer programs. Significant
bibliographies are given in Karabalis (1983) and
Aristizabal (1987).
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-17
4.6—STATIC ANALYSIS
4.6.1—Influence of Plan Geometry
4.6.1.1—Plan Aspect Ratio
If the span length of a superstructure with
torsionally stiff closed cross-sections exceeds 2.5 times
its width, the superstructure may be idealized as a
single-spine beam. The following dimensional
definitions shall be used to apply this criterion:
•
Width—the core width of a monolithic deck or the
average distance between the outside faces of
exterior webs.
•
Length for rectangular simply supported bridges—
the distance between deck joints.
•
Length for continuous and/or skewed bridges—the
length of the longest side of the rectangle that can
be drawn within the plan view of the width of the
smallest span, as defined herein.
The length-to-width restriction specified above does
not apply to cast-in-place multicell box girders concrete
box girder bridges.
C4.6.1.1
Where transverse distortion of a superstructure is
small in comparison with longitudinal deformation, the
former does not significantly affect load distribution,
hence, an equivalent beam idealization is appropriate.
The relative transverse distortion is a function of the
ratio between structural width and height, the latter, in
turn, depending on the length. Hence, the limits of such
idealization are determined in terms of the width-toeffective length ratio.
Simultaneous torsion, moment, shear, and reaction
forces and the attendant stresses are to be superimposed
as appropriate. The equivalent beam idealization does
not alleviate the need to investigate warping effects in
steel structures. In all equivalent beam idealizations, the
eccentricity of loads should be taken with respect to the
centerline of the equivalent beam. Asymmetrical
sections need to consider the relative location of the
shear center and center of gravity.
4.6.1.2—Structures Curved in Plan
4.6.1.2.1—General
C4.6.1.2.1
The moments, shears, and other force effects
required to proportion the superstructure components
shall be based on a rational analysis of the entire
superstructure. Analysis of sections with no axis of
symmetry should consider the relative locations of the
center of gravity and the shear center. The substructure
shall also be considered in the case of integral
abutments, piers, or bents.
The entire superstructure, including bearings, shall
be considered as an integral structural unit. Boundary
conditions shall represent the articulations provided by
the bearings and/or integral connections used in the
design. Analyses may be based on elastic smalldeflection theory, unless more rigorous approaches are
deemed necessary by the Engineer.
Analyses shall consider bearing orientation and
restraint of bearings afforded by the substructure. These
load effects shall be considered in designing bearings,
cross-frames, diaphragms, bracing, and the deck.
Distortion of the cross-section need not be
considered in the structural analysis.
Centrifugal force effects shall be considered in
accordance with Article 3.6.3.
Since equilibrium of horizontally curved I-girders is
developed by the transfer of load between the girders,
the analysis must recognize the integrated behavior of
all structural components. Equilibrium of curved box
girders may be less dependent on the interaction
between girders. Bracing members are considered
primary members in curved bridges since they transmit
forces necessary to provide equilibrium.
The deck acts in flexure, vertical shear, and
horizontal shear. Torsion increases the horizontal deck
shear, particularly in curved box girders. The lateral
restraint of the bearings may also cause horizontal shear
in the deck.
Small-deflection theory is adequate for the analysis
of most curved-girder bridges. However, curved Igirders are prone to deflect laterally when the girders are
insufficiently braced during erection. This behavior may
not be well recognized by small-deflection theory.
Classical methods of analysis usually are based on
strength of materials assumptions that do not recognize
cross-section deformation. Finite element analyses that
model the actual cross-section shape of the I- or box
girders can recognize cross-section distortion and its
effect on structural behavior. Cross-section deformation
of steel box girders may have a significant effect on
torsional behavior, but this effect is limited by the
provision of sufficient internal cross bracing.
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4-18
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
4.6.1.2.2—Single-Girder Torsionally Stiff
Superstructures
Except for concrete box girder bridges, a
horizontally curved, torsionally stiff single-girder
superstructure
meeting
the
requirements
of
Article 4.6.1.1 may be analyzed for global force effects
as a curved spine beam.
The location of the centerline of such a beam shall
be taken at the center of gravity of the cross-section, and
the eccentricity of dead loads shall be established by
volumetric consideration.
C4.6.1.2.2
In order to apply the aspect ratio provisions of
Article 4.6.1.1, as specified, the plan needs to be
hypothetically straightened. Force effects should be
calculated on the basis of the actual curved layout.
With symmetrical cross-sections, the center of
gravity of permanent loads falls outside the center of
gravity. Shear center of the cross-section and the
resulting eccentricity need to be investigated.
C4.6.1.2.3
4.6.1.2.3—Concrete Box Girder Bridges
Horizontally curved concrete box girders may be
designed with straight segments, for central angles up to
12 degrees within one span, unless concerns about other
force effects dictate otherwise.
Horizontally curved nonsegmental concrete box
girder bridge superstructures may be analyzed and
designed for global force effects as single-spine beams
with straight segments for central angles up to 34 degrees
within one span as shown in Figure 4.6.1.2.3-1, unless
concerns about local force effects dictate otherwise. The
location of the centerline of such a beam shall be taken at
the center of gravity of the cross-section and the
eccentricity of dead loads shall be established by
volumetric consideration. Where the substructure is
integral with the superstructure, the substructure elements
shall be included in the model and allowance made for
prestress friction loss due to horizontal curvature or
tendon deviation.
Concrete box girders generally behave as a singlegirder multi-web torsionally stiff superstructure. A
parameter study conducted by Song, Chai, and Hida
(2003) indicated that the distribution factors from the
LRFD formulae compared well with the distribution
factors from grillage analyses when using straight
segments on spans with central angles up to 34 degrees
in one span.
Nutt, Redfield, and Valentine (2008) studied the
limits of applicability for various methods of analyzing
horizontally curved concrete box girder bridges. The
focus of this study was on local as well as global force
effects and provided the basis for revisions in 2010.
They identified three approaches for the analysis of
concrete box girder bridges as follows:
1.
The first method allows bridges with a central angle
within one span of less than 12 degrees to be
analyzed as if they were straight because curvature
has a minor effect on response. This is typically
done with a plane frame analysis.
2.
The second method involves a spine beam analysis
which the superstructure is idealized as a series of
straight beam chorded segments of limited central
angle located along the bridge centerline. Where the
substructure is integral with the superstructure, a
space frame analysis is required. Whole-width
design as described in Article 4.6.2.2.1 was found
to yield conservative results when space frame
analysis was used. It is acceptable to reduce the
number of live load lanes applied to the wholewidth model to those that can fit on the bridge when
global response such as torsion or transverse
bending is being considered.
3.
Bridges with high curvatures or unusual plan
geometry require a third method of analysis that
utilizes sophisticated three-dimensional computer
models. Unusual plan geometry includes but is not
limited to bridges with variable widths or with
unconventional orientation of skewed supports.
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-19
The range of applicability using approximate methods
herein is expected to yield results within five percent of
the most detailed type of analysis. Analysis of force
effects in curved tendons is also addressed in
Article 5.10.4.3.
Centerline of Bridge
Pier
Pier
Central Angle
Abutment
Abutment
Center of Curve
Figure 4.6.1.2.3-1—Definition of Central Angle
Horizontally curved segmental concrete box girder
superstructures
meeting
the
requirements
of
Article 4.6.1.1, and whose central angle within one span
is between 12 degrees and 34 degrees may be analyzed
as a single-spine beam comprised of straight segments
provided no segment has a central angle greater than
3.5 degrees as shown in Figure 4.6.1.2.3-2. For integral
substructures, an appropriate three-dimensional model of
the structure shall be used. Redistribution of forces due
to the time-dependant properties of concrete shall be
accounted for.
ax
°M
3.5
nt
me
St
m
ea
tB
gh
rai
Ele
r
nte
Ce
e
urv
C
of
Figure 4.6.1.2.3-2—Three-Dimensional Spine Model of Curved Concrete Box Girder Bridge
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
4-20
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
For both segmental and nonsegmental box girder
bridges with central angles exceeding 34 degrees within
any one span or for bridges with a maximum central
angle in excess of 12 degrees with unusual plan
geometry, the bridge shall be analyzed using 6 degrees
of freedom in a proven three-dimensional analysis
method.
4.6.1.2.4—Steel Multiple-Beam Superstructures
4.6.1.2.4a—General
Horizontally curved superstructures may be
analyzed as grids or continuums in which the segments
of the longitudinal beams are assumed to be straight
between nodes. The actual eccentricity of the segment
between the nodes shall not exceed 2.5 percent of the
length of the segment.
C4.6.1.2.4a
An eccentricity of 2.5 percent of the length of the
segment corresponds to a central angle subtended by a
curved segment of about 12 degrees.
This Article applies only to major-axis bending
moment and does not apply to lateral flange bending, or
torsion, which should always be examined with respect
to curvature.
Bridges with even slight curvature may develop
large radial forces at the abutment bearings. Therefore,
thermal analysis of all curved bridges is recommended.
C4.6.1.2.4b
4.6.1.2.4b—I-Girders
The effect of curvature on stability shall be
considered for all curved I-girders.
Where I-girder bridges meet the following four
conditions, the effects of curvature may be ignored in
the analysis for determining the major-axis bending
moments and bending shears:
•
Girders are concentric;
•
Bearing lines are not skewed more than 10 degrees
from radial;
•
The stiffnesses of the girders are similar;
•
For all spans, the arc span divided by the girder
radius in feet is less than 0.06 radians where the arc
span, Las, shall be taken as follows:
For simple spans:
Las =
arc length of the girder (ft)
For end spans of continuous members:
Las =
0.9 times the arc length of the girder (ft)
For interior spans of continuous members:
Las =
0.8 times the arc length of the girder (ft)
The requirement for similar stiffness among the
girders is intended to avoid large and irregular changes
in stiffness which could alter transverse distribution of
load. Under such conditions, a refined analysis would be
appropriate. Noncomposite dead load preferably is to be
distributed uniformly to the girders since the crossframes provide restoring forces that prevent the girders
from deflecting independently. Certain dead loads
applied to the composite bridge may be distributed
uniformly to the girders as provided in Article 4.6.2.2.1.
However, heavier concentrated line loads such as
parapets, sidewalks, barriers, or sound walls should not
be distributed equally to the girders. Engineering
judgment must be used in determining the distribution
of these loads. Often the largest portion of the load on
an overhang is assigned to the exterior girder, or to the
exterior girder and the first interior girder. The exterior
girder on the outside of the curve is often critical in
curved girder bridges.
The effect of curvature on the torsional behavior of a
girder must be considered regardless of the amount of
curvature since stability and strength of curved girders is
different from that of straight girders (Hall and Yoo, 1996).
In lieu of a refined analysis, Eq. C4.6.1.2.4b-1 may
be appropriate for determining the lateral bending
moment in I-girder flanges due to curvature
(Richardson, Gordon, and Associates, 1976; United
States Steel, 1984).
M lat =
M 2
NRD
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
(C4.6.1.2.4b-1)
2012
Edition
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
An I-girder in a bridge satisfying these criteria may be
analyzed as an individual straight girder with span
length equal to the arc length. Lateral flange bending
effects should then be determined from an appropriate
approximation and considered in the design.
Cross-frame or diaphragm members shall be
designed in accordance with Articles 6.7.4 and 6.13 for
forces computed by rational means.
Cross-frame spacing shall be set to limit flange
lateral bending in the girders.
4.6.1.2.4c—Closed Box and Tub Girders
The effect of curvature on strength and stability
shall be considered for all curved box girders.
Where box girder bridges meet the following three
conditions, the effect of curvature may be ignored in the
analysis for determination of the major-axis bending
moments and bending shears:
•
Girders are concentric,
•
Bearings are not skewed, and
•
For all spans, the arc span divided by the girder
radius is less than 0.3 radians, and the girder depth is
less than the width of the box at mid-depth where the
arc span, Las, shall be taken as defined in
Article 4.6.1.2.4b.
4-21
where:
Mlat =
M =
ℓ =
R =
D =
N =
flange lateral bending moment (kip-ft)
major-axis bending moment (kip-ft)
unbraced length (ft)
girder radius (ft)
web depth (ft)
a constant taken as 10 or 12 in past practice
Although the depth to be used in computing the
flange lateral moment from Eq. C4.6.1.2.4b-1 is
theoretically equal to the depth, h, between the
midthickness of the top and bottom flanges, for
simplicity, the web depth, D, is conservatively used in
Eq. C4.6.1.2.4b-1. The Engineer may substitute the
depth, h, for D in Eq. C4.6.1.2.4b-1, if desired.
Eq. C4.6.1.2.4b-1 assumes the presence of a cross-frame
at the point under investigation, that the cross-frame
spacing is relatively uniform, and that the major-axis
bending moment, M, is constant between brace points.
Therefore, at points not actually located at cross-frames,
flange lateral moments from Eq. C4.6.1.2.4b-1 may not
be strictly correct. The constant, N, in Eq. C4.6.1.2.4b-1
has been taken as either 10 or 12 in past practice and
either value is considered acceptable depending on the
level of conservatism that is desired.
Other conditions that produce torsion, such as skew,
should be dealt with by other analytical means which
generally involve a refined analysis.
C4.6.1.2.4c
Although box-shaped girders have not been
examined as carefully as I-girders with regard to
approximate methods, bending moments in closed
girders are less affected by curvature than are I-girders
(Tung and Fountain, 1970). However, in a box shape,
torsion is much greater than in an open shape so that
web shears are affected by torsion due to curvature,
skew or loads applied away from the shear center of the
box. Double bearings resist significant torque compared
to a box-centered single bearing.
If the box is haunched or tapered, the shallowest
girder depth should be used in conjunction with the
narrowest width of the box at middepth in determining
whether the effects of curvature may be ignored in
calculating the major axis bending moments and
bending shears.
A box girder in a bridge satisfying these criteria may be
analyzed as an individual straight girder with span
length equal to the arc length. Lateral flange bending
effects should then be found from an appropriate
approximation and considered in the design.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
4-22
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Cross-frame or diaphragm members shall be
designed in accordance with the provisions of
Articles 6.7.4 and 6.13 and lateral bracing members
shall be designed in accordance with Articles 6.7.5 and
6.13 for forces computed by rational means.
4.6.2—Approximate Methods of Analysis
4.6.2.1—Decks
4.6.2.1.1—General
C4.6.2.1.1
An approximate method of analysis in which the
deck is subdivided into strips perpendicular to the
supporting components shall be considered acceptable
for decks other than:
•
fully filled and partially filled grids for which the
provisions of Article 4.6.2.1.8 shall apply, and
•
top slabs of segmental concrete box girders for
which the provisions of 4.6.2.9.4 shall apply.
Where the strip method is used, the extreme
positive moment in any deck panel between girders shall
be taken to apply to all positive moment regions.
Similarly, the extreme negative moment over any beam
or girder shall be taken to apply to all negative moment
regions.
This model is analogous to past AASHTO
Specifications.
In determining the strip widths, the effects of flexure
in the secondary direction and of torsion on the
distribution of internal force effects are accounted for to
obtain flexural force effects approximating those that
would be provided by a more refined method of analysis.
Depending on the type of deck, modeling and design
in the secondary direction may utilize one of the
following approximations:
•
Secondary strip designed in a manner like the
primary strip, with all the limit states applicable;
•
Resistance requirements in the secondary direction
determined as a percentage of that in the primary
one as specified in Article 9.7.3.2 (i.e., the
traditional approach for reinforced concrete slab in
the previous editions of the AASHTO Standard
Specifications); or
•
Minimum structural and/or geometry requirements
specified for the secondary direction independent of
actual force effects, as is the case for most wood
decks.
The approximate strip model for decks is based on
rectangular layouts. Currently about two-thirds of all
bridges nationwide are skewed. While skew generally
tends to decrease extreme force effects, it produces
negative moments at corners, torsional moments in the
end zones, substantial redistribution of reaction forces,
and a number of other structural phenomena that should
be considered in the design.
4.6.2.1.2—Applicability
The use of design aids for decks containing
prefabricated elements may be permitted in lieu of
analysis if the performance of the deck is documented
and supported by sufficient technical evidence. The
Engineer shall be responsible for the accuracy and
implementation of any design aids used.
For slab bridges and concrete slabs spanning more
than 15.0 ft and which span primarily in the direction
parallel to traffic, the provisions of Article 4.6.2.3 shall
apply.
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2012
Edition
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4.6.2.1.3—Width of Equivalent Interior Strips
The width of the equivalent strip of a deck may be
taken as specified in Table 4.6.2.1.3-1. Where decks
span primarily in the direction parallel to traffic, strips
supporting an axle load shall not be taken to be greater
than 40.0 in. for open grids and not greater than 144 in.
for all other decks where multilane loading is being
investigated. For deck overhangs, where applicable, the
provisions of Article 3.6.1.3.4 may be used in lieu of the
strip width specified in Table 4.6.2.1.3-1 for deck
overhangs. The equivalent strips for decks that span
primarily in the transverse direction shall not be subject
to width limits. The following notation shall apply to
Table 4.6.2.1.3-1:
S =
h =
L =
P =
Sb =
+M =
−M =
X =
4-23
C4.6.2.1.3
Values provided for equivalent strip widths and
strength requirements in the secondary direction are
based on past experience. Practical experience and
future research work may lead to refinement.
To get the load per unit width of the equivalent strip,
divide the total load on one design traffic lane by the
calculated strip width.
spacing of supporting components (ft)
depth of deck (in.)
span length of deck (ft)
axle load (kip)
spacing of grid bars (in.)
positive moment
negative moment
distance from load to point of support (ft)
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2012
Edition
4-24
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 4.6.2.1.3-1—Equivalent Strips
Type of Deck
Concrete:
•
Cast-in-place
Direction of Primary Strip
Relative to Traffic
Width of Primary Strip (in.)
Overhang
45.0 + 10.0X
Either Parallel or
Perpendicular
−M:
26.0 + 6.6S
48.0 + 3.0S
+M:
•
Cast-in-place with stay-in-place
concrete formwork
Either Parallel or
Perpendicular
+M:
−M:
26.0 + 6.6S
48.0 + 3.0S
•
Precast, post-tensioned
Either Parallel or
Perpendicular
+M:
−M:
26.0 + 6.6S
48.0 + 3.0S
Steel:
•
Open grid
•
Filled or partially filled grid
•
Unfilled, composite grids
Main Bars
1.25P + 4.0Sb
Main Bars
Article 4.6.2.1.8 applies
Main Bars
Article 4.6.2.1.8 applies
Parallel
Perpendicular
2.0h + 30.0
2.0h + 40.0
Parallel
Perpendicular
90.0 + 0.84L
4.0h + 30.0
Wood:
•
Prefabricated glulam
o Noninterconnected
o
Interconnected
•
Stress-laminated
Parallel
Perpendicular
0.8S + 108.0
10.0S + 24.0
•
Spike-laminated
o Continuous decks or
interconnected panels
Parallel
Perpendicular
2.0h + 30.0
4.0h + 40.0
Parallel
Perpendicular
2.0h + 30.0
2.0h + 40.0
o
Noninterconnected panels
Wood plank decks shall be designed for the wheel
load of the design truck distributed over the tire contact
area. For transverse planks, i.e., planks perpendicular to
traffic direction:
•
If wp ≥ 10.0 in., the full plank width shall be
assumed to carry the wheel load.
•
If wp < 10.0 in., the portion of the wheel load
carried by a plank shall be determined as the ratio of
wp and 10.0 in.
Only the wheel load is specified for plank decks.
Addition of lane load will cause a negligible increase in
force effects; however, it may be added for uniformity
of the Code.
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All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-25
For longitudinal planks:
•
If wp ≥ 20.0 in., the full plank width shall be
assumed to carry the wheel load.
•
If wp < 20.0 in., the portion of the wheel load
carried by a plank shall be determined as the ratio of
wp and 20.0 in.
where:
wp =
plank width (in.)
4.6.2.1.4—Width of Equivalent Strips at Edges of
Slabs
4.6.2.1.4a—General
For the purpose of design, the notional edge beam
shall be taken as a reduced deck strip width specified
herein. Any additional integral local thickening or
similar protrusion acting as a stiffener to the deck that is
located within the reduced deck strip width can be
assumed to act with the reduced deck strip width as the
notional edge beam.
4.6.2.1.4b—Longitudinal Edges
Edge beams shall be assumed to support one line of
wheels and, where appropriate, a tributary portion of the
design lane load.
Where decks span primarily in the direction of
traffic, the effective width of a strip, with or without an
edge beam, may be taken as the sum of the distance
between the edge of the deck and the inside face of the
barrier, plus 12.0 in., plus one-quarter of the strip width,
specified in either Article 4.6.2.1.3, Article 4.6.2.3, or
Article 4.6.2.10, as appropriate, but not exceeding either
one-half the full strip width or 72.0 in.
4.6.2.1.4c—Transverse Edges
Transverse edge beams shall be assumed to support one
axle of the design truck in one or more design lanes,
positioned to produce maximum load effects. Multiple
presence factors and the dynamic load allowance shall apply.
The effective width of a strip, with or without an
edge beam, may be taken as the sum of the distance
between the transverse edge of the deck and the
centerline of the first line of support for the deck,
usually taken as a girder web, plus one-half of the width
of strip as specified in Article 4.6.2.1.3. The effective
width shall not exceed the full strip width specified in
Article 4.6.2.1.3.
C4.6.2.1.4c
For decks covered by Table A4-1, the total moment
acting on the edge beam, including the multiple presence
factor and the dynamic load allowance, may be
calculated by multiplying the moment per unit width,
taken from Table A4-1, by the corresponding full strip
width specified in Article 4.6.2.1.3.
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2012
Edition
4-26
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
4.6.2.1.5—Distribution of Wheel Loads
C4.6.2.1.5
If the spacing of supporting components in the
secondary direction exceeds 1.5 times the spacing in the
primary direction, all of the wheel loads shall be
considered to be applied to the primary strip, and the
provisions of Article 9.7.3.2 may be applied to the
secondary direction.
If the spacing of supporting components in the
secondary direction is less than 1.5 times the spacing in
the primary direction, the deck shall be modeled as a
system of intersecting strips.
The width of the equivalent strips in both directions
may be taken as specified in Table 4.6.2.1.3-1. Each
wheel load shall be distributed between two intersecting
strips. The distribution shall be determined as the ratio
between the stiffness of the strip and the sum of
stiffnesses of the intersecting strips. In the absence of
more precise calculations, the strip stiffness, ks, may be
estimated as:
ks =
EI s
S
This Article attempts to clarify the application of
the traditional AASHTO approach with respect to
continuous decks.
(4.6.2.1.5-1)
3
where:
Is
S
=
=
moment of inertia of the equivalent strip (in.4)
spacing of supporting components (in.)
4.6.2.1.6—Calculation of Force Effects
The strips shall be treated as continuous beams or
simply supported beams, as appropriate. Span length
shall be taken as the center-to-center distance between
the supporting components. For the purpose of
determining force effects in the strip, the supporting
components shall be assumed to be infinitely rigid.
The wheel loads may be modeled as concentrated
loads or as patch loads whose length along the span shall
be the length of the tire contact area, as specified in
Article 3.6.1.2.5, plus the depth of the deck. The strips
should be analyzed by classical beam theory.
The design section for negative moments and shear
forces, where investigated, may be taken as follows:
•
For monolithic construction, closed steel boxes,
closed concrete boxes, open concrete boxes without
top flanges, and stemmed precast beams, i.e., Crosssections (b), (c), (d), (e), (f), (g), (h), (i), and (j)
from Table 4.6.2.2.1-1, at the face of the supporting
component,
•
For steel I-beams and steel tub girders,
i.e.,
Cross-sections
(a)
and
(c)
from
Table 4.6.2.2.1-1, one-quarter the flange width from
the centerline of support,
C4.6.2.1.6
This is a deviation from the traditional approach
based on a continuity correction applied to results
obtained for analysis of simply supported spans. In lieu
of more precise calculations, the unfactored design live
load moments for many practical concrete deck slabs
can be found in Table A4-1.
For short-spans, the force effects calculated using
the footprint could be significantly lower, and more
realistic, than force effects calculated using concentrated
loads.
Reduction in negative moment and shear replaces
the effect of reduced span length in the current code.
The design sections indicated may be applied to deck
overhangs and to portions of decks between stringers or
similar lines of support.
Past practice has been to not check shear in typical
decks. A design section for shear is provided for use in
nontraditional situations. It is not the intent to
investigate shear in every deck.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
•
For precast I-shaped concrete beams and open
concrete boxes with top flanges, i.e., Cross-sections
(c) and (k) from Table 4.6.2.2.1-1, one-third the
flange width, but not exceeding 15.0 in., from the
centerline of support,
•
For wood beams, i.e., Cross-section (l) from Table
4.6.2.2.1-1, one-fourth the top beam width from
centerline of beam.
4-27
For open box beams, each web shall be considered
as a separate supporting component for the deck. The
distance from the centerline of each web and the
adjacent design sections for negative moment shall be
determined based on the type of construction of the box
and the shape of the top of the web using the
requirements outlined above.
C4.6.2.1.7
4.6.2.1.7—Cross-Sectional Frame Action
Where decks are an integral part of box or cellular
cross-sections, flexural and/or torsional stiffnesses of
supporting components of the cross-section, i.e., the
webs and bottom flange, are likely to cause significant
force effects in the deck. Those components shall be
included in the analysis of the deck.
If the length of a frame segment is modeled as the
width of an equivalent strip, provisions of
Articles 4.6.2.1.3, 4.6.2.1.5, and 4.6.2.1.6 may be used.
The model used is essentially a transverse
segmental strip, in which flexural continuity provided by
the webs and bottom flange is included. Such modeling
is restricted to closed cross-sections only. In openframed structures, a degree of transverse frame action
also exists, but it can be determined only by complex,
refined analysis.
In normal beam-slab superstructures, crosssectional frame action may safely be neglected. If the
slab is supported by box beams or is integrated into a
cellular cross-section, the effects of frame action could
be considerable. Such action usually decreases positive
moments, but may increase negative moments resulting
in cracking of the deck. For larger structures, a threedimensional analysis may be appropriate. For smaller
structures, the analysis could be restricted to a segment
of the bridge whose length is the width of an equivalent
strip.
Extreme force effects may be calculated by
combining the:
• Longitudinal response of the superstructure
approximated by classical beam theory, and
•
4.6.2.1.8—Live Load Force Effects for Fully and
Partially Filled Grids and for Unfilled Grid Decks
Composite with Reinforced Concrete Slabs
Moments in kip-in./in. of deck due to live load may
be determined as:
•
Main bars perpendicular to traffic:
For L ≤ 120 in.
Transverse flexural response modeled as a crosssectional frame.
C4.6.2.1.8
The moment equations are based on orthotropic
plate theory considering vehicular live loads specified in
Article 3.6. The equations take into account relevant
factored load combinations including truck and tandem
loads. The moment equations also account for dynamic
load allowance, multiple presence factors, and load
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2012
Edition
4-28
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
M transverse = 1.28D 0.197 L0.459 C
(4.6.2.1.8-1)
For L > 120 in.
M transverse =
(
D 0.188 3.7 L1.35 − 956.3
)
L
(C )
(4.6.2.1.8-2)
•
Main bars parallel to traffic:
For L ≤ 120 in.
M parallel = 0.73D 0.123 L0.64 C
(4.6.2.1.8-3)
For L > 120 in.
(
D 0.138 3.1L1.429 − 1088.5
M parallel =
L
)
(C )
(4.6.2.1.8-4)
positioning on the deck surface to produce the largest
possible moment.
Negative moment can be determined as maximum
simple span positive moment times the continuity factor,
C.
The reduction factor of 1.5 in the last sentence of
Article 4.6.2.1.8 accounts for smaller dynamic load
allowance (15 percent vs. 33 percent), smaller load
factor (0.75 vs. 1.75) and no multiple presence
(1.0 vs. 1.2) when considering the Fatigue I limit state.
Use of Eqs. 4.6.2.1.8-1 and 4.6.2.1.8-3 for all spans is
appropriate as Eqs. 4.6.2.1.8-1 and 4.6.2.1.8-3 reflect an
individual design truck on short-span lengths while
Eqs. 4.6.2.1.8-2 and 4.6.2.1.8-4 reflect the influence of
multiple design tandems that control moment envelope
on longer span lengths. The approximation produces
reasonable estimates of fatigue moments, however,
improved estimates can be determined using fatigue
truck patch loads in the infinite series formula provided
by Higgins (2003).
where:
L
=
C
=
D =
Dx =
Dy =
span length from center-to-center of supports
(in.)
continuity factor; 1.0 for simply supported and
0.8 for continuous spans
Dx/Dy
flexural rigidity of deck in main bar direction
(kip-in.2/in.)
flexural rigidity of deck perpendicular to main
bar direction (kip-in.2/in.)
For grid decks, Dx and Dy should be calculated as
EIx and EIy where E is the modulus of elasticity and Ix
and Iy are the moment of inertia per unit width of deck,
considering the section as cracked and using the
transformed area method for the main bar direction and
perpendicular to main bar direction, respectively.
Moments for fatigue assessment may be estimated
for all span lengths by reducing Eq. 4.6.2.1.8-1 for main
bars perpendicular to traffic or Eq. 4.6.2.1.8-3 for main
bars parallel to traffic by a factor of 1.5.
Deflection in units of in. due to vehicular live load
may be determined as:
•
Main bars perpendicular to traffic:
Δ transverse =
•
0.0052 D 0.19 L3
Dx
(4.6.2.1.8-5)
Main bars parallel to traffic:
Δ parallel =
0.0072 D 0.11 L3
Dx
Actual Dx and Dy values can vary considerably
depending on the specific deck design, and using
assumed values based only on the general type of deck
can lead to unconservative design moments. Flexural
rigidity in each direction should be calculated
analytically as EI considering the section as cracked and
using the transformed area method.
The deflection equations permit calculation of the
midspan displacement for a deck under service load. The
equations are based on orthotropic plate theory and
consider both truck and tandem loads on a simply
supported deck.
Deflection may be reduced for decks continuous
over three or more supports. A reduction factor of 0.8 is
conservative.
(4.6.2.1.8-6)
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2012
Edition
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-29
4.6.2.1.9—Inelastic Analysis
The inelastic finite element analysis or yield line
analysis may be permitted by the Owner.
4.6.2.2—Beam-Slab Bridges
4.6.2.2.1—Application
C4.6.2.2.1
2013 Revision
The provisions of this Article may be applied to
straight girder bridges and horizontally curved concrete
bridges, as well as horizontally curved steel girder
bridges
complying
with
the
provisions
of
Article 4.6.1.2.4. The provisions of this Article may also
be used to determine a starting point for some methods
of analysis to determine force effects in curved girders
of any degree of curvature in plan.
Except as specified in Article 4.6.2.2.5, the
provisions of this Article shall be taken to apply to
bridges being analyzed for:
•
A single lane of loading, or
•
Multiple lanes of live load yielding approximately
the same force effect per lane.
If one lane is loaded with a special vehicle or
evaluation permit vehicle, the design force effect per
girder resulting from the mixed traffic may be
determined as specified in Article 4.6.2.2.5.
For beam spacing exceeding the range of
applicability as specified in tables in Articles 4.6.2.2.2
and 4.6.2.2.3, the live load on each beam shall be the
reaction of the loaded lanes based on the lever rule
unless specified otherwise herein.
The provisions of Article 3.6.1.1.2 specify that
multiple presence factors shall not be used with the
approximate load assignment methods other than statical
moment or lever arm methods because these factors are
already incorporated in the distribution factors.
Bridges not meeting the requirements of this Article
shall be analyzed as specified in Article 4.6.3.
The distribution of live load, specified in
Articles 4.6.2.2.2 and 4.6.2.2.3, may be used for girders,
beams, and stringers, other than multiple steel box
beams with concrete decks that meet the following
conditions and any other conditions identified in tables
of distribution factors as specified herein:
•
Width of deck is constant;
•
Unless otherwise specified, the number of beams is
not less than four;
The V-load method is one example of a method of
curved bridge analysis which starts with straight girder
distribution factors (United States Steel, 1984).
The lever rule involves summing moments about
one support to find the reaction at another support by
assuming that the supported component is hinged at
interior supports.
When using the lever rule on a three-girder bridge,
the notional model should be taken as shown in
Figure C4.6.2.2.1-1. Moments should be taken about the
assumed, or notional, hinge in the deck over the middle
girder to find the reaction on the exterior girder.
Figure C4.6.2.2.1-1—Notional Model for Applying Lever
Rule to Three-Girder Bridges
Provisions in Articles 4.6.2.2.2 and 4.6.2.2.3 that do
not appear in earlier editions of the Standard Specifications
come primarily from Zokaie et al. (1991). Correction
factors for continuity have been deleted for two reasons:
•
Correction factors dealing with five percent
adjustments were thought to imply misleading
levels of accuracy in an approximate method, and
•
Analyses of many continuous beam-slab-type
bridges indicate that the distribution coefficients for
negative moments exceed those obtained for
positive moments by approximately ten percent. On
the other hand, it has been observed that stresses at
or near an internal bearing are reduced due to the
fanning of the reaction force. This reduction is
about the same magnitude as the increase in
distribution factors, hence the two tend to cancel
each other out, and thus are omitted from these
Specifications.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
4-30
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
•
Beams are parallel and have approximately the
same stiffness;
•
Unless otherwise specified, the roadway part of the
overhang, de, does not exceed 3.0 ft;
•
Curvature in plan is less than the limit specified in
Article 4.6.1.2.4, or where distribution factors are
required in order to implement an acceptable
approximate or refined analysis method satisfying
the requirements of Article 4.4 for bridges of any
degree of curvature in plan; and
•
Cross-section is consistent with one of the crosssections shown in Table 4.6.2.2.1-1.
Where moderate deviations from a constant deck
width or parallel beams exist, the distribution factor may
either be varied at selected locations along the span or
else a single distribution factor may be used in
conjunction with a suitable value for beam spacing.
Cast-in-place multicell concrete box girder bridge
types may be designed as whole-width structures. Such
cross-sections shall be designed for the live load
distribution factors in Articles 4.6.2.2.2 and 4.6.2.2.3 for
interior girders, multiplied by the number of girders, i.e.,
webs.
Additional requirements for multiple steel box
girders with concrete decks shall be as specified in
Article 4.6.2.2.2b.
Where bridges meet the conditions specified herein,
permanent loads of and on the deck may be distributed
uniformly among the beams and/or stringers.
Live load distribution factors, specified herein, may
be used for permit and rating vehicles whose overall
width is comparable to the width of the design truck.
The following notation shall apply to tables in
Articles 4.6.2.2.2 and 4.6.2.2.3:
A
b
=
=
area of stringer, beam or girder (in.2)
width of beam (in.)
In Strength Load Combination II, applying a
distribution factor procedure to a loading involving a
heavy permit load can be overly conservative unless laneby-lane distribution factors are available. Use of a refined
method of analysis will circumvent this situation.
A rational approach may be used to extend the
provisions of this Article to bridges with splayed
girders. The distribution factor for live load at any point
along the span may be calculated by setting the girder
spacing in the equations of this Article equal to half the
sum of the center-to-center distance between the girder
under consideration and the two girders to either side.
This will result in a variable distribution factor along the
length of the girder. While the variable distribution
factor is theoretically correct, it is not compatible with
existing line girder computer programs that only allow
constant distribution factor. Further simplifications may
be used to allow the use of such computer programs.
One such simplification involves running the computer
program a number of times equal to the number of spans
in the bridge. For each run, the girder spacing is set
equal to the maximum girder spacing in one span and
the results from this run are applied to this span. This
approach is guaranteed to result in conservative design.
In the past, some jurisdictions applied the latter
approach, but used the girder spacing at the 2/3 or 3/4
points of the span; which will also be an acceptable
approximation.
Most of the equations for distribution factors were
derived for constant deck width and parallel beams.
Past designs with moderate exceptions to these two
assumptions have performed well when the S/D
distribution factors were used. While the distribution
factors specified herein are more representative of
actual bridge behavior, common sense indicates that
some exceptions are still possible, especially if the
parameter S is chosen with prudent judgment, or if the
factors are appropriately varied at selected locations
along the span.
Whole-width design is appropriate for torsionallystiff cross-sections where load-sharing between girders
is extremely high and torsional loads are hard to
estimate. Prestressing force should be evenly distributed
between girders. Cell width-to-height ratios should be
approximately 2:1.
In lieu of more refined information, the St. Venant
torsional inertia, J, may be determined as:
•
For thin-walled open beam:
J =
•
1
3
bt
3
(C4.6.2.2.1-1)
For stocky open sections, e.g., prestressed I-beams,
T-beams, etc., and solid sections:
J=
A4
40.0 I p
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All rights reserved. Duplication is a violation of applicable law.
(C4.6.2.2.1-2)
2012
Edition
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
C
D
d
de
=
=
=
=
e
g
Ip
J
K
Kg
L
Nb
Nc
NL
=
=
=
=
=
=
=
=
=
=
S
tg
=
=
to
ts
W
We
θ
μ
=
=
=
=
=
=
stiffness parameter
width of distribution per lane (ft)
depth of beam or stringer (in.)
horizontal distance from the centerline of the
exterior web of exterior beam at deck level to
the interior edge of curb or traffic barrier (ft)
correction factor
distribution factor
polar moment of inertia (in.4)
St. Venant’s torsional inertia (in.4)
constant for different types of construction
longitudinal stiffness parameter (in.4)
span of beam (ft)
number of beams, stringers or girders
number of cells in a concrete box girder
number of design lanes as specified in
Article 3.6.1.1.1
spacing of beams or webs (ft)
depth of steel grid or corrugated steel plank
including integral concrete overlay or structural
concrete component, less a provision for
grinding, grooving, or wear (in.)
depth of structural overlay (in.)
depth of concrete slab (in.)
edge-to-edge width of bridge (ft)
half the web spacing, plus the total overhang (ft)
skew angle (degrees)
Poisson’s ratio
Unless otherwise stated, the stiffness parameters for
area, moments of inertia and torsional stiffness used
herein and in Articles 4.6.2.2.2 and 4.6.2.2.3 shall be
taken as those of the cross-section to which traffic will
be applied, i.e., usually the composite section.
4-31
•
For closed thin-walled shapes:
J=
4 Ao 2
s
t
(C4.6.2.2.1-3)
where:
b
t
A
Ip
Ao
s
=
=
=
=
=
=
width of plate element (in.)
thickness of plate-like element (in.)
area of cross-section (in.2)
polar moment of inertia (in.4)
area enclosed by centerlines of elements (in.2)
length of a side element (in.)
Eq. C4.6.2.2.1-2 has been shown to substantially
underestimate the torsional stiffness of some concrete
I-beams and a more accurate, but more complex,
approximation can be found in Eby et al. (1973).
The transverse post-tensioning shown for some
cross-sections herein is intended to make the units act
together. A minimum 0.25 ksi prestress is
recommended.
For beams with variable moment of inertia, Kg may
be based on average properties.
For bridge types “f,” “g,” “h,” “i,” and “j,”
longitudinal joints between precast units of the crosssection are shown in Table 4.6.2.2.1-1. This type of
construction acts as a monolithic unit if sufficiently
interconnected. In Article 5.14.4.3.3f, a fully
interconnected joint is identified as a flexural
shear joint. This type of interconnection is
enhanced by either transverse post-tensioning of an
intensity specified above or by a reinforced structural
overlay, which is also specified in Article 5.14.4.3.3f, or
both. The use of transverse mild steel rods secured by
nuts or similar unstressed dowels should not be
considered sufficient to achieve full transverse flexural
continuity unless demonstrated by testing or experience.
Generally, post-tensioning is thought to be more
effective than a structural overlay if the intensity
specified above is achieved.
In some cases, the lower limit of deck slab
thickness, ts, shown in the range of applicability column
in tables in Articles 4.6.2.2.2 and 4.6.2.2.3 is less than
7.0 in. The research used to develop the equations in
those tables reflects the range of slab thickness shown.
Article 9.7.1.1 indicates that concrete decks less than
7.0 in. in thickness should not be used unless approved
by the Owner. Lesser values shown in tables in
Articles 4.6.2.2.2 and 4.6.2.2.3 are not intended to
override Article 9.7.1.1.
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2012
Edition
4-32
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The longitudinal stiffness parameter, Kg, shall be
taken as:
K g = n ( I + Aeg 2 )
(4.6.2.2.1-1)
in which:
n=
EB
ED
(4.6.2.2.1-2)
where:
EB =
modulus of elasticity of beam material (ksi)
ED =
modulus of elasticity of deck material (ksi)
I
=
moment of inertia of beam (in.4)
eg
=
distance between the centers of gravity of the
basic beam and deck (in.)
The load distribution factor equations for bridge
type “d”, cast-in-place multicell concrete box girders,
were derived by first positioning the vehicle
longitudinally, and then transversely, using an I-section
of the box. While it would be more appropriate to
develop an algorithm to find the peak of an influence
surface, using the present factor for the interior girders
multiplied by the number of girders is conservative in
most cases.
Table C4.6.2.2.1-1 describes how the term L
(length) may be determined for use in the live load
distribution factor equations given in Articles 4.6.2.2.2
and 4.6.2.2.3.
The parameters A and I in Eq. 4.6.2.2.1-1 shall be taken
as those of the noncomposite beam.
The bridge types indicated in tables in
Articles 4.6.2.2.2 and 4.6.2.2.3, with reference to
Table 4.6.2.2.1-1, may be taken as representative of the
type of bridge to which each approximate equation
applies.
Table C4.6.2.2.1-1— L for Use in Live Load Distribution Factor Equations
Force Effect
Positive Moment
Negative Moment—Near interior supports of
continuous spans from point of contraflexure to point
of contraflexure under a uniform load on all spans
Negative Moment—Other than near interior supports
of continuous spans
Shear
Exterior Reaction
Interior Reaction of Continuous Span
L (ft)
The length of the span for which moment is being calculated
The average length of the two adjacent spans
The length of the span for which moment is being calculated
The length of the span for which shear is being calculated
The length of the exterior span
The average length of the two adjacent spans
Except as permitted by Article 2.5.2.7.1, regardless
of the method of analysis used, i.e., approximate or
refined, exterior girders of multibeam bridges shall not
have less resistance than an interior beam.
In the rare occasion when the continuous span
arrangement is such that an interior span does not have
any positive uniform load moment (i.e., no uniform load
points of contraflexure), the region of negative moment
near the interior supports would be increased to the
centerline of the span, and the L used in determining the
live load distribution factors would be the average of the
two adjacent spans.
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2012
Edition
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-33
Table 4.6.2.2.1-1—Common Deck Superstructures Covered in Articles 4.6.2.2.2 and 4.6.2.2.3
Supporting Components
Steel Beam
Type Of Deck
Cast-in-place concrete slab,
precast concrete slab, steel
grid, glued/spiked panels,
stressed wood
Closed Steel or Precast Concrete
Boxes
Cast-in-place concrete slab
Open Steel or Precast Concrete
Boxes
Cast-in-place concrete slab,
precast concrete deck slab
Cast-in-Place Concrete Multicell
Box
Monolithic concrete
Cast-in-Place Concrete Tee Beam
Monolithic concrete
Precast Solid, Voided or Cellular
Concrete Boxes with Shear Keys
Cast-in-place concrete
overlay
Precast Solid, Voided, or Cellular
Concrete Box with Shear Keys and
with or without Transverse PostTensioning
Integral concrete
Precast Concrete Channel Sections
with Shear Keys
Cast-in-place concrete
overlay
Typical Cross-Section
Continued on next page
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All rights reserved. Duplication is a violation of applicable law.
2012
Edition
4-34
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 4.6.2.2.1-1 (continued)—Common Deck Superstructures Covered in Articles 4.6.2.2.2 and 4.6.2.2.3
Supporting Components
Precast Concrete Double Tee
Section with Shear Keys and with
or without Transverse PostTensioning
Type Of Deck
Integral concrete
Typical Cross-Section
Precast Concrete Tee Section with
Shear Keys and with or without
Transverse Post-Tensioning
Integral concrete
Precast Concrete I or Bulb-Tee
Sections
Cast-in-place concrete,
precast concrete
Wood Beams
Cast-in-place concrete or
plank, glued/spiked panels
or stressed wood
For cast-in-place concrete multicell box shown as
cross-section Type “d” in Table 4.6.2.2.1-1, the
distribution factors in Article 4.6.2.2.2 and 4.6.2.2.3
shall be taken to apply to a notional shape consisting of
a web, overhangs of an exterior web, and the associated
half flanges between a web under consideration and the
next adjacent web or webs.
With the owner’s concurrence, the simplifications
provided in Table 4.6.2.2.1-2 may be used:
Table 4.6.2.2.1-2—Constant Values for Articles 4.6.2.2.2 and 4.6.2.2.3
Equation
Parameters
Simplified Value
k
1.09
0.1
4.6.2.2.2b-1
0.25
4.6.2.2.2e-1
1.03
1.07
1.15
—
0.3
4.6.2.2.3c-1
0.97
0.93
0.85
—
4.6.2.2.2b-1,
4.6.2.2.3a-1
—
—
—
d
0.54 + 0.16
b
12.0 Lts3
Kg
I
J
e
1.05
a
1.02
Kg
3
12.0 Lts
Kg
12.0 Lts3
Table Reference
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
f,g,i,j
—
2012
Edition
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-35
4.6.2.2.2—Distribution Factor Method for Moment
and Shear
4.6.2.2.2a—Interior Beams with Wood Decks
2013 Revision
The live load flexural moment and shear for interior
beams with transverse wood decks may be determined
by applying the lane fraction specified in
Table 4.6.2.2.2a-1 and Eq. 4.6.2.2.2a-1.
When investigation of shear parallel to the grain in
wood components is required, the distributed live load
shear shall be determined by the following expression:
VLL = 0.50 ( 0.60VLU ) + VLD
(4.6.2.2.2a-1)
where:
VLL =
VLU =
VLD =
distributed live load vertical shear (kips)
maximum vertical shear at 3d or L/4 due to
undistributed wheel loads (kips)
maximum vertical shear at 3d or L/4 due to
wheel loads distributed laterally as specified
herein (kips)
For undistributed wheel loads, one line of wheels is
assumed to be carried by one bending member.
Table 4.6.2.2.2a-1—Distribution of Live Load for Moment and Shear in Interior Beams with Wood Decks
Type of Deck
Plank
Stressed Laminated
Spike Laminated
Glued Laminated Panels on
Glued Laminated Stringers
Glue Laminated Panels on
Steel Stringers
Applicable CrossSection from Table
4.6.2.2.1-1
a, l
a, l
a, l
a, l
a, l
4.6.2.2.2b—Interior Beams with Concrete
Decks
2013 Revision
One Design
Lane Loaded
S/6.7
S/9.2
S/8.3
S/10.0
S/8.8
Two or More
Design Lanes
Loaded
S/7.5
S/9.0
S/8.5
S/10.0
S/9.0
Range of
Applicability
S ≤ 5.0
S ≤ 6.0
S ≤ 6.0
S ≤ 6.0
S ≤ 6.0
C4.6.2.2.2b
The live load flexural moment for interior beams
with concrete decks may be determined by applying the
lane fraction specified in Table 4.6.2.2.2b-1.
For the concrete beams, other than box beams, used
in multibeam decks with shear keys:
•
Deep, rigid end diaphragms shall be provided to
ensure proper load distribution; and
•
If the stem spacing of stemmed beams is less than
4.0 ft or more than 10.0 ft, a refined analysis
complying with Article 4.6.3 shall be used.
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All rights reserved. Duplication is a violation of applicable law.
2012
Edition
4-36
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
For multiple steel box girders with a concrete
deck in bridges satisfying the requirements of
Article 6.11.2.3, the live load flexural moment may be
determined using the appropriate distribution factor
specified in Table 4.6.2.2.2b-1.
Where the spacing of the box girders varies along
the length of the bridge, the distribution factor may
either be varied at selected locations along the span or
else a single distribution factor may be used in
conjunction with a suitable value of NL. In either case,
the value of NL shall be determined as specified in
Article 3.6.1.1.1, using the width, w, taken at the section
under consideration.
The results of analytical and model studies of
simple span multiple box section bridges, reported in
Johnston and Mattock (1967), showed that folded plate
theory could be used to analyze the behavior of bridges
of this type. The folded plate theory was used to obtain
the maximum load per girder, produced by various
critical combinations of loading on 31 bridges having
various spans, numbers of box girders, and numbers of
traffic lanes.
Multiple
presence
factors,
specified
in
Table 3.6.1.1.2-1, are not applied because the multiple
factors in past editions of the Standard Specifications
were considered in the development of the equation in
Table 4.6.2.2.2b-1 for multiple steel box girders.
The lateral load distribution obtained for simple
spans is also considered applicable to continuous
structures.
The bridges considered in the development of the
equations had interior end diaphragms only, i.e., no
interior diaphragms within the spans, and no exterior
diaphragms anywhere between boxes. If interior or
exterior diaphragms are provided within the span, the
transverse load distribution characteristics of the bridge
will be improved to some degree. This improvement can
be evaluated, if desired, using the analysis methods
identified in Article 4.4.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-37
Table 4.6.2.2.2b-1—Distribution of Live Loads for Moment in Interior Beams
Type of Superstructure
Wood Deck on Wood
or Steel Beams
Concrete Deck on
Wood Beams
Applicable CrossSection from
Table 4.6.2.2.1-1
a, l
l
Concrete Deck, Filled
Grid, Partially Filled
Grid, or Unfilled Grid
Deck Composite with
Reinforced Concrete
Slab on Steel or
Concrete Beams;
Concrete T-Beams, Tand Double T-Sections
a, e, k and also i, j
if sufficiently
connected to act
as a unit
Cast-in-Place Concrete
Multicell Box
d
Distribution Factors
See Table 4.6.2.2.2a-1
One Design Lane Loaded:
S/12.0
Two or More Design Lanes Loaded:
S/10.0
One Design Lane Loaded:
0.4
0.3
S S
0.06 +
3
14
L
12.0
Lt
s
Two or More Design Lanes Loaded:
0.6
Kg
S ≤ 6.0
0.1
0.1
0.2
S S Kg
0.075 +
3
9.5 L 12.0 Lts
use lesser of the values obtained from the
equation above with Nb = 3 or the lever rule
One Design Lane Loaded:
0.45
0.35
S 1 1
1.75 +
3.6 L N c
Two or More Design Lanes Loaded:
0.3
Concrete Deck on
Concrete Spread Box
Beams
b, c
Concrete Beams used
in Multibeam Decks
f
13 S 1
N c 5.8 L
One Design Lane Loaded:
0.35
g
if sufficiently
connected to act
as a unit
Range of
Applicability
0.25
0.25
S Sd
2
3.0 12.0 L
Two or More Design Lanes Loaded:
0.6
0.125
S Sd
2
6.3 12.0 L
Use Lever Rule
One Design Lane Loaded:
0.5
0.25
b I
k
33.3L J
3.5 ≤ S ≤ 16.0
4.5 ≤ ts ≤ 12.0
20 ≤ L ≤ 240
Nb ≥ 4
10,000 ≤ Kg ≤
7,000,000
Nb = 3
7.0 ≤ S ≤ 13.0
60 ≤ L ≤ 240
Nc ≥ 3
If Nc > 8 use Nc = 8
6.0 ≤ S ≤ 18.0
20 ≤ L ≤ 140
18 ≤ d ≤ 65
Nb ≥ 3
S > 18.0
35 ≤ b ≤ 60
20 ≤ L ≤ 120
5 ≤ Nb ≤ 20
where: k = 2.5( N b ) −0.2 ≥ 1.5
Two or More Design Lanes Loaded:
0.6
0.2
0.06
b b I
k
305 12.0 L J
continued on next page
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2012
Edition
4-38
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 4.6.2.2.2b-1 (continued)—Distribution of Live Loads for Moment in Interior Beams
Type of Superstructure
Applicable CrossSection from
Table 4.6.2.2.1-1
h
Distribution Factors
Regardless of Number of Loaded Lanes:
S/D
where:
C = K (W / L) ≤ K
D = 11.5 − N L + 1.4 N L (1 − 0.2C )
g, i, j
if connected only
enough to prevent
relative vertical
displacement at
the interface
when C ≤ 5
D = 11.5 − N L when C > 5
K=
a
Concrete Deck on
Multiple Steel Box
Girders
b, c
Skew ≤ 45°
NL ≤ 6
(1 + μ ) I
J
for preliminary design, the following values
of K may be used:
Beam Type
Nonvoided rectangular beams
Rectangular beams with
circular voids:
Box section beams
Channel beams
T-beam
Double T-beam
Open Steel Grid Deck
on Steel Beams
2
Range of
Applicability
K
0.7
0.8
1.0
2.2
2.0
2.0
One Design Lane Loaded:
S/7.5 If tg< 4.0
S/10.0 If tg≥ 4.0
Two or More Design Lanes Loaded:
S/8.0 If tg< 4.0
S/10.0 If tg≥ 4.0
Regardless of Number of Loaded Lanes:
N
0.425
0.05 + 0.85 L +
Nb
NL
4.6.2.2.2c—Interior Beams with Corrugated
Steel Decks
S ≤ 6.0
S ≤ 10.5
0.5 ≤
NL
≤ 1.5
Nb
2013 Revision
The live load flexural moment for interior beams
with corrugated steel plank deck may be determined by
applying the lane fraction, g, specified in
Table 4.6.2.2.2c-1.
Table 4.6.2.2.2c-1—Distribution of Live Load for Moment
in Interior Beams with Corrugated Steel Plank Decks
One Design
Lane Loaded
Two or More
Design Lanes
Loaded
S/9.2
S/9.0
Range of
Applicability
S ≤ 5.5
tg ≥ 2.0
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4.6.2.2.2d—Exterior Beams
4-39
C4.6.2.2.2d
2013 Revision
The live load flexural moment for exterior beams
may be determined by applying the lane fraction, g,
specified in Table 4.6.2.2.2d-1.
The distance, de, shall be taken as positive if the
exterior web is inboard of the interior face of the traffic
railing and negative if it is outboard of the curb or traffic
barrier.
In beam-slab bridge cross-sections with diaphragms
or cross-frames, the distribution factor for the exterior
beam shall not be taken to be less than that which would
be obtained by assuming that the cross-section deflects
and rotates as a rigid cross-section. The provisions of
Article 3.6.1.1.2 shall apply.
This additional investigation is required because the
distribution factor for girders in a multigirder crosssection, Types “a,” “e,” and “k” in Table 4.6.2.2.1-1,
was determined without consideration of diaphragm or
cross-frames. The recommended procedure is an interim
provision until research provides a better solution.
The procedure outlined in this section is the same
as the conventional approximation for loads on piles.
NL
R=
NL
+
Nb
X ext e
Nb
x
(C4.6.2.2.2d-1)
2
where:
R =
NL =
e =
x
=
Xext =
Nb =
reaction on exterior beam in terms of lanes
number of loaded lanes under consideration
eccentricity of a design truck or a design lane
load from the center of gravity of the pattern of
girders (ft)
horizontal distance from the center of gravity of
the pattern of girders to each girder (ft)
horizontal distance from the center of gravity of
the pattern of girders to the exterior girder (ft)
number of beams or girders
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2012
Edition
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 4.6.2.2.2d-1—Distribution of Live Loads for Moment in Exterior Longitudinal Beams
Type of Superstructure
Wood Deck on Wood or
Steel Beams
Concrete Deck on Wood
Beams
Concrete Deck, Filled Grid,
Partially Filled Grid, or
Unfilled Grid Deck
Composite with Reinforced
Concrete Slab on Steel or
Concrete Beams; Concrete
T-Beams, T- and Double TSections
Applicable CrossSection from Table
4.6.2.2.1-1
a, l
One Design Lane
Loaded
Lever Rule
Two or More
Design Lanes
Loaded
Lever Rule
Range of
Applicability
N/A
l
Lever Rule
Lever Rule
N/A
a, e, k and
also i, j
if sufficiently
connected to act as a
unit
Lever Rule
Cast-in-Place Concrete
Multicell Box
d
Concrete Deck on Concrete
Spread Box Beams
b, c
f, g
Concrete Beams Other than
Box Beams Used in
Multibeam Decks
h
i, j
if connected only
enough to prevent
relative vertical
displacement at the
interface
a
Nb = 3
We ≤ S
0 ≤ de ≤ 4.5
6.0 < S ≤ 18.0
Use Lever Rule
S > 18.0
g = e ginterior
d
e = 1.04 + e ≥ 1.0
25
de ≤ 2.0
Lever Rule
Lever Rule
N/A
Lever Rule
Lever Rule
N/A
g = e ginterior
e = 1.125 +
4.6.2.2.2e—Skewed Bridges
−1.0 ≤ de ≤ 5.5
g = e ginterior
de
e = 0.97 +
28.5
Lever Rule
Concrete Box Beams Used
in Multibeam Decks
Open Steel Grid Deck on
Steel Beams
Concrete Deck on Multiple
Steel Box Girders
g = e ginterior
d
e = 0.77 + e
9.1
use lesser of the
values obtained
from the
equation above
with Nb = 3 or
the lever rule
We
W
g =
g = e
14
14
or the provisions for a whole-width
design specified in Article 4.6.2.2.1
b, c
de
≥ 1.0
30
As specified in Table 4.6.2.2.2b-1
2013 Revision
When the line supports are skewed and the
difference between skew angles of two adjacent lines of
supports does not exceed 10 degrees, the bending
moment in the beams may be reduced in accordance
with Table 4.6.2.2.2e-1.
C4.6.2.2.2e
Accepted reduction factors are not currently
available for cases not covered in Table 4.6.2.2.2e-1.
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2012
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-41
Table 4.6.2.2.2e-1—Reduction of Load Distribution Factors for Moment in Longitudinal Beams on Skewed Supports
Type of Superstructure
Concrete Deck, Filled Grid,
Partially Filled Grid, or Unfilled
Grid Deck Composite with
Reinforced Concrete Slab on
Steel or Concrete Beams;
Concrete T-Beams, T- and
Double T- Sections
Concrete Deck on Concrete
Spread Box Beams, Cast-inPlace Multicell Box Concrete
Box Beams and Double TSections used in Multibeam
Decks
Applicable CrossSection from Table
4.6.2.2.1-1
a, e, k and
also i, j
if sufficiently
connected to act as a
unit
Any Number of Design Lanes
Loaded
1 − c1 ( tan θ )
1.5
Kg
c1 = 0.25
3
12.0 Lts
0.25
S
L
0.5
If θ < 30° then c1 = 0.0
o
o
If θ > 60 use θ = 60
1.05 − 0.25 tan θ ≤ 1.0
b, c, d, f, g
o
Range of
Applicability
o
o
30 ≤ θ ≤ 60
3.5 ≤ S ≤ 16.0
20 ≤ L ≤ 240
Nb ≥ 4
o
o
0 ≤ θ ≤ 60
o
If θ > 60 use θ = 60
4.6.2.2.2f—Flexural Moments and Shear in
Transverse Floorbeams
2013 Revision
If the deck is supported directly by transverse
floorbeams, the floorbeams may be designed for loads
determined in accordance with Table 4.6.2.2.2f-1.
The fractions provided in Table 4.6.2.2.2f-1 shall be
used in conjunction with the 32.0-kip design axle load
alone. For spacings of floorbeams outside the given
ranges of applicability, all of the design live loads shall
be considered, and the lever rule may be used.
Table 4.6.2.2.2f-1—Distribution of Live Load for Transverse Beams for Moment and Shear
Type of Deck
Plank
Laminated Wood Deck
Concrete
Steel Grid and Unfilled Grid Deck Composite
with Reinforced Concrete Slab
Steel Grid and Unfilled Grid Deck Composite
with Reinforced Concrete Slab
Steel Bridge Corrugated Plank
Fraction of Wheel Load to
Each Floorbeam
S
4
S
5
S
6
S
4.5
S
6
S
5.5
Range of Applicability
N/A
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S ≤ 5.0
S ≤ 6.0
tg ≤ 4.0
S ≤ 5.0
tg > 4.0
S ≤ 6.0
tg ≥ 2.0
2012
Edition
4-42
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
4.6.2.2.3—Distribution Factor Method for Shear
4.6.2.2.3a—Interior Beams
2013 Revision
The live load shear for interior beams may be
determined by applying the lane fractions specified in
Table 4.6.2.2.3a-1. For interior beam types not listed in
Table 4.6.2.2.3a-1, lateral distribution of the wheel or
axle adjacent to the end of span shall be that produced
by use of the lever rule.
For concrete box beams used in multibeam decks, if
the values of I or J do not comply with the limitations in
Table 4.6.2.2.3a-1, the distribution factor for shear may
be taken as that for moment.
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2012
Edition
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-43
Table 4.6.2.2.3a-1—Distribution of Live Load for Shear in Interior Beams
Type of
Superstructure
Wood Deck on
Wood or Steel
Beams
Concrete Deck on
Wood Beams
Concrete Deck,
Filled Grid,
Partially Filled
Grid, or Unfilled
Grid Deck
Composite with
Reinforced
Concrete Slab on
Steel or Concrete
Beams; Concrete
T-Beams, T-and
Double T-Sections
Cast-in-Place
Concrete Multicell
Box
Concrete Deck on
Concrete Spread
Box Beams
Applicable
Cross-Section
from Table
4.6.2.2.1-1
a, l
One Design Lane
Loaded
Two or More Design Lanes
Loaded
See Table 4.6.2.2.2a-1
Range of
Applicability
l
Lever Rule
Lever Rule
N/A
a, e, k and also
i, j if
sufficiently
connected to
act as a unit
0.36 +
S
25.0
0.2 +
b, c
3.5 ≤ S ≤ 16.0
2.0
20 ≤ L ≤ 240
4.5 ≤ ts ≤ 12.0
Nb ≥ 4
Lever Rule
d
S S
−
12 35
Lever Rule
0.6
S d
9.5 12.0 L
0.6
S d
10 12.0 L
0.1
0.1
Nb = 3
0.9
0.1
0.8
0.1
S d
7.3 12.0 L
S d
7.4 12.0 L
6.0 ≤ S ≤ 13.0
20 ≤ L ≤ 240
35 ≤ d ≤ 110
Nc ≥ 3
6.0 ≤ S ≤ 18.0
20 ≤ L ≤ 140
18 ≤ d ≤ 65
Nb ≥ 3
Lever Rule
Concrete Box
Beams Used in
Multibeam Decks
f, g
b
130 L
0.15
I
J
Lever Rule
0.05
0.4
0.1
b b I
156 12.0 L J
b
≥ 1.0
48
S > 18.0
0.05
b
48
35 ≤ b ≤ 60
20 ≤ L ≤ 120
5 ≤ N b ≤ 20
25, 000 ≤ J ≤ 610, 000
40, 000 ≤ I ≤ 610, 000
Concrete Beams
Other Than Box
Beams Used in
Multibeam Decks
Open Steel Grid
Deck on Steel
Beams
Concrete Deck on
Multiple Steel Box
Beams
h
i, j if
connected only
enough to
prevent
relative
vertical
displacement
at the interface
a
b, c
Lever Rule
Lever Rule
N/A
Lever Rule
Lever Rule
N/A
As specified in Table 4.6.2.2.2b-1
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2012
Edition
4-44
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
4.6.2.2.3b—Exterior Beams
2013 Revision
The live load shear for exterior beams shall be
determined by applying the lane fractions specified in
Table 4.6.2.2.3b-1. For cases not addressed in
Table 4.6.2.2.3a-1 and Table 4.6.2.2.3b-1, the live load
distribution to exterior beams shall be determined by
using the lever rule.
The parameter de shall be taken as positive if the
exterior web is inboard of the curb or traffic barrier and
negative if it is outboard.
The additional provisions for exterior beams in
beam-slab bridges with cross-frames or diaphragms,
specified in Articles 4.6.2.2.2d, shall apply.
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2012
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-45
Table 4.6.2.2.3b-1—Distribution of Live Load for Shear in Exterior Beams
Type of Superstructure
Wood Deck on Wood or
Steel Beams
Concrete Deck on Wood
Beams
Concrete Deck, Filled
Grid, Partially Filled
Grid, or Unfilled Grid
Deck Composite with
Reinforced Concrete Slab
on Steel or Concrete
Beams; Concrete TBeams, T- and Double TBeams
Cast-in-Place Concrete
Multicell Box
Applicable CrossSection from
Table 4.6.2.2.1-1
a, l
One Design
Lane Loaded
Lever Rule
Two or More Design
Lanes Loaded
Lever Rule
Range of
Applicability
N/A
l
Lever Rule
Lever Rule
N/A
a, e, k and
also i, j
if sufficiently connected
to act as a unit
Lever Rule
g = e ginterior
d
e = 0.6 + e
10
−1.0 ≤ d e ≤ 5.5
Lever Rule
Nb = 3
g = e ginterior
d
e = 0.64 + e
12.5
−2.0 ≤ d e ≤ 5.0
d
Lever Rule
or the provisions for a whole-width
design specified in Article 4.6.2.2.1
Concrete Deck on
Concrete Spread Box
Beams
b, c
Concrete Box Beams
Used in Multibeam Decks
f, g
Lever Rule
g = e g interior
e = 1.25 +
de
≥ 1.0
20
g = e ginterior
d
e = 0.8 + e
10
0 ≤ d e ≤ 4.5
Lever Rule
S > 18.0
b
d e + 12 − 2.0
e = 1+
40
Concrete Beams Other
Than Box Beams Used in
Multibeam Decks
Open Steel Grid Deck on
Steel Beams
Concrete Deck on
Multiple Steel Box Beams
h
i, j
if connected only enough
to prevent relative
vertical displacement at
the interface
a
b, c
Lever Rule
Lever Rule
d e ≤ 2.0
35 ≤ b ≤ 60
48
g = e ginterior
b
48
≤ 1.0
b
0.5
≥ 1.0
Lever Rule
Lever Rule
N/A
N/A
As specified in Table 4.6.2.2.2b-1
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2012
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4-46
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
4.6.2.2.3c—Skewed Bridges
C4.6.2.2.3c
2013 Revision
Shear in the exterior beam at the obtuse corner of
the bridge shall be adjusted when the line of support is
skewed. The value of the correction factor shall be
obtained from Table 4.6.2.2.3c-1. It is applied to the
lane fraction specified in Table 4.6.2.2.3a-1 for interior
beams and in Table 4.6.2.2.3b-1 for exterior beams. This
factor should not be applied in addition to modeling
skewed supports.
In determining the end shear in multibeam bridges,
the skew correction at the obtuse corner shall be applied
to all the beams.
Verifiable correction factors are not available for
cases not covered in Table 4.6.2.2.3c-1.
The equal treatment of all beams in a multibeam
bridge is conservative regarding positive reaction and
shear. However, it is not necessarily conservative
regarding uplift in the case of large skew and short
exterior spans of continuous beams. A supplementary
investigation of uplift should be considered using the
correction factor from Table 4.6.2.2.3c-1, i.e., the terms
other than 1.0, taken as negative for the exterior beam at
the acute corner.
Chapter 4
Table 4.6.2.2.3c-1—Correction Factors for Load Distribution Factors for Support Shear of the Obtuse Corner
Type of Superstructure
Concrete Deck, Filled Grid,
Partially Filled Grid, or Unfilled
Grid Deck Composite with
Reinforced Concrete Slab on Steel
or Concrete Beams; Concrete TBeams, T- and Double T-Section
Applicable Cross-Section
from Table 4.6.2.2.1-1
a, e, k and also i, j
if sufficiently connected to
act as a unit
Correction Factor
0.3
12.0 Lts 3
1.0 + 0.20
tan θ
K g
Range of
Applicability
0° ≤ θ ≤ 60°
3.5 ≤ S ≤ 16.0
20 ≤ L ≤ 240
Nb ≥ 4
d
12.0 L
1.0 + 0.25 +
tan θ
70d
0° < θ ≤ 60°
6.0 < S ≤ 13.0
20 ≤ L ≤ 240
35 ≤ d ≤ 110
Nc ≥ 3
Concrete Deck on Spread Concrete
Box Beams
b, c
Ld
1.0 + 12.0 tan θ
6S
0° < θ ≤ 60°
6.0 ≤ S ≤ 11.5
20 ≤ L ≤ 140
18 ≤ d ≤ 65
Nb ≥ 3
Concrete Box Beams Used in
Multibeam Decks
f, g
12.0 L
tan θ
90d
0° < θ ≤ 60°
20 ≤ L ≤ 120
17 ≤ d ≤ 60
Cast-in-Place Concrete Multicell
Box
1.0 +
35 ≤ b ≤ 60
5 ≤ N b ≤ 20
4.6.2.2.4—Curved Steel Bridges
Approximate analysis methods may be used for
analysis of curved steel bridges. The Engineer shall
ascertain that the approximate analysis method used is
appropriate by confirming that the method satisfies the
requirements stated in Article 4.4.
In curved systems, consideration should be given to
placing parapets, sidewalks, barriers and other heavy
line loads at their actual location on the bridge. Wearing
surface and other distributed loads may be assumed
uniformly distributed to each girder in the cross-section.
C4.6.2.2.4
The V-load method (United States Steel, 1984) has
been a widely used approximate method for analyzing
horizontally curved steel I-girder bridges. The method
assumes that the internal torsional load on the bridge—
resulting solely from the curvature—is resisted by selfequilibrating sets of shears between adjacent girders.
The V-load method does not directly account for sources
of torque other than curvature and the method does not
account for the horizontal shear stiffness of the concrete
deck. The method is only valid for loads such as normal
highway loadings. For exceptional loadings, a more
refined analysis is required. The method assumes a linear
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2012
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-47
distribution of girder shears across the bridge section;
thus, the girders at a given cross-section should have
approximately the same vertical stiffness. The V-load
method is also not directly applicable to structures with
reverse curvature or to a closed-framed system with
horizontal lateral bracing near, or in the plane of one or
both flanges. The V-load method does not directly
account for girder twist; thus, lateral deflections, which
become important on bridges with large spans and/or
sharp skews and vertical deflections, may be significantly
underestimated. In certain situations, the V-load method
may not detect uplift at end bearings. The method is best
suited for preliminary design, but may also be suitable for
final design of structures with radial supports or supports
skewed less than approximately 10 degrees.
The M/R method provides a means to account for
the effect of curvature in curved box girder bridges. The
method and suggested limitations on its use are
discussed by Tung and Fountain (1970).
Vertical reactions at interior supports on the
concave side of continuous-span bridges may be
significantly underestimated by both the V-load and
M/R methods.
Live load distribution factors for use with the
V-load and M/R methods may be determined using the
appropriate provisions of Article 4.6.2.2.
Strict rules and limitations on the applicability of
both of these approximate methods do not exist. The
Engineer must determine when approximate methods of
analysis are appropriate.
4.6.2.2.5—Special Loads with Other Traffic
Except as specified herein, the provisions of this
Article may be applied where the approximate methods
of analysis for the analysis of beam-slab bridges
specified in Article 4.6.2.2 and slab-type bridges
specified in Article 4.6.2.3 are used. The provisions of
this Article shall not be applied where either:
•
the lever rule has been specified for both single lane
and multiple lane loadings, or
•
the special requirement for exterior girders of beamslab bridge cross-sections with diaphragms
specified in Article 4.6.2.2.2d has been utilized for
simplified analysis.
Force effects resulting from heavy vehicles in one
lane with routine traffic in adjacent lanes, such as might
be considered with Load Combination Strength II in
Table 3.4.1-1 may be determined as:
g
g
G = Gp 1 + GD gm − 1
Z
Z
(4.6.2.2.4-1)
C4.6.2.2.5
Because the number of loaded lanes used to
determine the multiple lane live load distribution factor,
gm, is not known, the multiple lane multiple presence
factor, m, is implicitly set equal to 1.0 in this equation,
which assumes only two lanes are loaded, resulting in a
conservative final force effect over using the multiple
presence factors for three or more lanes loaded.
The factor Z is used to distinguish between
situations where the single lane live load distribution
factor was determined from a specified algebraic
equation and situations where the lever rule was
specified for the determination of the single lane live
load distribution factor. In the situation where an
algebraic equation was specified, the multiple presence
factor of 1.20 for a single lane loaded has been included
in the algebraic equation and must be removed by using
Z = 1.20 in Eq. 4.6.2.2.4-1 so that the distribution factor
can be utilized in Eq. 4.6.2.2.4-1 to determine the force
effect resulting from a multiple lane loading.
This formula was developed from a similar formula
presented without investigation by Modjeski and Masters,
Inc. (1994) in a report to the Pennsylvania Department of
Transportation in 1994, as was examined in Zokaie (1998).
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
where:
G
=
Gp
g1
GD
gm
Z
=
=
=
=
=
final force effect applied to a girder (kip or
kip-ft)
force effect due to overload truck (kip or kip-ft)
single lane live load distribution factor
force effect due to design loads (kip or kip-ft)
multiple lane live load distribution factor
a factor taken as 1.20 where the lever rule was
not utilized, and 1.0 where the lever rule was
used for a single lane live load distribution
factor
4.6.2.3—Equivalent Strip Widths for Slab-Type
Bridges
C4.6.2.3
This Article shall be applied to the types of crosssections shown schematically in Table 4.6.2.3-1. For the
purpose of this Article, cast-in-place voided slab bridges
may be considered as slab bridges.
The equivalent width of longitudinal strips per lane
for both shear and moment with one lane, i.e., two lines
of wheels, loaded may be determined as:
(4.6.2.3-1)
E = 10.0 + 5.0 L1W1
In Eq. 4.6.2.3-1, the strip width has been divided by
1.20 to account for the multiple presence effect.
The equivalent width of longitudinal strips per lane
for both shear and moment with more than one lane
loaded may be determined as:
E = 84.0 + 1.44 L1W1 ≤
12.0W
NL
(4.6.2.3-2)
where:
E =
L1 =
W1 =
W =
NL =
equivalent width (in.)
modified span length taken equal to the lesser
of the actual span or 60.0 (ft)
modified edge-to-edge width of bridge taken to
be equal to the lesser of the actual width or 60.0
for multilane loading, or 30.0 for single-lane
loading (ft)
physical edge-to-edge width of bridge (ft)
number of design lanes as specified in
Article 3.6.1.1.1
For skewed bridges, the longitudinal force effects
may be reduced by the factor r:
r = 1.05 − 0.25tanθ ≤ 1.00
(4.6.2.3-3)
where:
θ
=
skew angle (degrees)
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2012
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-49
Table 4.6.2.3-1—Typical Schematic Cross-Section
Supporting Components
Cast-in-Place Concrete Slab or Voided Slab
Type of Deck
Monolithic
Stressed Wood Deck
Integral Wood
Glued/Spiked Wood Panels with Spreader Beam
Integral Wood
Typical Cross-Section
4.6.2.4—Truss and Arch Bridges
The lever rule may be used for the distribution of
gravity loads in trusses and arches when analyzed as
planar structures. If a space analysis is used, either the
lever rule or direct loading through the deck or deck
system may be used.
Where loads, other than the self-weight of the
members and wind loads there on, are transmitted to the
truss at the panel points, the truss may be analyzed as a
pin-connected assembly.
4.6.2.5—Effective Length Factor, K
Physical column lengths shall be multiplied by an
effective length factor, K, to compensate for rotational and
translational boundary conditions other than pinned ends.
In the absence of a more refined analysis, where
lateral stability is provided by diagonal bracing or other
suitable means, the effective length factor in the braced
plane, K, for the compression members in triangulated
trusses, trusses, and frames may be taken as:
•
For bolted or welded end connections at both ends:
K = 0.750
•
For pinned connections at both ends: K = 0.875
C4.6.2.5
Equations for the compressive resistance of
columns and moment magnification factors for beamcolumns include a factor, K, which is used to modify the
length according to the restraint at the ends of the
column against rotation and translation.
K is the ratio of the effective length of an idealized
pin-end column to the actual length of a column with
various other end conditions. KL represents the length
between inflection points of a buckled column influenced
by the restraint against rotation and translation of column
ends. Theoretical values of K, as provided by the Structural
Stability Research Council, are given in Table C4.6.2.5-1
for some idealized column end conditions.
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2012
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•
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
For single angles, regardless of end connection:
K = 1.0
Vierendeel trusses shall be treated as unbraced
frames.
Table C4.6.2.5-1—Effective Length Factors, K
(a)
(b)
(c)
(d)
(e)
(f)
0.5
0.7
1.0
1.0
2.0
2.0
0.65
0.80
1.0
1.2
2.1
2.0
Buckled shape of
column is shown
by dashed line
Theoretical K
value
Design value of
K when ideal
conditions are
approximated
Rotation fixed
Rotation free
Rotation fixed
Rotation free
End condition
code
Translation fixed
Translation fixed
Translation free
Translation free
Because actual column end conditions seldom
comply fully with idealized restraint conditions against
rotation and translation, the design values suggested by
the Structural Stability Research Council are higher than
the idealized values.
Lateral stability of columns in continuous frames,
unbraced by attachment to shear walls, diagonal bracing,
or adjacent structures, depends on the flexural stiffness
of the rigidly connected beams. Therefore, the effective
length factor, K, is a function of the total flexural
restraint provided by the beams at the ends of the
column. If the stiffness of the beams is small in relation
to that of the column, the value of K could exceed 2.0.
Single angles are loaded through one leg and are
subject to eccentricity and twist, which is often not
recognized. K is set equal to 1.0 for these members to
more closely match the strength provided in the Guide
for Design of Steel Transmission Towers (ASCE
Manual No. 52, 1971).
Assuming that only elastic action occurs and that all
columns buckle simultaneously, it can be shown that
(Chen and Liu, 1991; ASCE Task Committee on
Effective Length, 1997):
For braced frames:
2
Ga Gb π Ga + Gb
+
4 K
2
π
K
1 −
π
tan K
π
2tan
2K = 1
+
π
K
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(C4.6.2.5-1)
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-51
For unbraced frames:
2
§ π ·
Ga Gb ¨
¸ − 36
© K ¹
=
6 (Ga + Gb )
π
K
§ π ·
tan ¨
¸
© K ¹
(C4.6.2.5-2)
where subscripts a and b refer to the two ends of the
column under consideration
in which:
§E I ·
Σ¨ c c ¸
L
G= © c ¹
§ Eg I g ·
Σ¨
¨ Lg ¸¸
©
¹
(C4.6.2.5-3)
where:
Ȉ
=
Ec
Ic
Lc
Eg
=
=
=
=
Ig
=
Lg =
K
=
summation of the properties of components
rigidly connected to an end of the column in the
plane of flexure
modulus of elasticity of column (ksi)
moment of inertia of column (in.4)
unbraced length of column (in.)
modulus of elasticity of beam or other
restraining member (ksi)
moment of inertia of beam or other restraining
member (in.4)
unsupported length of beam or other restraining
member (in.)
effective length factor for the column under
consideration
Figures C4.6.2.5-1 and C4.6.2.5-2 are graphical
representations of the relationship among K, Ga, and Gb
for Eqs. C4.6.2.5-1 and C4.6.2.5-2, respectively. The
figures can be used to obtain values of K directly.
Eqs. C4.6.2.5-1, C4.6.2.5-2, and the alignment
charts in Figures C4.6.2.5-1 and C4.6.2.5-2 are based on
assumptions of idealized conditions. The development
of the chart and formula can be found in textbooks such
as Salmon and Johnson (1990) and Chen and Lui
(1991). When actual conditions differ significantly from
these idealized assumptions, unrealistic designs may
result. Galambos (1988), Yura (1971), Disque (1973),
Duan and Chen (1988), and AISC (1993) may be used
to evaluate end conditions more accurately.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure C4.6.2.5-1—Alignment Chart for Determining
Effective Length Factor, K, for Braced Frames
Figure C4.6.2.5-2—Alignment Chart for Determining
Effective Length Factor, K, for Unbraced Frames
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-53
The following applies to
Figures C4.6.2.5-1 and C4.6.2.5-2:
the
use
of
•
For column ends supported by but not rigidly
connected to a footing or foundation, G is
theoretically equal to infinity, but unless actually
designed as a true frictionless pin, may be taken
equal to 10 for practical design. If the column end is
rigidly attached to a properly designed footing, G
may be taken equal to 1.0. Smaller values may be
taken if justified by analysis.
•
In computing effective length factors for members
with monolithic connections, it is important to
properly evaluate the degree of fixity in the
foundation using engineering judgment. In absence
of a more refined analysis, the following values can
be used:
Condition
Footing anchored on rock 1.5
Footing not anchored on rock
Footing on soil
Footing on multiple rows of
end bearing piles
G
3.0
5.0
1.0
In lieu of the alignment charts, the following
alternative K-factor equations (Duan, King, and Chen,
1993) may be used.
For braced frames:
K =1−
1
1
1
−
−
5 + 9Ga 5 + 9Gb 10 + Ga Gb
(C4.6.2.5-4)
For unbraced frames:
•
For K < 2
K =4−
1
1 + 0.2Ga
−
1
1 + 0.2Gb
−
1
1 + 0.01Ga Gb
(C4.6.2.5-5)
For K ≥ 2
•
K=
2πa
0.9 + 0.81 + 4ab
(C4.6.2.5-6)
in which:
a=
Ga Gb
+3
Ga + Gb
(C4.6.2.5-7)
b=
36
+6
Ga + Gb
(C4.6.2.5-8)
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4-54
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Eq. C4.6.2.5-5 is used first. If the value of K calculated
by Eq. C4.6.2.5-5 is greater than 2, Eq. C4.6.2.5-6 is
used. The values for K calculated using Eqs. C4.6.2.5-5
and C4.6.2.5-6 are a good fit with results from the
alignment chart Eqs. C4.6.2.5-1, C4.6.2.5-2, C4.6.2.5-3,
and allow an Engineer to perform a direct noniterative
solution for K.
4.6.2.6—Effective Flange Width
C4.6.2.6.1
4.6.2.6.1—General
Unless specified otherwise in this Article or in
Articles 4.6.2.6.2, 4.6.2.6.3, or 4.6.2.6.5, the effective
flange width of a concrete deck slab in composite or
monolithic construction may be taken as the tributary
width perpendicular to the axis of the member for
determining cross-section stiffnesses for analysis and for
determining flexural resistances. The effective flange
width of orthotropic steel decks shall be as specified in
Article 4.6.2.6.4. For the calculation of live load
deflections, where required, the provisions of
Article 2.5.2.6.2 shall apply.
Where a structurally continuous concrete barrier is
present and is included in the structural analysis as
permitted in Article 4.5.1, the deck slab overhang width
used for the analysis as well as for checking the
composite girder resistance may be extended by:
Δw =
Ab
2t s
(4.6.2.6.1-1)
where:
Ab =
ts =
cross-sectional area of the barrier (in.2)
thickness of deck slab (in.)
The slab effective flange width in composite girder
and/or stringer systems or in the chords of composite
deck trusses may be taken as one-half the distance to the
adjacent stringer or girder on each side of the
component, or one-half the distance to the adjacent
stringer or girder plus the full overhang width.
Otherwise, the slab effective flange width should be
determined by a refined analysis when:
•
the composite or monolithic member cross-section
is subjected to significant combined axial force and
bending, with the exception that forces induced by
restraint of thermal expansion may be determined in
beam-slab systems using the slab tributary width,
•
the largest skew angle θ in the bridge system is
greater than 75 degrees, where θ is the angle of a
bearing line measured relative to a normal to the
centerline of a longitudinal component,
•
the slab spans longitudinally between transverse
floorbeams, or
Longitudinal stresses are distributed across the deck
of composite and monolithic flexural members by inplane shear stresses. Due to the corresponding shear
deformations, plane sections do not remain plane and the
longitudinal stresses across the deck are not uniform.
This phenomenon is referred to as shear lag. The
effective flange width is the width of the deck over
which the assumed uniformly distributed longitudinal
stresses result approximately in the same deck force and
member moments calculated from elementary beam
theory assuming plane sections remain plane, as are
produced by the nonuniform stress distribution.
The provisions of this Article apply to all
longitudinal flexural members composite or monolithic
with a deck slab, including girders and stringers. They
are based on finite element studies of various bridge
types and configurations, corroborated by experimental
tests, and sensitivity analysis of various candidate
regression equations (Chen et al., 2005). Chen et al.
(2005) found that bridges with larger L/S (ratio of span
length to girder spacing) consistently exhibited an
effective width be equal to the tributary width b.
Nonskewed bridges with L/S = 3.1, the smallest value of
L/S considered in the Chen et al. (2005) study, exhibited
be = b in the maximum positive bending regions and
approximately be = 0.9b in the maximum negative
bending regions under service limit state conditions.
However, they exhibited be = b in these regions in all
cases at the strength limit state. Bridges with large skew
angles often exhibited be < b in both the maximum
positive and negative moment regions, particularly in
cases with small L/S. However, when various potential
provisions were assessed using the Rating Factor (RF)
as a measure of impact, the influence of using full width
(be = b) was found to be minimal. Therefore, the use of
the tributary width is justified in all cases within the
limits specified in this Article. The Chen et al. (2005)
study demonstrated that there is no significant
relationship between the slab effective width and the
slab thickness, as implied by previous Specifications.
These provisions are considered applicable for skew
angles less than or equal to 75 degrees, L/S greater than or
equal to 2.0 and overhang widths less than or equal to
0.5S. In unusual cases where these limits are violated, a
refined analysis should be used to determine the slab
effective width. Furthermore, these provisions are
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
•
the slab is designed for two-way action.
4.6.2.6.2—Segmental Concrete Box Beams and
Single-Cell, Cast-in-Place Box Beams
The effective flange width may be assumed equal to
the physical flange width if:
•
b ≤ 0.1 li
•
b ≤ 0.3 do
Otherwise, the effective width of outstanding flanges
may be taken as specified in Figures 4.6.2.6.2-1 through
4.6.2.6.2-4, where:
do =
b =
depth of superstructure (in.)
physical flange width on each side of the web,
e.g., b1, b2, and b3, as shown in
Figure 4.6.2.6.2-3 (in.)
4-55
considered applicable for slab-beam bridges with unequal
skew angles of the bearing lines, splayed girders,
horizontally curved girders, cantilever spans, and various
unequal span lengths of continuous spans, although these
parameters have not been investigated extensively in
studies to date. These recommendations are based on the
fact that the participation of the slab in these broader
parametric cases is fundamentally similar to the
participation of the slab in the specific parametric cases
that have been studied.
The use of one-half the distance to the adjacent
stringer or girder in calculating the effective width of the
main girders in composite girder and/or stringer systems
or the truss chords in composite deck trusses is a
conservative assumption for the main structural
components, since typically a larger width of the slab
can be expected to participate with the main girders or
truss chords. However, this tributary width assumption
may lead to an underestimation of the shear connector
requirements and a lack of consideration of axial forces
and bending moments in the composite stringers or
girders due to the global effects. To utilize a larger slab
width for the main girders or truss chords, a refined
analysis should be considered.
The specific cases in which a refined analysis is
recommended are so listed because they are
significantly beyond the conventional application of
the concept of a slab effective width. These cases
include tied arches where the deck slab is designed to
contribute to the resistance of the tie girders and cable
stayed bridges with a composite deck slab. Chen et al.
(2005) provides a few case study results for simplified
lower-bound slab effective widths in composite deck
systems of cable stayed bridges with certain specific
characteristics.
C4.6.2.6.2
One possible alternative to the procedure specified
in this Article is contained in Clause 3-10.2 of the 1991
Ontario Highway Bridge Design Code, which provides
an equation for determining the effective flange width
for use in calculating flexural resistances and stresses.
Superposition of local two-way slab flexural
stresses due to wheel loads and the primary longitudinal
flexural stresses is not normally required.
The effective flange widths bm and bs are
determined as the product of the coefficient in
Figure 4.6.2.6.2-2 and the physical distance b, as
indicated in Figure 4.6.2.6.2-3.
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4-56
be
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
=
bm =
bs
=
a
=
ℓi
=
effective flange width corresponding to the
particular position of the section of interest in
the span as specified in Figure 4.6.2.6.2-1 (in.)
effective flange width for interior portions of a
span as determined from Figure 4.6.2.6.2-2; a
special case of be (in.)
effective flange width at interior support or for
cantilever
arm
as
determined
from
Figure 4.6.2.6.2-2; a special case of be (in.)
portion of span subject to a transition in
effective flange width taken as the lesser of the
physical flange width on each side of the web
shown in Figure 4.6.2.6.2-3 or one quarter of
the span length (in.)
a notional span length specified in
Figure 4.6.2.6.2-1 for the purpose of
determining effective flange widths using
Figure 4.6.2.6.2-2
The following interpretations apply:
•
In any event, the effective flange width shall not be
taken as greater than the physical width.
•
The effects of unsymmetrical loading on the
effective flange width may be disregarded.
•
The value of bs shall be determined using the
greater of the effective span lengths adjacent to the
support.
•
If bm is less than bs in a span, the pattern of the
effective width within the span may be determined
by the connecting line of the effective widths bs at
adjoining support points.
For the superposition of local and global force
effects, the distribution of stresses due to the global
force effects may be assumed to have a straight line
pattern in accordance with Figure 4.6.2.6.2-3c. The
linear stress distribution should be determined from the
constant stress distribution using the conditions that the
flange force remains unchanged and that the maximum
width of the linear stress distribution on each side of a
web is 2.0 times the effective flange width.
The section properties for normal forces may be
based on the pattern according to Figure 4.6.2.6.2-4 or
determined by more rigorous analysis.
If the linear stress distributions intersect a free edge
or each other before reaching the maximum width, the
linear stress distribution is a trapezoid; otherwise, it is a
triangle. This is shown in Figure 4.6.2.6.2-3c.
Figure 4.6.2.6.2-4 is intended only for calculation of
resistance due to anchorage of post-tensioning tendons
and other concentrated forces and may be disregarded in
the general analysis to determine force effects.
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
System
4-57
Pattern of bm/b
Single-Span Girder
ℓi = 1.0ℓ
Continuous
Girder
End Span
ℓi = 0.8ℓ
Interior Span
ℓi = 0.6ℓ
Cantilever Arm
ℓi = 1.5ℓ
Figure 4.6.2.6.2-1—Pattern of Effective Flange Width, be, bm, and bs
Figure 4.6.2.6.2-2—Values of the Effective Flange Width Coefficients for bm and bs for the Given Values of b/ℓi
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure 4.6.2.6.2-3—Cross-Sections and Corresponding Effective Flange Widths, be, for Flexure and Shear
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-59
Figure 4.6.2.6.2-4—Effective Flange Widths, bn, for Normal
Forces
4.6.2.6.3—Cast-in-Place Multicell Superstructures
The effective width for cast-in-place multiweb
cellular superstructures may be taken to be as specified
in Article 4.6.2.6.1, with each web taken to be a beam,
or it may be taken to be the full width of the deck slab.
In the latter case, the effects of shear lag in the end
zones shall be investigated.
4.6.2.6.4—Orthotropic Steel Decks
The effective width need not be determined when
using refined analysis as specified in Article 4.6.3.2.4.
For simplified analysis, the effective width of the deck,
including the deck plate and ribs, acting as the top flange
of a longitudinal superstructure component or a
transverse beam may be taken as:
•
L/B 5: fully effective
•
1
L/B < 5: bod = L
5
where:
L
=
B
=
bod =
span length of the orthotropic girder or
transverse beam (in.)
spacing between orthotropic girder web plates
or transverse beams (in.)
effective width of orthotropic deck (in.)
C4.6.2.6.4
Consideration of effective width of the deck plate
can be avoided by application of refined analysis
methods.
The procedures in Design Manual for Orthotropic
Steel Plate Deck Bridges (AISC, 1963) may be used as
an acceptable means of simplified analysis; however, it
has been demonstrated that using this procedure can
result in rib effective widths exceeding the rib spacing,
which may be unconservative.
Tests (Dowling et al., 1977) have shown that for
most practical cases, shear lag can be ignored in
calculating the ultimate compressive strength of
stiffened or unstiffened girder flanges (Lamas and
Dowling, 1980; Burgan and Dowling, 1985; Jetteur et
al., 1984; and Hindi, 1991). Thus, a flange may
normally be considered to be loaded uniformly across its
width. It necessary to consider the flange effectiveness
in greater detail only in the case of flanges with
particularly large aspect ratios (L/B < 5) or particularly
slender edge panels or stiffeners (Burgan and Dowling,
1985 and Hindi, 1991) is it necessary to consider the
flange effectiveness in greater detail.
Consideration of inelastic behavior can increase the
effective width as compared to elastic analysis. At
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
for strength limit states for positive and negative flexure.
For service and fatigue limit states in regions of high
shear, the effective deck width can be determined by
refined analysis or other accepted approximate methods.
4.6.2.6.5—Transverse Floorbeams and Integral
Bent Caps
For transverse floorbeams and for integral bent caps
designed with a composite concrete deck slab, the effective
flange width overhanging each side of the transverse
floorbeam or bent cap web shall not exceed six times the
least slab thickness or one-tenth of the span length. For
cantilevered transverse floorbeams or integral bent caps, the
span length shall be taken as two times the length of the
cantilever span.
ultimate loading, the region of the flange plate above the
web can yield and spread the plasticity (and distribute
stress) outward if the plate maintains local stability.
Results from studies by Chen et al. (2005) on composite
steel girders, which included several tub-girder bridges,
indicate that the full slab width may be considered
effective in both positive and negative moment regions.
Thus, orthotropic plates acting as flanges are
considered fully effective for strength limit state
evaluations from positive and negative flexure when the
L/B ratio is at least 5. For the case of L/B < 5, only a
width of one-fifth of the effective span should be
considered effective. For service and fatigue limit states
in regions of high shear, a special investigation into
shear lag should be done.
C4.6.2.6.5
The provisions for the effective flange width for
transverse floorbeams and integral bent caps are based
on past successful practice, specified by Article 8.10.1.4
of the 2002 AASHTO Standard Specifications.
[This space is intentionally left blank. —ed.]
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-61
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4-62
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
4.6.2.7—Lateral Wind Load Distribution in
Multibeam Bridges
4.6.2.7.1—I-Sections
In bridges with composite decks, noncomposite decks
with concrete haunches, and other decks that can provide
horizontal diaphragm action, wind load on the upper half of
the outside beam, the deck, vehicles, barriers, and
appurtenances shall be assumed to be directly transmitted to
the deck, acting as a lateral diaphragm carrying this load to
supports. Wind load on the lower half of the outside beam
shall be assumed to be applied laterally to the lower flange.
For bridges with decks that cannot provide horizontal
diaphragm action, the lever rule shall apply for distribution
of the wind load to the top and bottom flanges.
Bottom and top flanges subjected to lateral wind load
shall be assumed to carry that load to adjacent brace points
by flexural action. Such brace points occur at wind bracing
nodes or at cross-frames and diaphragm locations.
The lateral forces applied at brace points by the
flanges shall be transmitted to the supports by one of the
following load paths:
•
Truss action of horizontal wind bracing in the plane
of the flange;
•
Frame action of the cross-frames or diaphragms
transmitting the forces into the deck or the wind
bracing in the plane of the other flange, and then by
diaphragm action of the deck, or truss action of the
wind bracing, to the supports;
•
Lateral bending of the flange subjected to the lateral
forces and all other flanges in the same plane,
transmitting the forces to the ends of the span, for
example, where the deck cannot provide horizontal
diaphragm action, and there is no wind bracing in the
plane of either flange.
C4.6.2.7.1
Precast concrete plank decks and timber decks are
not solid diaphragms and should not be assumed to
provide horizontal diaphragm action unless evidence is
available to show otherwise.
Unless a more refined analysis is made, the
wind force, wind moment, horizontal force to be
transmitted by diaphragms and cross-frames, and
horizontal force to be transmitted by lateral bracing
may be calculated as indicated below. This
procedure is presented for beam bridges but may be
adapted for other types of bridges.
The wind force, W, may be applied to the flanges of
exterior members. For composite members and
noncomposite members with cast-in-place concrete or
orthotropic steel decks, W need not be applied to the top
flange.
W =
ηi γPD d
2
(C4.6.2.7.1-1)
where:
W =
factored wind force per unit length applied to
the flange (kip/ft)
design horizontal wind pressure specified in
Article 3.8.1 (ksf)
depth of the member (ft)
load factor specified in Table 3.4.1-1 for the
particular group loading combination
load modifier relating to ductility, redundancy, and
operational importance as specified in Article 1.3.2.1
PD =
d
Ȗ
=
=
Și
=
For the first two load paths, the maximum wind moment
on the loaded flange may be determined as:
Mw =
WLb 2
10
(C4.6.2.7.1-2)
where:
Mw =
maximum lateral moment in the flange due to
the factored wind loading (kip-ft)
factored wind force per unit length applied to
the flange (kip/ft)
spacing of brace points (ft)
W =
Lb =
For the third load path, the maximum wind moment
on the loaded flange may be computed as:
Mw =
WLb 2 WL2
+
10
8 Nb
(C4.6.2.7.1-3)
where:
Mw =
total lateral moment in the flange due to the
factored wind loading (kip-ft)
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-63
W =
Lb =
Nb =
L =
factored wind force per unit length applied to
the flange (kip/ft)
spacing of cross-frames or diaphragms (ft)
number of longitudinal members
span length (ft)
Eq. C4.6.2.7.1-3 is based on the assumption that
cross-frames and diaphragms act as struts in distributing
the wind force on the exterior flange to adjacent flanges.
If there are no cross-frames or diaphragms, the first term
should be taken as 0.0, and Nb should be taken as 1.0.
The horizontal wind force applied to each brace
point may be calculated as:
Pw = WLb
(C4.6.2.7.1-4)
where:
Pw =
W =
Lb =
4.6.2.7.2—Box Sections
lateral wind force applied to the brace point (kips)
wind force per unit length from Eq. C4.6.2.7.1-1
(kip/ft)
spacing of diaphragms or cross-frames (ft)
Lateral bracing systems required to support both
flanges due to transfer of wind loading through
diaphragms or cross-frames shall be designed for a
horizontal force of 2Pw at each brace point.
One quarter of the wind force on a box section shall
be applied to the bottom flange of the exterior box beam.
The section assumed to resist the wind force shall
consist of the bottom flange and a part of the web as
determined in Sections 5 and 6. The other three quarters
of the wind force on a box section, plus the wind force
on vehicles, barriers, and appurtenances, shall be
assumed to be transmitted to the supports by diaphragm
action of the deck.
Interbox lateral bracing shall be provided if the
section assumed to resist the wind force is not adequate.
4.6.2.7.3—Construction
The need for temporary wind bracing during
construction shall be investigated for I- and box-section
bridges.
4.6.2.8—Seismic Lateral Load Distribution
4.6.2.8.1—Applicability
These provisions shall apply to diaphragms, crossframes, and lateral bracing, which are part of the seismic
lateral force resisting system in common slab-on-girder
bridges in Seismic Zones 2, 3, and 4. The provisions of
Article 3.10.9.2 shall apply to Seismic Zone 1.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
4.6.2.8.2—Design Criteria
The Engineer shall demonstrate that a clear,
straightforward load path to the substructure exists and
that all components and connections are capable of
resisting the imposed load effects consistent with the
chosen load path.
The flow of forces in the assumed load path must be
accommodated through all affected components and
details including, but not limited to, flanges and webs of
main beams or girders, cross-frames, connections, slabto-girder interfaces, and all components of the bearing
assembly from top flange interface through the
confinement of anchor bolts or similar devices in the
substructure.
The analysis and design of end diaphragms and
cross-frames shall consider horizontal supports at an
appropriate number of bearings. Slenderness and
connection requirements of bracing members that are part
of the lateral force resisting system shall comply with
applicable provisions specified for main member design.
Members of diaphragms and cross-frames identified
by the Designer as part of the load path carrying seismic
forces from the superstructure to the bearings shall be
designed and detailed to remain elastic, based on the
applicable gross area criteria, under all design
earthquakes, regardless of the type of bearings used. The
applicable provisions for the design of main members
shall apply.
4.6.2.8.3—Load Distribution
A viable load path shall be established to transmit
lateral loads to the foundation based on the stiffness
characteristics of the deck, diaphragms, cross-frames,
and lateral bracing. Unless a more refined analysis is
made, an approximate load path shall be assumed as
noted below.
•
In bridges with:
o
A concrete deck that can provide
horizontal diaphragm action, or
o
A horizontal bracing system in the plane of
the top flange,
the lateral loads applied to the deck shall be
assumed to be transmitted directly to the bearings
through end diaphragms or cross-frames. The
development and analysis of the load path through
the deck or through the top lateral bracing, if
present, shall utilize assumed structural actions
analogous to those used for the analysis of wind
loadings.
C4.6.2.8.2
Diaphragms, cross-frames, lateral bracing, bearings,
and substructure elements are part of a seismic load
resisting system in which the lateral loads and
performance of each element are affected by the strength
and stiffness characteristics of the other elements. Past
earthquakes have shown that when one of these
elements responded in a ductile manner or allowed some
movement, damage was limited. In the strategy taken
herein, it is assumed that ductile plastic hinging in
substructure is the primary source of energy dissipation.
Alternative design strategies may be considered if
approved by the Owner.
C4.6.2.8.3
A continuous path is necessary for the transmission
of the superstructure inertia forces to the foundation.
Concrete decks have significant rigidity in their
horizontal plane, and in short to medium slab-on-girder
spans, their response approaches a rigid body motion.
Therefore, the lateral loading of the intermediate
diaphragms and cross-frames is minimal.
Bearings do not usually resist load simultaneously,
and damage to only some of the bearings at one end of a
span is not uncommon. When this occurs, high load
concentrations can result at the location of the other
bearings, which should be taken into account in the
design of the end cross-frames or diaphragms. Also, a
significant change in the load distribution among end
cross-frame members may occur. Although studies of
cyclic load behavior of bracing systems have shown that
with adequate details, bracing systems can allow for
ductile behavior, these design provisions require elastic
behavior in end diaphragms (Astaneh-Asl and Goel,
1984; Astaneh-Asl et al., 1985; Haroun and Sheperd,
1986; Goel and El-Tayem, 1986).
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
•
In bridges that have:
o
Decks that cannot provide horizontal
diaphragm action and
o
No lateral bracing in the plane of the top
flange,
the lateral loads applied to the deck shall be
distributed through the intermediate diaphragms and
cross-frames to the bottom lateral bracing or the
bottom flange, and then to the bearings, and through
the end diaphragms and cross-frames, in proportion
to their relative rigidity and the respective tributary
mass of the deck.
•
4-65
Because the end diaphragm is required to remain
elastic as part of the identified load path, stressing of
intermediate cross-frames need not be considered.
If a bottom lateral bracing system is not present, and
the bottom flange is not adequate to carry the
imposed force effects, the first procedure shall be
used, and the deck shall be designed and detailed to
provide the necessary horizontal diaphragm action.
4.6.2.9—Analysis of Segmental Concrete Bridges
4.6.2.9.1—General
C4.6.2.9.1
Elastic analysis and beam theory may be used to
determine design moments, shears, and deflections. The
effects of creep, shrinkage, and temperature differentials
shall be considered as well as the effects of shear lag.
Shear lag shall be considered in accordance with the
provisions of Article 4.6.2.9.3.
For spans in excess of 250 ft, results of elastic
analyses should be evaluated with consideration of
possible variations in the modulus of elasticity of the
concrete, variations in the concrete creep and shrinkage
properties, and the impact of variations in the
construction schedule on these and other design
parameters.
4.6.2.9.2—Strut-and-Tie Models
Strut-and-tie models may be used for analysis in
areas of load or geometrical discontinuity.
Analysis of concrete segmental bridges requires
consideration of variation of design parameters with
time as well as a specific construction schedule and
method of erection. This, in turn, requires the use of a
computer program developed to trace the timedependent response of segmentally erected, prestressed
concrete bridges through construction and under service
loads. Among the many programs developed for this
purpose, several are in the public domain and may be
purchased for a nominal amount, e.g., (Ketchum, 1986;
Shushkewich, 1986; Danon and Gamble, 1977).
C4.6.2.9.2
See references for background on transverse
analysis of concrete box girder bridges.
4.6.2.9.3—Effective Flange Width
Effective flange width for service load stress
calculations may be determined by the provisions of
Article 4.6.2.6.2.
The section properties for normal forces may be
based on Figure 4.6.2.6.2-4 or determined by more
rigorous analysis.
Bending, shear, and normal forces may be evaluated
by using the corresponding factored resistances.
The capacity of a cross-section at the strength limit
state may be determined by considering the full
compression flange width effect.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
4.6.2.9.4—Transverse Analysis
The transverse design of box girder segments for
flexure shall consider the segment as a rigid box frame.
Flanges shall be analyzed as variable depth sections,
considering the fillets between the flanges and webs.
Wheel loads shall be positioned to provide maximum
moments, and elastic analysis shall be used to determine
the effective longitudinal distribution of wheel loads for
each load location. Consideration shall be given to the
increase in web shear and other effects on the
cross-section resulting from eccentric loading or
unsymmetrical structure geometry.
The provisions of Articles 4.6.2.1 and 4.6.3.2,
influence surfaces such as those by Homberg (1968) and
Pucher (1964), or other elastic analysis procedures may
be used to evaluate live load plus impact moment effects
in the top flange of the box section.
Transverse elastic and creep shortening due to
prestressing and shrinkage shall be considered in the
transverse analysis.
The effect of secondary moments due to
prestressing shall be included in stress calculations at the
service limit state and construction evaluation. At the
strength limit state, the secondary force effects induced
by prestressing, with a load factor of 1.0, shall be added
algebraically to the force effects due to factored dead
and live loads and other applicable loads.
4.6.2.9.5—Longitudinal Analysis
4.6.2.9.5a—General
Longitudinal analysis of segmental concrete bridges
shall consider a specific construction method and
construction schedule as well as the time-related effects
of concrete creep, shrinkage, and prestress losses.
The effect of secondary moments due to
prestressing shall be included in stress calculations at the
service limit state. At the strength limit state, the
secondary force effects induced by prestressing, with a
load factor of 1.0, shall be added algebraically to other
applicable factored loads.
4.6.2.9.5b—Erection Analysis
Analysis of the structure during any construction
stage shall consider the construction load combinations,
stresses, and stability considerations specified in
Article 5.14.2.3.
4.6.2.9.5c—Analysis of the Final Structural
System
The provisions of Article 5.14.2.2.3 shall apply.
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-67
4.6.2.10—Equivalent Strip Widths for Box
Culverts
4.6.2.10.1—General
C4.6.2.10.1
This Article shall be applied to box culverts with
depths of fill less than 2.0 ft.
4.6.2.10.2—Case 1: Traffic Travels Parallel to Span
When traffic travels primarily parallel to the span,
culverts shall be analyzed for a single loaded lane with
the single lane multiple presence factor.
The axle load shall be distributed to the top slab for
determining moment, thrust, and shear as follows:
Perpendicular to the span:
E = 96 + 1.44 S
Parallel to the span:
(4.6.2.10.2-1)
Espan = LT + LLDF ( H )
(4.6.2.10.2-2)
Design for depths of fill of 2.0 ft or greater are
covered in Article 3.6.1.2.6.
C4.6.2.10.2
Culverts are designed under the provisions of
Section 12. Box culverts are normally analyzed as twodimensional frames. Equivalent strip widths are used to
simplify the analysis of the three-dimensional response
to live loads. Eqs. 4.6.2.10.2-1 and 4.6.2.10.2-2 are
based on research (McGrath et al., 2004) that
investigated the forces in box culverts with spans up to
24.0 ft.
The distribution widths are based on distribution of
shear forces. Distribution widths for positive and
negative moments are wider; however, using the
narrower width in combination with a single lane
multiple presence factor provides designs adequate for
multiple loaded lanes for all force effects.
Although past practice has been to ignore the
distribution of live load with depth of fill, consideration
of this effect, as presented in Eq. 4.6.2.10.2-2, produces
a more accurate model of the changes in design forces
with increasing depth of fill. The increased load length
parallel to the span, as allowed by Eq. 4.6.2.10.2-2, may
be conservatively neglected in design.
where:
E
=
S
Espan
=
=
LT
=
LLDF
=
H
=
equivalent distribution width perpendicular
to span (in.)
clear span (ft)
equivalent distribution length parallel to
span (in.)
length of tire contact area parallel to span,
as specified in Article 3.6.1.2.5 (in.)
factor for distribution of live load with
depth of fill, 1.15 or 1.00, as specified in
Article 3.6.1.2.6
depth of fill from top of culvert to top of
pavement (in.)
4.6.2.10.3—Case 2: Traffic Travels Perpendicular
to Span
When traffic travels perpendicular to the span, live
load shall be distributed to the top slab using the
equations specified in Article 4.6.2.1 for concrete decks
with primary strips perpendicular to the direction of
traffic.
C4.6.2.10.3
Culverts with traffic traveling perpendicular to the
span can have two or more trucks on the same design
strip at the same time. This must be considered, with the
appropriate multiple presence factor, in analysis of the
culvert structural response.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
4.6.2.10.4—Precast Box Culverts
For precast box culverts with top slabs having spanto-thickness ratios (s/t) of 18 or less and segment lengths
greater than or equal to 4 ft in length, shear transfer across
the joint need not be provided.
For precast box culverts not satisfying the
requirements noted above, the design shall incorporate
one of the following:
•
Provide the culvert with a means of shear transfer
between the adjacent sections. Shear transfer may
be provided by pavement, soil fill, or a physical
connection between adjacent sections.
•
Design the section ends as edge beams in
accordance with the provisions of Article 4.6.2.1.4b
using the distribution width computed from Eq.
4.6.2.10.2-1. The distribution width shall not exceed
the length between two adjacent joints.
C4.6.2.10.4
Precast box culverts manufactured in accordance
with AASHTO M 273 are often installed with joints
that do not provide a means of direct shear transfer
across the joints of adjacent sections under service
load conditions. This practice is based on research
(James, 1984; Frederick, et al., 1988) which indicated
significant shear transfer may not be necessary under
service loading. The response of the sections tested
was typified by small deflections and strains
indicating that cracking did not occur under service
wheel loads with no earth cover and that the demand
on the section was lower than predicted by the design,
which was based conservatively on a cracked section.
While there are no known service issues with
installation of standard box sections without means of
shear transfer across joints, analysis (McGrath et al.,
2004) shows that stresses are substantially higher
when a box culvert is subjected to a live load at a free
edge than when loaded away from a free edge.
However, research performed on precast box
culverts that were loaded at the edge of the section
(Abolmaali and Garg, 2007) has shown that no means of
load transfer across the joint is required when the live
load is distributed per Articles 4.6.2.10.2 and 4.6.2.10.3
and the top slab of the box culvert is designed in
accordance with Article 5.8.3. The tested boxes were
shown to have significantly more shear strength than
predicted by Article 5.8.3.
For box culverts outside of the normal
ASTM/AASHTO dimensional requirements, some fill
or pavement will likely provide sufficient shear transfer
to distribute live load to adjacent box sections without
shear keys to avoid higher stresses due to edge loading.
Otherwise, for box culverts outside of ASTM/AASHTO
dimensional requirements with zero depth of cover, and
no pavement, soil, or other means of shear transfer such
as shear keys, designers should design the culvert
section for the specified reduced distribution widths
lacking a more rigorous design method.
4.6.3—Refined Methods of Analysis
4.6.3.1—General
C4.6.3.1
Refined methods, listed in Article 4.4, may be used
for the analysis of bridges. In such analyses,
consideration shall be given to aspect ratios of elements,
positioning and number of nodes, and other features of
topology that may affect the accuracy of the analytical
solution.
The number of possible locations for positioning
the design vehicular live load will be large when
determining the extreme force effect in an element
using a refined method of analysis. The following are
variable:
•
The location of the design lanes when the available
deck width contains a fraction of a design lane
width,
•
Which of the design lanes are actually used,
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
A structurally continuous railing, barrier, or median,
acting compositely with the supporting components,
may be considered to be structurally active at service
and fatigue limit states.
When a refined method of analysis is used, a table
of live load distribution coefficients for extreme force
effects in each span shall be provided in the contract
documents to aid in permit issuance and rating of the
bridge.
4-69
•
The longitudinal location of the design vehicular
live load in each lane,
•
The longitudinal axle spacing of the design
vehicular live load,
•
The transverse location of the design vehicular live
load in each lane.
This provision reflects the experimentally observed
response of bridges. This source of stiffness has
traditionally been neglected but exists and may be
included, provided that full composite behavior is
assured.
These live load distribution coefficients should be
provided for each combination of component and lane.
4.6.3.2—Decks
C4.6.3.2.1
4.6.3.2.1—General
Unless otherwise specified, flexural and torsional
deformation of the deck shall be considered in the
analysis but vertical shear deformation may be
neglected.
Locations of flexural discontinuity through which
shear may be transmitted should be modeled as hinges.
In the analysis of decks that may crack and/or
separate along element boundaries when loaded,
Poisson’s ratio may be neglected. The wheel loads shall
be modeled as patch loads distributed over an area, as
specified in Article 3.6.1.2.5, taken at the contact
surface. This area may be extended by the thickness of
the wearing surface, integral or nonintegral, on all four
sides. When such extension is utilized, the thickness of
the wearing surface shall be reduced for any possible
wear at the time of interest. Other extended patch areas
may be utilized with the permission of the Owner
provided that such extended area is consistent with the
assumptions in, and application of, a particular refined
method of analysis.
4.6.3.2.2—Isotropic Plate Model
For the purpose of this section, bridge decks that are
solid, have uniform or close to uniform depth, and
whose stiffness is close to equal in every in-plane
direction shall be considered isotropic.
In many solid decks, the wheel load-carrying
contribution of torsion is comparable to that of flexure.
Large torsional moments exist in the end zones of
skewed girder bridges due to differential deflection. In
most deck types, shear stresses are rather low, and their
contribution to vertical deflection is not significant. Inplane shear deformations, which gave rise to the concept
of effective width for composite bridge decks, should
not be neglected.
C4.6.3.2.2
Analysis is rather insensitive to small deviations in
constant depth, such as those due to superelevation,
crown, and haunches. In slightly cracked concrete slabs,
even a large difference in the reinforcement ratio will
not cause significant changes in load distribution.
The torsional stiffness of the deck may be estimated
using Eq. C4.6.2.2.1-1 with b equal to 1.0.
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4-70
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
4.6.3.2.3—Orthotropic Plate Model
In orthotropic plate modeling, the flexural rigidity
of the elements may be uniformly distributed along the
cross-section of the deck. Where the torsional stiffness
of the deck is not contributed solely by a solid plate of
uniform thickness, the torsional rigidity should be
established by physical testing, three-dimensional
analysis, or generally accepted and verified
approximations.
C4.6.3.2.3
The accuracy of the orthotropic plate analysis is
sharply reduced for systems consisting of a small
number of elements subjected to concentrated loads.
4.6.3.2.4—Refined Orthotropic Deck Model
Refined analysis of orthotropic deck structures
subjected to direct wheel loads should be accomplished
using a detailed three-dimensional shell or solid finite
element structural model. The structural model should
include all components and connections and consider
local structural stress at fatigue prone details as shown in
Table 6.6.1.2.3-1. Structural modeling techniques that
utilize the following simplifying assumptions may be
applied:
•
Linear elastic material behavior,
•
Small deflection theory,
•
Plane sections remain plane,
•
Neglect residual stresses, and
•
Neglect imperfections and weld geometry.
C4.6.3.2.4
2013 Revision
Further guidance on evaluating local structural
stresses using finite element modeling is provided in
Manual for Design, Construction, and Maintenance of
Orthotropic Steel Bridges (FHWA, 2012).
Meshing shall be sufficiently detailed to calculate
local stresses at weld toes and to resolve the wheel patch
pressure loading with reasonable accuracy.
4.6.3.3—Beam-Slab Bridges
C4.6.3.3.1
4.6.3.3.1—General
The aspect ratio of finite elements and grid panels
should not exceed 5.0. Abrupt changes in size and/or shape
of finite elements and grid panels should be avoided.
Nodal loads shall be statically equivalent to the
actual loads being applied.
More restrictive limits for aspect ratio may be
specified for the software used.
In the absence of other information, the following
guidelines may be used at the discretion of the
Engineer:
•
A minimum of five, and preferably nine, nodes per
beam span should be used.
•
For finite element analyses involving plate and
beam elements, it is preferable to maintain the
relative vertical distances between various elements.
If this is not possible, longitudinal and transverse
elements may be positioned at the midthickness of
the plate-bending elements, provided that the
eccentricities are included in the equivalent
properties of those sections that are composite.
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4.6.3.3.2—Curved Steel Bridges
Refined analysis methods should be used for the
analysis of curved steel bridges unless the Engineer
ascertains that approximate analysis methods are
appropriate according to the provisions of
Article 4.6.2.2.4.
4-71
•
For grid analysis or finite element and finite
difference analyses of live load, the slab shall be
assumed to be effective for stiffness in both positive
and negative flexure. In a filled or partially filled
grid system, composite section properties should be
used.
•
In finite element analysis, an element should have
membrane capability with discretization sufficient
to properly account for shear lag. The force effects
so computed should be applied to the appropriate
composite or noncomposite section for computing
resistance.
•
For longitudinal composite members in grid
analyses, stiffness should be computed by assuming
a width of the slab to be effective, but it need not be
less than that specified in Article 4.6.2.6.
•
For K-frame and X-frame diaphragms, equivalent
beam flexure and shear stiffnesses should be
computed. For bridges with widely spaced
diaphragms, it may be desirable to use notional
transverse beam members to model the deck. The
number of such beams is to some extent
discretionary. The significance of shear lag in the
transverse beam-slab width as it relates to lateral
load distribution can be evaluated qualitatively by
varying the stiffness of the beam-slab elements
within reasonable limits and observing the results.
Such a sensitivity study often shows that this effect
is not significant.
•
Live load force effects in diaphragms should be
calculated by the grid or finite element analysis.
The easiest way to establish extreme force effects is
by using influence surfaces analogous to those
developed for the main longitudinal members.
•
The St. Venant torsional inertia may be determined
using the equation in Article C4.6.2.2.1.
Transformation of concrete and steel to a common
material should be on the basis of shear modulus, G,
which can be taken as G = 0.5E/(1+μ). It is
recommended that the St. Venant rigidity of
composite sections utilize only one-half of the
effective width of the flexural section, as described
above, before transformation.
C4.6.3.3.2
Refined analysis methods, identified in Article 4.4,
are generally computer-based. The finite strip and finite
element methods have been the most common. The
finite strip method is less rigorous than the finite
element method and has fallen into disuse with the
advent of more powerful computers. Finite element
programs may provide grid analyses using a series of
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4-72
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
beam elements connected in a plane. Refinements of the
grid model may include offset elements. Frequently, the
torsional warping degree of freedom is not available in
beam elements. The finite element method may be
applied to a three-dimensional model of the
superstructure. A variety of elements may be used in this
type of model. The three-dimensional model may be
made capable of recognizing warping torsion by
modeling each girder cross-section with a series of
elements.
The stiffness of supports, including lateral restraint
such as integral abutments or integral piers, should be
recognized in the analysis. Since bearing restraint is
offset from the neutral axis of the girders, large lateral
forces at the bearings often occur and may create
significant bending in the girders, which may lead to
lower girder moments than would be computed if the
restraints were not present. The Engineer should
ascertain that any such benefit recognized in the design
will be present throughout the useful life of the bridge.
Loads may be applied directly to the structural
model, or applied to influence lines or influence
surfaces. Only where small-deflection elastic solutions
are used are influence surfaces or influence lines
appropriate. The Engineer should ascertain that dead
loads are applied as accurately as possible.
4.6.3.4—Cellular and Box Bridges
A refined analysis of cellular bridges may be made
by any of the analytic methods specified in Article 4.4,
except the yield line method, which accounts for the two
dimensions seen in plan view and for the modeling of
boundary conditions. Models intended to quantify
torsional warping and/or transverse frame action should
be fully three-dimensional.
For single box cross-sections, the superstructure
may be analyzed as a spine beam for both flexural and
torsional effects. A steel box should not be considered to
be torsionally rigid unless internal bracing is provided to
maintain the box cross-section. The transverse position
of bearings shall be modeled.
4.6.3.5—Truss Bridges
A refined plane frame or space frame analysis shall
include consideration for the following:
•
Composite action with the deck or deck system;
•
Continuity among the components;
•
Force effects due to self-weight of components,
change in geometry due to deformation, and axial
offset at panel points; and
•
In-plane and out-of-plane buckling of components
including original out-of-straightness, continuity
among the components and the effect axial forces
present in those components.
C4.6.3.5
Load applied to deck or floorbeams instead of to
truss joints will yield results that more completely
quantify out-of-plane actions.
Experience has shown that dead load force effects
calculated using either plane frame or space frame
analysis in a truss with properly cambered primary and
secondary members and detailed to minimize
eccentricity at joints, will be quite close to those
calculated by the conventional approximations. In many
cases, a complete three-dimensional frame analysis may
be the only way to accurately calculate forces in
secondary members, particularly live load force effects.
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-73
Out-of-plane buckling of the upper chords of pony
truss bridges shall be investigated. If the truss derives its
lateral stability from transverse frames, of which the
floorbeams are a part, the deformation of the floorbeams
due to vehicular loading shall be considered.
4.6.3.6—Arch Bridges
C4.6.3.6
The provisions of Article 4.6.3.5 shall apply where
applicable.
The effect of the extension of cable hangers shall be
considered in the analysis of an arch tie.
Where not controlled through proper detailing, rib
shortening should be investigated.
The use of large deflection analysis of arches of
longer spans should be considered in lieu of the
moment magnification correction as specified in
Article 4.5.3.2.2c.
When the distribution of stresses between the top
and bottom chords of trussed arches is dependent on the
manner of erection, the manner of erection shall be
indicated in the contract documents.
4.6.3.7—Cable-Stayed Bridges
Rib shortening and arch design and construction are
discussed by Nettleton (1977).
Any single-step correction factor cannot be
expected to accurately model deflection effects over a
wide range of stiffnesses.
If a hinge is provided at the crown of the rib in addition
to hinges at the abutment, the arch becomes statically
determinate, and stresses due to change of temperature and
rib shortening are essentially eliminated.
Arches may be analyzed, designed, and constructed
as hinged under dead load or portions of dead load and
as fixed at some hinged locations for the remaining
design loads.
In trussed arches, considerable latitude is available
in design for distribution of stresses between the top and
bottom chords dependent on the manner of erection. In
such cases, the manner of erection should be indicated in
the contract documents.
C4.6.3.7
The distribution of force effects to the components
of a cable-stayed bridge may be determined by either
spatial or planar structural analysis if justified by
consideration of tower geometry, number of planes of
stays, and the torsional stiffness of the deck
superstructure.
Cable-stayed bridges shall be investigated for
nonlinear effects that may result from:
•
The change in cable sag at all limit states,
•
Deformation of deck superstructure and towers at
all limit states, and
•
Material nonlinearity at the extreme event limit
states.
Nonlinear effects on cable-stayed bridges are
treated in several texts, e.g., (Podolny and Scalzi, 1986;
Troitsky, 1977), and a report by the ASCE Committee
on Cable Suspended Bridges (ASCE, 1991), from which
the particular forms of Eqs. 4.6.3.7-1 and 4.6.3.7-2 were
taken.
Cable sag may be investigated using an equivalent
member modeled as a chord with modified modulus of
elasticity given by Eq. 4.6.3.7-1 for instantaneous
stiffness and Eq. 4.6.3.7-2, applied iteratively, for
changing cable loads.
EMOD
EAW 2(cos α ) 5
= E 1 +
12 H 3
−1
(4.6.3.7-1)
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EMOD
( H 1 + H 2 ) EAW 2 ( cos α )5
= E 1 +
24 H 12 H 2 2
−1
(4.6.3.7-2)
where:
E
W
A
α
H, H1,
H2
=
=
=
=
modulus of elasticity of the cable (ksi)
total weight of cable (kip)
cross-sectional area of cable (in.2)
angle between cable and horizontal (degrees)
=
horizontal component of cable force (kip)
The change in force effects due to deflection may
be investigated using any method that satisfies the
provisions of Article 4.5.3.2.1 and accounts for the
change in orientation of the ends of cable stays.
Cable-stayed bridges shall be investigated for the
loss of any one cable stay.
4.6.3.8—Suspension Bridges
Force effects in suspension bridges shall be
analyzed by the large deflection theory for vertical
loads. The effects of wind loads shall be analyzed, with
consideration of the tension stiffening of the cables. The
torsional rigidity of the deck may be neglected in
assigning forces to cables, suspenders, and components
of stiffening trusses.
C4.6.3.8
In the past, short suspension bridges have been
analyzed by conventional small deflection theories.
Correction factor methods have been used on short- to
moderate-span bridges to account for the effect of
deflection, which is especially significant for calculating
deck system moments. Any contemporary suspension
bridge would have a span such that the large deflection
theory should be used. Suitable computer programs are
commercially available. Therefore, there is little
rationale to use anything other than the large deflection
solution.
For the same economic reasons, the span would
probably be long enough that the influence of the
torsional rigidity of the deck, combined with the
relatively small effect of live load compared to dead
load, will make the simple sum-of-moments technique
suitable to assign loads to the cables and suspenders and
usually even to the deck system, e.g., a stiffening truss.
4.6.4—Redistribution of Negative Moments in
Continuous Beam Bridges
4.6.4.1—General
The Owner may permit the redistribution of force
effects in multispan, multibeam, or girder
superstructures. Inelastic behavior shall be restricted to
the flexure of beams or girders, and inelastic behavior
due to shear and/or uncontrolled buckling shall not be
permitted. Redistribution of loads shall not be
considered in the transverse direction.
The reduction of negative moments over the
internal supports due to the redistribution shall be
accompanied by a commensurate increase in the positive
moments in the spans.
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4.6.4.2—Refined Method
The negative moments over the support, as
established by linear elastic analysis, may be decreased
by a redistribution process considering the
moment-rotation characteristics of the cross-section or
by
a
recognized
mechanism
method.
The
moment-rotation relationship shall be established using
material characteristics, as specified herein, and/or
verified by physical testing.
4.6.4.3—Approximate Procedure
In lieu of the analysis described in Article 4.6.4.2,
simplified redistribution procedures for concrete and
steel beams, as specified in Sections 5 and 6,
respectively, may be used.
4.6.5—Stability
The investigation of stability shall utilize the large
deflection theory.
4.6.6—Analysis for Temperature Gradient
C4.6.6
Where determination of force effects due to vertical
temperature gradient is required, the analysis should
consider axial extension, flexural deformation, and
internal stresses.
Gradients shall be as specified in Article 3.12.3.
The response of a structure to a temperature
gradient can be divided into three effects as follows:
•
AXIAL EXPANSION—This is due to the uniform
component of the temperature distribution that
should be considered simultaneously with the
uniform temperature specified in Article 3.12.2. It
may be calculated as:
TUG =
1
TG dw dz
Ac
(C4.6.6-1)
The corresponding uniform axial strain is:
εu = α (TUG + Tu )
•
(C4.6.6-2)
FLEXURAL DEFORMATION—Because plane
sections remain plane, a curvature is imposed on the
superstructure to accommodate the linearly variable
component of the temperature gradient. The rotation
per unit length corresponding to this curvature may
be determined as:
φ=
α
Ic
TG z dw dz =
1
R
(C4.6.6-3)
If the structure is externally unrestrained, i.e.,
simply supported or cantilevered, no external force
effects are developed due to this superimposed
deformation.
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The axial strain and curvature may be used in both
flexibility and stiffness formulations. In the former,
εu may be used in place of P/AE, and φ may be used
in place of M/EI in traditional displacement
calculations. In the latter, the fixed-end force effects
for a prismatic frame element may be determined
as:
N = EAc εu
(C4.6.6-4)
M = EI c φ
(C4.6.6-5)
An expanded discussion with examples may be
found in Ghali and Neville (1989).
Strains induced by other effects, such as shrinkage
and creep, may be treated in a similar manner.
•
INTERNAL STRESS—Using the sign convention
that compression is positive, internal stresses in
addition to those corresponding to the restrained
axial expansion and/or rotation may be calculated
as:
σ E = E [ αTG − αTUG − φz ]
(C4.6.6-6)
where:
TG =
TUG =
Tu =
Ac =
Ic
=
α
E
R
w
z
=
=
=
=
=
temperature gradient (Δ°F)
temperature averaged across the cross-section
(°F)
uniform specified temperature (°F)
cross-section area—transformed for steel
beams (in.2)
inertia of cross-section—transformed for steel
beams (in.4)
coefficient of thermal expansion (in./in./°F)
modulus of elasticity (ksi)
radius of curvature (ft)
width of element in cross-section (in.)
vertical distance from center of gravity of
cross-section (in.)
For example, the flexural deformation part of the
gradient flexes a prismatic superstructure into a segment
of a circle in the vertical plane. For a two-span structure
with span length, L, in ft, the unrestrained beam would
lift off from the central support by Δ = 6 L2/R in in.
Forcing the beam down to eliminate Δ would develop a
moment whose value at the pier would be:
Mc =
3
EI c φ
2
(C4.6.6-7)
Therefore, the moment is a function of the beam rigidity
and imposed flexure. As rigidity approaches 0.0 at the
strength limit state, Mc tends to disappear. This behavior
also indicates the need for ductility to ensure structural
integrity as rigidity decreases.
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4.7—DYNAMIC ANALYSIS
4.7.1—Basic Requirements of Structural Dynamics
4.7.1.1—General
C4.7.1.1
For analysis of the dynamic behavior of bridges, the
stiffness, mass, and damping characteristics of the
structural components shall be modeled.
The minimum number of degrees-of-freedom
included in the analysis shall be based upon the number
of natural frequencies to be obtained and the reliability
of the assumed mode shapes. The model shall be
compatible with the accuracy of the solution method.
Dynamic models shall include relevant aspects of the
structure and the excitation. The relevant aspects of the
structure may include the:
•
Distribution of mass,
•
Distribution of stiffness, and
•
Damping characteristics.
The relevant aspects of excitation may include the:
•
Frequency of the forcing function,
•
Duration of application, and
•
Direction of application.
4.7.1.2—Distribution of Masses
The modeling of mass shall be made with
consideration of the degree of discretization in the
model and the anticipated motions.
Typically, analysis for vehicle- and wind-induced
vibrations is not to be considered in bridge design.
Although a vehicle crossing a bridge is not a static
situation, the bridge is analyzed by statically placing the
vehicle at various locations along the bridge and
applying a dynamic load allowance, as specified in
Article 3.6.2, to account for the dynamic responses
caused by the moving vehicle. However, in flexible
bridges and long slender components of bridges that
may be excited by bridge movement, dynamic force
effects may exceed the allowance for impact given in
Article 3.6.2. In most observed bridge vibration
problems, the natural structural damping has been very
low. Flexible continuous bridges may be especially
susceptible to vibrations. These cases may require
analysis for moving live load.
If the number of degrees-of-freedom in the model
exceeds the number of dynamic degrees-of-freedom used,
a standard condensation procedure may be employed.
Condensation procedures may be used to reduce the
number of degrees-of-freedom prior to the dynamic
analysis. Accuracy of the higher modes can be
compromised with condensation. Thus if higher modes are
required, such procedures should be used with caution.
The number of frequencies and mode shapes
necessary to complete a dynamic analysis should be
estimated in advance or determined as an early step in a
multistep approach. Having determined that number, the
model should be developed to have a larger number of
applicable degrees-of-freedom.
Sufficient degrees-of-freedom should be included to
represent the mode shapes relevant to the response
sought. One rule-of-thumb is that there should be twice
as many degrees-of-freedom as required frequencies.
The number of degrees-of-freedom and the
associated masses should be selected in a manner that
approximates the actual distributive nature of mass. The
number of required frequencies also depends on the
frequency content of the forcing function.
C4.7.1.2
The distribution of stiffness and mass should be
modeled in a dynamic analysis. The discretization of the
model should account for geometric and material
variation in stiffness and mass.
The selection of the consistent or lump mass
formulation is a function of the system and the response
sought and is difficult to generalize. For distributive
mass systems modeled with polynomial shape functions
in which the mass is associated with distributive
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stiffness, such as a beam, a consistent mass formulation
is recommended (Paz, 1985). In lieu of a consistent
formulation, lumped masses may be associated at the
translational degrees-of-freedom, a manner that
approximates the distributive nature of the mass (Clough
and Penzian, 1975).
For systems with distributive mass associated with
larger stiffness, such as in-plane stiffness of a bridge
deck, the mass may be properly modeled as lumped. The
rotational inertia effects should be included where
significant.
4.7.1.3—Stiffness
C4.7.1.3
The bridge shall be modeled to be consistent with
the degrees-of-freedom chosen to represent the natural
modes and frequencies of vibration. The stiffness of the
elements of the model shall be defined to be consistent
with the bridge being modeled.
4.7.1.4—Damping
In seismic analysis, nonlinear effects which
decrease stiffness, such as inelastic deformation and
cracking, should be considered.
Reinforced concrete columns and walls in Seismic
Zones 2, 3, and 4 should be analyzed using cracked
section properties. For this purpose, a moment of inertia
equal to one-half that of the uncracked section may be
used.
C4.7.1.4
Equivalent viscous damping may be used to
represent energy dissipation.
Damping may be neglected in the calculation of
natural frequencies and associated nodal displacements.
The effects of damping should be considered where a
transient response is sought.
Suitable damping values may be obtained from field
measurement of induced free vibration or by forced
vibration tests. In lieu of measurements, the following
values may be used for the equivalent viscous damping
ratio:
•
Concrete construction:
two percent
• Welded and bolted steel construction: one percent
•
Timber:
five percent
4.7.1.5—Natural Frequencies
For the purpose of Article 4.7.2, and unless
otherwise specified by the Owner, elastic undamped
natural modes and frequencies of vibration shall be used.
For the purpose of Articles 4.7.4 and 4.7.5, all relevant
damped modes and frequencies shall be considered.
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4.7.2—Elastic Dynamic Responses
4.7.2.1—Vehicle-Induced Vibration
When an analysis for dynamic interaction between a
bridge and the live load is required, the Owner shall
specify and/or approve surface roughness, speed, and
dynamic characteristics of the vehicles to be employed
for the analysis. Impact shall be derived as a ratio of the
extreme dynamic force effect to the corresponding static
force effect.
In no case shall the dynamic load allowance used in
design be less than 50 percent of the dynamic load
allowance specified in Table 3.6.2.1-1, except that no
reduction shall be allowed for deck joints.
C4.7.2.1
The limitation on the dynamic load allowance
reflects the fact that deck surface roughness is a major
factor in vehicle/bridge interaction and that it is difficult
to estimate long-term deck deterioration effects thereof
at the design stage.
The proper application of the provision for reducing
the dynamic load allowance is:
IM CALC ≥ 0.5IM Table 3-6
(C4.7.2.1-1)
not:
IM
IM
≥ 0.5 1 +
1 + 100
100
CALC
(C4.7.2.1-2)
4.7.2.2—Wind-Induced Vibration
4.7.2.2.1—Wind Velocities
For critical or essential structures, which may be
expected to be sensitive to wind effects, the location and
magnitude of extreme pressure and suction values shall
be established by simulated wind tunnel tests.
4.7.2.2.2—Dynamic Effects
Wind-sensitive structures shall be analyzed for
dynamic effects, such as buffeting by turbulent or
gusting winds, and unstable wind-structure interaction,
such as galloping and flutter. Slender or torsionally
flexible structures shall be analyzed for lateral buckling,
excessive thrust, and divergence.
4.7.2.2.3—Design Considerations
Oscillatory deformations under wind that may lead
to excessive stress levels, structural fatigue, and user
inconvenience or discomfort shall be avoided. Bridge
decks, cable stays, and hanger cables shall be protected
against excessive vortex and wind-rain-induced
oscillations. Where practical, the employment of
dampers shall be considered to control excessive
dynamic responses. Where dampers or shape
modification are not practical, the structural system shall
be changed to achieve such control.
C4.7.2.2.3
Additional information on design for wind may be
found in AASHTO (1985); Scanlan (1975); Simiu and
Scanlan (1978); Basu and Chi (1981a); Basu and Chi
(1981b); ASCE (1961); and ASCE (1991).
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4.7.3—Inelastic Dynamic Responses
4.7.3.1—General
During a major earthquake or ship collision, energy
may be dissipated by one or more of the following
mechanisms:
•
Elastic and inelastic deformation of the object that
may collide with the structure,
•
Inelastic deformation of the structure and its
attachments,
•
Permanent displacement of the masses of the
structure and its attachments, and
•
Inelastic deformation of special-purpose mechanical
energy dissipators.
4.7.3.2—Plastic Hinges and Yield Lines
For the purpose of analysis, energy absorbed by
inelastic deformation in a structural component may be
assumed to be concentrated in plastic hinges and yield
lines. The location of these sections may be established
by successive approximation to obtain a lower bound
solution for the energy absorbed. For these sections,
moment-rotation hysteresis curves may be determined
by using verified analytic material models.
4.7.4—Analysis for Earthquake Loads
4.7.4.1—General
Minimum analysis requirements for seismic effects
shall be as specified in Table 4.7.4.3.1-1.
For the modal methods of analysis, specified in
Articles 4.7.4.3.2 and 4.7.4.3.3, the design response
spectrum specified in Figure 3.10.4.1-1 and
Eqs. 3.10.4.2-1, 3.10.4.2-3, and 3.10.4.2.4 shall be used.
Bridges in Seismic Zone 1 need not be analyzed for
seismic loads, regardless of their operational
classification and geometry. However, the minimum
requirements, as specified in Articles 4.7.4.4 and 3.10.9,
shall apply.
4.7.4.2—Single-Span Bridges
Seismic analysis is not required for single-span
bridges, regardless of seismic zone.
Connections between the bridge superstructure and
the abutments shall be designed for the minimum force
requirements as specified in Article 3.10.9.
Minimum support length requirements shall be
satisfied at each abutment as specified in Article 4.7.4.4.
C4.7.4.2
A single-span bridge is comprised of a
superstructure unit supported by two abutments with no
intermediate piers.
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4.7.4.3—Multispan Bridges
4.7.4.3.1—Selection of Method
C4.7.4.3.1
For multispan structures, the minimum analysis
requirements shall be as specified in Table 4.7.4.3.1-1 in
which:
*
=
no seismic analysis required
UL
=
uniform load elastic method
SM
=
single-mode elastic method
MM
=
multimode elastic method
TH
=
time history method
The selection of the method of analysis depends on
seismic zone, regularity, and operational classification
of the bridge.
Regularity is a function of the number of spans and
the distribution of weight and stiffness. Regular bridges
have less than seven spans; no abrupt or unusual
changes in weight, stiffness, or geometry; and no large
changes in these parameters from span to span or
support-to-support, abutments excluded. A more
rigorous analysis procedure may be used in lieu of the
recommended minimum.
Table 4.7.4.3.1-1—Minimum Analysis Requirements for Seismic Effects
Seismic
Zone
1
2
3
4
Single-Span
Bridges
No seismic
analysis
required
Other Bridges
regular
irregular
*
*
SM/UL
SM
SM/UL
MM
SM/UL
MM
Multispan Bridges
Essential Bridges
regular
irregular
*
*
SM/UL
MM
MM
MM
MM
MM
Critical Bridges
regular
irregular
*
*
MM
MM
MM
TH
TH
TH
Except as specified below, bridges satisfying the
requirements of Table 4.7.4.3.1-2 may be taken as
“regular” bridges. Bridges not satisfying the
requirements of Table 4.7.4.3.1-2 shall be taken as
“irregular” bridges.
Table 4.7.4.3.1-2—Regular Bridge Requirements
Parameter
Number of Spans
Maximum subtended angle for a curved bridge
Maximum span length ratio from span to span
Maximum bent/pier stiffness ratio from span to span,
excluding abutments
2
90°
3
—
3
90°
2
4
Value
4
90°
2
4
5
90°
1.5
3
6
90°
1.5
2
Curved bridges comprised of multiple simple-spans
shall be considered to be “irregular” if the subtended
angle in plan is greater than 20 degrees. Such bridges
shall be analyzed by either the multimode elastic method
or the time-history method.
A curved continuous-girder bridge may be analyzed
as if it were straight, provided all of the following
requirements are satisfied:
•
The bridge is “regular” as defined in
Table 4.7.4.3.1-2, except that for a two-span bridge
the maximum span length ratio from span to span
must not exceed 2;
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•
The subtended angle in plan is not greater than
90 degrees; and
•
The span lengths of the equivalent straight bridge
are equal to the arc lengths of the curved bridge.
If these requirements are not satisfied, then curved
continuous-girder bridges must be analyzed using the
actual curved geometry.
4.7.4.3.2—Single-Mode Methods of Analysis
4.7.4.3.2a—General
Either of the two single-mode methods of analysis
specified herein may be used where appropriate.
C4.7.4.3.2b
4.7.4.3.2b—Single-Mode Spectral Method
The single-mode method of spectral analysis shall
be based on the fundamental mode of vibration in either
the longitudinal or transverse direction. For regular
bridges, the fundamental modes of vibration in the
horizontal plane coincide with the longitudinal and
transverse axes of the bridge structure. This mode shape
may be found by applying a uniform horizontal load to
the structure and calculating the corresponding
deformed shape. The natural period may be calculated
by equating the maximum potential and kinetic energies
associated with the fundamental mode shape. The
amplitude of the displaced shape may be found from the
elastic seismic response coefficient, Csm, specified in
Article 3.10.4.2, and the corresponding spectral
displacement. This amplitude shall be used to determine
force effects.
The single-mode spectral analysis method described
in the following steps may be used for both transverse
and longitudinal earthquake motions. Examples
illustrating its application are given in AASHTO (1983)
and ATC (1981).
•
Calculate the static displacements vs(x) due to an
assumed uniform loading po as shown in
Figure C4.7.4.3.2b-1:
Figure C4.7.4.3.2b-1—Bridge Deck Subjected to Assumed
Transverse and Longitudinal Loading
•
Calculate factors α, β, and γ as:
α = vs ( x ) dx
(C4.7.4.3.2b-1)
β = w ( x ) vs ( x ) dx
(C4.7.4.3.2b-2)
γ = w ( x ) vs 2 ( x ) dx
(C4.7.4.3.2b-3)
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where:
po
=
vs(x)
w(x)
=
=
a uniform load arbitrarily set equal to
1.0 (kip/ft)
deformation corresponding to po (ft)
nominal, unfactored dead load of the
bridge superstructure and tributary
substructure (kip/ft)
The computed factors, α, β, and γ have units of (ft2),
(kip-ft), and (kip-ft2), respectively.
•
Calculate the period of the bridge as:
Tm = 2π
γ
po g α
(C4.7.4.3.2b-4)
where:
acceleration of gravity (ft/sec.2)
g
=
•
Using Tm and Eqs. 3.10.4.2-1, 3.10.4.2-4, or
3.10.4.2-5, calculate Csm.
•
Calculate the equivalent static earthquake loading
pe(x) as:
pe ( x ) =
βCsm
w( x)vs ( x)
γ
(C4.7.4.3.2b-5)
where:
Csm
=
pe(x)
=
•
4.7.4.3.2c—Uniform Load Method
The uniform load method shall be based on the
fundamental mode of vibration in either the longitudinal
or transverse direction of the base structure. The period
of this mode of vibration shall be taken as that of an
equivalent single mass-spring oscillator. The stiffness of
this equivalent spring shall be calculated using the
maximum displacement that occurs when an arbitrary
uniform lateral load is applied to the bridge. The elastic
seismic response coefficient, Csm, specified in
Article 3.10.4.2 shall be used to calculate the equivalent
uniform seismic load from which seismic force effects
are found.
the dimensionless elastic seismic response
coefficient given by Eqs. 3.10.4.2-1,
3.10.4.2-4, or 3.10.4.2-5
the intensity of the equivalent static
seismic loading applied to represent the
primary mode of vibration (kip/ft)
Apply loading pe(x) to the structure, and determine
the resulting member force effects.
C4.7.4.3.2c
The uniform load method, described in the following
steps, may be used for both transverse and longitudinal
earthquake motions. It is essentially an equivalent static
method of analysis that uses a uniform lateral load to
approximate the effect of seismic loads. The method is
suitable for regular bridges that respond principally in their
fundamental mode of vibration. Whereas all displacements
and most member forces are calculated with good accuracy,
the method is known to overestimate the transverse shears at
the abutments by up to 100 percent. If such conservatism is
undesirable, then the single-mode spectral analysis method
specified in Article 4.7.4.3.2b is recommended.
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•
Calculate the static displacements vs(x) due to an
assumed uniform load po, as shown in
Figure C4.7.4.3.2b-1. The uniform loading po is
applied over the length of the bridge; it has units of
force per unit length and may be arbitrarily set
equal to 1.0. The static displacement vs(x) has units
of length.
•
Calculate the bridge lateral stiffness, K, and total
weight, W, from the following expressions:
po L
vs,MAX
(C4.7.4.3.2c-1)
W = w( x)dx
(C4.7.4.3.2c-2)
K=
where:
L
vs,MAX
w(x)
=
=
=
total length of the bridge (ft)
maximum value of vs(x) (ft)
nominal, unfactored dead load of the
bridge superstructure and tributary
substructure (kip/ft)
The weight should take into account structural
elements and other relevant loads including, but not
limited to, pier caps, abutments, columns, and footings.
Other loads, such as live loads, may be included.
Generally, the inertia effects of live loads are not
included in the analysis; however, the probability of a
large live load being on the bridge during an earthquake
should be considered when designing bridges with high
live-to-dead load ratios that are located in metropolitan
areas where traffic congestion is likely to occur.
•
Calculate the period of the bridge, Tm, using the
expression:
Tm = 2π
W
gK
(C4.7.4.3.2c-3)
where:
acceleration of gravity (ft/sec.2)
g
=
•
Calculate the equivalent static earthquake loading pe
from the expression:
pe =
CsmW
L
(C4.7.4.3.2c-4)
where:
Csm =
the dimensionless elastic seismic response
coefficient given by Eqs. 3.10.4.2-1, 3.10.4.2-4,
or 3.10.4.2-5
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pe
=
•
Calculate the displacements and member forces for
use in design either by applying pe to the structure
and performing a second static analysis or by
scaling the results of the first step above by the ratio
pe /po.
4.7.4.3.3—Multimode Spectral Method
The multimode spectral analysis method shall be
used for bridges in which coupling occurs in more than
one of the three coordinate directions within each mode
of vibration. As a minimum, linear dynamic analysis
using a three-dimensional model shall be used to
represent the structure.
The number of modes included in the analysis
should be at least three times the number of spans in the
model. The design seismic response spectrum as
specified in Article 3.10.4 shall be used for each mode.
The member forces and displacements may be
estimated by combining the respective response
quantities (moment, force, displacement, or relative
displacement) from the individual modes by the
Complete Quadratic Combination (CQC) method.
C4.7.4.3.3
Member forces and displacements obtained using
the CQC combination method are generally adequate for
most bridge systems (Wilson et al., 1981).
If the CQC method is not readily available,
alternative methods include the square root of the sum of
the squares method (SRSS), but this method is best
suited for combining responses from well-separated
modes. For closely spaced modes, the absolute sum of
the modal responses should be used.
4.7.4.3.4—Time-History Method
C4.7.4.3.4
4.7.4.3.4a—General
Any step-by-step time-history method of analysis
used for either elastic or inelastic analysis shall satisfy
the requirements of Article 4.7.
The sensitivity of the numerical solution to the size
of the time step used for the analysis shall be
determined. A sensitivity study shall also be carried out
to investigate the effects of variations in assumed
material hysteretic properties.
The time histories of input acceleration used to
describe the earthquake loads shall be selected in
accordance with Article 4.7.4.3.4b.
C4.7.4.3.4a
Rigorous methods of analysis are required for
critical structures, which are defined in Article 3.10.3,
and/or those that are geometrically complex or close to
active earthquake faults. Time history methods of
analysis are recommended for this purpose, provided
care is taken with both the modeling of the structure and
the selection of the input time histories of ground
acceleration.
C4.7.4.3.4b
4.7.4.3.4b—Acceleration Time Histories
Developed time histories shall have characteristics
that are representative of the seismic environment of the
site and the local site conditions.
Response-spectrum-compatible time histories shall
be used as developed from representative recorded
motions. Analytical techniques used for spectrum
matching shall be demonstrated to be capable of
equivalent uniform static seismic loading per
unit length of bridge applied to represent the
primary mode of vibration (kip/ft)
Characteristics of the seismic environment to be
considered in selecting time histories include:
•
Tectonic environment (e.g., subduction zone;
shallow crustal faults),
•
Earthquake magnitude,
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
achieving seismologically realistic time series that are
similar to the time series of the initial time histories
selected for spectrum matching.
Where recorded time histories are used, they shall
be scaled to the approximate level of the design response
spectrum in the period range of significance. Each time
history shall be modified to be response-spectrumcompatible using the time-domain procedure.
At least three response-spectrum-compatible time
histories shall be used for each component of motion in
representing the design earthquake (ground motions
having seven percent probability of exceedance in
75 yr). All three orthogonal components (x, y, and z) of
design motion shall be input simultaneously when
conducting a nonlinear time-history analysis. The design
actions shall be taken as the maximum response
calculated for the three ground motions in each principal
direction.
If a minimum of seven time histories are used for
each component of motion, the design actions may be
taken as the mean response calculated for each principal
direction.
For near-field sites (D < 6 mi), the recorded
horizontal components of motion that are selected
should represent a near-field condition and should be
transformed into principal components before making
them response-spectrum-compatible. The major
principal component should then be used to represent
motion in the fault-normal direction and the minor
principal component should be used to represent motion
in the fault-parallel direction.
•
Type of faulting (e.g., strike-slip; reverse; normal),
•
Seismic-source-to-site distance,
•
Local site conditions, and
•
Design or expected ground-motion characteristics
(e.g., design response spectrum, duration of strong
shaking, and special ground motion characteristics
such as near-fault characteristics)
Dominant earthquake magnitudes and distances,
which contribute principally to the probabilistic design
response spectra at a site, as determined from national
ground motion maps, can be obtained from
deaggregation information on the USGS website:
http://geohazards.cr.usgs.gov.
It is desirable to select time histories that have been
recorded under conditions similar to the seismic
conditions at the site listed above, but compromises are
usually required because of the multiple attributes of the
seismic environment and the limited data bank of
recorded time histories. Selection of time histories having
similar earthquake magnitudes and distances, within
reasonable ranges, are especially important parameters
because they have a strong influence on response spectral
content, response spectral shape, duration of strong
shaking, and near-source ground-motion characteristics. It
is desirable that selected recorded motions be somewhat
similar in overall ground motion level and spectral shape
to the design spectrum to avoid using very large scaling
factors with recorded motions and very large changes in
spectral content in the spectrum-matching approach. If the
site is located within 6 mi of an active fault, then
intermediate-to-long-period ground-motion pulses that are
characteristic of near-source time histories should be
included if these types of ground motion characteristics
could significantly influence structural response.
Similarly, the high short-period spectral content of nearsource vertical ground motions should be considered.
Ground motion modeling methods of strong motion
seismology are being increasingly used to supplement
the recorded ground motion database. These methods
are especially useful for seismic settings for which
relatively few actual strong motion recordings are
available, such as in the central and eastern United
States. Through analytical simulation of the earthquake
rupture and wave propagation process, these methods
can produce seismologically reasonable time series.
Response spectrum matching approaches include
methods in which time series adjustments are made in
the time domain (Lilhanand and Tseng, 1988;
Abrahamson, 1992) and those in which the adjustments
are made in the frequency domain (Gasparini and
Vanmarcke, 1976; Silva and Lee, 1987; Bolt and
Gregor, 1993). Both of these approaches can be used to
modify existing time histories to achieve a close match
to the design response spectrum while maintaining fairly
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-87
well the basic time domain character of the recorded or
simulated time histories. To minimize changes to the
time domain characteristics, it is desirable that the
overall shape of the spectrum of the recorded time
history not be greatly different from the shape of the
design response spectrum and that the time history
initially be scaled so that its spectrum is at the
approximate level of the design spectrum before
spectrum matching.
Where three-component sets of time histories are
developed by simple scaling rather than spectrum
matching, it is difficult to achieve a comparable
aggregate match to the design spectra for each
component of motion when using a single scaling factor
for each time history set. It is desirable, however, to use
a single scaling factor to preserve the relationship
between the components. Approaches for dealing with
this scaling issue include:
•
use of a higher scaling factor to meet the minimum
aggregate match requirement for one component
while exceeding it for the other two,
•
use of a scaling factor to meet the aggregate match
for the most critical component with the match
somewhat deficient for other components, and
•
Compromising on the scaling by using different
factors as required for different components of a
time-history set.
While the second approach is acceptable, it requires
careful examination and interpretation of the results and
possibly dual analyses for application of the higher
horizontal component in each principal horizontal
direction.
The requirements for the number of time histories to
be used in nonlinear inelastic dynamic analysis and for
the interpretation of the results take into account the
dependence of response on the time domain character of
the time histories (duration, pulse shape, pulse
sequencing) in addition to their response spectral content.
Additional guidance on developing acceleration
time histories for dynamic analysis may be found in
publications by the Caltrans Seismic Advisory Board
Adhoc Committee (CSABAC) on Soil-FoundationStructure Interaction (1999) and the U.S. Army Corps of
Engineers (2000). CSABAC (1999) also provides
detailed guidance on modeling the spatial variation of
ground motion between bridge piers and the conduct of
seismic soil-foundation-structure interaction (SFSI)
analyses. Both spatial variations of ground motion and
SFSI may significantly affect bridge response. Spatial
variations include differences between seismic wave
arrival times at bridge piers (wave passage effect),
ground motion incoherence due to seismic wave
scattering, and differential site response due to different
soil profiles at different bridge piers. For long bridges,
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
all forms of spatial variations may be important. For
short bridges, limited information appears to indicate
that wave passage effects and incoherence are, in
general, relatively unimportant in comparison to effects
of differential site response (Shinozuka et al., 1999;
Martin, 1998). Somerville et al. (1999) provide guidance
on the characteristics of pulses of ground motion that
occur in time histories in the near-fault region.
4.7.4.4—Minimum Support Length
Requirements
C4.7.4.4
Support lengths at expansion bearings without
restrainers, STUs, or dampers shall either accommodate
the greater of the maximum displacement calculated in
accordance with the provisions of Article 4.7.4.3, except
for bridges in Zone 1, or a percentage of the empirical
support length, N, specified by Eq. 4.7.4.4-1. Otherwise,
longitudinal restrainers complying with Article 3.10.9.5
shall be provided. Bearings restrained for longitudinal
movement shall be designed in compliance with
Article 3.10.9. The percentages of N, applicable to each
seismic zone, shall be as specified in Table 4.7.4.4-1.
The empirical support length shall be taken as:
N = ( 8 + 0.02 L + 0.08 H ) (1 + 0.000125S 2 )
Support lengths are equal to the length of the overlap
between the girder and the seat as shown in
Figure C4.7.4.4-1. To satisfy the minimum values for N in
this Article, the overall seat width will be larger than N by
an amount equal to movements due to prestress shortening,
creep, shrinkage, and thermal expansion/contraction. The
minimum value for N given in Eq. 4.7.4.4-1 includes an
arbitrary allowance for cover concrete at the end of the
girder and face of the seat. If above average cover is used at
these locations, N should be increased accordingly.
(4.7.4.4-1)
where:
N
=
L
=
H
=
minimum support length measured normal to
the centerline of bearing (in.)
length of the bridge deck to the adjacent
expansion joint, or to the end of the bridge
deck; for hinges within a span, L shall be the
sum of the distances to either side of the hinge;
for single-span bridges, L equals the length of
the bridge deck (ft)
for abutments, average height of columns
supporting the bridge deck from the abutment
to the next expansion joint (ft)
for columns and/or piers, column, or pier height
(ft)
Figure C4.7.4.4-1—Support Length, N
for hinges within a span, average height of the
adjacent two columns or piers (ft)
0.0 for single-span bridges (ft)
S
=
skew of support measured from line normal to
span (degrees)
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-89
Table 4.7.4.4-1—Percentage N by Zone and Acceleration
Coefficient AS, Specified in Eq. 3.10.4.2-2
Acceleration
Coefficient, AS
<0.05
≥0.05
All Applicable
All Applicable
All Applicable
Zone
1
1
2
3
4
Percent, N
≥75
100
150
150
150
4.7.4.5 P-∆ Requirements
C4.7.4.5
The displacement of any column or pier in the
longitudinal or transverse direction shall satisfy:
ΔPu < 0.25φM n
(4.7.4.5-1)
in which:
Δ = Rd Δ e
•
(4.7.4.5-2)
If T < 1.25Ts , then:
1 1.25Ts 1
Rd = 1 −
+
R
R T
•
(4.7.4.5-3)
If T ≥ 1.25Ts , then:
Rd = 1
(4.7.4.5-4)
where:
Δ
=
Δe =
T =
TS =
R =
Pu =
φ =
Mn =
displacement of the point of contraflexure in
the column or pier relative to the point of fixity
for the foundation (ft)
displacement calculated from elastic seismic
analysis (in.)
period of fundamental mode of vibration (sec.)
corner period specified in Article 3.10.4.2
(sec.)
R-factor specified in Article 3.10.7
axial load on column or pier (kip)
flexural resistance factor for column specified
in Article 5.10.11.4.1b
nominal flexural strength of column or pier
calculated at the axial load on the column or
pier (kip-ft)
Bridges subject to earthquake ground motion may
be susceptible to instability due to P-Δ effects.
Inadequate strength can result in ratcheting of structural
displacements to larger and larger values causing
excessive ductility demand on plastic hinges in the
columns, large residual deformations, and possibly
collapse. The maximum value for Δ given in this Article
is intended to limit the displacements such that P-Δ
effects will not significantly affect the response of the
bridge during an earthquake.
P-Δ effects lead to a loss in strength once yielding
occurs in the columns of a bridge. In severe cases, this
can result in the force-displacement relationship having
a negative slope once yield is fully developed. The value
for Δ given by Eq. 4.7.4.5-1 is such that this reduction in
strength is limited to 25 percent of the yield strength of
the pier or bent.
An explicit P-Δ check was not required in the
previous edition of these Specifications but has been
introduced herein because two conservative provisions
have been relaxed in this revised edition. These are:
•
The
shape
of
the
response
spectrum
(Figure 3.10.4.1-1) has been changed from being
proportional to 1/T2/3 to 1/T. The reason for the
1/T2/3 provision in the previous edition was to give
conservative estimates of force and displacement in
bridges with longer periods (>1.0 secs) which, in an
indirect way, provided for such effects as P-Δ. With
the change of the spectrum to being proportional to
1/T, an explicit check for P-Δ is now required.
•
The flexural resistance factor, φ, for seismic design of
columns with high axial loads has been increased from
a minimum value of 0.5 to 0.9 (Article 5.10.11.4.1b).
Use of a low resistance factor led to additional strength
being provided in heavily loaded columns that could
be used to offset reductions due to P-Δ, in the previous
edition. The increased value for φ now permitted in
Section 5 is a second reason for requiring an explicit
check for P-Δ.
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4.7.5—Analysis for Collision Loads
Where permitted by the provisions of Section 3,
dynamic analysis for ship collision may be replaced by
an equivalent static elastic analysis. Where an inelastic
analysis is specified, the effect of other loads that may
also be present shall be considered.
4.7.6—Analysis of Blast Effects
C4.7.6
As a minimum, bridge components analyzed for
blast forces should be designed for the dynamic effects
resulting from the blast pressure on the structure. The
results of an equivalent static analysis shall not be used
for this purpose.
Localized spall and breach damage should be
accounted for when designing bridge components for
blast forces. Data available at the time these provisions
were developed (winter 2010) are not sufficient to
develop expressions for estimating the extent of
spall/breach in concrete columns; however, spall and
breach damage can be estimated for other types of
components using guidelines found in Department of
Defense (2008a).
The highly impulsive nature of blast loads warrants
the consideration of inertial effects during the analysis
of a structural component. Past research has
demonstrated that, in general, an equivalent static
analysis is not acceptable for the design of any structural
member subjected to blast loads (Department of
Defense, 2008a; Department of Defense, 2002; Bounds,
1998; ASCE, 1997). Information on designing structures
to resist blast loads may be found in AASHTO’s Bridge
Security Guidelines (2011), ASCE (1997), Department
of Defense (2008a), Conrath, et al. (1999), Biggs (1964),
and Bounds (1998).
4.8—ANALYSIS BY PHYSICAL MODELS
4.8.1—Scale Model Testing
To establish and/or to verify structural behavior, the
Owner may require the testing of scale models of
structures and/or parts thereof. The dimensional and
material properties of the structure, as well as its
boundary conditions and loads, shall be modeled as
accurately as possible. For dynamic analysis, inertial
scaling, load/excitation, and damping functions shall be
applied as appropriate. For strength limit state tests,
factored dead load shall be simulated. The
instrumentation shall not significantly influence the
response of the model.
4.8.2—Bridge Testing
C4.8.2
Existing bridges may be instrumented and results
obtained under various conditions of traffic and/or
environmental loads or load tested with special purpose
vehicles to establish force effects and/or the loadcarrying capacity of the bridge.
These measured force effects may be used to project
fatigue life, to serve as a basis for similar designs, to
establish permissible weight limits, to aid in issuing
permits, or to establish a basis of prioritizing
rehabilitation or retrofit.
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4.9—REFERENCES
4-91
2013 Revision
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-93
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Hindi, W. A. 1991. “Behavior and Design of Stiffened Compression Flanges of Steel Box Girder Bridges.” Ph.D.
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Homberg, H. 1968. Fahrbahnplatten mit Verandlicher Dicke. Springer-Verlag, New York, NY.
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4-94
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
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SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-95
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2012
Edition
4-96
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
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2012
Edition
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4-97
APPENDIX A4—DECK SLAB DESIGN TABLE
Table A4-1 may be used in determining the design moments for different girder arrangements. The following
assumptions and limitations were used in developing this table and should be considered when using the listed values
for design:
•
The moments are calculated using the equivalent strip method as applied to concrete slabs supported on parallel
girders.
•
Multiple presence factors and the dynamic load allowance are included in the tabulated values.
•
See Article 4.6.2.1.6 for the distance between the center of the girders to the location of the design sections for
negative moments in the deck. Interpolation between the listed values may be used for distances other than those
listed in Table A4-1.
•
The moments are applicable for decks supported on at least three girders and having a width of not less than 14.0
ft between the centerlines of the exterior girders.
•
The moments represent the upper bound for the moments in the interior regions of the slab and, for any specific
girder spacing, were taken as the maximum value calculated, assuming different number of girders in the bridge
cross-section. For each combination of girder spacing and number of girders, the following two cases of overhang
width were considered:
(a) Minimum total overhang width of 21.0 in. measured from the center of the exterior girder, and
(b) Maximum total overhang width equal to the smaller of 0.625 times the girder spacing and 6.0 ft.
A railing system width of 21.0 in. was used to determine the clear overhang width. For other widths of
railing systems, the difference in the moments in the interior regions of the deck is expected to be within the
acceptable limits for practical design.
•
The moments do not apply to the deck overhangs and the adjacent regions of the deck that need to be designed
taking into account the provisions of Article A13.4.1.
•
It was found that the effect of two 25k axles of the tandem, placed at 4.0 ft from each other, produced maximum
effects under each of the tires approximately equal to the effect of the 32k truck axle. The tandem produces a
larger total moment, but this moment is spread over a larger width. It was concluded that repeating calculations
with a different strip width for the tandem would not result in a significant difference.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
4-98
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table A4-1—Maximum Live Load Moments per Unit Width, kip-ft/ft
Negative Moment
S
4’
4’
4’
4’
5’
5’
5’
5’
6’
6’
6’
6’
7’
7’
7’
7’
8’
8’
8’
8’
9’
9’
9’
9’
10’
10’
10’
10’
11’
11’
11’
11’
12’
12’
12’
12’
13’
13’
13’
13’
14’
14’
14’
14’
15’
–0”
–3”
–6”
–9”
–0”
–3”
–6”
–9”
–0”
–3”
–6”
–9”
–0”
–3”
–6”
–9”
–0”
–3”
–6”
–9”
–0”
–3”
–6”
–9”
–0”
–3”
–6”
–9”
–0”
–3”
–6”
–9”
–0”
–3”
–6”
–9”
–0”
–3”
–6”
–9”
–0”
–3”
–6”
–9”
–0”
Positive
Moment
4.68
4.66
4.63
4.64
4.65
4.67
4.71
4.77
4.83
4.91
5.00
5.10
5.21
5.32
5.44
5.56
5.69
5.83
5.99
6.14
6.29
6.44
6.59
6.74
6.89
7.03
7.17
7.32
7.46
7.60
7.74
7.88
8.01
8.15
8.28
8.41
8.54
8.66
8.78
8.90
9.02
9.14
9.25
9.36
9.47
Distance from CL of Girder to Design Section for Negative Moment
0.0 in.
2.68
2.73
3.00
3.38
3.74
4.06
4.36
4.63
4.88
5.10
5.31
5.50
5.98
6.13
6.26
6.38
6.48
6.58
6.66
6.74
6.81
6.87
7.15
7.51
7.85
8.19
8.52
8.83
9.14
9.44
9.72
10.01
10.28
10.55
10.81
11.06
11.31
11.55
11.79
12.02
12.24
12.46
12.67
12.88
13.09
3 in.
2.07
2.25
2.58
2.90
3.20
3.47
3.73
3.97
4.19
4.39
4.57
4.74
5.17
5.31
5.43
5.54
5.65
5.74
5.82
5.90
5.97
6.03
6.31
6.65
6.99
7.32
7.64
7.95
8.26
8.55
8.84
9.12
9.40
9.67
9.93
10.18
10.43
10.67
10.91
11.14
11.37
11.59
11.81
12.02
12.23
6 in.
1.74
1.95
2.19
2.43
2.66
2.89
3.11
3.31
3.50
3.68
3.84
3.99
4.36
4.49
4.61
4.71
4.81
4.90
4.98
5.06
5.13
5.19
5.46
5.80
6.13
6.45
6.77
7.08
7.38
7.67
7.96
8.24
8.51
8.78
9.04
9.30
9.55
9.80
10.03
10.27
10.50
10.72
10.94
11.16
11.37
9 in.
1.60
1.74
1.90
2.07
2.24
2.41
2.58
2.73
2.88
3.02
3.15
3.27
3.56
3.68
3.78
3.88
3.98
4.06
4.14
4.22
4.28
4.40
4.66
4.94
5.26
5.58
5.89
6.20
6.50
6.79
7.07
7.36
7.63
7.90
8.16
8.42
8.67
8.92
9.16
9.40
9.63
9.85
10.08
10.30
10.51
12 in.
1.50
1.57
1.65
1.74
1.83
1.95
2.07
2.19
2.31
2.42
2.53
2.64
2.84
2.96
3.15
3.30
3.43
3.53
3.61
3.67
3.71
3.82
4.04
4.21
4.41
4.71
5.02
5.32
5.62
5.91
6.19
6.47
6.74
7.02
7.28
7.54
7.79
8.04
8.28
8.52
8.76
8.99
9.21
9.44
9.65
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
18 in.
1.34
1.33
1.32
1.29
1.26
1.28
1.30
1.32
1.39
1.45
1.50
1.58
1.63
1.65
1.88
2.21
2.49
2.74
2.96
3.15
3.31
3.47
3.68
3.89
4.09
4.29
4.48
4.68
4.86
5.04
5.22
5.40
5.56
5.75
5.97
6.18
6.38
6.59
6.79
6.99
7.18
7.38
7.57
7.76
7.94
24 in.
1.25
1.20
1.18
1.20
1.12
0.98
0.99
1.02
1.07
1.13
1.20
1.28
1.37
1.51
1.72
1.94
2.16
2.37
2.58
2.79
3.00
3.20
3.39
3.58
3.77
3.96
4.15
4.34
4.52
4.70
4.87
5.05
5.21
5.38
5.54
5.70
5.86
6.01
6.16
6.30
6.45
6.58
6.72
6.86
7.02
2012
Edition
SECTION 5: CONCRETE STRUCTURES
TABLE OF CONTENTS
5
5.1—SCOPE ................................................................................................................................................................. 5-1
5.2—DEFINITIONS..................................................................................................................................................... 5-1
5.3—NOTATION ......................................................................................................................................................... 5-5
5.4—MATERIAL PROPERTIES .............................................................................................................................. 5-12
5.4.1—General ..................................................................................................................................................... 5-12
5.4.2—Normal Weight and Structural Lightweight Concrete ............................................................................. 5-13
5.4.2.1—Compressive Strength .................................................................................................................... 5-13
5.4.2.2—Coefficient of Thermal Expansion ................................................................................................. 5-15
5.4.2.3—Shrinkage and Creep ...................................................................................................................... 5-15
5.4.2.3.1—General ................................................................................................................................ 5-15
5.4.2.3.2—Creep ................................................................................................................................... 5-15
5.4.2.3.3—Shrinkage ............................................................................................................................. 5-17
5.4.2.4—Modulus of Elasticity ..................................................................................................................... 5-18
5.4.2.5—Poisson’s Ratio .............................................................................................................................. 5-18
5.4.2.6—Modulus of Rupture ....................................................................................................................... 5-18
5.4.2.7—Tensile Strength ............................................................................................................................. 5-19
5.4.3—Reinforcing Steel ..................................................................................................................................... 5-19
5.4.3.1—General .......................................................................................................................................... 5-19
5.4.3.2—Modulus of Elasticity ..................................................................................................................... 5-20
5.4.3.3—Special Applications ...................................................................................................................... 5-20
5.4.4—Prestressing Steel ..................................................................................................................................... 5-20
5.4.4.1—General .......................................................................................................................................... 5-20
5.4.4.2—Modulus of Elasticity ..................................................................................................................... 5-21
5.4.5—Post-Tensioning Anchorages and Couplers ............................................................................................. 5-21
5.4.6—Ducts ........................................................................................................................................................ 5-22
5.4.6.1—General .......................................................................................................................................... 5-22
5.4.6.2—Size of Ducts .................................................................................................................................. 5-22
5.4.6.3—Ducts at Deviation Saddles ............................................................................................................ 5-23
5.5—LIMIT STATES ................................................................................................................................................. 5-23
5.5.1—General ..................................................................................................................................................... 5-23
5.5.2—Service Limit State................................................................................................................................... 5-23
5.5.3—Fatigue Limit State................................................................................................................................... 5-23
5.5.3.1—General .......................................................................................................................................... 5-23
5.5.3.2—Reinforcing Bars ............................................................................................................................ 5-24
5.5.3.3—Prestressing Tendons ..................................................................................................................... 5-25
5.5.3.4—Welded or Mechanical Splices of Reinforcement.......................................................................... 5-25
5.5.4—Strength Limit State ................................................................................................................................. 5-26
5.5.4.1—General .......................................................................................................................................... 5-26
5.5.4.2—Resistance Factors ......................................................................................................................... 5-26
5.5.4.2.1—Conventional Construction .................................................................................................. 5-26
5.5.4.2.2—Segmental Construction ....................................................................................................... 5-28
5-i
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
5-ii
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
5.5.4.2.3—Special Requirements for Seismic Zones 2, 3, and 4 ........................................................... 5-28
5.5.4.3—Stability .......................................................................................................................................... 5-29
5.5.5—Extreme Event Limit State ....................................................................................................................... 5-29
5.6—DESIGN CONSIDERATIONS.......................................................................................................................... 5-29
5.6.1—General ..................................................................................................................................................... 5-29
5.6.2—Effects of Imposed Deformation .............................................................................................................. 5-29
5.6.3—Strut-and-Tie Model ................................................................................................................................. 5-29
5.6.3.1—General ........................................................................................................................................... 5-29
5.6.3.2—Structural Modeling ....................................................................................................................... 5-30
5.6.3.3—Proportioning of Compressive Struts ............................................................................................. 5-31
5.6.3.3.1—Strength of Unreinforced Strut............................................................................................. 5-31
5.6.3.3.2—Effective Cross-Sectional Area of Strut ............................................................................... 5-32
5.6.3.3.3—Limiting Compressive Stress in Strut .................................................................................. 5-33
5.6.3.3.4—Reinforced Strut ................................................................................................................... 5-33
5.6.3.4—Proportioning of Tension Ties ....................................................................................................... 5-33
5.6.3.4.1—Strength of Tie ..................................................................................................................... 5-33
5.6.3.4.2—Anchorage of Tie ................................................................................................................. 5-34
5.6.3.5—Proportioning of Node Regions ..................................................................................................... 5-34
5.6.3.6—Crack Control Reinforcement ........................................................................................................ 5-34
5.7—DESIGN FOR FLEXURAL AND AXIAL FORCE EFFECTS ........................................................................ 5-35
5.7.1—Assumptions for Service and Fatigue Limit States .................................................................................. 5-35
5.7.2—Assumptions for Strength and Extreme Event Limit States ..................................................................... 5-36
5.7.2.1—General ........................................................................................................................................... 5-36
5.7.2.2—Rectangular Stress Distribution...................................................................................................... 5-38
5.7.3—Flexural Members .................................................................................................................................... 5-39
5.7.3.1—Stress in Prestressing Steel at Nominal Flexural Resistance .......................................................... 5-39
5.7.3.1.1—Components with Bonded Tendons ..................................................................................... 5-39
5.7.3.1.2—Components with Unbonded Tendons ................................................................................. 5-40
5.7.3.1.3—Components with Both Bonded and Unbonded Tendons .................................................... 5-40
5.7.3.1.3a—Detailed Analysis ........................................................................................................ 5-40
5.7.3.1.3b—Simplified Analysis .................................................................................................... 5-41
5.7.3.2—Flexural Resistance ........................................................................................................................ 5-41
5.7.3.2.1—Factored Flexural Resistance ............................................................................................... 5-41
5.7.3.2.2—Flanged Sections .................................................................................................................. 5-41
5.7.3.2.3—Rectangular Sections............................................................................................................ 5-42
5.7.3.2.4—Other Cross-Sections ........................................................................................................... 5-43
5.7.3.2.5—Strain Compatibility Approach ............................................................................................ 5-43
5.7.3.3—Limits for Reinforcement ............................................................................................................... 5-43
5.7.3.3.1—Maximum Reinforcement .................................................................................................... 5-43
5.7.3.3.2 Minimum Reinforcement ....................................................................................................... 5-43
5.7.3.4—Control of Cracking by Distribution of Reinforcement ................................................................. 5-45
5.7.3.5—Moment Redistribution .................................................................................................................. 5-47
5.7.3.6—Deformations.................................................................................................................................. 5-47
5.7.3.6.1—General ................................................................................................................................. 5-47
5.7.3.6.2—Deflection and Camber ........................................................................................................ 5-47
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
TABLE OF CONTENTS
5-iii
5.7.3.6.3—Axial Deformation ............................................................................................................... 5-48
5.7.4—Compression Members ............................................................................................................................ 5-48
5.7.4.1—General .......................................................................................................................................... 5-48
5.7.4.2—Limits for Reinforcement............................................................................................................... 5-49
5.7.4.3—Approximate Evaluation of Slenderness Effects ........................................................................... 5-50
5.7.4.4—Factored Axial Resistance ............................................................................................................. 5-51
5.7.4.5—Biaxial Flexure .............................................................................................................................. 5-52
5.7.4.6—Spirals and Ties ............................................................................................................................. 5-53
5.7.4.7—Hollow Rectangular Compression Members ................................................................................. 5-53
5.7.4.7.1—Wall Slenderness Ratio ........................................................................................................ 5-53
5.7.4.7.2—Limitations on the Use of the Rectangular Stress Block Method ........................................ 5-54
5.7.4.7.2a—General ....................................................................................................................... 5-54
5.7.4.7.2b—Refined Method for Adjusting Maximum Usable Strain Limit .................................. 5-54
5.7.4.7.2c—Approximate Method for Adjusting Factored Resistance ........................................... 5-55
5.7.5—Bearing ..................................................................................................................................................... 5-55
5.7.6—Tension Members .................................................................................................................................... 5-56
5.7.6.1—Factored Tension Resistance ......................................................................................................... 5-56
5.7.6.2—Resistance to Combinations of Tension and Flexure ..................................................................... 5-56
5.8—SHEAR AND TORSION................................................................................................................................... 5-56
5.8.1—Design Procedures ................................................................................................................................... 5-56
5.8.1.1—Flexural Regions ............................................................................................................................ 5-56
5.8.1.2—Regions Near Discontinuities ........................................................................................................ 5-57
5.8.1.3—Interface Regions ........................................................................................................................... 5-57
5.8.1.4—Slabs and Footings ......................................................................................................................... 5-57
5.8.1.5—Webs of Curved Post-Tensioned Box Girder Bridges ................................................................... 5-57
5.8.2—General Requirements.............................................................................................................................. 5-57
5.8.2.1—General .......................................................................................................................................... 5-57
5.8.2.2—Modifications for Lightweight Concrete ....................................................................................... 5-59
5.8.2.3—Transfer and Development Lengths ............................................................................................... 5-60
5.8.2.4—Regions Requiring Transverse Reinforcement .............................................................................. 5-60
5.8.2.5—Minimum Transverse Reinforcement ............................................................................................ 5-60
5.8.2.6—Types of Transverse Reinforcement .............................................................................................. 5-61
5.8.2.7—Maximum Spacing of Transverse Reinforcement ......................................................................... 5-62
5.8.2.8—Design and Detailing Requirements .............................................................................................. 5-62
5.8.2.9—Shear Stress on Concrete ............................................................................................................... 5-63
5.8.3—Sectional Design Model ........................................................................................................................... 5-64
5.8.3.1—General .......................................................................................................................................... 5-64
5.8.3.2—Sections Near Supports .................................................................................................................. 5-65
5.8.3.3—Nominal Shear Resistance ............................................................................................................. 5-67
5.8.3.4—Procedures for Determining Shear Resistance ............................................................................... 5-68
5.8.3.4.1—Simplified Procedure for Nonprestressed Sections.............................................................. 5-69
5.8.3.4.2—General Procedure ............................................................................................................... 5-69
5.8.3.4.3—Simplified Procedure for Prestressed and Nonprestressed Sections ................................... 5-73
5.8.3.5—Longitudinal Reinforcement .......................................................................................................... 5-75
5.8.3.6—Sections Subjected to Combined Shear and Torsion ..................................................................... 5-77
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
5-iv
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
5.8.3.6.1—Transverse Reinforcement ................................................................................................... 5-77
5.8.3.6.2—Torsional Resistance ............................................................................................................ 5-77
5.8.3.6.3—Longitudinal Reinforcement ................................................................................................ 5-77
5.8.4—Interface Shear Transfer—Shear Friction ................................................................................................ 5-78
5.8.4.1—General ........................................................................................................................................... 5-78
5.8.4.2—Computation of the Factored Interface Shear Force, Vui, for Girder/Slab Bridges......................... 5-80
5.8.4.3—Cohesion and Friction Factors ....................................................................................................... 5-82
5.8.4.4—Minimum Area of Interface Shear Reinforcement ......................................................................... 5-83
5.8.5—Principal Stresses in Webs of Segmental Concrete Bridges..................................................................... 5-84
5.8.6—Shear and Torsion for Segmental Box Girder Bridges ............................................................................. 5-85
5.8.6.1—General ........................................................................................................................................... 5-85
5.8.6.2—Loading .......................................................................................................................................... 5-85
5.8.6.3—Regions Requiring Consideration of Torsional Effects.................................................................. 5-86
5.8.6.4—Torsional Reinforcement................................................................................................................ 5-87
5.8.6.5—Nominal Shear Resistance ............................................................................................................. 5-88
5.8.6.6—Reinforcement Details.................................................................................................................... 5-89
5.9—PRESTRESSING ............................................................................................................................................... 5-90
5.9.1—General Design Considerations ................................................................................................................ 5-90
5.9.1.1—General ........................................................................................................................................... 5-90
5.9.1.2—Specified Concrete Strengths ......................................................................................................... 5-91
5.9.1.3—Buckling ......................................................................................................................................... 5-91
5.9.1.4—Section Properties .......................................................................................................................... 5-91
5.9.1.5—Crack Control ................................................................................................................................. 5-91
5.9.1.6—Tendons with Angle Points or Curves............................................................................................ 5-91
5.9.2—Stresses Due to Imposed Deformation ..................................................................................................... 5-92
5.9.3—Stress Limitations for Prestressing Tendons ............................................................................................ 5-92
5.9.4—Stress Limits for Concrete ........................................................................................................................ 5-93
5.9.4.1—For Temporary Stresses before Losses—Fully Prestressed Components ...................................... 5-93
5.9.4.1.1—Compression Stresses........................................................................................................... 5-93
5.9.4.1.2—Tension Stresses ................................................................................................................... 5-93
5.9.4.2—For Stresses at Service Limit State after Losses—Fully Prestressed Components ........................ 5-95
5.9.4.2.1—Compression Stresses........................................................................................................... 5-95
5.9.4.2.2—Tension Stresses ................................................................................................................... 5-97
5.9.5—Loss of Prestress....................................................................................................................................... 5-98
5.9.5.1—Total Loss of Prestress ................................................................................................................... 5-98
5.9.5.2—Instantaneous Losses ...................................................................................................................... 5-98
5.9.5.2.1—Anchorage Set ...................................................................................................................... 5-98
5.9.5.2.2—Friction ................................................................................................................................. 5-99
5.9.5.2.2a—Pretensioned Construction .......................................................................................... 5-99
5.9.5.2.2b—Post-Tensioned Construction ...................................................................................... 5-99
5.9.5.2.3—Elastic Shortening .............................................................................................................. 5-101
5.9.5.2.3a—Pretensioned Members ..............................................................................................5-101
5.9.5.2.3b—Post-Tensioned Members ......................................................................................... 5-102
5.9.5.2.3c—Combined Pretensioning and Post-Tensioning ......................................................... 5-103
5.9.5.3—Approximate Estimate of Time-Dependent Losses...................................................................... 5-103
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
TABLE OF CONTENTS
5-v
5.9.5.4—Refined Estimates of Time-Dependent Losses ............................................................................ 5-104
5.9.5.4.1—General .............................................................................................................................. 5-104
5.9.5.4.2—Losses: Time of Transfer to Time of Deck Placement ...................................................... 5-105
5.9.5.4.2a—Shrinkage of Girder Concrete ................................................................................... 5-105
5.9.5.4.2b—Creep of Girder Concrete ......................................................................................... 5-106
5.9.5.4.2c—Relaxation of Prestressing Strands ........................................................................... 5-106
5.9.5.4.3—Losses: Time of Deck Placement to Final Time ............................................................... 5-107
5.9.5.4.3a—Shrinkage of Girder Concrete ................................................................................... 5-107
5.9.5.4.3b—Creep of Girder Concrete ......................................................................................... 5-108
5.9.5.4.3c—Relaxation of Prestressing Strands ........................................................................... 5-108
5.9.5.4.3d—Shrinkage of Deck Concrete ..................................................................................... 5-108
5.9.5.4.4—Precast Pretensioned Girders without Composite Topping ............................................... 5-109
5.9.5.4.5—Post-Tensioned Nonsegmental Girders ............................................................................. 5-109
5.9.5.5—Losses for Deflection Calculations .............................................................................................. 5-109
5.10—DETAILS OF REINFORCEMENT .............................................................................................................. 5-110
5.10.1—Concrete Cover .................................................................................................................................... 5-110
5.10.2—Hooks and Bends ................................................................................................................................. 5-110
5.10.2.1—Standard Hooks.......................................................................................................................... 5-110
5.10.2.2—Seismic Hooks ........................................................................................................................... 5-110
5.10.2.3—Minimum Bend Diameters......................................................................................................... 5-110
5.10.3—Spacing of Reinforcement.................................................................................................................... 5-111
5.10.3.1 Minimum Spacing of Reinforcing Bars ....................................................................................... 5-111
5.10.3.1.1—Cast-in-Place Concrete .................................................................................................... 5-111
5.10.3.1.2—Precast Concrete .............................................................................................................. 5-111
5.10.3.1.3—Multilayers ....................................................................................................................... 5-111
5.10.3.1.4—Splices.............................................................................................................................. 5-112
5.10.3.1.5—Bundled Bars ................................................................................................................... 5-112
5.10.3.2—Maximum Spacing of Reinforcing Bars .................................................................................... 5-112
5.10.3.3—Minimum Spacing of Prestressing Tendons and Ducts ............................................................. 5-112
5.10.3.3.1—Pretensioning Strand ........................................................................................................ 5-112
5.10.3.3.2—Post-Tensioning Ducts—Girders Straight in Plan ........................................................... 5-113
5.10.3.3.3—Post-Tensioning Ducts—Girders Curved in Plan ............................................................ 5-113
5.10.3.4—Maximum Spacing of Prestressing Tendons and Ducts in Slabs ............................................... 5-113
5.10.3.5—Couplers in Post-Tensioning Tendons ....................................................................................... 5-114
5.10.4—Tendon Confinement ........................................................................................................................... 5-114
5.10.4.1—General....................................................................................................................................... 5-114
5.10.4.2—Wobble Effect in Slabs .............................................................................................................. 5-114
5.10.4.3—Effects of Curved Tendons ........................................................................................................ 5-114
5.10.4.3.1—Design for In-Plane Force Effects ................................................................................... 5-115
5.10.4.3.1a—In-Plane Force Effects ............................................................................................ 5-115
5.10.4.3.1b— Shear Resistance to Pull-out .................................................................................. 5-116
5.10.4.3.1c— Cracking of Cover Concrete .................................................................................. 5-117
5.10.4.3.1d—Regional Bending ................................................................................................... 5-118
5.10.4.3.2—Out-of-Plane Force Effects .............................................................................................. 5-118
5.10.5—External Tendon Supports.................................................................................................................... 5-119
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
5-vi
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
5.10.6—Transverse Reinforcement for Compression Members ........................................................................ 5-119
5.10.6.1—General ....................................................................................................................................... 5-119
5.10.6.2—Spirals ........................................................................................................................................ 5-119
5.10.6.3—Ties............................................................................................................................................. 5-120
5.10.7—Transverse Reinforcement for Flexural Members ................................................................................ 5-121
5.10.8—Shrinkage and Temperature Reinforcement ......................................................................................... 5-121
5.10.9—Post-Tensioned Anchorage Zones ........................................................................................................ 5-122
5.10.9.1—General ....................................................................................................................................... 5-122
5.10.9.2—General Zone and Local Zone .................................................................................................... 5-123
5.10.9.2.1—General ............................................................................................................................. 5-123
5.10.9.2.2—General Zone.................................................................................................................... 5-124
5.10.9.2.3—Local Zone ....................................................................................................................... 5-124
5.10.9.2.4—Responsibilities ................................................................................................................ 5-125
5.10.9.3—Design of the General Zone ....................................................................................................... 5-125
5.10.9.3.1—Design Methods ............................................................................................................... 5-125
5.10.9.3.2—Design Principles ............................................................................................................. 5-126
5.10.9.3.3—Special Anchorage Devices ............................................................................................. 5-129
5.10.9.3.4—Intermediate Anchorages ................................................................................................. 5-129
5.10.9.3.4a—General .................................................................................................................... 5-129
5.10.9.3.4b—Tie-Backs ................................................................................................................ 5-130
5.10.9.3.4c—Blister and Rib Reinforcement ................................................................................ 5-130
5.10.9.3.5—Diaphragms ...................................................................................................................... 5-131
5.10.9.3.6—Multiple Slab Anchorages................................................................................................ 5-131
5.10.9.3.7—Deviation Saddles ............................................................................................................ 5-132
5.10.9.4—Application of the Strut-and-Tie Model to the Design of General Zone.................................... 5-132
5.10.9.4.1—General ............................................................................................................................. 5-132
5.10.9.4.2—Nodes ............................................................................................................................... 5-134
5.10.9.4.3—Struts ................................................................................................................................ 5-136
5.10.9.4.4—Ties .................................................................................................................................. 5-136
5.10.9.5—Elastic Stress Analysis ............................................................................................................... 5-136
5.10.9.6—Approximate Stress Analyses and Design ................................................................................. 5-137
5.10.9.6.1—Limitations of Application ............................................................................................... 5-137
5.10.9.6.2—Compressive Stresses ....................................................................................................... 5-138
5.10.9.6.3—Bursting Forces ................................................................................................................ 5-140
5.10.9.6.4—Edge Tension Forces ........................................................................................................ 5-141
5.10.9.7—Design of Local Zones ............................................................................................................... 5-142
5.10.9.7.1—Dimensions of Local Zone ............................................................................................... 5-142
5.10.9.7.2—Bearing Resistance ........................................................................................................... 5-143
5.10.9.7.3—Special Anchorage Devices ............................................................................................. 5-144
5.10.10—Pretensioned Anchorage Zones .......................................................................................................... 5-144
5.10.10.1—Splitting Resistance .................................................................................................................. 5-144
5.10.10.2—Confinement Reinforcement .................................................................................................... 5-146
5.10.11—Provisions for Seismic Design ........................................................................................................... 5-147
5.10.11.1—General ..................................................................................................................................... 5-147
5.10.11.2—Seismic Zone 1 ......................................................................................................................... 5-148
5.10.11.3—Seismic Zone 2 ......................................................................................................................... 5-148
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
TABLE OF CONTENTS
5-vii
5.10.11.4—Seismic Zones 3 and 4 ............................................................................................................. 5-149
5.10.11.4.1—Column Requirements ................................................................................................... 5-149
5.10.11.4.1a—Longitudinal Reinforcement ................................................................................. 5-149
5.10.11.4.1b—Flexural Resistance............................................................................................... 5-149
5.10.11.4.1c—Column Shear and Transverse Reinforcement...................................................... 5-150
5.10.11.4.1d—Transverse Reinforcement for Confinement at Plastic Hinges ............................. 5-151
5.10.11.4.1e—Spacing of Transverse Reinforcement for Confinement ....................................... 5-153
5.10.11.4.1f—Splices ................................................................................................................... 5-153
5.10.11.4.2—Requirements for Wall-Type Piers ................................................................................ 5-154
5.10.11.4.3—Column Connections ..................................................................................................... 5-155
5.10.11.4.4—Construction Joints in Piers and Columns ..................................................................... 5-155
5.10.12—Reinforcement for Hollow Rectangular Compression Members ....................................................... 5-156
5.10.12.1—General..................................................................................................................................... 5-156
5.10.12.2—Spacing of Reinforcement ....................................................................................................... 5-156
5.10.12.3—Ties .......................................................................................................................................... 5-156
5.10.12.4—Splices ...................................................................................................................................... 5-156
5.10.12.5—Hoops ....................................................................................................................................... 5-157
5.11—DEVELOPMENT AND SPLICES OF REINFORCEMENT........................................................................ 5-157
5.11.1—General ................................................................................................................................................. 5-157
5.11.1.1—Basic Requirements ................................................................................................................... 5-157
5.11.1.2—Flexural Reinforcement ............................................................................................................. 5-157
5.11.1.2.1—General ............................................................................................................................ 5-157
5.11.1.2.2—Positive Moment Reinforcement ..................................................................................... 5-158
5.11.1.2.3—Negative Moment Reinforcement.................................................................................... 5-159
5.11.1.2.4—Moment Resisting Joints.................................................................................................. 5-159
5.11.2—Development of Reinforcement ........................................................................................................... 5-160
5.11.2.1—Deformed Bars and Deformed Wire in Tension ........................................................................ 5-160
5.11.2.1.1—Tension Development Length.......................................................................................... 5-160
5.11.2.1.2—Modification Factors which Increase ℓd........................................................................... 5-161
5.11.2.1.3—Modification Factors which Decrease ℓd ........................................................................... 5-161
5.11.2.2—Deformed Bars in Compression ................................................................................................. 5-162
5.11.2.2.1—Compressive Development Length .................................................................................. 5-162
5.11.2.2.2—Modification Factors........................................................................................................ 5-162
5.11.2.3—Bundled Bars ............................................................................................................................. 5-162
5.11.2.4—Standard Hooks in Tension ........................................................................................................ 5-163
5.11.2.4.1—Basic Hook Development Length .................................................................................... 5-163
5.11.2.4.2—Modification Factors........................................................................................................ 5-163
5.11.2.4.3—Hooked-Bar Tie Requirements ........................................................................................ 5-164
5.11.2.5—Welded Wire Fabric ................................................................................................................... 5-164
5.11.2.5.1—Deformed Wire Fabric ..................................................................................................... 5-164
5.11.2.5.2—Plain Wire Fabric ............................................................................................................. 5-165
5.11.2.6—Shear Reinforcement ................................................................................................................. 5-165
5.11.2.6.1—General ............................................................................................................................ 5-165
5.11.2.6.2—Anchorage of Deformed Reinforcement.......................................................................... 5-166
5.11.2.6.3—Anchorage of Wire Fabric Reinforcement....................................................................... 5-166
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
5-viii
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
5.11.2.6.4—Closed Stirrups................................................................................................................. 5-167
5.11.3—Development by Mechanical Anchorages ............................................................................................ 5-167
5.11.4—Development of Prestressing Strand .................................................................................................... 5-167
5.11.4.1—General ....................................................................................................................................... 5-167
5.11.4.2—Bonded Strand ............................................................................................................................ 5-168
5.11.4.3—Partially Debonded Strands ........................................................................................................ 5-169
5.11.5—Splices of Bar Reinforcement .............................................................................................................. 5-170
5.11.5.1—Detailing..................................................................................................................................... 5-170
5.11.5.2—General Requirements ................................................................................................................ 5-170
5.11.5.2.1—Lap Splices....................................................................................................................... 5-170
5.11.5.2.2—Mechanical Connections .................................................................................................. 5-171
5.11.5.2.3—Welded Splices ................................................................................................................ 5-171
5.11.5.3—Splices of Reinforcement in Tension ......................................................................................... 5-171
5.11.5.3.1—Lap Splices in Tension ..................................................................................................... 5-171
5.11.5.3.2—Mechanical Connections or Welded Splices in Tension .................................................. 5-172
5.11.5.4—Splices in Tension Tie Members ................................................................................................ 5-172
5.11.5.5—Splices of Bars in Compression ................................................................................................. 5-172
5.11.5.5.1—Lap Splices in Compression............................................................................................. 5-172
5.11.5.5.2—Mechanical Connections or Welded Splices in Compression .......................................... 5-173
5.11.5.5.3—End-Bearing Splices......................................................................................................... 5-173
5.11.6—Splices of Welded Wire Fabric ............................................................................................................ 5-173
5.11.6.1—Splices of Welded Deformed Wire Fabric in Tension ............................................................... 5-173
5.11.6.2—Splices of Welded Smooth Wire Fabric in Tension ................................................................... 5-173
5.12—DURABILITY ............................................................................................................................................... 5-174
5.12.1—General ................................................................................................................................................. 5-174
5.12.2—Alkali-Silica Reactive Aggregates ....................................................................................................... 5-175
5.12.3—Concrete Cover .................................................................................................................................... 5-175
5.12.4—Protective Coatings .............................................................................................................................. 5-176
5.12.5—Protection for Prestressing Tendons ..................................................................................................... 5-176
5.13—SPECIFIC MEMBERS .................................................................................................................................. 5-177
5.13.1—Deck Slabs............................................................................................................................................ 5-177
5.13.2—Diaphragms, Deep Beams, Brackets, Corbels, and Beam Ledges ....................................................... 5-177
5.13.2.1—General ....................................................................................................................................... 5-177
5.13.2.2—Diaphragms ................................................................................................................................ 5-177
5.13.2.3—Detailing Requirements for Deep Beams ................................................................................... 5-178
5.13.2.4—Brackets and Corbels ................................................................................................................. 5-179
5.13.2.4.1—General ............................................................................................................................. 5-179
5.13.2.4.2—Alternative to Strut-and-Tie Model.................................................................................. 5-181
5.13.2.5—Beam Ledges .............................................................................................................................. 5-182
5.13.2.5.1—General ............................................................................................................................. 5-182
5.13.2.5.2—Design for Shear .............................................................................................................. 5-183
5.13.2.5.3—Design for Flexure and Horizontal Force......................................................................... 5-184
5.13.2.5.4—Design for Punching Shear .............................................................................................. 5-184
5.13.2.5.5—Design of Hanger Reinforcement .................................................................................... 5-185
5.13.2.5.6—Design for Bearing ........................................................................................................... 5-186
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
TABLE OF CONTENTS
5-ix
5.13.3—Footings ............................................................................................................................................... 5-187
5.13.3.1—General....................................................................................................................................... 5-187
5.13.3.2—Loads and Reactions .................................................................................................................. 5-187
5.13.3.3—Resistance Factors ..................................................................................................................... 5-187
5.13.3.4—Moment in Footings ................................................................................................................... 5-187
5.13.3.5—Distribution of Moment Reinforcement..................................................................................... 5-188
5.13.3.6—Shear in Slabs and Footings ....................................................................................................... 5-188
5.13.3.6.1—Critical Sections for Shear ............................................................................................... 5-188
5.13.3.6.2—One-Way Action .............................................................................................................. 5-189
5.13.3.6.3—Two-Way Action ............................................................................................................. 5-189
5.13.3.7—Development of Reinforcement ................................................................................................. 5-190
5.13.3.8—Transfer of Force at Base of Column ......................................................................................... 5-190
5.13.4—Concrete Piles ...................................................................................................................................... 5-191
5.13.4.1—General....................................................................................................................................... 5-191
5.13.4.2—Splices........................................................................................................................................ 5-191
5.13.4.3—Precast Reinforced Piles ............................................................................................................ 5-192
5.13.4.3.1—Pile Dimensions ............................................................................................................... 5-192
5.13.4.3.2—Reinforcing Steel ............................................................................................................. 5-192
5.13.4.4—Precast Prestressed Piles ............................................................................................................ 5-192
5.13.4.4.1—Pile Dimensions ............................................................................................................... 5-192
5.13.4.4.2—Concrete Quality .............................................................................................................. 5-192
5.13.4.4.3—Reinforcement ................................................................................................................. 5-193
5.13.4.5—Cast-in-Place Piles ..................................................................................................................... 5-193
5.13.4.5.1—Pile Dimensions ............................................................................................................... 5-194
5.13.4.5.2—Reinforcing Steel ............................................................................................................. 5-194
5.13.4.6—Seismic Requirements ............................................................................................................... 5-194
5.13.4.6.1—Zone 1 .............................................................................................................................. 5-194
5.13.4.6.2—Zone 2 .............................................................................................................................. 5-194
5.13.4.6.2a—General.................................................................................................................... 5-194
5.13.4.6.2b—Cast-in-Place Piles .................................................................................................. 5-195
5.13.4.6.2c—Precast Reinforced Piles ......................................................................................... 5-195
5.13.4.6.2d—Precast Prestressed Piles ......................................................................................... 5-195
5.13.4.6.3—Zones 3 and 4................................................................................................................... 5-195
5.13.4.6.3a—General.................................................................................................................... 5-195
5.13.4.6.3b—Confinement Length ............................................................................................... 5-195
5.13.4.6.3c—Volumetric Ratio for Confinement ......................................................................... 5-196
5.13.4.6.3d—Cast-in-Place Piles .................................................................................................. 5-196
5.13.4.6.3e—Precast Piles ............................................................................................................ 5-196
5.14—PROVISIONS FOR STRUCTURE TYPES .................................................................................................. 5-196
5.14.1—Beams and Girders ............................................................................................................................... 5-196
5.14.1.1—General....................................................................................................................................... 5-196
5.14.1.2—Precast Beams ............................................................................................................................ 5-197
5.14.1.2.1—Preservice Conditions ...................................................................................................... 5-197
5.14.1.2.2—Extreme Dimensions........................................................................................................ 5-197
5.14.1.2.3—Lifting Devices ................................................................................................................ 5-197
© 2012 by the American Association of State Highway and Transportation Officials.
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Edition
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
5.14.1.2.4—Detail Design ................................................................................................................... 5-197
5.14.1.2.5—Concrete Strength............................................................................................................. 5-198
5.14.1.3—Spliced Precast Girders .............................................................................................................. 5-198
5.14.1.3.1—General ............................................................................................................................. 5-198
5.14.1.3.2—Joints between Segments ................................................................................................. 5-199
5.14.1.3.2a—General .................................................................................................................... 5-199
5.14.1.3.2b—Details of Closure Joints ......................................................................................... 5-199
5.14.1.3.2c—Details of Match-Cast Joints ................................................................................... 5-200
5.14.1.3.2d—Joint Design ............................................................................................................ 5-200
5.14.1.3.3—Girder Segment Design .................................................................................................... 5-200
5.14.1.3.4—Post-Tensioning ............................................................................................................... 5-201
5.14.1.4—Bridges Composed of Simple Span Precast Girders Made Continuous ..................................... 5-201
5.14.1.4.1—General ............................................................................................................................. 5-201
5.14.1.4.2—Restraint Moments ........................................................................................................... 5-202
5.14.1.4.3—Material Properties ........................................................................................................... 5-203
5.14.1.4.4—Age of Girder When Continuity Is Established ............................................................... 5-203
5.14.1.4.5—Degree of Continuity at Various Limit States .................................................................. 5-204
5.14.1.4.6—Service Limit State........................................................................................................... 5-205
5.14.1.4.7—Strength Limit State ......................................................................................................... 5-206
5.14.1.4.8—Negative Moment Connections........................................................................................5-206
5.14.1.4.9—Positive Moment Connections ......................................................................................... 5-206
5.14.1.4.9a—General .................................................................................................................... 5-206
5.14.1.4.9b—Positive Moment Connection Using Mild Reinforcement ...................................... 5-207
5.14.1.4.9c—Positive Moment Connection Using Prestressing Strand ........................................ 5-208
5.14.1.4.9d—Details of Positive Moment Connection ................................................................. 5-208
5.14.1.4.10—Continuity Diaphragms .................................................................................................. 5-209
5.14.1.5—Cast-in-Place Girders and Box and T-Beams ............................................................................ 5-210
5.14.1.5.1—Flange and Web Thickness .............................................................................................. 5-210
5.14.1.5.1a—Top Flange .............................................................................................................. 5-210
5.14.1.5.1b—Bottom Flange ........................................................................................................ 5-210
5.14.1.5.1c—Web ......................................................................................................................... 5-210
5.14.1.5.2—Reinforcement .................................................................................................................. 5-210
5.14.1.5.2a—Deck Slab Reinforcement Cast-in-Place in T-Beams and Box Girders .................. 5-210
5.14.1.5.2b—Bottom Slab Reinforcement in Cast-in-Place Box Girders..................................... 5-211
5.14.2—Segmental Construction ....................................................................................................................... 5-211
5.14.2.1—General ....................................................................................................................................... 5-211
5.14.2.2—Analysis of Segmental Bridges .................................................................................................. 5-212
5.14.2.2.1—General ............................................................................................................................. 5-212
5.14.2.2.2—Construction Analysis ...................................................................................................... 5-212
5.14.2.2.3—Analysis of the Final Structural System ...........................................................................5-212
5.14.2.3—Design ........................................................................................................................................ 5-213
5.14.2.3.1—Loads................................................................................................................................ 5-213
5.14.2.3.2—Construction Loads .......................................................................................................... 5-213
5.14.2.3.3—Construction Load Combinations at the Service Limit State ........................................... 5-214
5.14.2.3.4—Construction Load Combinations at Strength Limit States .............................................. 5-217
5.14.2.3.4a—Superstructures ........................................................................................................ 5-217
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2012
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TABLE OF CONTENTS
5-xi
5.14.2.3.4b—Substructures .......................................................................................................... 5-217
5.14.2.3.5—Thermal Effects During Construction.............................................................................. 5-217
5.14.2.3.6—Creep and Shrinkage ........................................................................................................ 5-217
5.14.2.3.7—Prestress Losses ............................................................................................................... 5-218
5.14.2.3.8—Provisional Post-Tensioning Ducts and Anchorages ....................................................... 5-219
5.14.2.3.8a—General.................................................................................................................... 5-219
5.14.2.3.8b—Bridges with Internal Ducts .................................................................................... 5-219
5.14.2.3.8c—Provision for Future Dead Load or Deflection Adjustment .................................... 5-219
5.14.2.3.9—Plan Presentation ............................................................................................................. 5-219
5.14.2.3.10—Box Girder Cross-Section Dimensions and Details ....................................................... 5-220
5.14.2.3.10a—Minimum Flange Thickness ................................................................................. 5-220
5.14.2.3.10b—Minimum Web Thickness .................................................................................... 5-220
5.14.2.3.10c—Length of Top Flange Cantilever .......................................................................... 5-221
5.14.2.3.10d—Overall Cross-Section Dimensions ....................................................................... 5-221
5.14.2.3.10e—Overlays ................................................................................................................ 5-222
5.14.2.3.11—Seismic Design .............................................................................................................. 5-222
5.14.2.4—Types of Segmental Bridges ...................................................................................................... 5-223
5.14.2.4.1—General ............................................................................................................................ 5-223
5.14.2.4.2—Details for Precast Construction ...................................................................................... 5-223
5.14.2.4.3—Details for Cast-in-Place Construction ............................................................................ 5-225
5.14.2.4.4—Cantilever Construction ................................................................................................... 5-225
5.14.2.4.5—Span-by-Span Construction ............................................................................................. 5-225
5.14.2.4.6—Incrementally Launched Construction ............................................................................. 5-226
5.14.2.4.6a—General.................................................................................................................... 5-226
5.14.2.4.6b—Force Effects Due to Construction Tolerances ....................................................... 5-226
5.14.2.4.6c—Design Details......................................................................................................... 5-227
5.14.2.4.6d—Design of Construction Equipment ........................................................................ 5-228
5.14.2.5—Use of Alternative Construction Methods ................................................................................. 5-228
5.14.2.6—Segmentally Constructed Bridge Substructures ......................................................................... 5-230
5.14.2.6.1—General ............................................................................................................................ 5-230
5.14.2.6.2—Construction Load Combinations .................................................................................... 5-230
5.14.2.6.3—Longitudinal Reinforcement of Hollow, Rectangular Precast Segmental Piers .............. 5-230
5.14.3—Arches .................................................................................................................................................. 5-231
5.14.3.1—General....................................................................................................................................... 5-231
5.14.3.2—Arch Ribs ................................................................................................................................... 5-231
5.14.4—Slab Superstructures ............................................................................................................................ 5-231
5.14.4.1—Cast-in-Place Solid Slab Superstructures................................................................................... 5-231
5.14.4.2—Cast-in-Place Voided Slab Superstructures ............................................................................... 5-232
5.14.4.2.1—Cross-Section Dimensions ............................................................................................... 5-232
5.14.4.2.2—Minimum Number of Bearings ........................................................................................ 5-233
5.14.4.2.3—Solid End Sections ........................................................................................................... 5-233
5.14.4.2.4—General Design Requirements ......................................................................................... 5-233
5.14.4.2.5—Compressive Zones in Negative Moment Area ............................................................... 5-234
5.14.4.2.6—Drainage of Voids ............................................................................................................ 5-234
5.14.4.3—Precast Deck Bridges ................................................................................................................. 5-234
5.14.4.3.1—General ............................................................................................................................ 5-234
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5-xii
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
5.14.4.3.2—Shear Transfer Joints........................................................................................................ 5-235
5.14.4.3.3—Shear-Flexure Transfer Joints .......................................................................................... 5-235
5.14.4.3.3a—General .................................................................................................................... 5-235
5.14.4.3.3b—Design ..................................................................................................................... 5-235
5.14.4.3.3c—Post-Tensioning ...................................................................................................... 5-235
5.14.4.3.3d—Longitudinal Construction Joints ............................................................................ 5-235
5.14.4.3.3e—Cast-in-Place Closure Joint ..................................................................................... 5-236
5.14.4.3.3f—Structural Overlay ................................................................................................... 5-236
5.14.5—Additional Provisions for Culverts ....................................................................................................... 5-236
5.14.5.1—General ....................................................................................................................................... 5-236
5.14.5.2—Design for Flexure ..................................................................................................................... 5-236
5.14.5.3—Design for Shear in Slabs of Box Culverts ................................................................................ 5-236
5.15—REFERENCES ............................................................................................................................................... 5-237
APPENDIX A5—BASIC STEPS FOR CONCRETE BRIDGES ............................................................................ 5-247
A5.1—GENERAL .................................................................................................................................................... 5-247
A5.2—GENERAL CONSIDERATIONS ................................................................................................................. 5-247
A5.3—BEAM AND GIRDER SUPERSTRUCTURE DESIGN .............................................................................. 5-247
A5.4—SLAB BRIDGES........................................................................................................................................... 5-248
A5.5—SUBSTRUCTURE DESIGN ........................................................................................................................ 5-249
APPENDIX B5—GENERAL PROCEDURE FOR SHEAR DESIGN WITH TABLES......................................... 5-251
B5.1—BACKGROUND ........................................................................................................................................... 5-251
B5.2—SECTIONAL DESIGN MODEL—GENERAL PROCEDURE ................................................................... 5-251
APPENDIX C5—UPPER LIMITS FOR ARTICLES AFFECTED BY CONCRETE COMPRESSIVE
STRENGTH .............................................................................................................................................................. 5-259
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
SECTION 5
CONCRETE STRUCTURES
5.1—SCOPE
The provisions in this section apply to the design of
bridge and retaining wall components constructed of
normal weight or lightweight concrete and reinforced
with steel bars, welded wire reinforcement, and/or
prestressing strands, bars, or wires. The provisions are
based on concrete strengths varying from 2.4 ksi to
10.0 ksi, except where higher strengths are allowed for
normal weight concrete.
The provisions of this section combine and unify
the requirements for reinforced, prestressed, and
partially prestressed concrete. Provisions for seismic
design, analysis by the strut-and-tie model, and design
of segmentally constructed concrete bridges and bridges
made from precast concrete elements have been added.
A brief outline for the design of some routine
concrete components is contained in Appendix A.
5.2—DEFINITIONS
2013 Revision
Anchorage—In post-tensioning, a mechanical device used to anchor the tendon to the concrete; in pretensioning, a
device used to anchor the tendon until the concrete has reached a predetermined strength, and the prestressing force
has been transferred to the concrete; for reinforcing bars, a length of reinforcement, or a mechanical anchor or hook,
or combination thereof at the end of a bar needed to transfer the force carried by the bar into the concrete.
Anchorage Blister—A build-out area in the web, flange, or flange-web junction for the incorporation of tendon
anchorage fittings.
Anchorage Zone—The portion of the structure in which the prestressing force is transferred from the anchorage
device onto the local zone of the concrete, and then distributed more widely into the general zone of the structure.
At Jacking—At the time of tensioning, the prestressing tendons.
At Loading—The maturity of the concrete when loads are applied. Such loads include prestressing forces and
permanent loads but generally not live loads.
At Transfer—Immediately after the transfer of prestressing force to the concrete.
Blanketed Strand—See Partially Debonded Strand.
Bonded Tendon—A tendon that is bonded to the concrete, either directly or by means of grouting.
Bursting Force—Tensile forces in the concrete in the vicinity of the transfer or anchorage of prestressing forces.
Cast-in-Place Concrete—Concrete placed in its final location in the structure while still in a plastic state.
Closely Spaced Anchorages—Anchorage devices are defined as closely spaced if their center-to-center spacing does
not exceed 1.5 times the width of the anchorage devices in the direction considered.
Closure—A placement of cast-in-place concrete used to connect two or more previously cast portions of a structure.
Composite Construction—Concrete components or concrete and steel components interconnected to respond to force
effects as a unit.
Compression-Controlled Section—A cross-section in which the net tensile strain in the extreme tension steel at
nominal resistance is less than or equal to the compression-controlled strain limit.
5-1
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5-2
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Compression-Controlled Strain Limit—The net tensile strain in the extreme tension steel at balanced strain conditions.
See Article 5.7.2.1.
Concrete Cover—The specified minimum distance between the surface of the reinforcing bars, strands, posttensioning ducts, anchorages, or other embedded items, and the surface of the concrete.
Confinement—A condition where the disintegration of the concrete under compression is prevented by the
development of lateral and/or circumferential forces such as may be provided by appropriate reinforcing, steel or
composite tubes, or similar devices.
Confinement Anchorage—Anchorage for a post-tensioning tendon that functions on the basis of containment of the
concrete in the local anchorage zone by special reinforcement.
Creep—Time-dependent deformation of concrete under permanent load.
Curvature Friction—Friction resulting from the tendon moving against the duct when tensioned due to the curvature
of the duct.
Deck Slab—A solid concrete slab resisting and distributing wheel loads to the supporting components.
Decompression—The stage at which the compressive stresses, induced by prestress, are overcome by the tensile
stresses.
Deep Component—Components in which the distance from the point of 0.0 shear to the face of the support is less than
2d or components in which a load causing more than one-third of the shear at a support is closer than 2d from the face
of the support.
Deviation Saddle—A concrete block build-out in a web, flange, or web-flange junction used to control the geometry
of, or to provide a means for changing direction of, external tendons.
Development Length—The distance required to develop the specified strength of a reinforcing bar or prestressing
strand.
Direct Loading/Supporting—Application of a load or use of a support external to the member, as in the case of point
or uniform loads applied directly to the deck surface, simply-supported girder ends, bent (pier) cap supported on
pinned columns.
Duct Stack—A vertical group of tendons in which the space between individual tendons is less than 1.5 in.
Edge Distance—The minimum distance between the centerline of reinforcement or other embedded elements and the
edge of the concrete.
Effective Depth—The depth of a component effective in resisting flexural or shear forces.
Effective Prestress—The stress or force remaining in the prestressing steel after all losses have occurred.
Embedment Length—The length of reinforcement or anchor provided beyond a critical section over which transfer of
force between concrete and reinforcement may occur.
External Tendon—A post-tensioning tendon placed outside of the body of concrete, usually inside a box girder.
Extreme Tension Steel—The reinforcement (prestressed or nonprestressed) that is farthest from the extreme
compression fiber.
Fully Prestressed Component—Prestressed concrete component in which stresses satisfy the tensile stress limits at
Service Limit State specified herein. Such components are assumed to remain uncracked at the Service Limit State.
General Zone—Region adjacent to a post-tensioned anchorage within which the prestressing force spreads out to an
essentially linear stress distribution over the cross-section of the component.
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2012
Edition
SECTION 5: CONCRETE STRUCTURES
5-3
Intermediate Anchorage—Anchorage not located at the end surface of a member or segment for tendons that do not
extend over the entire length of the member or segment; usually in the form of embedded anchors, blisters, ribs, or
recess pockets.
Indirect Loading/Supporting—Application of a load or use of a support internally such as girders framing into an
integral bent (pier) cap, dapped or spliced-girders where load transfer is between the top and bottom face of the
member, or utility loads hung from the web of a girder.
Internal Tendon—A post-tensioning tendon placed within the body of concrete.
Isotropic Reinforcement—An arrangement of reinforcement in which the bars are orthogonal, and the reinforcement
ratios in the two directions are equal.
Jacking Force—The force exerted by the device that introduces tension into the tendons.
Launching Bearing—Temporary bearings with low friction characteristics used for construction of bridges by the
incremental launching method.
Launching Nose—Temporary steel assembly attached to the front of an incrementally launched bridge to reduce
superstructure force effects during launching.
Lightweight Concrete—Concrete containing lightweight aggregate and having an air-dry unit weight not exceeding
0.120 kcf, as determined by ASTM C567. Lightweight concrete without natural sand is termed “all-lightweight
concrete” and lightweight concrete in which all of the fine aggregate consists of normal weight sand is termed “sandlightweight concrete.”
Local Bending—The lateral flexural bending caused by curved post-tensioning tendons on the concrete cover between
the internal ducts and the inside face of the curved element (usually webs).
Local Shear—The lateral shear caused by curved post-tensioning tendons on the concrete cover between the internal
ducts and the inside face of the curved element (usually webs).
Local Zone—The volume of concrete that surrounds and is immediately ahead of the anchorage device and that is
subjected to high compressive stresses.
Low Relaxation Steel—Prestressing strand in which the steel relaxation losses have been substantially reduced by
stretching at an elevated temperature.
Net Tensile Strain—The tensile strain at nominal resistance exclusive of strains due to effective prestress, creep,
shrinkage, and temperature.
Normal Weight Concrete—Concrete having a weight between 0.135 and 0.155 kcf.
Partially Debonded Strand—A pretensioned prestressing strand that is bonded for a portion of its length and
intentionally debonded elsewhere through the use of mechanical or chemical means. Also called shielded or blanketed
strand.
Post-Tensioning—A method of prestressing in which the tendons are tensioned after the concrete has reached a
predetermined strength.
Post-Tensioning Duct—A form device used to provide a path for post-tensioning tendons or bars in hardened
concrete. The following types are in general use:
Rigid Duct—Seamless tubing stiff enough to limit the deflection of a 20.0-ft length supported at its ends to not more
than 1.0 in.
Semirigid Duct—A corrugated duct of metal or plastic sufficiently stiff to be regarded as not coilable into
conventional shipping coils without damage.
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5-4
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Flexible Duct—A loosely interlocked duct that can be coiled into a 4.0-ft diameter without damage.
Precast Members—Concrete elements cast in a location other than their final position.
Precompressed Tensile Zone—Any region of a prestressed component in which prestressing causes compressive
stresses and service load effects cause tensile stresses.
Prestressed Concrete—Concrete components in which stresses and deformations are introduced by application of
prestressing forces.
Pretensioning—A method of prestressing in which the strands are tensioned before the concrete is placed.
Regional Bending—Transverse bending of a concrete box girder web due to concentrated lateral prestress forces
resisted by the frame action of the box acting as a whole.
Reinforced Concrete—Structural concrete containing no less than the minimum amounts of prestressing tendons or
nonprestressed reinforcement specified herein.
Reinforcement—Reinforcing bars and/or prestressing steel.
Relaxation—The time-dependent reduction of stress in prestressing tendons.
Resal Effect—The reduction or addition of shear based on the bottom slab compression angle with the center of
gravity.
Segmental Construction—The fabrication and erection of a structural element (superstructure and/or substructure)
using individual elements, which may be either precast or cast-in-place. The completed structural element acts as a
monolithic unit under some or all design loads. Post-tensioning is typically used to connect the individual elements.
For superstructures, the individual elements are typically short (with respect to the span length), box-shaped segments
with monolithic flanges that comprise the full width of the structure. (See Article 5.14.2.)
Seismic Hoop—A cylindrical noncontinuously wound tie with closure made using a butt weld or a mechanical
coupler.
Shielded Strand—See Partially Debonded Strand.
Slab—A component having a width of at least four times its effective depth.
Special Anchorage Device—Anchorage device whose adequacy should be proven in a standardized acceptance test.
Most multiplane anchorages and all bond anchorages are special anchorage devices.
Specified Strength of Concrete—The nominal compressive strength of concrete specified for the work and assumed
for design and analysis of new structures.
Spiral—Continuously wound bar or wire in the form of a cylindrical helix.
Spliced Precast Girder—A type of superstructure in which precast concrete beam-type elements are joined
longitudinally, typically using post-tensioning, to form the completed girder. The bridge cross-section is typically a
conventional structure consisting of multiple precast girders. This type of construction is not considered to be
segmental construction for the purposes of these Specifications. (See Article 5.14.1.3.)
Splitting Tensile Strength—The tensile strength of concrete that is determined by a splitting test made in accordance
with AASHTO T 198 (ASTM C496).
Stress Range—The algebraic difference between the maximum and minimum stresses due to transient loads.
Structural Concrete—All concrete used for structural purposes.
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2012
Edition
SECTION 5: CONCRETE STRUCTURES
5-5
Structural Mass Concrete—Any large volume of concrete where special materials or procedures are required to cope
with the generation of heat of hydration and attendant volume change to minimize cracking.
Strut-and-Tie Model—A model used principally in regions of concentrated forces and geometric discontinuities to
determine concrete proportions and reinforcement quantities and patterns based on assumed compression struts in the
concrete, tensile ties in the reinforcement, and the geometry of nodes at their points of intersection.
Temperature Gradient—Variation of temperature of the concrete over the cross-section.
Tendon—A high-strength steel element used to prestress the concrete.
Tension-Controlled Section—A cross-section in which the net tensile strain in the extreme tension steel at nominal
resistance is greater than or equal to 0.005.
Transfer—The operation of imparting the force in a pretensioning anchoring device to the concrete.
Transfer Length—The length over which the pretensioning force is transferred to the concrete by bond and friction in
a pretensioned member.
Transverse Reinforcement—Reinforcement used to resist shear, torsion, and lateral forces or to confine concrete in a
structural member. The terms “stirrups” and “web reinforcement” are usually applied to transverse reinforcement in
flexural members and the terms “ties,” “hoops,” and “spirals” are applied to transverse reinforcement in compression
members.
Wobble Friction—The friction caused by the deviation of a tendon duct or sheath from its specified profile.
Yield Strength—The specified yield strength of reinforcement.
5.3—NOTATION
A
=
Ab
=
Ac
=
Acb
=
Acp
=
Acs
Acv
Ad
Ag
Ah
Ahr
AI
=
=
=
=
=
=
=
A
=
An
Ao
Aoh
=
=
=
Aps
Apsb
Apsu
=
=
=
2013 Revision
the maximum area of the portion of the supporting surface that is similar to the loaded area and
concentric with it and that does not overlap similar areas for adjacent anchorage devices (in.2); for
segmental construction: static weight of precast segment being handled (kip) (5.10.9.7.2) (5.14.2.3.2)
area of an individual bar (in.2); effective bearing area (in.2); net area of a bearing plate (in.2) (5.10.9.6.2)
(5.10.9.7.2)
area of core of spirally reinforced compression member measured to the outside diameter of the spiral
(in.2); gross area of concrete deck slab (in.2) (5.7.4.6) (C5.14.1.4.3)
the area of the continuing cross-section within the extensions of the sides of the anchor plate or blister,
i.e., the area of the blister or rib shall not be taken as part of the cross-section (in.2) (5.10.9.3.4b)
area enclosed by outside perimeter of concrete cross-section, including area of holes, if any (in.2)
(5.8.2.1) (5.8.6.3)
cross-sectional area of a concrete strut in strut-and-tie model (in.2) (5.6.3.3.1)
area of concrete section resisting shear transfer (in.2) (5.8.4.1)
area of deck concrete (in.2) (5.9.5.4.3d)
gross area of section (in.2); gross area of bearing plate (in.2) (5.5.4.2.1) (5.10.9.7.2)
area of shear reinforcement parallel to flexural tension reinforcement (in.2) (5.13.2.4.1)
area of one leg of hanger reinforcement in beam ledges and inverted T-beams (in.2) (5.13.2.5.5)
for segmental construction: dynamic response due to accidental release or application of a precast
segment (kip) (5.14.2.3.2)
area of longitudinal torsion reinforcement in the exterior web of the box girder (in.2); area of longitudinal
column reinforcement (in.2) (5.8.3.6.3) (5.11.5.2.1)
area of reinforcement in bracket or corbel resisting tensile force Nuc (in.2) (5.13.2.4.2)
area enclosed by shear flow path, including area of holes, if any (in.2) (5.8.2.1)
area enclosed by centerline of exterior closed transverse torsion reinforcement, including area of holes, if
any (in.2) (5.8.2.1)
area of prestressing steel (in.2); area of prestressing steel (in.2) (5.5.4.2.1) (5.7.4.4)
area of bonded prestressing steel (in.2) (5.7.3.1.3b)
area of unbonded prestressing steel (in.2) (5.7.3.1.3b)
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
5-6
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
As
=
A's
Ash
Ask
Asp
Asp1
Asp2
Ass
Ast
As-BW
As-SD
At
Atr
Av
Avf
=
=
=
=
=
=
=
=
=
=
=
=
=
=
Aw
A1
A2
=
=
=
a
=
aeff
=
af
av
b
=
=
=
be
beff
=
=
bo
bv
bw
CEQ
CLE
CLL
CR
c
=
=
=
=
=
=
=
=
D
DC
DIFF
Dr
DW
d
db
dburst
dc
=
=
=
=
=
=
=
=
=
de
=
area of nonprestressed tension reinforcement (in.2); total area of longitudinal deck reinforcement (in.2)
(5.5.4.2.1) (C5.14.1.4.3)
area of compression reinforcement (in.2) (5.7.3.1.1)
cross-sectional area of column tie reinforcements (in.2) (5.10.11.4.1d)
area of skin reinforcement per unit height in one side face (in.2) (5.7.3.4)
area of shaft spiral or transverse reinforcement (in.2) (5.11.5.2.1)
cross-sectional area of a tendon in the larger group (in.2) (C5.9.5.2.3b)
cross-sectional area of a tendon in the smaller group (in.2) (C5.9.5.2.3b)
area of reinforcement in an assumed strut of a strut-and-tie model (in.2) (5.6.3.3.4)
total area of longitudinal mild steel reinforcement (in.2) (5.6.3.4.1)
area of steel in the footing band width (in.2) (5.13.3.5)
total area of steel in short direction of a footing (in.2) (5.13.3.5)
area of one leg of closed transverse torsion reinforcement (in.2) (5.8.3.6.2)
area of concrete deck slab with transformed longitudinal deck reinforcement (in.2) (C5.14.1.4.3)
area of a transverse reinforcement within distance s (in.2) (5.8.2.5)
area of shear-friction reinforcement (in.2); area of reinforcement for interface shear between concretes of slab
and beam (in.2/in.); total area of reinforcement, including flexural reinforcement (in.2) (5.8.4.1) (5.10.11.4.4)
area of an individual wire to be developed or spliced (in.2) (5.11.2.5.1)
loaded area (in.2) (5.7.5)
area of the lower base of the largest frustum of a pyramid, cone, or tapered wedge contained wholly
within the support and having for its upper base the loaded area and having side slopes of 1 vertical to
2 horizontal (in.2) (5.7.5)
depth of equivalent rectangular stress block (in.); the anchor plate width (in.); the lateral dimension of
the anchorage device measured parallel to the larger dimension of the cross-section (in.) (5.7.2.2)
(5.10.9.3.6) (5.10.9.6.1)
lateral dimension of the effective bearing area measured parallel to the larger dimension of the crosssection (in.) (5.10.9.6.2)
distance between concentrated load and reinforcement parallel to load (in.) (5.13.2.5.1)
shear span: distance between concentrated load and face of support (in.) (5.13.2.4.1)
for rectangular sections, the width of the compression face of the member; for a flange section in
compression, the effective width of the flange as specified in Article 4.6.2.6 (in.); least width of
component section (in.); the lateral dimension of the anchorage device measured parallel to the smaller
dimension of the cross-section (in.) (5.7.3) (5.10.8) (5.10.9.6.2)
effective width of the shear flow path (in.) (5.8.6.3)
lateral dimension of the effective bearing area measured parallel to the smaller dimension of the crosssection (in.) (5.10.9.6.2)
perimeter of critical section for slabs and footings (in.) (5.13.3.6.1)
width of web adjusted for the presence of ducts (in.); width of the interface (in.) (5.8.2.9) (5.8.4.1)
width of member’s web (in.); web width or diameter of a circular section (in.) (5.6.3.6) (5.7.3.1.1)
for segmental construction: specialized construction equipment (kip) (5.14.2.3.2)
for segmental construction: longitudinal construction equipment load (kip) (5.14.2.3.2)
for segmental construction: distributed construction live load (ksf) (5.14.2.3.2)
loss of prestress due to creep of concrete (ksi) (5.14.2.3.2)
distance from the extreme compression fiber to the neutral axis (in.); cohesion factor (ksi); required
concrete cover over the reinforcing steel (in.); spacing from centerline of bearing to end of beam (in.)
(5.5.4.2.1) (5.7.2.2) (5.8.4.1) (C5.10.9.7.1) (5.13.2.5.2)
external diameter of the circular member (in.) (C5.8.2.9)
weight of supported structure (kip) (5.14.2.3.2)
for segmental construction: differential load (kip) (5.14.2.3.2)
diameter of the circle passing through the centers of the longitudinal reinforcement (in.) (C5.8.2.9)
superimposed dead load (kip) or (klf) (5.14.2.3.2)
distance from compression face to centroid of tension reinforcement (in.) (5.7.3.4)
nominal diameter of a reinforcing bar, wire, or prestressing strand (in.) (5.10.2.1)
distance from anchorage device to the centroid of the bursting force, Tburst (in.) (5.10.9.3.2)
thickness of concrete cover measured from extreme tension fiber to center of bar or wire located closest
thereto (in.); minimum concrete cover over the tendon duct, plus one-half of the duct diameter (in.)
(5.7.3.4) (5.10.4.3.1)
effective depth from extreme compression fiber to the centroid of the tensile force in the tensile
reinforcement (in.) (5.8.2.9)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 5: CONCRETE STRUCTURES
df
dℓ
=
=
dp
ds
=
=
d's
dt
dv
deff
dduct
Eb
Ec
Ecd
Ec deck
Eci
Ect
Eeff
EI
Ep
Es
e
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
ed
=
em
epc
epg
F
F′
Fε
Fu-in
Fu-out
fb
f ′c
fca
fcb
fcgp
=
=
=
=
=
=
=
=
=
=
=
=
=
f′ci
=
fcpe
=
fcr
=
fct
fcu
fmin
fn
fpbt
fpc
=
=
=
=
=
=
5-7
distance from top of ledge to compression reinforcement (in.) (5.13.2.5.5)
distance from the extreme compression fiber to the centroid of extreme tension steel element (in.)
(5.7.3.4)
distance from extreme compression fiber to the centroid of the prestressing tendons (in.) (5.7.3.1.1)
distance from extreme compression fiber to the centroid of the nonprestressed tensile reinforcement (in.)
(5.7.3.2.2)
distance from extreme compression fiber to the centroid of compression reinforcement (in.) (5.7.3.2.2)
distance from extreme compression fiber to centroid of extreme tension steel (in.) (5.5.4.2.1)
effective shear depth (in.) (5.8.2.9)
one-half the effective length of the failure plane in shear and tension for curved element (in.) (5.10.4.3.1)
outside diameter of post-tensioning duct (in.) (5.10.4.3.1)
modulus of elasticity of the bearing plate material (ksi) (5.10.9.7.2)
modulus of elasticity of concrete (ksi) (5.4.2.4)
modulus of elasticity of deck concrete (ksi) (5.9.5.4.3d)
modulus of elasticity of deck concrete (ksi) (C5.14.1.4.3)
modulus of elasticity of concrete at transfer (ksi) (C5.9.5.2.3a)
modulus of elasticity of concrete at transfer or time of load application (ksi) (5.9.5.2.3a)
effective modulus of elasticity (ksi) (C5.14.2.3.6)
flexural stiffness (kip-in.2) (5.7.4.3)
modulus of elasticity of prestressing tendons (ksi) (5.4.4.2) (5.7.4.4)
modulus of elasticity of reinforcing bars (ksi) (5.4.3.2)
base of Napierian logarithms; eccentricity of the anchorage device or group of devices with respect to
the centroid of the cross-section; always taken as positive (in.); minimum edge distance for anchorage
devices as specified by the supplier (in.) (5.9.2) (5.10.9.6.3) (C5.10.9.7.1)
eccentricity of deck with respect to the transformed composite section, taken as negative in common
construction (in.) (5.9.5.4.3d)
average eccentricity at midspan (in.) (C5.9.5.2.3a)
eccentricity of strands with respect to centroid of composite section (in.) (5.9.5.4.3a)
eccentricity of strands with respect to centroid of girder (in.) (5.9.5.4.2a)
force effect calculated using instantaneous modulus of elasticity at time loading is applied (kip) (5.9.2)
reduced force resultant accounting for creep in time corresponding to the φ used (kip) (5.9.2)
reduction factor (5.8.3.4.2)
in-plane deviation force effect per unit length of tendon (kips/ft) (5.10.4.3.1)
out-of-plane force effect per unit length of tendon (kips/ft) (5.10.4.3.2)
stress in anchor plate at a section taken at the edge of the wedge hole or holes (ksi) (5.10.9.7.2)
specified compressive strength of concrete for use in design (ksi) (5.4.2.1)
concrete compressive stress ahead of the anchorage devices (ksi) (5.10.9.6.2)
unfactored dead load compressive stress in the region behind the anchor (ksi) (5.10.9.3.4b)
concrete stress at the center of gravity of prestressing tendons, that results from the prestressing force at
either transfer or jacking and the self-weight of the member at sections of maximum moment (ksi)
(5.9.5.2.3a)
specified compressive strength of concrete at time of initial loading or prestressing (ksi); nominal
concrete strength at time of application of tendon force (ksi) (5.4.2.3.2) (5.10.9.7.2)
compressive stress in concrete due to effective prestress forces only (after allowance for all prestress
losses) at extreme fiber of section where tensile stress is caused by externally applied loads (ksi)
(5.7.3.3.2)
design flexural cracking stress of the hypothetical unreinforced concrete beam consisting of the cover
concrete over the inside face of a stack of horizontally curved post-tensioned tendons (ksi) (5.10.4.3.1)
average splitting tensile strength of lightweight aggregate concrete (ksi) (5.8.2.2)
limiting concrete compressive stress for design by strut-and-tie model (ksi) (5.6.3.3.1)
algebraic minimum stress level (ksi) (5.5.3.2)
nominal concrete bearing stress (ksi) (5.10.9.7.2)
stress in prestressing steel immediately prior to transfer (ksi) (C5.9.5.2.3a)
compressive stress in concrete after all prestress losses have occurred either at the centroid of the crosssection resisting live load or at the junction of the web and flange when the centroid lies in the flange
(ksi); in a composite section, fpc is the resultant compressive stress at the centroid of the composite
section or at the junction of the web and flange when the centroid lies within the flange, that results from
both prestress and the bending moments resisted by the precast member acting alone (ksi) (C5.6.3.5)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
5-8
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
fpe
fpj
fpo
=
=
=
fps
=
fpsl
fpt
fpu
fpul
fpx
=
=
=
=
=
fpy
fr
fs
f ′s
fss
fuℓ
=
=
=
=
=
=
fy
=
fytr
f ′y
fyh
H
h
=
=
=
=
=
hc
hc
=
=
hds
hf
h1
h2
Ic
=
=
=
=
=
Icr
IE
Ie
Ig
=
=
=
=
Is
K
=
=
Kdf
=
Kid
=
KL
=
K′L
K1
k
=
=
=
kc
kf
khc
=
=
=
effective stress in the prestressing steel after losses (ksi) (5.6.3.4.1) (5.7.4.4)
stress in the prestressing steel at jacking (ksi) (5.9.3)
a parameter taken as modulus of elasticity of prestressing tendons multiplied by the locked-in difference
in strain between the prestressing tendons and the surrounding concrete (ksi) (5.8.3.4.2)
average stress in prestressing steel at the time for which the nominal resistance of member is required
(ksi) (C5.6.3.3.3)
stress in the strand at the Service limit state. Cracked section shall be assumed (ksi) (C5.14.1.4.9)
stress in prestressing steel immediately after transfer (ksi) (5.9.3)
specified tensile strength of prestressing steel (ksi) (5.4.4.1)
stress in the strand at the Strength limit state (ksi) (C5.14.1.4.9)
design stress in pretensioned strand at nominal flexural strength at section of member under
consideration (ksi) (C5.11.4.2)
yield strength of prestressing steel (ksi) (5.4.4.1)
modulus of rupture of concrete (ksi) (5.4.2.6)
stress in the mild tension reinforcement at nominal flexural resistance (ksi) (5.7.3.1) (5.7.3.2)
stress in the mild steel compression reinforcement at nominal flexural resistance (ksi) (5.7.3.1) (5.7.3.2)
tensile stress in mild steel reinforcement at the service limit state (ksi) (5.7.3.4)
specified minimum tensile strength of column longitudinal reinforcement (ksi), 90 ksi for ASTM A615
and 80 ksi for ASTM A706 (5.11.5.2.1)
specified minimum yield strength of reinforcing bars (ksi); specified yield strength of reinforcing bars
≤75 ksi (5.5.4.2.1) (5.10.8)
specified minimum yield strength of shaft transverse reinforcement (ksi) (5.11.5.2.1)
specified minimum yield strength of compression reinforcement (ksi) (5.7.3.1.1)
specified yield strength of transverse reinforcement (ksi) (5.7.4.6)
average annual ambient mean relative humidity (percent) (5.4.2.3.2)
overall thickness or depth of a member (in.); least thickness of component section (in.); lateral
dimension of the cross-section in the direction considered (in.) (5.7.3.4) (5.10.8) (5.10.9.6.3)
core dimension of tied column in direction under consideration (in.) (5.10.11.4.1d)
clear span of the web of concrete box girder bridges between the top and bottom slabs measured along
the axis of the webs (in.) (C5.10.4.3.1)
height of a vertical group of ducts (in.) (C5.10.4.3.1)
compression flange depth (in.) (5.7.3.1.1)
largest lateral dimension of member (in.) (C5.10.9.3.2)
least lateral dimension of member (in.) (C5.10.9.3.2)
moment of inertia of section calculated using the net concrete section properties of the girder and the
deck and the deck-to-girder modular ratio at service (in.4) (5.9.5.4.3a)
moment of inertia of the cracked section, transformed to concrete (in.4) (5.7.3.6.2)
for segmental construction: dynamic load from equipment (kip) (5.14.2.3.2)
effective moment of inertia (in.4) (5.7.3.6.2)
moment of inertia of the gross concrete section about the centroidal axis, neglecting the reinforcement
(in.4) (5.7.3.6.2)
moment of inertia of the reinforcing taken about the centroid of the column (in.4) (5.7.4.3)
effective length factor for compression members; stress variable used in calculating torsional cracking
moment; wobble friction coefficient (per ft of tendon) (5.7.4.1) (5.8.6.3) (5.9.5.2.2b)
transformed section coefficient that accounts for time-dependent interaction between concrete and
bonded steel in the section being considered for time period between deck placement and final time
(5.9.5.4.3a)
transformed section coefficient that accounts for time-dependent interaction between concrete and
bonded steel in the section being considered for time period between transfer and deck placement
(5.9.5.4.2a)
factor accounting for type of steel taken as 30 for low relaxation strands and 7 for other prestressing
steel, unless more accurate manufacturer's data are available (5.9.5.4.2c)
factor accounting for type of steel (C5.9.5.4.2c)
correction factor for source of aggregate (5.4.2.4)
factor representing the ratio of column tensile reinforcement to total column reinforcement at the
nominal resistance (5.11.5.2.1)
factor for the effect of the volume-to-surface ratio (C5.4.2.3.2)
factor for the effect of concrete strength (5.4.2.3.2)
humidity factor for creep (5.4.2.3.2)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 5: CONCRETE STRUCTURES
khs
ks
ktd
kvs
L
ℓa
ℓc
=
=
=
=
=
=
=
ℓd
ℓdb
=
=
ℓdh
=
ℓdsh
ℓe
=
=
ℓhb
ℓhd
ℓi
ℓpx
ℓs
ℓu
Ma
Mc
Mcr
Mdnc
Mend
=
=
=
=
=
=
=
=
=
=
=
Mg
Mmid
=
=
Mn
Mr
Mrx
Mry
Mu
Mux
Muy
M1
=
=
=
=
=
=
=
=
M2
=
m
N
NR
Ns
=
=
=
=
Nu
Nuc
=
=
N1
N2
n
=
=
=
φcont
=
5-9
humidity factor for shrinkage (5.4.2.3.3)
factor for the effect of the volume-to-surface ratio (C5.4.2.3.2)
time development factor (5.4.2.3.2)
factor for the effect of the volume-to-surface ratio of the component (5.4.2.3.2)
span length (ft or in.); length of bearing plate or pad (in.) (5.7.3.1.2) (5.13.2.5.4)
additional embedment length at support or at point of inflection (in.) (C5.11.1.2.2)
longitudinal extent of confining reinforcement of the local zone but not more than the larger of 1.15 aeff
or 1.15 beff (in.); length of lap for compression lap splices (in.) (5.10.9.6.2) (5.11.5.5.1)
development length (in.) (5.11.1.2.1)
basic development length for straight reinforcement to which modification factors are applied to
determine ℓd (in.) (5.11.2.1.1)
development length of standard hook in tension as measured from critical section to outside end of hook
(in.) (5.11.2.4.1)
total length of extended strand (in.) (C5.14.1.4.9)
effective tendon length (in.); embedment length beyond standard stirrup hook (in.) (5.7.3.1.2)
(5.11.2.6.2)
basic development length of standard hook in tension (in.) (5.11.2.4.1)
development length for deformed wire fabric (in.) (5.11.2.5.1)
length of tendon between anchorages (in.) (5.7.3.1.2)
distance from free end of pretensioned strand to section of member under consideration (in.) (C5.11.4.2)
Class C tension lap splice length of the column longitudinal reinforcement (in.) (5.11.5.2.1)
unsupported length of a compression member (in.) (5.7.4.1)
maximum moment in a member at the stage for which deformation is computed (kip-in.) (5.7.3.6.2)
magnified moment used for proportioning slender compression members (kip-in.) (5.7.4.3)
cracking moment (kip-in.) (5.7.3.3.2) (5.7.3.6.2)
total unfactored dead load moment acting on the monolithic or noncomposite section (kip-in.) (5.7.3.3.2)
moment at the ends of a hypothetical unreinforced concrete beam consisting of the cover concrete over
the inside face of a stack of horizontally curved post-tensioned tendons (in.-k) (5.10.4.3.1)
midspan moment due to member self-weight (kip-in.) (C5.9.5.2.3a)
moment at the midpoint of a hypothetical unreinforced concrete beam consisting of the cover concrete
over the inside face of a stack of horizontally curved prestress post-tensioned (in.-k) (5.10.4.3.1)
nominal flexural resistance (kip-in.) (5.7.3.2.1)
factored flexural resistance of a section in bending (kip-in.) (5.7.3.2.1)
uniaxial factored flexural resistance of a section in the direction of the x-axis (kip-in.) (5.7.4.5)
uniaxial factored flexural resistance of a section in the direction of the y-axis (kip-in.) (5.7.4.5)
factored moment at the section (kip-in.) (C5.6.3.1)
component of moment due to factored load in the direction of the x-axis (kip-in.) (5.7.4.5)
component of moment due to factored load in the direction of the y-axis (kip-in.) (5.7.4.5)
smaller end moment at the strength limit state due to factored load acting on a compression member;
positive if the member is bent in single curvature and negative if bent in double curvature (kip-in.)
(5.7.4.3)
larger end moment at the strength limit state due to factored load acting on a compression member;
always positive (kip-in.) (5.7.4.3)
modification factor (5.7.5)
the number of cycles of stress range; the number of identical prestressing tendons (5.5.3.4) (5.9.5.2.3b)
factored tensile resistance of transverse pair of reinforcing bars (kip) (5.13.2.3)
number of support hinges crossed by the tendon between anchorages or discretely bonded points
(5.7.3.1.2)
applied factored axial force taken as positive if tensile (kip) (5.8.3.4.2)
factored axial force normal to the cross-section, occurring simultaneously with Vu; taken to be positive
for tension and negative for compression; includes effects of tension due to creep and shrinkage (kip)
(5.13.2.4.1)
number of tendons in the larger group (C5.9.5.2.3b)
number of tendons is the smaller group (C5.9.5.2.3b)
modular ratio = Es /Ec or Ep /Ec; number of anchorages in a row; projection of base plate beyond the
wedge hole or wedge plate, as appropriate (in.); modular ratio between deck concrete and reinforcement
(5.7.1) (5.10.9.6.2) (5.10.9.7.2) (C5.14.1.4.3)
girder web continuity factor for evaluating regional bending (5.10.4.3.1)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
5-10
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Pc
Pn
=
=
Po
Pr
=
=
Prx
Prxy
Pry
Ps
Pu
=
=
=
=
=
pc
ph
=
=
Q
R
r
r /h
S
Sc
=
=
=
=
=
=
SH
Snc
=
=
Str
s
=
=
smax
sw
sx
sxe
Tburst
=
=
=
=
=
Tcr
Tia
Tn
Tr
Tu
T1
T2
t
=
=
=
=
=
=
=
=
td
tf
ti
U
Vc
Vn
Vp
=
=
=
=
=
=
=
Vr
V/S
Vs
Vu
=
=
=
=
permanent net compressive force (kip) (5.8.4.1)
nominal axial resistance of a section (kip); nominal axial resistance of strut or tie (kip); nominal bearing
resistance (kip) (5.5.4.2.1) (5.6.3.2) (5.7.5)
nominal axial resistance of a section at 0.0 eccentricity (kip) (5.7.4.5)
factored axial resistance of strut or tie (kip); factored bearing resistance of anchorages (kip); factored
bursting resistance of pretensioned anchorage zone provided by transverse reinforcement (kip) (5.6.3.2)
(5.10.9.7.2) (5.10.10.1)
factored axial resistance corresponding to Mrx (kip) (5.7.4.5)
factored axial resistance with biaxial loading (kip) (5.7.4.5)
factored axial resistance corresponding to Mry (kip) (5.7.4.5)
maximum unfactored anchorage stressing force (kip) (5.10.9.3.4b)
factored axial force effect or factored tendon force (kip); factored tendon load on an individual anchor
(kip) (5.7.4.3) (5.10.9.3.6)
length of outside perimeter of the concrete section (in.) (5.8.2.1) (5.8.6.3)
perimeter of the centerline of the closed transverse torsion reinforcement (in.); perimeter of the polygon
defined by the centroids of the longitudinal chords of the space truss resisting torsion (in.) (5.8.2.1)
(5.8.6.4)
force effect in associated units (5.14.2.3.4)
radius of curvature of the tendon at the considered location (ft) (5.10.4.3.1)
radius of gyration of gross cross-section (in.) (5.7.4.1)
ratio of base radius to height of rolled-on transverse deformations (5.5.3.2)
center-to-center spacing of bearing along a beam ledge (in.) (5.13.2.5.2)
section modulus for the extreme fiber of the composite section where tensile stress is caused by
externally applied loads (in.3) (5.7.3.3.2)
shrinkage (5.14.2.3.2)
section modulus for the extreme fiber of the monolithic or noncomposite section where tensile stress is
caused by externally applied loads (in.3) (5.7.3.3.2)
spacing of transverse shaft reinforcement (in.) (5.11.5.2.1)
average spacing of mild steel reinforcement in layer closest to tension face (in.); spacing of reinforcing bars
(in.); spacing of rows of ties (in.); anchorage spacing (in.); center-to-center spacing of anchorages (in.);
spacing of hanger reinforcing bars (in.) (5.7.3.4) (5.8.2.5) (5.8.4.1) (5.10.9.3.6) (5.10.9.6.2) (5.13.2.5.5)
maximum permitted spacing of transverse reinforcement (in.) (5.8.2.7)
spacing of wires to be developed or spliced (in.) (5.11.2.5.1)
crack spacing parameter (in.) (C5.8.3.4.2)
equivalent value of sx which allows for influence of aggregate size (in.) (5.8.3.4.2)
tensile force in the anchorage zone acting ahead of the anchorage device and transverse to the tendon
axis (kip) (5.10.9.6.3)
torsional cracking resistance (kip-in.) (5.8.2.1)
tie-back tension force at the intermediate anchorage (kip) (5.10.9.3.4b)
nominal torsion resistance (kip-in.) (5.8.2.1)
factored torsional resistance provided by circulatory shear flow (kip-in.) (5.8.2.1)
factored torsional moment (kip-in.) (C5.6.3.1)
edge tension force (kip) (5.10.9.3.6)
bursting force (kip) (5.10.9.3.6)
time (day); thickness of wall (in.); thickness of the section (in.); average thickness of bearing plate (in.)
(5.4.2.3.2) (5.7.4.7.1) (5.10.9.6.2) (5.10.9.7.2)
age at deck placement (day) (5.9.5.4.2b)
final age (day) (5.9.5.4.2a)
age of concrete when load is initially applied (day) (5.4.2.3.2)
for segmental construction: segment unbalance (kip) (5.14.2.3.2)
nominal shear resistance provided by tensile stresses in the concrete (kip) (5.8.2.4)
nominal shear resistance of the section considered (kip) (5.8.2.1)
component in the direction of the applied shear of the effective prestressing force; positive if resisting
the applied shear (kip) (C5.8.2.3)
factored shear resistance (kip) (5.8.2.1)
volume-to-surface ratio (5.4.2.3.2)
shear resistance provided by shear reinforcement (kip) (5.8.3.3)
factored shear force at section (kip) (C5.6.3.1)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 5: CONCRETE STRUCTURES
vu
W
W/C
WE
WUP
wc
Xu
=
=
=
=
=
=
=
x
yt
α
=
=
=
αh
=
αs
αv
=
=
β
=
βb
βc
βd
=
=
=
β1
=
βs
=
γ
γe
Δf
(ΔF)TH
Δfcd
=
=
=
=
=
Δfcdf
=
Δfcdp
=
ΔfpA
ΔfpCD
=
=
ΔfpCR
ΔfpES
ΔfpF
ΔfpR1
=
=
=
=
ΔfpR2
=
ΔfpSD
=
ΔfpSR
ΔfpSS
ΔfpT
=
=
=
=
=
=
=
εbdf
εbid
εcu
εddf
5-11
average factored shear stress on the concrete (ksi) (5.8.2.7) (5.8.2.9)
width of bearing plate measured along the length of a corbel, bracket, or beam ledge (in.) (C5.13.2.5.1)
water–cement ratio (5.12.3)
for segmental construction: horizontal wind load on equipment (kip) (5.14.2.3.2)
for segmental construction: wind uplift on cantilever (ksf) (5.14.2.3.2)
unit weight of concrete (kcf) (5.4.2.4)
clear length of the constant thickness portion of a wall between other walls or fillers between walls (in.)
(5.7.4.7.1)
length of a prestressing tendon from the jacking end to any point under consideration (ft) (5.9.5.2.2b)
distance from the neutral axis to the extreme tension fiber (in.) (5.7.3.6.2)
angle of inclination of transverse reinforcement to longitudinal axis (degrees); total angular change of
prestressing steel path from jacking end to a point under investigation (rad.); the angle of inclination of a
tendon force with respect to the centerline of the member (degrees) (5.8.3.3) (5.9.5.2.2b) (5.10.9.6.3)
total horizontal angular change of prestressing steel path from jacking end to a point under investigation
(rad.) (5.9.5.2.2b)
angle between compressive strut and adjoining tension tie (degrees) (5.6.3.3.3)
total vertical angular change of prestressing steel path from jacking end to a point under investigation
(rad.) (5.9.5.2.2b)
factor relating effect of longitudinal strain on the shear capacity of concrete, as indicated by the ability of
diagonally cracked concrete to transmit tension; ratio of long side to short side of footing (5.8.3.3)
(5.13.3.5)
ratio of the area of reinforcement cut off to the total area of tension reinforcement at the section (5.11.1.2.1)
ratio of the long side to the short side of the concentrated load or reaction area (5.13.3.6.3)
ratio of maximum factored dead load moments to maximum factored total load moment; always positive
(5.7.4.3)
ratio of the depth of the equivalent uniformly stressed compression zone assumed in the strength limit
state to the depth of the actual compression zone (5.7.2.2)
ratio of flexural strain at the extreme tension face to the strain at the centroid of the reinforcement layer
nearest the tension face (5.7.3.4)
load factor
crack control exposure condition factor (5.7.3.4)
live load stress range due to fatigue load (ksi) (5.5.3.1)
constant-amplitude fatigue threshold (ksi) (5.5.3.1)
change in concrete stress at centroid of prestressing strands due to long-term losses between transfer and
deck placement, combined with deck weight and superimposed loads (ksi) (5.9.5.4.3b)
change in concrete stress at centroid of prestressing strands due to shrinkage of deck concrete (ksi)
(5.9.5.4.3d)
change in concrete stress at c.g. of prestressing steel due to all dead loads, except dead load acting at the
time the prestressing force is applied (ksi) (5.9.5.4.3)
loss in prestressing steel stress due to anchorage set (ksi) (5.9.5.1)
prestress loss due to creep of girder concrete between time of deck placement and final time (ksi)
(5.9.5.4.1)
prestress loss due to creep of girder concrete between transfer and deck placement (ksi) (5.9.5.4.1)
loss in prestressing steel stress due to elastic shortening (ksi) (5.9.5.1)
loss in prestressing steel stress due to friction (ksi) (5.9.5.1)
prestress loss due to relaxation of prestressing strands between transfer and deck placement (ksi)
(5.9.5.4.1)
prestress loss due to relaxation of prestressing strands in composite section between time of deck
placement and final time (ksi) (5.9.5.4.1)
prestress loss due to shrinkage of girder concrete between time of deck placement and final time (ksi)
(5.9.5.4.1)
prestress loss due to shrinkage of girder concrete between transfer and deck placement (ksi) (5.9.5.4.1)
prestress loss due to shrinkage of deck composite section (ksi) (5.9.5.4.1)
total loss in prestressing steel stress (ksi) (5.9.5.1)
shrinkage strain of girder between time of deck placement and final time (in./in.) (5.9.5.4.3a)
concrete shrinkage strain of girder between transfer and deck placement (in./in.) (5.9.5.4.2a)
failure strain of concrete in compression (in./in.) (5.7.3.1.2) (5.7.4.4)
shrinkage strain of deck concrete between placement and final time (in./in.) (5.9.5.4.3d)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
5-12
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
εeffective =
=
εs
εsh
=
εt
θ
θs
=
=
=
=
=
κ
=
λ
λw
μ
ρh
=
=
=
=
ρmin
ρs
ρv
φ
φw
Ψ(t, ti)
=
=
=
=
=
=
εx
ε1
Ψb(td, ti) =
Ψb(tf, td) =
Ψb(tf, ti) =
effective concrete shrinkage strain (in./in.) (C5.14.1.4.3)
tensile strain in cracked concrete in direction of tension tie (in./in.); net longitudinal tensile strain in the
section at the centroid of the tension reinforcement (in./in.) (5.6.3.3.3) (5.8.3.4.2)
concrete shrinkage strain at a given time (in./in.); net longitudinal tensile strain in the section at the
centroid of the tension reinforcement (in./in.) (5.4.2.3.3) (C5.14.1.4.3)
net tensile strain in extreme tension steel at nominal resistance (C5.5.4.2.1)
longitudinal strain in the web of the member (in./in.) (Appendix B5)
principal tensile strain in cracked concrete due to factored loads (in./in.) (5.6.3.3.3)
angle of inclination of diagonal compressive stresses (degrees) (5.8.3.3)
angle between compression strut and longitudinal axis of the member in a shear truss model of a beam
(degrees) (5.6.3.3.2)
correction factor for closely spaced anchorages; multiplier for strand development length (5.10.9.6.2)
(5.11.4.2)
parameter used to determine friction coefficient μ (5.8.4.2)
wall slenderness ratio for hollow columns (5.7.4.7.1)
coefficient of friction (5.8.4.1)
ratio of area of horizontal shear reinforcement to area of gross concrete area of a vertical section
(5.10.11.4.2)
minimum ratio of tension reinforcement to effective concrete area (5.7.3.3.2)
ratio of spiral reinforcement to total volume of column core (5.7.4.6)
ratio of area of vertical shear reinforcement to area of gross concrete area of a horizontal section (5.10.11.4.2)
resistance factor (5.5.4.2.1)
hollow column reduction factor (5.7.4.7.2)
creep coefficient—the ratio of the creep strain that exists t days after casting to the elastic strain caused
when load pi is applied ti days after casting (5.4.2.3.2)
girder creep coefficient at time of deck placement due to loading introduced at transfer (5.9.5.4.2b)
girder creep coefficient at final time due to loading at deck placement; creep coefficient of deck concrete
at final time due to loading introduced shortly after deck placement (i.e., overlays, barriers, etc.)
(5.9.5.4.3b) (5.9.5.4.3d)
girder creep coefficient at final time due to loading introduced at transfer (5.9.5.4.2a)
5.4—MATERIAL PROPERTIES
5.4.1—General
C5.4.1
Designs should be based on the material properties
cited herein and on the use of materials that conform to
the standards for the grades of construction materials as
specified in AASHTO LRFD Bridge Construction
Specifications.
When other grades or types of materials are used,
their properties, including statistical variability, shall be
established prior to design. The minimum acceptable
properties and test procedures for such materials shall be
specified in the contract documents.
The contract documents shall define the grades or
properties of all materials to be used.
According to AASHTO LRFD Bridge Construction
Specifications, all materials and tests must conform to the
appropriate standards included in the AASHTO Standard
Specifications for Transportation Materials and Methods
of Sampling and Testing and/or the standards of the
American Society for Testing and Materials.
Occasionally, it may be appropriate to use materials
other than those included in the AASHTO LRFD Bridge
Construction Specifications; for example, when
concretes are modified to obtain very high-strengths
through the introduction of special materials, such as:
•
Silica fume,
•
Cements other than Portland or blended hydraulic
cements,
•
Proprietary high early strength cements,
•
Ground granulated blast-furnace slag, and
•
Other types of cementitious and/or Pozzolanic
materials.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 5: CONCRETE STRUCTURES
5-13
In these cases, the specified properties of such
materials should be measured using the testing
procedures defined in the contract documents.
5.4.2—Normal Weight and Structural Lightweight
Concrete
5.4.2.1—Compressive Strength
For each component, the specified compressive
strength, f ′c, or the class of concrete shall be shown in
the contract documents.
Design concrete strengths above 10.0 ksi for normal
weight concrete shall be used only when allowed by
specific Articles or when physical tests are made to
establish the relationships between the concrete strength
and other properties. Specified concrete with strengths
below 2.4 ksi should not be used in structural
applications.
The specified compressive strength for prestressed
concrete and decks shall not be less than 4.0 ksi.
For lightweight structural concrete, air dry unit
weight, strength and any other properties required for
the application shall be specified in the contract
documents.
C5.4.2.1
The evaluation of the strength of the concrete used
in the work should be based on test cylinders produced,
tested, and evaluated in accordance with Section 8 of the
AASHTO LRFD Bridge Construction Specifications.
This Section was originally developed based on an
upper limit of 10.0 ksi for the design concrete
compressive strength. As research information for
concrete compressive strengths greater than 10.0 ksi
becomes available, individual Articles are being revised
or extended to allow their use with higher strength
concretes. Appendix C5 contains a listing of the Articles
affected by concrete compressive strength and their
current upper limit.
It is common practice that the specified strength be
attained 28 days after placement. Other maturity ages
may be assumed for design and specified for
components that will receive loads at times appreciably
different than 28 days after placement.
It is recommended that the classes of concrete shown
in Table C5.4.2.1-1 and their corresponding specified
strengths be used whenever appropriate. The classes of
concrete indicated in Table C5.4.2.1-1 have been
developed for general use and are included in AASHTO
LRFD Bridge Construction Specifications, Section 8,
“Concrete Structures,” from which Table C5.4.2.1-1
was taken.
These classes are intended for use as follows:
•
Class A concrete is generally used for all elements
of structures, except when another class is more
appropriate, and specifically for concrete exposed to
saltwater.
•
Class B concrete is used in footings, pedestals,
massive pier shafts, and gravity walls.
•
Class C concrete is used in thin sections, such as
reinforced railings less than 4.0 in. thick, for filler in
steel grid floors, etc.
•
Class P concrete is used when strengths in excess of
4.0 ksi are required. For prestressed concrete,
consideration should be given to limiting the
nominal aggregate size to 0.75 in.
•
Class S concrete is used for concrete deposited
underwater in cofferdams to seal out water.
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2012
Edition
5-14
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
For concrete Classes A, A(AE), and P used in or
over saltwater, the W/C ratio shall be specified not to
exceed 0.45.
The sum of Portland cement and other cementitious
materials shall be specified not to exceed 800 pcy,
except for Class P (HPC) concrete where the sum of
Portland cement and other cementitious materials shall
be specified not to exceed 1000 pcy.
Air-entrained concrete, designated “AE” in
Table C5.4.2.1-1, shall be specified where the concrete
will be subject to alternate freezing and thawing and
exposure to deicing salts, saltwater, or other potentially
damaging environments.
Strengths above 5.0 ksi should be used only when
the availability of materials for such concrete in the
locale is verified.
Lightweight concrete is generally used only under
conditions where weight is critical.
In the evaluation of existing structures, it may be
appropriate to modify the f ′c and other attendant
structural properties specified for the original
construction to recognize the strength gain or any
strength loss due to age or deterioration after 28 days.
Such modified f ′c should be determined by core samples
of sufficient number and size to represent the concrete in
the work, tested in accordance with AASHTO
T 24M/T 24 (ASTM C42/C42M).
There is considerable evidence that the durability of
reinforced concrete exposed to saltwater, deicing salts,
or sulfates is appreciably improved if, as recommended
by ACI 318, either or both the cover over the reinforcing
steel is increased or the W/C ratio is limited to 0.40. If
materials, with reasonable use of admixtures, will
produce a workable concrete at W/C ratios lower than
those listed in Table C5.4.2.1-1, the contract documents
should alter the recommendations in Table C5.4.2.1-1
appropriately.
The specified strengths shown in Table C5.4.2.1-1
are generally consistent with the W/C ratios shown.
However, it is possible to satisfy one without the other.
Both are specified because W/C ratio is a dominant
factor contributing to both durability and strength;
simply obtaining the strength needed to satisfy the
design assumptions may not ensure adequate durability.
Table C5.4.2.1-1—Concrete Mix Characteristics by Class
Minimum
Cement
Content
Maximum W/C
Ratio
pcy
611
611
517
lbs. Per lbs.
0.49
0.45
0.58
B(AE)
517
0.55
C
C(AE)
P
P(HPC)
658
658
564
0.49
0.45
0.49
S
Lightweight
658
564
0.58
Class of
Concrete
A
A(AE)
B
Coarse
Aggregate
Per AASHTO M 43
(ASTM D448)
Square Size of
%
Openings (in.)
—
1.0 to No. 4
6.0 ± 1.5
1.0 to No. 4
—
2.0 to No. 3 and No. 3
to No. 4
5.0 ± 1.5
2.0 to No. 3 and No. 3
to No. 4
—
0.5 to No. 4
7.0 ± 1.5
0.5 to No. 4
As specified
1.0 to No. 4
elsewhere
or
0.75 to No. 4
—
1.0 to No. 4
As specified in the contract documents
Air
Content
Range
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
28-Day
Compressive
Strength
ksi
4.0
4.0
2.4
2.4
4.0
4.0
As specified
elsewhere
—
2012
Edition
SECTION 5: CONCRETE STRUCTURES
5-15
5.4.2.2—Coefficient of Thermal Expansion
The coefficient of thermal expansion should be
determined by the laboratory tests on the specific mix to
be used.
In the absence of more precise data, the thermal
coefficient of expansion may be taken as:
•
For normal weight concrete: 6.0 × 10–6/°F, and
•
For lightweight concrete: 5.0 × 10–6/°F
C5.4.2.2
The thermal coefficient depends primarily on the
types and proportions of aggregates used and on the
degree of saturation of the concrete.
The thermal coefficient of normal weight concrete
can vary between 3.0 to 8.0 × 10.0–6/°F, with limestone
and marble aggregates producing the lower values, and
chert and quartzite the higher. Only limited
determinations of these coefficients have been made for
lightweight concretes. They are in the range of 4.0 to
6.0 × 10–6/°F and depend on the amount of natural sand
used.
Additional information may be found in ACI 209,
ACI 343 and ACI 213.
5.4.2.3—Shrinkage and Creep
C5.4.2.3.1
5.4.2.3.1—General
Values of shrinkage and creep, specified herein and
in Articles 5.9.5.3 and 5.9.5.4, shall be used to
determine the effects of shrinkage and creep on the loss
of prestressing force in bridges other than segmentally
constructed ones. These values in conjunction with the
moment of inertia, as specified in Article 5.7.3.6.2, may
be used to determine the effects of shrinkage and creep
on deflections.
These provisions shall be applicable for specified
concrete strengths up to 15.0 ksi. In the absence of more
accurate data, the shrinkage coefficients may be
assumed to be 0.0002 after 28 days and 0.0005 after one
year of drying.
When mix-specific data are not available, estimates
of shrinkage and creep may be made using the
provisions of:
•
Articles 5.4.2.3.2 and 5.4.2.3.3,
•
The CEB-FIP model code, or
•
ACI 209.
Creep and shrinkage of concrete are variable
properties that depend on a number of factors, some of
which may not be known at the time of design.
Without specific physical tests or prior experience
with the materials, the use of the empirical methods
referenced in these Specifications cannot be expected to
yield results with errors less than ±50 percent.
For segmentally constructed bridges, a more precise
estimate shall be made, including the effect of:
•
Specific materials,
•
Structural dimensions,
•
Site conditions, and
•
Construction methods, and
•
Concrete age at various stages of erection.
5.4.2.3.2—Creep
C5.4.2.3.2
The creep coefficient may be taken as:
ψ ( t ,ti ) = 1.9k s khc k f ktd ti −0.118
(5.4.2.3.2-1)
The methods of determining creep and shrinkage, as
specified herein and in Article 5.4.2.3.3, are based on
Huo et al. (2001), Al-Omaishi (2001), Tadros (2003),
and Collins and Mitchell (1991). These methods are
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
5-16
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
in which:
ks = 1.45 – 0.13(V/S) ≥ 1.0
(5.4.2.3.2-2)
khc = 1.56 – 0.008H
(5.4.2.3.2-3)
5
1 + f ci′
(5.4.2.3.2-4)
t
ktd =
61 − 4 f ci′ + t
(5.4.2.3.2-5)
kf =
where:
H
=
ks
=
kf
khc
ktd
t
=
=
=
=
ti
=
V/S =
f ′ci =
relative humidity (%). In the absence of better
information, H may be taken from
Figure 5.4.2.3.3-1.
factor for the effect of the volume-to-surface
ratio of the component
factor for the effect of concrete strength
humidity factor for creep
time development factor
maturity of concrete (day), defined as age of
concrete between time of loading for creep
calculations, or end of curing for shrinkage
calculations, and time being considered for
analysis of creep or shrinkage effects
age of concrete at time of load application
(day)
volume-to-surface ratio (in.)
specified compressive strength of concrete at
time of prestressing for pretensioned members
and at time of initial loading for nonprestressed
members. If concrete age at time of initial
loading is unknown at design time, f ′ci may be
taken as 0.80 f ′c (ksi).
The surface area used in determining the volume-tosurface ratio should include only the area that is exposed
to atmospheric drying. For poorly ventilated enclosed
cells, only 50 percent of the interior perimeter should be
used in calculating the surface area. For precast
members with cast-in-place topping, the total precast
surface should be used. For pretensioned stemmed
members (I-beams, T-beams, and box beams), with an
average web thickness of 6.0 to 8.0 in., the value of kvs
may be taken as 1.00.
based on the recommendation of ACI Committee 209 as
modified by additional recently published data. Other
applicable references include Rusch et al. (1983), Bazant
and Wittman (1982), and Ghali and Favre (1986).
The creep coefficient is applied to the compressive
strain caused by permanent loads in order to obtain the
strain due to creep.
Creep is influenced by the same factors as
shrinkage, and also by:
•
Magnitude and duration of the stress,
•
Maturity of the concrete at the time of loading, and
•
Temperature of concrete.
Creep shortening of concrete under permanent loads
is generally in the range of 0.5 to 4.0 times the initial
elastic shortening, depending primarily on concrete
maturity at the time of loading.
The time development of shrinkage, given by
Eq. 5.4.2.3.2-5, is proposed to be used for both precast
concrete and cast-in-place concrete components of a
bridge member, and for both accelerated curing and
moist curing conditions. This simplification is based on
a parametric study documented in Tadros (2003), on
prestress losses in high strength concrete. It was found
that various time development prediction methods have
virtually no impact on the final creep and shrinkage
coefficients, prestress losses, or member deflections.
It was also observed in that study that use of modern
concrete mixtures with relatively low water/cement
ratios and with high range water reducing admixtures,
has caused time development of both creep and
shrinkage to have similar patterns. They have a
relatively rapid initial development in the first several
weeks after concrete placement and a slow further
growth thereafter. For calculation of intermediate values
of prestress losses and deflections in cast-in-place
segmental bridges constructed with the balanced
cantilever method, it may be warranted to use actual test
results for creep and shrinkage time development using
local conditions. Final losses and deflections would be
substantially unaffected whether Eq. 5.4.2.3.2-5 or
another time-development formula is used.
The factors for the effects of volume-to-surface
ratio are an approximation of the following formulas:
For creep:
t
26 e 0.36(V/S ) + t 1.80 + 1.77 e −0.54(V/S )
kc =
t
2.587
45 + t
(C5.4.2.3.2-1)
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2012
Edition
SECTION 5: CONCRETE STRUCTURES
5-17
For shrinkage:
t
26e0.36(V/S ) + t 1064 − 94(V/S )
ks =
t
923
45 + t
(C5.4.2.3.2-2)
The maximum V/S ratio considered in the
development of Eqs. C5.4.2.3.2-1 and C5.4.2.3.2-2 was
6.0 in.
Ultimate creep and shrinkage are less sensitive to
surface exposure than intermediate values at an early
age of concrete. For accurately estimating intermediate
deformations of such specialized structures as
segmentally constructed balanced cantilever box girders,
it may be necessary to resort to experimental data or use
the more detailed Eqs. C5.4.2.3.2-1 and C5.4.2.3.2-2.
C5.4.2.3.3
5.4.2.3.3—Shrinkage
For concretes devoid of shrinkage-prone aggregates,
the strain due to shrinkage, εsh, at time, t, may be taken
as:
ε sh = k s khs k f ktd 0.48 × 10−3
(5.4.2.3.3-1)
in which:
khs
=
(2.00 – 0.014 H)
(5.4.2.3.3-2)
where:
khs =
humidity factor for shrinkage
If the concrete is exposed to drying before 5 days of
curing have elapsed, the shrinkage as determined in
Eq. 5.4.2.3.3-1 should be increased by 20 percent.
Shrinkage of concrete can vary over a wide range
from nearly nil if continually immersed in water to in
excess of 0.0008 for thin sections made with high
shrinkage aggregates and sections that are not properly
cured.
Shrinkage is affected by:
•
Aggregate characteristics and proportions,
•
Average humidity at the bridge site,
•
W/C ratio,
•
Type of cure,
•
Volume to surface area ratio of member, and
•
Duration of drying period.
Large concrete members may undergo substantially
less shrinkage than that measured by laboratory testing
of small specimens of the same concrete. The
constraining effects of reinforcement and composite
actions with other elements of the bridge tend to reduce
the dimensional changes in some components.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
5-18
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure 5.4.2.3.3-1—Annual Average Ambient Relative
Humidity in Percent
5.4.2.4—Modulus of Elasticity
C5.4.2.4
In the absence of measured data, the modulus of
elasticity, Ec, for concretes with unit weights between
0.090 and 0.155 kcf and specified compressive strengths
up to 15.0 ksi may be taken as:
1.5
E c = 33,000 K1 wc
f c′
(5.4.2.4-1)
where:
K1 =
wc =
f ′c =
correction factor for source of aggregate to be
taken as 1.0 unless determined by physical test,
and as approved by the authority of jurisdiction
unit weight of concrete (kcf); refer to
Table 3.5.1-1 or Article C5.4.2.4
specified compressive strength of concrete (ksi)
5.4.2.5—Poisson’s Ratio
Unless determined by physical tests, Poisson’s ratio
may be assumed as 0.2. For components expected to be
subject to cracking, the effect of Poisson’s ratio may be
neglected.
5.4.2.6—Modulus of Rupture
Unless determined by physical tests, the modulus of
rupture, fr, for specified concrete strengths up to 15.0 ksi
may be taken as:
•
For normal-weight concrete:
o
Except as specified below .............. 0.24√f ′c
See commentary for specified strength in
Article 5.4.2.1.
For normal weight concrete with wc = 0.145 kcf, Ec
may be taken as:
Ec = 1,820 f c′
(C5.4.2.4-1)
Test data show that the modulus of elasticity of
concrete is influenced by the stiffness of the aggregate.
The factor K1 is included to allow the calculated
modulus to be adjusted for different types of aggregate
and local materials. Unless a value has been determined
by physical tests, K1 should be taken as 1.0. Use of a
measured K1 factor permits a more accurate prediction
of modulus of elasticity and other values that utilize it.
C5.4.2.5
This is a ratio between the lateral and axial strains
of an axially and/or flexurally loaded structural element.
C5.4.2.6
Most modulus of rupture test data on normal weight
concrete is between 0.24√f ′c and 0.37√f ′c (ksi) (Walker
and Bloem, 1960; Khan, Cook, and Mitchell, 1996). A
value of 0.37√f ′c has been recommended for the
prediction of the tensile strength of high-strength
concrete (ACI, 1992). However, the modulus of rupture
is sensitive to curing methods and nearly all of the test
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2012
Edition
SECTION 5: CONCRETE STRUCTURES
o
•
When used to calculate the cracking
moment of a member in
Article 5.8.3.4.3 ............................ 0.20√f ′c
For lightweight concrete:
o
For sand—lightweight concrete .... 0.20√f ′c
o
For all—lightweight concrete ....... 0.17√f ′c
When physical tests are used to determine modulus of
rupture, the tests shall be performed in accordance with
AASHTO T 97 and shall be performed on concrete
using the same proportions and materials as specified for
the structure.
5-19
units in the dataset mentioned previously were moist
cured until testing. Carrasquillio et al. (1981) noted a
26 percent reduction in the 28-day modulus of rupture if
high-strength units were allowed to dry after 7 days of
moist curing over units that were moist cured until
testing.
The flexural cracking stress of concrete members
has been shown to significantly reduce with increasing
member depth. Shioya et al. (1989) observed that the
flexural cracking strength is proportional to H-0.25 where
H is the overall depth of the flexural member in inches.
Based on this observation, a 36.0 in. deep girder should
achieve a flexural cracking stress that is 36 percent
lower than that of a 6.0 in. deep modulus of rupture test.
Since modulus of rupture units were either 4.0 or
6.0 in. deep and moist cured up to the time of testing,
the modulus of rupture should be significantly greater
than that of an average size bridge member composed of
the same concrete. Therefore, 0.24√f ′c is appropriate for
checking minimum reinforcement in Article 5.7.3.3.2.
The properties of higher-strength concretes are
particularly sensitive to the constitutive materials. If test
results are to be used in design, it is imperative that tests
be made using concrete with not only the same mix
proportions but also the same materials as the concrete
used in the structure.
The given values may be unconservative for tensile
cracking caused by restrained shrinkage, anchor zone
splitting, and other such tensile forces caused by effects
other than flexure. The direct tensile strength stress
should be used for these cases.
C5.4.2.7
5.4.2.7—Tensile Strength
Direct tensile strength may be determined by either
using ASTM C900, or the split tensile strength method
in accordance with AASHTO T 198 (ASTM C496).
For normal-weight concrete with specified
compressive strengths up to 10 ksi, the direct tensile
strength may be estimated as fr = 0.23√f ′c.
5.4.3—Reinforcing Steel
5.4.3.1—General
2013 Revision
C5.4.3.1
2013 Revision
Reinforcing bars, deformed wire, cold-drawn wire,
welded plain wire fabric, and welded deformed wire
fabric shall conform to the material standards as
specified in Article 9.2 of the AASHTO LRFD Bridge
Construction Specifications.
Reinforcement shall be deformed, except that plain
bars or plain wire may be used for spirals, hoops, and
wire fabric.
The nominal yield strength shall be the minimum as
specified for the grade of steel selected, except that yield
strengths in excess of 75.0 ksi shall not be used for
design purposes. The yield strength or grade of the bars
or wires shall be shown in the contract documents. Bars
with yield strengths less than 60.0 ksi shall be used only
with the approval of the Owner.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
5-20
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Where ductility is to be assured or where welding is
required, steel conforming to the requirements of ASTM
A706, “Low Alloy Steel Deformed Bars for Concrete
Reinforcement,” should be specified.
5.4.3.2—Modulus of Elasticity
ASTM A706 reinforcement should be considered
for seismic design because of the greater quality control
by which unanticipated overstrength is limited.
2013 Revision
The modulus of elasticity, Es, of steel reinforcing
shall be assumed as 29,000 ksi.
5.4.3.3—Special Applications
2013 Revision
Reinforcement to be welded shall be indicated in
the contract documents, and the welding procedure to be
used shall be specified.
Reinforcement conforming to ASTM A1035/
A1035M may only be used as top and bottom flexural
reinforcement in the longitudinal and transverse
directions of bridge decks in Seismic Zones 1 and 2.
C5.4.3.3
2013 Revision
In 2004, ASTM published A1035/A1035M,
Standard Specification for Deformed and Plain, Lowcarbon, Chromium, Steel Bars for Concrete
Reinforcement. This reinforcement offers the potential
for corrosion resistance.
Epoxy-coated reinforcing steel provides a physical
barrier to inhibit corrosion of the steel in the presence of
chlorides. The handling, placement, and repair of epoxycoated reinforcing steel requires significant care and
attention.
Reinforcement conforming to ASTM A1035/
A1035M has a specified minimum yield strength of
100 ksi determined by the 0.2 percent offset method, a
specified minimum tensile strength of 150 ksi, and a
specified minimum elongation of six or seven percent
depending on bar size. There is also a requirement that
the stress corresponding to a tensile strain of 0.0035
shall be a minimum of 80 ksi. The reinforcement has a
non-linear stress-strain relationship. Article 5.4.3.1 of
the Design Specifications states that yield strengths in
excess of 75.0 ksi shall not be used for design purposes.
Consequently, design is based on a stress of 75.0 ksi, but
the actual strength is at least twice that value. This has
lead to concerns about the applicability of the existing
specifications with ASTM A1035 reinforcement.
Consequently, it is proposed that initial usage of the
reinforcement be restricted to top and bottom flexural
reinforcement in the transverse and longitudinal
directions of bridge decks in Seismic Zones 1 and 2.
5.4.4—Prestressing Steel
C5.4.4.1
5.4.4.1—General
Uncoated, stress-relieved or low-relaxation,
seven-wire strand, or uncoated plain or deformed,
high-strength bars, shall conform to the following
materials standards, as specified for use in AASHTO
LRFD Bridge Construction Specifications:
•
AASHTO M 203/M 203M (ASTM A416/A416M),
or
•
AASHTO M 275/M 275M (ASTM A722/A722M).
Low relaxation strand shall be regarded as the
standard type. Stress-relieved (normal relaxation) strand
will not be furnished unless specifically ordered, or by
arrangement between purchaser and supplier.
Tensile and yield strengths for these steels may be
taken as specified in Table 5.4.4.1-1.
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2012
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SECTION 5: CONCRETE STRUCTURES
5-21
Table 5.4.4.1-1—Properties of Prestressing Strand and Bar
Material
Strand
Bar
Grade or Type
Diameter (in.)
Tensile Strength,
fpu (ksi)
Yield Strength,
fpy (ksi)
250 ksi
270 ksi
1/4 to 0.6
3/8 to 0.6
250
270
Type 1, Plain
Type 2, Deformed
3/4 to 1-3/8
5/8 to 1-3/8
150
150
85% of fpu, except 90% of
fpu for low-relaxation
strand
85% of fpu
80% of fpu
Where complete prestressing details are included in
the contract documents, the size and grade or type of
steel shall be shown. If the plans indicate only the
prestressing forces and locations of application, the
choice of size and type of steel shall be left to the
Contractor, subject to the Engineer's approval.
5.4.4.2—Modulus of Elasticity
If more precise data are not available, the modulus
of elasticity for prestressing steels, based on nominal
cross-sectional area, may be taken as:
for strand:
for bar:
Ep = 28,500 ksi, and
Ep = 30,000 ksi
C5.4.4.2
The suggested modulus of elasticity of 28,500 ksi
for strands is based on recent statistical data. This value
is higher than that previously assumed because of the
slightly different characteristics and the near universal
use of low-relaxation strands.
As shown in Figure C5.4.4.2-1, there is no sharp
break in the curves to indicate a distinct elastic limit or
yield point. Arbitrary methods of establishing yield
strength, based on a specific set or measured strain, are
generally used. The 0.2 percent offset and the one
percent extension methods are the most common.
Figure C5.4.4.2-1—Typical Stress-Strain Curve for
Prestressing Steels
5.4.5—Post-Tensioning Anchorages and Couplers
C5.4.5
Anchorages and tendon couplers shall conform to
the requirements of Article 10.3.2 of AASHTO LRFD
Bridge Construction Specifications.
Corrosion protection shall be provided for tendons,
anchorages, end fittings, and couplers.
Complete details for qualification testing of
anchorages and couplers are included in Article 10.3.2
of AASHTO LRFD Bridge Construction Specifications.
Characteristics of anchorages and couplers related
to design and detailing are summarized below from
AASHTO LRFD Bridge Construction Specifications:
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2012
Edition
5-22
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
•
Anchorages and couplers are to develop at least 95
percent of the minimum specified ultimate strength
of the prestressing steel without exceeding the
anchorage set movement assumed for the design.
Unbonded systems are to also pass a dynamic
loading test.
•
Couplers are not to be used at points of sharp
tendon curvature.
•
Couplers are to be used only at locations shown on
the contract documents or approved by the
Engineer.
•
Couplers are to be enclosed in housings long
enough to permit the necessary movements.
•
Where bonded anchorages or couplers are located at
sections that are critical at strength limit state, the
strength required of the bonded tendons is not to
exceed the resistance of the tendon assembly,
including the anchorage or coupler, tested in an
unbonded state.
•
Bearing stresses on concrete under anchorage
distribution plates are not to exceed specified limits.
•
Unless waived by the Engineer because of suitable
previous tests and/or experience, qualification of
anchorages and couplers are to be verified by
testing.
5.4.6—Ducts
C5.4.6.1
5.4.6.1—General
Ducts for tendons shall be rigid or semirigid either
galvanized ferrous metal or polyethylene, or they shall
be formed in the concrete with removable cores.
The radius of curvature of tendon ducts shall not be
less than 20.0 ft, except in the anchorage areas where
12.0 ft may be permitted.
Polyethylene ducts shall not be used when the
radius of curvature of the tendon is less than 30.0 ft.
Where polyethylene ducts are used and the tendons
are to be bonded, the bonding characteristics of
polyethylene ducts to the concrete and the grout should
be investigated.
The effects of grouting pressure on the ducts and
the surrounding concrete shall be investigated.
The maximum support interval for the ducts during
construction shall be indicated in the contract documents
and shall conform to Article 10.4.1.1 of the AASHTO
LRFD Bridge Construction Specifications.
5.4.6.2—Size of Ducts
The inside diameter of ducts shall be at least
0.25 in. larger than the nominal diameter of single bar or
strand tendons. For multiple bar or strand tendons, the
inside cross-sectional area of the duct shall be at least
The use of polyethylene duct is generally
recommended in corrosive environments. Pertinent
requirements for ducts can be found in Article 10.8.2 in
AASHTO LRFD Bridge Construction Specifications.
Polyethylene duct should not be used on radii under
30.0 ft because of its lower resistance to abrasion during
pulling-through and stressing tendons.
The contract documents should indicate the specific
type of duct material to be used when only one type is to
be allowed.
C5.4.6.2
The pull-through method of tendon placement is
usually employed by contractors where tendons exceed
400 ft in length.
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2012
Edition
SECTION 5: CONCRETE STRUCTURES
5-23
2.0 times the net area of the prestressing steel with one
exception where tendons are to be placed by the pullthrough method, the duct area shall be at least 2.5 times
the net area of the prestressing steel.
The size of ducts shall not exceed 0.4 times the least
gross concrete thickness at the duct.
5.4.6.3—Ducts at Deviation Saddles
Ducts at deviation saddles shall be galvanized steel
pipe conforming to the requirements of ASTM A53,
Type E, Grade B. The nominal wall thickness of the
pipe shall be not less than 0.125 in.
5.5—LIMIT STATES
5.5.1—General
Structural components shall be proportioned to
satisfy the requirements at all appropriate service,
fatigue, strength, and extreme event limit states.
Prestressed and partially prestressed concrete
structural components shall be investigated for stresses
and deformations for each stage that may be critical
during construction, stressing, handling, transportation,
and erection as well as during the service life of the
structure of which they are part.
Stress concentrations due to prestressing or other
loads and to restraints or imposed deformations shall be
considered.
5.5.2—Service Limit State
Actions to be considered at the service limit state
shall be cracking, deformations, and concrete stresses, as
specified in Articles 5.7.3.4, 5.7.3.6, and 5.9.4,
respectively.
The cracking stress shall be taken as the modulus of
rupture specified in Article 5.4.2.6.
5.5.3—Fatigue Limit State
C5.5.3.1
5.5.3.1—General
Fatigue need not be investigated for concrete deck
slabs in multigirder applications or reinforced-concrete
box culverts.
In regions of compressive stress due to permanent
loads and prestress in reinforced concrete components,
fatigue shall be considered only if this compressive
stress is less than the maximum tensile live load stress
resulting from the Fatigue I load combination as
specified in Table 3.4.1-1 in combination with the
provisions of Article 3.6.1.4.
Stresses measured in concrete deck slabs of bridges
in service are far below infinite fatigue life, most probably
due to internal arching action; see Article C9.7.2.
Fatigue evaluation for reinforced-concrete box
culverts showed that the live load stresses in the
reinforcement due to Fatigue I load combination did not
reduce the member resistance at the strength limit state.
In determining the need to investigate fatigue,
Table 3.4.1-1 specifies a load factor of 1.50 on the live
load force effect resulting from the fatigue truck for the
Fatigue I load combination. This factored live load force
effect represents the greatest fatigue stress that the
bridge will experience during its life.
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2012
Edition
5-24
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Fatigue of the reinforcement need not be checked
for fully prestressed components designed to have
extreme fiber tensile stress due to Service III Limit State
within the tensile stress limit specified in Table
5.9.4.2.2-1. Structural components with a combination
of prestressing strands and reinforcing bars that allow
the tensile stress in the concrete to exceed the Service III
limit specified in Table 5.9.4.2.2-1 shall be checked for
fatigue.
For fatigue considerations, concrete members shall
satisfy:
γ ( Δf ) ≤ ( ΔF )TH
Fatigue limit state load factor, girder distribution
factors, and dynamic allowance cause fatigue limit state
stress to be considerably less than the corresponding
value determined from Service Limit State III. For fully
prestressed components, the net concrete stress is
usually significantly less than the concrete tensile stress
limit specified in Table 5.9.4.2.2-1. Therefore, the
calculated flexural stresses are significantly reduced. For
this situation, the calculated steel stress range, which is
equal to the modular ratio times the concrete stress
range, is almost always less than the steel fatigue stress
range limit specified in Article 5.5.3.3.
(5.5.3.1-1)
where:
γ
=
Δf
=
(ΔF)TH =
load factor specified in Table 3.4.1-1 for
the Fatigue I load combination
force effect, live load stress range due to
the passage of the fatigue load as specified
in Article 3.6.1.4 (ksi)
constant-amplitude fatigue threshold, as
specified in Article 5.5.3.2, 5.5.3.3, or
5.5.3.4, as appropriate (ksi)
For fully prestressed components in other than
segmentally constructed bridges, the compressive stress
due to the Fatigue I load combination and one-half the
sum of effective prestress and permanent loads shall not
exceed 0.40f ′c after losses.
The section properties for fatigue investigations
shall be based on cracked sections where the sum of
stresses, due to unfactored permanent loads and
prestress, and the Fatigue I load combination is tensile
and exceeds 0.095√f ′c.
5.5.3.2—Reinforcing Bars
2013 Revision
The constant-amplitude fatigue threshold, (ΔF)TH,
for straight reinforcement and welded wire
reinforcement without a cross weld in the high-stress
region shall be taken as:
( ΔF )TH
= 24 − 0.33 f min
(5.5.3.2-1)
The constant-amplitude fatigue threshold, (ΔF)TH,
for straight welded wire reinforcement with a cross weld
in the high-stress region shall be taken as:
( ΔF )TH
where:
= 16 − 0.33 f min
(5.5.3.2-2)
C5.5.3.2
2013 Revision
Bends in primary reinforcement should be avoided
in regions of high stress range.
Structural welded wire reinforcement has been
increasingly used in bridge applications in recent years,
especially as auxiliary reinforcement in bridge I- and
box beams and as primary reinforcement in slabs.
Design for shear has traditionally not included a fatigue
check of the reinforcement as the member is expected to
be uncracked under service conditions and the stress
range in steel minimal. The stress range for steel bars
has existed in previous editions. It is based on Hansen et
al. (1976). The simplified form in this edition replaces
the (r/h) parameter with the default value 0.3
recommended by Hansen et al. Inclusion of limits for
WWR is based on recent studies by Hawkins et al.
(1971, 1987) and Tadros et al. (2004).
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2012
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
SECTION 5: CONCRETE STRUCTURES
fmin =
5-25
minimum live-load stress resulting from the
Fatigue I load combination, combined with the
more severe stress from either the permanent
loads or the permanent loads, shrinkage, and
creep-induced external loads; positive if
tension, negative if compression (ksi)
Since the fatigue provisions were developed based
primarily on ASTM A615 steel reinforcement, their
applicability to other types of reinforcement is largely
unknown. Consequently, a cautionary note is added to
the Commentary.
The definition of the high-stress region for application of
Eqs. 5.5.3.2-1 and 5.5.3.2-2 for flexural reinforcement
shall be taken as one-third of the span on each side of the
section of maximum moment.
5.5.3.3—Prestressing Tendons
C5.5.3.3
The constant-amplitude fatigue threshold, (ǻF)TH,
for prestressing tendons shall be taken as:
•
18.0 ksi for radii of curvature in excess of 30.0 ft,
and
•
10.0 ksi for radii of curvature not exceeding 12.0 ft.
A linear interpolation may be used for radii between
12.0 and 30.0 ft.
5.5.3.4—Welded or Mechanical Splices of
Reinforcement
For welded or mechanical connections that are
subject to repetitive loads, the constant-amplitude
shall be as given in
fatigue threshold, (ǻF)TH,
Table 5.5.3.4-1.
Table 5.5.3.4-1—Constant-Amplitude Fatigue Threshold of
Splices
Type of Splice
Grout-filled sleeve, with or without
epoxy coated bar
Cold-swaged coupling sleeves
without threaded ends and with or
without epoxy-coated bar;
Integrally-forged coupler with upset
NC threads; Steel sleeve with a
wedge; One-piece taper-threaded
coupler; and Single V-groove direct
butt weld
All other types of splices
(ǻF)TH
for greater
than
1,000,000
cycles
18 ksi
12 ksi
4 ksi
Where the total cycles of loading, N, as specified in
Eq. 6.6.1.2.5-2, are less than one million, (ǻF)TH in
Table 5.5.3.4-1 may be increased by the quantity
24 (6ílogN) ksi to a total not greater than the value
given by Eq. 5.5.3.2-1 in Article 5.5.3.2. Higher values
Where the radius of curvature is less than shown, or
metal-to-metal fretting caused by prestressing tendons
rubbing on hold-downs or deviations is apt to be a
consideration, it will be necessary to consult the
literature for more complete presentations that will allow
the increased bending stress in the case of sharp
curvature, or fretting, to be accounted for in the
development of permissible fatigue stress ranges. Metalto-metal fretting is not normally expected to be a
concern in conventional pretensioned beams.
C5.5.3.4
Review of the available fatigue and static test data
indicates that any splice, that develops 125 percent of
the yield strength of the bar will sustain one million
cycles of a 4 ksi constant amplitude stress range. This
lower limit is a close lower bound for the splice fatigue
data obtained in NCHRP Project 10-35, and it also
agrees well with the limit of 4.5 ksi for Category E from
the provisions for fatigue of structural steel weldments.
The strength requirements of Articles 5.11.5.2.2 and
5.11.5.2.3 also will generally ensure that a welded splice
or mechanical connector will also meet certain minimum
requirements for fabrication and installation, such as
sound welding and proper dimensional tolerances.
Splices that do not meet these requirements for
fabrication and installation may have reduced fatigue
performance. Further, splices designed to the lesser
force requirements of Article 5.11.5.3.2 may not have
the same fatigue performance as splices designed for the
greater force requirement. Consequently, the minimum
strength requirement indirectly provides for a minimum
fatigue performance.
It was found in NCHRP Project 10-35 that there is
substantial variation in the fatigue performance of
different types of welds and connectors. However, all
types of splices appeared to exhibit a constant amplitude
fatigue limit for repetitive loading exceeding about
one million cycles. The stress ranges for over one million
cycles of loading given in Table 5.5.3.4-1 are based on
statistical tolerance limits to constant amplitude staircase
test data, such that there is a 95 percent level of
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2012
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
5-26
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
of (ǻF)TH, up to the value given by Eq. 5.5.3.2-1, may
be used if justified by fatigue test data on splices that are
the same as those that will be placed in service.
Welded or mechanical splices shall not be used with
ASTM A1035/A1035M reinforcement.
confidence that 95 percent of the data would exceed the
given values for five million cycles of loading. These
values may, therefore, be regarded as a fatigue limit
below which fatigue damage is unlikely to occur during
the design lifetime of the structure. This is the same basis
used to establish the fatigue design provisions for
unspliced reinforcing bars in Article 5.5.3.2, which is
based on fatigue tests reported in NCHRP Report 164,
Fatigue Strength of High-Yield Reinforcing Bars.
5.5.4—Strength Limit State
5.5.4.1—General
C5.5.4.1
The strength limit state issues to be considered shall
be those of strength and stability.
Factored resistance shall be the product of nominal
resistance as determined in accordance with the
applicable provisions of Articles 5.6, 5.7, 5.8, 5.9, 5.10,
5.13, and 5.14, unless another limit state is specifically
identified, and the resistance factor is as specified in
Article 5.5.4.2.
Additional resistance factors are specified in
Article 12.5.5 for buried pipes and box structures made
of concrete.
5.5.4.2—Resistance Factors
5.5.4.2.1—Conventional Construction
2013 Revision
Resistance factor φ shall be taken as:
•
For tension-controlled reinforced concrete sections
as defined in Article 5.7.2.1 ............................... 0.90
•
For tension-controlled prestressed concrete
sections as defined in Article 5.7.2.1 ................. 1.00
•
For shear and torsion:
normal weight concrete ............................... 0.90
lightweight concrete .................................... 0.80
•
For compression-controlled sections with spirals or
ties, as defined in Article 5.7.2.1, except as
specified in Articles 5.10.11.3 and 5.10.11.4.1b for
Seismic Zones 2, 3, and 4 at the extreme event limit
state .................................................................... 0.75
•
For bearing on concrete...................................... 0.70
•
For compression in strut-and-tie models ............ 0.70
C5.5.4.2.1
2013 Revision
In applying the resistance factors for tensioncontrolled and compression-controlled sections, the
axial tensions and compressions to be considered are
those caused by external forces. Effects of primary
prestressing forces are not included.
In editions of and interims to the LRFD
Specifications prior to 2005, the provisions specified the
magnitude of the resistance factor for cases of axial load
or flexure, or both, it terms of the type of loading. For
these cases, the φ-factor is now determined by the strain
conditions at a cross-section, at nominal strength. The
background and basis for these provisions are given in
Mast (1992) and ACI 318-02.
A lower φ-factor is used for compression-controlled
sections than is used for tension-controlled sections
because compression-controlled sections have less
ductility, are more sensitive to variations in concrete
strength, and generally occur in members that support
larger loaded areas than members with tensioncontrolled sections.
For sections subjected to axial load with flexure,
factored resistances are determined by multiplying both
Pn and Mn by the appropriate single value of φ.
Compression-controlled and tension-controlled sections
are defined in Article 5.7.2.1 as those that have net
tensile strain in the extreme tension steel at nominal
strength less than or equal to the compression-controlled
strain limit, and equal to or greater than 0.005,
respectively. For sections with net tensile strain İt in the
extreme tension steel at nominal strength between the
above limits, the value of φ may be determined by linear
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SECTION 5: CONCRETE STRUCTURES
5-27
interpolation, as shown in Figure C5.5.4.2.1-1. The
concept of net tensile strain εt is discussed in
Article C5.7.2.1. Classifying sections as tensioncontrolled, transition or compression-controlled, and
linearly varying the resistance factor in the transition
zone between reasonable values for the two extremes,
provides a rational approach for determining φ and
limiting the capacity of over-reinforced sections.
1.2
dt
− 1
c
φ = 0. 58 3 + 0 .2 5
1.1
Prestressed
1
Non-prestressed
0.9
φ
0.8
dt
− 1
c
φ = 0. 65 + 0.1 5
0.7
0.6
Transition
Compression
Tension
Controlled
Controlled
0.5
0.001
0.002
0.003
0.004
0.005
0.006
0.007
εt
Figure C5.5.4.2.1-1—Variation of φ with Net Tensile Strain εt and dt /c for Grade 60 Reinforcement and for Prestressing
Steel
•
For compression in anchorage zones:
normal weight concrete ....................... 0.80
lightweight concrete ............................ 0.65
•
For tension in steel in anchorage zones ............. 1.00
•
For resistance during pile driving ...................... 1.00
For sections in which the net tensile strain in the
extreme tension steel at nominal resistance is between
the limits for compression-controlled and tensioncontrolled sections, φ may be linearly increased from
0.75 to that for tension-controlled sections as the net
tensile strain in the extreme tension steel increases from
the compression-controlled strain limit to 0.005.
This variation φ may be computed for prestressed
members such that:
d
0.75 ≤ φ = 0.583 + 0.25 t − 1 ≤ 1.0
c
(5.5.4.2.1-1)
and for nonprestressed members such that:
d
0.75 ≤ φ = 0.65 + 0.15 t − 1 ≤ 0.9
c
The φ-factor of 0.8 for normal weight concrete
reflects the importance of the anchorage zone, the brittle
failure mode for compression struts in the anchorage
zone, and the relatively wide scatter of results of
experimental anchorage zone studies. The φ-factor of
0.65 for lightweight concrete reflects its often lower
tensile strength and is based on the multipliers used in
ACI 318-89, Section 11.2.1.2.
The design of intermediate anchorages, anchorages,
diaphragms, and multiple slab anchorages are addressed
in Breen et al. (1994).
The typical cross-section of a continuous concrete
box girder often shows both conventional bar
reinforcing
and
post-tensioning
ducts.
This
superstructure, however, is first designed to satisfy the
Service limit state by determining the number of tendons
required to satisfy allowable stress limits. Then, the
strength limit state is checked. Mild steel may or may
not need to be added. If mild steel is required to satisfy
the Strength but not the service limit state, the member
is still considered fully prestressed for the purpose of
determining the appropriate resistance factor.
(5.5.4.2.1-2)
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
where:
c
=
dt
=
distance from the extreme compression fiber to
the neutral axis (in.)
distance from the extreme compression fiber to
the centroid of the extreme tension steel
element (in.)
C5.5.4.2.2
5.5.4.2.2—Segmental Construction
Resistance factors for the strength limit state shall
be taken as provided in Table 5.5.4.2.2-1 for the
conditions indicated and in Article 5.5.4.2.1 for
conditions not covered in Table 5.5.4.2.2-1.
In selecting resistance factors for flexure, φf, and
shear and torsion, φv, the degree of bonding of the posttensioning system shall be considered. In order for a
tendon to be considered as fully bonded at a section, it
should be fully developed at that section for a
development length not less than that required by
Article 5.11.4. Shorter embedment lengths may be
permitted if demonstrated by full-size tests and approved
by the Engineer.
Where the post-tensioning is a combination of fully
bonded tendons and unbonded or partially bonded
tendons, the resistance factor at any section shall be
based upon the bonding conditions for the tendons
providing the majority of the prestressing force at the
section.
Joints between precast units shall be either cast-inplace closures or match cast and epoxied joints.
Comprehensive tests of a large continuous
three-span model of a twin-cell box girder bridge built
from precast segments with fully bonded internal
tendons and epoxy joints indicated that cracking was
well distributed through the segment lengths. No epoxy
joint opened at failure, and the load deflection curve was
identical to that calculated for a monolithic specimen.
The complete ultimate strength of the tendons was
developed at failure. The model had substantial ductility
and full development of calculated deflection at failure.
Flexural cracking concentrated at joints and final failure
came when a central joint opened widely and crushing
occurred at the top of the joint. Based on the observation
of this limited test data, a maximum φ of 0.95 was
selected.
Table 5.5.4.2.2-1—Resistance Factor for Joints in
Segmental Construction
φf
Flexure
Normal Weight Concrete
Fully Bonded Tendons
0.95
φv
Shear
Unbonded or Partially
0.90
Bonded Tendons
Sand-Lightweight Concrete
Fully Bonded Tendons
0.90
0.85
Unbonded or Partially
Bonded Tendons
0.85
0.90
0.70
0.65
5.5.4.2.3—Special Requirements for Seismic
Zones 2, 3, and 4
A modified resistance factor for columns in Seismic
Zones 2, 3, and 4 shall be taken as specified in
Articles 5.10.11.3 and 5.10.11.4.1b.
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SECTION 5: CONCRETE STRUCTURES
5-29
5.5.4.3—Stability
The structure as a whole and its components shall
be designed to resist sliding, overturning, uplift and
buckling. Effects of eccentricity of loads shall be
considered in the analysis and design.
Buckling of precast members during handling,
transportation, and erection shall be investigated.
5.5.5—Extreme Event Limit State
The structure as a whole and its components shall
be proportioned to resist collapse due to extreme events,
specified in Table 3.4.1-1, as may be appropriate to its
site and use.
5.6—DESIGN CONSIDERATIONS
5.6.1—General
C5.6.1
Components and connections shall be designed to
resist load combinations, as specified in Section 3, at all
stages during the life of the structure, including those
during construction. Load factors shall be as specified in
Section 3.
As specified in Section 4, equilibrium and strain
compatibility shall be maintained in the analysis.
This Article reflects the AASHTO Standard
Specifications for Highway Bridges (1996), the
AASHTO Guide Specifications for Design and
Construction of Segmental Concrete Bridges (1989) and
the Ontario Highway Bridge Design Code (1991).
5.6.2—Effects of Imposed Deformation
C5.6.2
The effects of imposed deformations due to
shrinkage, temperature change, creep, prestressing, and
movements of supports shall be investigated.
For common structure types, experience may show
that evaluating the redistribution of force effects as a
result of creep and shrinkage is unnecessary.
5.6.3—Strut-and-Tie Model
C5.6.3.1
5.6.3.1—General
Strut-and-tie models may be used to determine
internal force effects near supports and the points of
application of concentrated loads at strength and
extreme event limit states.
The strut-and-tie model should be considered for
the design of deep footings and pile caps or other
situations in which the distance between the centers of
applied load and the supporting reactions is less than
about twice the member thickness.
Where the conventional methods of strength of
materials are not applicable because of nonlinear strain
distribution, the strut-and-tie modeling may provide a
convenient way of approximating load paths and force
effects in the structure. In fact, the load paths may be
visualized and the geometry of concrete and steel
selected to implement the load path.
The strut-and-tie model is new to these
Specifications. More detailed information on this
method is given by Schlaich et al. (1987) and Collins
and Mitchell (1991).
Traditional section-by-section design is based on
the assumption that the reinforcement required at a
particular section depends only on the separated values
of the factored section force effects Vu, Mu, and Tu and
does not consider the mechanical interaction among
these force effects as the strut-and-tie model does. The
traditional method further assumes that shear
distribution remains uniform and that the longitudinal
strains will vary linearly over the depth of the beam.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
If the strut-and-tie model is selected for structural
analysis, Articles 5.6.3.2 through 5.6.3.6 shall apply.
C5.6.3.2
5.6.3.2—Structural Modeling
The structure and a component or region, thereof,
may be modeled as an assembly of steel tension ties and
concrete compressive struts interconnected at nodes to
form a truss capable of carrying all the applied loads to
the supports. The required widths of compression struts
and tension ties shall be considered in determining the
geometry of the truss.
The factored resistance, Pr, of struts and ties shall
be taken as that of axially loaded components:
Pr = φPn
(5.6.3.2-1)
where:
Pn =
φ =
For members such as the deep beam shown in
Figure C5.6.3.2-1, these assumptions are not valid. The
shear stresses on a section just to the right of a support
will be concentrated near the bottom face. The behavior
of a component, such as the deep beam, can be predicted
more accurately if the flow of forces through the
complete structure is studied. Instead of determining Vu
and Mu at different sections along the span, the flow of
compressive stresses going from the loads P to the
supports and the required tension force to be developed
between the supports should be established.
For additional applications of the strut-and-tie
model see Articles 5.10.9.4, 5.13.2.3, and 5.13.2.4.1.
nominal resistance of strut or tie (kip)
resistance factor for tension or compression
specified in Article 5.5.4.2, as appropriate
Cracked reinforced concrete carries load principally
by compressive stresses in the concrete and tensile
stresses in the reinforcement. After significant cracking
has occurred, the principal compressive stress
trajectories in the concrete tend toward straight lines and
hence can be approximated by straight compressive
struts. Tension ties are used to model the principal
reinforcement.
A strut-and-tie truss model is shown in
Figures C5.6.3.2-1 and C5.6.3.2-2. The zones of high
unidirectional compressive stress in the concrete are
represented by compressive struts. The regions of the
concrete subjected to multidirectional stresses, where the
struts and ties meet the joints of the truss, are
represented by nodal zones.
Because of the significant transverse dimensions of
the struts and ties, a “truss joint” becomes a “nodal
zone” with finite dimensions. Establishing the geometry
of the truss usually involves trial and error in which
member sizes are assumed, the truss geometry is
established, member forces are determined, and the
assumed member sizes are verified.
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SECTION 5: CONCRETE STRUCTURES
5-31
Figure C5.6.3.2-1—Strut-and-Tie Model for a Deep Beam
Figure C5.6.3.2-2—Strut-and-Tie Model for Continuous
Deep Beam
5.6.3.3—Proportioning of Compressive Struts
5.6.3.3.1—Strength of Unreinforced Strut
The nominal resistance of
compressive strut shall be taken as:
Pn = f cu Acs
an
unreinforced
(5.6.3.3.1-1)
where:
Pn =
fcu =
Acs =
nominal resistance of a compressive strut (kip)
limiting compressive stress as specified in
Article 5.6.3.3.3 (ksi)
effective cross-sectional area of strut as
specified in Article 5.6.3.3.2 (in.2)
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
5.6.3.3.2—Effective Cross-Sectional Area of Strut
The value of Acs shall be determined by considering
both the available concrete area and the anchorage
conditions at the ends of the strut, as shown in
Figure 5.6.3.3.2-1.
When a strut is anchored by reinforcement, the
effective concrete area may be considered to extend a
distance of up to six bar diameters from the anchored
bar, as shown in Figure 5.6.3.3.2-1 (a).
Figure 5.6.3.3.2-1—Influence of Anchorage Conditions on Effective Cross-Sectional Area of Strut
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SECTION 5: CONCRETE STRUCTURES
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5.6.3.3.3—Limiting Compressive Stress in Strut
as:
The limiting compressive stress, fcu, shall be taken
f cu =
f c′
≤ 0.85 f c′
0.8 + 170 ε1
(5.6.3.3.3-1)
in which:
ε1 = ε s + ( ε s + 0.002 ) cot 2 α s
(5.6.3.3.3-2)
where:
αs
=
εs
=
f ′c =
the smallest angle between the compressive
strut and adjoining tension ties (degrees)
the tensile strain in the concrete in the direction
of the tension tie (in./in.)
specified compressive strength (ksi)
C5.6.3.3.3
If the concrete is not subjected to principal tensile
strains greater than about 0.002, it can resist a
compressive stress of 0.85 f ′c. This will be the limit for
regions of the struts not crossed by or joined to tension
ties. The reinforcing bars of a tension tie are bonded to
the surrounding concrete. If the reinforcing bars are to
yield in tension, there should be significant tensile
strains imposed on the concrete. As these tensile strains
increase, fcu decreases.
The expression for ε1 is based on the assumption
that the principal compressive strain ε2 in the direction
of the strut equals 0.002 and that the tensile strain in the
direction of the tension tie equals εs. As the angle
between the strut-and-tie decreases, ε1 increases and
hence fcu decreases. In the limit, no compressive stresses
would be permitted in a strut that is superimposed on a
tension tie, i.e., αs = 0, a situation that violates
compatibility.
For a tension tie consisting of reinforcing bars, εs
can be taken as the tensile strain due to factored loads in
the reinforcing bars. For a tension tie consisting of
prestressing, εs can be taken as 0.0 until the
precompression of the concrete is overcome. For higher
stresses, εs would equal (fps − fpe) /Ep.
If the strain εs varies over the width of the strut, it is
appropriate to use the value at the centerline of the strut.
5.6.3.3.4—Reinforced Strut
If the compressive strut contains reinforcement that
is parallel to the strut and detailed to develop its yield
stress in compression, the nominal resistance of the strut
shall be taken as:
(5.6.3.3.4-1)
Pn = f cu Acs + f y Ass
where:
Ass =
area of reinforcement in the strut (in.2)
5.6.3.4—Proportioning of Tension Ties
C5.6.3.4.1
5.6.3.4.1—Strength of Tie
Tension tie reinforcement shall be anchored to the
nodal zones by specified embedment lengths, hooks, or
mechanical anchorages. The tension force shall be
developed at the inner face of the nodal zone.
The nominal resistance of a tension tie in kips shall
be taken as:
Pn = f y Ast + Aps f pe + f y
where:
(5.6.3.4.1-1)
The second term of the equation for Pn is intended
to ensure that the prestressing steel does not reach its
yield point, thus a measure of control over unlimited
cracking is maintained. It does, however, acknowledge
that the stress in the prestressing elements will be
increased due to the strain that will cause the concrete to
crack. The increase in stress corresponding to this action
is arbitrarily limited to the same increase in stress that
the mild steel will undergo. If there is no mild steel, fy
may be taken as 60.0 ksi for the second term of the
equation.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Ast =
Aps =
fy =
fpe =
total area of longitudinal mild steel
reinforcement in the tie (in.2)
area of prestressing steel (in.2)
yield strength of mild steel longitudinal
reinforcement (ksi)
stress in prestressing steel due to prestress after
losses (ksi)
5.6.3.4.2—Anchorage of Tie
The tension tie reinforcement shall be anchored to
transfer the tension force therein to the node regions of
the truss in accordance with the requirements for
development of reinforcement as specified in
Article 5.11.
C5.6.3.5
5.6.3.5—Proportioning of Node Regions
Unless confining reinforcement is provided and its
effect is supported by analysis or experimentation, the
concrete compressive stress in the node regions of the
strut shall not exceed:
•
For node regions bounded by compressive struts
and bearing areas: 0.85φf ′c
•
•
•
Size of the bearing plates,
For node regions anchoring a one-direction tension
tie: 0.75φf ′c
•
Dimensions of the compressive struts, and
For node regions anchoring tension ties in more
than one direction: 0.65φf ′c
•
Dimensions of the tension ties.
The reduced stress limits on nodes anchoring
tension ties are based on the detrimental effect of the
tensile straining caused by these ties. If the ties consist
of post-tensioned tendons and the stress in the concrete
does not need to be above fpc, no tensile straining of the
nodal zone will be required. For this case, the 0.85φf ′c
limit is appropriate.
where:
φ
The limits in concrete compressive stresses in nodal
zones are related to the degree of expected confinement
in these zones provided by the concrete in compression.
The stresses in the nodal zones can be reduced by
increasing the:
=
the resistance factor for bearing on concrete as
specified in Article 5.5.4.2.
The tension tie reinforcement shall be uniformly
distributed over an effective area of concrete at least
equal to the tension tie force divided by the stress limits
specified herein.
In addition to satisfying strength criteria for
compression struts and tension ties, the node regions
shall be designed to comply with the stress and
anchorage limits specified in Articles 5.6.3.4.1 and
5.6.3.4.2.
The bearing stress on the node region produced by
concentrated loads or reaction forces shall satisfy the
requirements specified in Article 5.7.5.
5.6.3.6—Crack Control Reinforcement
Structures and components or regions thereof,
except for slabs and footings, which have been designed
in accordance with the provisions of Article 5.6.3, shall
contain orthogonal grids of reinforcing bars. The
spacing of the bars in these grids shall not exceed the
smaller of d/4 and 12.0 in.
The reinforcement in the vertical and horizontal
direction shall satisfy the following:
C5.6.3.6
This reinforcement is intended to control the width
of cracks and to ensure a minimum ductility for the
member so that, if required, significant redistribution of
internal stresses is possible.
The total horizontal reinforcement can be calculated
as 0.003 times the effective area of the strut denoted by
the shaded portion of the cross-section in
Figure C5.6.3.6-1. For thinner members, this crack
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SECTION 5: CONCRETE STRUCTURES
5-35
Av
≥ 0.003
bw sv
(5.6.3.6-1)
Ah
≥ 0.003
bw sh
(5.6.3.6-2)
control reinforcement will consist of two grids of
reinforcing bars, one near each face. For thicker
members, multiple grids of reinforcement through the
thickness may be required in order to achieve a practical
layout.
where:
Ah
=
Av
=
bw
sv , s h
=
=
total area of horizontal crack control
reinforcement
within
spacing
sh,
respectively (in.2)
total area of vertical crack control
reinforcement
within
spacing
sv,
respectively (in.2)
width of member’s web (in.)
spacing of vertical and horizontal crack
control reinforcement, respectively (in.)
Crack control reinforcement shall be distributed
evenly within the strut area.
Figure C5.6.3.6-1—Distribution of Crack Control
Reinforcement in Compression Strut
5.7—DESIGN FOR FLEXURAL AND AXIAL
FORCE EFFECTS
2013 Revision
5.7.1—Assumptions for Service and Fatigue Limit
States
C5.7.1
The following assumptions may be used in the
design of reinforced, prestressed, and partially
prestressed concrete components for all compressive
strength levels:
Prestressing is treated as part of resistance, except
for anchorages and similar details, where the design is
totally a function of the tendon force and for which a
load factor is specified in Article 3.4.3. External
reactions caused by prestressing induce force effects that
normally are taken to be part of the loads side of
Eq. 1.3.2.1-1. This represents a philosophical
dichotomy. In lieu of more precise information, in these
Specifications the load factor for these induced force
effects should be taken as that for the permanent loads.
Examples of components for which the assumption
of linearly varying strains may not be suitable include
deep components such as deep beams, corbels, and
brackets.
•
Prestressed concrete resists tension at sections that
are uncracked, except as specified in Article 5.7.6.
•
The strains in the concrete vary linearly, except in
components or regions of components for which
conventional strength of materials is inappropriate.
•
The modular ratio, n, is rounded to the nearest
integer number.
•
The modular ratio is calculated as follows:
•
o
Es /Ec for reinforcing bars
o
Ep /Ec for prestressing tendons
An effective modular ratio of 2n is applicable to
permanent loads and prestress.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
5.7.2—Assumptions for Strength and Extreme Event
Limit States
5.7.2.1—General
2013 Revision
Factored resistance of concrete components shall be
based on the conditions of equilibrium and strain
compatibility, the resistance factors as specified in
Article 5.5.4.2, and the following assumptions:
•
In components with fully bonded reinforcement or
prestressing, or in the bonded length of locally
debonded or shielded strands, strain is directly
proportional to the distance from the neutral axis,
except for deep members that shall satisfy the
requirements of Article 5.13.2, and for other
disturbed regions.
•
In components with fully unbonded or partially
unbonded prestressing tendons, i.e., not locally
debonded or shielded strands, the difference in
strain between the tendons and the concrete section
and the effect of deflections on tendon geometry are
included in the determination of the stress in the
tendons.
•
If the concrete is unconfined, the maximum usable
strain at the extreme concrete compression fiber is
not greater than 0.003.
•
If the concrete is confined, a maximum usable strain
exceeding 0.003 in the confined core may be
utilized if verified. Calculation of the factored
resistance shall consider that the concrete cover
may be lost at strains compatible with those in the
confined concrete core.
•
Except for the strut-and-tie model, the stress in the
reinforcement is based on a stress-strain curve
representative of the steel or on an approved
mathematical representation, including development
of reinforcing and prestressing elements and
transfer of pretensioning.
•
The tensile strength of the concrete is neglected.
•
The concrete compressive stress-strain distribution
is assumed to be rectangular, parabolic, or any other
shape that results in a prediction of strength in
substantial agreement with the test results.
•
The development of reinforcing and prestressing
elements and transfer of pretensioning are
considered.
•
Balanced strain conditions exist at a cross-section
when tension reinforcement reaches the strain
corresponding to its specified yield strength fy just
as the concrete in compression reaches its assumed
ultimate strain of 0.003.
C5.7.2.1
2013 Revision
The first paragraph of C5.7.1 applies.
Research by Bae and Bayrak (2003) has shown that,
for well-confined High Strength Concrete (HSC)
columns, the concrete cover may be lost at maximum
useable strains at the extreme concrete compression
fiber as low as 0.0022. The heavy confinement steel
causes a weak plane between the concrete core and
cover, causing high shear stresses and the resulting early
loss of concrete cover.
The nominal flexural strength of a member is
reached when the strain in the extreme compression
fiber reaches the assumed strain limit of 0.003. The net
tensile strain εt is the tensile strain in the extreme tension
steel at nominal strength, exclusive of strains due to
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SECTION 5: CONCRETE STRUCTURES
•
Sections are compression-controlled when the net
tensile strain in the extreme tension steel is equal to
or less than the compression-controlled strain limit
at the time the concrete in compression reaches its
assumed strain limit of 0.003. The compressioncontrolled strain limit is the net tensile strain in the
reinforcement at balanced strain conditions. For
Grade 60 reinforcement, and for all prestressed
reinforcement, the compression-controlled strain
limit may be set equal to 0.002.
5-37
prestress, creep, shrinkage, and temperature. The net
tensile strain in the extreme tension steel is determined
from a linear strain distribution at nominal strength, as
shown in Figure C5.7.2.1-1, using similar triangles.
Figure C5.7.2.1-1—Strain Distribution and Net Tensile
Strain
•
Sections are tension-controlled when the net tensile
strain in the extreme tension steel is equal to or
greater than 0.005 just as the concrete in
compression reaches its assumed strain limit of
0.003. Sections with net tensile strain in the extreme
tension steel between the compression-controlled
strain limit and 0.005 constitute a transition region
between compression-controlled and tensioncontrolled sections.
•
The use of compression reinforcement in
conjunction with additional tension reinforcement is
permitted to increase the strength of flexural
members.
When the net tensile strain in the extreme tension
steel is sufficiently large (equal to or greater than 0.005),
the section is defined as tension-controlled where ample
warning of failure with excessive deflection and
cracking may be expected. When the net tensile strain in
the extreme tension steel is small (less than or equal to
the compression-controlled strain limit), a brittle failure
condition may be expected, with little warning of
impending failure. Flexural members are usually
tension-controlled, while compression members are
usually compression-controlled. Some sections, such as
those with small axial load and large bending moment,
will have net tensile strain in the extreme tension steel
between the above limits. These sections are in a
transition region between compression- and tensioncontrolled sections. Article 5.5.4.2.1 specifies the
appropriate resistance factors for tension-controlled and
compression-controlled sections, and for intermediate
cases in the transition region.
Before the development of these provisions, the
limiting tensile strain for flexural members was not
stated, but was implicit in the maximum reinforcement
limit that was given as c/de ≤ 0.42, which corresponded
to a net tensile strain at the centroid of the tension
reinforcement of 0.00414. The net tensile strain limit of
0.005 for tension-controlled sections was chosen to be a
single value that applies to all types of steel (prestressed
and nonprestressed) permitted by this Specification.
Unless unusual amounts of ductility are required,
the 0.005 limit will provide ductile behavior for most
designs. One condition where greater ductile behavior is
required is in design for redistribution of moments in
continuous members and frames. Article 5.7.3.5 permits
redistribution of negative moments. Since moment
redistribution is dependent on adequate ductility in
hinge regions, moment redistribution is limited to
sections that have a net tensile strain of at least 0.0075.
For beams with compression reinforcement, or
T-beams, the effects of compression reinforcement and
flanges are automatically accounted for in the
computation of net tensile strain εt.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
5-38
•
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
In the approximate flexural resistance equations of
Articles 5.7.3.1 and 5.7.3.2, fy and f ′y may replace fs
and f ′s, respectively, subject to the following
conditions:
o
fy may replace fs when, using fy in the
calculation, the resulting ratio c/ds does not
exceed 0.6. If c/ds exceeds 0.6, strain
compatibility shall be used to determine the
stress in the mild steel tension reinforcement.
o
f ′y may replace f ′s when, using f ′y in the
calculation, c ≥ 3d ′s. If c < 3d ′s, strain
compatibility shall be used to determine the
stress in the mild steel compression
reinforcement. The compression reinforcement
shall be conservatively ignored, i.e., A′s = 0.
Additional limitations on the maximum usable
extreme concrete compressive strain in hollow
rectangular compression members shall be investigated
as specified in Article 5.7.4.7.
5.7.2.2—Rectangular Stress Distribution
The natural relationship between concrete stress and
strain may be considered satisfied by an equivalent
rectangular concrete compressive stress block of 0.85f ′c
over a zone bounded by the edges of the cross-section
and a straight line located parallel to the neutral axis at
the distance a = β1c from the extreme compression fiber.
The distance c shall be measured perpendicular to the
neutral axis. The factor β1 shall be taken as 0.85 for
concrete strengths not exceeding 4.0 ksi. For concrete
strengths exceeding 4.0 ksi, β1 shall be reduced at a rate
of 0.05 for each 1.0 ksi of strength in excess of 4.0 ksi,
except that β1 shall not be taken to be less than 0.65.
Additional limitations on the use of the rectangular
stress block when applied to hollow rectangular
compression members shall be investigated as specified
in Article 5.7.4.7.
When using the approximate flexural resistance
equations in Articles 5.7.3.1 and 5.7.3.2, it is important
to assure that both the tension and compression mild
steel reinforcement are yielding to obtain accurate
results. In previous editions of the AASHTO LRFD
Bridge
Design
Specifications,
the
maximum
reinforcement limit of c/de ≤ 0.42 assured that the mild
tension steel would yield at nominal flexural resistance,
but this limit was eliminated in the 2006 interim
revisions. The current limit of c/ds ≤ 0.6 assures that the
mild tension steel will be at or near yield, while c ≥ 3d ′s
assures that the mild compression steel will yield. It is
conservative to ignore the compression steel when
calculating flexural resistance. In cases where either the
tension or compression steel does not yield, it is more
accurate to use a method based on the conditions of
equilibrium and strain compatibility to determine the
flexural resistance.
The mild steel tension reinforcement limitation does
not apply to prestressing steel used as tension
reinforcement. The equations used to determine the
stress in the prestressing steel at nominal flexural
resistance already consider the effect of the depth to the
neutral axis.
C5.7.2.2
For practical design, the rectangular compressive
stress distribution defined in this Article may be used in
lieu of a more exact concrete stress distribution. This
rectangular stress distribution does not represent the
actual stress distribution in the compression zone at
ultimate, but in many practical cases it does provide
essentially the same results as those obtained in tests.
All strength equations presented in Article 5.7.3 are
based on the rectangular stress block.
The factor β1 is basically related to rectangular
sections; however, for flanged sections in which the
neutral axis is in the web, β1 has experimentally been
found to be an adequate approximation.
For sections that consist of a beam with a composite
slab of different concrete strength, and the compression
block includes both types of concrete, it is conservative
to assume the composite beam to be of uniform strength
at the lower of the concrete strengths in the flange and
web. If a more refined estimate of flexural capacity is
warranted, a more rigorous analysis method should be
used. Examples of such analytical techniques are
presented in Weigel, Seguirant, Brice, and Khaleghi
(2003) and Seguirant, Brice, and Khaleghi (2004).
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2012
Edition
LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
SECTION 5: CONCRETE STRUCTURES
5-39
5.7.3—Flexural Members
5.7.3.1—Stress in Prestressing Steel at Nominal
Flexural Resistance
5.7.3.1.1—Components with Bonded Tendons
For rectangular or flanged sections subjected to
flexure about one axis where the approximate stress
distribution specified in Article 5.7.2.2 is used and for
which fpe is not less than 0.5 fpu, the average stress in
prestressing steel, fps, may be taken as:
§
c ·
f ps = f pu ¨ 1 k
¸
¨
d p ¸¹
©
(5.7.3.1.1-1)
in which:
§
f py
k = 2 ¨1.04
¨
f pu
©
·
¸¸
¹
(5.7.3.1.1-2)
for T-section behavior:
c
Aps f pu As f s Asc f sc 0.85 f cc (b bw ) h f
0.85 f ccE1bw kAps
f pu
Aps f pu + As f s Asc f sc
f
0.85 f ccE1b+ kAps pu
dp
Equations in this Article and subsequent equations
for flexural resistance are based on the assumption that
the distribution of steel is such that it is reasonable to
consider all of the tensile reinforcement to be lumped at
the location defined by ds and all of the prestressing
steel can be considered to be lumped at the location
defined by dp. Therefore, in the case where a significant
number of prestressing elements are on the compression
side of the neutral axis, it is more appropriate to use a
method based on the conditions of equilibrium and
strain compatibility as indicated in Article 5.7.2.1.
The background and basis for Eqs. 5.7.3.1.1-1 and
5.7.3.1.2-1 can be found in Naaman (1985), Loov
(1988), Naaman (1989), and Naaman (1990–1992).
Values of fpy /fpu are defined in Table C5.7.3.1.1-1.
Therefore, the values of k from Eq. 5.7.3.1.1-2 depend
only on the type of tendon used.
Table C5.7.3.1.1-1—Values of k
(5.7.3.1.1-3)
dp
for rectangular section behavior:
c
C5.7.3.1.1
(5.7.3.1.1-4)
Type of Tendon
fpy/fpu
Value of k
Low relaxation strand
Stress-relieved strand and
Type 1 high-strength bar
0.90
0.85
0.28
0.38
Type 2 high-strength bar
0.80
0.48
where:
Aps =
fpu =
fpy
As
A's
fs
=
=
=
=
f cs =
b
=
bw =
hf =
dp =
area of prestressing steel (in.2)
specified tensile strength of prestressing steel
(ksi)
yield strength of prestressing steel (ksi)
area of mild steel tension reinforcement (in.2)
area of compression reinforcement (in.2)
stress in the mild steel tension reinforcement at
nominal flexural resistance (ksi), as specified in
Article 5.7.2.1
stress in the mild steel compression
reinforcement at nominal flexural resistance
(ksi), as specified in Article 5.7.2.1
width of the compression face of the member;
for a flange section in compression, the
effective width of the flange as specified in
Article 4.6.2.6 (in.)
width of web (in.)
depth of compression flange (in.)
distance from extreme compression fiber to the
centroid of the prestressing tendons (in.)
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2012
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
5-40
c
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
=
distance between the neutral axis and the
compressive face (in.)
stress block factor specified in Article 5.7.2.2
ȕ1 =
5.7.3.1.2—Components with Unbonded Tendons
For rectangular or flanged sections subjected to
flexure about one axis and for biaxial flexure with axial
load as specified in Article 5.7.4.5, where the
approximate
stress
distribution
specified
in
Article 5.7.2.2 is used, the average stress in unbonded
prestressing steel may be taken as:
§ dp − c ·
f ps = f pe + 900 ¨
¸ ≤ f py
© Ae ¹
(5.7.3.1.2-1)
C5.7.3.1.2
A first estimate of the average stress in unbonded
prestressing steel may be made as:
f ps = f pe + 15.0 (ksi)
(C5.7.3.1.2-1)
In order to solve for the value of fps in
Eq. 5.7.3.1.2-1, the equation of force equilibrium at
ultimate is needed. Thus, two equations with two
unknowns (fps and c) need to be solved simultaneously
to achieve a closed-form solution.
in which:
§ 2Ai ·
¸
© 2 + Ns ¹
(5.7.3.1.2-2)
Ae = ¨
for T-section behavior:
c=
Aps f ps + As f s − As′ f s′ − 0.85 f c′ (b − bw ) h f
0.85 f c′ β1 b w
(5.7.3.1.2-3)
for rectangular section behavior:
c=
Aps f ps + As f s − As′ f s′
0.85 f c′ β1 b
(5.7.3.1.2-4)
where:
c
=
Ɛe =
Ɛi =
Ns =
fpy =
fpe =
distance from extreme compression fiber to the
neutral axis assuming the tendon prestressing
steel has yielded, given by Eqs. 5.7.3.1.2-3 and
5.7.3.1.2-4 for T-section behavior and
rectangular section behavior, respectively (in.)
effective tendon length (in.)
length of tendon between anchorages (in.)
number of support hinges crossed by the tendon
between anchorages or discretely bonded points
yield strength of prestressing steel (ksi)
effective stress in prestressing steel at section
under consideration after all losses (ksi)
5.7.3.1.3—Components with Both Bonded and
Unbonded Tendons
5.7.3.1.3a—Detailed Analysis
Except as specified in Article 5.7.3.1.3b, for
components with both bonded and unbonded tendons, the
stress in the prestressing steel shall be computed by
detailed analysis. This analysis shall take into account the
strain compatibility between the section and the bonded
prestressing steel. The stress in the unbonded prestressing
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2012
Edition
SECTION 5: CONCRETE STRUCTURES
5-41
steel shall take into account the global displacement
compatibility between bonded sections of tendons located
within the span. Bonded sections of unbonded tendons
may be anchorage points and any bonded section, such as
deviators. Consideration of the possible slip at deviators
shall be taken into consideration. The nominal flexural
strength should be computed directly from the stresses
resulting from this analysis.
5.7.3.1.3b—Simplified Analysis
In lieu of the detailed analysis described in
Article 5.7.3.1.3a, the stress in the unbonded tendons
may be conservatively taken as the effective stress in the
prestressing steel after losses, fpe. In this case, the stress
in the bonded prestressing steel shall be computed using
Eqs. 5.7.3.1.1-1 through 5.7.3.1.1-4, with the term Aps fpu
in Eqs. 5.7.3.1.1-3 and 5.7.3.1.1-4 replaced with the
term Apsb fpu + Apsu fpe.
where:
Apsb =
Apsu =
area of bonded prestressing steel (in.2)
area of unbonded prestressing steel (in.2)
When computing the nominal flexural resistance
using Eq. 5.7.3.2.2-1, the average stress in the
prestressing steel shall be taken as the weighted average
of the stress in the bonded and unbonded prestressing
steel, and the total area of bonded and unbonded
prestressing shall be used.
5.7.3.2—Flexural Resistance
5.7.3.2.1—Factored Flexural Resistance
The factored resistance Mr shall be taken as:
(5.7.3.2.1-1)
M r = φM n
where:
Mn =
φ =
nominal resistance (kip-in.)
resistance factor as specified in Article 5.5.4.2
5.7.3.2.2—Flanged Sections
For flanged sections subjected to flexure about one
axis and for biaxial flexure with axial load as specified
in Article 5.7.4.5, where the approximate stress
distribution specified in Article 5.7.2.2 is used and
where the compression flange depth is less than a = β1c,
as determined in accordance with Eqs. 5.7.3.1.1-3,
5.7.3.1.1-4, 5.7.3.1.2-3, or 5.7.3.1.2-4, the nominal
flexural resistance may be taken as:
C5.7.3.2.1
Moment at the face of the support may be used for
design. Where fillets making an angle of 45 degrees or
more with the axis of a continuous or restrained member
are built monolithic with the member and support, the
face of support should be considered at a section where
the combined depth of the member and fillet is at least
one and one-half times the thickness of the member. No
portion of a fillet should be considered as adding to the
effective depth when determining the nominal
resistance.
C5.7.3.2.2
In previous editions and interims of the LRFD
Specifications, the factor β1 was applied to the flange
overhang term of Eqs. 5.7.3.2.2-1, 5.7.3.1.1-3, and
5.7.3.1.2-3. This was not consistent with the original
derivation of the equivalent rectangular stress block as it
applies to flanged sections (Mattock, Kriz, and
Hognestad. 1961). For the current LRFD Specifications,
the β1 factor has been removed from the flange overhang
term of these equations. See also Seguirant (2002),
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2012
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5-42
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
( ) ( )
( ) ( )
M n = Aps f ps d p −
As′ f s ′ d s′ −
a
2
a
2
+ As f s d s −
+ 0.85 fc′ b − bw h f
a
2
a
2
−
−
hf
2
Girgis, Sun, and Tadros (2002), Naaman (2002),
Weigel, Seguirant, Brice, and Khaleghi (2003), Baran,
Schultz, and French (2004), and Seguirant, Brice, and
Khaleghi (2004).
(5.7.3.2.2-1)
where:
Aps =
fps =
dp =
As =
fs
=
ds
=
A′s =
f ′s =
d ′s =
f ′c =
b
=
bw =
β1 =
hf =
a
=
area of prestressing steel (in.2)
average stress in prestressing steel at nominal
bending resistance specified in Eq. 5.7.3.1.1-1
(ksi)
distance from extreme compression fiber to the
centroid of prestressing tendons (in.)
area of nonprestressed tension reinforcement
(in.2)
stress in the mild steel tension reinforcement at
nominal flexural resistence (ksi), as specified in
Article 5.7.2.1
distance from extreme compression fiber to the
centroid
of
nonprestressed
tensile
reinforcement (in.)
area of compression reinforcement (in.2)
stress in the mild steel compression
reinforcement at nominal flexural resistance
(ksi), as specified in Article 5.7.2.1
distance from extreme compression fiber to the
centroid of compression reinforcement (in.)
specified compressive strength of concrete at
28 days, unless another age is specified (ksi)
width of the compression face of the member;
for a flange section in compression, the
effective width of the flange as specified in
Article 4.6.2.6 (in.)
web width or diameter of a circular section (in.)
stress block factor specified in Article 5.7.2.2
compression flange depth of an I or T member
(in.)
cβ1; depth of the equivalent stress block (in.)
5.7.3.2.3—Rectangular Sections
For rectangular sections subjected to flexure about
one axis and for biaxial flexure with axial load as
specified in Article 5.7.4.5, where the approximate stress
distribution specified in Article 5.7.2.2 is used and where
the compression flange depth is not less than a = β1c as
determined in accordance with Eqs. 5.7.3.1.1-4 or
5.7.3.1.2-4, the nominal flexural resistance Mn may be
determined by using Eqs. 5.7.3.1.1-1 through 5.7.3.2.2-1,
in which case bw shall be taken as b.
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2012
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SECTION 5: CONCRETE STRUCTURES
5-43
5.7.3.2.4—Other Cross-Sections
For cross-sections other than flanged or essentially
rectangular sections with vertical axis of symmetry or
for sections subjected to biaxial flexure without axial
load, the nominal flexural resistance, Mn, shall be
determined by an analysis based on the assumptions
specified in Article 5.7.2. The requirements of
Article 5.7.3.3 shall apply.
5.7.3.2.5—Strain Compatibility Approach
2013 Revision
Alternatively, the strain compatibility approach may
be used if more precise calculations are required. The
appropriate provisions of Article 5.7.2.1 shall apply.
The stress and corresponding strain in any given
layer of reinforcement may be taken from any
representative stress-strain formula or graph for mild
reinforcement and prestressing strands.
5.7.3.3—Limits for Reinforcement
5.7.3.3.1—Maximum Reinforcement
[PROVISION DELETED IN 2005]
5.7.3.3.2 Minimum Reinforcement
Unless otherwise specified, at any section of a
noncompression-controlled flexural component, the
amount of prestressed and nonprestressed tensile
reinforcement shall be adequate to develop a factored
flexural resistance, Mr, at least equal to the lesser of:
C5.7.3.3.1
2013 Revision
In editions of and interims to the LRFD
Specifications prior to 2005, Article 5.7.3.3.1 limited the
tension reinforcement quantity to a maximum amount
such that the ratio c/de did not exceed 0.42. Sections
with c/de > 0.42 were considered over-reinforced. Overreinforced nonprestressed members were not allowed,
whereas prestressed and partially prestressed members
with PPR greater than 50 percent were if “it is shown by
analysis and experimentation that sufficient ductility of
the structure can be achieved.” No guidance was given
for what “sufficient ductility” should be, and it was not
clear what value of φ should be used for such overreinforced members.
The current provisions of LRFD eliminate this limit
and unify the design of prestressed and nonprestressed
tension- and compression-controlled members. The
background and basis for these provisions are given in
Mast (1992). Below a net tensile strain in the extreme
tension steel of 0.005, as the tension reinforcement
quantity increases, the factored resistance of prestressed
and nonprestressed sections is reduced in accordance
with Article 5.5.4.2.1. This reduction compensates for
decreasing ductility with increasing overstrength. Only
the addition of compression reinforcement in
conjunction with additional tension reinforcement can
result in an increase in the factored flexural resistance of
the section.
C5.7.3.3.2
Minimum reinforcement provisions are intended to
reduce the probability of brittle failure by providing
flexural capacity greater than the cracking moment.
Testing of a large number of lightly reinforced and
prestressed concrete members at the University of
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2012
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5-44
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
•
•
1.33 times the factored moment required by the
applicable strength load combination specified
in Table 3.4.1-1; and
S
M cr = γ 3 ( γ 1 f r + γ 2 f cpe ) Sc − M dnc c − 1
S nc
(5.7.3.3.2-1)
where:
fr
=
fcpe =
Mdnc =
Sc
=
Snc =
modulus of rupture of concrete specified in
Article 5.4.2.6
compressive stress in concrete due to effective
prestress forces only (after allowance for all
prestress losses) at extreme fiber of section
where tensile stress is caused by externally
applied loads (ksi)
total unfactored dead load moment acting on
the monolithic or noncomposite section (kipin.)
section modulus for the extreme fiber of the
composite section where tensile stress is caused
by externally applied loads (in.3)
section modulus for the extreme fiber of the
monolithic or noncomposite section where
tensile stress is caused by externally applied
loads (in.3)
Illinois demonstrated that significant inelastic
displacements can be achieved, and none of the beams
tested failed without large warning deflections
(Freyermuth and Alami, 1997). If these experiments
were conducted in load control, a number of specimens
would have failed without warning because the ultimate
strength (including the effects of strain hardening) was
less than the cracking strength. Based on this
observation, the ultimate strength should be used instead
of the nominal strength as a true measure of brittle
response. The ratio of steel stress at yield to ultimate (γ3)
sufficiently approximates the nominal to ultimate
strength for lightly reinforced concrete members.
The sources of variability in computing the cracking
moment and resistance are appropriately factored
(Holombo and Tadros, 2009). The factor applied to the
modulus of rupture (γ1) is greater than the factor applied
to the amount of prestress (γ2) to account for greater
variability.
For precast segmental construction, cracking
generally starts at the segment joints. Research at the
University of California, San Diego, has shown that
flexure cracks occur adjacent to the epoxy-bonded
match-cast face, where the accumulation of fines
reduces the tensile strength (Megally et al., 2003). Based
on this observation, a reduced (γ1) factor of 1.2 is
justified.
Appropriate values for Mdnc and Snc shall be used for
any intermediate composite sections. Where the beams
are designed for the monolithic or noncomposite section
to resist all loads, Snc shall be substituted for Sc in the
above equation for the calculation of Mcr.
The following factors shall be used to account for
variability in the flexural cracking strength of concrete,
variability of prestress, and the ratio of nominal yield
stress of reinforcement to ultimate:
γ1 = flexural cracking variability factor
=
=
γ2 =
=
=
1.2 for precast segmental structures
1.6 for all other concrete structures
prestress variability factor
1.1 for bonded tendons
1.0 for unbonded tendons
γ3 = ratio of specified minimum yield strength
=
=
=
to ultimate tensile strength of the
reinforcement
0.67 for A615, Grade 60 reinforcement
0.75 for A706, Grade 60 reinforcement
1.00 for prestressed concrete structures
The provisions of Article 5.10.8 shall apply.
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2012
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
SECTION 5: CONCRETE STRUCTURES
5-45
5.7.3.4—Control of Cracking by Distribution of
Reinforcement
2013 Revision
The provisions specified herein shall apply to the
reinforcement of all concrete components, except that of
deck slabs designed in accordance with Article 9.7.2, in
which tension in the cross-section exceeds 80 percent of
the modulus of rupture, specified in Article 5.4.2.6, at
applicable service limit state load combination specified
in Table 3.4.1-1.
The spacing s of mild steel reinforcement in the
layer closest to the tension face shall satisfy the
following:
s ≤
700 γ e
β s f ss
− 2d c
(5.7.3.4-1)
in which:
ȕs = 1 +
dc
0.7( h − d c )
where:
dc
=
=
=
=
fss
=
h
=
Ȗe
dƐ =
exposure factor
1.00 for Class 1 exposure condition
0.75 for Class 2 exposure condition
thickness of concrete cover measured from
extreme tension fiber to center of the flexural
reinforcement located closest thereto (in.)
tensile stress in steel reinforcement at the
service limit state (ksi)
overall thickness or depth of the component
(in.)
distance from the extreme compression fiber to
the centroid of extreme tension steel element
(in.)
C5.7.3.4
2013 Revision
All reinforced concrete members are subject to
cracking under any load condition, including thermal
effects and restraint of deformations, which produces
tension in the gross section in excess of the cracking
strength of the concrete. Locations particularly
vulnerable to cracking include those where there is an
abrupt change in section and intermediate posttensioning anchorage zones.
Provisions specified, herein, are used for the
distribution of tension reinforcement to control flexural
cracking.
Crack width is inherently subject to wide scatter,
even in careful laboratory work, and is influenced by
shrinkage and other time-dependent effects. Steps
should be taken in detailing of the reinforcement to
control cracking. From the standpoint of appearance,
many fine cracks are preferable to a few wide cracks.
Improved crack control is obtained when the steel
reinforcement is well distributed over the zone of
maximum concrete tension. Several bars at moderate
spacing are more effective in controlling cracking than
one or two larger bars of equivalent area.
Extensive laboratory work involving deformed
reinforcing bars has confirmed that the crack width at
the service limit state is proportional to steel stress.
However, the significant variables reflecting steel
detailing were found to be the thickness of concrete
cover and spacing of the reinforcement.
Eq. 5.7.3.4-1 is expected to provide a distribution of
reinforcement that will control flexural cracking. The
equation is based on a physical crack model (Frosch,
2001) rather than the statistically-based model used in
previous editions of the specifications. It is written in a
form emphasizing reinforcement details, i.e., limiting bar
spacing, rather than crack width. Furthermore, the physical
crack model has been shown to provide a more realistic
estimate of crack widths for larger concrete covers
compared to the previous equation (Destefano, 2003).
Eq. 5.7.3.4-1 with Class 1 exposure condition is
based on an assumed crack width of 0.017 in. Previous
research indicates that there appears to be little or no
correlation between crack width and corrosion, however,
the different classes of exposure conditions have been so
defined in order to provide flexibility in the application of
these provisions to meet the needs of the Authority having
jurisdiction. Class 1 exposure condition could be thought
of as an upper bound in regards to crack width for
appearance and corrosion. Areas that the Authority
having jurisdiction may consider for Class 2 exposure
condition would include decks and substructures exposed
to water. The crack width is directly proportional to the Ȗe
exposure factor, therefore, if the individual Authority with
jurisdiction desires an alternate crack width, the Ȗe factor
can be adjusted directly. For example a Ȗe factor of 0.5
will result in an approximate crack width of 0.0085 in.
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2012
Edition
LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
5-46
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Class 1 exposure condition applies when cracks can
be tolerated due to reduced concerns of appearance
and/or corrosion. Class 2 exposure condition applies to
transverse design of segmental concrete box girders for
any loads applied prior to attaining full nominal concrete
strength and when there is increased concern of
appearance and/or corrosion.
In the computation of dc, the actual concrete cover
thickness is to be used.
When computing the actual stress in the steel
reinforcement, axial tension effects shall be considered,
while axial compression effects may be considered.
The minimum and maximum spacing of
reinforcement shall also comply with the provisions of
Articles 5.10.3.1 and 5.10.3.2, respectively.
The effects of bonded prestressing steel may be
considered, in which case the value of fs used in
Eq. 5.7.3.4-1, for the bonded prestressing steel, shall be
the stress that develops beyond the decompression state
calculated on the basis of a cracked section or strain
compatibility analysis.
Where flanges of reinforced concrete T-girders and
box girders are in tension at the service limit state, the
flexural tension reinforcement shall be distributed over
the lesser of:
•
The effective flange
Article 4.6.2.6, or
•
A width equal to 1/10 of the average of adjacent
spans between bearings.
width,
specified
in
If the effective flange width exceeds 1/10 the span,
additional longitudinal reinforcement, with area not less
than 0.4 percent of the excess slab area, shall be
provided in the outer portions of the flange.
If dƐ of nonprestressed or partially prestressed
concrete members exceeds 3.0 ft, longitudinal skin
reinforcement shall be uniformly distributed along both
side faces of the component for a distance dƐ /2 nearest
the flexural tension reinforcement. The area of skin
reinforcement Ask in in.2/ft of height on each side face
shall satisfy:
Ask ≥ 0.012 (d A − 30) ≤
As + Aps
4
Where members are exposed to aggressive exposure
or corrosive environments, additional protection beyond
that provided by satisfying Eq. 5.7.3.4-1 may be
provided by decreasing the permeability of the concrete
and/or waterproofing the exposed surface.
Cracks in segmental concrete box girders may result
from stresses due to handling and storing segments for
precast construction and to stripping forms and supports
from cast-in-place construction before attainment of the
nominal f ƍc.
The ȕs factor, which is a geometric relationship
between the crack width at the tension face versus the
crack width at the reinforcement level, has been
incorporated into the basic crack control equation in
order to provide uniformity of application for flexural
member depths ranging from thin slabs in box culverts
to deep pier caps and thick footings. The theoretical
definition of ȕs may be used in lieu of the approximate
expression provided.
Distribution of the negative reinforcement for
control of cracking in T-girders should be made in the
context of the following considerations:
•
Wide spacing of the reinforcement across the full
effective width of flange may cause some wide
cracks to form in the slab near the web.
•
Close spacing near the web leaves the outer regions
of the flange unprotected.
The 1/10 of the span limitation is to guard against
an excessive spacing of bars, with additional
reinforcement required to protect the outer portions of
the flange.
The requirements for skin reinforcement are based
upon ACI 318-95. For relatively deep flexural members,
some reinforcement should be placed near the vertical
faces in the tension zone to control cracking in the web.
Without such auxiliary steel, the width of the cracks in
the web may greatly exceed the crack widths at the level
of the flexural tension reinforcement.
(5.7.3.4-2)
where:
Aps =
As =
area of prestressing steel (in.2)
area of tensile reinforcement (in.2)
However, the total area of longitudinal skin
reinforcement (per face) need not exceed one-fourth of
the required flexural tensile reinforcement As + Aps.
The maximum spacing of the skin reinforcement
shall not exceed either dƐ /6 or 12.0 in.
Such reinforcement may be included in strength
computations if a strain compatibility analysis is made
to determine stresses in the individual bars or wires.
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2012
Edition
SECTION 5: CONCRETE STRUCTURES
5.7.3.5—Moment Redistribution
5-47
2013 Revision
In lieu of more refined analysis, where bonded
reinforcement that satisfies the provisions of
Article 5.11 is provided at the internal supports of
continuous reinforced concrete beams, negative
moments determined by elastic theory at strength limit
states may be increased or decreased by not more than
1000εt percent, with a maximum of 20 percent.
Redistribution of negative moments shall be made only
when εt is equal to or greater than 0.0075 at the section
at which moment is reduced.
Positive moments shall be adjusted to account for
the changes in negative moments to maintain
equilibrium of loads and force effects.
C5.7.3.5
2013 Revision
In editions and interims to the LRFD Specifications
prior to 2005, Article 5.7.3.5 specified the permissible
redistribution percentage in terms of the c/de ratio. The
current specification specifies the permissible
redistribution percentage in terms of net tensile strain εt.
The background and basis for these provisions are given
in Mast (1992).
5.7.3.6—Deformations
5.7.3.6.1—General
C5.7.3.6.1
The provisions of Article 2.5.2.6 shall be
considered.
Deck joints and bearings shall accommodate the
dimensional changes caused by loads, creep, shrinkage,
thermal changes, settlement, and prestressing.
5.7.3.6.2—Deflection and Camber
C5.7.3.6.2
Deflection and camber calculations shall consider
dead load, live load, prestressing, erection loads,
concrete creep and shrinkage, and steel relaxation.
For determining deflection and camber, the
provisions of Articles 4.5.2.1, 4.5.2.2, and 5.9.5.5 shall
apply.
In the absence of a more comprehensive analysis,
instantaneous deflections may be computed using the
modulus of elasticity for concrete as specified in
Article 5.4.2.4 and taking the moment of inertia as either
the gross moment of inertia, Ig, or an effective moment
of inertia, Ie, given by Eq. 5.7.3.6.2-1:
3
M cr 3
M cr
I e=
I g + 1 −
I cr ≤ I g
M a
Ma
For more precise determinations of long-term
deflections, the creep and shrinkage coefficients cited in
Article 5.4.2.3 should be utilized. These coefficients
include the effects of aggregate characteristics, humidity
at the structure site, relative thickness of member,
maturity at time of loading, and length of time under
loads.
For structures such as segmentally constructed
bridges, camber calculations should be based on the
modulus of elasticity and the maturity of the concrete
when each increment of load is added or removed, as
specified in Articles 5.4.2.3 and 5.14.2.3.6.
(5.7.3.6.2-1)
in which:
M cr = f r
Ig
yt
(5.7.3.6.2-2)
where:
Mcr =
fr =
cracking moment (kip-in.)
modulus of rupture of concrete as specified in
Article 5.4.2.6 (ksi)
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2012
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5-48
yt
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
=
Ma =
distance from the neutral axis to the extreme
tension fiber (in.)
maximum moment in a component at the stage
for which deformation is computed (kip-in.)
For prismatic members, effective moment of inertia
may be taken as the value obtained from Eq. 5.7.3.6.2-1
at midspan for simple or continuous spans, and at
support for cantilevers. For continuous nonprismatic
members, the effective moment of inertia may be taken
as the average of the values obtained from
Eq. 5.7.3.6.2-1 for the critical positive and negative
moment sections.
Unless a more exact determination is made, the
long-time deflection may be taken as the instantaneous
deflection multiplied by the following factor:
•
If the instantaneous deflection is based on Ig: 4.0
•
If the instantaneous deflection is based on Ie: 3.0–
1.2(A's /As) ≥1.6
In prestressed concrete, the long-term deflection is
usually based on mix-specific data, possibly in
combination with the calculation procedures in
Article 5.4.2.3. Other methods of calculating deflections
which consider the different types of loads and the
sections to which they are applied, such as that found in
(PCI, 1992), may also be used.
where:
A 's =
As =
area of compression reinforcement (in.2)
area of nonprestressed tension reinforcement
(in.2)
The contract documents shall require that
deflections of segmentally constructed bridges shall be
calculated prior to casting of segments based on the
anticipated casting and erection schedules and that they
shall be used as a guide against which actual deflection
measurements are checked.
5.7.3.6.3—Axial Deformation
Instantaneous shortening or expansion due to loads
shall be determined using the modulus of elasticity of
the materials at the time of loading.
Instantaneous shortening or expansion due to
temperature shall be determined in accordance with
Articles 3.12.2, 3.12.3, and 5.4.2.2.
Long-term shortening due to shrinkage and creep
shall be determined as specified in Article 5.4.2.3.
5.7.4—Compression Members
5.7.4.1—General
C5.7.4.1
Unless otherwise permitted, compression members
shall be analyzed with consideration of the effects of:
•
Eccentricity,
•
Axial loads,
•
Variable moments of inertia,
•
Degree of end fixity,
Compression members are usually prestressed only
where they are subjected to a high level of flexure or
when they are subjected to driving stresses, as is the case
with prestressed concrete piles.
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2012
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SECTION 5: CONCRETE STRUCTURES
•
Deflections,
•
Duration of loads, and
•
Prestressing.
5-49
In lieu of a refined procedure, nonprestressed
columns with the slenderness ratio, Kℓu /r < 100, may be
designed by the approximate procedure specified in
Article 5.7.4.3.
where:
=
K
effective
length
factor
Article 4.6.2.5
unbraced length (in.)
radius of gyration (in.)
ℓu =
r =
specified
in
The requirements of this Article shall be
supplemented and modified for structures in Seismic
Zones 2, 3, and 4, as specified in Article 5.10.11.
Provisions shall be made to transfer all force effects
from compression components, adjusted for secondorder moment magnification, to adjacent components.
Where the connection to an adjacent component is
by a concrete hinge, longitudinal reinforcement shall be
centralized within the hinge to minimize flexural
resistance and shall be developed on both sides of the
hinge.
C5.7.4.2
5.7.4.2—Limits for Reinforcement
Additional limits on reinforcement for compression
members in Seismic Zones 2, 3, and 4 shall be
considered as specified in Articles 5.10.11.3 and
5.10.11.4.1a.
The maximum area of prestressed and
nonprestressed
longitudinal
reinforcement
for
noncomposite compression components shall be such
that:
As Aps f pu
+
≤ 0.08
Ag
Ag f y
(5.7.4.2-1)
and:
Aps f pe
Ag f c′
(5.7.4.2-2)
≤ 0.30
The minimum area of prestressed and
nonprestressed
longitudinal
reinforcement
for
noncomposite compression components shall be such
that:
As f y
Ag f c′
where:
+
Aps f pu
Ag f c′
≥ 0.135
(5.7.4.2-3)
According to current ACI codes, the area of
longitudinal
reinforcement
for
nonprestressed
noncomposite compression components should be not
less than 0.01 Ag. Because the dimensioning of columns
is primarily controlled by bending, this limitation does
not account for the influence of the concrete
compressive strength. To account for the compressive
strength of concrete, the minimum reinforcement in
flexural members is shown to be proportional to f ′c /fy in
Article 5.7.3.3.2. This approach is also reflected in the
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5-50
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
area of nonprestressed tension steel (in.2)
gross area of section (in.2)
area of prestressing steel (in.2)
specified tensile strength of prestressing steel
(ksi)
specified yield strength of reinforcing bars (ksi)
specified compressive strength of concrete (ksi)
effective prestress (ksi)
first term of Eq. 5.7.4.2-3. For fully prestressed
members, current codes specify a minimum average
prestress of 0.225 ksi. Here also the influence of
compressive strength is not accounted for. A
compressive strength of 5.0 ksi has been used as a basis
for these provisions, and a weighted averaging
procedure was used to arrive at the equation.
The minimum number of longitudinal reinforcing
bars in the body of a column shall be six in a circular
arrangement and four in a rectangular arrangement. The
minimum size of bar shall be No. 5.
For bridges in Seismic Zone 1, a reduced effective
area may be used when the cross-section is larger than
that required to resist the applied loading. The minimum
percentage of total (prestressed and nonprestressed)
longitudinal reinforcement of the reduced effective area
is to be the greater of one percent or the value obtained
from Eq. 5.7.4.2-3. Both the reduced effective area and
the gross area must be capable of resisting all applicable
load combinations from Table 3.4.1-1.
Where columns are pinned to their foundations, a
small number of central bars have sometimes been used
as a connection between footing and column.
As
Ag
Aps
fpu
=
=
=
=
fy =
f ′c =
fpe =
5.7.4.3—Approximate Evaluation of Slenderness
Effects
For members not braced against sidesway, the
effects of slenderness may be neglected where the
slenderness ratio, Kℓu/r, is less than 22.
For members braced against sidesway, the effects of
slenderness may be neglected where Kℓu/r is less than
34−12(M1 /M2), in which M1 and M2 are the smaller and
larger end moments, respectively, and the term (M1 /M2)
is positive for single curvature flexure.
The following approximate procedure may be used
for the design of nonprestressed compression members
with Kℓu /r less than 100:
•
The design is based on a factored axial load, Pu,
determined by elastic analysis and a magnified
as
specified
in
factored
moment,
Mc,
Article 4.5.3.2.2b.
•
The unsupported length, ℓu, of a compression
member is taken as the clear distance between
components capable of providing lateral support for
the compression components. Where haunches are
present, the unsupported length is taken to the
extremity of any haunches in the plane considered.
•
The radius of gyration, r, is computed for the gross
concrete section.
For low risk seismic zones, the one percent reduced
effective area rule, which has been used successfully
since 1957 in the Standard Specifications, is
implemented, but modified to account for the
dependency of the minimum reinforcement on the ratio
of f ′c /fy.
For columns subjected to high, permanent axial
compressive stresses where significant concrete creep is
likely, using an amount of longitudinal reinforcement
less than that given by Eq. 5.7.4.2-3 is not recommended
because of the potential for significant transfer of load
from the concrete to the reinforcement as discussed in
the report of ACI Committee 105.
C5.7.4.3
These procedures were developed for reinforced
concrete columns but are currently used for prestressed
concrete columns as well.
For members in structures, which undergo
appreciable lateral deflections resulting from
combinations of vertical load or combinations of vertical
and lateral loads, force effects should be determined
using a second-order analysis.
For a rectangular compression member, r may be
taken as 0.30 times the overall dimension in the
direction in which stability is being considered. For a
circular compression member, r may be taken as 0.25
times the diameter.
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SECTION 5: CONCRETE STRUCTURES
5-51
•
For members braced against sidesway, the effective
length factor, K, is taken as 1.0, unless it is shown
by analysis that a lower value may be used.
•
For members not braced against sidesway, K is
determined with due consideration for the effects of
cracking and reinforcement on relative stiffness and
is taken as not less than 1.0.
In lieu of a more precise calculation, EI for use in
determining Pe, as specified in Eq. 4.5.3.2.2b-5, shall be
taken as the greater of:
Ec I g
+ Es I s
EI = 5
1 + βd
(5.7.4.3-1)
Ec I g
EI = 2.5
1+ β d
(5.7.4.3-2)
where:
Ec =
Ig =
Es =
Is =
βd =
modulus of elasticity of concrete (ksi)
moment of inertia of the gross concrete section
about the centroidal axis (in.4)
modulus of elasticity of longitudinal steel (ksi)
moment of inertia of longitudinal steel about
the centroidal axis (in.4)
ratio of maximum factored permanent load
moments to maximum factored total load
moment; always positive
For
eccentrically
prestressed
members,
consideration shall be given to the effect of lateral
deflection due to prestressing in determining the
magnified moment.
C5.7.4.4
5.7.4.4—Factored Axial Resistance
The factored axial resistance of concrete
compressive components, symmetrical about both
principal axes, shall be taken as:
(5.7.4.4-1)
Pr = φPn
in which:
•
For members with spiral reinforcement:
0.85 f c′ ( Ag − Ast − Aps )
+ f y Ast − Aps ( f pe − E p ε cu )
Pn = 0.85
•
(5.7.4.4-2)
For members with tie reinforcement:
0.85 f c′ ( Ag − Ast − Aps )
+ f y Ast − Aps ( f pe − E p ε cu )
Pn = 0.80
(5.7.4.4-3)
2013 Revision
The values of 0.85 and 0.80 in Eqs. 5.7.4.4-2 and
5.7.4.4-3 place upper limits on the usable resistance of
compression members to allow for unintended
eccentricity.
In the absence of concurrent bending due to external
loads or eccentric application of prestress, the ultimate
strain on a compression member is constant across the
entire cross-section. Prestressing causes compressive
stresses in the concrete, which reduces the resistance of
compression members to externally applied axial loads.
The term, Epεcu, accounts for the fact that a column or
pile also shortens under externally applied loads, which
serves to reduce the level of compression due to
prestress. Assuming a concrete compressive strain at
ultimate, εcu = 0.003, and a prestressing steel modulus,
Ep = 28,500 ksi, gives a relatively constant value of 85.0
ksi for the amount of this reduction. Therefore, it is
acceptable to reduce the effective prestressing by this
amount. Conservatively, this reduction can be ignored.
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5-52
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
where:
Pr =
Pn =
f ′c =
Ag
Ast
fy
φ
Aps
Ep
=
=
=
=
=
=
fpe =
εcu =
factored axial resistance, with or without
flexure (kip)
nominal axial resistance, with or without
flexure (kip)
specified strength of concrete at 28 days, unless
another age is specified (ksi)
gross area of section (in.2)
total area of longitudinal reinforcement (in.2)
specified yield strength of reinforcement (ksi)
resistance factor specified in Article 5.5.4.2
area of prestressing steel (in.2)
modulus of elasticity of prestressing tendons
(ksi)
effective stress in prestressing steel after losses
(ksi)
failure strain of concrete in compression
(in./in.)
5.7.4.5—Biaxial Flexure
C5.7.4.5
In lieu of an analysis based on equilibrium and
strain compatibility for biaxial flexure, noncircular
members subjected to biaxial flexure and compression
may be proportioned using the following approximate
expressions:
•
If the factored axial load is not less than
0.10 φ f ′c Ag:
1
1
1
1
=
+
−
Prxy
Prx
Pry φ Po
Eqs. 5.7.3.2.1-1 and 5.7.4.4-1 relate factored
resistances, given in Eqs. 5.7.4.5-1 and 5.7.4.5-2 by the
subscript r, e.g., Mrx, to the nominal resistances and the
resistance factors. Thus, although previous editions of
the Standard Specifications included the resistance
factor explicitly in equations corresponding to
Eqs. 5.7.4.5-1 and 5.7.4.5-2, these Specifications
implicitly include the resistance factor by using factored
resistances in the denominators.
(5.7.4.5-1)
in which:
Po =
0.85 f c′ ( Ag − Ast − Aps ) + f y Ast − Aps ( f pe − E p ε cu )
•
If the factored
0.10 φ f ′c Ag:
M ux + M uy ≤ 1.0
M rx
M ry
axial
load
is
(5.7.4.5-2)
less
than
The procedure for calculating corresponding values
of Mrx and Prx or Mry and Pry can be found in most texts
on reinforced concrete design.
(5.7.4.5-3)
where:
φ
=
Prxy =
Prx =
Pry =
Pu =
resistance factor for members in axial
compression
factored axial resistance in biaxial flexure (kip)
factored axial resistance determined on the
basis that only eccentricity ey is present (kip)
factored axial resistance determined on the
basis that only eccentricity ex is present (kip)
factored applied axial force (kip)
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2012
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SECTION 5: CONCRETE STRUCTURES
Mux =
Muy =
ex
=
ey
=
Po =
5-53
factored applied moment about the x-axis
(kip-in.)
factored applied moment about the y-axis
(kip-in.)
eccentricity of the applied factored axial force
in the x direction, i.e., = Muy /Pu (in.)
eccentricity of the applied factored axial force
in the y direction, i.e., = Mux /Pu (in.)
nominal axial resistance of a section at 0.0
eccentricity
The factored axial resistance Prx and Pry shall not be
taken to be greater than the product of the resistance
factor, φ, and the maximum nominal compressive
resistance given by either Eqs. 5.7.4.4-2 or 5.7.4.4-3, as
appropriate.
5.7.4.6—Spirals and Ties
2013 Revision
The area of steel for spirals and ties in bridges in
Seismic Zones 2, 3, or 4 shall comply with the
requirements specified in Article 5.10.11.
Where the area of spiral and tie reinforcement is not
controlled by:
•
Seismic requirements,
•
Shear or torsion as specified in Article 5.8, or
•
Minimum
requirements
Article 5.10.6,
as
specified
in
the ratio of spiral reinforcement to total volume of
concrete core, measured out-to-out of spirals, shall
satisfy:
A g f c′
− 1
ρ s ≥ 0.45
Ac
f yh
(5.7.4.6-1)
where:
Ag =
Ac =
f ′c =
fyh =
gross area of concrete section (in.2)
area of core measured to the outside diameter
of the spiral (in.2)
specified strength of concrete at 28 days, unless
another age is specified (ksi)
specified yield strength of spiral reinforcement
(ksi)
Other details of spiral and tie reinforcement shall
conform to the provisions of Articles 5.10.6 and 5.10.11.
5.7.4.7—Hollow Rectangular Compression
Members
5.7.4.7.1—Wall Slenderness Ratio
The wall slenderness ratio of a hollow rectangular
cross-section shall be taken as:
C5.7.4.7.1
The definition of the parameter Xu is illustrated in
Figure C5.7.4.7.1-1, taken from Taylor et al. (1990).
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2012
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5-54
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
λw =
Xu
t
(5.7.4.7.1-1)
where:
Xu =
t
=
λw =
the clear length of the constant thickness
portion of a wall between other walls or fillets
between walls (in.)
thickness of wall (in.)
wall slenderness ratio for hollow columns
Wall slenderness greater than 35 may be used only
when the behavior and resistance of the wall is
documented by analytic and experimental evidence
acceptable to the Owner.
Figure C5.7.4.7.1-1—Illustration of Xu
The test program, reported in Taylor et al. (1990),
was limited to the case of loading under simultaneous
axial and uniaxial bending about the weak axis of the
section. The results of the study have not been
confirmed for the case of biaxial bending. Until such a
study is completed, the Designer should investigate the
effects of biaxial loading on hollow sections.
5.7.4.7.2—Limitations on the Use of the
Rectangular Stress Block Method
5.7.4.7.2a—General
Except as specified in Article 5.7.4.7.2c, the
equivalent rectangular stress block method shall not be
employed in the design of hollow rectangular
compression members with a wall slenderness ratio ≥15.
Where the wall slenderness ratio is less than 15, the
rectangular stress block method may be used based on a
compressive strain of 0.003.
5.7.4.7.2b—Refined Method for Adjusting
Maximum Usable Strain Limit
Where the wall slenderness ratio is 15 or greater,
the maximum usable strain at the extreme concrete
compression fiber is equal to the lesser of the computed
local buckling strain of the widest flange of the crosssection, or 0.003.
The local buckling strain of the widest flange of the
cross-section may be computed assuming simply
supported boundary conditions on all four edges of the
flange. Nonlinear material behavior shall be considered
by incorporating the tangent material moduli of the
concrete and reinforcing steel in computations of the
local buckling strain.
Discontinuous, nonpost-tensioned reinforcement in
segmentally constructed hollow rectangular compression
members shall be neglected in computations of member
strength.
Flexural resistance shall be calculated using the
principles of Article 5.7.3 applied with anticipated
stress-strain curves for the types of material to be used.
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2012
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SECTION 5: CONCRETE STRUCTURES
5-55
5.7.4.7.2c—Approximate Method for Adjusting
Factored Resistance
The provisions of this Article and the rectangular
stress block method may be used in lieu of the
provisions of Articles 5.7.4.7.2a and 5.7.4.7.2b where
the wall slenderness is ≤ 35.
The factored resistance of a hollow column,
determined using a maximum usable strain of 0.003, and
the resistance factors specified in Article 5.5.4.2 shall be
further reduced by a factor φw taken as:
•
If λ w ≤ 15, then φ w = 1.0
(5.7.4.7.2c-1)
•
If 15 < λ w ≤ 25, then φ w = 1 − 0.025 ( λ w − 15 )
(5.7.4.7.2c-2)
•
If 25 < λ w ≤ 35, then φ w = 0.75
(5.7.4.7.2c-3)
5.7.5—Bearing
C5.7.5
In the absence of confinement reinforcement in the
concrete supporting the bearing device, the factored
bearing resistance shall be taken as:
(5.7.5-1)
Pr = φPn
in which:
(5.7.5-2)
Pn = 0.85 f c′A1m
where:
Pn
A1
m
A2
=
=
=
=
nominal bearing resistance (kip)
area under bearing device (in.2)
modification factor
a notional area defined herein (in.2)
The modification factor may be determined as
follows:
•
Where the supporting surface is wider on all sides
than the loaded area:
m=
•
A2
≤ 2.0
A1
(5.7.5-3)
Where the loaded area is subjected to nonuniformly
distributed bearing stresses:
m = 0.75
A2
≤ 1.50
A1
(5.7.5-4)
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Where the supporting surface is sloped or stepped, A2
may be taken as the area of the lower base of the largest
frustum of a right pyramid, cone, or tapered wedge
contained wholly within the support and having for its
upper base the loaded area, as well as side slopes of 1.0
vertical to 2.0 horizontal.
Where the factored applied load exceeds the
factored resistance, as specified herein, provisions shall
be made to resist the bursting and spalling forces in
accordance with Article 5.10.9.
Figure C5.7.5-1—Determination of A2 for a Stepped
Support
5.7.6—Tension Members
5.7.6.1—Factored Tension Resistance
Members in which the factored loads induce tensile
stresses throughout the cross-section shall be regarded as
tension members, and the axial force shall be assumed to
be resisted only by the steel elements. The provisions of
Article 5.11.5.4 shall apply.
The factored resistance to uniform tension shall be
taken as:
(5.7.6.1-1)
Pr = φPn
where:
Pn =
φ
=
nominal tension resistance specified in
Article 5.6.3.4
resistance factor specified in Article 5.5.4.2
5.7.6.2—Resistance to Combinations of Tension
and Flexure
Members subjected to eccentric tension loading,
which induces both tensile and compressive stresses in
the cross-section, shall be proportioned in accordance
with the provisions of Article 5.7.2.
5.8—SHEAR AND TORSION
5.8.1—Design Procedures
5.8.1.1—Flexural Regions
Where it is reasonable to assume that plane sections
remain plane after loading, regions of components shall
be designed for shear and torsion using either the
sectional model as specified in Article 5.8.3 or the strutand-tie model as specified in Article 5.6.3. The
requirements of Article 5.8.2 shall apply.
In lieu of the provisions of Article 5.8.3, segmental
post-tensioned concrete box girder bridges may be
designed for shear and torsion using the provisions of
Article 5.8.6.
C5.8.1.1
The sectional model is appropriate for the design of
typical bridge girders, slabs, and other regions of
components where the assumptions of traditional
engineering beam theory are valid. This theory assumes
that the response at a particular section depends only on
the calculated values of the sectional force effects, i.e.,
moment, shear, axial load, and torsion, and does not
consider the specific details of how the force effects
were introduced into the member. Although the strutand-tie model can be applied to flexural regions, it is
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SECTION 5: CONCRETE STRUCTURES
5-57
Components in which the distance from the point of
zero shear to the face of the support is less than 2d, or
components in which a load causing more than 1/2 (1/3
in case of segmental box girders) of the shear at a
support is closer than 2d from the face of the support,
may be considered to be deep components for which the
provisions of Article 5.6.3 and the detailing
requirements of Article 5.13.2.3 apply.
5.8.1.2—Regions Near Discontinuities
more appropriate and generally yields less conservative
designs for regions near discontinuities where the actual
flow of forces should be considered in more detail.
C5.8.1.2
Where the plane sections assumption of flexural
theory is not valid, regions of members shall be
designed for shear and torsion using the strut-and-tie
model as specified in Article 5.6.3. The provisions of
Article 5.13.2 shall apply.
The response of regions adjacent to abrupt changes
in cross-section, openings, dapped ends, deep beams,
and corbels is influenced significantly by the details of
how the loads are introduced into the region and how the
region is supported.
5.8.1.3—Interface Regions
Interfaces between elements shall be designed for
shear transfer in accordance with the provisions of
Article 5.8.4.
5.8.1.4—Slabs and Footings
Slab-type regions shall be designed for shear in
accordance with the provisions of Article 5.13.3.6 or
Article 5.6.3.
5.8.1.5—Webs of Curved Post-Tensioned Box
Girder Bridges
Curved post-tensioned box girders having an overall
clear height, hc, in excess of 4 ft shall be designed for
the following combined effects before and after losses:
•
The combined effects of global shear resulting from
vertical shear and torsion,
•
Transverse web regional bending resulting from
lateral prestress force, and
•
Transverse web bending from vertical loads and
transverse post-tensioning.
C5.8.1.5
Transverse web bending is a function of the vertical
loads, restoring effect of the longitudinal prestressing,
the Resal effect, and any transverse prestressing.
Considering global web shear and regional web
transverse bending alone will tend to underestimate the
amount of vertical reinforcing steel required in the webs.
More rigorous approaches that consider the interaction
of these combined forces are presented in Menn (1990)
and Nutt (2008).
5.8.2—General Requirements
5.8.2.1—General
as:
C5.8.2.1
The factored torsional resistance, Tr, shall be taken
Tr = φTn
(5.8.2.1-1)
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where:
Tn =
nominal torsional resistance specified in
Article 5.8.3.6 (kip-in.)
resistance factor specified in Article 5.5.4.2
=
φ
The factored shear resistance, Vr, shall be taken as:
(5.8.2.1-2)
Vr = φVn
Vn =
nominal shear resistance specified in
Article 5.8.3.3 (kip)
resistance factor as specified in Article 5.5.4.2
=
φ
For normal weight concrete, torsional effects shall
be investigated where:
(5.8.2.1-3)
Tu > 0.25φTcr
in which:
Tcr = 0.125 f c′
Acp 2
pc
1+
f pc
0.125 f c′
(5.8.2.1-4)
where:
Tu =
Tcr =
Acp =
factored torsional moment (kip-in.)
torsional cracking moment (kip-in.)
total area enclosed by outside perimeter of
concrete cross-section (in.2)
the length of the outside perimeter of the
concrete section (in.)
compressive stress in concrete after prestress
losses have occurred either at the centroid of
the cross-section resisting transient loads or at
the junction of the web and flange where the
centroid lies in the flange (ksi)
resistance factor specified in Article 5.5.4.2
=
pc
fpc =
=
φ
If the factored torsional moment is less than onequarter of the factored pure torsional cracking moment,
it will cause only a very small reduction in shear
capacity or flexural capacity and, hence, can be
neglected.
Sections that are designed for live loads using
approximate methods of analysis in Article 4.6.2.2 need
not be investigated for torsion.
The limit to Eq. 5.8.2.1-4 was added to avoid overestimating Tcr in the case of cellular structures.
Eq. 5.8.2.1-4 was derived from a solid section assuming
an equivalent thin wall tube. When the actual bv and Acp2
is considered, torsional resistance can be much less. The
resulting expression matches that in the current edition
of AASHTO’s Guide Specifications for Design and
Construction of Segmental Bridges.
For cellular structures:
Acp 2
pc
30 ft
19 ft
≤ 2 Aobv
0.75 ft
(5.8.2.1-5)
1 ft
Ao
where:
Ao =
area enclosed by the shear flow path, including
any area of holes therein (in.2)
The equivalent factored shear force, Vu, shall be
taken equal to:
For solid sections:
0.75 ft
6 ft
3 ft
6 ft
7 ft
Acp
12 ft
Figure C5.8.2.1-1—Sketch Showing Data Used in Sample
Calculation for Ao Shown Below
Ao =
1
2
(11 ft + 18 ft )( 6.25 ft ) = 90.6 ft
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SECTION 5: CONCRETE STRUCTURES
0.9 phTu
V +
2 Ao
5-59
2
2
u
(5.8.2.1-6)
For box sections:
Vu +
Tu d s
2 Ao
(5.8.2.1-7)
where:
ph =
Tu =
perimeter of the centerline of the closed
transverse torsion reinforcement (in.)
factored torsional moment (kip-in.)
5.8.2.2—Modifications for Lightweight Concrete
Where lightweight aggregate concretes are used, the
following modifications shall apply in determining
resistance to torsion and shear:
•
Where the average splitting tensile strength of
lightweight concrete, fct, is specified, the term √f ′c
in the expressions given in Articles 5.8.2 and 5.8.3
shall be replaced by:
4.7 f ct ≤
•
Alternatively, the term Ao can usually be taken as
85 percent of the area enclosed by the centerline of the
exterior closed transverse torsion reinforcement,
including area of any holes. The justification for this
generally conservative substitution is given in Collins
and Mitchell (1991).
A stress limit for principal tension at the neutral axis
in the web was added in 2004. This check requires shear
demand, and not the resistance, to be modified for torsion.
Eqs. 5.8.2.1-6 and 5.8.2.1-7 were added to clarify how
demand is modified for torsion. Note that the Vu in
Eqs. 5.8.3.4.2-1, 5.8.3.4.2-2, and 5.8.3.4.2-3 for εx, and in
Eq. 5.8.2.9-1 for vu, are not modified for torsion.
For solid cross-section shapes, such as a rectangle
or an “I,” there is the possibility of considerable
redistribution of shear stresses. To make some
allowance for this favorable redistribution it is safe to
use a root-mean-square approach in calculating the
nominal shear stress for these cross-sections, as
indicated in Eq. 5.8.2.1-6. The 0.9ph comes from
90 percent of the perimeter of the spalled concrete
section. This is similar to multiplying 0.9 times the lever
arm in flexural calculations.
For a box girder, the shear flow due to torsion is
added to the shear flow due to flexure in one exterior
web, and subtracted from the opposite exterior web. In
the controlling web, the second term in Eq. 5.8.2.1-7
comes from integrating the distance from the centroid of
the section, to the center of the shear flow path around
the circumference of the section. The stress is converted
to a force by multiplying by the web height measured
between the shear flow paths in the top and bottom
slabs, which has a value approximately equal that of ds.
If the exterior web is sloped, this distance should be
divided by the sine of the web angle from horizontal.
C5.8.2.2
The tensile strength and shear capacity of
lightweight concrete is typically somewhat less than that
of normal weight concrete having the same compressive
strength.
f c′
Where fct is not specified, the term 0.75√f ′c for all
for sandlightweight concrete, and 0.85√f ′c
lightweight concrete shall be substituted for √f ′c in
the expressions given in Articles 5.8.2 and 5.8.3
Linear interpolation may be employed when partial
sand replacement is used.
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5.8.2.3—Transfer and Development Lengths
C5.8.2.3
The provisions of Article 5.11.4 shall be considered.
5.8.2.4—Regions Requiring Transverse
Reinforcement
2013 Revision
C5.8.2.4
Except for slabs, footings, and culverts, transverse
reinforcement shall be provided where:
•
Vu > 0.5φ (Vc + V p )
The reduced prestress in the transfer length reduces
Vp, fpc, and fpe. The transfer length influences the tensile
force that can be resisted by the tendons at the inside
edge of the bearing area, as described in Article 5.8.3.5.
2013 Revision
Transverse reinforcement, which usually consists of
stirrups, is required in all regions where there is a
significant chance of diagonal cracking.
(5.8.2.4-1)
or
•
Where consideration of torsion is required by
Eq. 5.8.2.1-3 or Eq. 5.8.6.3-1
where:
Vu =
Vc =
Vp =
φ
=
factored shear force (kip)
nominal shear resistance of the concrete (kip)
component of prestressing force in direction of
the shear force; Vp = 0 when the simplified
method of 5.8.3.4.3 is used (kip)
resistance factor specified in Article 5.5.4.2
5.8.2.5—Minimum Transverse Reinforcement
2013 Revision
Except for segmental post-tensioned concrete box
girder bridges, where transverse reinforcement is required,
as specified in Article 5.8.2.4, the area of steel shall satisfy:
Av ≥ 0.0316
f c′
bv s
fy
(5.8.2.5-1)
where:
Av =
bv
=
s
fy
=
=
C5.8.2.5
2013 Revision
A minimum amount of transverse reinforcement is
required to restrain the growth of diagonal cracking and
to increase the ductility of the section. A larger amount
of transverse reinforcement is required to control
cracking as the concrete strength is increased.
Additional transverse reinforcement may be
required for transverse web bending.
area of a transverse reinforcement within
distance s (in.2)
width of web adjusted for the presence of ducts
as specified in Article 5.8.2.9 (in.)
spacing of transverse reinforcement (in.)
yield strength of transverse reinforcement (ksi)
For segmental post-tensioned concrete box girder
bridges, where transverse reinforcement is required, as
specified in Article 5.8.6.5, the area of transverse
reinforcement shall satisfy:
Av ≥ 0.05
bw s
fy
(5.8.2.5-2)
where:
Av =
bw =
area of a transverse shear reinforcement per
web within distance s (in.2)
width of web (in.)
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SECTION 5: CONCRETE STRUCTURES
s
fy
=
=
5-61
spacing of transverse reinforcement (in.)
yield strength of transverse reinforcement (ksi)
For segmental post-tensioned concrete box girder
bridges, where transverse reinforcement is not required,
as specified in Article 5.8.6.5, the minimum area of
transverse shear reinforcement per web shall not be less
than the equivalent of two No. 4 Grade 60 reinforcement
bars per foot of length.
5.8.2.6—Types of Transverse Reinforcement
Transverse reinforcement to resist shear may consist of:
•
Stirrups perpendicular to the longitudinal axis of the
member;
•
Welded wire reinforcement, with wires located
perpendicular to the longitudinal axis of the
member, provided that the transverse wires are
certified to undergo a minimum elongation of
four percent, measured over a gage length of at least
4.0 in. including at least one cross wire;
•
Anchored prestressed tendons, detailed and
constructed to minimize seating and time-dependent
losses, which make an angle not less than 45 degrees
with the longitudinal tension reinforcement;
•
Combinations of stirrups, tendons, and bent
longitudinal bars;
•
Spirals or hoops;
•
Inclined stirrups making an angle of not less than
45 degrees with the longitudinal tension
reinforcement; or
•
Bent longitudinal bars in nonprestressed members
with the bent portion making an angle of 30 degrees
or more with the longitudinal tension reinforcement.
C5.8.2.6
Stirrups inclined at less than 45 degrees to the
longitudinal reinforcement are difficult to anchor
effectively against slip and, hence, are not permitted.
Inclined stirrups and prestressed tendons should be
oriented to intercept potential diagonal cracks at an
angle as close to normal as practical.
To increase shear capacity, transverse reinforcement
should be capable of undergoing substantial strain prior
to failure. Welded wire fabric, particularly if fabricated
from small wires and not stress-relieved after
fabrication, may fail before the required strain is
reached. Such failures may occur at or between the
cross-wire intersections.
For some large bridge girders, prestressed tendons
perpendicular to the member axis may be an efficient
form of transverse reinforcement. Because the tendons
are short, care must be taken to avoid excessive loss of
prestress due to anchorage slip or seating losses. The
requirements for transverse reinforcement assume it is
perpendicular to the longitudinal axis of prismatic
members or vertical for nonprismatic or tapered members.
Requirements for bent bars were added to make the
provisions consistent with those in AASHTO (2002).
Inclined stirrups and bent longitudinal reinforcement
shall be spaced so that every 45-degree line, extending
towards the reaction from mid-depth of the member, h/2,
to the longitudinal tension reinforcement shall be
crossed by at least one line of transverse reinforcement.
Transverse reinforcement shall be detailed such that
the shear force between different elements or zones of a
member are effectively transferred.
Torsional reinforcement shall consist of both
transverse and longitudinal reinforcement. Longitudinal
reinforcement shall consist of bars and/or tendons.
Transverse reinforcement may consist of:
•
Closed stirrups or closed ties, perpendicular to the
longitudinal axis of the member, as specified in
Article 5.11.2.6.4,
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
•
A closed cage of welded wire reinforcement with
transverse wires perpendicular to the longitudinal
axis of the member, or
•
Spirals or hoops.
5.8.2.7—Maximum Spacing of Transverse
Reinforcement
C5.8.2.7
The spacing of the transverse reinforcement shall
not exceed the maximum permitted spacing, smax,
determined as:
•
Sections that are highly stressed in shear require
more closely spaced reinforcement to provide crack
control.
If vu < 0.125 f ′c, then:
smax = 0.8d v ≤ 24.0 in.
•
2013 Revision
(5.8.2.7-1)
If vu ≥ 0.125 f ′c, then:
smax = 0.4d v ≤ 12.0 in.
(5.8.2.7-2)
where:
vu
=
dv
=
the shear stress calculated in accordance with
Article 5.8.2.9 (ksi)
effective shear depth as defined in
Article 5.8.2.9 (in.)
For segmental post-tensioned concrete box girder
bridges, spacing of closed stirrups or closed ties required
to resist shear effects due to torsional moments shall not
exceed one-half of the shortest dimension of the crosssection, nor 12.0 in.
5.8.2.8—Design and Detailing Requirements
2013 Revision
Transverse reinforcement shall be anchored at both
ends in accordance with the provisions of
Article 5.11.2.6. For composite flexural members,
extension of beam shear reinforcement into the deck
slab may be considered when determining if the
development
and
anchorage
provisions
of
Article 5.11.2.6 are satisfied.
The design yield strength of nonprestressed
transverse reinforcement shall be taken equal to the
specified yield strength when the latter does not exceed
60.0 ksi. For nonprestressed transverse reinforcement
with yield strength in excess of 60.0 ksi, the design yield
strength shall be taken as the stress corresponding to a
strain of 0.0035, but not to exceed 75.0 ksi. The design
yield strength of prestressed transverse reinforcement
shall be taken as the effective stress, after allowance for
all prestress losses, plus 60.0 ksi, but not greater than fpy.
C5.8.2.8
2013 Revision
To be effective, the transverse reinforcement should
be anchored at each end in a manner that minimizes slip.
Fatigue of welded wire reinforcement is not a concern in
prestressed members as long as the specially fabricated
reinforcement is detailed to have welded joints only in
the flanges where shear stress is low.
Some of the provisions of Article 5.8.3 are based on
the assumption that the strain in the transverse
reinforcement has to attain a value of 0.002 to develop
its yield strength. For prestressed tendons, it is the
additional strain required to increase the stress above the
effective stress caused by the prestress that is of
concern. Limiting the design yield strength of
nonprestressed transverse reinforcement to 75.0 ksi or a
stress corresponding to a strain of 0.0035 provides
control of crack widths at service limit state. For
reinforcement without a well-defined yield point, the
yield strength is determined at a strain of 0.0035 at
strength limit state. Research by Griezic (1994), Ma
(2000), and Bruce (2003) has indicated that the
performance of higher strength steels as shear
reinforcement has been satisfactory. Use of relatively
small diameter deformed welded wire reinforcement at
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SECTION 5: CONCRETE STRUCTURES
5-63
When welded wire reinforcement is used as
transverse reinforcement, it shall be anchored at both
ends in accordance with Article 5.11.2.6.3. No welded
joints other than those required for anchorage shall be
permitted.
Components of inclined flexural compression
and/or flexural tension in variable depth members shall
be considered when calculating shear resistance.
5.8.2.9—Shear Stress on Concrete
as:
relatively small spacing, compared to individually field
tied reinforcing bars results in improved quality control
and improved member performance in service.
The components in the direction of the applied
shear of inclined flexural compression and inclined
flexural tension can be accounted for in the same
manner as the component of the longitudinal
prestressing force, Vp.
C5.8.2.9
The shear stress on the concrete shall be determined
vu =
Vu − φV p
φbv d v
(5.8.2.9-1)
where:
φ
=
bv
=
dv
=
resistance factor for shear specified in
Article 5.5.4.2
effective web width taken as the minimum web
width, measured parallel to the neutral axis,
between the resultants of the tensile and
compressive forces due to flexure, or for
circular sections, the diameter of the section,
modified for the presence of ducts where
applicable (in.)
effective shear depth taken as the distance,
measured perpendicular to the neutral axis,
between the resultants of the tensile and
compressive forces due to flexure; it need not
be taken to be less than the greater of 0.9 de or
0.72h (in.)
in which:
de =
Aps f ps d p + As f y d s
Aps f ps + As f y
(5.8.2.9-2)
In determining the web width at a particular level,
one-half the diameters of ungrouted ducts or one-quarter
the diameter of grouted ducts at that level shall be
subtracted from the web width.
Figure C5.8.2.9-1—Illustration of the Terms bv and dv
For flexural members, the distance between the
resultants of the tensile and compressive forces due to
flexure can be determined as:
dv =
Mn
As f y + Aps f ps
(C5.8.2.9-1)
In continuous members near the point of inflection,
if Eq. C5.8.2.9-1 is used, it should be evaluated in terms
of both the top and the bottom reinforcement. Note that
other limitations on the value of dv to be used are
specified and that dv is the value at the section at which
shear is being investigated.
Previous editions of the Standard Specifications
permitted d for prestressed members to be taken as 0.8h.
The 0.72h limit on dv is 0.9 × 0.8h.
Post-tensioning ducts act as discontinuities and
hence, can reduce the crushing strength of concrete
webs. In determining which level over the effective
depth of the beam has the minimum width, and hence
controls bv, levels which contain a post-tensioning duct
or several ducts shall have their widths reduced. Thus,
for the section shown in Figure C5.8.2.9-1, the posttensioning duct in the position shown would not reduce
bv, because it is not at a level where the width of the
section is close to the minimum value. If the location of
the tendon was raised such that the tendon is located
within the narrow portion of the web, the value of bv
would be reduced.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
For circular members, such as reinforced concrete
columns or prestressed concrete piles, dv can be
determined from Eq. C5.8.2.9-1 provided that Mn is
calculated ignoring the effects of axial load and that the
reinforcement areas, As and Aps, are taken as the
reinforcement in one-half of the section. Alternatively,
dv can be taken as 0.9de, where:
de =
D Dr
+
π
2
(C5.8.2.9-2)
where:
D =
Dr =
external diameter of the circular member (in.)
diameter of the circle passing through the
centers of the longitudinal reinforcement (in.)
Figure C5.8.2.9-2—Illustration of Terms bv, dv, and de for
Circular Sections
Circular members usually have the longitudinal
reinforcement uniformly distributed around the
perimeter of the section. When the member cracks, the
highest shear stresses typically occur near the middepth
of the section. This is also true when the section is not
cracked. It is for this reason that the effective web width
can be taken as the diameter of the section.
5.8.3—Sectional Design Model
5.8.3.1—General
C5.8.3.1
The sectional design model may be used for shear
design where permitted in accordance with the
provisions of Article 5.8.1.
In lieu of the methods specified herein, the
resistance of members in shear or in shear combined
with torsion may be determined by satisfying the
conditions of equilibrium and compatibility of strains
and by using experimentally verified stress-strain
relationships for reinforcement and for diagonally
cracked concrete. Where consideration of simultaneous
In the sectional design approach, the component is
investigated by comparing the factored shear force and
the factored shear resistance at a number of sections
along its length. Usually this check is made at the tenth
points of the span and at locations near the supports.
See Articles 5.10.11.3 and 5.10.11.4.1c for
additional requirements for Seismic Zones 2, 3, and 4
and Articles 5.8.1.2 and 5.8.3.2 for additional
requirements for member end regions.
An appropriate nonlinear finite element analysis or a
detailed sectional analysis would satisfy the requirements
of this Article. More information on appropriate
procedures and a computer program that satisfies these
requirements are given by Collins and Mitchell (1991).
One possible approach to the analysis of biaxial shear and
other complex loadings on concrete members is outlined
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SECTION 5: CONCRETE STRUCTURES
shear in a second direction is warranted, investigation
shall be based either on the principles outlined above or
on a three-dimensional strut-and-tie model.
5.8.3.2—Sections Near Supports
The provisions of Article 5.8.1.2 shall be
considered.
Where the reaction force in the direction of the
applied shear introduces compression into the end region
of a member, the location of the critical section for shear
shall be taken as dv from the internal face of the support
as illustrated in Figure 5.8.3.2-1.
5-65
in Rabbat and Collins (1978), and a corresponding
computer-aided solution is presented in Rabbat and
Collins (1976). A discussion of the effect of biaxial shear
on the design of reinforced concrete beam-to-column
joints can be found in Paulay and Priestley (1992).
C5.8.3.2
Loads close to the support are transferred directly to
the support by compressive arching action without
causing additional stresses in the stirrups.
The traditional approach to proportioning transverse
reinforcement involves the determination of the required
stirrup spacing at discrete sections along the member.
The stirrups are then detailed such that this spacing is
not exceeded over a length of the beam extending from
the design section to the next design section out into the
span. In such an approach, the shear demand and
resistance provided is assumed to be as shown in
Figure C5.8.3.2-1.
Figure C5.8.3.2-1—Traditional Shear Design
Figure 5.8.3.2-1—Critical Section for Shear
Otherwise, the design section shall be taken at the
internal face of the support. Where the beam-type
element extends on both sides of the reaction area, the
design section on each side of the reaction shall be
determined separately based upon the loads on each side
of the reaction and whether their respective contribution
to the total reaction introduces tension or compression
into the end region.
For post-tensioned beams, anchorage zone
reinforcement shall be provided as specified in
Article 5.10.9. For pretensioned beams, a reinforcement
cage confining the ends of strands shall be provided as
specified in Article 5.10.10. For nonprestressed beams
supported on bearings that introduce compression into
the member, only minimal transverse reinforcement may
be provided between the inside edge of the bearing plate
or pad and the end of the beam.
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For typical cases where the applied load acts at or
above the middepth of the member, it is more practical
to take the traditional approach as shown in
Figure C5.8.3.2-1 or a more liberal yet conservative
approach as shown in Figure C5.8.3.2-2. The approach
taken in Figure C5.8.3.2-2 has the effect of extending
the required stirrup spacing for a distance of 0.5dv cot θ
toward the bearing.
Figure C5.8.3.2-2—Simplified Design Section for Loads
Applied at or above the Middepth of the Member
Figure C5.8.3.2-3 shows a case where an inverted
T-beam acts as a pier cap and the longitudinal members
are supported by the flange of the T. In this case, a
significant amount of the load is applied below the
middepth of the member, and it is more appropriate to
use the traditional approach to shear design shown in
Figure C5.8.3.2-1.
Figure C5.8.3.2-3—Inverted T-Beam Pier Cap
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SECTION 5: CONCRETE STRUCTURES
5-67
If the shear stress at the design section calculated in
accordance with Article 5.8.2.9 exceeds 0.18f ′c and the
beam-type element is not built integrally with the
support, its end region shall be designed using the strutand-tie model specified in Article 5.6.3.
5.8.3.3—Nominal Shear Resistance
C5.8.3.3
The nominal shear resistance, Vn, shall be
determined as the lesser of:
Vn = Vc + Vs + V p
(5.8.3.3-1)
Vn = 0.25 f c′bv d v + V p
(5.8.3.3-2)
in which:
V c = 0.0316 β f c′ b v d v , if the procedures of
Articles 5.8.3.4.1 or 5.8.3.4.2 are used
(5.8.3.3-3)
Vc = the lesser of Vci and Vcw, if the procedures of
Article 5.8.3.4.3 are used
Vs =
Av f y d v (cot θ + cot α) sin α
s
(5.8.3.3-4)
Where transverse reinforcement consists of a single
longitudinal bar or a single group of parallel longitudinal
bars bent up at the same distance from the support, the
shear resistance Vs provided by these bars shall be
determined as:
Vs = Av f y sin α ≤ 0.095 f c′bv d v
The T-beam pier cap shown in Figure C5.8.3.2-3
acts as a beam ledge and should be designed for the
localized effects caused by the concentrated load applied
to the T-beam flange. Provisions for beam ledge design
are given in Article 5.13.2.5.
Where a beam is loaded on top and its end is not
built integrally into the support, all the shear funnels
down into the end bearing. Where the beam has a thin
web so that the shear stress in the beam exceeds 0.18 f ′c,
there is the possibility of a local diagonal compression
or horizontal shear failure along the interface between
the web and the lower flange of the beam. Usually the
inclusion of additional transverse reinforcement cannot
prevent this type of failure and either the section size
must be increased or the end of the beam designed using
a strut-and-tie model.
2013 Revision
The shear resistance of a concrete member may be
separated into a component, Vc, that relies on tensile
stresses in the concrete, a component, Vs, that relies on
tensile stresses in the transverse reinforcement, and a
component, Vp, that is the vertical component of the
prestressing force.
The expressions for Vc and Vs apply to both
prestressed and nonprestressed sections, with the terms β
and θ depending on the applied loading and the
properties of the section.
The upper limit of Vn, given by Eq. 5.8.3.3-2, is
intended to ensure that the concrete in the web of the
beam will not crush prior to yield of the transverse
reinforcement.
where α = 90 degrees, Eq. 5.8.3.3-4 reduces to:
Vs =
Av f y d v cot θ
s
(C5.8.3.3-1)
(5.8.3.3-5)
where:
bv
=
dv
=
s
=
β
=
effective web width taken as the minimum web
width within the depth dv as determined in
Article 5.8.2.9 (in.)
effective shear depth as determined in
Article 5.8.2.9 (in.)
spacing of transverse reinforcement measured
in a direction parallel to the longitudinal
reinforcement (in.)
factor indicating ability of diagonally cracked
concrete to transmit tension and shear as
specified in Article 5.8.3.4
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
θ
=
α
=
Av =
Vp =
angle of inclination of diagonal compressive
stresses as determined in Article 5.8.3.4
(degrees); if the procedures of Article 5.8.3.4.3
are used, cot θ is defined therein
angle of inclination of transverse reinforcement
to longitudinal axis (degrees)
area of shear reinforcement within a distance s
(in.2)
component in the direction of the applied shear
of the effective prestressing force; positive if
resisting the applied shear; Vp = 0 when
Article 5.8.3.4.3 is applied (kip)
Where bent longitudinal reinforcement is used, only
the center three-fourths of the inclined portion of the
bent bar shall be considered effective for transverse
reinforcement.
Where more than one type of transverse
reinforcement is used to provide shear resistance in the
same portion of a member, the shear resistance Vs shall
be determined as the sum of Vs values computed from
each type.
Where shear resistance is provided by bent
longitudinal reinforcement or a combination of bent
longitudinal reinforcement and stirrups, the nominal
shear resistance shall be determined using the simplified
procedure in accordance with Article 5.8.3.4.1.
5.8.3.4—Procedures for Determining Shear
Resistance
Design for shear may utilize any of the three
methods identified herein provided that all requirements
for usage of the chosen method are satisfied.
The angle θ is, therefore, also taken as the angle
between a strut and the longitudinal axis of a member.
Vp is part of Vcw by the method in Article 5.8.3.4.3
and thus Vp need be taken as zero in Eq. 5.8.3.3-1.
Requirements for bent bars were added to make the
provisions consistent with those in AASHTO (2002).
C5.8.3.4
Three complementary methods are given for evaluating
shear resistance. Method 1, specified in Article 5.8.3.4.1, as
described herein, is only applicable for nonprestressed
sections. Method 2, as described in Article 5.8.3.4.2, is
applicable for all prestressed and nonprestressed members,
with and without shear reinforcement, with and without
axial load. Two approaches are presented in Method 2: a
direct calculation, specified in Article 5.8.3.4.2, and an
evaluation using tabularized values presented in
Appendix B5. The approaches to Method 2 may be
considered statistically equivalent. Method 3, specified in
Article 5.8.3.4.3, is applicable for both prestressed and
nonprestressed sections in which there is no net axial tensile
load and at least minimum shear reinforcement is provided.
Axial load effects can otherwise be accounted for through
adjustments to the level of effective precompression stress,
fpc. In regions of overlapping applicability between the latter
two methods, Method 3 will generally lead to somewhat
more shear reinforcement being required, particularly in
areas of negative moment and near points of contraflexure.
If Method 3 leads to an unsatisfactory rating, it is
permissible to use Method 2.
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SECTION 5: CONCRETE STRUCTURES
5-69
5.8.3.4.1—Simplified Procedure for Nonprestressed
Sections
For concrete footings in which the distance from
point of zero shear to the face of the column, pier or wall
is less than 3dv with or without transverse reinforcement,
and for other nonprestressed concrete sections not
subjected to axial tension and containing at least the
minimum amount of transverse reinforcement specified
in Article 5.8.2.5, or having an overall depth of less than
16.0 in., the following values may be used:
C5.8.3.4.1
With β taken as 2.0 and θ as 45 degrees, the
expressions for shear strength become essentially
identical to those traditionally used for evaluating shear
resistance. Recent large-scale experiments (Shioya et al.,
1989), however, have demonstrated that these traditional
expressions can be seriously unconservative for large
members not containing transverse reinforcement.
β = 2.0
θ = 45°
5.8.3.4.2—General Procedure
C5.8.3.4.2
The parameters β and θ may be determined either
by the provisions herein, or alternatively by the
provisions of Appendix B5.
For sections containing at least the minimum
amount of transverse reinforcement specified in
Article 5.8.2.5, the value of β may be determined by
Eq. 5.8.3.4.2-1:
β=
4.8
(1 + 750ε s )
(5.8.3.4.2-1)
When sections do not contain at least the minimum
amount of shear reinforcement, the value of β may be as
specified in Eq. 5.8.3.4.2-2:
β=
4.8
51
(5.8.3.4.2-2)
(1 + 750ε s ) ( 39 + s xe )
The value of θ in both cases may be as specified in
Eq. 5.8.3.4.2-3:
(5.8.3.4.2-3)
θ = 29 + 3500ε s
In Eqs. 5.8.3.4.2-1 through 5.8.3.4.2-3, εs is the net
longitudinal tensile strain in the section at the centroid of
the tension reinforcement as shown in Figures 5.8.3.4.2-1
and 5.8.3.4.2-2. In lieu of more involved procedures, εs
may be determined by Eq. 5.8.3.4.2-4:
Mu
+ 0.5 N u + Vu − V p − Aps f po
d
εs = v
Es As + E p Aps
(5.8.3.4.2-4)
The crack spacing parameter, sxe, shall be
determined as:
sxe = sx
where:
1.38
ag + 0.63
(5.8.3.4.2-5)
The shear resistance of a member may be determined
by performing a detailed sectional analysis that satisfies
the requirements of Article 5.8.3.1. Such an analysis, see
Figure C5.8.3.4.2-1, would show that the shear stresses
are not uniform over the depth of the web and that the
direction of the principal compressive stresses changes
over the depth of the beam. The more direct procedure
given herein assumes that the concrete shear stresses are
uniformly distributed over an area bv wide and dv deep,
that the direction of principal compressive stresses
(defined by angle θ and shown as D) remains constant
over dv, and that the shear strength of the section can be
determined by considering the biaxial stress conditions at
just one location in the web. See Figure C5.8.3.4.2-2.
This design procedure (Collins et al, 1994) was
derived from the Modified Compression Field Theory
(MCFT, Vecchio, and Collins, 1986) which is a
comprehensive behavioral model for the response of
diagonally cracked concrete subject to in-plane shear and
normal stresses. Prior to the 2008 interim revisions, the
General Procedure for shear design was iterative and
required the use of tables for the evaluation of β and θ.
With the 2008 revisions, this design procedure was
modified to be non-iterative and algebraic equations were
introduced for the evaluation of β and θ. These equations
are functionally equivalent to those used in the Canadian
design code (A23.2-M04, 2004), were also derived from
the MCFT (Bentz et al. 2006), and were evaluated as
appropriate for use in the AASHTO LRFD Bridge Design
Specifications (Hawkins et al., 2006, 2007).
The longitudinal strain, εs, can be determined by the
procedure illustrated in Figure C5.8.3.4.2-3. The actual
section is represented by an idealized section consisting
of a flexural tension flange, a flexural compression
flange, and a web. The area of the compression flange is
taken as the area on the flexure compression side of the
member, i.e., the total area minus the area of the tension
flange as defined by Ac. After diagonal cracks have
formed in the web, the shear force applied to the web
concrete, Vu − Vp, will primarily be carried by
diagonal compressive stresses in the web concrete.
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12.0 in. ≤ sxe ≤ 80.0 in.
where:
Ac =
Aps =
As =
ag =
fpo =
Nu =
Mu =
area of concrete on the flexural tension side of
the member as shown in Figure 5.8.3.4.2-1
(in.2)
area of prestressing steel on the flexural tension
side of the member, as shown in
Figure 5.8.3.4.2-1 (in.2)
area of nonprestressed steel on the flexural
tension side of the member at the section under
consideration, as shown in Figure 5.8.3.4.2-1
(in.2)
maximum aggregate size (in.)
a parameter taken as modulus of elasticity of
prestressing tendons multiplied by the lockedin difference in strain between the prestressing
tendons and the surrounding concrete (ksi). For
the usual levels of prestressing, a value of 0.7
fpu will be appropriate for both pretensioned
and post-tensioned members
factored axial force, taken as positive if tensile
and negative if compressive (kip)
absolute value of the factored moment, not to
These diagonal compressive stresses will result in a
longitudinal compressive force in the web concrete of
(Vu − Vp) cot θ. Equilibrium requires that this
longitudinal compressive force in the web needs to be
balanced by tensile forces in the two flanges, with half
the force, that is 0.5 (Vu − Vp) cot θ, being taken by each
flange. For simplicity, 0.5 cot θ may be taken as = 2.0
and the longitudinal demand due to shear in the
longitudinal tension reinforcement becomes Vu – Vp
without significant loss of accuracy. After the required
axial forces in the two flanges are calculated, the
resulting axial strains, εt and εc, can be calculated based
on the axial force-axial strain relationship shown in
Figure C5.8.3.4.2-3.
For pretensioned members, fpo can be taken as the
stress in the strands when the concrete is cast around
them, i.e., approximately equal to the jacking stress. For
post-tensioned members, fpo can be conservatively taken
as the average stress in the tendons when the posttensioning is completed.
be taken less than Vu − Vp dv (kip-in.)
sx
=
Vu =
the lesser of either dv or the maximum distance
between layers of longitudinal crack control
reinforcement, where the area of the
reinforcement in each layer is not less than
0.003bvsx, as shown in Figure 5.8.3.4.2-3 (in.)
factored shear force (kip)
Within the transfer length, fpo shall be increased
linearly from zero at the location where the bond
between the strands and concrete commences to its full
value at the end of the transfer length.
The flexural tension side of the member shall be
taken as the half-depth containing the flexural tension
zone, as illustrated in Figure 5.8.3.4.2-1.
In the use of Eqs. 5.8.3.4.2-1 through 5.8.3.4.2-5,
the following should be considered:
•
Mu should not be taken less than Vu − Vp dv .
•
In calculating As and Aps the area of bars or tendons
terminated less than their development length from
the section under consideration should be reduced
in proportion to their lack of full development.
•
If the value of εs calculated from Eq. 5.8.3.4.2-4 is
negative, it should be taken as zero or the value
should be recalculated with the denominator of
Eq. 5.8.3.4.2-4 replaced by (EsAs + EpAps + EcAct).
However, εs should not be taken as less than
–0.40 × 10–3.
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SECTION 5: CONCRETE STRUCTURES
•
For sections closer than dv to the face of the support,
the value of εs calculated at dv from the face of the
support may be used in evaluating β and θ.
•
If the axial tension is large enough to crack the
flexural compression face of the section, the value
calculated from Eq. 5.8.3.4.2-4 should be doubled.
•
It is permissible to determine β and θ from
Eqs. 5.8.3.4.2-1 through 5.8.3.4.2-3 using a value of
εs which is greater than that calculated from
Eq. 5.8.3.4.2-4 However εs should not be taken
greater than 6.0 × 10–3.
5-71
Figure 5.8.3.4.2-1—Illustration of Shear Parameters for Section Containing at Least the Minimum Amount of Transverse
Reinforcement, Vp = 0
Figure 5.8.3.4.2-2—Longitudinal Strain, εs, for Sections
Containing Less than the Minimum Amount of Transverse
Reinforcement
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The relationships for evaluating β and θ in
Eqs. 5.8.3.4.2-1 and 5.8.3.4.2-2 are based on calculating
the stresses that can be transmitted across diagonally
cracked concrete. As the cracks become wider, the
stress that can be transmitted decreases. For members
containing at least the minimum amount of transverse
reinforcement, it is assumed that the diagonal cracks
will be spaced about 12.0 in. apart. For members
without transverse reinforcement, the spacing of
diagonal cracks inclined at θ degrees to the longitudinal
reinforcement is assumed to be sx /sin θ, as shown in
Figure 5.8.3.4.2-3. Hence, deeper members having
larger values of sx are calculated to have more widely
spaced cracks and hence, cannot transmit such high
shear stresses. The ability of the crack surfaces to
transmit shear stresses is influenced by the aggregate
size of the concrete. Members made from concretes that
have a smaller maximum aggregate size will have a
larger value of sxe and hence, if there is no transverse
reinforcement, will have a smaller shear strength.
Figure 5.8.3.4.2-3—Definition of Crack Spacing
Parameter, sx
Figure C5.8.3.4.2-1—Detailed Sectional Analysis to Determine Shear Resistance in Accordance with Article 5.8.3.1
Figure C5.8.3.4.2-2—More Direct Procedure to Determine Shear Resistance in Accordance with Article 5.8.3.4.2
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SECTION 5: CONCRETE STRUCTURES
5-73
Figure C5.8.3.4.2-3—More Accurate Calculation Procedure for Determining εs
5.8.3.4.3—Simplified Procedure for Prestressed
and Nonprestressed Sections
For concrete beams not subject to significant axial
tension, prestressed and nonprestressed, and containing
at least the minimum amount of transverse
reinforcement specified in Article 5.8.2.5, Vn in
Article 5.8.3.3 may be determined with Vp taken as zero
and Vc taken as the lesser of Vci and Vcw, where:
Vci =
Vcw =
nominal shear resistance provided by concrete
when inclined cracking results from combined
shear and moment (kip)
nominal shear resistance provided by concrete
when inclined cracking results from excessive
principal tensions in web (kip)
Vci shall be determined as:
Vci = 0.02 f c′bv d v + Vd +
Vi M cre
M max
≥ 0.06 f c′bv d v
(5.8.3.4.3-1)
C5.8.3.4.3
Article 5.8.3.4.3 is based on the recommendations
of NCHRP Report 549 (Hawkins et al., 2005). The
concepts of this Article are compatible with the concepts
of ACI Code 318-05 and AASHTO Standard
Specifications for Highway Bridges (2002) for
evaluations of the shear resistance of prestressed
concrete members. However, those concepts are
modified so that this Article applies to both prestressed
and nonprestressed sections.
The nominal shear resistance Vn is the sum of the
shear resistances Vc and Vs provided by the concrete and
shear reinforcement, respectively. Both Vc and Vs
depend on the type of inclined cracking that occurs at
the given section. There are two types of inclined
cracking: flexure-shear cracking and web-shear cracking
for which the associated resistances are Vci and Vcw,
respectively.
Figure
C5.8.3.4.3-1
shows
the
development of both types of cracking when increasing
uniform load was applied to a 63-in. bulb-tee girder.
NCHRP Report XX2 (Hawkins et al., 2005).
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
where:
C
L
31
Vd
=
Vi
=
Mcre
=
Mmax
=
shear force at section due to unfactored
dead load and includes both DC and DW
(kip)
factored shear force at section due to
externally applied loads occurring
simultaneously with Mmax (kip)
moment causing flexural cracking at
section due to externally applied loads
(kip-in)
maximum factored moment at section due
to externally applied loads (kip-in)
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
(a) Load 1
C
L
31
32
33
34
35
36
37
38
39
(b) Load 2
C
L
31
32
33
34
35
36
37
38
39
Mcre shall be determined as:
M dnc
S nc
M cre = Sc f r + f cpe −
(5.8.3.4.3-2)
Figure C5.8.3.4.3-1—Development of Shear Cracking with
Increasing Loads for Uniformly Loaded Bulb Tee Beam;
Load 1 < Load 2 < Load 3
where:
fcpe
=
Mdnc
=
Sc
=
Snc
=
compressive stress in concrete due to
effective prestress forces only (after
allowance for all prestress losses) at
extreme fiber of section where tensile stress
is caused by externally applied loads (ksi)
total unfactored dead load moment acting
on the monolithic or noncomposite section
(kip-in.)
section modulus for the extreme fiber of
the composite section where tensile
stress is caused by externally applied
loads (in.3)
section modulus for the extreme fiber of
the monolithic or noncomposite section
where tensile stress is caused by externally
applied loads (in.3)
In Eq. 5.8.3.4.3-1, Mmax and Vi shall be determined
from the load combination causing maximum moment at
the section.
Vcw shall be determined as:
(
)
Vcw = 0.06 f c′ + 0.30 f pc bv dv + V p
(5.8.3.4.3-3)
where:
fpc =
(c) Load 3
compressive stress in concrete (after allowance
for all prestresss losses) at centroid of cross
section resisting externally applied loads or at
junction of web and flange when the centroid
lies within the flange (ksi). In a composite
member, fpc is the resultant compressive stress
at the centroid of the composite section, or at
junction of web and flange, due to both
Web-shear cracking begins from an interior point in
the web of the member before either flange in that
region cracks in flexure. In Figure C5.8.3.4.3-1, at
load 1, web-shear cracking developed in the web of the
member adjacent to the end support. Flexure-shear
cracking is initiated by flexural cracking. Flexural
cracking increases the shear stresses in the concrete
above the flexural crack. In Figure C5.8.3.4.3-1, flexural
cracking had developed in the central region of the beam
by load 2 and by load 3, the flexural cracks had become
inclined cracks as flexural cracking extended towards
the end support with increasing load.
For sections with shear reinforcement equal to or
greater than that required by Article 5.8.2.5, the shear
carried by the concrete may drop below Vc shortly after
inclined cracking, and the shear reinforcement may yield
locally. However, sections continue to resist increasing
shears until resistances provided by the concrete again
reach Vc. Thus, Vci and Vcw are measures of the
resistance that can be provided by the concrete at the
nominal shear resistance of the section and are not
directly equal to the shears at inclined cracking.
The angle θ of the inclined crack, and therefore of
the diagonal compressive stress, is less for a web-shear
crack than a flexure-shear crack. Consequently, for a
given section the value of Vs associated with web-shear
cracking is greater than that associated with flexureshear cracking.
Vci is the sum of the shear (ViMcr /Mmax) required to
cause flexural cracking at the given section plus the
increment of shear necessary to develop the flexural crack
into a shear crack, For a non-composite beam, the total
cross section resists all applied shears, dead and live, Ic
equals the moment of inertia of the gross section and Vd
equals the unfactored dead load shear acting on the
section. In this case Eq. 5.8.3.4.3-1 can be used directly.
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SECTION 5: CONCRETE STRUCTURES
5-75
prestresss and moments resisted by precast
member acting alone.
Vs shall be determined using Eq. 5.8.3.3-4 with cot θ
taken as follows:
where Vci < Vcw:
cot θ
=
1.0
where Vci > Vcw:
f pc
f ′ ≤ 1.8
c
cot θ = 1.0 + 3
(5.8.3.4.3-4)
For a composite beam, part of the dead load is
resisted by only part of the final section. Where the final
gross concrete section is achieved with only one
addition to the initial concrete section (two-stage
construction), Eq. 5.8.3.4.3-1 can be used directly. In
Eq. 5.8.3.4.3-2 appropriate section properties are used to
compute fd and in Eq. 5.8.3.4.3-1 the shear due to dead
load Vd and that due to other loads Vi are separated. Vd is
the total shear force due to unfactored dead loads acting
on the part of the section carrying the dead loads acting
prior to composite action plus the unfactored
superimposed dead load acting on the composite
member. The term Vi may be taken as (Vu – Vd) and Mmax
as Mu – Md where Vu and Mu are the factored shear and
moment at the given section due to the total factored
loads Md is the moment due to unfactored dead load at
the same section.
Where the final gross section is developed with more
than one concrete composite addition to the initial section
(multiple-stage construction), it is necessary to trace the
build up of the extreme fiber flexural stresses to compute
Mcr. For each stage in the life history of the member, the
increments in the extreme fiber flexural stress at the given
section due to the unfactored loads acting on that section
are calculated using the section properties existing at that
stage. Vd, Vi, and Mmax are calculated in the same manner
as for two-stage construction.
A somewhat lower modulus of rupture is used in
evaluating Mcre by Eq. 5.8.3.4.3-2 to account for the
effects of differential shrinkage between the slab and the
girder, and the effects of thermal gradients that can
occur over the depth of the girder.
5.8.3.5—Longitudinal Reinforcement 2013 Revision
At each section the tensile capacity of the
longitudinal reinforcement on the flexural tension side
of the member shall be proportioned to satisfy:
Aps f ps + As f y ≥
Mu
dv φ f
+ 0.5
Nu Vu
+ − Vp − 0.5Vs cot θ
φc φv
(5.8.3.5-1)
where:
Vs
=
shear resistance provided by the transverse
reinforcement at the section under
investigation as given by Eq. 5.8.3.3-4,
except Vs shall not be taken as greater than
Vu /φ (kip)
C5.8.3.5
2013 Revision
Shear causes tension in the longitudinal
reinforcement. For a given shear, this tension becomes
larger as θ becomes smaller and as Vc becomes larger.
The tension in the longitudinal reinforcement caused by
the shear force can be visualized from a free-body
diagram such as that shown in Figure C5.8.3.5-1.
Taking moments about Point 0 in Figure C5.8.3.5-1,
assuming that the aggregate interlock force on the crack,
which contributes to Vc, has a negligible moment about
Point 0, and neglecting the small difference in location
of Vu and Vp leads to the requirement for the tension
force in the longitudinal reinforcement caused by shear.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
θ
=
φfφvφc
=
angle of inclination of diagonal
compressive stresses used in determining
the nominal shear resistance of the section
under investigation as determined by
Article 5.8.3.4 (degrees); if the procedures
of Article 5.8.3.4.3 are used, cot θ is
defined therein
resistance
factors
taken
from
Article 5.5.4.2 as appropriate for moment,
shear and axial resistance
Figure C5.8.3.5-1—Forces Assumed in Resistance Model
Caused by Moment and Shear
The area of longitudinal reinforcement on the
flexural tension side of the member need not exceed the
area required to resist the maximum moment acting
alone. This provision applies where the reaction force or
the load introduces direct compression into the flexural
compression face of the member.
Eq. 5.8.3.5-1 shall be evaluated where simplysupported girders are made continuous for live loads.
Where longitudinal reinforcement is discontinuous,
Eq. 5.8.3.5-1 shall be re-evaluated.
At maximum moment locations, the shear force
changes sign, and hence the inclination of the diagonal
compressive stresses changes. At direct supports
including simply-supported girder ends and bent/pier
caps pinned to columns, and at loads applied directly to
the top or bottom face of the member, this change of
inclination is associated with a fan-shaped pattern of
compressive stresses radiating from the point load or the
direct support as shown in Figure C5.8.3.5-2. This
fanning of the diagonal stresses reduces the tension in
the longitudinal reinforcement caused by the shear; i.e.,
angle θ becomes steeper. The tension in the
reinforcement does not exceed that due to the maximum
moment alone. Hence, the longitudinal reinforcement
requirements can be met by extending the flexural
reinforcement for a distance of dvcotθ or as specified in
Article 5.11, whichever is greater.
Figure C5.8.3.5-2—Force Variation in Longitudinal
Reinforcement Near Maximum Moment Locations
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SECTION 5: CONCRETE STRUCTURES
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At the inside edge of the bearing area of simple end
supports to the section of critical shear, the longitudinal
reinforcement on the flexural tension side of the member
shall satisfy:
V
As f y + Aps f ps ≥ u − 0.5Vs − V p cot θ
φv
(5.8.3.5-2)
Eqs. 5.8.3.5-1 and 5.8.3.5-2 shall be taken to apply
to sections not subjected to torsion. Any lack of full
development shall be accounted for.
In determining the tensile force that the
reinforcement is expected to resist at the inside edge of
the bearing area, the values of Vu, Vs, Vp, and θ,
calculated for the section dv from the face of the support
may be used. In calculating the tensile resistance of the
longitudinal reinforcement, a linear variation of
resistance over the development length of
Article 5.11.2.1.1 or the bi-linear variation of resistance
over the transfer and development length of
Article 5.11.4.2 may be assumed.
5.8.3.6—Sections Subjected to Combined Shear
and Torsion
C5.8.3.6.1
5.8.3.6.1—Transverse Reinforcement
The transverse reinforcement shall not be less than
the sum of that required for shear, as specified in
Article 5.8.3.3, and for the concurrent torsion, as
specified in Articles 5.8.2.1 and 5.8.3.6.2.
The shear stresses due to torsion and shear will add
on one side of the section and offset on the other side.
The transverse reinforcement is designed for the side
where the effects are additive.
Usually the loading that causes the highest torsion
differs from the loading that causes the highest shear.
Although it is sometimes convenient to design for the
highest torsion combined with the highest shear, it is
only necessary to design for the highest shear and its
concurrent torsion, and the highest torsion and its
concurrent shear.
5.8.3.6.2—Torsional Resistance
The nominal torsional resistance shall be taken as:
Tn =
2 Ao At f y cot θ
(5.8.3.6.2-1)
s
where:
Ao =
At
=
θ
=
area enclosed by the shear flow path, including
any area of holes therein (in.2)
area of one leg of closed transverse torsion
reinforcement in solid members, or total area of
transverse torsion reinforcement in the exterior
web of cellular members (in.2)
angle of crack as determined in accordance
with the provisions of Article 5.8.3.4 with the
modifications to the expressions for v and Vu
herein (degrees)
5.8.3.6.3—Longitudinal Reinforcement
The provisions of Article 5.8.3.5 shall apply as
amended, herein, to include torsion.
The longitudinal reinforcement in solid sections
shall be proportioned to satisfy Eq. 5.8.3.6.3-1:
C5.8.3.6.3
To account for the fact that on one side of the
section the torsional and shear stresses oppose each
other, the equivalent tension used in the design equation
is taken as the square root of the sum of the squares of
the individually calculated tensions in the web.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Aps f ps + As f y ≥
M u 0.5 N u
+
+
φ dv
φ
2
V
0.45 ph Tu
cot θ u − V p − 0.5Vs +
φ
2 Ao φ
2
(5.8.3.6.3-1)
In box sections, longitudinal reinforcement for
torsion, in addition to that required for flexure, shall not
be less than:
A =
Tn ph
2 Ao f y
(5.8.3.6.3-2)
where:
ph =
perimeter of the centerline of the closed
transverse torsion reinforcement (in.)
5.8.4—Interface Shear Transfer—Shear Friction
5.8.4.1—General
2013 Revision
Interface shear transfer shall be considered across a
given plane at:
•
An existing or potential crack,
•
An interface between dissimilar materials,
•
An interface between two concretes cast at different
times, or
•
The interface between different elements of the
cross-section.
C5.8.4.1
Shear displacement along an interface plane may be
resisted by cohesion, aggregate interlock, and shearfriction developed by the force in the reinforcement
crossing the plane of the interface. Roughness of the
shear plane causes interface separation in a direction
perpendicular to the interface plane. This separation
induces tension in the reinforcement balanced by
compressive stresses on the interface surfaces.
Adequate shear transfer reinforcement must be
provided perpendicular to the vertical planes of
web/flange interfaces in box girders to transfer flange
longitudinal forces at the strength limit state. The
factored design force for the interface reinforcement is
calculated to account for the interface shear force, ΔF,
as shown in Figure C5.8.4.1-1, as well as any localized
shear effects due to the prestressing force anchorages at
the section.
Figure C5.8.4.1-1—Longitudinal Shear Transfer between
Flanges and Webs of Box Girder Bridges
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SECTION 5: CONCRETE STRUCTURES
5-79
Reinforcement for interface shear may consist of
single bars, multiple leg stirrups, or welded wire fabric.
All reinforcement present where interface shear
transfer is to be considered shall be fully developed on
both sides of the interface by embedment, hooks,
mechanical methods such as headed studs or welding to
develop the design yield stress.
Any reinforcement crossing the interface is subject
to the same strain as the designed interface
reinforcement. Insufficient anchorage of any
reinforcement crossing the interface could result in
localized fracture of the surrounding concrete.
When the required interface shear reinforcement in
girder/slab design exceeds the area required to satisfy
vertical (transverse) shear requirements, additional
reinforcement must be provided to satisfy the interface
shear requirements. The additional interface shear
reinforcement need only extend into the girder a
sufficient depth to develop the design yield stress of the
reinforcement rather than extending the full depth of the
girder as is required for vertical shear reinforcement.
The minimum area of interface shear reinforcement
specified in Article 5.8.4.4 shall be satisfied.
The factored interface shear resistance, Vri, shall be
taken as:
Vri = φVni
(5.8.4.1-1)
and the design shall satisfy:
Vri ≥ Vui
(5.8.4.1-2)
where:
Vni =
Vui =
φ
=
nominal interface shear resistance (kip)
factored interface shear force due to total load
based on the applicable strength and extreme
event load combinations in Table 3.4.1-1 (kip)
resistance factor for shear specified in
Article 5.5.4.2.1. In cases where different
weight concretes exist on the two sides of an
interface, the lower of the two values of φ shall
be used.
The nominal shear resistance of the interface plane
shall be taken as:
Vni = cAcv + μ (Avf fy + Pc)
(5.8.4.1-3)
The nominal shear resistance, Vni, used in the design
shall not be greater than the lesser of:
Vni ≤ K1 f ƍc Acv, or
(5.8.4.1-4)
Vni ≤ K2 Acv
(5.8.4.1-5)
in which:
Acv = bvi Lvi
(5.8.4.1-6)
Total load shall include all noncomposite and
composite loads.
For the extreme limit state event φ may be taken
as 1.0.
A pure shear friction model assumes interface shear
resistance is directly proportional to the net normal
clamping force (Avf fy + Pc), through a friction coefficient
(μ). Eq. 5.8.4.1-3 is a modified shear-friction model
accounting for a contribution, evident in the
experimental data, from cohesion and/or aggregate
interlock depending on the nature of the interface under
consideration given by the first term. For simplicity, the
term “cohesion factor” is used throughout the body of
this Article to capture the effects of cohesion and/or
aggregate interlock such that Eq. 5.8.4.1-3 is analogous
to the vertical shear resistance expression of Vc + Vs.
Eq. 5.8.4.1-4 limits Vni to prevent crushing or
shearing of aggregate along the shear plane.
Eqs. 5.8.4.1-3 and 5.8.4.1-4 are sufficient, with
an appropriate value for K1, to establish a lower bound
for the available experimental data; however,
Eq. 5.8.4.1-5 is necessitated by the sparseness of
available experimental data beyond the limiting K2
values provided in Article 5.8.4.3.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
where:
Acv =
area of concrete considered to be engaged in
interface shear transfer (in.2)
area of interface shear reinforcement crossing
the shear plane within the area Acv (in.2)
interface width considered to be engaged in
shear transfer (in.)
Avf =
bvi =
Lvi =
c
ȝ
fy
interface length considered to be engaged in
shear transfer (in.)
cohesion factor specified in Article 5.8.4.3 (ksi)
friction factor specified in Article 5.8.4.3 (dim.)
yield stress of reinforcement but design value
not to exceed 60 (ksi)
=
=
=
Pc =
permanent net compressive force normal to the
shear plane; if force is tensile, Pc = 0.0 (kip)
f ƍc =
specified 28-day compressive strength of the
weaker concrete on either side of the interface
(ksi)
fraction of concrete strength available to resist
interface shear, as specified in Article 5.8.4.3.
limiting interface shear resistance specified in
Article 5.8.4.3 (ksi)
K1 =
K2 =
5.8.4.2—Computation of the Factored Interface
Shear Force, Vui, for Girder/Slab Bridges
Based on consideration of a free body diagram and
utilizing the conservative envelope value of Vu1, the
factored interface shear stress for a concrete girder/slab
bridge may be determined as:
Vui =
Vu1
bvi d v
where:
(5.8.4.2-1)
The interface shear strength Eqs. 5.8.4.1-3,
5.8.4.1-4, and 5.8.4.1-5 are based on experimental data
for normal weight, nonmonolithic concrete strengths
ranging from 2.5 ksi to 16.5 ksi; normal weight,
monolithic concrete strengths from 3.5 ksi to 18.0 ksi;
sand-lightweight concrete strengths from 2.0 ksi to 6.0
ksi; and all-lightweight concrete strengths from 4.0 ksi
to 5.2 ksi.
Composite section design utilizing full-depth
precast deck panels is not addressed by these provisions.
Design specifications for such systems should be
established by, or coordinated with, the Owner.
Avf used in Eq. 5.8.4.1-3 is the interface shear
reinforcement within the interface area Acv. For a
girder/slab interface, the area of the interface shear
reinforcement per foot of girder length is calculated by
replacing Acv in Eq. 5.8.4.1-3 with 12bvi and Pc
corresponding to the same one foot of girder length.
In consideration of the use of stay-in-place deck
panels, or any other interface details, the Designer shall
determine the width of interface, bvi, effectively acting to
resist interface shear.
The interface reinforcement is assumed to be
stressed to its design yield stress, fy. However, fy used in
determining the interface shear resistance is limited to
60 ksi because interface shear resistance computed using
higher values have overestimated the interface shear
resistance experimentally determined in a limited
number of tests of pre-cracked specimens.
It is conservative to neglect Pc if it is compressive,
however, if included, the value of Pc shall be computed
as the force acting over the area, Acv. If Pc is tensile,
additional reinforcement is required to resist the net
tensile force as specified in Article 5.8.4.2.
C5.8.4.2
The following illustrates a free body diagram
approach to computation of interface shear in a
girder/slab bridge. In reinforced concrete, or prestressed
concrete, girder bridges, with a cast-in-place slab,
horizontal shear forces develop along the interface
between the girders and the slab. The classical strength
of materials approach, which is based on elastic
behavior of the section, has been used successfully in
the past to determine the design interface shear force. As
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SECTION 5: CONCRETE STRUCTURES
dv
=
5-81
the distance between the centroid of the tension
steel and the mid-thickness of the slab to
compute a factored interface shear stress
The factored interface shear force in kips/ft for a
concrete girder/slab bridge may be determined as:
Vui = vui Acv = vui 12bvi
(5.8.4.2-2)
If the net force, Pc, across the interface shear plane
is tensile, additional reinforcement, Avpc, shall be
provided as:
Avpc =
Pc
φf y
(5.8.4.2-3)
For beams and girders, the longitudinal spacing of
the rows of interface shear transfer reinforcing bars shall
not exceed 24.0 in.
an alternative to the classical elastic strength of
materials approach, a reasonable approximation of the
factored interface shear force at the strength or extreme
event limit state for either elastic or inelastic behavior
and cracked or uncracked sections, can be derived with
the defined notation and the free body diagram shown in
Figure C5.8.4.2-1 as follows:
Mu2 =
V1 =
maximum factored moment at section 2
the factored vertical shear at section 1 concurrent
with Mu2
the factored moment at section 1 concurrent
with Mu2
unit length segment of girder
compression force above the shear plane
associated with M1
compression force above the shear plane
associated with Mu2
M1 =
Δl =
C1 =
Cu2 =
Mu2 = M1 + V1 Δl
Cu 2 =
Cu 2 =
C1 =
Mu2
(C5.8.4.2-2)
dv
M1
dv
+
(C5.8.4.2-1)
V1Δ1
dv
M1
dv
(C5.8.4.2-3)
(C5.8.4.2-4)
Figure C5.8.4.2-1—Free Body Diagrams
Vh = Cu2 – C1
Vh =
V1Δ1
dv
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(C5.8.4.2-5)
(C5.8.4.2-6)
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Such that for a unit length segment:
Vhi =
V1
(C5.8.4.2-7)
dv
where:
Vhi =
factored interface shear force per unit length
(kips/length)
The variation of V1 over the length of any girder
segment reflects the shear flow embodied in the classical
strength of materials approach. For simplicity of design,
V1 can be conservatively taken as Vu1 (since Vu1, the
maximum factored vertical shear at section 1, is not
likely to act concurrently with the factored moment at
section 2); and further, the depth, dv, can be taken as the
distance between the centroid of the tension steel and the
mid-thickness of the slab to compute a factored interface
shear stress.
For design purposes, the computed factored
interface shear stress of Eq. 5.8.4.2-1 is converted to a
resultant interface shear force computed with
Eq. 5.8.4.2-1 acting over an area, Acv, within which the
computed area of reinforcement, Avf, shall be located.
The resulting area of reinforcement, Avf, then defines the
area of interface reinforcement required per foot of
girder for direct comparison with vertical shear
reinforcement requirements.
5.8.4.3—Cohesion and Friction Factors
The following values shall be taken for cohesion, c,
and friction factor, ȝ:
•
For a cast-in-place concrete slab on clean concrete
girder surfaces, free of laitance with surface
roughened to an amplitude of 0.25 in.
c
ȝ
K1
K2
•
=
=
=
=
=
0.28 ksi
1.0
0.3
1.8 ksi for normal-weight concrete
1.3 ksi for lightweight concrete
For normal-weight concrete placed monolithically:
c
ȝ
K1
K2
=
=
=
=
0.40 ksi
1.4
0.25
1.5 ksi
C5.8.4.3
The values presented provide a lower bound of the
substantial body of experimental data available in the
literature (Loov and Patnaik, 1994; Patnaik, 1999;
Mattock, 2001; Slapkus and Kahn, 2004). Furthermore,
the inherent redundancy of girder/slab bridges
distinguishes this system from other structural
interfaces.
The values presented apply strictly to monolithic
concrete. These values are not applicable for situations
where a crack may be anticipated to occur at a Service
Limit State.
The factors presented provide a lower bound of the
experimental data available in the literature (Hofbeck,
Ibrahim, and Mattock, 1969; Mattock, Li, and Wang,
1976; Mitchell and Kahn, 2001).
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SECTION 5: CONCRETE STRUCTURES
•
For lightweight concrete placed monolithically, or
nonmonolithically, against a clean concrete surface,
free of laitance with surface intentionally roughened
to an amplitude of 0.25 in.:
c
ȝ
K1
K2
•
0.24 ksi
1.0
0.25
1.0 ksi
=
=
=
=
0.24 ksi
1.0
0.25
1.5 ksi
Available experimental data demonstrates that only
one modification factor is necessary, when coupled with
the resistance factors of Article 5.5.4.2, to accommodate
both all-lightweight and sand-lightweight concrete. Note
this deviates from earlier specifications that
distinguished between all-lightweight and sandlightweight concrete.
Due to the absence of existing data, the prescribed
cohesion and friction factors for nonmonolithic
lightweight concrete are accepted as conservative for
application to monolithic lightweight concrete.
Tighter constraints have been adopted for
roughened interfaces, other than cast-in-place slabs on
roughened girders, even though available test data does
not indicate more severe restrictions are necessary. This
is to account for variability in the geometry, loading and
lack of redundancy at other interfaces.
For concrete placed against a clean concrete
surface, free of laitance, but not intentionally
roughened:
c
ȝ
K1
K2
•
=
=
=
=
For normal-weight concrete placed against a clean
concrete surface, free of laitance, with surface
intentionally roughened to an amplitude of 0.25 in.:
c
ȝ
K1
K2
•
5-83
=
=
=
=
0.075 ksi
0.6
0.2
0.8 ksi
For concrete anchored to as-rolled structural steel
by headed studs or by reinforcing bars where all
steel in contact with concrete is clean and free of
paint:
c
ȝ
K1
K2
=
=
=
=
0.025 ksi
0.7
0.2
0.8 ksi
For brackets, corbels, and ledges, the cohesion
factor, c, shall be taken as 0.0.
5.8.4.4—Minimum Area of Interface Shear
Reinforcement
Except as provided herein, the cross-sectional area
of the interface shear reinforcement, Avf, crossing the
interface area, Acv, shall satisfy:
Avf ≥
0.05 Acv
fy
Since the effectiveness of cohesion and aggregate
interlock along a vertical crack interface is unreliable the
cohesion component in Eq. 5.8.4.1-3 is set to 0.0 for
brackets, corbels, and ledges.
C5.8.4.4
For a girder/slab interface, the minimum area of
interface shear reinforcement per foot of girder length is
calculated by replacing Acv in Eq. 5.8.4.4-1 with 12bvi.
(5.8.4.4-1)
For a cast-in-place concrete slab on clean concrete
girder surfaces free of laitance, the following provisions
shall apply:
Previous editions of these specifications and of the
AASHTO Standard Specifications have required a
minimum area of reinforcement based on the full
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•
•
The minimum interface shear reinforcement,
Avf, need not exceed the lesser of the amount
determined using Eq. 5.8.4.4-1 and the amount
needed to resist 1.33Vui /φ as determined using
Eq. 5.8.4.1-3.
The minimum reinforcement provisions specified
herein shall be waived for girder/slab interfaces
with surface roughened to an amplitude of 0.25 in.
where the factored interface shear stress, vui of
Eq. 5.8.4.2-1, is less than 0.210 ksi, and all vertical
(transverse) shear reinforcement required by the
provisions of Article 5.8.2.5 is extended across the
interface and adequately anchored in the slab.
interface area; similar to Eq. 5.8.4.4-1, irrespective of
the need to mobilize the strength of the full interface
area to resist the applied factored interface shear. In
2006, the additional minimum area provisions,
applicable only to girder/slab interfaces, were
introduced. The intent of these provisions was to
eliminate the need for additional interface shear
reinforcement due simply to a beam with a wider top
flange being utilized in place of a narrower flanged
beam.
The additional provision establishes a rational upper
bound for the area of interface shear reinforcement
required based on the interface shear demand rather than
the interface area as stipulated by Eq. 5.8.4.4-1. This
treatment is analogous to minimum reinforcement
provisions for flexural capacity where a minimum
additional overstrength factor of 1.33 is required beyond
the factored demand.
With respect to a girder/slab interface, the intent is
that the portion of the reinforcement required to resist
vertical shear which is extended into the slab also serves
as interface shear reinforcement.
5.8.5—Principal Stresses in Webs of Segmental
Concrete Bridges
C5.8.5
The provisions specified herein shall apply to all
types of segmental bridges with internal and/or external
tendons.
The principal tensile stress resulting from the longterm residual axial stress and maximum shear and/or
maximum shear combined with shear from torsion stress
at the neutral axis of the critical web shall not exceed the
tensile stress limit of Table 5.9.4.2.2-1 at the Service III
limit state of Article 3.4.1 at all stages during the life of
the structure, excluding those during construction. When
investigating principal stresses during construction, the
tensile stress limits of Table 5.14.2.3.3-1 shall apply.
The principal stress shall be determined using
classical beam theory and the principles of Mohr’s
Circle. The width of the web for these calculations shall
be measured perpendicular to the plane of the web.
Compressive stress due to vertical tendons provided
in the web shall be considered in the calculation of the
principal stress. The vertical force component of draped
longitudinal tendons shall be considered as a reduction
in the shear force due to the applied loads.
Local tensions produced in webs resulting from
anchorage of tendons as discussed in Article 5.10.9.2
shall be included in the principal tension check.
Local transverse flexural stress due to out-of-plane
flexure of the web itself at the critical section may be
neglected in computing the principal tension in webs.
This principal stress check is introduced to verify
the adequacy of webs of segmental concrete bridges for
longitudinal shear and torsion.
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SECTION 5: CONCRETE STRUCTURES
5-85
5.8.6—Shear and Torsion for Segmental Box Girder
Bridges
5.8.6.1—General
C5.8.6.1
Where it is reasonable to assume that plane sections
remain plane after loading, the provisions presented
herein shall be used for the design of segmental posttensioned concrete box girder bridges for shear and
torsion in lieu of the provisions of Article 5.8.3.
The applicable provisions of Articles 5.8.1, 5.8.2,
5.8.4, and 5.8.5 may apply, as modified by the
provisions herein.
Discontinuity regions (where the plane sections
assumption of flexural theory is not applicable) shall be
designed using the provisions of Article 5.8.6.2 and the
strut-and-tie model approach of Article 5.6.3. The
provisions of Article 5.13.2 shall apply to special
discontinuity regions such as deep beams, brackets and
corbels, as appropriate.
The effects of any openings or ducts in members
shall be considered. In determining the effective web or
flange thickness, be, the diameters of ungrouted ducts or
one-half the diameters of grouted ducts shall be
subtracted from the web or flange thickness at the
location of these ducts.
The values of √f 'c used in any part of Article 5.8.6
shall not exceed 3.16.
The design yield strength of transverse shear or
torsion reinforcement shall be in accordance with
Article 5.8.2.8.
5.8.6.2—Loading
2013 Revision
Design for shear and torsion shall be performed at
the strength limit state load combinations as defined in
Article 3.4.1.
The shear component of the primary effective
longitudinal prestress force acting in the direction of the
applied shear being examined, Vp, shall be added to the
load effect, with a load factor of 1.0.
The secondary shear effects from prestressing shall
be included in the PS load defined in Article 3.3.2.
The vertical component of inclined tendons shall
only be considered to reduce the applied shear on the
webs for tendons which are anchored or fully developed
by anchorages, deviators, or internal ducts located in the
top or bottom 1/3 of the webs.
The effects of factored torsional moments, Tu, shall
be considered in the design when their magnitude
exceeds the value specified in Article 5.8.6.3.
For types of construction other than segmental box
girders, the provisions of Article 5.8.3 may be applied in
lieu of the provisions of Article 5.8.6.
Discontinuity regions where the plane sections
assumption of flexural theory is not applicable include
regions adjacent to abrupt changes in cross-sections,
openings, dapped ends, regions where large
concentrated loads, reactions, or post-tensioning forces
are applied or deviated, diaphragms, deep beams,
corbels or joints.
The effects of using concrete with √f ′c > 3.16 on the
allowable stress limits is not well known.
C5.8.6.2
Design of prestressed concrete segmental bridges
for shear and torsion is based on the strength limit state
conditions because little information is available
concerning actual shear stress distributions at the service
limit state.
This load effect should only be added to the box
girder analysis and not transferred into the substructure.
Some designers prefer to add this primary prestress
force shear component to the resistance side of the
equation.
For members subjected to combined shear and
torsion, the torsional moments produce shear forces in
different elements of the structure that, depending on the
direction of torsion, may add to or subtract from the
shear force in the element due to vertical shear. Where it
is required to consider the effects of torsional moments,
the shear forces from torsion need to be added to those
from the vertical shear when determining the design
shear force acting on a specific element. The possibility
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
In a statically indeterminate structure where
significant reduction of torsional moment in a member
can occur due to redistribution of internal forces upon
cracking, the applied factored torsion moment at a
section, Tu, may be reduced to φTcr, provided that
moments and forces in the member and in adjoining
members are adjusted to account for the redistribution.
of the torsional moment reversing direction should be
investigated.
where:
Tu =
Tcr =
φ
=
factored torsional moment (kip-in.)
torsional cracking moment calculated using
Eq. 5.8.6.3-2 (kip-in.)
resistance factor for shear specified in
Article 5.5.4.2
In lieu of a more refined analysis, the torsional
loading from a slab may be assumed as linearly
distributed along the member.
The effects of axial tension due to creep, shrinkage,
and thermal effects in restrained members shall be
considered wherever applicable.
The component of inclined flexural compression or
tension, in the direction of the applied shear, in variable
depth members shall be considered when determining
the design factored shear force.
5.8.6.3—Regions Requiring Consideration of
Torsional Effects
For normal weight concrete, torsional effects shall
be investigated where:
Tu > 1/3 φTcr
(5.8.6.3-1)
in which:
T c r = 0 .0 6 3 2 K
K = 1+
f pc
0.0632 f
'
c
f c′ 2 A o b e
(5.8.6.3-2)
≤ 2.0
(5.8.6.3-3)
where:
Tu =
Tcr =
K =
Ao =
factored torsional moment (kip-in.)
torsional cracking moment (kip-in.)
stress variable K shall not be taken greater than
1.0 for any section where the stress in the
extreme tension fiber, calculated on the basis of
gross section properties, due to factored load
and effective prestress force after losses
exceeds 0.19√f ′c in tension.
area enclosed by the shear flow path of a closed
box section, including any holes therein (in.2)
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SECTION 5: CONCRETE STRUCTURES
be
=
pc
=
effective width of the shear flow path, but not
exceeding the minimum thickness of the webs
or flanges comprising the closed box section
(in.). be shall be adjusted to account for the
presence of ducts as specified in Article 5.8.6.1.
the length of the outside perimeter of the
concrete section (in.)
unfactored compressive stress in concrete after
prestress losses have occurred either at the
centroid of the cross-section resisting transient
loads or at the junction of the web and flange
where the centroid lies in the flange (ksi)
resistance factor for shear specified in
Article 5.5.4.2
fpc =
φ
5-87
=
In lieu of a more refined analysis, be may be taken
as Acp /Pe, where Acp is the area enclosed by the outside
perimeter of the concrete cross-section and Pc is the
outside perimeter of the concrete cross-section.
When calculating K for a section subject to factored
axial force, Nu, fpc shall be replaced with fpc – Nu/Ag. Nu
shall be taken as a positive value when the axial force is
tensile and negative when it is compressive.
5.8.6.4—Torsional Reinforcement
C5.8.6.4
Where consideration of torsional effects is required
by Article 5.8.6.3, torsion reinforcement shall be
provided, as specified herein. This reinforcement shall
be in addition to the reinforcement required to resist the
factored shear, as specified in Article 5.8.6.5, flexure
and axial forces that may act concurrently with the
torsion.
The longitudinal and transverse reinforcement
required for torsion shall satisfy:
Tu ≤ φTn
(5.8.6.4-1)
The nominal torsional resistance from transverse
reinforcement shall be based on a truss model with
45-degree diagonals and shall be computed as:
Tn =
2 Ao Av f y
s
(5.8.6.4-2)
The minimum additional longitudinal reinforcement
for torsion, Aℓ , shall satisfy:
A ≥
Tu ph
2 φ Ao f y
(5.8.6.4-3)
where:
Av =
Aℓ =
In determining the required amount of longitudinal
reinforcement, the beneficial effect of longitudinal
prestressing is taken into account by considering it
equivalent to an area of reinforcing steel with a yield
force equal to the effective prestressing force.
area of transverse shear reinforcement (in.2)
total area of longitudinal torsion reinforcement
in the exterior web of the box girder (in.2)
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Tu =
ph =
Ao =
fy
=
φ
=
applied factored torsional moment (kip-in.)
perimeter of the polygon defined by the
centroids of the longitudinal chords of the
space truss resisting torsion. ph may be taken as
the perimeter of the centerline of the outermost
closed stirrups (in.)
area enclosed by shear flow path, including
area of holes, if any (in.2)
yield strength of additional longitudinal
reinforcement (ksi)
resistance factor for shear specified in
Article 5.5.4.2
Aℓ shall be distributed around the perimeter of the
closed stirrups in accordance with Article 5.8.6.6.
Subject to the minimum reinforcement requirements
of Article 5.8.6.6, the area of additional longitudinal
torsion reinforcement in the flexural compression zone
may be reduced by an amount equal to:
Mu
(0.9d e f y )
(5.8.6.4-4)
where:
Mu =
de
=
fy
=
the factored moment acting at that section
concurrent with Tu (kip-in.)
effective depth from extreme compression
fiber to the centroid of the tensile force in the
tensile reinforcement (in.)
specified minimum yield strength of
reinforcing bars (ksi)
5.8.6.5—Nominal Shear Resistance
C5.8.6.5
In lieu of the provisions of Article 5.8.3, the
provisions herein shall be used to determine the nominal
shear resistance of post-tensioned concrete box girders
in regions where it is reasonable to assume that plane
sections remain plane after loading.
Transverse reinforcement shall be provided when
Vu > 0.5φVc , where Vc is computed by Eq. 5.8.6.5-4.
The nominal shear resistance, Vn, shall be
determined as the lesser of:
Vn = Vc + Vs
(5.8.6.5-1)
Vn = 0.379 f c′ bv dv
(5.8.6.5-2)
The expression for Vc has been checked against a
wide range of test data and has been found to be a
conservative expression.
and, where the effects of torsion are required to be
considered by Article 5.8.6.2, the cross-sectional
dimensions shall be such that:
Vc = 0.0632 K f c′ bv d v
(5.8.6.5-3)
in which:
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SECTION 5: CONCRETE STRUCTURES
Vs =
Av f y d v
s
Vu Tu
+
≤ 0.474 f c′
bv d v 2 Ao be
5-89
(5.8.6.5-4)
Eq. 5.8.6.5-4 is based on an assumed 45-degree
truss model.
(5.8.6.5-5)
Eq. 5.8.6.4-5 is only used to establish appropriate
concrete section dimensions.
where:
bv
=
dv
=
s
K
=
=
Av =
Vu =
Tu =
Ao =
be
=
φ
=
effective web width taken as the minimum web
width within the depth dv as determined in
Article 5.8.6.1 (in.)
0.8h or the distance from the extreme
compression fiber to the centroid of the
prestressing reinforcement, whichever is
greater (in.)
spacing of stirrups (in.)
stress variable computed in accordance with
Article 5.8.6.3.
area of shear reinforcement within a distance s
(in.2)
factored design shear including any normal
component from the primary prestressing force
(kip)
applied factored torsional moment (kip-in.)
area enclosed by shear flow path, including
area of holes, if any (in.2)
the effective thickness of the shear flow path of
the elements making up the space truss model
resisting torsion calculated in accordance with
Article 5.8.6.3 (in.)
resistance factor for shear specified in
Article 5.5.4.2
The factored nominal shear resistance, φVn, shall be
greater than or equal to Vu.
The applied factored shear, Vu, in regions near
supports may be computed at a distance h/2 from the
support when the support reaction, in the direction of the
applied shear, introduces compression into the support
region of the member and no concentrated load occurs
within a distance, h, from the face of the support.
5.8.6.6—Reinforcement Details
In addition to the provisions herein, the provisions
of Article 5.10 and 5.11 shall also apply to segmental
post-tensioned box girders, as applicable.
At any place on the cross-section where the axial
tension due to torsion and bending exceeds the axial
compression due to prestressing and bending, either
supplementary tendons to counter the tension or local
longitudinal reinforcement, which is continuous across
the joints between segments, shall be required.
Where supplementary tendons are added, they shall
be located to provide compression around the perimeter
of the closed box section.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Where local longitudinal reinforcement is added,
the bars shall be distributed around the perimeter formed
by the closed stirrups. Perimeter bar spacing shall not
exceed 18.0 in. At least one longitudinal bar shall be
placed in each corner of the stirrups. The minimum
diameter of the corner bars shall be 1/24 of the stirrup
spacing but no less than that of a #5 bar.
The spacing of the transverse reinforcement shall
not exceed the maximum permitted spacing, smax,
determined as:
•
If vu < 0.19√f ′c, then:
smax = 0.8d ≤ 36.0 in.
•
(5.8.6.6-1)
If vu ≥ 0.19 √f ′c, then:
smax = 0.4d ≤ 18.0 in.
(5.8.6.6-2)
where:
vu
=
dv
=
the shear stress calculated in accordance with
Eq. 5.8.6.5-5 (ksi)
effective shear depth as defined in
Article 5.8.6.5 (in.)
Transverse reinforcement for shear and torsion shall
be provided for a distance at least h/2 beyond the point
they are theoretically required.
Interface shear transfer reinforcement shall be
provided as specified in Article 5.8.4.
5.9—PRESTRESSING
5.9.1—General Design Considerations
5.9.1.1—General
C5.9.1.1
The provisions herein specified shall apply to
structural concrete members reinforced with any
combination of prestressing tendons and conventional
reinforcing bars acting together to resist common force
effects. Prestressed structural components shall be
designed for both initial and final prestressing forces.
They shall satisfy the requirements at service, fatigue,
strength, and extreme event limit states, as specified in
Article 5.5, and in accordance with the assumptions
provided in Articles 5.6, 5.7, and 5.8.
Unstressed prestressing tendons or reinforcing bars
may be used in combination with stressed tendons,
provided it is shown that performance of the structure
satisfies all limit states and the requirements of
Articles 5.4 and 5.6.
Compressive stress limits, specified in Article 5.9.4,
shall be used with any applicable service load
combination in Table 3.4.1-1, except Service Load
Combination III, which shall not apply to the
investigation of compression.
Tensile stress limits, specified in Article 5.9.4, shall
be used with any applicable service load combination in
The background material in this Article is based on
previous editions of the Standard Specifications and on
ACI 343, ACI 318, and the Ontario Highway Bridge
Design Code.
Prestressing tendons of high-strength steel bars or
strands are generally used but other materials satisfying
desired strength, stiffness, and ductility requirements
could also be used, provided that they meet the intent of
Article 5.4.1.
A unified theory of concrete structures recognizes
conventional reinforced concrete and fully prestressed
concrete as limiting cases encompassing levels of
precompression ranging from none to that necessary to
satisfy the Service III limit state specified in Table
5.9.4.2.2-1. Prior to 2011, these Specifications
identified intermediate cases between these two
extremes as partially prestressed concrete including:
•
A concrete member designed with a combination of
prestressed and nonprestressed reinforcement that
act together to resist common force effects at the
strength limit state and
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SECTION 5: CONCRETE STRUCTURES
Table 3.4.1-1. Service Load Combination III shall apply
when investigating tension under live load.
5-91
•
A prestressed concrete member designed to crack in
tension under the combination of effective prestress
and full service load at the Service III limit state
while satisfying the requirements for the fatigue
limit states.
5.9.1.2—Specified Concrete Strengths
The specified strengths, f ′c and f ′ci, shall be
identified in the contract documents for each
component. Stress limits relating to specified strengths
shall be as specified in Article 5.9.4.
Concrete strength at transfer shall be adequate for
the requirements of the anchorages or for transfer
through bond as well as for camber or deflection
requirements.
5.9.1.3—Buckling
Buckling of a member between points where
concrete and tendons are in contact, buckling during
handling and erection, and buckling of thin webs and
flanges shall be investigated.
5.9.1.4—Section Properties
For section properties prior to bonding of posttensioning tendons, effects of loss of area due to open
ducts shall be considered.
For both pretensioned or post-tensioned members
after bonding of tendons, section properties may be
based on either the gross or transformed section.
C5.9.1.4
Bonding means that the grout in the duct has
attained its specified strength.
5.9.1.5—Crack Control
Where cracking is permitted under service loads,
crack width, fatigue of reinforcement, and corrosion
considerations shall be investigated in accordance with
the provisions of Articles 5.5, 5.6, and 5.7.
5.9.1.6—Tendons with Angle Points or Curves
The provisions of Article 5.4.6 for the curvature of
ducts shall apply.
The provisions of Article 5.10.4 shall apply to the
investigation of stress concentrations due to changes in
the direction of prestressing tendons.
For tendons in draped ducts that are not nominally
straight, consideration shall be given to the difference
between the center of gravity of the tendon and the
center of gravity of the duct when determining
eccentricity.
The provisions of Article 5.8.1.5 for the webs of
curved post-tensioned box girder bridges shall apply.
C5.9.1.6
Vertically draped strand tendons should be assumed
to be at the bottom of the duct in negative moment areas
and at the top of the duct in positive moment areas. The
location of the tendon center of gravity, with respect to
the centerline of the duct, is shown for negative moment
in Figure C5.9.1.6-1.
Figure C5.9.1.6-1—Location of Tendon in Duct
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
5.9.2—Stresses Due to Imposed Deformation
C5.9.2
The effects on adjoining elements of the structure of
elastic and inelastic deformations due to prestressing
shall be investigated. The restraining forces produced in
the adjoining structural elements may be reduced due to
the effects of creep.
In monolithic frames, force effects in columns and
piers resulting from prestressing the superstructure may
be based on the initial elastic shortening.
For conventional monolithic frames, any increase in
column moments due to long-term creep shortening of
the prestressed superstructure is considered to be offset
by the concurrent relaxation of deformation moments in
the columns due to creep in the column concrete.
The reduction of restraining forces in other
members of a structure that are caused by the prestress
in a member may be taken as:
Additional information is contained in Leonhardt
(1964).
•
For suddenly imposed deformations
(
F′ = F 1− e
•
−ψ ( t , ti )
) , or
(5.9.2-1)
For slowly imposed deformations
(
)
F ′ = F 1 − e −ψ (t ,ti ) / ψ ( t , ti )
(5.9.2-2)
where:
F
=
F′
=
Ψ(t, ti) =
e
=
force effect determined using the modulus
of elasticity of the concrete at the time
loading is applied (kip)
reduced force effect (kip)
creep coefficient at time t for loading
applied at time ti as specified in
Article 5.4.2.3.2
base of Napierian logarithms
5.9.3—Stress Limitations for Prestressing Tendons
C5.9.3
The tendon stress due to prestress or at the service
limit state shall not exceed the values:
For post-tensioning, the short-term allowable of
0.90fpy may be allowed for short periods of time prior to
seating to offset seating and friction losses, provided
that the other values in Table 5.9.3-1 are not exceeded.
•
Specified in Table 5.9.3-1, or
•
Recommended by the manufacturer of the tendons
or anchorages.
The tendon stress at the strength and extreme event
limit states shall not exceed the tensile strength limit
specified in Table 5.4.4.1-1.
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2012
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SECTION 5: CONCRETE STRUCTURES
5-93
Table 5.9.3-1—Stress Limits for Prestressing Tendons
Condition
Immediately prior to transfer (fpbt)
At service limit state after all losses (fpe)
Prior to seating—short-term fpbt may be
allowed
At anchorages and couplers immediately
after anchor set
Elsewhere along length of member away
from anchorages and couplers immediately
after anchor set
At service limit state after losses (fpe)
Tendon Type
Stress-Relieved Strand and
Low
Plain
Relaxation
High-Strength Bars
Strand
Pretensioning
0.70 fpu
0.75 fpu
0.80 fpy
0.80 fpy
Post-Tensioning
0.90 fpy
Deformed HighStrength Bars
—
0.80 fpy
0.90 fpy
0.90 fpy
0.70 fpu
0.70 fpu
0.70 fpu
0.70 fpu
0.74 fpu
0.70 fpu
0.80 fpy
0.80 fpy
0.80 fpy
5.9.4—Stress Limits for Concrete
5.9.4.1—For Temporary Stresses before
Losses—Fully Prestressed Components
5.9.4.1.1—Compression Stresses
The compressive stress limit for pretensioned and
post-tensioned concrete components, including
segmentally constructed bridges, shall be 0.60 f ′ci
(ksi).
5.9.4.1.2—Tension Stresses
The limits in Table 5.9.4.1.2-1 shall apply for
tensile stresses.
C5.9.4.1.2
Where bonded reinforcement is provided to allow
use of the increased tensile limiting stress in areas with
bonded reinforcement, the tensile force must be
computed. The first step in computing the tensile force,
T, is to determine the depth of the tensile zone using the
extreme fiber stresses at the location being considered,
fci top and fci bot. An area is then defined over which the
average tensile stress is assumed to act. The tensile force
is computed as the product of the average tensile stress
and the computed area, as illustrated below. The
required area of reinforcement, As, is computed by
dividing the tensile force by the permitted stress in the
reinforcement.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
T=
fci top
As =
2
btop x
T
fs
where fs = 0.5 fy ≤ 30 ksi
Figure C5.9.4.1.2-1—Calculation of Tensile Force and
Required Area of Reinforcement
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SECTION 5: CONCRETE STRUCTURES
5-95
Table 5.9.4.1.2-1—Temporary Tensile Stress Limits in Prestressed Concrete before Losses, Fully Prestressed Components
Bridge Type
Other Than
Segmentally
Constructed Bridges
Segmentally
Constructed Bridges
Location
tensile
zone
without
bonded
Stress Limit
N/A
•
In precompressed
reinforcement
•
In areas other than the precompressed tensile zone and
without bonded reinforcement
0.0948√f ′ci ≤ 0.2 (ksi)
•
In areas with bonded reinforcement (reinforcing bars or
prestressing steel) sufficient to resist the tensile force in the
concrete computed assuming an uncracked section, where
reinforcement is proportioned using a stress of 0.5 fy, not to
exceed 30 ksi.
0.24√f ′ci (ksi)
•
For handling stresses in prestressed piles
0.158√ f ′ci (ksi)
Longitudinal Stresses through Joints in the Precompressed
Tensile Zone
•
Joints with minimum bonded auxiliary reinforcement
through the joints, which is sufficient to carry the calculated
tensile force at a stress of 0.5 fy; with internal tendons or
external tendons
0.0948√f ′ci maximum
tension (ksi)
•
Joints without the minimum bonded auxiliary reinforcement
through the joints
No tension
Transverse Stresses through Joints
•
For any type of joint
0.0948√f ′ci (ksi)
Stresses in Other Areas
•
For areas without bonded nonprestressed reinforcement
•
In areas with bonded reinforcement (reinforcing bars or
prestressing steel) sufficient to resist the tensile force in the
concrete computed assuming an uncracked section, where
reinforcement is proportioned using a stress of 0.5 fy, not to
exceed 30 ksi.
No tension
0.19√f ′ci (ksi)
Principal Tensile Stress at Neutral Axis in Web
•
All types of segmental concrete bridges with internal and/or
external tendons, unless the Owner imposes other criteria
for critical structures
0.110√f ′ci (ksi)
5.9.4.2—For Stresses at Service Limit State after
Losses—Fully Prestressed Components
5.9.4.2.1—Compression Stresses
C5.9.4.2.1
Compression shall be investigated using the
Service Limit State Load Combination I specified in
Table 3.4.1-1. The limits in Table 5.9.4.2.1-1 shall
apply.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The reduction factor, φw, shall be taken to be equal
to 1.0 when the web and flange slenderness ratios,
calculated according to Article 5.7.4.7.1, are not greater
than 15. When either the web or flange slenderness ratio
is greater than 15, the reduction factor, φw, shall be
calculated according to Article 5.7.4.7.2.
Unlike solid rectangular beams that were used in the
development of concrete design codes, the unconfined
concrete of the compression sides of box girders are
expected to creep to failure at a stress far lower than the
nominal strength of the concrete. This behavior is
similar to the behavior of the concrete in thin-walled
columns. The reduction factor, φw, was originally
developed to account for the reduction in the usable
strain of concrete in thin-walled columns at the strength
limit state. The use of φw to reduce the stress limit in box
girders at the service limit state is not theoretically
correct. However, due to the lack of information about
the behavior of the concrete at the service limit state, the
use of φw provides a rational approach to account for the
behavior of thin components.
The application of Article 5.7.4.7.2 to flanged,
strutted, and variable thickness elements requires some
judgment. Consideration of appropriate lengths of walltype element is illustrated in Figure C5.9.4.2.1-1. For
constant thickness lengths, the wall thickness associated
with that length should be used. For variable thickness
lengths, e.g., L4, an average thickness could be used. For
multilength components, such as the top flange, the
highest ratio should be used. The beneficial effect of
support by struts should be considered. There are no
effective length factors shown. The free edge of the
cantilever overhang is assumed to be supported by the
parapet in Figure C5.9.4.2.1-1.
Figure C5.9.4.2.1-1—Suggested Choices for Wall Lengths
to be Considered
Table 5.9.4.2.1-1—Compressive Stress Limits in Prestressed Concrete at Service Limit State after Losses, Fully Prestressed
Components
Location
In other than segmentally constructed bridges due to the sum of effective prestress
and permanent loads
Stress Limit
0.45 f ′c (ksi)
•
In segmentally constructed bridges due to the sum of effective prestress and
permanent loads
0.45 f ′c (ksi)
•
Due to the sum of effective prestress, permanent loads, and transient loads as well as
during shipping and handling
0.60 φw f ′c (ksi)
•
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SECTION 5: CONCRETE STRUCTURES
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C5.9.4.2.2
5.9.4.2.2—Tension Stresses
For longitudinal service load combinations that
involve traffic loading tension stresses in members with
bonded or unbounded prestressing tendons should be
investigated using load combination Service III
specificied in Table 3.4.1-1. Load combination Service I
should be investigated for load combinations that
involve traffic loadings in transverse analyses of box
girder bridges.
The limits in Table 5.9.4.2.2-1 shall apply.
Severe corrosive conditions include exposure to
deicing salt, water, or airborne sea salt and airborne
chemicals in heavy industrial areas.
See Figure C5.9.4.1.2-1 for calculation of required
area of bonded reinforcement.
Table 5.9.4.2.2-1—Tensile Stress Limits in Prestressed Concrete at Service Limit State after Losses, Fully Prestressed
Components
Bridge Type
Location
Other Than Segmentally
Constructed Bridges
Tension in the Precompressed Tensile Zone Bridges,
Assuming Uncracked Sections
•
Segmentally Constructed
Bridges
Stress Limit
For components with bonded prestressing tendons or
reinforcement that are subjected to not worse than
moderate corrosion conditions
•
For components with bonded prestressing tendons or
reinforcement that are subjected to severe corrosive
conditions
•
For components with unbonded prestressing tendons
Longitudinal Stresses through Joints in the Precompressed
Tensile Zone
•
Joints with minimum bonded auxiliary reinforcement
through the joints sufficient to carry the calculated
longitudinal tensile force at a stress of 0.5 fy; internal
tendons or external tendons
0.19√ f ′c (ksi)
0.0948√ f ′c (ksi)
No tension
0.0948√ f ′c (ksi)
Joints without the minimum bonded auxiliary
reinforcement through joints
Transverse Stresses through Joints
No tension
Tension in the transverse direction in precompressed
tensile zone
Stresses in Other Areas
0.0948√ f ′c (ksi)
•
•
•
For areas without bonded reinforcement
No tension
In areas with bonded reinforcement sufficient to resist
the tensile force in the concrete computed assuming an
uncracked
section,
where
reinforcement
is
proportioned using a stress of 0.5 fy, not to exceed
30 ksi
Principal Tensile Stress at Neutral Axis in Web
0.19√ f ′c (ksi)
All types of segmental concrete bridges with internal
and/or external tendons, unless the Owner imposes
other criteria for critical structures.
0.110√ f ′c (ksi)
•
•
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5.9.5—Loss of Prestress
5.9.5.1—Total Loss of Prestress
C5.9.5.1
Values of prestress losses specified herein shall be
applicable to normal weight concrete only and for
specified concrete strengths up to 15.0 ksi, unless stated
otherwise.
In lieu of more detailed analysis, prestress losses in
members constructed and prestressed in a single stage,
relative to the stress immediately before transfer, may be
taken as:
• In pretensioned members:
Δf pT = Δf pES + Δf pLT
•
(5.9.5.1-1)
In post-tensioned members:
Δf pT = Δf pF + Δf pA + Δf pES + Δf pLT
(5.9.5.1-2)
where:
ΔfpT
ΔfpF
ΔfpA
ΔfpES
ΔfpLT =
=
=
=
=
total loss (ksi)
loss due to friction (ksi)
loss due to anchorage set (ksi)
sum of all losses or gains due to elastic
shortening or extension at the time of
application of prestress and/or external
loads (ksi)
losses due to long-term shrinkage and
creep of concrete, and relaxation of the
steel (ksi)
For segmental construction, lightweight concrete
construction, multi-stage prestressing, and bridges where
more exact evaluation of prestress losses is desired,
calculations for loss of prestress should be made in
accordance with a time-step method supported by
proven research data. See references cited in
Article C5.4.2.3.2.
Data from control tests on the materials to be used,
the methods of curing, ambient service conditions, and
pertinent structural details for the construction should be
considered.
Accurate estimate of total prestress loss requires
recognition that the time-dependent losses resulting
from creep, shrinkage, and relaxation are also
interdependent. However, undue refinement is seldom
warranted or even possible at the design stage because
many of the component factors are either unknown or
beyond the control of the Designer.
Losses due to anchorage set, friction, and elastic
shortening are instantaneous, whereas losses due to
creep, shrinkage, and relaxation are time-dependent.
This Article has been revised on the basis of new
analytical investigations. The presence of a substantial
amount of nonprestressed reinforcement, such as in
partially prestressed concrete, influences stress
redistribution along the section due to creep of concrete
with time, and generally leads to smaller loss of
prestressing steel pretension and larger loss of concrete
precompression.
The loss across stressing hardware and anchorage
devices has been measured from two to six percent
(Roberts, 1993) of the force indicated by the ram
pressure times the calibrated ram area. The loss varies
depending on the ram and the anchor. An initial design
value of three percent is recommended.
The extension of the provisions to 15.0 ksi was
based on Tadros (2003), which only included normal
weight concrete. Consequently, the extension to 15.0 ksi
is only valid for members made with normal weight
concrete.
5.9.5.2—Instantaneous Losses
5.9.5.2.1—Anchorage Set
The magnitude of the anchorage set shall be the
greater of that required to control the stress in the
prestressing steel at transfer or that recommended by the
manufacturer of the anchorage. The magnitude of the set
assumed for the design and used to calculate set loss
shall be shown in the contract documents and verified
during construction.
C5.9.5.2.1
Anchorage set loss is caused by the movement of
the tendon prior to seating of the wedges or the
anchorage gripping device. The magnitude of the
minimum set depends on the prestressing system used.
This loss occurs prior to transfer and causes most of the
difference between jacking stress and stress at transfer.
A common value for anchor set is 0.375 in., although
values as low as 0.0625 in. are more appropriate for
some anchorage devices, such as those for bar tendons.
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SECTION 5: CONCRETE STRUCTURES
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For wedge-type strand anchors, the set may vary
between 0.125 in. and 0.375 in., depending on the type
of equipment used. For short tendons, a small anchorage
seating value is desirable, and equipment with power
wedge seating should be used. For long tendons, the
effect of anchorage set on tendon forces is insignificant,
and power seating is not necessary. The 0.25-in.
anchorage set value, often assumed in elongation
computations, is adequate but only approximate.
Due to friction, the loss due to anchorage set may
affect only part of the prestressed member.
Losses due to elastic shortening may also be
calculated in accordance with Article 5.9.5.2.3 or other
published guidelines (PCI 1975; Zia et. al. 1979). Losses
due to elastic shortening for external tendons may be
calculated in the same manner as for internal tendons.
5.9.5.2.2—Friction
5.9.5.2.2a—Pretensioned Construction
For draped prestressing tendons, losses that may
occur at the hold-down devices should be considered.
5.9.5.2.2b—Post-Tensioned Construction
Losses due to friction between the internal
prestressing tendons and the duct wall may be taken as:
Δf pF = f pj ( 1 − e −( Kx + μ α ) )
C5.9.5.2.2b
Where large discrepancies occur between measured
and calculated tendon elongations, in-place friction tests
are required.
(5.9.5.2.2b-1)
Losses due to friction between the external tendon
across a single deviator pipe may be taken as:
Δf pF = f pj (1 − e −μ ( α+ 0.04) )
(5.9.5.2.2b-2)
where:
fpj
x
=
=
K
μ
α
=
=
=
e
=
stress in the prestressing steel at jacking (ksi)
length of a prestressing tendon from the jacking
end to any point under consideration (ft)
wobble friction coefficient (per ft of tendon)
coefficient of friction
sum of the absolute values of angular change of
prestressing steel path from jacking end, or
from the nearest jacking end if tensioning is
done equally at both ends, to the point under
investigation (rad.)
base of Napierian logarithms
Values of K and μ should be based on experimental
data for the materials specified and shall be shown in the
contract documents. In the absence of such data, a value
within the ranges of K and μ as specified in
Table 5.9.5.2.2b-1 may be used.
The 0.04 radians in Eq. 5.9.5.2.2b-2 represents an
inadvertent angle change. This angle change may vary
depending on job-specific tolerances on deviator pipe
placement and need not be applied in cases where the
deviation angle is strictly controlled or precisely known,
as in the case of continuous ducts passing through
separate longitudinal bell-shaped holes at deviators. The
inadvertent angle change need not be considered for
calculation of losses due to wedge seating movement.
For slender members, the value of x may be taken
as the projection of the tendon on the longitudinal axis
of the member. A friction coefficient of 0.25 is
appropriate for 12 strand tendons. A lower coefficient
may be used for larger tendon and duct sizes. See also
Article C5.14.2.3.7 for further discussion of friction and
wobble coefficients.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
For tendons confined to a vertical plane, α shall be
taken as the sum of the absolute values of angular
changes over length x.
For tendons curved in three dimensions, the total
tridimensional angular change α shall be obtained by
vectorially adding the total vertical angular change, αv,
and the total horizontal angular change, αh.
αv and αh may be taken as the sum of absolute
values of angular changes over length, x, of the
projected tendon profile in the vertical and horizontal
planes, respectively.
The scalar sum of αv and αh may be used as a first
approximation of α.
When the developed elevation and plan of the
tendons are parabolic or circular, the α can be computed
from:
α =
(C5.9.5.2.2b-1)
2
2
αv + αh
When the developed elevation and the plan of the
tendon are generalized curves, the tendon may be split
into small intervals, and the above formula can be
applied to each interval so that:
α = ΣΔα = Σ Δ α v2 + Δ α 2h
(C5.9.5.2.2b-2)
As an approximation, the tendon may be replaced by
a series of chords connecting nodal points. The angular
changes, Δαv and Δαh, of each chord may be obtained
from its slope in the developed elevation and in plan.
Field tests conducted on the external tendons of a
segmental viaduct in San Antonio, Texas, indicate that
the loss of prestress at deviators is higher than the usual
friction coefficient (μ = 0.25) would estimate.
This additional loss appears to be due, in part, to the
tolerances allowed in the placement of the deviator
pipes. Small misalignments of the pipes can result in
significantly increased angle changes of the tendons at
the deviation points. The addition of an inadvertent
angle change of 0.04 radians to the theoretical angle
change accounts for this effect based on typical deviator
length of 3.0 ft and placement tolerance of ±3/8 in. The
0.04 value is to be added to the theoretical value at each
deviator. The value may vary with tolerances on pipe
placement.
The measurements also indicated that the friction
across the deviators was higher during the stressing
operations than during the seating operations.
See Podolny (1986) for a general development of
friction loss theory for bridges with inclined webs and
for horizontally curved bridges.
Table 5.9.5.2.2b-1—Friction Coefficients for Post-Tensioning Tendons
Type of Steel
Wire or strand
High-strength bars
Type of Duct
Rigid and semirigid galvanized metal
sheathing
Polyethylene
Rigid steel pipe deviators for external
tendons
Galvanized metal sheathing
K
μ
0.0002
0.15–0.25
0.0002
0.0002
0.23
0.25
0.0002
0.30
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SECTION 5: CONCRETE STRUCTURES
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5.9.5.2.3—Elastic Shortening
5.9.5.2.3a—Pretensioned Members
The loss due to elastic shortening in pretensioned
members shall be taken as:
Δf pES =
Ep
E ct
f cgp
(5.9.5.2.3a-1)
where:
fcgp =
Ep =
Ect =
the concrete stress at the center of gravity of
prestressing tendons due to the prestressing
force immediately after transfer and the selfweight of the member at the section of
maximum moment (ksi).
modulus of elasticity of prestressing steel (ksi)
modulus of elasticity of concrete at transfer or
time of load application (ksi)
The total elastic loss or gain may be taken as the
sum of the effects of prestress and applied loads.
C5.9.5.2.3a
Changes in prestressing steel stress due to the
elastic deformations of the section occur at all stages of
loading. Historically, it has been conservative to account
for this effect implicitly in the calculation of elastic
shortening and creep losses considering only the
prestress force present after transfer.
The change in prestressing steel stress due to the
elastic deformations of the section may be determined
for any load applied. The resulting change may be a
loss, at transfer, or a gain, at time of superimposed load
application. Where a more detailed analysis is desired,
Eq. 5.9.5.2.3a-1 may be used at each section along the
beam, for the various loading conditions.
In calculating fcgp, using gross (or net) crosssection properties, it may be necessary to perform a
separate calculation for each different elastic
deformation to be included. For the combined effects
of initial prestress and member weight, an initial
estimate of prestress after transfer is used. The
prestress may be assumed to be 90 percent of the initial
prestress before transfer and the analysis iterated until
acceptable accuracy is achieved. To avoid iteration
altogether, Eq. C5.9.5.2.3a-1 may be used for the
initial section. If the inclusion of an elastic gain due to
the application of the deck weight is desired, the
change in prestress force can be directly calculated.
The same is true for all other elastic gains with
appropriate consideration for composite sections.
When calculating concrete stresses using
transformed section properties, the effects of losses and
gains due to elastic deformations are implicitly
accounted for and ΔfpES should not be included in the
prestressing force applied to the transformed section at
transfer. Nevertheless, the effective prestress in the
strands can be determined by subtracting losses (elastic
and time-dependent) from the jacking stress. In other
words, when using transformed section properties, the
prestressing strand and the concrete are treated together
as a composite section in which both the concrete and
the prestressing strand are equally strained in
compression by a prestressing force conceived as a
fictitious external load applied at the level of the strands.
To determine the effective stress in the prestressing
strands (neglecting time-dependent losses for simplicity)
the sum of the ΔfpES values considered must be included.
In contrast, analysis with gross (or net) section
properties involves using the effective stress in the
strands at any given stage of loading to determine the
prestress force and resulting concrete stresses.
The loss due to elastic shortening in pretensioned
members may be determined by the following
alternative equation:
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Δf pES =
Aps f pbt ( I g + em 2 Ag ) − em M g Ag
Ag I g Eci
Aps ( I g + em 2 Ag ) +
Ep
(C5.9.5.2.3a-1)
where:
Aps =
Ag =
Eci =
Ep =
em =
fpbt =
Ig
=
Mg =
5.9.5.2.3b—Post-Tensioned Members
The loss due to elastic shortening in post-tensioned
members, other than slab systems, may be taken as:
Δf pES =
where:
N =
fcgp =
N − 1 Ep
f cgp
2 N E ci
area of prestressing steel (in.2)
gross area of section (in.2)
modulus of elasticity of concrete at transfer
(ksi)
modulus of elasticity of prestressing tendons
(ksi)
average prestressing steel eccentricity at
midspan (in.)
stress in prestressing steel immediately prior to
transfer (ksi)
moment of inertia of the gross concrete section
(in.4)
midspan moment due to member self-weight
(kip-in.)
C5.9.5.2.3b
The loss due to elastic shortening in post-tensioned
members, other than slab systems, may be determined
by the following alternative equation:
(5.9.5.2.3b-1)
number of identical prestressing tendons
sum of concrete stresses at the center of gravity
of prestressing tendons due to the prestressing
force after jacking and the self-weight of the
member at the sections of maximum moment
(ksi)
fcgp values may be calculated using a steel stress
reduced below the initial value by a margin dependent
on elastic shortening, relaxation, and friction effects.
For post-tensioned structures with bonded tendons,
fcgp may be taken at the center section of the span or, for
continuous construction, at the section of maximum
moment.
For post-tensioned structures with unbonded
tendons, the fcgp value may be calculated as the stress at
the center of gravity of the prestressing steel averaged
along the length of the member.
For slab systems, the value of ΔfpES may be taken as
25 percent of that obtained from Eq. 5.9.5.2.3b-1.
Δf pES =
2
N − 1 Aps f pbt ( I g + em Ag ) − em M g Ag
Ag I g Eci
2N
Aps ( I g + em 2 Ag ) +
Ep
(C5.9.5.2.3b-1)
where:
Aps =
Ag =
Eci =
Ep =
em =
fpbt =
Ig
=
Mg =
N
fpj
=
=
area of prestressing steel (in.2)
gross area of section (in.2)
modulus of elasticity of concrete at transfer
(ksi)
modulus of elasticity of prestressing tendons
(ksi)
average eccentricity at midspan (in.)
stress in prestressing steel immediately prior to
transfer as specified in Table 5.9.3-1 (ksi)
moment of inertia of the gross concrete section
(in.4)
midspan moment due to member self-weight
(kip-in.)
number of identical prestressing tendons
stress in the prestressing steel at jacking (ksi)
For post-tensioned structures with bonded tendons,
ΔfpES may be calculated at the center section of the span
or, for continuous construction, at the section of
maximum moment.
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SECTION 5: CONCRETE STRUCTURES
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For post-tensioned structures with unbonded
tendons, ΔfpES can be calculated using the eccentricity of
the prestressing steel averaged along the length of the
member.
For slab systems, the value of ΔfpES may be taken as
25 percent of that obtained from Eq. C5.9.5.2.3b-1.
For post-tensioned construction, ΔfpES losses can be
further reduced below those implied by Eq. 5.9.5.2.3b-1
with proper tensioning procedures such as stage
stressing and retensioning.
If tendons with two different numbers of strand per
tendon are used, N may be calculated as:
A
N = N 1 + N 2 sp2
(C5.9.5.2.3b-2)
Asp1
where:
N1 =
N2 =
Asp1 =
Asp2 =
5.9.5.2.3c—Combined Pretensioning and PostTensioning
In applying the provisions of Articles 5.9.5.2.3a and
5.9.5.2.3b to components with combined pretensioning
and post-tensioning, and where post-tensioning is not
applied in identical increments, the effects of subsequent
post-tensioning on the elastic shortening of previously
stressed prestressing tendons shall be considered.
5.9.5.3—Approximate Estimate of
Time-Dependent Losses
made
from
•
members
concrete,
•
the concrete is either steam- or moist-cured,
•
prestressing is by bars or strands with normal
and low relaxation properties, and
•
average exposure conditions and temperatures
characterize the site,
normal-weight
the long-term prestress loss, ∆fpLT, due to creep of
concrete, shrinkage of concrete, and relaxation of steel
shall be estimated using the following formula:
Δf pLT = 10.0
in which:
f pi Aps
Ag
γ h γ st + 12.0 γ h γ st + Δf pR
C5.9.5.2.3c
See Castrodale and White (2004) for information on
computing the effect of subsequent post-tensioning on
the elastic shortening of previously stressed prestressing
tendons.
C5.9.5.3
For standard precast, pretensioned members subject
to normal loading and environmental conditions, where:
are
number of tendons in the larger group
number of tendons in the smaller group
cross-sectional area of a tendon in the larger
group (in.2)
cross-sectional area of a tendon in the smaller
group (in.2)
(5.9.5.3-1)
The losses or gains due to elastic deformations at
the time of transfer or load application should be added
to the time-dependent losses to determine total losses.
However, these elastic losses (or gains) must be taken
equal to zero if transformed section properties are used
in stress analysis.
The approximate estimates of time-dependent
prestress losses given in Eq. 5.9.5.3-1 are intended for
sections with composite decks only. The losses in
Eq. 5.9.5.3-1 were derived as approximations of the
terms in the refined method for a wide range of standard
precast prestressed concrete I-beams and inverted tee
beams. The members were assumed to be fully utilized,
i.e., level of prestressing is such that concrete tensile
stress at full service loads is near the maximum limit. It
is further assumed in the development of the
approximate method that live load moments produce
about one-third of the total load moments, which is
reasonable for I-beam and inverted tee composite
construction and conservative for noncomposite boxes
and voided slabs. They were calibrated with full-scale
test results and with the results of the refined method,
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γ h = 1.7 − 0.01H
γ st =
5
(1 + f ci′ )
(5.9.5.3-2)
(5.9.5.3-3)
where:
fpi
=
H
=
γh
=
γst =
ΔfpR =
prestressing steel stress immediately prior to
transfer (ksi)
the average annual ambient relative humidity
(%)
correction factor for relative humidity of the
ambient air
correction factor for specified concrete strength
at time of prestress transfer to the concrete
member
an estimate of relaxation loss taken as 2.4 ksi
for low relaxation strand, 10.0 ksi for stress
relieved strand, and in accordance with
manufacturers recommendation for other types
of strand (ksi)
and found to give conservative results (Al-Omaishi,
2001; Tadros, 2003). The approximate method should
not be used for members of uncommon shapes, i.e.,
having V/S ratios much different from 3.5 in., level of
prestressing, or construction staging. The first term in
Eq. 5.9.5.3-1 corresponds to creep losses, the second
term to shrinkage losses, and the third to relaxation
losses.
The commentary to Article 5.9.5.4.2 also gives an
alternative relaxation loss prediction method.
For girders other than those made with composite
slabs, the time-dependent prestress losses resulting from
creep and shrinkage of concrete and relaxation of steel
shall be determined using the refined method of
Article 5.9.5.4.
For segmental concrete bridges, lump sum losses
may be used only for preliminary design purposes.
For members of unusual dimensions, level of
prestressing, construction staging, or concrete
constituent materials, the refined method of
Article 5.9.5.4 or computer time-step methods shall be
used.
5.9.5.4—Refined Estimates of Time-Dependent
Losses
5.9.5.4.1—General
C5.9.5.4.1
For nonsegmental prestressed members, more
accurate values of creep-, shrinkage-, and relaxationrelated losses, than those specified in Article 5.9.5.3
may be determined in accordance with the provisions of
this Article. For precast pretensioned girders without a
composite topping and for precast or cast-in-place
nonsegmental post-tensioned girders, the provisions of
Articles 5.9.5.4.4 and 5.9.5.4.5, respectively, shall be
considered before applying the provisions of this
Article.
For segmental construction and post-tensioned
spliced precast girders, other than during preliminary
design, prestress losses shall be determined by the timestep method and the provisions of Article 5.9.5,
including consideration of the time-dependent
construction stages and schedule shown in the contract
documents.
For
components
with
combined
pretensioning and post-tensioning, and where post-
See Castrodale and White (2004) for information on
computing the interaction of creep effects for
prestressing applied at different times.
Estimates of losses due to each time-dependent
source, such as creep, shrinkage, or relaxation, can lead
to a better estimate of total losses compared with the
values obtained using Article 5.9.5.3. The individual
losses are based on research published in Tadros (2003),
which aimed at extending applicability of the provisions
of these Specifications to high-strength concrete.
The new approach additionally accounts for interaction
between the precast and the cast-in-place concrete
components of a composite member and for variability
of creep and shrinkage properties of concrete by linking
the loss formulas to the creep and shrinkage prediction
formulae of Article 5.4.2.3.
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2012
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SECTION 5: CONCRETE STRUCTURES
5-105
tensioning is applied in more than one stage, the effects
of subsequent prestressing on the creep loss for previous
prestressing shall be considered.
The change in prestressing steel stress due to timedependent loss, ΔfpLT, shall be determined as follows:
ΔfpLT = (ΔfpSR + ΔfpCR + ΔfpR1)id +
(ΔfpSD + ΔfpCD + ΔfpR2 – ΔfpSS)df
(5.9.5.4.1-1)
where:
prestress loss due to shrinkage of girder
concrete between transfer and deck
placement (ksi)
= prestress loss due to creep of girder
ΔfpCR
concrete between transfer and deck
placement (ksi)
= prestress loss due to relaxation of
ΔfpR1
prestressing strands between time of
transfer and deck placement (ksi)
= prestress loss due to relaxation of
ΔfpR2
prestressing strands in composite section
between time of deck placement and final
time (ksi)
= prestress loss due to shrinkage of girder
ΔfpSD
concrete between time of deck placement
and final time (ksi)
ΔfpCD = prestress loss due to creep of girder
concrete between time of deck placement
and final time (ksi)
= prestress gain due to shrinkage of deck in
ΔfpSS
composite section (ksi)
(ΔfpSR + ΔfpCR + ΔfpR1)id
= sum of time-dependent prestress losses
between transfer and deck placement (ksi)
(ΔfpSD + ΔfpCD + ΔfpR2 – ΔfpSS)df
= sum of time-dependent prestress losses
after deck placement (ksi)
ΔfpSR
=
For concrete containing lightweight aggregates,
very hard aggregates, or unusual chemical admixtures,
the estimated material properties used in this Article and
Article 5.4.2.3 may be inaccurate. Actual test results
should be used for their estimation.
For segmental construction, for all considerations
other than preliminary design, prestress losses shall be
determined as specified in Article 5.9.5, including
consideration of the time-dependent construction
method and schedule shown in the contract documents.
5.9.5.4.2—Losses: Time of Transfer to Time of Deck
Placement
5.9.5.4.2a—Shrinkage of Girder Concrete
The prestress loss due to shrinkage of girder
concrete between time of transfer and deck placement,
ΔfpSR, shall be determined as:
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Δf pSR = εbid E p K id
(5.9.5.4.2a-1)
in which:
1
K id =
1+
E p Aps
Ag e 2pg
Eci Ag
Ig
1 +
[1 + 0.7ψ b ( t f ,ti )]
where:
εbid
=
Kid
=
epg
=
Ψb(tf, ti) =
=
=
tf
ti
(5.9.5.4.2a-2)
concrete shrinkage strain of girder between
the time of transfer and deck placement per
Eq. 5.4.2.3.3-1
transformed section coefficient that
accounts for time-dependent interaction
between concrete and bonded steel in the
section being considered for time period
between transfer and deck placement
eccentricity of prestressing force with
respect to centroid of girder (in.); positive
in common construction where it is below
girder centroid
girder creep coefficient at final time due to
loading introduced at transfer per
Eq. 5.4.2.3.2-1
final age (days)
age at transfer (days)
5.9.5.4.2b—Creep of Girder Concrete
The prestress loss due to creep of girder concrete
between time of transfer and deck placement, ΔfpCR,
shall be determined as:
Δf pCR =
Ep
Eci
f cgp ψb ( td , ti ) K id
(5.9.5.4.2b-1)
where:
Ψb(td, ti) =
td
=
girder creep coefficient at time of deck
placement due to loading introduced at
transfer per Eq. 5.4.2.3.2-1
age at deck placement (days)
5.9.5.4.2c—Relaxation of Prestressing Strands
The prestress loss due to relaxation of prestressing
strands between time of transfer and deck placement,
ΔfpR1, shall be determined as:
Δf pR1 =
f pt
− 0.55
K L f py
f pt
(5.9.5.4.2c-1)
C5.9.5.4.2c
Eqs. 5.9.5.4.2c-1 and 5.9.5.4.3c-1 are given for
relaxation losses and are appropriate for normal
temperature ranges only. Relaxation losses increase with
increasing temperatures.
A more accurate equation for prediction of
relaxation loss between transfer and deck placement is
given in Tadros et al. (2003):
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
SECTION 5: CONCRETE STRUCTURES
5-107
where:
fpt
=
stress in prestressing strands immediately after
transfer, taken not less than 0.55fpy in
Eq. 5.9.5.4.2c-1
30 for low relaxation strands and 7 for other
prestressing steel, unless more accurate
manufacturer's data are available
KL =
The relaxation loss, ΔfpR1, may be assumed equal to
1.2 ksi for low-relaxation strands.
ª f pt log (24t ) § f pt
· º ª 3(Δf pSR + Δf pCR ) º
Δf pR1 = «
− 0.55 ¸ » «1 −
¨¨
» K id
¸» «
′
f pt
¹¼ ¬
¼»
¬« K L log(24ti ) © f py
(C5.9.5.4.2c-1)
where the KƍL is a factor accounting for type of steel,
equal to 45 for low relaxation steel and 10 for stress
relieved steel, t is time in days between strand
tensioning and deck placement. The term in the first
square brackets is the intrinsic relaxation without
accounting for strand shortening due to creep and
shrinkage of concrete. The second term in square
brackets accounts for relaxation reduction due to creep
and shrinkage of concrete. The factor Kid accounts for
the restraint of the concrete member caused by bonded
reinforcement. It is the same factor used for the creep
and shrinkage components of the prestress loss. The
equation given in Article 5.9.5.4.2c is an approximation
of the above formula with the following typical values
assumed:
ti
=
0.75 day
t
=
120 days
ª 3(Δf pSR + Δf pCR ) º
«1 −
» = 0.67
f pt
¬
¼
Kid =
0.8
5.9.5.4.3—Losses: Time of Deck Placement to
Final Time
5.9.5.4.3a—Shrinkage of Girder Concrete
The prestress loss due to shrinkage of girder
concrete between time of deck placement and final time,
ΔfpSD, shall be determined as:
Δf pSD = ε bdf E p K df
(5.9.5.4.3a-1)
in which:
1
K df =
1+
E p Aps §
2
Ac e pc ·
¨1 +
¸ [1 + 0.7ȥ b ( t f , ti )]
Eci Ac ©
Ic ¹
(5.9.5.4.3a-2)
where:
İbdf =
Kdf =
shrinkage strain of girder between time of deck
placement and final time per Eq. 5.4.2.3.3-1
transformed section coefficient that accounts
for time-dependent interaction between
concrete and bonded steel in the section being
considered for time period between deck
placement and final time
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5-108
epc =
Ac =
Ic
=
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
eccentricity of prestressing force with respect
to centroid of composite section (in.), positive
in typical construction where prestressing force
is below centroid of section
area of section calculated using the gross
composite concrete section properties of the
girder and the deck and the deck-to-girder
modular ratio (in.2)
moment of inertia of section calculated using
the gross composite concrete section properties
of the girder and the deck and the deck-togirder modular ratio at service (in.4)
5.9.5.4.3b—Creep of Girder Concrete
The prestress (loss is positive, gain is negative) due
to creep of girder concrete between time of deck
placement and final time, ǻfpCD, shall be determined as:
Δf pCD =
Ep
f ª ȥ t , t − ȥb ( td , ti ) º» K df
¼
Eci cgp «¬ b f i
Ep
+
Δf ȥ §¨ t , t ·¸ K
Ec cd b © f d ¹ df
( )
(5.9.5.4.3b-1)
where:
Δfcd
=
change in concrete stress at centroid of
prestressing strands due to long-term
losses between transfer and deck
placement, combined with deck weight and
superimposed loads (ksi)
girder creep coefficient at final time due to
loading
at
deck
placement
per
Eq. 5.4.2.3.2-1
Ȍb(tf, td) =
5.9.5.4.3c—Relaxation of Prestressing Strands
The prestress loss due to relaxation of prestressing
strands in composite section between time of deck
placement and final time, ΔfpR2, shall be determined as:
Δf pR 2 = Δf pR1
C5.9.5.4.3.c
Research indicates that about one-half of the losses
due to relaxation occur before deck placement;
therefore, the losses after deck placement are equal to
the prior losses.
(5.9.5.4.3c-1)
5.9.5.4.3d—Shrinkage of Deck Concrete
The prestress gain due to shrinkage of deck
composite section, ΔfpSS, shall be determined as:
Δf pSS =
Ep
Ec
(
)
Δf cdf K df ª¬1 + 0.7ȥ b t f , t d º¼
(5.9.5.4.3d-1)
in which:
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2012
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SECTION 5: CONCRETE STRUCTURES
ε ddf Ad Ecd
Δf cdf =
[1 + 0.7ψ ( t
d
f
, td )
]
5-109
1 e pc ed
−
Ic
Ac
(5.9.5.4.3d-2)
where:
Δfcdf
=
εddf
=
Ad
Ecd
ed
=
=
=
Ψb(tf, td) =
change in concrete stress at centroid of
prestressing strands due to shrinkage of
deck concrete (ksi)
shrinkage strain of deck concrete between
placement
and
final
time
per
Eq. 5.4.2.3.3-1
area of deck concrete (in.2)
modulus of elasticity of deck concrete (ksi)
eccentricity of deck with respect to the
gross composite section, positive in typical
construction where deck is above girder
(in.)
creep coefficient of deck concrete at final
time due to loading introduced shortly after
deck placement (i.e. overlays, barriers,
etc.) per Eq. 5.4.2.3.2-1
5.9.5.4.4—Precast Pretensioned Girders without
Composite Topping
The equations in Article 5.9.5.4.2 and
Article 5.9.5.4.3 are applicable to girders with
noncomposite deck or topping, or with no topping. The
values for time of “deck placement” in Article 5.9.5.4.2
may be taken as values at time of noncomposite deck
placement or values at time of installation of precast
members without topping. Time of “deck placement” in
Article 5.9.5.4.3 may be taken as time of noncomposite
deck placement or values at time of installation of
precast members without topping. Area of “deck” for
these applications shall be taken as zero.
5.9.5.4.5—Post-Tensioned Nonsegmental Girders
Long-term prestress losses for post-tensioned
members after tendons have been grouted may be
calculated using the provisions of Articles 5.9.5.4.1
through 5.9.5.4.4. In Eq. 5.9.5.4.1-1, the value of the
term (ΔfpSR + ΔfpCR + ΔfpR1)id shall be taken as zero.
5.9.5.5—Losses for Deflection Calculations
For camber and deflection calculations of
prestressed nonsegmental members made of normal
weight concrete with a strength in excess of 3.5 ksi at
the time of prestress, fcgp and Δfcdp may be computed as
the stress at the center of gravity of prestressing steel
averaged along the length of the member.
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
5.10—DETAILS OF REINFORCEMENT
5.10.1—Concrete Cover
Minimum concrete cover shall be as specified in
Article 5.12.3.
5.10.2—Hooks and Bends
5.10.2.1—Standard Hooks
2013 Revision
For the purpose of these Specifications, the term
“standard hook” shall mean one of the following:
•
For longitudinal reinforcement:
C5.10.2.1
2013 Revision
These requirements are consistent with the
requirements of ACI 318 and CRSI's Manual of
Standard Practice.
(a) 180-degree bend, plus a 4.0db extension, but
not less than 2.5 in. at the free end of the bar, or
(b) 90-degree bend, plus a 12.0db extension at the
free end of the bar.
•
For transverse reinforcement:
(a) No. 5 bar and smaller—90-degree bend, plus a
6.0db extension at the free end of the bar,
(b) No. 6, No. 7 and No. 8 bars—90-degree bend,
plus a 12.0db extension at the free end of the
bar; and
(c) No. 8 bar and smaller—135-degree bend, plus a
6.0 db extension at the free end of the bar.
where:
db =
nominal diameter of reinforcing bar (in.)
5.10.2.2—Seismic Hooks
2013 Revision
Seismic hooks shall consist of a 135-degree bend,
plus an extension of not less than the larger of 6.0db or
3.0 in. Seismic hooks shall be used for transverse
reinforcement in regions of expected plastic hinges.
Such hooks and their required locations shall be detailed
in the contract documents.
5.10.2.3—Minimum Bend Diameters
The diameter of a bar bend, measured on the inside
of the bar, shall not be less than that specified in
Table 5.10.2.3-1.
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SECTION 5: CONCRETE STRUCTURES
5-111
Table 5.10.2.3-1—Minimum Diameters of Bend
Bar Size and Use
Minimum
Diameter
No. 3 through No. 5—General
No. 3 through No. 5—Stirrups and Ties
No. 6 through No. 8—General
No. 9, No. 10, and No. 11
No. 14 and No. 18
6.0db
4.0db
6.0db
8.0db
10.0db
The inside diameter of bend for stirrups and ties in
plain or deformed welded wire fabric shall not be less
than 4.0db for deformed wire larger than D6 and 2.0db
for all other wire sizes. Bends with inside diameters of
less than 8.0db shall not be located less than 4.0db from
the nearest welded intersection.
5.10.3—Spacing of Reinforcement
5.10.3.1 Minimum Spacing of Reinforcing Bars
5.10.3.1.1—Cast-in-Place Concrete
For cast-in-place concrete, the clear distance
between parallel bars in a layer shall not be less than:
•
1.5 times the nominal diameter of the bars,
•
1.5 times the maximum size of the coarse aggregate,
or
•
1.5 in.
5.10.3.1.2—Precast Concrete
For precast concrete manufactured under plant
control conditions, the clear distance between parallel
bars in a layer shall not be less than:
•
The nominal diameter of the bars,
•
1.33 times the maximum size of the coarse
aggregate, or
•
1.0 in.
5.10.3.1.3—Multilayers
Except in decks where parallel reinforcing is placed
in two or more layers, with clear distance between layers
not exceeding 6.0 in., the bars in the upper layers shall
be placed directly above those in the bottom layer, and
the clear distance between layers shall not be less than
1.0 in. or the nominal diameter of the bars.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
5.10.3.1.4—Splices
The clear distance limitations between bars that are
specified in Articles 5.10.3.1.1 and 5.10.3.1.2 shall also
apply to the clear distance between a contact lap splice
and adjacent splices or bars.
5.10.3.1.5—Bundled Bars
C5.10.3.1.5
The number of parallel reinforcing bars bundled in
contact to act as a unit shall not exceed four in any one
bundle, except that in flexural members, the number of
bars larger than No. 11 shall not exceed two in any one
bundle.
ties.
Bundled bars shall be enclosed within stirrups or
Individual bars in a bundle, cut off within the span
of a member, shall be terminated at different points with
at least a 40-bar diameter stagger. Where spacing
limitations are based on bar size, a unit of bundled bars
shall be treated as a single bar of a diameter derived
from the equivalent total area.
Bundled bars should be tied, wired, or otherwise
fastened together to ensure that they remain in their
relative position, regardless of their inclination.
5.10.3.2—Maximum Spacing of Reinforcing Bars
Unless otherwise specified, the spacing of the
reinforcement in walls and slabs shall not exceed 1.5
times the thickness of the member or 18.0 in. The
maximum spacing of spirals, ties, and temperature
shrinkage reinforcement shall be as specified in
Articles 5.10.6, 5.10.7, and 5.10.8.
5.10.3.3—Minimum Spacing of Prestressing
Tendons and Ducts
C5.10.3.3.1
5.10.3.3.1—Pretensioning Strand
The distance between pretensioning strands,
including shielded ones, at each end of a member within
the transfer length, as specified in Article 5.11.4.1, shall
not be less than a clear distance taken as 1.33 times the
maximum size of the aggregate nor less than the centerto-center distances specified in Table 5.10.3.3.1-1.
Table 5.10.3.3.1-1—Center-to-Center Spacings
Strand Size (in.)
Spacing (in.)
0.6
0.5625 Special
0.5625
0.5000
0.4375
0.50 Special
0.3750
2.000
The requirement to maintain the clear spacing
within the transfer zone is to ensure the strands are
separated sufficiently to properly transfer their
prestressing force to the surrounding concrete and to
reduce the stress concentration around the strands at the
ends of pretensioned components at release.
Some jurisdictions limit the clear distance between
pretensioning strands to not less than twice the nominal
size of aggregate to facilitate placing and compaction of
concrete.
1.750
1.500
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SECTION 5: CONCRETE STRUCTURES
5-113
If justified by performance tests of full-scale
prototypes of the design, the clear distance between
strands at the end of a member may be decreased.
The minimum clear distance between groups of
bundled strands shall not be less than 1.33 times the
maximum size of the aggregate or 1.0 in.
Pretensioning strands in a member may be bundled
to touch one another in an essentially vertical plane at
and between hold-down locations. Strands bundled in
any manner, other than a vertical plane, shall be limited
to four strands per bundle.
5.10.3.3.2—Post-Tensioning Ducts—Girders
Straight in Plan
Unless otherwise specified herein, the clear distance
between straight post-tensioning ducts shall not be less
than 1.5 in. or 1.33 times the maximum size of the
coarse aggregate. For precast segmental construction
when post-tensioning tendons extend through an epoxy
joint between components, the clear spacing between
post-tensioning ducts shall not be less than the greater of
the duct internal diameter or 4.0 in.
Ducts may be bundled together in groups not
exceeding three, provided that the spacing, as specified
between individual ducts, is maintained between each
duct in the zone within 3.0 ft of anchorages.
For groups of bundled ducts in construction other
than segmental, the minimum clear horizontal distance
between adjacent bundles shall not be less than 4.0 in.
When groups of ducts are located in two or more
horizontal planes, a bundle shall contain no more than
two ducts in the same horizontal plan.
The minimum vertical clear distance between
bundles shall not be less than 1.5 in. or 1.33 times the
maximum size of coarse aggregate.
For precast construction, the minimum clear
horizontal distance between groups of ducts may be
reduced to 3.0 in.
C5.10.3.3.2
Figure C5.10.3.3.2-1—Examples of Acceptable
Arrangements for Ducts Not Curved in the Horizontal
Plan
5.10.3.3.3—Post-Tensioning Ducts—Girders
Curved in Plan
The minimum clear distance between curved ducts
shall be as required for tendon confinement as specified
in Article 5.10.4.3. The spacing for curved ducts shall
not be less than that required for straight ducts.
5.10.3.4—Maximum Spacing of Prestressing
Tendons and Ducts in Slabs
Pretensioning strands for precast slabs shall be
spaced symmetrically and uniformly and shall not be
farther apart than 1.5 times the total composite slab
thickness or 18.0 in.
Post-tensioning tendons for slabs shall not be
farther apart, center-to-center, than 4.0 times the total
composite minimum thickness of the slab.
C5.10.3.4
The 4.0 times depth of slab requirement for the
maximum spacing of transverse post-tensioning ducts in
deck slabs is new and reflects common practice. The
composite thickness refers to slabs with bonded overlays.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
5.10.3.5—Couplers in Post-Tensioning Tendons
The contract documents shall specify that not more
than 50 percent of the longitudinal post-tensioning
tendons be coupled at one section and that the spacing
between adjacent coupler locations be not closer than
the segment length or twice the segment depth. The void
areas around couplers shall be deducted from the gross
section area and moment of inertia when computing
stresses at the time post-tensioning force is applied.
C5.10.3.5
European experience indicates that the prestressing
force decreases locally in the region of a coupler. This is
believed to result, in part, from increased creep caused
by high compressive stresses in the reduced concrete
section due to coupling of tendons. Cracking has not
been observed in bridges where the number of tendons
coupled at a section has been limited to 50 percent of the
total number of tendons.
5.10.4—Tendon Confinement
5.10.4.1—General
C5.10.4.1
Tendons shall be located within the reinforcing steel
stirrups in webs, and, where applicable, between layers of
transverse reinforcing steel in flanges and slabs. For ducts
in the bottom flanges of variable depth segments, nominal
confinement reinforcing shall be provided around the duct
at each segment face. The reinforcement shall not be less
than two rows of No. 4 hairpin bars at both sides of each
duct with vertical dimension equal to the slab thickness,
less top and bottom cover dimensions.
The effects of grouting pressure in the ducts shall be
considered.
5.10.4.2—Wobble Effect in Slabs
For the purpose of this Article, ducts spaced closer
than 12.0 in. center-to-center in either direction shall be
considered as closely spaced.
Where closely spaced transverse or longitudinal
ducts are located in the flanges, and no provisions to
minimize wobble of ducts are included in the contract
documents, the top and bottom reinforcement mats
should be tied together with No. 4 hairpin bars. The
spacing between the hairpin bars shall not exceed
18.0 in. or 1.5 times the slab thickness in each direction.
5.10.4.3—Effects of Curved Tendons
Reinforcement shall be used to confine curved
tendons if required by Article 5.8.1.5. The reinforcement
shall be proportioned to ensure that the steel stress at
service limit state does not exceed 0.6 fy, and the
assumed value of fy shall not exceed 60.0 ksi. Unless a
strut-and-tie analysis is done and indicates otherwise,
Spacing of the confinement reinforcement shall not
exceed either 3.0 times the outside diameter of the duct
or 24.0 in.
Tendons shall not be bundled in groups greater than
three when girders are curved in horizontal plane.
This Article is based primarily on
recommendation from Breen and Kashima (1991).
the
C5.10.4.2
The hairpin bars are provided to prevent slab
delamination along the plane of the post-tensioning
ducts.
C5.10.4.3
Curved tendons induce deviation forces that are
radial to the tendon in the plane of tendon curvature.
Curved tendons with multiple strands or wires also
induce out-of-plane forces that are perpendicular to the
plane of tendon curvature.
Resistance to in-plane forces in curved girders may
be provided by increasing the concrete cover over the
duct, by adding confinement tie reinforcement or by a
combination thereof.
It is not the purpose of this Article to encourage the
use of curved tendons around re-entrant corners or
voids. Where possible, this type of detail should be
avoided.
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SECTION 5: CONCRETE STRUCTURES
5-115
5.10.4.3.1—Design for In-Plane Force Effects
5.10.4.3.1a—In-Plane Force Effects
In-plane deviation force effects due to the change in
direction of tendons shall be taken as:
Pu
F u-i n =
R
(5.10.4.3.1a-1)
where:
Fu-in
=
Pu
=
R
=
the in-plane deviation force effect per unit
length of tendon (kips/ft)
the tendon force factored as specified in
Article 3.4.3 (kip)
the radius of curvature of the tendon at the
considered location (ft)
The maximum deviation force shall be determined
on the basis that all the tendons, including provisional
tendons, are stressed. The provisions of Article 5.10.9
shall apply to design for in-plane force effects due to
tendons curved at the tendon anchorage.
C5.10.4.3.1a
In-plane forces occur, for example, in anchorage
blisters
or
curved
webs,
as
shown
in
Figures C5.10.4.3.1a-1 and C5.10.4.3.1a-2. Without
adequate reinforcement, the tendon deviation forces may
rip through the concrete cover on the inside of the
tendon curve, or unbalanced compressive forces may
push off the concrete on the outside of the curve. Small
radial tensile stresses may be resisted by concrete in
tension.
The load factor of 1.2 taken from Article 3.4.3 and
applied to the maximum tendon jacking force results in a
design load of about 96 percent of the nominal ultimate
strength of the tendon. This number compares well with
the maximum attainable jacking force, which is limited
by the anchor efficiency factor.
Deviation forces push off
concrete cover on inside
of curvature
(a)
(b)
Unbalanced compression force
components push off concrete
cover on outside of curvature
Reinforcement for
in-plane forces
(c)
Figure C5.10.4.3.1a-1—In-Plane Forces in a Soffit Blister
The radial component from the longitudinal web
stress in the concrete due to the compression in the
cylindrical web must be subtracted.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure C5.10.4.3.1a-2—In-Plane Force Effects in Curved
Girders Due to Horizontally Curved Tendons
5.10.4.3.1b—Shear Resistance to Pull-out
The shear resistance per unit length of the concrete
cover against pull-out by deviation forces, Vr, shall be
taken as:
(5.10.4.3.1b-1)
Vr = φVn
in which:
Vn = 0.15deff√f’ci Vn = 0.15deff
f ci′
(5.10.4.3.1b-2)
where:
Vn =
φ =
deff =
nominal shear resistance of two shear planes
per unit length (kips/in.)
resistance factor for shear, 0.75
one-half the effective length of the failure plane
in shear and tension for a curved element (in.)
C5.10.4.3.1b
The two shear planes for which Eq. 5.10.4.3.1b-3
gives Vn are as indicated in Figure 5.10.4.3.1b-1 for
single and multiple tendons.
Where a staggered or side-by-side group of ducts is
located side by side in a single web, all possible shear
and tension failure planes should be considered in
determining deff.
A generic stirrup and duct tie detail is shown in
Figure C5.10.4.3.1b-1. Small diameter reinforcing bars
should be used for better development of these bars.
There have been no reported web failures when this
detail has been used.
12” Web
3” clr
to Duct
Inside of Curve
2” clr to
Stirrup
For single duct stack or for sduct < dduct, deff, shown in
Detail (a) in Figure 5.10.4.3.1b-1, shall be taken as:
d eff = d c +
d duct
4
(5.10.4.3.1b-3)
For sduct ≥ dduct, deff shall be taken as the lesser of the
following based on Paths 1 and 2 shown in Detail (b) in
Figure 5.10.4.3.1b-1:
d eff = t w −
d duct
2
d eff = d c +
d duct
+
4
(5.10.4.3.1b-4)
s
duct
2
#4
Duct Tie
#4
Stirrup Tie, Typ
#5 Stirrups
Figure C5.10.4.3.1b-1—Typical Stirrup and Duct Tie
Detail
(5.10.4.3.1b-5)
where:
sduct =
clear distance between tendon ducts in vertical
direction (in.)
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SECTION 5: CONCRETE STRUCTURES
dduct =
dc =
tw =
5-117
outside diameter of prestress duct (in.)
cover on duct (in.)
web thickness (in.)
deff
dc
dc
1
sduct
R
inside face
R
inside face
sduct
2
tw
dduct
(a)
dduct
(b)
Figure 5.10.4.3.1b-1—Definition of deff
If the factored in-plane deviation force exceeds the
factored shear resistance of the concrete cover, as
specified in Eq. 5.10.4.3.1b-2, fully anchored stirrup and
duct ties hooked around the outermost stirrup legs to
resist the in-plane deviation forces shall be provided in
the form of either nonprestressed or prestressed
reinforcement.
5.10.4.3.1c—Cracking of Cover Concrete
When the clear distance between ducts oriented in a
vertical column is less than 1.5 in., the ducts shall be
considered stacked. Resistance to cracking shall be
investigated at the ends and at midheight of the
unreinforced cover concrete.
The applied local moment per unit length at the
ends of the cover shall be taken as:
M end
ΣFu − in h 2
hds ds
=
12
(5.10.4.3.1c-1)
M mid
Figure C5.10.4.3.1c-1 illustrates the concept of an
unreinforced cover concrete beam to be investigated for
cracking. Experience has shown that a vertical stack of
more than three ducts can result in cracking of the cover
concrete. When more than three ducts are required, it is
recommended that at least 1.5 in. spacing be provided
between the upper and lower ducts of the two stacks.
The resistance factor is based on successful
performance of curved post-tensioned box girder bridges
in California.
dc
And the applied local moment per unit length at the
midheight of the cover shall be taken as:
ΣFu − in h 2
hds ds
=
24
C5.10.4.3.1c
Ignore Concrete
near Ducts for
Regional Bending
hds
W = Fu-in
(5.10.4.3.1c-2)
Web and Ducts
where:
hds = the height of the duct stack as shown in
Figure C5.10.4.3.1b-1
Equivalent Beam
Figure C5.10.4.3.1c-1—Hypothetical Unreinforced
Concrete Cover Beam
Tensile stresses in the unreinforced concrete cover
resulting from Eqs. 5.10.4.3.1c-1 and 5.10.4.3.1c-2 shall
be combined with the tensile stresses from regional
bending of the web as defined in Article 5.10.4.3.1d to
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
evaluate the potential for cracking of the cover concrete.
If combined tensile stresses exceed the cracking stresses
given by Eq. 5.10.4.3.1c-4, ducts shall be restrained by
stirrup and duct tie reinforcement.
(5.10.4.3.1c-3)
f cr = φf r
where:
φ = 0.85
(5.10.4.3.1c-4)
C5.10.4.3.1d
5.10.4.3.1d—Regional Bending
The regional flexural effects of in-plane forces shall
be taken as:
Mu =
φΣFu −in hc
4
(5.10.4.3.1d-1)
where:
φcont
=
hc
=
0.6 continuity factor for interior webs; 0.7
continuity factor for exterior webs
span of the web between the top and bottom
slabs measured along the axis of the web as
shown in Figure C5.10.4.3.1c-1.
When determining tensile stresses for the purpose
of evaluating the potential for cracking of the cover
concrete as specified in Article 5.10.4.3.1c, the effect of
regional bending is combined with bending of the local
concrete cover beam. It is recommended that the effect
of stirrups in resisting bending be ignored, and that the
ducts be considered as voids in the transverse section of
the webs.
The wedging action of strands within the duct due
to vertical curvature of the tendon can exacerbate tendon
pullout resulting from horizontal curvature of the tendon
as described in Articles 5.10.4.3.1b and 5.10.4.3.1c.
For curved girders, the local flexural and shear
effects of out-of-plane forces as described in Article
5.10.4.3.2 shall be evaluated.
When curved ducts for tendons other than those
crossing at approximately 90 degrees are located so that
the direction of the radial force from one tendon is
toward another, confinement of the ducts shall be
provided by:
•
Spacing the ducts to ensure adequate nominal shear
resistance, as specified in Eq. 5.10.4.3.1b-1 or
•
Providing confinement reinforcement to resist the
radial force.
5.10.4.3.2—Out-of-Plane Force Effects
Out-of-plane force effects due to the wedging action
of strands against the duct wall may be estimated as:
F u -out =
Pu
πR
(5.10.4.3.2-1)
where:
Fu-out
=
Pu
=
R
=
out-of-plane force effect per unit length of
tendon (kip/ft)
tendon force, factored as specified in
Article 3.4.3 (kip)
radius of curvature of the tendon in a
vertical plane at the considered location
(ft)
C5.10.4.3.2
Out-of-plane forces in multistrand, post-tensioning
tendons are caused by the spreading of the strands or
wires within the duct, as shown in Figure C5.10.4.3.2-1.
Small out-of-plane forces may be resisted by concrete in
shear; otherwise, spiral reinforcement is most effective
to resist out-of-plane forces. In horizontally curved
bridges, out-of-plane forces due to the vertical curvature
of tendons should be added to in-plane forces resulting
from horizontal curvature of the tendons.
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SECTION 5: CONCRETE STRUCTURES
5-119
If the factored shear resistance given by
Eq. 5.10.4.3.1b-1 is not adequate, local confining
reinforcement shall be provided throughout the curved
tendon segments to resist all of the out-of-plane forces,
preferably in the form of spiral reinforcement.
Figure C5.10.4.3.2-1—Effects of Out-of-Plane Forces
5.10.5—External Tendon Supports
Unless a vibration analysis indicates otherwise, the
unsupported length of external tendons shall not exceed
25.0 ft.
5.10.6—Transverse Reinforcement for Compression
Members
5.10.6.1—General
2013 Revision
The provisions of Article 5.10.11 shall also apply to
design and detailing in Seismic Zones 2, 3, and 4.
Transverse reinforcement for compression members
may consist of either spirals or ties.
C5.10.6.1
2013 Revision
Article 5.10.11.2 applies to Seismic Zone 1 but has
no additional requirements for transverse reinforcement
for compression members.
5.10.6.2—Spirals
Spiral reinforcement for compression members
other than piles shall consist of one or more evenly
spaced continuous spirals of either deformed or plain bar
or wire with a minimum diameter of 0.375 in. The
reinforcement shall be arranged so that all primary
longitudinal reinforcement is contained on the inside of,
and in contact with, the spirals.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The clear spacing between the bars of the spiral
shall not be less than either 1.0 in. or 1.33 times the
maximum size of the aggregate. The center-to-center
spacing shall not exceed 6.0 times the diameter of the
longitudinal bars or 6.0 in.
Except as specified in Articles 5.10.11.3 and
5.10.11.4.1 for Seismic Zones 2, 3, and 4, spiral
reinforcement shall extend from the footing or other
support to the level of the lowest horizontal
reinforcement of the supported members.
Anchorage of spiral reinforcement shall be provided
by 1.5 extra turns of spiral bar or wire at each end of the
spiral unit. For Seismic Zones 2, 3, and 4, the extension
of transverse reinforcement into connecting members
shall meet the requirements of Article 5.10.11.4.3.
Splices in spiral reinforcement may be one of the
following:
•
Lap splices of 48.0 uncoated bar diameters, 72.0
coated bar diameters, or 48.0 wire diameters;
•
Approved mechanical connectors; or
•
Approved welded splices.
C5.10.6.3
5.10.6.3—Ties
In tied compression members, all longitudinal bars
or bundles shall be enclosed by lateral ties that shall be
equivalent to:
•
No. 3 bars for No. 10 or smaller bars,
•
No. 4 bars for No. 11 or larger bars, and
•
No. 4 bars for bundled bars.
Figure C5.10.6.3-1 illustrates the placement of
restraining ties in compression members which are not
designed for plastic hinging.
The spacing of ties along the longitudinal axis of
the compression member shall not exceed the least
dimension of the compression member or 12.0 in.
Where two or more bars larger than No. 10 are bundled
together, the spacing shall not exceed half the least
dimension of the member or 6.0 in.
Deformed wire or welded wire fabric of equivalent
area may be used instead of bars.
Figure C5.10.6.3-1—Acceptable Tie Arrangements
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SECTION 5: CONCRETE STRUCTURES
5-121
No longitudinal bar or bundle shall be more than
24.0 in., measured along the tie, from a restrained bar or
bundle. A restrained bar or bundle is one which has
lateral support provided by the corner of a tie having an
included angle of not more than 135 degrees. Where the
column design is based on plastic hinging capability, no
longitudinal bar or bundle shall be farther than 6.0 in.
clear on each side along the tie from such a laterally
supported bar or bundle and the tie reinforcement shall
meet the requirements of Articles 5.10.11.4.1d through
5.10.11.4.1f. Where the bars or bundles are located
around the periphery of a circle, a complete circular tie
may be used if the splices in the ties are staggered.
Ties shall be located vertically not more than half a
tie spacing above the footing or other support and not
more than half a tie spacing below the lowest horizontal
reinforcement in the supported member.
Columns in Seismic Zones 2, 3, and 4 are designed
for plastic hinging. The plastic hinge zone is defined in
Article 5.10.11.4.1c. Additional requirements for
transverse reinforcement for bridges in Seismic Zones 2,
3, and 4 are specified in Articles 5.10.11.3 and
5.10.11.4.1. Plastic hinging may be used as a design
strategy for other extreme events, such as ship collision.
5.10.7—Transverse Reinforcement for Flexural
Members
Compression reinforcement in flexural members,
except deck slabs, shall be enclosed by ties or stirrups
satisfying the size and spacing requirements of
Article 5.10.6 or by welded wire fabric of equivalent
area.
5.10.8—Shrinkage and Temperature Reinforcement
Reinforcement for shrinkage and temperature
stresses shall be provided near surfaces of concrete
exposed to daily temperature changes and in structural
mass
concrete.
Temperature
and
shrinkage
reinforcement to ensure that the total reinforcement on
exposed surfaces is not less than that specified herein.
Reinforcement for shrinkage and temperature may
be in the form of bars, welded wire fabric, or
prestressing tendons.
For bars or welded wire fabric, the area of
reinforcement per foot, on each face and in each
direction, shall satisfy:
1.30bh
2 (b + h) f y
(5.10.8-1)
0.11 ≤ As ≤ 0.60
(5.10.8-2)
As ≥
where:
As =
b
=
h
fy
=
=
area of reinforcement in each direction and
each face (in.2/ft)
least width of component section (in.)
least thickness of component section (in.)
specified yield strength of reinforcing bars
75 ksi
C5.10.8
The comparable equation in ACI was written for
slabs with the reinforcement being distributed equally to
both surfaces of the slabs.
The requirements of this Article are based on ACI
318 and 207.2R. The coefficient in Eq. 5.10.8-1 is the
product of 0.0018, 60 ksi, and 12.0 in./ft and, therefore,
has the units kips/in.-ft.
Eq. 5.10.8-1 is written to show that the total required
reinforcement, As,= 0.0018bh, is distributed uniformly
around the perimeter of the component. It provides a
more uniform approach for components of any size. For
example, a 30.0 ft high × 1.0 ft thick wall section requires
0.126 in.2/ft in each face and each direction; a 4.0 ft × 4.0
ft component requires 0.260 in.2/ft in each face and each
direction; and a 5.0 ft × 20.0 ft footing requires
0.520 in.2/ft in each face and each direction. For circular
or other shapes the equation becomes:
As ≥
1.3 Ag
Perimeter ( f y )
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(C5.10.8-1)
2012
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
5-122
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Where the least dimension varies along the length of
wall, footing, or other component, multiple sections
should be examined to represent the average condition at
each section. Spacing shall not exceed:
•
3.0 times the component thickness, or 18.0 in.
•
12.0 in. for walls and footings greater than 18.0 in.
thick
•
12.0 in. for other components greater than 36.0 in.
thick
For components 6.0 in. or less in thickness the minimum
steel specified may be placed in a single layer.
Shrinkage and temperature steel shall not be required
for:
•
End face of walls 18 in. or less in thickness
•
Side faces of buried footings 36 in. or less in
thickness
•
Faces of all other components, with smaller
dimension less than or equal to 18.0 in.
Permanent prestress of 0.11 ksi is equivalent to the
resistance of the steel specified in Eq. 5.10.8-1 at the
strength limit state. The 0.11 ksi prestress should not be
added to that required for the strength or service limit
states. It is a minimum requirement for shrinkage and
temperature crack control.
The spacing of stress-relieving joints should be
considered in determining the area of shrinkage and
temperature reinforcement.
Surfaces of interior walls of box girders need not be
considered to be exposed to daily temperature changes.
See also Article 12.14.5.8 for additional
requirements for three-sided buried structures.
If prestressing tendons are used as steel for
shrinkage and temperature reinforcement, the tendons
shall provide a minimum average compressive stress of
0.11 ksi on the gross concrete area through which a
crack plane may extend, based on the effective prestress
after losses. Spacing of tendons should not exceed either
72.0 in. or the distance specified in Article 5.10.3.4.
Where the spacing is greater than 54.0 in., bonded
reinforcement shall be provided between tendons, for a
distance equal to the tendon spacing.
5.10.9—Post-Tensioned Anchorage Zones
5.10.9.1—General
C5.10.9.1
Anchorages shall be designed at the strength limit
states for the factored jacking forces as specified in
Article 3.4.3.
For anchorage zones at the end of a component or
segment, the transverse dimensions may be taken as the
depth and width of the section but not larger than the
longitudinal dimension of the component or segment.
The longitudinal extent of the anchorage zone in the
direction of the tendon shall not be less than the greater
of the transverse dimensions of the anchorage zone and
shall not be taken as more than one and one-half times
that dimension.
For intermediate anchorages, the anchorage zone
shall be considered to extend in the direction opposite to
the anchorage force for a distance not less than the
larger of the transverse dimensions of the anchorage
zone.
With slight modifications, the provisions of
Article 5.10.9 are also applicable to the design of
reinforcement under high-load capacity bearings.
The anchorage zone is geometrically defined as the
volume of concrete through which the concentrated
prestressing force at the anchorage device spreads
transversely to a more linear stress distribution across
the entire cross-section at some distance from the
anchorage device.
Within the anchorage zone, the assumption that
plane sections remain plane is not valid.
The dimensions of the anchorage zone are based on
the principle of St. Venant. Provisions for components
with a length smaller than one of its transverse
dimensions were included to address cases such as
transverse prestressing of bridge decks, as shown in
Figure C5.10.9.1-1.
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SECTION 5: CONCRETE STRUCTURES
5-123
Figure C5.10.9.1-1—Geometry of the Anchorage Zones
5.10.9.2—General Zone and Local Zone
C5.10.9.2.1
5.10.9.2.1—General
For design purposes, the anchorage zone shall be
considered as comprised of two regions:
•
The general zone, for which the provisions of
Article 5.10.9.2.2 apply, and
•
The local zone, for which the provisions of Article
5.10.9.2.3 apply.
For intermediate anchorages, large tensile stresses
may exist behind the anchor. These tensile stresses result
from the compatibility of deformations ahead of and
behind the anchorage.
Figure C5.10.9.1-1 illustrates the distinction
between the local and the general zone. The region
subjected to tensile stresses due to spreading of the
tendon force into the structure is the general zone
(Figure C5.10.9.1-1a). The region of high compressive
stresses immediately ahead of the anchorage device is
the local zone (Figure C5.10.9.1-1b).
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
General Zone
a)
Principal Tensile Stresses and the General Zone
Local Zone
b) Principal Compressive Stresses and the Local Zone
Figure C5.10.9.2.1-1—General Zone and Local Zone
5.10.9.2.2—General Zone
The extent of the general zone shall be taken as
identical to that of the overall anchorage zone including
the local zone, defined in Article 5.10.9.1.
Design of general zones shall comply with the
requirements of Article 5.10.9.3.
5.10.9.2.3—Local Zone
Design of local zones shall either comply with the
requirements of Article 5.10.9.7 or be based on the
results of acceptance tests as specified in
Article 5.10.9.7.3 and described in Article 10.3.2.3 of
AASHTO LRFD Bridge Construction Specifications.
For design of the local zone, the effects of high
bearing pressure and the application of confining
reinforcement shall be considered.
Anchorage devices based on the acceptance test of
AASHTO LRFD Bridge Construction Specifications,
Article 10.3.2.3, shall be referred to as special anchorage
devices.
C5.10.9.2.2
In many cases, the general zone and the local zone
can be treated separately, but for small anchorage zones,
such as in slab anchorages, local zone effects, such as high
bearing and confining stresses, and general zone effects,
such as tensile stresses due to spreading of the tendon
force, may occur in the same region. The designer should
account for the influence of overlapping general zones.
C5.10.9.2.3
The local zone is defined as either the rectangular
prism, or, for circular or oval anchorages, the equivalent
rectangular prism of the concrete surrounding and
immediately ahead of the anchorage device and any
integral confining reinforcement. The dimensions of the
local zone are defined in Article 5.10.9.7.1.
The local zone is expected to resist the high local
stresses introduced by the anchorage device and to
transfer them to the remainder of the anchorage zone.
The resistance of the local zone is more influenced by
the characteristics of the anchorage device and its
confining reinforcement than by either the geometry or
the loading of the structure.
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SECTION 5: CONCRETE STRUCTURES
5-125
C5.10.9.2.4
5.10.9.2.4—Responsibilities
The Engineer of Record shall be responsible for the
overall design and approval of working drawings for the
general zone, including the location of the tendons and
anchorage devices, general zone reinforcement, the
stressing sequence, and the design of the local zone for
anchorage devices based on the provisions of
Article 5.10.9.7. The contract documents shall specify
that all working drawings for the local zone must be
approved by the Engineer of Record.
The anchorage device Supplier shall be responsible
for furnishing anchorage devices that satisfy the anchor
efficiency requirements of AASHTO LRFD Bridge
Construction Specifications, Article 10.3.2. If special
anchorage devices are used, the anchorage device
Supplier shall be responsible for furnishing anchorage
devices that also satisfy the acceptance test requirements
of Article 5.10.9.7.3 and of AASHTO LRFD Bridge
Construction Specifications, Article 10.3.2.3. This
acceptance test and the anchor efficiency test shall be
conducted by an independent testing agency acceptable
to the Engineer of Record. The anchorage device
supplier shall provide records of the acceptance test in
conformance with AASHTO LRFD Bridge Construction
Specifications, Article 10.3.2.3.12, to the Engineer of
Record and to the Constructor and shall specify
auxiliary and confining reinforcement, minimum edge
distance, minimum anchor spacing, and minimum
concrete strength at time of stressing required for proper
performance of the local zone.
The responsibilities of the Constructor shall be as
specified in the AASHTO LRFD Bridge Construction
Specifications, Article 10.4.
The Engineer of Record has the responsibility to
indicate the location of individual tendons and
anchorage devices. Should the Designer initially choose
to indicate only total tendon force and eccentricity, he
still retains the responsibility of approving the specific
tendon layout and anchorage arrangement submitted by
a post-tensioning specialist or the Contractor. The
Engineer is responsible for the design of general zone
reinforcement required by the approved tendon layout
and anchorage device arrangement.
The use of special anchorage devices does not
relieve the Engineer of Record from his responsibility to
review the design and working drawings for the
anchorage zone to ensure compliance with the
anchorage device Supplier's specifications.
The anchorage device Supplier has to provide
information regarding all requirements necessary for the
satisfactory performance of the local zone to the
Engineer of Record and to the Contractor. Necessary
local zone confinement reinforcement has to be
specified by the Supplier.
5.10.9.3—Design of the General Zone
5.10.9.3.1—Design Methods
C5.10.9.3.1
For the design of general zones, the following
design methods, conforming to the requirements of
Article 5.10.9.3.2, may be used:
•
Equilibrium-based inelastic models,
termed as “strut-and-tie models;”
generally
•
Refined elastic stress analyses as specified in
Section 4; or
•
Other approximate methods, where applicable.
The effects of stressing sequence and
three-dimensional effects due to concentrated jacking
loads shall be investigated. Three-dimensional effects
may be analyzed using three-dimensional analysis
procedures or may be approximated by considering
separate submodels for two or more planes, in which
case the interaction of the submodels should be
The design methods referred to in this Article are
not meant to preclude other recognized and verified
procedures. In many anchorage applications where
substantial or massive concrete regions surround the
anchorages and where the members are essentially
rectangular without substantial deviations in the force
flow
path,
the
approximate
procedures of
Article 5.10.9.6 can be used. However, in the posttensioning of thin sections, flanged sections, and
irregular sections or where the tendons have appreciable
curvature, the more general procedures of
Article 5.10.9.4 and 5.10.9.5 may be required.
Different anchorage force combinations have a
significant effect on the general zone stresses. Therefore,
it is important to consider not only the final stage of a
stressing sequence with all tendons stressed but also the
intermediate stages.
The provision concerning three-dimensional effects
was included to alert the Designer to effects
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 6: STEEL STRUCTURES
TABLE OF CONTENTS
6
6.1—SCOPE ................................................................................................................................................................. 6-1
6.2—DEFINITIONS ..................................................................................................................................................... 6-1
6.3—NOTATION ....................................................................................................................................................... 6-10
6.4—MATERIALS ..................................................................................................................................................... 6-22
6.4.1—Structural Steels ....................................................................................................................................... 6-22
6.4.2—Pins, Rollers, and Rockers ....................................................................................................................... 6-25
6.4.3—Bolts, Nuts, and Washers ......................................................................................................................... 6-25
6.4.3.1—Bolts ............................................................................................................................................... 6-25
6.4.3.2—Nuts................................................................................................................................................ 6-26
6.4.3.2.1—Nuts Used with Structural Fasteners .................................................................................... 6-26
6.4.3.2.2—Nuts Used with Anchor Bolts .............................................................................................. 6-26
6.4.3.3—Washers ......................................................................................................................................... 6-26
6.4.3.4—Alternative Fasteners ..................................................................................................................... 6-27
6.4.3.5—Load Indicator Devices .................................................................................................................. 6-27
6.4.4—Stud Shear Connectors ............................................................................................................................. 6-27
6.4.5—Weld Metal .............................................................................................................................................. 6-27
6.4.6—Cast Metal ................................................................................................................................................ 6-28
6.4.6.1—Cast Steel and Ductile Iron ............................................................................................................ 6-28
6.4.6.2—Malleable Castings......................................................................................................................... 6-28
6.4.6.3—Cast Iron ........................................................................................................................................ 6-28
6.4.7—Stainless Steel .......................................................................................................................................... 6-28
6.4.8—Cables ...................................................................................................................................................... 6-28
6.4.8.1—Bright Wire .................................................................................................................................... 6-28
6.4.8.2—Galvanized Wire ............................................................................................................................ 6-28
6.4.8.3—Epoxy-Coated Wire ....................................................................................................................... 6-29
6.4.8.4—Bridge Strand ................................................................................................................................. 6-29
6.5—LIMIT STATES ................................................................................................................................................. 6-29
6.5.1—General ..................................................................................................................................................... 6-29
6.5.2—Service Limit State ................................................................................................................................... 6-29
6.5.3—Fatigue and Fracture Limit State .............................................................................................................. 6-29
6.5.4—Strength Limit State ................................................................................................................................. 6-29
6.5.4.1—General........................................................................................................................................... 6-29
6.5.4.2—Resistance Factors ......................................................................................................................... 6-30
6.5.5—Extreme Event Limit State ....................................................................................................................... 6-31
6.6—FATIGUE AND FRACTURE CONSIDERATIONS ........................................................................................ 6-31
6.6.1—Fatigue ..................................................................................................................................................... 6-31
6.6.1.1—General........................................................................................................................................... 6-31
6.6.1.2—Load-Induced Fatigue .................................................................................................................... 6-32
6.6.1.2.1—Application .......................................................................................................................... 6-32
6.6.1.2.2—Design Criteria ..................................................................................................................... 6-33
6-i
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
6-ii
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6.6.1.2.3—Detail Categories ..................................................................................................................6-34
6.6.1.2.4—Detailing to Reduce Constraint ............................................................................................6-48
6.6.1.2.5—Fatigue Resistance ...............................................................................................................6-48
6.6.1.3—Distortion-Induced Fatigue ............................................................................................................ 6-51
6.6.1.3.1—Transverse Connection Plates ..............................................................................................6-52
6.6.1.3.2—Lateral Connection Plates ....................................................................................................6-52
6.6.1.3.3—Orthotropic Decks ................................................................................................................6-53
6.6.2—Fracture ....................................................................................................................................................6-53
6.7—GENERAL DIMENSION AND DETAIL REQUIREMENTS .......................................................................... 6-57
6.7.1—Effective Length of Span ..........................................................................................................................6-57
6.7.2—Dead Load Camber...................................................................................................................................6-57
6.7.3—Minimum Thickness of Steel....................................................................................................................6-59
6.7.4—Diaphragms and Cross-Frames.................................................................................................................6-59
6.7.4.1—General ........................................................................................................................................... 6-59
6.7.4.2—I-Section Members ......................................................................................................................... 6-60
6.7.4.3—Box Section Members .................................................................................................................... 6-62
6.7.4.4—Trusses and Arches ........................................................................................................................ 6-64
6.7.5—Lateral Bracing .........................................................................................................................................6-65
6.7.5.1—General ........................................................................................................................................... 6-65
6.7.5.2—I-Section Members ......................................................................................................................... 6-65
6.7.5.3—Tub Section Members .................................................................................................................... 6-66
6.7.5.4—Trusses ........................................................................................................................................... 6-68
6.7.6—Pins ...........................................................................................................................................................6-68
6.7.6.1—Location ......................................................................................................................................... 6-68
6.7.6.2—Resistance ...................................................................................................................................... 6-69
6.7.6.2.1—Combined Flexure and Shear ...............................................................................................6-69
6.7.6.2.2—Bearing .................................................................................................................................6-69
6.7.6.3—Minimum Size Pin for Eyebars ...................................................................................................... 6-69
6.7.6.4—Pins and Pin Nuts ........................................................................................................................... 6-70
6.7.7—Heat-Curved Rolled Beams and Welded Plate Girders ............................................................................6-70
6.7.7.1—Scope .............................................................................................................................................. 6-70
6.7.7.2—Minimum Radius of Curvature....................................................................................................... 6-70
6.7.7.3—Camber ........................................................................................................................................... 6-71
6.8—TENSION MEMBERS ...................................................................................................................................... 6-71
6.8.1—General .....................................................................................................................................................6-71
6.8.2—Tensile Resistance ....................................................................................................................................6-72
6.8.2.1—General ........................................................................................................................................... 6-72
6.8.2.2—Reduction Factor, U ....................................................................................................................... 6-73
6.8.2.3—Combined Tension and Flexure ..................................................................................................... 6-76
6.8.3—Net Area ...................................................................................................................................................6-77
6.8.4—Limiting Slenderness Ratio ......................................................................................................................6-77
6.8.5—Builtup Members ......................................................................................................................................6-78
6.8.5.1—General ........................................................................................................................................... 6-78
6.8.5.2—Perforated Plates ............................................................................................................................ 6-78
6.8.6—Eyebars .....................................................................................................................................................6-78
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 6: STEEL STRUCTURES
6-iii
6.8.6.1—Factored Resistance ....................................................................................................................... 6-78
6.8.6.2—Proportions ..................................................................................................................................... 6-78
6.8.6.3—Packing .......................................................................................................................................... 6-79
6.8.7—Pin-Connected Plates ............................................................................................................................... 6-79
6.8.7.1—General........................................................................................................................................... 6-79
6.8.7.2—Pin Plates ....................................................................................................................................... 6-79
6.8.7.3—Proportions ..................................................................................................................................... 6-80
6.8.7.4—Packing .......................................................................................................................................... 6-80
6.9—COMPRESSION MEMBERS ........................................................................................................................... 6-80
6.9.1—General ..................................................................................................................................................... 6-80
6.9.2—Compressive Resistance ........................................................................................................................... 6-81
6.9.2.1—Axial Compression ........................................................................................................................ 6-81
6.9.2.2—Combined Axial Compression and Flexure ................................................................................... 6-81
6.9.3—Limiting Slenderness Ratio ...................................................................................................................... 6-82
6.9.4—Noncomposite Members .......................................................................................................................... 6-82
6.9.4.1—Nominal Compressive Resistance .................................................................................................. 6-82
6.9.4.1.1—General ................................................................................................................................ 6-82
6.9.4.1.2—Elastic Flexural Buckling Resistance................................................................................... 6-86
6.9.4.1.3—Elastic Torsional Buckling and Flexural-Torsional Buckling Resistance ............................ 6-86
6.9.4.2—Nonslender and Slender Member Elements ................................................................................... 6-88
6.9.4.2.1—Nonslender Member Elements ............................................................................................. 6-88
6.9.4.3—Built-up Members .......................................................................................................................... 6-93
6.9.4.3.1—General ................................................................................................................................ 6-93
6.9.4.3.2—Perforated Plates .................................................................................................................. 6-94
6.9.4.4—Single-Angle Members .................................................................................................................. 6-95
6.9.5—Composite Members ................................................................................................................................ 6-98
6.9.5.1—Nominal Compressive Resistance .................................................................................................. 6-98
6.9.5.2—Limitations ..................................................................................................................................... 6-99
6.9.5.2.1—General ................................................................................................................................ 6-99
6.9.5.2.2—Concrete-Filled Tubes ......................................................................................................... 6-99
6.9.5.2.3—Concrete-Encased Shapes .................................................................................................... 6-99
6.10—I-SECTION FLEXURAL MEMBERS .......................................................................................................... 6-100
6.10.1—General ................................................................................................................................................. 6-100
6.10.1.1—Composite Sections.................................................................................................................... 6-102
6.10.1.1.1—Stresses ............................................................................................................................ 6-102
6.10.1.1.1a—Sequence of Loading .............................................................................................. 6-102
6.10.1.1.1b—Stresses for Sections in Positive Flexure ................................................................ 6-102
6.10.1.1.1c—Stresses for Sections in Negative Flexure ............................................................... 6-103
6.10.1.1.1d—Concrete Deck Stresses .......................................................................................... 6-103
6.10.1.1.1e—Effective Width of Concrete Deck .......................................................................... 6-103
6.10.1.2—Noncomposite Sections .............................................................................................................. 6-103
6.10.1.3—Hybrid Sections.......................................................................................................................... 6-104
6.10.1.4—Variable Web Depth Members .................................................................................................. 6-104
6.10.1.5—Stiffness ..................................................................................................................................... 6-106
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
6-iv
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6.10.1.6—Flange Stresses and Member Bending Moments ....................................................................... 6-106
6.10.1.7—Minimum Negative Flexure Concrete Deck Reinforcement ...................................................... 6-108
6.10.1.8—Net Section Fracture ................................................................................................................... 6-110
6.10.1.9—Web Bend-Buckling Resistance ................................................................................................. 6-110
6.10.1.9.1—Webs without Longitudinal Stiffeners .............................................................................6-110
6.10.1.9.2—Webs with Longitudinal Stiffeners ..................................................................................6-112
6.10.1.10—Flange-Strength Reduction Factors .......................................................................................... 6-113
6.10.1.10.1—Hybrid Factor, Rh ...........................................................................................................6-113
6.10.1.10.2—Web Load-Shedding Factor, Rb ......................................................................................6-114
6.10.2—Cross-Section Proportion Limits ..........................................................................................................6-118
6.10.2.1—Web Proportions ........................................................................................................................ 6-118
6.10.2.1.1—Webs without Longitudinal Stiffeners .............................................................................6-118
6.10.2.1.2—Webs with Longitudinal Stiffeners ..................................................................................6-119
6.10.2.2—Flange Proportions ..................................................................................................................... 6-119
6.10.3—Constructibility .....................................................................................................................................6-120
6.10.3.1—General ....................................................................................................................................... 6-120
6.10.3.2—Flexure ....................................................................................................................................... 6-121
6.10.3.2.1—Discretely Braced Flanges in Compression......................................................................6-121
6.10.3.2.2—Discretely Braced Flanges in Tension ..............................................................................6-123
6.10.3.2.3 Continuously Braced Flanges in Tension or Compression .................................................6-123
6.10.3.2.4—Concrete Deck ..................................................................................................................6-123
6.10.3.3—Shear .......................................................................................................................................... 6-124
6.10.3.4—Deck Placement.......................................................................................................................... 6-124
6.10.3.5—Dead Load Deflections ............................................................................................................... 6-126
6.10.4—Service Limit State ...............................................................................................................................6-127
6.10.4.1—Elastic Deformations .................................................................................................................. 6-127
6.10.4.2—Permanent Deformations ............................................................................................................ 6-127
6.10.4.2.1—General .............................................................................................................................6-127
6.10.4.2.2—Flexure .............................................................................................................................6-127
6.10.5—Fatigue and Fracture Limit State ..........................................................................................................6-130
6.10.5.1—Fatigue........................................................................................................................................ 6-130
6.10.5.2—Fracture ...................................................................................................................................... 6-130
6.10.5.3—Special Fatigue Requirement for Webs ...................................................................................... 6-130
6.10.6—Strength Limit State..............................................................................................................................6-131
6.10.6.1—General ....................................................................................................................................... 6-131
6.10.6.2—Flexure ....................................................................................................................................... 6-132
6.10.6.2.1—General .............................................................................................................................6-132
6.10.6.2.2—Composite Sections in Positive Flexure ...........................................................................6-132
6.10.6.2.3—Composite Sections in Negative Flexure and Noncomposite Sections ............................6-134
6.10.6.3—Shear .......................................................................................................................................... 6-136
6.10.6.4—Shear Connectors ....................................................................................................................... 6-136
6.10.7—Flexural Resistance—Composite Sections in Positive Flexure ............................................................6-136
6.10.7.1—Compact Sections ....................................................................................................................... 6-136
6.10.7.1.1—General .............................................................................................................................6-136
6.10.7.1.2—Nominal Flexural Resistance ...........................................................................................6-137
6.10.7.2—Noncompact Sections ................................................................................................................. 6-139
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 6: STEEL STRUCTURES
6-v
6.10.7.2.1—General ............................................................................................................................ 6-139
6.10.7.2.2—Nominal Flexural Resistance ........................................................................................... 6-140
6.10.7.3—Ductility Requirement ................................................................................................................ 6-140
6.10.8—Flexural Resistance—Composite Sections in Negative Flexure and Noncomposite Sections ............. 6-141
6.10.8.1—General....................................................................................................................................... 6-141
6.10.8.1.1—Discretely Braced Flanges in Compression ..................................................................... 6-141
6.10.8.1.2—Discretely Braced Flanges in Tension ............................................................................. 6-141
6.10.8.1.3—Continuously Braced Flanges in Tension or Compression .............................................. 6-141
6.10.8.2 Compression-Flange Flexural Resistance ..................................................................................... 6-142
6.10.8.2.1—General ............................................................................................................................ 6-142
6.10.8.2.2—Local Buckling Resistance............................................................................................... 6-143
6.10.8.2.3—Lateral Torsional Buckling Resistance ............................................................................ 6-144
6.10.8.3—Tension-Flange Flexural Resistance .......................................................................................... 6-150
6.10.9—Shear Resistance .................................................................................................................................. 6-151
6.10.9.1—General....................................................................................................................................... 6-151
6.10.9.2—Nominal Resistance of Unstiffened Webs ................................................................................. 6-152
6.10.9.3—Nominal Resistance of Stiffened Webs...................................................................................... 6-152
6.10.9.3.1—General ............................................................................................................................ 6-152
6.10.9.3.2—Interior Panels .................................................................................................................. 6-153
6.10.9.3.3—End Panels ....................................................................................................................... 6-154
6.10.10—Shear Connectors ............................................................................................................................... 6-154
6.10.10.1—General..................................................................................................................................... 6-154
6.10.10.1.1—Types ............................................................................................................................. 6-155
6.10.10.1.2—Pitch ............................................................................................................................... 6-155
6.10.10.1.3—Transverse Spacing ........................................................................................................ 6-156
6.10.10.1.4—Cover and Penetration .................................................................................................... 6-157
6.10.10.2—Fatigue Resistance ................................................................................................................... 6-157
6.10.10.3—Special Requirements for Points of Permanent Load Contraflexure ........................................ 6-158
6.10.10.4—Strength Limit State ................................................................................................................. 6-158
6.10.10.4.1—General .......................................................................................................................... 6-158
6.10.10.4.2—Nominal Shear Force ..................................................................................................... 6-159
6.10.10.4.3—Nominal Shear Resistance ............................................................................................. 6-161
6.10.11—Stiffeners ............................................................................................................................................ 6-161
6.10.11.1—Transverse Stiffeners ............................................................................................................... 6-161
6.10.11.1.1—General .......................................................................................................................... 6-161
6.10.11.1.2—Projecting Width ............................................................................................................ 6-162
6.10.11.1.3—Moment of Inertia .......................................................................................................... 6-162
6.10.11.2—Bearing Stiffeners .................................................................................................................... 6-165
6.10.11.2.1—General .......................................................................................................................... 6-165
6.10.11.2.2—Projecting Width ............................................................................................................ 6-165
6.10.11.2.3—Bearing Resistance......................................................................................................... 6-165
6.10.11.2.4—Axial Resistance of Bearing Stiffeners .......................................................................... 6-166
6.10.11.2.4a—General.................................................................................................................. 6-166
6.10.11.2.4b—Effective Section................................................................................................... 6-166
6.10.11.3—Longitudinal Stiffeners ............................................................................................................ 6-166
6.10.11.3.1—General .......................................................................................................................... 6-166
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
6-vi
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6.10.11.3.2—Projecting Width ............................................................................................................6-169
6.10.11.3.3—Moment of Inertia and Radius of Gyration ....................................................................6-169
6.10.12—Cover Plates .......................................................................................................................................6-170
6.10.12.1—General ..................................................................................................................................... 6-170
6.10.12.2—End Requirements .................................................................................................................... 6-170
6.10.12.2.1—General ...........................................................................................................................6-170
6.10.12.2.2—Welded Ends ..................................................................................................................6-171
6.10.12.2.3—Bolted Ends ....................................................................................................................6-171
6.11—BOX-SECTION FLEXURAL MEMBERS ................................................................................................... 6-171
6.11.1—General .................................................................................................................................................6-171
6.11.1.1—Stress Determinations................................................................................................................. 6-173
6.11.1.2—Bearings ..................................................................................................................................... 6-176
6.11.1.3—Flange-to-Web Connections ....................................................................................................... 6-176
6.11.1.4—Access and Drainage .................................................................................................................. 6-177
6.11.2—Cross-Section Proportion Limits ..........................................................................................................6-177
6.11.2.1—Web Proportions ........................................................................................................................ 6-177
6.11.2.1.1—General .............................................................................................................................6-177
6.11.2.1.2—Webs without Longitudinal Stiffeners .............................................................................6-178
6.11.2.1.3—Webs with Longitudinal Stiffeners ..................................................................................6-178
6.11.2.2—Flange Proportions ..................................................................................................................... 6-178
6.11.2.3—Special Restrictions on Use of Live Load Distribution Factor for Multiple Box Sections ......... 6-178
6.11.3—Constructibility .....................................................................................................................................6-179
6.11.3.1—General ....................................................................................................................................... 6-179
6.11.3.2—Flexure ....................................................................................................................................... 6-179
6.11.3.3—Shear .......................................................................................................................................... 6-182
6.11.4—Service Limit State ...............................................................................................................................6-182
6.11.5—Fatigue and Fracture Limit State ..........................................................................................................6-183
6.11.6—Strength Limit State..............................................................................................................................6-185
6.11.6.1—General ....................................................................................................................................... 6-185
6.11.6.2—Flexure ....................................................................................................................................... 6-185
6.11.6.2.1—General .............................................................................................................................6-185
6.11.6.2.2—Sections in Positive Flexure .............................................................................................6-185
6.11.6.2.3—Sections in Negative Flexure ...........................................................................................6-186
6.11.6.3—Shear .......................................................................................................................................... 6-186
6.11.6.4—Shear Connectors ....................................................................................................................... 6-186
6.11.7—Flexural Resistance—Sections in Positive Flexure ..............................................................................6-187
6.11.7.1—Compact Sections ....................................................................................................................... 6-187
6.11.7.1.1—General .............................................................................................................................6-187
6.11.7.1.2—Nominal Flexural Resistance ...........................................................................................6-187
6.11.7.2—Noncompact Sections ................................................................................................................. 6-187
6.11.7.2.1—General .............................................................................................................................6-187
6.11.7.2.2—Nominal Flexural Resistance ...........................................................................................6-188
6.11.8—Flexural Resistance—Sections in Negative Flexure.............................................................................6-189
6.11.8.1—General ....................................................................................................................................... 6-189
6.11.8.1.1—Box Flanges in Compression ...........................................................................................6-189
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 6: STEEL STRUCTURES
6-vii
6.11.8.1.2—Continuously Braced Flanges in Tension ........................................................................ 6-190
6.11.8.2—Flexural Resistance of Box Flanges in Compression ................................................................. 6-190
6.11.8.2.1—General ............................................................................................................................ 6-190
6.11.8.2.2—Unstiffened Flanges ......................................................................................................... 6-190
6.11.8.2.3—Longitudinally Stiffened Flanges ..................................................................................... 6-192
6.11.8.3—Tension-Flange Flexural Resistance .......................................................................................... 6-193
6.11.9—Shear Resistance .................................................................................................................................. 6-194
6.11.10—Shear Connectors ............................................................................................................................... 6-194
6.11.11—Stiffeners ............................................................................................................................................ 6-195
6.11.11.1—Web Stiffeners ......................................................................................................................... 6-195
6.11.11.2—Longitudinal Compression-Flange Stiffeners .......................................................................... 6-196
6.12—MISCELLANEOUS FLEXURAL MEMBERS ............................................................................................ 6-199
6.12.1—General ................................................................................................................................................. 6-199
6.12.1.1—Scope ......................................................................................................................................... 6-199
6.12.1.2—Strength Limit State ................................................................................................................... 6-199
6.12.1.2.1—Flexure ............................................................................................................................. 6-199
6.12.1.2.2—Combined Flexure and Axial Load .................................................................................. 6-199
6.12.1.2.3—Shear ................................................................................................................................ 6-200
6.12.1.2.3a—General.................................................................................................................... 6-200
6.12.1.2.3b—Square and Rectangular HSS .................................................................................. 6-200
6.12.1.2.3c—Circular Tubes ........................................................................................................ 6-200
6.12.2—Nominal Flexural Resistance ............................................................................................................... 6-201
6.12.2.1—General....................................................................................................................................... 6-201
6.12.2.2—Noncomposite Members ............................................................................................................ 6-201
6.12.2.2.1—I- and H-Shaped Members ............................................................................................... 6-201
6.12.2.2.2—Box-Shaped Members...................................................................................................... 6-202
6.12.2.2.3—Circular Tubes ................................................................................................................. 6-204
6.12.2.2.4—Tees and Double Angles .................................................................................................. 6-205
6.12.2.2.5—Channels .......................................................................................................................... 6-207
6.12.2.2.6—Single Angles ................................................................................................................... 6-209
6.12.2.2.7—Rectangular Bars and Solid Rounds ................................................................................ 6-210
6.12.2.3—Composite Members .................................................................................................................. 6-211
6.12.2.3.1—Concrete-Encased Shapes ................................................................................................ 6-211
6.12.2.3.2—Concrete-Filled Tubes...................................................................................................... 6-212
6.12.3—Nominal Shear Resistance of Composite Members ............................................................................. 6-212
6.12.3.1—Concrete-Encased Shapes .......................................................................................................... 6-212
6.12.3.2—Concrete-Filled Tubes ................................................................................................................ 6-213
6.12.3.2.1—Rectangular Tubes ........................................................................................................... 6-213
6.12.3.2.2—Circular Tubes ................................................................................................................. 6-213
6.13—CONNECTIONS AND SPLICES.................................................................................................................. 6-213
6.13.1—General ................................................................................................................................................. 6-213
6.13.2—Bolted Connections .............................................................................................................................. 6-214
6.13.2.1—General....................................................................................................................................... 6-214
6.13.2.1.1—Slip-Critical Connections ................................................................................................. 6-214
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
6-viii
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6.13.2.1.2—Bearing-Type Connections...............................................................................................6-215
6.13.2.2—Factored Resistance.................................................................................................................... 6-215
6.13.2.3—Bolts, Nuts, and Washers ........................................................................................................... 6-216
6.13.2.3.1—Bolts and Nuts ..................................................................................................................6-216
6.13.2.3.2—Washers............................................................................................................................6-216
6.13.2.4—Holes .......................................................................................................................................... 6-217
6.13.2.4.1—Type .................................................................................................................................6-217
6.13.2.4.1a—General .................................................................................................................... 6-217
6.13.2.4.1b—Oversize Holes ........................................................................................................ 6-217
6.13.2.4.1c—Short-Slotted Holes ................................................................................................. 6-217
6.13.2.4.1d—Long-Slotted Holes ................................................................................................. 6-217
6.13.2.4.2—Size ..................................................................................................................................6-217
6.13.2.5—Size of Bolts ............................................................................................................................... 6-218
6.13.2.6—Spacing of Bolts ......................................................................................................................... 6-218
6.13.2.6.1—Minimum Spacing and Clear Distance .............................................................................6-218
6.13.2.6.2—Maximum Spacing for Sealing Bolts ...............................................................................6-218
6.13.2.6.3—Maximum Pitch for Stitch Bolts.......................................................................................6-219
6.13.2.6.4—Maximum Pitch for Stitch Bolts at the End of Compression Members............................6-219
6.13.2.6.5—End Distance ....................................................................................................................6-219
6.13.2.6.6—Edge Distances .................................................................................................................6-220
6.13.2.7—Shear Resistance ........................................................................................................................ 6-220
6.13.2.8—Slip Resistance ........................................................................................................................... 6-221
6.13.2.9—Bearing Resistance at Bolt Holes ............................................................................................... 6-224
6.13.2.10—Tensile Resistance .................................................................................................................... 6-225
6.13.2.10.1—General ...........................................................................................................................6-225
6.13.2.10.2—Nominal Tensile Resistance ...........................................................................................6-225
6.13.2.10.3—Fatigue Resistance .........................................................................................................6-225
6.13.2.10.4—Prying Action .................................................................................................................6-225
6.13.2.11—Combined Tension and Shear................................................................................................... 6-226
6.13.2.12—Shear Resistance of Anchor Bolts ............................................................................................ 6-226
6.13.3—Welded Connections ............................................................................................................................6-227
6.13.3.1—General ....................................................................................................................................... 6-227
6.13.3.2—Factored Resistance.................................................................................................................... 6-227
6.13.3.2.1—General .............................................................................................................................6-227
6.13.3.2.2—Complete Penetration Groove-Welded Connections ........................................................6-227
6.13.3.2.2a—Tension and Compression ....................................................................................... 6-227
6.13.3.2.2b—Shear ....................................................................................................................... 6-227
6.13.3.2.3—Partial Penetration Groove-Welded Connections .............................................................6-228
6.13.3.2.3a—Tension or Compression.......................................................................................... 6-228
6.13.3.2.3b—Shear ....................................................................................................................... 6-228
6.13.3.2.4—Fillet-Welded Connections...............................................................................................6-228
6.13.3.2.4a—Tension and Compression ....................................................................................... 6-228
6.13.3.2.4b—Shear ....................................................................................................................... 6-229
6.13.3.3—Effective Area ............................................................................................................................ 6-229
6.13.3.4—Size of Fillet Welds .................................................................................................................... 6-229
6.13.3.5—Minimum Effective Length of Fillet Welds ............................................................................... 6-230
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 6: STEEL STRUCTURES
6-ix
6.13.3.6—Fillet Weld End Returns............................................................................................................. 6-230
6.13.3.7—Seal Welds ................................................................................................................................. 6-230
6.13.4—Block Shear Rupture Resistance .......................................................................................................... 6-230
6.13.5—Connection Elements ........................................................................................................................... 6-231
6.13.5.1—General....................................................................................................................................... 6-231
6.13.5.2—Tension ...................................................................................................................................... 6-231
6.13.5.3—Shear .......................................................................................................................................... 6-232
6.13.6—Splices .................................................................................................................................................. 6-232
6.13.6.1—Bolted Splices ............................................................................................................................ 6-232
6.13.6.1.1—General ............................................................................................................................ 6-232
6.13.6.1.2—Tension Members ............................................................................................................ 6-232
6.13.6.1.3—Compression Members .................................................................................................... 6-233
6.13.6.1.4—Flexural Members ............................................................................................................ 6-233
6.13.6.1.4a—General.................................................................................................................... 6-233
6.13.6.1.4b—Web Splices ............................................................................................................ 6-234
6.13.6.1.4c—Flange Splices ......................................................................................................... 6-238
6.13.6.1.5—Fillers ............................................................................................................................... 6-241
6.13.6.2—Welded Splices .......................................................................................................................... 6-242
6.13.7—Rigid Frame Connections..................................................................................................................... 6-243
6.13.7.1—General....................................................................................................................................... 6-243
6.13.7.2—Webs .......................................................................................................................................... 6-243
6.14—PROVISIONS FOR STRUCTURE TYPES .................................................................................................. 6-244
6.14.1—Through-Girder Spans.......................................................................................................................... 6-244
6.14.2—Trusses ................................................................................................................................................. 6-244
6.14.2.1—General....................................................................................................................................... 6-244
6.14.2.2—Truss Members .......................................................................................................................... 6-245
6.14.2.3—Secondary Stresses ..................................................................................................................... 6-245
6.14.2.4—Diaphragms ................................................................................................................................ 6-245
6.14.2.5—Camber ....................................................................................................................................... 6-245
6.14.2.6—Working Lines and Gravity Axes .............................................................................................. 6-245
6.14.2.7—Portal and Sway Bracing ............................................................................................................ 6-246
6.14.2.7.1—General ............................................................................................................................ 6-246
6.14.2.7.2—Through-Truss Spans ....................................................................................................... 6-246
6.14.2.7.3—Deck Truss Spans ............................................................................................................ 6-246
6.14.2.8—Gusset Plates .............................................................................................................................. 6-246
6.14.2.9—Half Through-Trusses ................................................................................................................ 6-247
6.14.2.10—Factored Resistance ................................................................................................................. 6-247
6.14.3—Orthotropic Deck Superstructures ........................................................................................................ 6-247
6.14.3.1—General....................................................................................................................................... 6-247
6.14.3.2—Decks in Global Compression.................................................................................................... 6-247
6.14.3.2.1—General ............................................................................................................................ 6-247
6.14.3.2.2—Local Buckling ................................................................................................................ 6-248
6.14.3.2.3—Panel Buckling ................................................................................................................. 6-248
6.14.3.3—Effective Width of Deck ............................................................................................................ 6-249
6.14.3.4—Superposition of Global and Local Effects ................................................................................ 6-249
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
6-x
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6.14.4—Solid Web Arches ................................................................................................................................6-249
6.14.4.1—Moment Amplification for Deflection ........................................................................................ 6-249
6.14.4.2—Web Slenderness ........................................................................................................................ 6-249
6.14.4.3—Flange Stability .......................................................................................................................... 6-250
6.15—PILES ............................................................................................................................................................. 6-250
6.15.1—General .................................................................................................................................................6-250
6.15.2—Structural Resistance ............................................................................................................................6-250
6.15.3—Compressive Resistance .......................................................................................................................6-252
6.15.3.1—Axial Compression ..................................................................................................................... 6-252
6.15.3.2—Combined Axial Compression and Flexure................................................................................ 6-252
6.15.3.3—Buckling ..................................................................................................................................... 6-252
6.15.4—Maximum Permissible Driving Stresses ...............................................................................................6-252
6.16—PROVISIONS FOR SEISMIC DESIGN ........................................................................................................ 6-252
6.16.1—General .................................................................................................................................................6-252
6.16.2—Materials...............................................................................................................................................6-254
6.16.3—Design Requirements for Seismic Zone 1 ............................................................................................6-254
6.16.4—Design Requirements for Seismic Zones 2, 3, or 4 ..............................................................................6-254
6.16.4.1—General ....................................................................................................................................... 6-254
6.16.4.2—Deck ........................................................................................................................................... 6-255
6.16.4.3—Shear Connectors ....................................................................................................................... 6-256
6.16.4.4—Elastic Superstructures ............................................................................................................... 6-259
6.17—REFERENCES ............................................................................................................................................... 6-259
APPENDIX A6—FLEXURAL RESISTANCE OF STRAIGHT COMPOSITE I-SECTIONS IN
NEGATIVE FLEXURE AND STRAIGHT NONCOMPOSITE I-SECTIONS WITH COMPACT OR
NONCOMPACT WEBS ........................................................................................................................................... 6-271
A6.1—GENERAL .................................................................................................................................................... 6-271
A6.1.1—Sections with Discretely Braced Compression Flanges.......................................................................6-272
A6.1.2—Sections with Discretely Braced Tension Flanges ...............................................................................6-273
A6.1.3 Sections with Continuously Braced Compression Flanges ....................................................................6-274
A6.1.4 Sections with Continuously Braced Tension Flanges.............................................................................6-274
A6.2—WEB PLASTIFICATION FACTORS .......................................................................................................... 6-274
A6.2.1—Compact Web Sections .......................................................................................................................6-274
A6.2.2—Noncompact Web Sections..................................................................................................................6-275
A6.3—FLEXURAL RESISTANCE BASED ON THE COMPRESSION FLANGE ............................................... 6-277
A6.3.1—General ................................................................................................................................................6-277
A6.3.2—Local Buckling Resistance ..................................................................................................................6-278
A6.3.3—Lateral Torsional Buckling Resistance ................................................................................................6-279
A6.4—FLEXURAL RESISTANCE BASED ON TENSION FLANGE YIELDING .............................................. 6-282
APPENDIX B6—MOMENT REDISTRIBUTION FROM INTERIOR–PIER I-SECTIONS IN STRAIGHT
CONTINUOUS-SPAN BRIDGES............................................................................................................................ 6-283
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
SECTION 6: STEEL STRUCTURES
6-xi
B6.1—GENERAL .................................................................................................................................................... 6-283
B6.2—SCOPE .......................................................................................................................................................... 6-283
B6.2.1—Web Proportions .................................................................................................................................. 6-284
B6.2.2—Compression Flange Proportions......................................................................................................... 6-284
B6.2.3—Section Transitions .............................................................................................................................. 6-285
B6.2.4—Compression Flange Bracing .............................................................................................................. 6-285
B6.2.5—Shear.................................................................................................................................................... 6-285
B6.2.6—Bearing Stiffeners ................................................................................................................................ 6-285
B6.3—SERVICE LIMIT STATE ............................................................................................................................. 6-286
B6.3.1—General ................................................................................................................................................ 6-286
B6.3.2—Flexure ................................................................................................................................................ 6-286
B6.3.2.1—Adjacent to Interior-Pier Sections ............................................................................................. 6-286
B6.3.2.2—At All Other Locations .............................................................................................................. 6-286
B6.3.3—Redistribution Moments ...................................................................................................................... 6-287
B6.3.3.1—At Interior-Pier Sections ............................................................................................................ 6-287
B6.3.3.2—At All Other Locations .............................................................................................................. 6-287
B6.4—STRENGTH LIMIT STATE .......................................................................................................................... 6-288
B6.4.1—Flexural Resistance ............................................................................................................................. 6-288
B6.4.1.1—Adjacent to Interior-Pier Sections ............................................................................................. 6-288
B6.4.1.2—At All Other Locations .............................................................................................................. 6-288
B6.4.2—Redistribution Moments ...................................................................................................................... 6-288
B6.4.2.1—At Interior-Pier Sections ............................................................................................................ 6-288
B6.4.2.2—At All Other Sections ................................................................................................................ 6-289
B6.5—EFFECTIVE PLASTIC MOMENT .............................................................................................................. 6-289
B6.5.1—Interior-Pier Sections with Enhanced Moment-Rotation Characteristics ............................................ 6-289
B6.5.2—All Other Interior-Pier Sections ........................................................................................................... 6-290
B6.6—REFINED METHOD .................................................................................................................................... 6-290
B6.6.1—General ................................................................................................................................................ 6-290
B6.6.2—Nominal Moment-Rotation Curves ..................................................................................................... 6-292
APPENDIX C6—BASIC STEPS FOR STEEL BRIDGE SUPERSTRUCTURES ................................................. 6-295
C6.1—GENERAL .................................................................................................................................................... 6-295
C6.2—GENERAL CONSIDERATIONS ................................................................................................................. 6-295
C6.3—SUPERSTRUCTURE DESIGN .................................................................................................................... 6-295
C6.4—FLOWCHARTS FOR FLEXURAL DESIGN OF I-SECTIONS.................................................................. 6-300
C6.4.1—Flowchart for LRFD Article 6.10.3 ..................................................................................................... 6-300
C6.4.2—Flowchart for LRFD Article 6.10.4 ..................................................................................................... 6-301
C6.4.3—Flowchart for LRFD Article 6.10.5 ..................................................................................................... 6-302
C6.4.4—Flowchart for LRFD Article 6.10.6 ..................................................................................................... 6-303
C6.4.5—Flowchart for LRFD Article 6.10.7 ..................................................................................................... 6-304
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
6-xii
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
C6.4.6—Flowchart for LRFD Article 6.10.8 .....................................................................................................6-305
C6.4.7—Flowchart for Appendix A6 .................................................................................................................6-307
C6.4.8—Flowchart for Article D6.4.1 ...............................................................................................................6-309
C6.4.9—Flowchart for Article D6.4.2 ...............................................................................................................6-310
C6.4.10—Moment Gradient Modifier, Cb (Sample Cases) ................................................................................6-311
APPENDIX D6—FUNDAMENTAL CALCULATIONS FOR FLEXURAL MEMBERS ..................................... 6-313
D6.1—PLASTIC MOMENT .................................................................................................................................... 6-313
D6.2—YIELD MOMENT ........................................................................................................................................ 6-315
D6.2.1—Noncomposite Sections .......................................................................................................................6-315
D6.2.2—Composite Sections in Positive Flexure ..............................................................................................6-316
D6.2.3—Composite Sections in Negative Flexure .............................................................................................6-316
D6.2.4—Sections with Cover Plates ..................................................................................................................6-317
D6.3—DEPTH OF THE WEB IN COMPRESSION ................................................................................................ 6-317
D6.3.1—In the Elastic Range (Dc) .....................................................................................................................6-317
D6.3.2—At Plastic Moment (Dcp) ......................................................................................................................6-318
D6.4—LATERAL TORSIONAL BUCKLING EQUATIONS FOR CB > 1.0, WITH EMPHASIS
ON UNBRACED LENGTH REQUIREMENTS FOR DEVELOPMENT OF THE MAXIMUM FLEXURAL
RESISTANCE........................................................................................................................................................... 6-319
D6.4.1—By the Provisions of Article 6.10.8.2.3 ...............................................................................................6-319
D6.4.2—By the Provisions of Article A6.3.3 ....................................................................................................6-320
D6.5—CONCENTRATED LOADS APPLIED TO WEBS WITHOUT BEARING STIFFENERS ....................... 6-320
D6.5.1—General ................................................................................................................................................6-320
D6.5.2—Web Local Yielding ............................................................................................................................6-321
D6.5.3—Web Crippling .....................................................................................................................................6-321
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 6
STEEL STRUCTURES
6.1—SCOPE
C6.1
This Section covers the design of steel components,
splices and connections for straight or horizontally curved
beam and girder structures, frames, trusses and arches,
cable-stayed and suspension systems, and metal deck
systems, as applicable.
When applied to curved steel girders, these provisions
shall be taken to apply to the design and construction of
highway superstructures with horizontally curved steel
I-shaped or single-cell box-shaped longitudinal girders
with radii greater than 100 ft. Exceptions to this limit shall
be based on a thorough evaluation of the application of the
bridge under consideration consistent with basic structural
fundamentals.
A brief outline for the design of steel girder bridges is
presented in Appendix C6.
The LRFD provisions have no span limit. There has
been a history of construction problems associated with
curved bridges with spans greater than about 350 ft. Large
girder self-weight may cause critical stresses and
deflections during erection when the steel work is
incomplete. Large lateral deflections and girder rotations
associated with longer spans tend to make it difficult to fit
up cross-frames. Large curved steel bridges have been
built successfully; however, these bridges deserve special
considerations such as the possible need for more than one
temporary support in large spans.
Most of the provisions for proportioning main
elements are grouped by structural action:
•
Tension and
(Article 6.8)
combined
tension
and
•
Compression and combined compression and flexure
(Article 6.9)
•
Flexure, flexural shear, and torsion:
o
I-sections (Article 6.10)
o
Box sections (Article 6.11)
o
Miscellaneous sections (Article 6.12)
flexure
Provisions for connections and splices are contained
in Article 6.13.
Article 6.14 contains provisions specific to particular
assemblages or structural types, e.g., through-girder spans,
trusses, orthotropic deck systems, and arches.
6.2—DEFINITIONS
2013 Revision
Abutment—An end support for a bridge superstructure.
Aspect Ratio—In any rectangular configuration, the ratio of the lengths of the sides.
Beam—A structural member whose primary function is to transmit loads to the support primarily through flexure and
shear. Generally, this term is used when the component is made of rolled shapes.
Beam-Column—A structural member whose primary function is to resist both axial loads and bending moments.
Bend-Buckling Resistance—The maximum load that can be carried by a web plate without experiencing theoretical elastic
local buckling due to bending.
Biaxial Bending—Simultaneous bending of a member or component about two perpendicular axes.
Bifurcation—The phenomenon whereby an ideally straight or flat member or component under compression may either
assume a deflected position or may remain undeflected, or an ideally straight member under flexure may either deflect and
twist out-of-plane or remain in its in-plane deflected position.
6-1
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
6-2
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Bifurcation Analysis—An analysis used to determine the buckling or bifurcation load.
Block Shear Rupture—Failure of a bolted web connection of coped beams or any tension connection by the tearing out of a
portion of a plate along the perimeter of the connecting bolts.
Bolt Assembly—The bolt, nut(s), and washer(s).
Box Flange—A flange that is connected to two webs. The flange may be a flat unstiffened plate, a stiffened plate or a flat
plate with reinforced concrete attached to the plate with shear connectors.
Bracing Member—A member intended to brace a main member or part thereof against lateral movement.
Buckling Load—The load at which an ideally straight member or component under compression assumes a deflected
position.
Built-Up Member—A member made of structural steel elements that are welded, bolted or riveted together.
Charpy V-Notch Impact Requirement—The minimum energy required to be absorbed in a Charpy V-notch test conducted
at a specified temperature.
Charpy V-Notch Test—An impact test complying with AASHTO T 243M/T 243 (ASTM A673/A673M).
Clear Distance of Bolts—The distance between edges of adjacent bolt holes.
Clear End Distance of Bolts—The distance between the edge of a bolt hole and the end of a member.
Closed-Box Section—A flexural member having a cross-section composed of two vertical or inclined webs which has at
least one completely enclosed cell. A closed-section member is effective in resisting applied torsion by developing shear
flow in the webs and flanges.
Collapse Load—That load that can be borne by a structural member or structure just before failure becomes apparent.
Compact Flange—For a composite section in negative flexure or a noncomposite section, a discretely braced compression
flange with a slenderness at or below which the flange can sustain sufficient strains such that the maximum potential
flexural resistance is achieved prior to flange local buckling having a statistically significant influence on the response,
provided that sufficient lateral bracing requirements are satisfied to develop the maximum potential flexural resistance.
Compact Section—A composite section in positive flexure satisfying specific steel grade, web slenderness and ductility
requirements that is capable of developing a nominal resistance exceeding the moment at first yield, but not to exceed the
plastic moment.
Compact Unbraced Length—For a composite section in negative flexure or a noncomposite section, the limiting unbraced
length of a discretely braced compression flange at or below which the maximum potential flexural resistance can be
achieved prior to lateral torsional buckling having a statistically significant influence on the response, provided that
sufficient flange slenderness requirements are satisfied to develop the maximum potential flexural resistance.
Compact Web—For a composite section in negative flexure or a noncomposite section, a web with a slenderness at or
below which the section can achieve a maximum flexural resistance equal to the plastic moment prior to web bendbuckling having a statistically significant influence on the response, provided that sufficient steel grade, ductility, flange
slenderness and/or lateral bracing requirements are satisfied.
Component—A constituent part of a structure.
Composite Beam—A steel beam connected to a deck so that they respond to force effects as a unit.
Composite Column—A structural compression member consisting of either structural shapes embedded in concrete, or a
steel tube filled with concrete designed to respond to force effects as a unit.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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SECTION 6: STEEL STRUCTURES
6-3
Composite Girder—A steel flexural member connected to a concrete slab so that the steel element and the concrete
slab, or the longitudinal reinforcement within the slab, respond to force effects as a unit.
Connection—A weld or arrangement of bolts that transfers normal and/or shear stresses from one element to another.
Constant Amplitude Fatigue Threshold—The nominal stress range below which a particular detail can withstand an infinite
number of repetitions without fatigue failure.
Continuously Braced Flange—A flange encased in concrete or anchored by shear connectors for which flange lateral
bending effects need not be considered. A continuously braced flange in compression is also assumed not to be subject to
local or lateral torsional buckling.
Controlling Flange—Top or bottom flange for the smaller section at a point of splice, whichever flange has the maximum
ratio of the elastic flexural stress at its midthickness due to the factored loads to its factored flexural resistance.
Cracked Section—A composite section in which the concrete is assumed to carry no tensile stress.
Critical Load—The load at which bifurcation occurs as determined by a theoretical stability analysis.
Cross-Frame—A transverse truss framework connecting adjacent longitudinal flexural components or inside a tub section
or closed box used to transfer and distribute vertical and lateral loads and to provide stability to the compression flanges.
Sometimes synonymous with the term diaphragm.
Cross-Section Distortion—Change in shape of the cross-section profile due to torsional loading.
Curved Girder—An I-, closed-box, or tub girder that is curved in a horizontal plane.
Deck—A component, with or without wearing surface, that supports wheel loads directly and is supported by other
components.
Deck System—A superstructure, in which the deck is integral with its supporting components, or in which the effects of
deformation of supporting components on the behavior of the deck is significant.
Deck Truss—A truss system in which the roadway is at or above the level of the top chord of the truss.
Detail Category—A grouping of components and details having essentially the same fatigue resistance.
Diaphragm—A vertically oriented solid transverse member connecting adjacent longitudinal flexural components or inside
a closed-box or tub section to transfer and distribute vertical and lateral loads and to provide stability to the compression
flanges.
Discretely Braced Flange—A flange supported at discrete intervals by bracing sufficient to restrain lateral deflection of the
flange and twisting of the entire cross-section at the brace points.
Distortion-Induced Fatigue—Fatigue effects due to secondary stresses not normally quantified in the typical analysis and
design of a bridge.
Edge Distance of Bolts—The distance perpendicular to the line of force between the center of a hole and the edge of the
component.
Effective Length—The equivalent length KL used in compression formulas and determined by a bifurcation analysis.
Effective Length Factor—The ratio between the effective length and the unbraced length of the member measured between
the centers of gravity of the bracing members.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
6-4
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Effective Net Area—Net area modified to account for the effect of shear lag.
Effective Width—The reduced width of a plate or concrete slab which, with an assumed uniform stress distribution,
produces the same effect on the behavior of a structural member as the actual plate width with its nonuniform stress
distribution.
Elastic—A structural response in which stress is directly proportional to strain and no deformation remains upon removal
of loading.
Elastic Analysis—Determination of load effects on members and connections based on the assumption that the material
stress-strain response is linear and the material deformation disappears on removal of the force that produced it.
Elastic-Perfectly Plastic (Elastic-Plastic)—An idealized material stress-strain curve that varies linearly from the point of
zero strain and zero stress up to the yield point of the material, and then increases in strain at the value of the yield stress
without any further increases in stress.
End Distance of Bolts—The distance along the line of force between the center of a hole and the end of the component.
End Panel—The end section of a truss or girder.
Engineer—A licensed structural engineer responsible for the design of the bridge or review of the bridge construction.
Eyebar—A tension member with a rectangular section and enlarged ends for a pin connection.
Factored Load—The product of the nominal load and a load factor.
Fastener—Generic term for welds, bolts, rivets, or other connecting device.
Fatigue—The initiation and/or propagation of cracks due to a repeated variation of normal stress with a tensile component.
Fatigue Design Life—The number of years that a detail is expected to resist the assumed traffic loads without fatigue
cracking. In the development of these Specifications it has been taken as 75 years.
Fatigue Life—The number of repeated stress cycles that results in fatigue failure of a detail.
Fatigue Resistance—The maximum stress range that can be sustained without failure of the detail for a specified number of
cycles.
Finite Fatigue Life—The number of cycles to failure of a detail when the maximum probable stress range exceeds the
constant amplitude fatigue threshold.
First-Order Analysis—Analysis in which equilibrium conditions are formulated on the undeformed structure; that is, the
effect of deflections is not considered in writing equations of equilibrium.
Flange Lateral Bending—Bending of a flange about an axis perpendicular to the flange plate due to lateral loads applied to
the flange and/or nonuniform torsion in the member.
Flexural Buckling—A buckling mode in which a compression member deflects laterally without twist or change in crosssectional shape.
Flexural-Torsional Buckling—A buckling mode in which a compression member bends and twists simultaneously without
a change in cross-sectional shape.
Force—Resultant of distribution of stress over a prescribed area. Generic term signifying axial loads, bending moment,
torques, and shears.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 6: STEEL STRUCTURES
6-5
Fracture-Critical Member (FCM)—Component in tension whose failure is expected to result in the collapse of the bridge
or the inability of the bridge to perform its function.
Fracture Toughness—A measure of the ability of a structural material or element to absorb energy without fracture. It is
generally determined by the Charpy V-notch test.
Gage of Bolts—The distance between adjacent lines of bolts; the distance from the back of an angle or other shape to the
first line of bolts.
Girder—A structural component whose primary function is to resist loads in flexure and shear. Generally, this term is used
for fabricated sections.
Grip—Distance between the nut and the bolt head.
Gusset Plate—Plate material used to interconnect vertical, diagonal, and horizontal truss members at a panel point.
Half Through-Truss Spans—A truss system with the roadway located somewhere between the top and bottom chords. It
precludes the use of a top lateral system.
HSS—A square, rectangular, or hollow structural steel section produced in accordance with a pipe or tubing product
specification.
Hybrid Section—A fabricated steel section with a web that has a specified minimum yield strength lower than one or both
flanges.
Inelastic Action—A condition in which deformation is not fully recovered upon removal of the load that produced it.
Inelastic Redistribution—The redistribution of internal force effects in a component or structure caused by inelastic
deformations at one or more sections.
Instability—A condition reached in the loading of a component or structure in which continued deformation results in a
decrease of load-resisting capacity.
Interior Panel—The interior section of a truss or girder component.
Joint—Area where two or more ends, surfaces, or edges are attached. Categorized by type of fastener used and method of
force transfer.
Lacing—Plates or bars to connect components of a member.
Lateral Bending Stress—The normal stress caused by flange lateral bending.
Lateral Bracing—A truss placed in a horizontal plane between two I-girders or two flanges of a tub girder to maintain
cross-sectional geometry, and provide additional stiffness and stability to the bridge system.
Lateral Bracing Component—A component utilized individually or as part of a lateral bracing system to prevent buckling
of components and/or to resist lateral loads.
Lateral-Torsional Buckling—Buckling of a component involving lateral deflection and twist.
Level—That portion of a rigid frame that includes one horizontal member and all columns between that member and the
base of the frame or the next lower horizontal member.
Limit State—A condition in which a component or structure becomes unfit for service and is judged either to be no longer
useful for its intended function or to be unsafe. Limits of structural usefulness include brittle fracture, plastic collapse,
excessive deformation, durability, fatigue, instability, and serviceability.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
6-6
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Load Effect—Moment, shear, axial force or torque induced in a member by loads applied to the structure.
Load Path—A succession of components and joints through which a load is transmitted from its origin to its destination.
Load-Induced Fatigue—Fatigue effects due to the in-plane stresses for which components and details are explicitly
designed.
Local Buckling—The buckling of a plate element in compression.
Longitudinally Loaded Weld—Weld with applied stress parallel to the longitudinal axis of the weld.
Major Axis—The centroidal axis about which the moment of inertia is a maximum; also referred to as the major principal
axis.
Net Tensile Stress—The algebraic sum of two or more stresses in which the total is tension.
Noncompact Flange—For a composite section in negative flexure or a noncomposite section, a discretely braced
compression flange with a slenderness at or below the limit at which localized yielding within the member cross-section
associated with a hybrid web, residual stresses and/or cross-section monosymmetry has a statistically significant effect on
the nominal flexural resistance.
Noncompact Section—A composite section in positive flexure for which the nominal resistance is not permitted to exceed
the moment at first yield.
Noncompact Unbraced Length—For a composite section in negative flexure or a noncomposite section, the limiting
unbraced length of a discretely braced compression flange at or below the limit at which the onset of yielding in either
flange of the cross-section with consideration of compression-flange residual stress effects has a statistically significant
effect on the nominal flexural resistance.
Noncompact Web—For a composite section in negative flexure or a noncomposite section, a web satisfying steel grade
requirements and with a slenderness at or below the limit at which theoretical elastic web bend-buckling does not occur for
elastic stress values, computed according to beam theory, smaller than the limit of the nominal flexural resistance.
Noncomposite Section—A steel beam where the deck is not connected to the steel section by shear connectors.
Noncontrolling Flange—The flange at a point of splice opposite the controlling flange.
Nonslender Element Section—Cross-section of a compression member composed of plate components of sufficient
slenderness such that they are able to develop their full nominal yield strength prior to the onset of local buckling.
Nonuniform Torsion—An internal resisting torsion in thin-walled sections, also known as warping torsion, producing shear
stress and normal stresses, and under which cross-sections do not remain plane. Members developing nonuniform torsion
resist the externally applied torsion by warping torsion and St. Venant torsion. Each of these components of internal
resisting torsion varies along the member length, although the externally applied concentrated torsion may be uniform
along the member between two adjacent points of torsional restraint. Warping torsion is dominant over St. Venant torsion
in members having open cross-sections, whereas St. Venant torsion is dominant over warping torsion in members having
closed cross-sections.
Open Section—A flexural member having a cross-section which has no enclosed cell. An open-section member resists
torsion primarily by nonuniform torsion, which causes normal stresses at the flange tips.
Orthotropic Deck—A deck made of a steel plate stiffened with open or closed steel ribs welded to the underside of a steel
plate.
Permanent Deflection—A type of inelastic action in which a deflection remains in a component or system after the load is
removed.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 6: STEEL STRUCTURES
6-7
Pier—A column or connected group of columns or other configuration designed to be an interior support for a bridge
superstructure.
Pitch—The distance between the centers of adjacent bolt holes or shear connectors along the line of force.
Plastic Analysis—Determination of load effects on members and connections based on the assumption of rigid-plastic
behavior; i.e., that equilibrium is satisfied throughout the structure and yield is not exceeded anywhere. Second-order
effects may need to be considered.
Plastic Hinge—A yielded zone which forms in a structural member when the plastic moment is attained. The beam is
assumed to rotate as if hinged, except that the plastic moment capacity is maintained within the hinge.
Plastic Moment—The resisting moment of a fully-yielded cross-section.
Plastic Strain—The difference between total strain and elastic strain.
Plastification—The process of successive yielding of fibers in the cross-section of a member as bending moment is
increased.
Plate—A flat rolled product whose thickness exceeds 0.25 in.
Portal Frames—End transverse truss bracing or Vierendeel bracing to provide for stability and to resist wind or seismic
loads.
Post-Buckling Resistance—The load that can be carried by a member or component after buckling.
Primary Member—A member designed to carry the internal forces determined from an analysis.
Prying Action—Lever action that exists in connections in which the line of application of the applied load is eccentric to
the axis of the bolt, causing deformation of the fitting and an amplification of the axial force in the bolt.
Redistribution Moment—An internal moment caused by yielding in a continuous span bending component and held in
equilibrium by external reactions.
Redistribution of Moments—A process that results from formation of inelastic deformations in continuous structures.
Redistribution Stress—The bending stress resulting from the redistribution moment.
Redundancy—The quality of a bridge that enables it to perform its design function in a damaged state.
Redundant Member—A member whose failure does not cause failure of the bridge.
Required Fatigue Life—A product of the single-lane average daily truck traffic, the number of cycles per truck passage,
and the design life in days.
Residual Stress—The stresses that remain in an unloaded member or component after it has been formed into a finished
product by cold bending, and/or cooling after rolling or welding.
Reverse Curvature Bending—A bending condition in which end moments on a member cause the member to assume an S
shape.
Rigid Frame—A structure in which connections maintain the angular relationship between beam and column members
under load.
St. Venant Torsion—That portion of the internal resisting torsion in a member producing only pure shear stresses on a
cross-section, also referred to as pure torsion or uniform torsion.
Second-Order Analysis—Analysis in which equilibrium conditions are formulated on the deformed structure; that is, in
which the deflected position of the structure is used in writing the equations of equilibrium.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
6-8
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Secondary Member—A member in which stress is not normally evaluated in the analysis.
Service Loads—Loads expected to be supported by the structure under normal usage.
Shape Factor—The ratio of the plastic moment to the yield moment, or the ratio of the plastic section modulus to the
elastic section modulus.
Shear-Buckling Resistance—The maximum load that can be supported by a web plate without experiencing theoretical
buckling due to shear.
Shear Connector—A mechanical device that prevents relative movements both normal and parallel to an interface.
Shear Flow—Shear force per unit width acting parallel to the edge of a plate element.
Shear Lag—Nonlinear distribution of normal stress across a component due to shear distortions.
Sheet—A flat rolled product whose thickness is between 0.006 and 0.25 in.
Single Curvature Bending—A deformed shape of a member in which the center of curvature is on the same side of the
member throughout the unbraced length.
Skew Angle—The angle between the axis of support relative to a line normal to the longitudinal axis of the bridge, i.e. a
zero-degree skew denotes a rectangular bridge.
Slab—A deck composed of concrete and reinforcement.
Slender Element Section—Cross-section of a compression member composed of plate components of sufficient slenderness
such that local buckling in the elastic range will occur.
Slender Flange—For a composite section in negative flexure or a noncomposite section, a discretely braced compression
flange with a slenderness at or above which the nominal flexural resistance is governed by elastic flange local buckling,
provided that sufficient lateral bracing requirements are satisfied.
Slender Unbraced Length—For a composite section in negative flexure or a noncomposite section, the limiting unbraced
length of a discretely braced compression flange at or above which the nominal flexural resistance is governed by elastic
lateral torsional buckling.
Slender Web—For a composite section in negative flexure or a noncomposite section, a web with a slenderness at or above
which the theoretical elastic bend-buckling stress in flexure is reached in the web prior to reaching the yield strength of the
compression flange.
Slenderness Ratio—The ratio of the effective length of a member to the radius of gyration of the member cross-section,
both with respect to the same axis of bending, or the full or partial width or depth of a component divided by its thickness.
Splice—A group of bolted connections, or a welded connection, sufficient to transfer the moment, shear, axial force, or
torque between two structural elements joined at their ends to form a single, longer element.
Stay-in-Place Formwork—Permanent metal or precast concrete forms that remain in place after construction is finished.
Stiffened Element—A flat compression element with adjoining out-of-plane elements along both edges parallel to the
direction of loading.
Stiffener—A member, usually an angle or plate, attached to a plate or web of a beam or girder to distribute load, to transfer
shear, or to prevent buckling of the member to which it is attached.
Stiffness—The resistance to deformation of a member or structure measured by the ratio of the applied force to the
corresponding displacement.
Strain Hardening—Phenomenon wherein ductile steel, after undergoing considerable deformation at or just above the yield
point, exhibits the capacity to resist substantially higher loading than that which caused initial yielding.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 6: STEEL STRUCTURES
6-9
Strain-Hardening Strain—For structural steels that have a flat or nearly flat plastic region in the stress-strain relationship,
the value of the strain at the onset of strain hardening.
Stress Range—The algebraic difference between extreme stresses resulting from the passage of a load.
Strong-Axis—The centroidal axis about which the moment of inertia is a maximum.
Subpanel—A stiffened web panel divided by one or more longitudinal stiffeners.
Sway Bracing—Transverse vertical bracing between truss members.
Tensile Strength—The maximum tensile stress that a material is capable of sustaining.
Tension-Field Action—The behavior of a girder panel under shear in which diagonal tensile stresses develop in the web
and compressive forces develop in the transverse stiffeners in a manner analogous to a Pratt truss.
Through-Girder Spans—A girder system where the roadway is below the top flange.
Through-Thickness Stress—Bending stress in a web or box flange induced by distortion of the cross-section.
Through-Truss Spans—A truss system where the roadway is located near the bottom chord and where a top chord lateral
system is provided.
Tie Plates—Plates used to connect components of a member.
Tied Arch—An arch in which the horizontal thrust of the arch rib is resisted by a horizontal tie.
Toe of the Fillet—Termination point of a fillet weld or a rolled section fillet.
Torsional Buckling—A buckling mode in which a compression member twists about its shear center.
Torsional Shear Stress—Shear stress induced by St. Venant torsion.
Transversely Loaded Weld—Weld with applied stress perpendicular to the longitudinal axis of the weld.
Trough-Type Box Section—A U-shaped section without a common top flange.
True Arch—An arch in which the horizontal component of the force in the arch rib is resisted by an external force supplied
by its foundation.
Tub Section—An open-topped steel girder which is composed of a bottom flange plate, two inclined or vertical web plates,
and an independent top flange attached to the top of each web. The top flanges are connected with lateral bracing members.
Unbraced Length—Distance between brace points resisting the mode of buckling or distortion under consideration;
generally, the distance between panel points or brace locations.
Unstiffened Element—A flat compression element with an adjoining out-of-plane element along one edge parallel to the
direction of loading.
Von Mises Yield Criterion—A theory which states that the inelastic action at a point under a combination of stresses begins
when the strain energy of distortion per unit volume is equal to the strain energy of distortion per unit volume in a simple
tensile bar stressed to the elastic limit under a state of uniaxial stress. This theory is also called the maximum strain-energyof-distortion theory. Accordingly, shear yield occurs at 0.58 times the yield strength.
Warping Stress—Normal stress induced in the cross-section by warping torsion and/or by distortion of the cross-section.
Warping Torsion—That portion of the total resistance to torsion in a member producing shear and normal stresses that is
provided by resistance to out-of-plane warping of the cross-section.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
6-10
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Web Crippling—The local failure of a web plate in the immediate vicinity of a concentrated load or bearing reaction due to
the transverse compression introduced by this load.
Web Slenderness Ratio—The depth of a web between flanges divided by the web thickness.
Yield Moment—In a member subjected to flexure, the moment at which an outer fiber first attains the yield stress.
Yield Strength—The stress at which a material exhibits a specified limiting deviation from the proportionality of stress to
strain.
Yield-Stress Level—The stress determined in a tension test when the strain reaches 0.005 in. per in.
6.3—NOTATION
A
=
Ab
Abot
Ac
Ad
=
=
=
=
Aeff
=
ADTT =
ADTTSL =
Ae
Af
=
Afn
=
Ag
=
An
Ao
Ap
=
=
=
Apn
=
Ar
Arb
Ars
Art
As
=
=
=
=
=
Asc
At
Atn
Av
=
=
=
=
Avg
=
Avn
=
Aw
=
2013 Revision
detail category constant; area enclosed within centerlines of plates of box members (in.2); total gross crosssectional area of the member (in.2) (6.6.1.2.5) (6.9.4.2.2) (6.12.2.2.2)
projected bearing area on a pin plate (in.2); cross-sectional area of a bolt (in.2) (6.8.7.2) (6.13.2.7)
area of the bottom flange (in.2) (6.10.10.1.2)
area of concrete (in.2); area of the concrete deck (in.2) (6.9.5.1) (D6.3.2)
minimum required cross-sectional area of a diagonal member of top lateral bracing for tub sections (in.2)
(C6.7.5.3)
summation of the effective areas of the cross-section based on an effective width for each slender stiffened
element in the cross-section = ( b − be )t (in.2) (6.9.4.2.2)
average daily truck traffic over the design life (6.6.1.2.5)
single-lane ADTT (6.6.1.2.5)
= effective net area (in.2); effective flange area (in.2) (6.6.1.2.3) (6.13.6.1.4c)
area of the inclined bottom flange (in.2); area of a box flange including longitudinal flange stiffeners (in.2);
sum of the area of fillers on the top and bottom of a connecting plate (in.2); area of flange transmitting a
concentrated load (in.2) (C6.10.1.4) (C6.11.11.2) (6.13.6.1.5) (6.13.7.2)
sum of the flange area and the area of any cover plates on the side of the neutral axis corresponding to Dn in a
hybrid section (in.2) (6.10.1.10.1)
gross area of a member (in.2); gross cross-sectional area of the member (in.2); gross area of the tension flange
(in.2); gross area of the section based on the design wall thickness (in.) (6.6.1.2.3) (6.8.2.1) (6.9.4.1.1)
(6.9.4.1.3) (6.10.1.8) (6.12.1.2.3c) (6.13.6.1.4c)
net cross-section area of a tension member (in.2); net area of a flange (in.2) (6.6.1.2.3) (6.8.2.1) (6.10.1.8)
enclosed area within a box section (in.2) (C6.7.4.3) (6.11.8.2.2)
smaller of either the connected plate area or the sum of the splice plate area on the top and bottom of the
connected plate (in.2) (6.13.6.1.5)
area of the projecting elements of a stiffener outside of the web-to-flange welds but not beyond the edge of
the flange (in.2) (6.10.11.2.3)
area of the longitudinal reinforcement (in.2) (6.9.5.1)
area of the bottom layer of longitudinal reinforcement within the effective concrete deck width (in.2) (D6.1)
total area of the longitudinal reinforcement within the effective concrete deck width (in.2) (D6.3.2)
area of the top layer of longitudinal reinforcement within the effective concrete deck width (in.2) (D6.1)
area of a structural steel shape (in.2); total area of longitudinal reinforcement over the interior support within
the effective concrete deck width (in.2); gross area of a splice plate (in.2); area of the concrete deck (in.2)
(6.10.10.3) (6.13.6.1.4c) (D6.3.2)
cross-sectional area of a stud shear connector (in.2) (6.10.10.4.3)
area of the tension flange (in.2) (D6.3.2)
net area along the cut carrying tension stress in block shear (in.2) (6.13.4)
cross-sectional area of transverse reinforcement that intercepts a diagonal shear crack in a concrete-encased
shape (in.2) (6.12.3.1)
gross area along the cut carrying shear stress in block shear (in.2); gross area of the connection element
subject to shear (in.2) (6.13.4) (6.13.5.3)
net area along the cut carrying shear stress in block shear (in.2); net area of the connection element subject to
shear (in.2) (6.13.4) (6.13.5.3)
area of the web of a steel section (in.2) (6.12.2.3.1)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 6: STEEL STRUCTURES
a
=
awc
B
=
=
b
=
b1, b2
bc
bf
=
=
=
bfc
=
bft
bℓ
=
=
=
bs
=
bs
=
bt
C
=
=
Cb
=
Cw
C1,C2,C3 =
c
=
crb
=
crt
=
D
=
D′
=
Dc
DC1
DC2
Dcp
Dn
=
=
=
=
=
Dp
=
Dt
DW
=
=
6-11
distance between connectors (in.); center-to-center distance between flanges of adjacent boxes in a multiple
box section (in.); longitudinal spacing of transverse flange stiffeners (in.); distance from the center of a bolt
to the edge of a plate subject to a tensile force due to prying action (in.) (6.9.4.3.1) (6.11.2.3) (C6.11.11.2)
(6.13.2.10.4)
ratio of two times the web area in compression to the area of the compression flange (6.10.1.10.2)
outside width of a rectangular Hollow Structural Section (HSS) perpendicular to the plane of the gusset
plate(s) (in.) (6.8.2.2)
width of a rectangular plate element (in.); width of the body of an eyebar (in.); widest flange width (in.);
distance from the edge of a plate or the edge of a perforation to the point of support or distance between
supports (in.); clear distance between plates (in.); the smaller of do and D (in.); width of a rectangular tube
(in.); overall thickness of the composite cross-section of a concrete-encased steel shape in the plane of
buckling (in.); distance from the center of a bolt to the toe of the fillet of a connected part (in.); distance
between the toe of the flange and the centerline of the web (in.) (C6.7.4.3) (6.7.6.3) (6.7.7.2) (6.10.11.1.3)
(6.12.2.2.2) (6.12.2.2.5) (6.12.2.3.1) (6.13.2.10.4) (6.14.4.2)
individual flange widths (in.) (C6.9.4.1.3)
full width of the compression flange (in.) (D6.1)
full width of the flange (in.); for I-sections, full width of the widest flange within the field section under
consideration (in.); for tub sections, full width of the widest top flange within the field section under
consideration (in.); for closed box sections, the limit of bf /4 does not apply (in.) (C6.7.4.2) (6.10.11.1.2)
(6.12.2.2.4) (6.12.2.2.5)
full width of the compression flange; compression-flange width between webs; clear width of the
compression flange between the webs less the inside corner radius on each side (in.) (6.10.1.10.2)
(6.11.8.2.2) (6.12.2.2.2)
full width of the tension flange (in.); width of a box flange in tension between webs (in.) (C6.10.9.1) (6.11.9)
projecting width of a longitudinal stiffener (in.); length of the longer leg of an unequal-leg angle (in.)
(6.9.4.4) (6.10.11.1.3)
effective width of the concrete deck (in.) (6.10.1.10.2)
length of the shorter leg of an unequal-leg angle (in.) (6.9.4.4)
projecting width of a transverse or bearing stiffener (in.); full width of the tension flange (in.) (6.10.11.1.2) (D6.1)
ratio of the shear-buckling resistance to the shear specified minimum yield strength (6.10.9.2)
moment gradient modifier (6.10.1.6) (6.12.2.2.5) (6.12.2.2.7)
warping torsional constant (in.6) (6.9.4.1.3) (6.12.2.2.5)
composite column constants specified in Table 6.9.5.1-1 (6.9.5.1)
distance from the center of the longitudinal reinforcement to the nearest face of a concrete-encased shape in
the plane of bending (in.) (6.12.2.3.1)
distance from the top of the concrete deck to the centerline of the bottom layer of longitudinal concrete deck
reinforcement (in.) (D6.1)
distance from the top of the concrete deck to the centerline of the top layer of longitudinal concrete deck
reinforcement (in.) (D6.1)
diameter of a pin (in.); clear distance between flanges (in.); outside diameter of a circular Hollow Structural
Section (HSS) (in.); outside diameter of a circular steel tube (in.); outside diameter of tube (in.); web depth
(in.); depth of the web plate measured along the slope (in.); clear distance between the flanges less the inside
corner radius on each side (in.) (6.7.6.2.1) (6.7.7.2) (6.8.2.2) (6.9.4.2) (6.9.4.2.1) (6.10.1.9.1) (6.11.9)
(6.12.1.2.3c) (6.12.2.2.2) (6.12.2.2.3) (6.12.2.2.5)
depth at which a composite section reaches its theoretical plastic moment capacity when the maximum strain
in the concrete deck is at its theoretical crushing strain (in.) (C6.10.7.3)
depth of the web in compression in the elastic range (in.) (6.10.1.9.1)
permanent load acting on the noncomposite section (C6.10.11.3.1)
permanent load acting on the long-term composite section (C6.10.11.3.1)
depth of the web in compression at the plastic moment (in.) (6.10.6.2.2)
larger of the distances from the elastic neutral axis of the cross-section to the inside face of either flange in a
hybrid section, or the distance from the neutral axis to the inside face of the flange on the side of the neutral
axis where yielding occurs first when the neutral axis is at the mid-depth of the web (in.) (6.10.1.10.1)
distance from the top of the concrete deck to the neutral axis of the composite section at the plastic moment
(in.) (6.10.7.1.2)
total depth of the composite section (in.) (6.10.7.1.2)
wearing surface load (C6.10.11.3.1)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
6-12
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
d
=
db
dc
=
=
do
drb
=
=
drt
=
ds
=
dt
=
dw
=
E
Ec
Ee
EXX
Fcf
FCM
Fcb
Fcr
=
=
=
=
=
=
=
=
Fcrs
Fcrw
Fcv
Fe
Fexx
Ffat
Ffat1
=
=
=
=
=
=
=
Ffat2
=
Fℓ
=
FLB
Fmax
Fn
Fnc
Fnc(FLB)
Fnt
Fp
=
=
=
=
=
=
=
Frc
Fs
=
=
FT
=
total depth of the steel section (in.); diameter of a stud shear connector (in.); depth of the member in the plane
of flexure (in.); depth of the member in the plane of shear (in.); nominal diameter of a bolt (in.); total depth
of the section (in.) depth of the rectangular bar (in.) (C6.10.8.2.3) (6.10.10.2) (6.12.2.2.4) (6.12.2.2.7)
(6.12.2.3.1) (6.12.3.1) (6.13.2.4.2)
depth of a beam in a rigid frame (in.) (6.13.7.2)
depth of a column in a rigid frame (in.); distance from the plastic neutral axis to the midthickness of the
compression flange used to compute the plastic moment (in.) (6.13.7.2) (D6.1)
transverse stiffener spacing (in.); the smaller of the adjacent web panel widths (in.) (6.10.9.3.2) (6.10.11.1.3)
distance from the plastic neutral axis to the centerline of the bottom layer of longitudinal concrete deck
reinforcement used to compute the plastic moment (in.) (D6.1)
distance from the plastic neutral axis to the centerline of the top layer of longitudinal concrete deck
reinforcement used to compute the plastic moment (in.) (D6.1)
distance from the centerline of the closest plate longitudinal stiffener or from the gage line of the closest
angle longitudinal stiffener to the inner surface or leg of the compression-flange element (in.); distance from
the plastic neutral axis to the midthickness of the concrete deck used to compute the plastic moment (in.)
(6.10.1.9.2) (D6.1)
distance from the plastic neutral axis to the midthickness of the tension flange used to compute the plastic
moment (in.) (D6.1)
distance from the plastic neutral axis to the middepth of the web used to compute the plastic moment (in.)
(D6.1)
modulus of elasticity of steel (ksi) (6.7.7.3)
modulus of elasticity of concrete (ksi) (6.10.1.1.1b)
modified modulus of elasticity of steel for a composite column (ksi) (6.9.5.1)
classification number for weld metal (C6.13.3.2.1)
design stress for the controlling flange at a point of splice (ksi) (C6.13.6.1.4b)
fracture-critical member (6.6.2)
nominal axial compression buckling resistance of the flange (6.11.8.2.2)
critical buckling stress for plates (ksi); elastic lateral torsional buckling stress (ksi); shear buckling resistance
(ksi); elastic local buckling stress (ksi) (C6.9.4.2) (6.10.1.6) (6.12.1.2.3c) (6.12.2.2.3) (6.12.2.2.5)
local buckling stress for the stiffener (ksi) (6.10.11.1.3)
nominal web bend-buckling resistance (ksi) (6.10.1.9.1)
nominal shear buckling resistance of the flange (6.11.8.2.2)
nominal compressive resistance of composite members (ksi) (6.9.5.1)
classification strength of weld metal (ksi) (6.13.3.2.2b)
radial fatigue shear range per unit length, taken as the larger of either Ffat1 or Ffat2 (kip/in.) (6.10.10.1.2)
radial fatigue shear range per unit length due to the effect of any curvature between brace points (kip/in.)
(6.10.10.1.2)
radial fatigue shear range per unit length due to torsion caused by effects other than curvature, such as skew
(kip/in.) (6.10.10.1.2)
statically equivalent uniformly distributed lateral force due to the factored loads from concrete deck overhang
brackets (kip/in.) (C6.10.3.4)
flange local buckling (C6.10.8.2.1) (CA6.3.1) (CD6.4.1) (CD6.4.2)
maximum potential compression-flange flexural resistance (ksi) (C6.10.8.2.1)
nominal flexural resistance of a flange (ksi) (C6.10.8.2.1)
nominal flexural resistance of a compression flange (ksi) (C6.8.2.3)
nominal compression-flange local buckling flexural resistance (ksi) (CD6.4.1)
nominal flexural resistance of a tension flange (ksi) (C6.8.2.3)
total radial force in the concrete deck at the point of maximum positive live load plus impact moment for the
design of the shear connectors at the strength limit state, taken equal to zero for straight spans or segments
(kip) (6.10.10.4.2)
net range of cross-frame force at the top flange (kip) (6.10.10.1.2)
vertical force on the connection between a longitudinal and a transverse flange stiffener (kip); Service II
design stress for the flange under consideration at a point of splice (ksi) (C6.11.11.2) (6.13.6.1.4c)
total radial force in the concrete deck between the point of maximum positive live load plus impact moment
and the centerline of an adjacent interior support for the design of shear connectors at the strength limit state,
taken equal to zero for straight spans or segments (kip) (6.10.10.4.2)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 6: STEEL STRUCTURES
Fu
=
Fub
Fvr
Fw
=
=
=
Fy
=
Fyc
Fyf
Fyr
=
=
=
Fyrb
=
Fyrs
Fyrt
Fys
=
=
=
Fyt
Fyw
f
=
=
=
f0
=
f1
=
f2
=
fa
fb
=
=
fbu
=
fby
=
fc
=
f′c
fcf
=
=
fd
=
fDC1
=
6-13
specified minimum tensile strength of steel (ksi); specified minimum tensile strength of a stud shear
connector (ksi); specified minimum tensile strength of a connected part (ksi); tensile strength of the
connection element (ksi) (6.4.1) (6.10.10.4.3) (6.13.2.9) (6.13.5.3)
specified minimum tensile strength of a bolt (ksi) (6.13.2.7)
factored torsional shear resistance of a box flange (ksi) (6.11.1.1)
vertical force on the connection between a transverse flange stiffener and a box section web (kip)
(C6.11.11.2)
specified minimum yield strength of steel (ksi); specified minimum yield strength of a pin (ksi); specified
minimum yield strength of a pin plate (ksi); specified minimum yield strength of a connected part (ksi);
specified minimum yield strength of a splice plate (ksi); specified minimum yield strength (ksi) (6.4.1)
(6.7.6.2.1) (6.8.7.2) (6.9.4.1.1) (6.12.2.2.4) (6.12.2.2.5) (6.12.2.2.7) (6.13.4) (6.13.6.1.4c)
specified minimum yield strength of a compression flange (ksi) (C6.8.2.3)
specified minimum yield strength of a flange (ksi) (6.7.7.3)
compression-flange stress at the onset of nominal yielding within the cross-section, including residual stress
effects but not including compression-flange lateral bending, taken as the smaller of 0.7Fyc and Fyw, but not
less than 0.5Fyc; smaller of the compression-flange stress at the onset of nominal yielding, with consideration
of residual stress effects, or the specified minimum yield strength of the web (ksi) (6.10.8.2.2) (6.11.8.2.2)
specified minimum yield strength of the bottom layer of longitudinal concrete deck reinforcement (ksi)
(D6.1)
specified minimum yield strength of the longitudinal concrete deck reinforcement (ksi) (D6.3.2)
specified minimum yield strength of the top layer of longitudinal concrete deck reinforcement (ksi) (D6.1)
specified minimum yield strength of a stiffener (ksi); specified minimum yield strength of the stiffener (ksi)
(6.10.11.1.2) (6.10.11.1.3)
specified minimum yield strength of a tension flange (ksi) (C6.8.2.3)
specified minimum yield strength of a web (ksi) (6.7.7.2)
axial or interaction stress range in various components of an orthotropic deck (ksi); shear flow in a box
section (kip/in.); QsFy (ksi) (6.6.1.2.3) (C6.11.1.1) (6.9.4.2.2)
stress due to the factored loads without consideration of flange lateral bending at a brace point opposite to the
one corresponding to f2, calculated from the moment envelope value that produces the largest compression at
this point in the flange under consideration, or the smallest tension if this point is never in compression;
positive for compression and negative for tension (ksi) (6.10.8.2.3)
axial stress range in various components of an orthotropic deck (ksi); stress at the opposite end of an
unbraced length from f2 representing the intercept of the most critical assumed linear stress distribution
through either f2 and fmid, or through f2 and f0, taken as 2fmid – f2 ≥ f0 (ksi) (C6.6.1.2.3) (6.10.8.2.3)
local bending stress range in various components of an orthotropic deck caused by rib-floorbeam interaction
(ksi); largest compressive stress due to the factored loads without consideration of lateral bending at either
end of an unbraced length calculated from the critical moment envelope value; always taken as positive
unless stress is zero or tensile at both ends of the unbraced length in which case f2 is taken as zero (ksi)
(C6.6.1.2.3) (6.10.8.2.3)
axial stress due to the factored loads in a solid web arch (ksi) (6.14.4.2)
maximum stress due to factored loadings, including moment amplification, in a solid web arch (ksi)
(6.14.4.2)
largest value of the compressive stress throughout the unbraced length in the flange under consideration,
calculated without consideration of flange lateral bending (ksi) (6.10.1.6)
stress in a box flange at an interior pier due to the factored loads caused by major-axis bending of the internal
diaphragm over the bearing sole plate (ksi) (C6.11.8.1.1)
compression-flange stress due to the Service II loads calculated without consideration of flange lateral
bending (ksi); sum of the various compression-flange flexural stresses caused by the different loads, i.e.,
DC1, DC2, DW and LL+IM, acting on their respective sections (ksi); compression-flange stress at the section
under consideration (6.10.4.2.2) (6.12.2.2.2) (D6.3.1)
minimum specified 28-day compressive strength of concrete (ksi) (6.9.5.1) (6.10.4.2.1)
maximum flexural stress due to the factored loads at the midthickness of the controlling flange at a point of
splice (ksi) (6.13.6.1.4c)
shear stress in a box flange at an interior pier caused by the internal diaphragm vertical shear due to the
factored loads (ksi) (C6.11.8.1.1)
compression-flange stress caused by the factored permanent load applied before the concrete deck has
hardened or is made composite, calculated without consideration of flange lateral bending (ksi) (6.10.1.10.2)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
6-14
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
fDC2
=
ff
=
fℓ
=
fℓ1
=
fLL+IM
=
fmid
=
fn
=
fncf
=
fos
=
fr
fs
=
=
fsr
ft
=
=
fv
=
fxx
=
G
=
g
H
=
=
Huw
h
=
=
ho
I
=
=
Iℓ
=
Ip
=
compression-flange stress caused by the factored permanent load acting on the long-term composite section,
calculated without consideration of flange lateral bending (ksi) (C6.10.11.3.1)
flange stress due to the Service II loads calculated without consideration of flange lateral bending (ksi)
(6.10.4.2.2)
flange lateral bending stress (ksi); second-order compression-flange lateral bending stress (ksi); flange lateral
bending stress due to the Service II loads (ksi); lateral bending stress in the flange under consideration at an
interior-pier section (ksi) (6.10.1.6) (6.10.4.2.2) (B6.4.2.1)
first-order compression-flange lateral bending stress at a section, or the maximum first-order lateral bending
stress in the compression flange throughout the unbraced length, as applicable (ksi) (6.10.1.6)
compression-flange stress caused by the factored vehicular live load plus impact acting on the short-term
composite section, calculated without consideration of flange lateral bending (ksi) (C6.10.11.3.1)
stress due to the factored loads without consideration of flange lateral bending at the middle of the unbraced
length of the flange under consideration, calculated from the moment envelope value that produces the
largest compression at this point, or the smallest tension if this point is never in compression; positive for
compression and negative for tension (ksi) (6.10.8.2.3)
normal stress in the inclined bottom flange of a variable web depth member (ksi); largest of the specified
minimum yield strengths of each component included in the calculation of Afn for a hybrid section when
yielding occurs first in one of the components, or the largest of the elastic stresses in each component on the
side of the neutral axis corresponding to Dn at first yield on the opposite side of the neutral axis (ksi)
(C6.10.1.4) (6.10.1.10.1)
flexural stress due to the factored loads at the midthickness of the noncontrolling flange at a point of splice
concurrent with fcf (ksi) (C6.13.6.1.4b)
flexural stress due to the Service II loads at the midthickness of the other flange at a point of splice
concurrent with fs in the flange under consideration (ksi) (C6.13.6.1.4b)
modulus of rupture of concrete (ksi) (6.10.1.7) (6.10.4.2.1)
flexural stress due to the factored loads in a longitudinal web stiffener (ksi); largest of the longitudinal
stresses due to the factored loads in the panels of a box flange on either side of a transverse flange stiffener
(ksi); maximum flexural stress due to the Service II loads at the midthickness of the flange under
consideration at a point of splice (ksi) (6.10.11.3.1) (C6.11.11.2) (C6.13.6.1.4b)
bending stress range in the longitudinal reinforcement over an interior pier (ksi) (6.10.10.3)
stress due to the factored loads on the gross area of a tension flange calculated without consideration of
flange lateral bending (ksi); sum of the various tension-flange flexural stresses caused by the different loads,
i.e., DC1, DC2, DW, and LL+IM, acting on their respective sections (ksi) (6.10.1.8) (D6.3.1)
St. Venant torsional shear stress in a box flange due to the factored loads; St. Venant torsional shear stress in
the flange due to the factored loads at the section under consideration (ksi) (6.11.3.2) (6.11.8.2.2)
various compression-flange flexural stresses caused by the different factored loads, i.e., DC1, DC2, DW, and
LL+IM, acting on their respective sections (ksi) (C6.10.11.3.1)
shear modulus of steel (ksi); shear modulus of elasticity for steel = 0.385E (ksi) (6.9.4.1.3) (C6.12.2.2.2)
(6.12.2.2.4)
distance between lines of bolts (in.); horizontal pitch of bolts in a web splice (in.) (6.8.3) (C6.13.6.1.4b)
effective throat of a fillet weld (in.); outside width of a rectangular Hollow Structural Section (HSS) parallel
to the plane of an end gusset plate(s) (in.) (6.6.1.2.5) (6.8.2.2)
design horizontal force resultant at the middepth of the web at a point of splice (kip) (C6.13.6.1.4b)
distance between centroids of individual component shapes perpendicular to the member axis of buckling
(in.); depth between the centerline of the flanges (in.); distance between flange centroids (in.) (6.9.4.3.1)
(C6.9.4.1.3) (C6.10.8.2.3)
distance between flange centroids (in.) (6.12.2.2.5)
moment of inertia of the short-term composite section, or optionally in regions of negative flexure of straight
girders only, the moment of inertia of the steel section plus the longitudinal reinforcement if the concrete is
not considered to be effective in tension in computing the range of longitudinal stress (in.4); moment of
inertia of the effective internal interior-pier diaphragm within a box section (in.4) (6.10.10.1.2) (C6.11.8.1.1)
moment of inertia of a longitudinal web stiffener including an effective width of web taken about the neutral
axis of the combined section (in.4); required moment of inertia of a longitudinal flange stiffener taken about
an axis parallel to a box flange and taken at the base of the stiffener (in.4) (6.10.11.1.3) (6.11.11.2)
polar moment of inertia of a web-splice bolt group (in.2) (C6.13.6.1.4b)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 6: STEEL STRUCTURES
6-15
Is
=
It
=
Ix
Iy
=
=
Iyc
=
Iyt
=
IM
J
=
=
K
=
Kh
Ks
Kxx
=
=
=
actual moment of inertia of a longitudinal flange stiffener taken about an axis parallel to a box flange and
taken at the base of the stiffener (in.4); moment of inertia of an arch rib stiffener (in.4) (6.11.8.2.3) (6.14.4.2)
moment of inertia of the transverse web stiffener taken about the edge in contact with the web for single
stiffeners and about the mid-thickness of the web for stiffener pairs (in.4); moment of inertia of a transverse
flange stiffener taken about an axis through its centroid and parallel to its bottom edge (in.4) (6.10.11.1.3)
(C6.11.11.2)
moments of inertia about the major principal axis of the cross-section (in.4) (6.9.4.1.3)
moment of inertia of a box-shaped member about an axis perpendicular to the axis of bending (in.4);
moments of inertia about the minor principal axis of the cross-section (in.4) moment of inertia about the yaxis (in.4) (6.9.4.1.3) (6.12.2.2.2) (6.12.2.2.4) (6.12.2.2.5)
moment of inertia of the compression flange of a steel section about the vertical axis in the plane of the web
(in.4) (6.10.2.2)
moment of inertia of the tension flange of a steel section about the vertical axis in the plane of the web (in.4)
(6.10.2.2)
dynamic load allowance from Article 3.6.2
St. Venant torsional constant (in.4); stiffener bending rigidity parameter (C6.7.4.3) (6.9.4.1.3) (6.10.11.1.3)
(6.12.2.2.4) (6.12.2.2.5)
effective length factor; effective length factor in the plane of buckling determined as specified in
Article 4.6.2.5 (6.9.3) (6.9.4.1.2)
hole size factor for bolted connections (6.13.2.8)
surface condition factor for bolted connections (6.13.2.8)
effective length for flexural buckling about the x-axis (in.) (6.9.4.1.3)
Kyy
=
effective length for flexural buckling about the y-axis (in.) (6.9.4.1.3)
Kzz
Kℓ/r
k
=
=
=
kc
ks
ksf
kss
L
=
=
=
=
=
Lb
=
Lc
=
Lcp
LFD
LL
Ln
=
=
=
=
Lp
=
Lr
=
LRFD
=
effective length for torsional buckling (in.) (6.9.4.1.3)
slenderness ratio (6.9.3)
plate buckling coefficient specified in Table 6.9.4.2.1-1; elastic web bend-buckling coefficient; shearbuckling coefficient for webs; plate-buckling coefficient for uniform normal stress in box flanges; distance
from the outer face of the flange to the toe of a web fillet of a rigid frame member to be stiffened (in.); platebuckling coefficient for uniform normal stress; distance from the outer face of a flange resisting a
concentrated load or a bearing reaction to the web toe of the fillet (in.) (6.9.4.2.1) (6.9.4.3.2) (6.10.1.9.1)
(6.10.9.3.2) (6.11.8.2.2) (6.13.7.2) (6.14.4.2) (D6.5.2)
flange local buckling coefficient (6.9.4.2.1)
plate-buckling coefficient for shear stress (6.11.8.2.2)
elastic web bend-buckling coefficient for fully restrained longitudinal edge conditions (C6.10.1.9.1)
elastic web bend-buckling coefficient for simply-supported longitudinal edge conditions (C6.10.1.9.1)
effective span length for determining additional camber to compensate for possible loss of camber in a heatcurved girder (in.); maximum length of the connection longitudinal welds or the out-to-out distance between
the bolts in the connection parallel to the line of force (in.); length of a girder shipping piece (in.); distance
from a single bolt to the free edge of the member measured parallel to the line of applied force (in.)
(6.6.1.2.3) (6.7.7.3) (6.8.2.2) (C6.10.3.4) (C6.13.2.9)
unbraced length (in.); unbraced length for lateral displacement or twist, as applicable (in.) (6.7.4.2)
(6.12.2.2.4) (6.12.2.2.5) (6.12.2.2.7)
length of a channel shear connector (in.); clear distance between bolt holes or between the bolt hole and the
end of the member in the direction of the applied bearing force (in.) (6.10.10.4.3) (6.13.2.9)
length of a cover plate (ft) (6.10.12.1)
load factor design
vehicular live load
arc length between the point of maximum positive live load plus impact moment and the centerline of an
adjacent interior support (ft) (6.10.10.4.2)
limiting unbraced length to achieve the nominal flexural resistance of RbRhFyc under uniform bending (in.);
arc length between an end of the girder and an adjacent point of maximum positive live load plus impact
moment (ft); limiting unbraced length to achieve the nominal flexural resistance Mp under uniform bending
(in.) (6.10.1.6) (6.10.10.4.2) (6.12.2.2.5)
limiting unbraced length to achieve the onset of nominal yielding in either flange under uniform bending
with consideration of compression-flange residual stress effects (in.) (6.7.4.2) (6.12.2.2.5)
load and resistance factor design
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
6-16
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
LTB
Lv
ℓ
=
=
=
M
M0
=
=
M1
=
M2
=
MAD
=
Mc
Mcr
MD1
=
=
=
MD2
=
Me
=
Mfb
=
Mft
=
Mℓ
=
Mmax
Mmid
=
=
Mn
Mnc
Mnc(FLB)
Mnt
Mp
Mpe
=
=
=
=
=
=
Mps
Mr
Mrb
Mrd
Mrt
=
=
=
=
=
lateral torsional buckling (C6.10.8.2.1) (C6.10.8.2.3) (CA6.3.1) (CA6.3.3) (CD6.4.1) (CD6.4.2)
distance between points of maximum and zero shear (in.) (6.12.1.2.3c)
unbraced member length (in.); distance between the work points of the joints measured along the length of
the angle (in.); unbraced length in the plane of buckling (in.) (6.8.4) (6.9.4.1.2) (6.9.4.4)
bending moment about the major-axis of the cross-section (k-in.) (C6.10.1.4)
bending moment due to the factored loads at a brace point opposite to the one corresponding to M2,
calculated from the moment envelope value that produces the largest compression at this point in the flange
under consideration, or the smallest tension if this point is never in compression; positive when it causes
compression and negative when it causes tension in the flange under consideration (k-in.) (A6.3.3)
bending moment at the opposite end of an unbraced length from M2 representing the intercept of the most
critical assumed linear stress distribution through either M2 and Mmid, or through M2 and M0, taken as
2Mmid – M2 ≥ M0 (k-in.); bending moment about the major-axis of the cross-section at the brace point with the
lower moment due to the factored loads adjacent to an interior-pier section from which moments are
redistributed taken as either the maximum or minimum moment envelope value, whichever produces the
smallest permissible unbraced length (k-in.) (A6.3.3) (B6.2.4)
largest major-axis bending moment due to the factored loads at either end of an unbraced length causing
compression in the flange under consideration, calculated from the critical moment envelope value; always
taken as positive unless the moment is zero or causes tension in the flange under consideration at both ends
of the unbraced length in which case M2 is taken as zero (k-in.); bending moment about the major-axis of the
cross-section at the brace point with the higher moment due to the factored loads adjacent to an interior-pier
section from which moments are redistributed taken as the critical moment envelope value (k-in.) (A6.3.3)
(B6.2.4)
additional bending moment that must be applied to the short-term composite section to cause nominal
yielding in either steel flange (k-in.) (D6.2.2)
column moment due to the factored loading in a rigid frame (k-in.) (6.13.7.2)
elastic lateral-torsional buckling moment (k-in.) (C6.12.2.2.2)
bending moment caused by the factored permanent load applied before the concrete deck has hardened or is
made composite (k-in.) (D6.2.2)
bending moment caused by the factored permanent load applied to the long-term composite section (k-in.)
(D6.2.2)
critical elastic moment envelope value due to the factored loads at an interior-pier section from which
moments are redistributed (k-in.) (B6.3.3.1)
applied moment due to the factored loads in a transverse beam supporting an orthotropic deck (k-in.)
(6.14.3.4)
applied transverse moment due to the factored loads in an orthotropic deck plate as a result of the plate
carrying wheel loads to adjacent longitudinal ribs (k-in.) (6.14.3.4)
lateral bending moment in the flanges due to the eccentric loadings from concrete deck overhang brackets (kin.) (C6.10.3.4)
maximum potential flexural resistance based on the compression flange (k-in.) (C6.10.8.2.1)
major-axis bending moment due to the factored loads at the middle of an unbraced length, calculated from
the moment envelope value that produces the largest compression at this point in the flange under
consideration, or the smallest tension if this point is never in compression; positive when it causes
compression and negative when it causes tension in the flange under consideration (k-in.) (A6.3.3)
nominal flexural resistance of a section (k-in.) (6.10.7.1.1)
nominal flexural resistance based on the compression flange (k-in.) (C6.8.2.3)
nominal flexural resistance based on compression flange local buckling (k-in.) (CD6.4.2)
nominal flexural resistance based on the tension flange (k-in.) (C6.8.2.3)
plastic moment (k-in.) (6.10.7.1.2) (6.12.2.2.2) (6.12.2.2.3) (6.12.2.2.4) (6.12.2.2.5) (6.12.2.2.7)
negative-flexure effective plastic moment at interior-pier sections from which moments are redistributed
(k-in.) (B6.3.3.1)
plastic moment resistance of the steel section of a concrete-encased member (k-in.) (6.12.2.3.1)
factored flexural resistance (k-in.) (6.12.1.2.1)
factored flexural resistance of a transverse beam supporting an orthotropic deck (k-in.) (6.14.3.4)
redistribution moment (k-in.) (B6.3.3.1)
factored flexural resistance of an orthotropic deck plate in carrying wheel loads to adjacent ribs (k-in.)
(6.14.3.4)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 6: STEEL STRUCTURES
Mrx
=
Mry
=
Mrx, Mry =
=
Mu
=
Muw
Mux, Muy =
=
Mux
=
Muy
=
My
Myc
=
Myt
m
N
=
=
=
NDT
Ns
n
=
=
=
nac
=
P
=
P1n
=
P1p
=
P2n
=
P2p
=
Pc
Pe
=
=
Ph
=
Pℓ
=
Pn
=
Pny
Po
Pp
=
=
=
6-17
factored flexural resistance about the x-axis taken equal to φf times the nominal flexural resistance about the
x-axis determined as specified in Article 6.10, 6.11 or 6.12, as applicable (kip-in.) (6.9.4.2.1)
factored flexural resistance about the y-axis taken equal to φf times the nominal flexural resistance about the
y-axis determined as specified in Article 6.12, as applicable (kip-in.) (6.9.4.2.1)
factored flexural resistance about the x- and y-axes, respectively (k-in.) (6.8.2.3)
moment due to the factored loads (k-in.); largest value of the major-axis bending moment throughout the
unbraced length causing compression in the flange under consideration (k-in.) (6.7.6.2.1) (6.10.1.6)
design moment at the middepth of the web at a point of splice (k-in.) (C6.13.6.1.4b)
flexural moments due to the factored loads about the x- and y-axes, respectively (k-in.) (6.8.2.3)
flexural moment about the x-axis resulting from factored loads (kip-in.) (6.9.4.2.1)
flexural moment about the y-axis resulting from factored loads (kip-in.) (6.9.4.2.1)
yield moment (k-in.); yield moment based on the distance to the tip of the stem (kip-in.) (6.10.7.1.2)
(6.12.2.2.4) (6.12.2.2.7)
yield moment with respect to the compression flange (k-in.); yield moment of the composite section of a
concrete-encased shape (k-in.) (C6.8.2.3) (6.12.2.3.1)
yield moment with respect to the tension flange (k-in.) (C6.8.2.3)
number of vertical rows of bolts in a web splice (C6.13.6.1.4b)
number of cycles of stress range; length of bearing, taken greater than or equal to k at end bearing locations
(in.) (6.6.1.2.5) (D6.5.2)
nondestructive testing
number of shear planes per bolt; number of slip planes per bolt (6.13.2.7) (6.13.2.8)
number of cycles per truck passage; modular ratio; number of shear connectors in a cross-section; minimum
number of shear connectors over the region under consideration; number of equally spaced longitudinal
flange stiffeners; number of bolts in one vertical row of a web splice (6.6.1.2.5) (6.9.5.1) (6.10.10.1.2)
(6.10.10.4.1) (6.11.8.2.3) (C6.13.6.1.4b)
number of additional shear connectors required in the regions of points of permanent load contraflexure for
sections that are noncomposite in negative-flexure regions (6.10.10.3)
total nominal shear force in the concrete deck for the design of the shear connectors at the strength limit state
(kip) (6.10.10.4.1)
longitudinal force in the girder over an interior support for the design of the shear connectors at the strength
limit state (kip) (6.10.10.4.2)
longitudinal force in the concrete deck at the point of maximum positive live load plus impact moment for
the design of the shear connectors at the strength limit state (kip) (6.10.10.4.2)
longitudinal force in the concrete deck over an interior support for the design of the shear connectors at the
strength limit state (kip) (6.10.10.4.2)
longitudinal force in the girder at the point of maximum positive live load plus impact moment for the design
of the shear connectors at the strength limit state (kip) (6.10.10.4.2)
plastic force in the compression flange used to compute the plastic moment (kip) (D6.1)
elastic critical buckling resistance determined as specified in Article 6.9.4.1.2 for flexural buckling, and as
specified in Article 6.9.4.1.3 for torsional bucking or flexural-torsional buckling, as applicable (kips)
(6.9.4.1.1)
horizontal component of the flange force in the inclined bottom flange of a variable web depth member (kip)
(C6.10.1.4)
statically equivalent concentrated lateral concrete deck overhang bracket force placed at the middle of the
unbraced length (kip) (C6.10.3.4)
nominal bearing resistance on pin plates (kip); nominal axial compressive resistance (kip); total longitudinal
force in the concrete deck over an interior support for the design of the shear connectors at the strength limit
state, taken as the lesser of either P1n or P2n (kip) (6.8.7.2) (6.9.2.1) (6.10.10.4.2)
nominal axial tensile resistance for yielding in the gross section (kip) (6.8.2.1)
equivalent nominal yield resistance = QFyAg (kips) (6.9.4.1.1)
total longitudinal force in the concrete deck at the point of maximum positive live load plus impact moment
for the design of the shear connectors at the strength limit state, taken as the lesser of either P1p or P2p (kip)
(6.10.10.4.2)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
6-18
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Pr
=
Prb
=
Prt
=
Ps
PT
=
=
Pt
=
Pu
=
Pv
=
Pw
p
=
=
Q
=
Qn
Qr
Qu
R
=
=
=
=
R1
=
factored axial tensile or compressive resistance (kip); factored bearing resistance on pin plates (kip); factored
axial resistance of bearing stiffeners (kip); nominal flexural resistance of an orthotropic deck, with
consideration of the effective width of the deck (kip); factored axial compressive resistance of a steel pile
(kip); factored compressive resistance determined as specified in Article 6.9.2.1 (kip) (6.8.2.1) (6.8.7.2)
(6.9.2.2) (6.9.4.2.1) (6.9.4.3.2) (6.10.11.2.4a) (6.15.3.1)
plastic force in the bottom layer of longitudinal deck reinforcement used to compute the plastic moment (kip)
(D6.1)
plastic force in the top layer of longitudinal deck reinforcement used to compute the plastic moment (kip)
(D6.1)
plastic compressive force in the concrete deck used to compute the plastic moment (kip) (D6.1)
total longitudinal force in the concrete deck between the point of maximum positive live load plus impact
moment and the centerline of an adjacent interior support for the design of the shear connectors at the
strength limit state, taken as the sum of Pp and Pn (kip) (6.10.10.4.2)
minimum required bolt tension (kip); plastic force in the tension flange used to compute the plastic moment
(kip) (6.13.2.8) (D6.1)
applied axial force due to the factored loads (kip); direct tension or shear force on a bolt due to the factored
loads (kip); global tension due to the factored loads on an orthotropic deck (kip); axial compressive force
effect resulting from factored loads (kip) (6.8.2.3) (6.9.4.2.1) (6.13.2.10.4) (6.13.2.11)
vertical component of the flange force in the inclined bottom flange of a variable web depth member
(kip) (C6.10.1.4)
plastic force in the web used to compute the plastic moment (kip) (D6.1)
pitch of shear connectors along the longitudinal axis (in.); staggered pitch between two adjacent lines of
staggered bolt holes (in.) (6.10.10.1.2) (6.13.2.6.3)
first moment of the transformed short-term area of the concrete deck about the neutral axis of the short-term
composite section, or optionally in regions of negative flexure of straight girders only, the first moment of the
longitudinal reinforcement about the neutral axis of the composite section if the concrete is not considered to
be effective in tension in computing the range of longitudinal stress (in.3); first moment of one-half the
effective box-flange area at an interior pier about the neutral axis of the effective internal diaphragm section
(in.3); slender element reduction factor determined as specified in Article 6.9.4.2. Q shall be taken equal to
1.0 for bearing stiffeners (6.9.4.1.1) (6.10.10.1.2) (C6.11.8.1.1)
nominal shear resistance of a single shear connector (kip) (6.10.10.4.1)
factored shear resistance of a single shear connector (kip) (6.10.10.4.1)
prying tension per bolt due to the factored loads (kip) (6.13.2.10.4)
transition radius of welded attachments as shown in Table 6.6.1.2.3-1 (in.); minimum girder radius within a
panel (ft); radius of curvature (ft); reduction factor applied to the factored shear resistance of bolts passing
through fillers (6.6.1.2.3) (6.7.4.2) (6.7.7.2) (6.13.6.1.5)
constant which when multiplied by kE Fyc defines the slenderness ratio for a box flange equal to 0.6 times
the flange slenderness at which the elastic buckling stress for the flange equals the resistance for yielding
under combined normal and shear stress (6.11.8.2.2)
R2
=
Rb
Rcf
Rh
Rn
=
=
=
=
Rp
=
(RpB)n
(RpB)r
Rpc
Rpt
Rr
(Rsb)n
(Rsb)r
=
=
=
=
=
=
=
constant which when multiplied by
kE Fyc defines the slenderness ratio for a box flange equal to the flange
slenderness at which the elastic buckling stress for the flange equals Fyr (6.11.8.2.2)
web load-shedding factor (6.10.1.6) (6.10.1.10.2) (6.11.8.2.2)
absolute value of the ratio of Fcf to fcf at a point of splice (C6.13.6.1.4b)
hybrid factor (6.10.1.10.1) (6.11.8.2.2)
nominal resistance of a bolt, connection or connected material (kip) or (ksi); nominal resistance to a
concentrated loading (kip) (6.13.2.2) (D6.5.2)
reduction factor for holes taken equal to 0.90 for bolt holes punched full size and 1.0 for bolt holes drilled
full size or subpunched and reamed to size (6.8.2.1) (6.13.4) (6.13.5.3)
nominal bearing resistance on pins (kip) (6.7.6.2.2)
factored bearing resistance on pins (kip) (6.7.6.2.2)
web plastification factor for the compression flange (A6.1.3)
web plastification factor for the tension flange (A6.1.4)
factored resistance of a bolt, connection or connected material (kip) or (ksi) (6.13.2.2)
nominal bearing resistance for the fitted end of bearing stiffeners (kip) (6.10.11.2.3)
factored bearing resistance for the fitted end of bearing stiffeners (kip) (6.10.11.2.3)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 6: STEEL STRUCTURES
Ru
r
ri
rib
rn
rs
rt
rts
rx
ry
ryc
rz
rσ
ro
S
Seff
SLT
SNC
Ss
SST
Sx
Sxc
Sxt
Sy
s
st
T
Tn
Tr
Tu
t
tb
tc
tf
6-19
=
=
factored concentrated load or bearing reaction (kip) (D6.5.2)
minimum radius of gyration of a tension or compression member (in.); radius of gyration of a built-up
member about an axis perpendicular to a perforated plate (in.); radius of gyration of a longitudinal web
stiffener including an effective width of web taken about the neutral axis of the combined section (in.) (6.8.4)
(6.9.4.3.2) (6.10.11.3.3)
= minimum radius of gyration of an individual component shape (in.) (C6.9.4.3.1)
= radius of gyration of an individual component shape relative to its centroidal axis parallel to the member axis
of buckling (in.) (6.9.4.3.1)
= nominal bearing pressure at bolt holes (ksi) (C6.13.2.9)
= radius of gyration of a structural steel shape, pipe or tubing about the plane of buckling (in.); radius of
gyration about the axis normal to the plane of buckling (in.) (6.9.4.1.2)
= effective radius of gyration for lateral torsional buckling (in.) (6.10.8.2.3)
= radius of gyration used in the determination of Lr (in.) (6.12.2.2.5)
= radius of gyration about the geometric axis of the angle parallel to the connected leg (in.); radius of gyration
about the x-axis (in.) (6.9.4.1.3) (6.9.4.4)
= radius of gyration of a steel section with respect to a vertical axis in the plane of the web (in.); radius of
gyration about the y-axis (in.) (6.9.4.1.3) (6.12.2.2.5) (CB6.2.4)
= radius of gyration of the compression flange with respect to a vertical axis in the plane of the web (in.)
(C6.10.8.2.3)
= radius of gyration about the minor principal axis of the angle (in.) (6.9.4.4)
= desired bending stress ratio in a horizontally curved I-girder, taken equal to |fℓ/fbu| (C6.7.4.2)
= polar radius of gyration about the shear center (in.) (6.9.4.1.3)
= elastic section modulus (in.3); elastic section modulus about the axis of bending (in.3) (C6.12.2.2.1)
(6.12.2.2.2) (6.12.2.2.3)
= effective elastic section modulus about the axis of bending determined using an effective width of the
compression flange be (in.3) (6.12.2.2.2)
= long-term composite elastic section modulus (in.3) (D6.2.2)
= noncomposite elastic section modulus (in.3) (D6.2.2)
= elastic section modulus of a transverse flange stiffener (in.3) (C6.11.11.2)
= short-term composite elastic section modulus (in.3) (D6.2.2)
= elastic section modulus to an inclined bottom flange of a variable web depth member (in.3) elastic section
modulus about the x-axis (in.3); section modulus about the major geometric axis (in.3) (6.12.2.2.5)
(6.12.2.2.7) (C6.10.1.4)
= elastic section modulus about the major axis of the section to the compression flange taken as Myc/Fyc (in.3);
elastic section modulus with respect to the compression flange (in.3) (C6.8.2.3) (6.12.2.2.4)
= elastic section modulus about the major axis of the section to the tension flange taken as Myt/Fyt (in.3) (C6.8.2.3)
= elastic section modulus about the axis parallel with the web (in.3) (6.12.2.2.1)
= pitch of any two consecutive bolts in a staggered chain (in.); longitudinal spacing of transverse reinforcement in a
concrete-encased shape (in.); spacing of bolts on a single line or in a staggered pattern adjacent to a free edge of an
outside plate or shape (in.); vertical pitch of bolts in a web splice (in.) (6.8.3) (6.12.3.1) (6.13.2.6.2) (C6.13.6.1.4b)
= maximum transverse spacing between shear connectors on a composite box flange (in.) (6.11.10)
= internal torque in a box section due to the factored loads (kip-in.); internal torque due to the factored loads
(kip-in.); base metal thickness of the thicker part joined in a fillet-welded connection given in Table 6.13.3.4-1
(in.) (C6.11.1.1) (6.13.3.4)
= nominal resistance of a bolt in axial tension or in combined axial tension and shear (kip) (6.13.2.2)
= factored resistance of a bolt in axial tension or in combined axial tension and shear (kip) (6.13.2.2)
= tensile force per bolt due to Load Combination Service II (kip) (6.13.2.11)
= thickness of plate or plates (in.); thickness of tube or wall (in.); thickness of the thinner outside plate or shape
(in.); thickness of the connected material (in.); thickness of the thinnest connected part (in.); thickness of tube
(in.); width of the rectangular bar parallel to the axis of bending (in.) (C6.7.4.3) (6.9.4.2.1) (6.12.1.2.3c)
(6.12.2.2.3) (6.12.2.2.7) (6.13.2.6.2) (6.13.2.9) (6.13.2.10.4)
= thickness of the flange transmitting the concentrated force in a rigid-frame connection (in.) (6.13.7.2)
= thickness of the flange of the member to be stiffened in a rigid-frame connection (in.) (6.13.7.2)
= flange thickness (in.); flange thickness of a channel shear connector (in.); thickness of the flange resisting a
concentrated load or bearing reaction (in.) (C6.9.4.1.3) (6.10.2.2) (6.10.10.4.3) (6.12.2.2.4) (6.12.2.2.5)
(D6.5.3)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
6-20
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
tfc
=
tft
tp
ts
=
=
=
tw
=
U
Ubs
=
=
V
=
Vcr
Vf
Vfat
Vn
Vp
Vr
Vsr
=
=
=
=
=
=
=
Vu
=
Vui
Vuw
w
=
=
=
xo
x
=
=
Yo
yo
y
Z
=
=
=
=
Zr
Zx
Zy
α
=
=
=
=
β
=
η
γ
=
=
thickness of the compression flange (in.); design wall thickness of the compression flange taken equal to 0.93
times the nominal wall thickness for electric-resistance-welded HSS and taken equal to the nominal wall
thickness for all others (in.) (6.10.1.10.2) (6.12.2.2.2)
thickness of the tension flange (in.) (C6.10.9.1)
thickness of a transversely loaded plate (in.); thickness of a projecting stiffener element (in.) (6.6.1.2.5) (6.10.11.1.2)
thickness of a concrete deck (in.); thickness of a longitudinal web or flange stiffener (in.); thickness of an
arch-rib stiffener (in.) (6.10.1.10.2) (6.10.11.3.2) (6.14.4.2)
web thickness (in.); web or tube thickness (in.); web thickness of a channel shear connector (in.); thickness
of the web to be stiffened in a rigid-frame connection (in.); web thickness of an arch rib (in.); design wall
thickness of the web taken equal to 0.93 times the nominal wall thickness for electric-resistance-welded HSS
and taken equal to the nominal wall thickness for all others (in.) (6.7.7.2) (6.9.4.2) (6.10.10.4.3) (6.12.2.2.2)
(6.12.2.2.5) (6.13.7.2) (6.14.4.2)
reduction factor to account for shear lag in connections subjected to a tension load (6.6.1.2.3) (6.8.2.1)
reduction factor for block shear rupture resistance taken equal to 0.50 when the tension stress is non-uniform
and1.0 when the tension stress is uniform (6.13.4)
additional shear force for built-up members with perforated plates (kip); factored vertical shear force in the internal
interior-pier diaphragm of a box section due to flexure plus St. Venant torsion (kip) (6.9.4.3.2) (C6.11.8.1.1)
shear-buckling resistance (kip) (6.10.3.3)
vertical shear force range under the Fatigue Load Combination (kip) (6.10.10.1.2)
longitudinal fatigue shear range per unit length (kip/in.) (6.10.10.1.2)
nominal shear resistance (kip) (6.10.9.1) (6.12.1.2.3a)
plastic shear force (kip) (6.10.9.2)
factored shear resistance (kip) (6.12.1.2.3)
horizontal fatigue shear range per unit length (kip/in.); vector sum of the horizontal fatigue shear range and the
torsional fatigue shear range in the concrete deck for a composite box flange (kip/in.) (6.10.10.1.2) (6.11.10)
shear due to the factored loads (kip); vertical shear due to the factored loads on one inclined web of a box
section (kip) (6.7.6.2.1) (6.11.9)
shear due to the factored loads along one inclined web of a box section (kip) (6.11.9)
design shear for the web at a point of splice (kip) (6.13.6.1.4b)
center-to-center distance between the top flanges of a box section (in.); plate width (in.); effective length of
deck assumed acting radial to the girder (in.); larger of the width of a box flange between longitudinal flange
stiffeners or the distance from a web to the nearest longitudinal flange stiffener (in.) (C6.7.5.3) (6.8.2.2)
(6.10.10.1.2) (6.11.8.2.3)
distance along the x-axis between the shear center and centroid of the cross-section (in.) (6.9.4.1.3)
distance from the centroid of the member to the surface of the gusset or connection plate (in.); perpendicular
distance from the plane of the connection to the centroid of the tension member cross-section or the portion
of the cross-section tributary to the connection (in.); dimensional parameter used in calculating the shear lag
reduction factor U (in.) (6.6.1.2.3) (6.8.2.2)
distance from the neutral axis to the extreme outer fiber of the cross-section (in.) (6.7.7.3)
distance along the y-axis between the shear center and centroid of the cross-section (in.) (6.9.4.1.3)
distance from the plastic neutral axis to the top of the element where the plastic neutral axis is located (in.) (D6.1)
curvature parameter for determining required longitudinal web stiffener rigidity; plastic section modulus
(in.3); plastic section modulus about the axis of bending (in.3) (6.10.11.3.3) (6.12.2.2.2) (6.12.2.2.3)
(6.12.2.2.7) (6.12.2.3.1)
shear fatigue resistance of an individual shear connector (kip) (6.10.10.1.2)
plastic section modulus about the x-axis (in.3) (6.12.2.2.4) (6.12.2.2.5)
plastic section modulus about the axis parallel with the web (in.3) (6.12.2.2.1)
separation ratio = h/2rib; factor defining the sloping straight line representing the finite-life portion of the
fatigue shear resistance of an individual stud shear connector; factor for flange splice design generally equal
to 1.0, except that a lower value equal to Fn/Fyf may be used for flanges where Fn is less than Fyf (6.9.4.3.1)
(6.10.10.2) (6.13.6.1.4c)
factor equal to two times the area of the web based on Dn divided by Afn used in computing the hybrid factor;
factor defining the approximate ratio of Dp to Dt/7.5 at which a composite section in positive flexure reaches Mp;
curvature correction factor for longitudinal web stiffener rigidity (6.10.1.10.1) (C6.10.7.1.2) (6.10.11.3.3)
load modifier related to ductility, redundancy and operational importance (C6.6.1.2.2)
load factor specified in Table 3.4.1-1; the ratio of Af to Ap for filler plate design (6.6.1.2.2) (6.13.6.1.5)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 6: STEEL STRUCTURES
Δ
=
ΔDL
=
(Δf)
(ΔF)cn
(ΔF)n
(ΔFTH)
ΔM
ΔR
λ
λf
=
=
=
=
=
=
=
=
λpf
=
λpw
λpw(Dc)
λpw(Dcp)
λrf
=
=
=
=
λrw
λw
ψ
=
=
=
ρ
ρt
θ
=
=
=
θp
θRL
=
=
σflg
=
φ
=
φb
φbb
φbs
φc
φe1
=
=
=
=
=
φe2
=
φf
φs
φsc
φsd
φt
φu
φv
φvu
=
=
=
=
=
=
=
=
6-21
total camber at any section along the effective span length of a heat-curved girder, including compensatory
camber to account for possible camber loss (in.); reduction factor for the maximum stress in a box flange
(6.7.7.3) (6.11.3.2)
camber at any point along the effective span length of a heat-curved girder to compensate for deflection due
to dead load or any other specified loads (in.) (6.7.7.3)
live load stress range due to the passage of the fatigue load (ksi) (6.6.1.2.2)
nominal fatigue resistance for Detail Category C (ksi) (6.6.1.2.5)
nominal fatigue resistance (ksi) (6.6.1.2.2) (6.6.1.2.5)
constant amplitude fatigue threshold (ksi) (6.6.1.2.5)
maximum value of ΔDL within the effective span length of a heat-curved girder (in.) (6.7.7.3)
additional camber to compensate for the possible loss of camber in a heat-curved girder (in.) (6.7.7.3)
normalized column slenderness factor (6.9.5.1)
slenderness ratio for the compression flange; slenderness ratio for the flange; compression-flange slenderness
= bfc/tfc; flange slenderness = bf /2tf; flange slenderness of the channel = bf /tf (6.10.8.2.2) (6.11.8.2.2)
(6.12.2.2.1) (6.12.2.2.2) (6.12.2.2.4) (6.12.2.2.5)
limiting slenderness ratio for a compact flange; limiting slenderness for a compact flange (6.10.8.2.2)
(6.12.2.2.2) (6.12.2.2.4) (6.12.2.2.5)
limiting slenderness for a compact web (6.12.2.2.2) (6.12.2.2.5)
limiting slenderness ratio for a compact web corresponding to 2Dc/tw (A6.2.2)
limiting slenderness ratio for a compact web corresponding to 2Dcp/tw (A6.2.1)
limiting slenderness ratio for a noncompact flange; limiting slenderness for a noncompact flange (6.10.8.2.2)
(6.12.2.2.2) (6.12.2.2.4)
limiting slenderness ratio for a noncompact web (6.10.1.10.2)
slenderness ratio for the web based on the elastic moment (A6.2.2)
ratio of the total cross-sectional area to the cross-sectional area of both flanges; constant used in determining
the required moment of inertia of longitudinal stiffeners for box flanges (6.7.7.2) (6.11.11.2)
factor equal to the smaller of Fyw/fn and 1.0 used in computing the hybrid factor (6.10.1.10.1)
the larger of Fyw/Fcrs and 1.0 (6.10.11.1.3)
angle of inclination of the bottom flange of a variable web depth member (degrees); angle of inclination of
the web plate of a box section to the vertical (degrees) (C6.10.1.4) (6.11.9)
plastic rotation at an interior-pier section (radians) (B6.6.2)
plastic rotation at which the moment at an interior-pier section nominally begins to decrease with increasing
θp (radians) (6.10.7.1.2)
range of longitudinal fatigue stress in the bottom flange without consideration of flange lateral bending (ksi)
(6.10.10.1.2)
resistance factor; resistance factor for resistance during pile driving; resistance factor for concrete in tension
specified in Article 5.5.4.2.1 (6.5.4.2) (6.10.1.7)
resistance factor for bearing (6.5.4.2)
resistance factor for bolts bearing on material (6.5.4.2)
resistance factor for block shear (6.5.4.2)
resistance factor for axial compression (6.5.4.2)
resistance factor for shear on the effective area of the weld metal in complete penetration welds; resistance
factor for tension normal to the effective area of the weld metal in partial penetration welds (6.5.4.2)
resistance factor for shear parallel to the axis of the weld metal in partial penetration welds; resistance factor
for shear in the throat of the weld metal in fillet welds (6.5.4.2)
resistance factor for flexure (6.5.4.2) (6.11.8.2.2)
resistance factor for shear in bolts (6.5.4.2)
resistance factor for shear connectors (6.5.4.2)
resistance factor for shakedown (CB6.4.2.1)
resistance factor for tension in bolts (6.5.4.2)
resistance factor for fracture on the net section of tension members (6.5.4.2)
resistance factor for shear (6.5.4.2) (6.11.8.2.2)
resistance factor for shear rupture of connection elements as specified in Article 6.5.4.2 (6.13.5.3)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
6-22
φw
φy
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
=
=
resistance factor for web crippling (6.5.4.2)
resistance factor for yielding on the gross section of tension members (6.5.4.2)
6.4—MATERIALS
6.4.1—Structural Steels
2013 Revision
Structural steels shall conform to the requirements
specified in Table 6.4.1-1, and the design shall be based on
the minimum properties indicated.
The modulus of elasticity and the thermal coefficient
of expansion of all grades of structural steel shall be
assumed as 29,000 ksi and 6.5×10–6 in./in./°F, respectively.
AASHTO M 270M/M 270, Grade 36 (ASTM
A709/A709M, Grade 36), may be used in thicknesses over
4.0 in. for nonstructural applications or bearing assembly
components.
C6.4.1
2013 Revision
The term yield strength is used in these Specifications
as a generic term to denote either the minimum specified
yield point or the minimum specified yield strength.
The main difference, and in most cases the only
difference, between AASHTO and ASTM requirements is
the inclusion of mandatory notch toughness and
weldability requirements in the AASHTO Material
Standards. Steels meeting the AASHTO Material
requirements are prequalified for use in welded bridges.
The yield strength in the direction parallel to the
direction of rolling is of primary interest in the design of
most steel structures. In welded bridges, notch toughness is
of equal importance. Other mechanical and physical
properties of rolled steel, such as anisotropy, ductility,
formability, and corrosion resistance, may also be
important to ensure the satisfactory performance of the
structure.
No specification can anticipate all of the unique or
especially demanding applications that may arise. The
literature on specific properties of concern and appropriate
supplementary material production or quality
requirements, provided in the AASHTO and ASTM
Material Specifications and the AASHTO/AWS
D1.5M/D1.5 Bridge Welding Code, should be considered,
if appropriate.
AASHTO M 270M/M 270 (ASTM A709/A709M),
Grade HPS 70W, has replaced AASHTO M 270M/M 270
(ASTM A709/A709M), Grade 70W, and AASHTO
M 270M/M 270 (ASTM A709/A709M), Grade HPS
100W, has replaced AASHTO M 270M/M 270 (ASTM
A709/A709M), Grade 100 and 100W in Table 6.4.1-1. The
intent of these replacements is to encourage the use of HPS
steel over the older bridge steels of the same strength level
due to its enhanced properties. The older steels are still
available, but are not recommended for use and should be
used only with the approval of the Owner. The maximum
available plate lengths of AASHTO M 270M/M 270
(ASTM A709/A709M), Grade HPS 70W and HPS 100W,
are a function of the processing of the plate, with longer
lengths of Grade HPS 70W produced as as-rolled plate.
The maximum available plate lengths of these steels
should be determined in consultation with the material
producers.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
SECTION 6: STEEL STRUCTURES
6-23
Quenched and tempered alloy steel structural shapes
and seamless mechanical tubing with a specified maximum
tensile strength not exceeding 140 ksi for structural shapes
or 145 ksi for seamless mechanical tubing may be used,
provided that:
•
The material meets all other mechanical and chemical
requirements of AASHTO M 270M/M 270 (ASTM
A709/A709M), Grade HPS 100W, and
•
The design is based upon the minimum properties
specified for AASHTO M 270M/M 270 (ASTM
A709/A709M), Grade HPS 100W.
Structural tubing shall be either cold-formed welded
or seamless tubing conforming to ASTM A500, Grade B
or Grade C, or ASTM A847; or hot-formed welded or
seamless tubing conforming to ASTM A501 or ASTM
A618.
Thickness limitations relative to rolled shapes and
groups shall comply with AASHTO M 160M/M 160
(ASTM A6/A6M).
ASTM A500 cautions that structural tubing
manufactured to that specification may not be suitable for
applications involving dynamically loaded elements in
welded structures where low-temperature notch-toughness
properties may be important. As such, the use of this
material should be carefully examined with respect to its
specific application in consultation with the Owner. Where
this material is contemplated for use in applications where
low-temperature notch-toughness properties are deemed
important, consideration should be given to requiring that
the material satisfy the Charpy V-notch toughness
requirements specified in Article 6.6.2.
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2012
Edition
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6-24
Table 6.4.1-1—Minimum Mechanical Properties of Structural Steel by Shape, Strength, and Thickness
AASHTO
Designation
M 270M/
M 270
Grade 36
A709/
A709M
Grade 36
Up to 4.0 incl.
M 270M/
M 270
Grade 50
A709/
A709M
Grade 50
Up to
4.0 incl.
M 270M/
M 270
Grade 50S
A709/
A709M
Grade 50S
Not
Applicable
M 270M/
M 270
Grade 50W
A709/
A709M
Grade 50W
Up to
4.0 incl.
M 270M/
M 270
Grade HPS 50W
A709/
A709M
Grade HPS 50W
Up to 4.0
incl.
M 270M/
M 270
Grade HPS 70W
A709/
A709M
Grade HPS 70W
Up to
4.0 incl.
All Groups
All
Groups
All
Groups
All
Groups
Not Applicable
Not Applicable
Not
Applicable
Not
Applicable
Minimum Tensile
Strength, Fu, ksi
58
65
65
70
70
85
110
100
Specified
Minimum Yield
Point or Specified
Minimum Yield
Strength, Fy, ksi
36
50
50
50
50
70
100
90
Equivalent ASTM
Designation
Thickness of
Plates, in.
Shapes
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M 270M/
M 270
Grade HPS 100W
A709/
A709M
Grade HPS 100W
Up to 2.5
Over 2.5 to
incl.
4.0 incl.
2012
Edition
SECTION 6: STEEL STRUCTURES
6-25
6.4.2—Pins, Rollers, and Rockers
Steel for pins, rollers, and expansion rockers shall
conform to the requirements in Table 6.4.2-1, Table 6.4.1-1,
or Article 6.4.7.
Expansion rollers shall be not less than 4.0 in. in
diameter.
Table 6.4.2-1—Minimum Mechanical Properties of Pins, Rollers, and Rockers by Size and Strength
AASHTO Designation with Size
Limitations
M 169
4.0 in. in dia.
or less
ASTM Designation
Grade or Class
A108
Grades 1016
to 1030 incl.
36
Specified Minimum Yield Point,
Fy, ksi
M 102M/
M 102
to 20.0 in.
in dia.
A668/
A668M
Class C
33
M 102M/
M 102
to 20.0 in.
in dia.
A668/
A668M
Class D
37.5
M 102M/
M 102
to 10.0 in.
in dia.
A668/
A668M
Class F
50
M 102M/
M 102
to 20.0 in.
in dia.
A668/
A668M
Class G
50
6.4.3—Bolts, Nuts, and Washers
6.4.3.1—Bolts
C6.4.3.1
Bolts used as structural fasteners shall conform to one
of the following:
•
The Standard Specification for Carbon Steel Bolts and
Studs, 60 ksi Tensile Strength, ASTM A307 Grade A
or B,
•
The Standard Specification for Structural Bolts, Steel,
Heat-Treated, 120/105 ksi Minimum Tensile Strength
with a required minimum tensile strength of 120 ksi
for diameters 0.5 through 1.0 in. and 105 ksi for
diameters 1.125 through 1.5 in., AASHTO M 164
(ASTM A325), or
•
The Standard Specification for Heat-Treated Steel
Structural Bolts, 150 ksi Minimum Tensile Strength,
AASHTO M 253 (ASTM A490).
The ASTM standard for A307 bolts covers three
grades of fasteners, A, B, and C. Grade A and B bolts may
be used under this Specification as appropriate. There is no
AASHTO standard corresponding to ASTM A307.
Type 1 bolts should be used with steels other than
weathering steel. Type 3 bolts conforming with either
AASHTO M 164 (ASTM A325) or AASHTO M 253
(ASTM A490) shall be used with weathering steels.
AASHTO M 164 (ASTM A325) Type 1 bolts may be
either hot-dip galvanized in accordance with AASHTO
M 232M/M 232 (ASTM A153/A153M), Class C, or
mechanically galvanized in accordance with AASHTO
M 298 (ASTM B695), Class 50, when approved by the
Engineer. Galvanized bolts shall be retested after
galvanizing, as required by AASHTO M 164 (ASTM
A325).
AASHTO M 253 (ASTM A490) bolts shall not be
galvanized.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
6-26
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Washers, nuts, and bolts of any assembly shall be
galvanized by the same process. The nuts should be
overtapped to the minimum amount required for the
fastener assembly and shall be lubricated with a lubricant
containing a visible dye.
Anchor Bolts shall conform to one of the following:
•
ASTM A307 Grade C, or
•
ASTM F1554.
6.4.3.2—Nuts
The purpose of the dye is to allow a visual check to be
made for the lubricant at the time of field installation.
Black bolts must be oily to the touch when delivered
and installed.
ASTM A307 Grade C are nonheaded anchor bolts
intended for structural anchorage purposes. There is no
AASHTO standard corresponding to ASTM F1554.
C6.4.3.2
6.4.3.2.1—Nuts Used with Structural Fasteners
Nuts used with structural fasteners shall conform to
the following as appropriate.
Except as noted below, nuts for AASHTO M 164
(ASTM A325) bolts shall conform to the Standard
Specification for Carbon and Alloy Steel Nuts, AASHTO
M 291 (ASTM A563), Grades DH, DH3, C, C3, and D.
Nuts for AASHTO M 253 (ASTM A490) bolts shall
conform to the requirements of AASHTO M 291 (ASTM
A563), Grades DH and DH3.
Nuts to be galvanized shall be heat treated Grade DH.
The provisions of Article 6.4.3.1 shall apply. All
galvanized nuts shall be lubricated with a lubricant
containing a visible dye.
Plain nuts shall have a minimum hardness of 89 HRB.
Nuts to be used with AASHTO M 164 (ASTM A325)
Type 3 bolts shall be of Grade C3 or DH3. Nuts to be used
with AASHTO M 253 (ASTM A490) Type 3 bolts shall be
of Grade DH3.
6.4.3.2.2—Nuts Used with Anchor Bolts
Nuts used with anchor bolts shall conform to the
following as appropriate.
Nuts for ASTM A307 Grade C and for ASTM F1554
anchor bolts shall conform to AASHTO M 291 (ASTM
A563) for appropriate grade and size of anchor bolt.
Nuts to be galvanized shall be heat treated Grade DH
or DH3. The provisions of Article 6.4.3.1 shall apply. All
galvanized nuts should be lubricated with a lubricant
containing a visible dye.
6.4.3.3—Washers
C6.4.3.3
Washers shall conform to the Standard Specification
for Hardened Steel Washers, AASHTO M 293 (ASTM
F436).
The provisions of Article 6.4.3.1 shall apply to
galvanized washers.
Installation provisions for washers are covered in the
AASHTO LRFD Bridge Construction Specifications
(2010).
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2012
Edition
SECTION 6: STEEL STRUCTURES
6-27
6.4.3.4—Alternative Fasteners
Other fasteners or fastener assemblies not specified
heretofore, such as those conforming to the requirements
of ASTM F1852, may be used subject to the approval of
the Engineer, provided that:
•
They meet materials, manufacturing, and chemical
composition requirements of AASHTO M 164
(ASTM A325) or AASHTO M 253 (ASTM A490),
•
They meet mechanical property requirements of the
same specification in full size tests, and
•
The body diameter and bearing areas under the head
and nut, or their equivalent, shall not be less than
those provided by a bolt and nut of the same nominal
dimensions prescribed in Articles 6.4.3.1 and 6.4.3.2,
Such alternate fasteners may differ in other dimensions
from those of the bolts, nuts, and washers specified in
Articles 6.4.3.1 through 6.4.3.3.
6.4.3.5—Load Indicator Devices
C6.4.3.5
Load-indicating devices conforming to the
requirements of ASTM F959 may be used in conjunction
with bolts, nuts and washers. Load-indicating devices
which are incorporated into assemblies with hardened
heavy hex AASHTO M 291 (ASTM A563) Grade DH nuts
shall be considered permissible for use, provided both the
load-indicating device and heavy hex nut meet the
mechanical property requirements of their respective
ASTM standards.
Alternate direct tension indicating devices may be
used, subject to the approval of the Engineer.
Installation provisions for load-indicating devices are
covered in the AASHTO LRFD Bridge Construction
Specifications (2010).
An assembly comprised of a load-indicating device
affixed to a hardened heavy hex structural nut by the
fastener manufacturer is also referred to as a captive
DTI/nut.
6.4.4—Stud Shear Connectors
C6.4.4
Shear connector studs shall be made from cold-drawn
bars, Grades 1015, 1018, or 1020, either semi or fully
killed, conforming to AASHTO M 169 (ASTM A108),
and shall have a specified minimum yield and tensile
strength of 50.0 ksi and 60.0 ksi, respectively. If flux
retaining caps are used, the steel for the caps shall be of a
low carbon grade suitable for welding and shall conform to
ASTM A109.
Physical properties, test methods, and certification of
steel shear connectors are covered in the AASHTO LRFD
Bridge Construction Specifications (2010).
6.4.5—Weld Metal
C6.4.5
Weld metal shall conform to the requirements of the
AASHTO/AWS D1.5M/D1.5 Bridge Welding Code.
The AWS designation systems are not consistent. For
example, there are differences between the system used for
designating electrodes for shielded metal arc welding and
the system used for designating submerged arc welding.
Therefore, when specifying weld metal and/or flux by
AWS designation, the applicable specification should be
reviewed to ensure a complete understanding of the
designation reference.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
6-28
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6.4.6—Cast Metal
6.4.6.1—Cast Steel and Ductile Iron
Cast steel shall conform to one of the following:
•
AASHTO M 103M/M 103 (ASTM A27/A27M),
Grade 70-36, unless otherwise specified;
•
AASHTO M 163M/M 163 (ASTM A743/A743M)
Grade CA15, unless otherwise specified.
Ductile iron castings shall conform to ASTM A536,
Grade 60-40-18, unless otherwise specified.
6.4.6.2—Malleable Castings
Malleable castings shall conform to ASTM A47,
Grade 35018. The specified minimum yield strength shall
not be less than 35.0 ksi.
6.4.6.3—Cast Iron
Cast iron castings shall conform to AASHTO M 105
(ASTM A48), Class 30.
6.4.7—Stainless Steel
Stainless steel may conform to one of the following:
•
ASTM A176,
•
ASTM A240,
•
ASTM A276, or
•
ASTM A666.
Stainless steel not conforming to the above-listed
specifications may be used, provided that it conforms to
the chemical and mechanical requirements of one of the
above-listed specifications or other published
specifications that establish its properties and suitability
and that it is subjected to analyses, tests, and other controls
to the extent and in the manner prescribed by one of the
listed specifications.
6.4.8—Cables
6.4.8.1—Bright Wire
Bright wire shall conform to ASTM A510.
6.4.8.2—Galvanized Wire
Galvanized wire shall conform to ASTM A641.
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2012
Edition
SECTION 6: STEEL STRUCTURES
6-29
6.4.8.3—Epoxy-Coated Wire
Epoxy-coated wire shall conform to ASTM A99.
6.4.8.4—Bridge Strand
Bridge strand shall conform to ASTM A586 or ASTM
A603.
6.5—LIMIT STATES
6.5.1—General
The structural behavior of components made of steel
or steel in combination with other materials shall be
investigated for each stage that may be critical during
construction, handling, transportation, and erection as well
as during the service life of the structure of which they are
part.
Structural components shall be proportioned to satisfy
the requirements at strength, extreme event, service, and
fatigue limit states.
6.5.2—Service Limit State
C6.5.2
The provisions of Article 2.5.2.6 shall apply as
applicable.
Flexural members shall be investigated at the service
limit state as specified in Articles 6.10 and 6.11.
The intent of the service limit state provisions
specified for flexural members in Articles 6.10 and 6.11 is
primarily to prevent objectionable permanent deformations
due to localized yielding that would impair rideability
under expected severe traffic loadings.
6.5.3—Fatigue and Fracture Limit State
Components and details shall be investigated for
fatigue as specified in Article 6.6.
The fatigue load combinations specified in
Table 3.4.1-1 and the fatigue live load specified in
Article 3.6.1.4 shall apply.
Flexural members shall be investigated at the fatigue
and fracture limit state as specified in Articles 6.10 and
6.11.
Bolts subject to tensile fatigue shall satisfy the
provisions of Article 6.13.2.10.3.
Fracture toughness requirements shall be in
conformance with Article 6.6.2.
6.5.4—Strength Limit State
6.5.4.1—General
Strength and stability shall be considered using the
applicable strength load combinations specified in
Table 3.4.1-1.
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2012
Edition
6-30
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6.5.4.2—Resistance Factors
Resistance factors, φ, for the strength limit state shall
be taken as follows:
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
C6.5.4.2
Base metal φ as appropriate for resistance under
consideration.
For flexure
φf = 1.00
For shear
φv = 1.00
For axial compression, steel only
φc = 0.90
For axial compression, composite
φc = 0.90
For tension, fracture in net section
φu = 0.80
For tension, yielding in gross section
φy = 0.95
For bearing on pins in reamed, drilled
or bored holes and on milled surfaces
φb = 1.00
For bolts bearing on material
φbb = 0.80
For shear connectors
φsc = 0.85
For A 325 and A 490 bolts in tension
φt = 0.80
For A 307 bolts in tension
φt = 0.80
For F 1554 bolts in tension
φt = 0.80
For A 307 bolts in shear
φs = 0.75
For F 1554 bolts in shear
φs = 0.75
For A 325 and A 490 bolts in shear
φs = 0.80
For block shear
φbs = 0.80
For shear, rupture in connection
element
φvu = 0.80
For web crippling
φw = 0.80
For weld metal in complete penetration welds:
o shear on effective area
φe1 = 0.85
o tension or compression normal to
effective area
same as base metal
o tension or compression parallel
to axis of the weld
same as base metal
For weld metal in partial penetration welds:
o shear parallel to axis of weld
φe2 = 0.80
o tension or compression parallel
to axis of weld
same as base metal
o compression normal to the
effective area
same as base metal
o tension normal to the effective
area
φe1 = 0.80
For weld metal in fillet welds:
o tension or compression parallel to
axis of the weld
same as base metal
o shear in throat of weld metal
φe2 = 0.80
For resistance during pile driving
φ = 1.00
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2012
Edition
LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
SECTION 6: STEEL STRUCTURES
•
•
•
•
For axial resistance of piles in compression and
subject to damage due to severe driving conditions
where use of a pile tip is necessary:
o H-piles
φc = 0.50
o pipe piles
φc = 0.60
For axial resistance of piles in compression under
good driving conditions where use of a pile tip is not
necessary:
o H-piles
φc = 0.60
o pipe piles
φc = 0.70
For combined axial and flexural resistance of
undamaged piles:
o axial resistance for H-piles
φc = 0.70
o axial resistance for pipe piles
φc = 0.80
o flexural resistance
φf = 1.00
For shear connectors in tension
φst = 0.75
6-31
The basis for the resistance factors for driven steel
piles is described in Article 6.15.2. Further limitations on
usable resistance during driving are specified in
Article 10.7.8.
Indicated values of φc and φf for combined axial and
flexural resistance are for use in interaction equations in
Article 6.9.2.2.
6.5.5—Extreme Event Limit State
C6.5.5
All applicable extreme event load combinations in
Table 3.4.1-1 shall be investigated. For Extreme Event I, γp
for DC and DW loads shall be taken to be 1.0.
All resistance factors for the extreme event limit state,
except those specified for bolts and shear connectors, shall
be taken to be 1.0.
All resistance factors for ASTM A307 Grade C and
ASTM F1554 bolts used as anchor bolts for the extreme
event limit state shall be taken to be 1.0.
Bolted slip-critical connections within a seismic load
path shall be proportioned according to the requirements of
Article 6.13.2.1.1. The connections shall also be
proportioned to provide shear, bearing, and tensile
resistance in accordance with Articles 6.13.2.7, 6.13.2.9,
and 6.13.2.10, as applicable, at the extreme event limit
state. Standard holes or short-slotted holes normal to the
line of force shall be used in such connections.
During earthquake motion, there is the potential for
full reversal of design load and inelastic deformations of
members orconnections, or both. Therefore, slip of bolted
joints located within a seismic load path cannot and need
not be prevented during a seismic event. A special
inspection of joints and connections, particularly in
fracture critical members, should be performed as
described in The Manual for Bridge Evaluation (2011)
after a seismic event.
To prevent excessive deformations of bolted joints
due to slip between the connected plies under earthquake
motions, only standard holes or short-slotted holes normal
to the line of force are permitted in bolted joints located
within a seismic load path. For such holes, the upper limit
of 2.4dtFu on the bearing resistance is intended to prevent
elongations due to bearing deformations from exceeding
approximately 0.25 in. It should be recognized, however,
that the actual bearing load in a seismic event may be
much larger than that anticipated in design and the actual
deformation of the holes may be larger than this theoretical
value. Nonetheless, the specified upper limit on the
nominal bearing resistance should effectively minimize
damage in moderate seismic events.
6.6—FATIGUE AND FRACTURE
CONSIDERATIONS
6.6.1—Fatigue
6.6.1.1—General
C6.6.1.1
Fatigue shall be categorized as load- or distortioninduced fatigue.
In the AASHTO Standard Specifications for Highway
Bridges (2002), the provisions explicitly relating to fatigue
deal only with load-induced fatigue.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6-32
6.6.1.2—Load-Induced Fatigue
6.6.1.2.1—Application
2013 Revision
The force effect considered for the fatigue design of a
steel bridge detail shall be the live load stress range. For
flexural members with shear connectors provided
throughout their entire length, and with concrete deck
reinforcement satisfying the provisions of Article 6.10.1.7,
live load stresses and stress ranges for fatigue design may
be computed using the short-term composite section
assuming the concrete deck to be effective for both
positive and negative flexure.
Residual stresses shall not be considered in
investigating fatigue.
These provisions shall be applied only to details
subjected to a net applied tensile stress. In regions where
the unfactored permanent loads produce compression,
fatigue shall be considered only if the compressive stress is
less than the maximum live load tensile stress caused by
the Fatigue I load combination specified in Table 3.4.1-1.
C6.6.1.2.1
Concrete can provide significant resistance to tensile
stress at service load levels. Recognizing this behavior will
have a significantly beneficial effect on the computation of
fatigue stress ranges in top flanges in regions of stress
reversal and in regions of negative flexure. By utilizing shear
connectors in these regions to ensure composite action in
combination with the required one percent longitudinal
reinforcement wherever the longitudinal tensile stress in the
concrete deck exceeds the factored modulus of rupture of the
concrete, crack length and width can be controlled so that
full-depth cracks should not occur. When a crack does
occur, the stress in the longitudinal reinforcement increases
until the crack is arrested. Ultimately, the cracked concrete
and the reinforcement reach equilibrium. Thus, the concrete
deck may contain a small number of staggered cracks at any
given section. Properly placed longitudinal reinforcement
prevents coalescence of these cracks.
It has been shown that the level of total applied stress is
insignificant for a welded steel detail. Residual stresses due
to welding are implicitly included through the specification
of stress range as the sole dominant stress parameter for
fatigue design. This same concept of considering only stress
range has been applied to rolled, bolted, and riveted details
where far different residual stress fields exist. The
application to nonwelded details is conservative. A complete
stress range cycle may include both a tensile and
compressive component. Only the live load plus dynamic
load allowance effects need be considered when
computing a stress range cycle; permanent loads do not
contribute to the stress range. Tensile stresses propagate
fatigue cracks. Material subjected to a cyclical loading at
or near an initial flaw will be subject to a fully effective
stress cycle in tension, even in cases of stress reversal,
because the superposition of the tensile residual stress
elevates the entire cycle into the tensile stress region.
Fatigue design criteria need only be considered for
components or details subject to effective stress cycles in
tension and/or stress reversal. If a component or detail is
subject to stress reversal, fatigue is to be considered no
matter how small the tension component of the stress cycle
is since a flaw in the tensile residual stress zone could still
be propagated by the small tensile component of stress.
The decision on whether or not a tensile stress could exist
is based on the Fatigue I Load Combination because this is
the largest stress range a detail is expected to experience
often enough to propogate a crack. When the tensile
component of the stress range cycle resulting from this
load combination exceeds the compressive stress due to
the unfactored permanent loads, there is a net tensile stress
in the component or at the detail under consideration, and
therefore, fatigue must be considered. If the tensile
component of the stress range does not exceed the
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SECTION 6: STEEL STRUCTURES
6-33
compressive stress due to the unfactored permanent loads
there is no net tensile stress. In this case, the stress cycle is
compression—compression and a fatigue crack will not
propogate beyond a heat-affected zone.
Cross-frames and diaphragms connecting adjacent girders
are stressed when one girder deflects with respect to the
adjacent girder connected by the diaphragm or cross-frame.
The sense of stress is reversed when the vehicle is positioned
over the adjacent girder. Since it is the total stress range that
produces fatigue, the effects of trucks in different transverse
positions usually creates the largest stress range in these
bracing members. To cause one cycle of the stress range so
computed requires two vehicles to traverse the bridge in
separate transverse positions with one vehicle leading the
other. For cases where the force effects in these members are
available from an analysis, such as in horizontally curved or
sharply skewed bridges, it may be desirable in some instances
to check fatigue-sensitive details on a bracing member
subjected to a net applied tensile stress determined as specified
herein. In lieu of more specific owner supplied guidance, it is
recommended that one cycle of stress be taken as 75 percent of
the stress range in the member determined by the passage of
the factored fatigue load in the two different transverse
positions just described. The factor of 0.75 is distinct from the
load factor specified for the applicable fatigue load
combination in Table 3.4.1-1; i.e., both factors may be applied
simultaneously. The reduction is intended to approximate the
low probability of two vehicles being located in the critical
relative positions, such as outside of a striped lane, over
millions of cycles. However, in no case should the calculated
range of stress be less than the stress range caused by loading
of only one lane. There is no provision in this recommended
procedure to account for the need for two trucks to cause a
single cycle of stress. For cases where the nominal fatigue
resistance is calculated based on a finite life, the Engineer may
wish to consider a reduction in the number of cycles whenever
two trucks are required to cause a single cycle of stress.
C6.6.1.2.2
6.6.1.2.2—Design Criteria
For load-induced fatigue considerations, each detail
shall satisfy:
γ ( Δf ) ≤ ( ΔF )n
(6.6.1.2.2-1)
where:
Ȗ
=
(ǻf)
=
(ǻF)n
=
load factor specified in Table 3.4.1-1 for the
fatigue load combination
force effect, live load stress range due to the
passage of the fatigue load as specified in
Article 3.6.1.4 (ksi)
nominal fatigue resistance as specified in
Article 6.6.1.2.5 (ksi)
6.6.1.2.3—Detail Categories
2013 Revision
Components and details shall be designed to satisfy
the requirements of their respective detail categories
summarized in Table 6.6.1.2.3-1. Where bolt holes are
Eq. 6.6.1.2.2-1 may be developed by rewriting
Eq. 1.3.2.1-1 in terms of fatigue load and resistance
parameters:
ηγ ( Δf ) ≤ φ ( ΔF )n
(C6.6.1.2.2-1)
but for the fatigue limit state,
Ș = 1.0
φ = 1.0
C6.6.1.2.3
Components and details susceptible to load-induced
fatigue cracking have been grouped into eight categories,
called detail categories, by fatigue resistance.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6-34
depicted in Table 6.6.1.2.3-1, their fabrication shall
conform to the provisions of Article 11.4.8.5 of the
AASHTO LRFD Bridge Construction Specifications.
Where permitted for use, unless specific information is
available to the contrary, bolt holes in cross-frame,
diaphragm, and lateral bracing members and their
connection plates shall be assumed for design to be
punched full size.
Except as specified herein for fracture critical
members, where the projected 75-year single lane Average
Daily Truck Traffic (ADTT)SL is less than or equal to that
specified in Table 6.6.1.2.3-2 for the component or detail
under consideration, that component or detail should be
designed for finite life using the Fatigue II load
combination specified in Table 3.4.1-1. Otherwise, the
component or detail shall be designed for infinite life using
the Fatigue I load combination. The single-lane Average
Daily Truck Traffic (ADTT)SL shall be computed as
specified in Article 3.6.1.4.2.
For components and details on fracture-critical
members, the Fatigue I load combination specified in
Table 3.4.1-1 should be used in combination with the
nominal fatigue resistance for infinite life specified in
Article 6.6.1.2.5.
Orthotropic deck components and details shall be
designed to satisfy the requirements of their respective
detail categories summarized in Table 6.6.1.2.3-1 for the
chosen design level shown in the table and as specified in
Article 9.8.3.4.
Experience indicates that in the design process the
fatigue considerations for Detail Categories A through B′
rarely, if ever, govern. Nevertheless, Detail Categories A
through B′ have been included in Table 6.6.1.2.3-1 for
completeness. Investigation of components and details
with a fatigue resistance based on Detail Categories A
through B′ may be appropriate in unusual design cases.
Table 6.6.1.2.3-1 illustrates many common details
found in bridge construction and identifies potential crack
initiation points for each detail. In Table 6.6.1.2.3-1,
“Longitudinal” signifies that the direction of applied stress
is parallel to the longitudinal axis of the detail.
“Transverse” signifies that the direction of applied stress is
perpendicular to the longitudinal axis of the detail.
Category F for allowable shear stress range on the throat
of a fillet weld has been eliminated from Table 6.6.1.2.3-1.
When fillet welds are properly sized for strength
considerations, Category F should not govern. Fatigue will be
governed by cracking in the base metal at the weld toe and
not by shear on the throat of the weld. Research on endbolted cover plates is discussed in Wattar et al. (1985).
Where the design stress range calculated using the
Fatigue I load combination is less than (ǻF)TH, the detail will
theoretically provide infinite life. Except for Categories E
and E′, for higher traffic volumes, the design will most often
be governed by the infinite life check. Table 6.6.1.2.3-2
shows for each detail category the values of (ADTT)SL above
which the infinite life check governs, assuming a 75-yr
design life and one stress range cycle per truck.
The values in the second column of Table 6.6.1.2.3-2
were computed as follows:
75 _ Year ( ADTT ) SL =
A
ª (ΔF )TH º
« 2 » (365)(75)(n )
¬
¼
3
(C6.6.1.2.3-1)
using the values for A and (ΔF)TH specified in
Tables 6.6.1.2.5-1 and 6.6.1.2.5-3, respectively, a fatigue
design life of 75 yr and a number of stress range cycles per
truck passage, n, equal to one. These values were rounded up
to the nearest five trucks per day. That is, the indicated values
were determined by equating infinite life and finite life
resistances with due regard to the difference in load factors
used with the Fatigue I and Fatigue II load combinations. For
other values of n, the values in Table 6.6.1.2.3-2 should be
modified by dividing by the appropriate value of n taken from
Table 6.6.1.2.5-2. For other values of the fatigue design life,
the values in Table 6.6.1.2.3-2 should be modified by
multiplying the values by the ratio of 75 divided by the
fatigue life sought in years.
The procedures for load-induced fatigue are followed
for orthotropic deck design. Although the local structural
stress range for certain fatigue details can be caused by
distortion of the deck plate, ribs, and floorbeams, research
has demonstrated that load-induced fatigue analysis
produces a reliable assessment of fatigue performance.
Considering the increased γLL and cycles per truck
passage (n) in orthotropic decks, the 75-yr ADTTSL
equivalent to infinite life (trucks per day) results in 870 for
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SECTION 6: STEEL STRUCTURES
6-35
deck plate details and 4350 for all other details, based on
Category C. Thus, finite life design may produce more
economical designs on lower-volume roadways.
Table 6.6.1.2.3-1—Detail Categories for Load-Induced Fatigue
Description
Category
Constant
A
(ksi3)
Threshold
(ǻF)TH
ksi
Potential Crack
Initiation Point
Illustrative Examples
Section 1—Plain Material away from Any Welding
1.1 Base metal, except noncoated
weathering steel, with rolled or
cleaned surfaces. Flame-cut
edges with surface roughness
value of 1,000 μ-in. or less, but
without re-entrant corners.
A
250 × 108
24
Away from all
welds or
structural
connections
1.2 Noncoated weathering steel
base metal with rolled or cleaned
surfaces designed and detailed in
accordance with FHWA (1989).
Flame-cut edges with surface
roughness value of 1,000 μ-in. or
less, but without re-entrant
corners.
B
120 × 108
16
Away from all
welds or
structural
connections
1.3 Member with re-entrant
corners at copes, cuts, block-outs
or other geometrical
discontinuities made to the
requirements of AASHTO/AWS
D1.5, except weld access holes.
C
44 × 108
10
At any external
edge
1.4 Rolled cross sections with
weld access holes made to the
requirements of AASHTO/AWS
D1.5, Article 3.2.4.
C
44 x 108
10
In the base
metal at the
re-entrant
corner of the
weld access
hole
1.5 Open holes in members
(Brown et al., 2007).
D
22 × 108
7
In the net
section
originating at
the side of the
hole
Section 2—Connected Material in Mechanically Fastened Joints
2.1 Base metal at the gross section
of high-strength bolted joints
designed as slip-critical
connections with pretensioned
high-strength bolts installed in
holes drilled full size or
subpunched and reamed to size—
e.g., bolted flange and web splices
and bolted stiffeners. (Note: see
Condition 2.3 for bolt holes
punched full size; see Condition
2.5 for bolted angle or tee section
member connections to gusset or
connection plates.)
B
120 × 108
16
Through the
gross section
near the hole
continued on next page
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Table 6.6.1.2.3-1 (continued)—Detail Categories for Load-Induced Fatigue
Description
Category
Constant
A
(ksi3)
Threshold
(ǻF)TH
ksi
Potential
Crack
Initiation Point
Illustrative Examples
Section 2—Connected Material in Mechanically Fastened Joints (continued)
2.2 Base metal at the net section of
high-strength bolted joints designed
as bearing-type connections but
fabricated and installed to all
requirements for slip-critical
connections with pretensioned highstrength bolts installed in holes
drilled full size or subpunched and
reamed to size. (Note: see Condition
2.3 for bolt holes punched full size;
see Condition 2.5 for bolted angle or
tee section member connections to
gusset or connection plates.)
2.3 Base metal at the net section of all
bolted connections in hot dipped
galvanized members (Huhn and
Valtinat, 2004); base metal at the
appropriate section defined in
Condition 2.1 or 2.2, as applicable, of
high-strength bolted joints with
pretensioned bolts installed in holes
punched full size (Brown et al., 2007);
and base metal at the net section of
other mechanically fastened joints,
except for eyebars and pin plates, e.g.,
joints using ASTM A307 bolts or
non-pretensioned high-strength bolts.
(Note: see Condition 2.5 for bolted
angle or tee section member
connections to gusset or connection
plates).
2.4 Base metal at the net section of
eyebar heads or pin plates (Note: for
base metal in the shank of eyebars
or through the gross section of pin
plates, see Condition 1.1 or 1.2, as
applicable.)
2.5 Base metal in angle or tee
section members connected to a
gusset or connection plate with
high-strength bolted slip-critical
connections. The fatigue stress
range shall be calculated on the
effective net area of the member,
Ae = UAg, in which U=(1- x /L) and
where Ag is the gross area of the
member. x is the distance from the
centroid of the member to the
surface of the gusset or connection
plate and L is the out-to-out distance
between the bolts in the connection
parallel to the line of force. The
effect of the moment due to the
eccentricities in the connection shall
be ignored in computing the stress
range (McDonald and Frank, 2009).
B
120 × 108
16
In the net
section
originating at
the side of the
hole
D
22 × 108
7
In the net
section
originating at
the side of the
hole or
through the
gross section
near the hole,
as applicable
E
11 × 108
4.5
In the net
section
originating at
the side of the
hole
See
applicable
Category
above
See
applicable
Constant
above
See
applicable
Threshold
above
Through the
gross section
near the hole,
or in the net
section
originating at
the side of the
hole, as
applicable
L
x
c.g.
L
c.g.
x
continued on next page
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SECTION 6: STEEL STRUCTURES
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Table 6.6.1.2.3-1 (continued)—Detail Categories for Load-Induced Fatigue
Description
Category
Constant
A
(ksi3)
Threshold
(ǻF)TH
ksi
Potential
Crack
Initiation Point
Illustrative Examples
2.5 (continued) The fatigue category
shall be taken as that specified for
Condition 2.1. For all other types of
bolted connections, replace Ag with
the net area of the member, An, in
computing the effective net area
according to the preceding equation
and use the appropriate fatigue
category for that connection type
specified for Condition 2.2 or 2.3, as
applicable.
Section 3—Welded Joints Joining Components of Built-Up Members
3.1 Base metal and weld metal in
members without attachments built
up of plates or shapes connected by
continuous longitudinal complete
joint penetration groove welds
back-gouged and welded from the
second side, or by continuous fillet
welds parallel to the direction of
applied stress.
B
120 × 108
16
From surface
or internal
discontinuities
in the weld
away from the
end of the
weld
3.2 Base metal and weld metal in
members without attachments built
up of plates or shapes connected by
continuous longitudinal complete
joint penetration groove welds with
backing bars not removed, or by
continuous partial joint penetration
groove welds parallel to the
direction of applied stress.
Bƍ
61 × 108
12
From surface
or internal
discontinuities
in the weld,
including weld
attaching
backing bars
3.3 Base metal and weld metal at
the termination of longitudinal
welds at weld access holes made to
the requirements of AASHTO/AWS
D1.5, Article 3.2.4 in built-up
members. (Note: does not include
the flange butt splice).
D
22 × 108
7
From the weld
termination
into the web or
flange
3.4 Base metal and weld metal in
partial length welded cover plates
connected by continuous fillet
welds parallel to the direction of
applied stress.
B
120 × 108
16
From surface
or internal
discontinuities
in the weld
away from the
end of the
weld
continued on next page
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Table 6.6.1.2.3-1 (continued)—Detail Categories for Load-Induced Fatigue
Description
Category
Constant
A
(ksi3)
Threshold
(ǻf)TH
ksi
Potential
Crack
Initiation Point
Illustrative Examples
Section 3—Welded Joints Joining Components of Built-Up Members (continued)
In the flange at
the toe of the
end weld or in
the flange at the
termination of
the longitudinal
weld or in the
edge of the
flange with
wide cover
plates
3.5 Base metal at the termination of
partial length welded cover plates
having square or tapered ends that
are narrower than the flange, with
or without welds across the ends, or
cover plates that are wider than the
flange with welds across the ends:
Flange thickness ≤ 0.8 in.
Flange thickness > 0.8 in.
E
11 × 108
4.5
E′
8
2.6
8
16
In the flange at
the termination
of the
longitudinal
weld
2.6
In the edge of
the flange at
the end of the
cover plate
weld
3.9 × 10
3.6 Base metal at the termination of
partial length welded cover plates
with slip-critical bolted end
connections satisfying the
requirements of Article 6.10.12.2.3.
B
120 × 10
3.7 Base metal at the termination of
partial length welded cover plates
that are wider than the flange and
without welds across the ends.
E′
3.9 × 108
Section 4—Welded Stiffener Connections
4.1 Base metal at the toe of
transverse stiffener-to-flange fillet
welds and transverse stiffener-toweb fillet welds. (Note: includes
similar welds on bearing stiffeners
and connection plates).
C′
44 × 108
12
Initiating from
the
geometrical
discontinuity
at the toe of
the fillet weld
extending into
the base metal
4.2 Base metal and weld metal in
longitudinal web or longitudinal
box-flange stiffeners connected by
continuous fillet welds parallel to
the direction of applied stress.
B
120 × 108
16
From the
surface or
internal
discontinuities
in the weld
away from the
end of the
weld
continued on next page
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SECTION 6: STEEL STRUCTURES
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Table 6.6.1.2.3-1 (continued)—Detail Categories for Load-Induced Fatigue
Description
Category
Constant
A
(ksi3)
Threshold
(ǻf)TH
ksi
Potential
Crack
Initiation Point
Illustrative Examples
Section 4—Welded Stiffener Connections (continued)
4.3 Base metal at the termination of
longitudinal stiffener-to-web or
longitudinal stiffener-to-box flange
welds:
With the stiffener attached by fillet
welds and with no transition radius
provided at the termination:
Stiffener thickness < 1.0 in.
Stiffener thickness ≥ 1.0 in.
E
11 × 108
4.5
E′
3.9 × 10
8
2.6
B
120 × 108
16
In the primary
member at the
end of the
weld at the
weld toe
With the stiffener attached by welds
and with a transition radius R
provided at the termination with the
weld termination ground smooth:
R ≥ 24 in.
C
24 in. > R ≥ 6 in.
D
6 in. > R ≥ 2 in.
E
2 in. > R
44 × 10
8
10
22 × 10
8
7
11 × 10
8
4.5
In the primary
member near
the point of
tangency of
the radius
Section 5—Welded Joints Transverse to the Direction of Primary Stress
5.1 Base metal and weld metal in or
adjacent to complete joint
penetration groove welded butt
splices, with weld soundness
established by NDT and with welds
ground smooth and flush parallel to
the direction of stress. Transitions in
thickness or width shall be made on
a slope no greater than 1:2.5 (see
also Figure 6.13.6.2-1).
From internal
discontinuities
in the filler
metal or along
the fusion
boundary or at
the start of the
transition
Fy < 100 ksi
B
120 ×
108
16
Fy ≥ 100 ksi
B′
61 × 108
12
B
120 ×
108
16
5.2 Base metal and weld metal in
or adjacent to complete joint
penetration groove welded butt
splices, with weld soundness
established by NDT and with
welds ground parallel to the
direction of stress at transitions in
width made on a radius of not less
than 2 ft with the point of tangency
at the end of the groove weld (see
also Figure 6.13.6.2-1).
From internal
discontinuities
in the filler
metal or
discontinuities
along the fusion
boundary
continued on next page
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Table 6.6.1.2.3-1 (continued)—Detail Categories for Load-Induced Fatigue
Description
Category
Constant
A
(ksi3)
Threshold
(ǻf)TH
ksi
Potential Crack
Initiation Point
8
10
From the
surface
discontinuity at
the toe of the
weld extending
into the base
metal or along
the fusion
boundary
10
Initiating from
the geometrical
discontinuity at
the toe of the
weld extending
into the base
metal or
initiating at the
weld root subject
to tension
extending up and
then out through
the weld
5.3 Base metal and weld metal in
or adjacent to the toe of complete
joint penetration groove welded T
or corner joints, or in complete
joint penetration groove welded
butt splices, with or without
transitions in thickness having
slopes no greater than 1:2.5 when
weld reinforcement is not removed.
(Note: cracking in the flange of the
“T” may occur due to out-of-plane
bending stresses induced by the
stem).
C
44 × 10
5.4 Base metal and weld metal at
details where loaded discontinuous
plate elements are connected with a
pair of fillet welds or partial joint
penetration groove welds on
opposite sides of the plate normal
to the direction of primary stress.
C as
adjusted
in Eq.
6.6.1.2.5-4
44 × 108
Illustrative Examples
Section 6—Transversely Loaded Welded Attachments
6.1 Base metal in a longitudinally
loaded component at a transversely
loaded detail (e.g. a lateral
connection plate) attached by a
weld parallel to the direction of
primary stress and incorporating a
transition radius R with the weld
termination ground smooth.
Near point of
tangency of the
radius at the
edge of the
longitudinally
loaded
component or at
the toe of the
weld at the
weld
termination if
not ground
smooth
R ≥ 24 in.
B
120 ×
108
16
24 in. > R ≥ 6 in.
C
44 × 108
10
6 in. > R ≥ 2 in.
D
22 × 108
7
2 in. > R
E
11 × 108
4.5
E
11 × 108
4.5
For any transition radius with the
weld termination not ground
smooth (Note: Condition 6.2, 6.3
or 6.4, as applicable, shall also be
checked.)
continued on next page
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SECTION 6: STEEL STRUCTURES
6-41
Table 6.6.1.2.3-1 (continued)—Detail Categories for Load-Induced Fatigue
Description
Category
Constant
A
(ksi3)
Threshold
(ǻf)TH
ksi
Potential Crack
Initiation Point
Illustrative Examples
Section 6—Transversely Loaded Welded Attachments (continued)
6.2 Base metal in a transversely
loaded detail (e.g. a lateral
connection plate) attached to a
longitudinally loaded component of
equal thickness by a complete joint
penetration groove weld parallel to
the direction of primary stress and
incorporating a transition radius R,
with weld soundness established by
NDT and with the weld termination
ground smooth:
With the weld reinforcement
removed:
B
R ≥ 24 in.
C
24 in. > R ≥ 6 in.
D
6 in. > R ≥ 2 in.
2 in. > R
E
120 × 108
16
44 × 10
8
10
22 × 10
8
7
11 × 10
8
4.5
With the weld reinforcement not
removed:
R ≥ 24 in.
24 in. > R ≥ 6 in.
C
44 × 108
10
C
44 × 10
8
10
22 × 10
8
7
11 × 10
8
4.5
D
6 in. > R ≥ 2 in.
2 in. > R
E
Near points of
tangency of the
radius or in the
weld or at the
fusion boundary of
the longitudinally
loaded component
or the transversely
loaded attachment
At the toe of the
weld either along
the edge of the
longitudinally
loaded component
or the transversely
loaded attachment
(Note: Condition 6.1 shall also be
checked.)
At the toe of the
weld along the
edge of the thinner
plate
6.3 Base metal in a transversely
loaded detail (e.g. a lateral
connection plate) attached to a
longitudinally loaded component
of unequal thickness by a
complete joint penetration groove
weld parallel to the direction of
primary stress and incorporating a
weld transition radius R, with
weld soundness established by
NDT and with the weld
termination ground smooth:
In the weld
termination of
small radius weld
transitions
At the toe of the
weld along the
edge of the thinner
plate
With the weld reinforcement removed:
R ≥ 2 in.
R < 2 in.
For any weld transition radius
with the weld reinforcement not
removed (Note: Condition 6.1
shall also be checked.)
D
22 × 108
E
11 × 10
8
4.5
E
11 × 108
4.5
7
continued on next page
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6-42
Table 6.6.1.2.3-1 (continued)—Detail Categories for Load-Induced Fatigue
Description
Category
Constant
A
(ksi3)
Threshold
(ǻf)TH
ksi
Potential Crack
Initiation Point
Illustrative Examples
Section 6—Transversely Loaded Welded Attachments (continued)
6.4 Base metal in a transversely
loaded detail (e.g. a lateral
connection plate) attached to a
longitudinally loaded component by
a fillet weld or a partial joint
penetration groove weld, with the
weld parallel to the direction of
primary stress (Note: Condition 6.1
shall also be checked.)
See
Condition
5.4
Section 7—Longitudinally Loaded Welded Attachments
7.1 Base metal in a longitudinally
loaded component at a detail with a
length L in the direction of the
primary stress and a thickness t
attached by groove or fillet welds
parallel or transverse to the direction
of primary stress where the detail
incorporates no transition radius:
L < 2 in.
2 in. ≤ L ≤ 12t or 4 in
In the primary
member at the
end of the weld
at the weld toe
C
44 × 108
D
22 × 10
8
E
11 × 108
4.5
E′
3.9 × 10
8
2.6
E
11x108
10
7
L > 12t or 4 in.
t < 1.0 in.
t 1.0 in.
(Note: see Condition 7.2 for welded
angle or tee section member
connections to gusset or connection
plates.)
7.2 Base metal in angle or tee section
members connected to a gusset or
connection plate by longitudinal fillet
welds along both sides of the
connected element of the member
cross-section. The fatigue stress
range shall be calculated on the
effective net area of the member, Ae =
UAg, in which U = (1– x /L) and
where Ag is the gross area of the
member. x is the distance from the
centroid of the member to the surface
of the gusset or connection plate and
L is the maximum length of the
longitudinal welds. The effect of the
moment due to the eccentricities in
the connection shall be ignored in
computing the stress range
(McDonald and Frank, 2009).
4.5
Toe of fillet
welds in
connected
element
L
L
x
c.g.
L
c.g.
x
L
continued on next page
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SECTION 6: STEEL STRUCTURES
6-43
Table 6.6.1.2.3-1 (continued)—Detail Categories for Load-Induced Fatigue
Description
Category
Constant
A
(ksi3)
Threshold
(ǻf)TH
ksi
Potential Crack
Initiation Point
Illustrative Examples
Section 8—Miscellaneous
8.1 Rib to Deck Weld—One-sided
80% (70% min) penetration weld
with root gap 0.02 in. prior to
welding
C
44 × 108
10
See Figure
D
22 × 108
7
See Figure
B
120 ×
108
16
See Figure
D
22 × 108
7
See Figure
C
44 × 108
10
See Figure
Allowable Design Level
1, 2, or 3
8.2 Rib Splice (Welded)—Single
groove butt weld with permanent
backing bar left in place. Weld gap
> rib wall thickness
Allowable Design Level
1, 2, or 3
8.3 Rib Splice (Bolted)—Base
metal at gross section of high
strength slip critical connection
Allowable Design Level
1, 2, or 3
8.4 Deck Plate Splice (in Plane)—
Transverse or Longitudinal single
groove butt splice with permanent
backing bar left in place
Allowable Design Level
1, 2, or 3
8.5 Rib to FB Weld (Rib)—Rib wall
at rib to FB weld (fillet or CJP)
Allowable Design Level
1, 2, or 3
continued on next page
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6-44
Table 6.6.1.2.3-1 (continued)—Detail Categories for Load-Induced Fatigue
Description
Constant
A
(ksi3)
Threshold
(ǻf)TH
ksi
Potential Crack
Initiation Point
44 × 108
10
See Figure
A
250 ×
108
24
See Figure
C
44 × 108
10
See Figure
C
44 × 108
10
See Figure
Category
8.6 Rib to FB Weld (FB Web)—FB
web at rib to FB weld (fillet, PJP, or
CJP)
C
Illustrative Examples
(see
Note 1)
Allowable Design Level
1 or 3
8.7 FB Cutout—Base metal at edge
with “smooth” flame cut finish as
per AWS D1.5
Allowable Design Level
1 or 3
8.8 Rib Wall at Cutout—Rib wall at
rib to FB weld (fillet, PJP, or CJP)
Allowable Design Level
1 or 3
8.9 Rib to Deck Plate at FB
Allowable Design Level
1 or 3
Note 1: Where stresses are dominated by in-plane component at fillet or PJP welds, Eq. 6.6.1.2.5-4 shall be considered. In this case, Δf should
be calculated at the mid-thickness and the extrapolation procedure as per Article 9.8.3.4.3 need not be applied.
Section 9—Miscellaneous
9.1 Base metal at stud-type shear
connectors attached by fillet or
automatic stud welding
44 × 108
10
At the toe of
the weld in the
base metal
continued on next page
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SECTION 6: STEEL STRUCTURES
6-45
Table 6.6.1.2.3-1 (continued)—Detail Categories for Load-Induced Fatigue
Description
Category
Constant
A
(ksi3)
Threshold
(ǻF)TH
ksi
Potential Crack
Initiation Point
Illustrative Examples
Section 9—Miscellaneous (continued)
9.2 Nonpretensioned high-strength
bolts, common bolts, threaded
anchor rods, and hanger rods with
cut, ground, or rolled threads. Use
the stress range acting on the tensile
stress area due to live load plus
prying action when applicable.
At the root of
the threads
extending into
the tensile
stress area
(Fatigue II) Finite Life
E′
3.9 × 108
N/A
(Fatigue I) Infinite Life
D
N/A
7
Table 6.6.1.2.3-2—75-yr (ADTT)SL Equivalent to Infinite
Life
Detail
Category
A
B
Bƍ
C
Cƍ
D
E
Eƍ
75-yrs (ADTT)SL Equivalent to Infinite
Life (trucks per day)
530
860
1035
1290
745
1875
3530
6485
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
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SECTION 6: STEEL STRUCTURES
6-47
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6-48
6.6.1.2.4—Detailing to Reduce Constraint
To the extent practical, welded structures shall be
detailed to avoid conditions that create highly constrained
joints and crack-like geometric discontinuities that are
susceptible to constraint-induced fracture. Welds that are
parallel to the primary stress but interrupted by intersecting
members shall be detailed to allow a minimum gap of 1 in.
between weld toes.
C6.6.1.2.4
The objective of this Article is to provide
recommended detailing guidelines for common joints to
avoid details susceptible to brittle fracture.
The form of brittle fracture being addressed has been
termed “constraint-induced fracture” and can occur
without any perceptible fatigue crack growth and, more
importantly, without any warning. This type of failure was
documented during the Hoan Bridge failure investigation
by Wright, Kaufmann, and Fisher (2003) and Kaufmann,
Connor, and Fisher (2004). Criteria have been developed
to identify bridges and details susceptible to this failure
mode as discussed in Mahmoud, Connor and Fisher
(2005).
Intersecting welds should be avoided.
Attached elements parallel to the primary stress are
sometimes interrupted when intersecting a full-depth
transverse member. These elements are less susceptible to
fracture and fatigue if the attachment parallel to the
primary stress is continuous and the transverse attachment
is discontinuous as shown in Figure C6.6.1.2.4-1. Also
shown is the space between the weld of the transverse
stiffener to the web and the weld of the longitudinal
stiffener to the web required to reduce constraint.
Figure C6.6.1.2.4-1—A Weld Detail where the
Longitudinal Stiffener Is Continuous
6.6.1.2.5—Fatigue Resistance
2013 Revision
Except as specified below, nominal fatigue resistance
shall be taken as:
•
For the Fatigue I load combination and infinite life:
(ΔF )n = (ΔF )TH
•
(6.6.1.2.5-1)
For the Fatigue II load combination and finite life:
C6.6.1.2.5
2013 Revision
The requirement on higher-traffic-volume bridges that
the maximum stress range experienced by a detail be less
than the constant-amplitude fatigue threshold provides a
theoretically infinite fatigue life. This requirement is
reflected in Eq. 6.6.1.2.5-1.
The fatigue resistance above the constant amplitude
fatigue threshold, in terms of cycles, is inversely
proportional to the cube of the stress range, e.g., if the
stress range is reduced by a factor of 2, the fatigue life
increases by a factor of 23. This is reflected in
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SECTION 6: STEEL STRUCTURES
6-49
1
(ΔF )n
A 3
=
N
(6.6.1.2.5-2)
in which:
N = ( 365 )( 75 ) n ( ADTT )SL
(6.6.1.2.5-3)
where:
=
=
A
n
(ADTT)SL=
(ΔF)TH =
constant taken from Table 6.6.1.2.5-1 (ksi3)
number of stress range cycles per truck
passage taken from Table 6.6.1.2.5-2
single-lane ADTT as specified in
Article 3.6.1.4
constant-amplitude fatigue threshold taken
from Table 6.6.1.2.5-3 (ksi)
Eq. 6.6.1.2.5-2. Orthotropic deck details that are connected
to the deck plate (e.g., the rib-to-deck weld) are subjected
to cycling from direct individual wheel loads. Thus, the
passage of one design truck results in five fatigue load
cycles as each axle produces one load cycle. The force
effect (Δf) can be conservatively taken as the worst case
from the five wheels or by application of Miner’s Rule to
determine the effective stress range from the group of
wheels.
In the AASHTO 2002 Standard Specifications, the
constant amplitude fatigue threshold is termed the
allowable fatigue stress range for more than 2 million
cycles on a redundant load path structure.
The fatigue design life has been considered to be
75 years in the overall development of the Specifications.
If a fatigue design life other than 75 years is sought, a
number other than 75 may be inserted in the equation
for N.
Figure C6.6.1.2.5-1 is a graphical representation of the
nominal fatigue resistance for Categories A through E′.
Figure C6.6.1.2.5-1—Stress Range Versus Number of
Cycles
The nominal fatigue resistance for base metal and
weld metal at details where loaded discontinuous plate
elements are connected with a pair of fillet welds or partial
joint penetration groove welds on opposite sides of the
plate normal to the direction of primary stress shall be
taken as:
(ΔF )n
0.65 − 0.59 2a + 0.72 w
tp
tp
c
≤ (ΔF )c
= (ΔF )n
n
t 0p.167
(6.6.1.2.5-4)
where:
(ΔF )
c
n
Eq. 6.6.1.2.5-4 accounts for the potential of a crack
initiating from the weld root and includes the effects of
weld penetration. Therefore, Eq. 6.6.1.2.5-4 is also
applicable to partial joint penetration groove welds, as
shown in Figure C6.6.1.2.5-2.
=
nominal fatigue resistance for Detail
Category C (ksi)
Figure C6.6.1.2.5-2—Loaded Discontinuous Plate Element
Connected by a Pair of Partial Joint Penetration Groove
Welds
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
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2a
=
tp
w
=
=
length of the non-welded root face in the
direction of the thickness of the loaded plate
(in.) For fillet welded connections, the
quantity (2a/tp) shall be taken equal to 1.0.
thickness of loaded plate (in.)
leg size of the reinforcement or contour
fillet, if any, in the direction of the thickness
of the loaded plate (in.)
The effect of any weld penetration may be conservatively
ignored in the calculation of (ΔF)n from Eq. 6.6.1.2.5-4 by
taking the quantity (2a/tp) equal to 1.0. The nominal
fatigue resistance based on the crack initiating from the
weld root in Eq. 6.6.1.2.5-4 is limited to the nominal
fatigue resistance for Detail Category C, which assumes
crack initiation from the weld toe. The development of
Eq. 6.6.1.2.5-4 is discussed in Frank and Fisher (1979).
In the AASHTO 2002 Standard Specifications,
allowable stress ranges are specified for both redundant
and nonredundant members. The allowables for
nonredundant members are arbitrarily specified as
80 percent of those for redundant members due to the
more severe consequences of failure of a nonredundant
member. However, greater fracture toughness is also
specified for nonredundant members. In combination, the
reduction in allowable stress range and the greater
fracture toughness constitute an unnecessary double
penalty for nonredundant members. The requirement for
greater fracture toughness has been maintained in these
Specifications. Therefore, the allowable stress ranges
represented by Eqs. 6.6.1.2.5-1 and 6.6.1.2.5-2 are
applicable to both redundant and nonredundant members.
Table 6.6.1.2.5-1—Detail Category Constant, A
Constant, A
times 108 (ksi3)
Detail Category
A
B
B′
C
C′
D
E
E′
M 164 (A325) Bolts in
Axial Tension
M 253 (A490) Bolts in
Axial Tension
250.0
120.0
61.0
44.0
44.0
22.0
11.0
3.9
17.1
31.5
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SECTION 6: STEEL STRUCTURES
6-51
Table 6.6.1.2.5-2—Cycles per Truck Passage, n
Longitudinal
Members
Simple Span
Girders
Continuous
Girders
Span Length
>40.0 ft
≤40.0 ft
1.0
2.0
1) near interior
support
1.5
2) elsewhere
Cantilever
Girders
1.0
Orthotropic
Deck Plate
Connections
Subjected
to Wheel Load
Cycling
Trusses
Transverse
Members
2.0
2.0
5.0
5.0
For the purpose of determining the stress-range cycles
per truck passage for continuous spans, a distance equal to
one-tenth the span on each side of an interior support
should be considered to be near the support.
The number of stress-range cycles per passage is taken
as 5.0 for cantilever girders because this type of bridge is
susceptible to large vibrations, which cause additional
cycles after the truck has left the bridge (Moses et al.,
1987; Schilling, 1990).
Orthotropic deck details that are connected to the deck
plate (e.g., the rib-to-deck weld) are subjected to cycling
from direct individual wheel loads. Thus, the passage of
one design truck results in five fatigue load cycles as each
axle produces one load cycle. The force effect (Δf) can be
conservatively taken as the worst case from the five wheels
or by application of Miner’s Rule to determine the
effective stress range from the group of wheels.
1.0
Spacing
> 20.0 ft
1.0
≤20.0 ft
2.0
Table 6.6.1.2.5-3—Constant-Amplitude Fatigue Thresholds
Detail Category
A
B
B′
C
C′
D
E
E′
M 164 (A 325) Bolts in
Axial Tension
M 253 (A 490) Bolts in
Axial Tension
Threshold (ksi)
24.0
16.0
12.0
10.0
12.0
7.0
4.5
2.6
31.0
38.0
6.6.1.3—Distortion-Induced Fatigue
Load paths that are sufficient to transmit all intended
and unintended forces shall be provided by connecting all
transverse members to appropriate components comprising
the cross-section of the longitudinal member. The load
paths shall be provided by attaching the various
components through either welding or bolting.
To control web buckling and elastic flexing of the
web, the provision of Article 6.10.5.3 shall be satisfied.
C6.6.1.3
When proper detailing practices are not followed,
fatigue cracking has been found to occur due to strains not
normally computed in the design process. This type of
fatigue cracking is called distortion-induced fatigue.
Distortion-induced fatigue often occurs in the web near a
flange at a welded connection plate for a cross-frame
where a rigid load path has not been provided to
adequately transmit the force in the transverse member
from the web to the flange.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6-52
These rigid load paths are required to preclude the
development of significant secondary stresses that could
induce fatigue crack growth in either the longitudinal or
the transverse member (Fisher et al., 1990).
6.6.1.3.1—Transverse Connection Plates
Except as specified herein, connection plates shall be
welded or bolted to both the compression and tension
flanges of the cross-section where:
•
Connecting diaphragms or cross-frames are attached
to transverse connection plates or to transverse
stiffeners functioning as connection plates,
•
Internal or external diaphragms or cross-frames are
attached to transverse connection plates or to
transverse stiffeners functioning as connection plates,
and
•
Floorbeams or stringers are attached to transverse
connection plates or to transverse stiffeners
functioning as connection plates.
In the absence of better information, the welded or
bolted connection should be designed to resist a 20.0-kip
lateral load for straight, nonskewed bridges.
Where intermediate connecting diaphragms are used:
•
On rolled beams in straight bridges with composite
reinforced decks whose supports are normal or
skewed not more than 10 degrees from normal and
•
With the intermediate diaphragms placed in
contiguous lines parallel to the supports.
less than full-depth end angles or connection plates may be
bolted or welded to the beam web to connect the
diaphragms. The end angles or plates shall be at least twothirds the depth of the web. For bolted angles, a minimum
gap of 3.0 in. shall be provided between the top and
bottom bolt holes and each flange. Bolt spacing
requirements specified in Article 6.13.2.6 shall be
satisfied. For welded angles or plates, a minimum gap of
3.0 in. shall be provided between the top and bottom of the
end-angle or plate welds and each flange; the heel and toe
of the end angles or both sides of the connection plate, as
applicable, shall be welded to the beam web. Welds shall
not be placed along the top and bottom of the end angles or
connection plates.
6.6.1.3.2—Lateral Connection Plates
If it is not practical to attach lateral connection plates to
flanges, lateral connection plates on stiffened webs should
be located a vertical distance not less than one-half the width
of the flange above or below the flange. Lateral connection
plates attached to unstiffened webs should be located at least
6.0 in. above or below the flange but not less than one-half
of the width of the flange, as specified above.
C6.6.1.3.1
These provisions appear in Article 10.20 of the
AASHTO Standard Specifications “Diaphragms and Cross
Frames” with no explanation as to the rationale for the
requirements and no reference to distortion-induced
fatigue.
These provisions apply to both diaphragms between
longitudinal members and diaphragms internal to
longitudinal members.
The 20.0-kip load represents a rule of thumb for
straight, nonskewed bridges. For curved or skewed
bridges, the diaphragm forces should be determined by
analysis (Keating et al., 1990). It is noted that the stiffness
of this connection is critical to help control relative
displacement between the components. Hence, where
possible, a welded connection is preferred as a bolted
connection possessing sufficient stiffness may not be
economical.
For box sections, webs are often joined to top flanges
and cross-frame connection plates and transverse stiffeners
are installed, and then these assemblies are attached to the
common box flange. In order to weld the webs
continuously to the box flange inside the box section, the
details in this case should allow the welding head to clear
the bottom of the connection plates and stiffeners. A
similar detail may also be required for any intermediate
transverse stiffeners that are to be attached to the box
flange. Suggested details are shown in AASHTO/NSBA
(2003). The Engineer is advised to consult with fabricators
regarding the preferred approach for fabricating the box
section and provide alternate details on the plans, if
necessary.
C6.6.1.3.2
The specified minimum distance from the flange is
intended to reduce the concentration of out-of-plane
distortion in the web between the lateral connection plate
and the flange to a tolerable magnitude. It also provides
adequate electrode access and moves the connection plate
closer to the neutral axis of the girder to reduce the impact
of the weld termination on fatigue strength.
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SECTION 6: STEEL STRUCTURES
6-53
The ends of lateral bracing members on the lateral
connection plate shall be kept a minimum of 4.0 in. from
the web and any transverse stiffener.
Where stiffeners are used, lateral connection plates
shall be centered on the stiffener, whether or not the plate
is on the same side of the web as the stiffener. Where the
lateral connection plate is on the same side of the web as
the stiffener, the transverse stiffener at this location shall
be discontinuous and attached to both flanges and the
connection plate. The detailing of welded lateral
connection plates shall also satisfy the provisions of
Article 6.6.1.2.4.
This requirement reduces potential distortion-induced
stresses in the gap between the web or stiffener and the
lateral members on the lateral plate. These stresses may
result from vibration of the lateral system. It also facilitates
painting and field inspection.
The typical detail where the lateral connection plate is
on the same side of the web as the stiffener is illustrated in
Figure C6.6.1.3.2-1.
Figure C6.6.1.3.2-1—Typical Discontinuous Transverse
Stiffener Detail at a Lateral Connection Plate
6.6.1.3.3—Orthotropic Decks
Detailing shall
Article 9.8.3.6.
satisfy
all
C6.6.1.3.3
requirements
of
The purpose of this provision is to control distortioninduced fatigue of deck details subject to local secondary
stresses due to out-of-plane bending.
6.6.2—Fracture
C6.6.2
Except as specified herein, all primary longitudinal
superstructure components and connections sustaining
tensile stress due to Strength Load Combination I, as
specified in Table 3.4.1-1, and transverse floorbeams
subject to such stress, shall require mandatory Charpy
V-notch testing. Other primary components and
connections sustaining tensile stresses due to the
Strength Load Combination I may require mandatory
Charpy V-notch testing at the discretion of the Owner.
All components and connections requiring Charpy Vnotch testing shall be so designated on the contract plans.
Unless otherwise indicated on the contract plans,
Charpy V-notch requirements shall not be considered
mandatory for the following items:
The basis and philosophy for the supplemental impact
requirements specified in the AASHTO Material
Specifications is given in AISI (1975).
The specification of mandatory Charpy V-notch
testing requirements for primary components and
connections sustaining tensile stress under the specified
load combination that are transverse to the primary
longitudinal components, other than transverse floorbeams,
is at the discretion of the Owner.
•
Splice plates and filler plates in bolted splices
connected in double shear;
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
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•
Intermediate transverse web stiffeners not serving as
connection plates;
•
Bearings, sole plates, and masonry plates;
•
Expansion dams; and
•
Drainage material.
The appropriate temperature zone shall be determined
from the applicable minimum service temperature specified
in Table 6.6.2-1 and shall be designated in the contract
documents.
Charpy V-notch impact energy requirements shall be
in accordance with Table 6.6.2-2 for the appropriate
temperature zone. The yield strength shall be taken as the
value given in the certified Mill Test Report.
The Engineer shall have the responsibility for
determining which, if any, component is a fracture-critical
member (FCM). Unless a rigorous analysis with assumed
hypothetical cracked components confirms the strength
and stability of the hypothetically damaged structure, the
location of all FCMs shall be clearly delineated on the
contract plans. The contract documents shall require that
FCMs shall be fabricated according to Section 12 of the
AASHTO/AWS D1.5M/D1.5 Bridge Welding Code.
Any attachment having a length in the direction of the
tension stress greater than 4.0 in. that is welded to a
tension area of a component of a FCM shall be considered
part of the tension component and shall be considered
fracture-critical.
Table 6.6.2-1—Temperature Zone Designations for
Charpy V-Notch Requirements
Minimum Service Temperature
0°F and above
−1°F to −30°F
−31°F to −60°F
Temperature Zone
1
2
3
The Charpy V-notch impact energy requirements are
the same regardless of whether the component is welded or
mechanically fastened, but vary depending on the type of
steel, type of construction, and the applicable minimum
service temperature. FCMs are subject to more stringent
Charpy V-notch impact energy requirements than
nonfracture-critical components.
Material for fracture-critical members or components
designated FCM is to be tested in conformance with
AASHTO T 243M/T 243 (ASTM A673/A673M)
Frequency P, except for plates of AASHTO
M 270M/M 270 (ASTM A709/A709M) Grade 36, 50,
50W, HPS 50W, and HPS 70W material, in which case
specimens are to be selected as follows:
•
As-rolled plates shall be sampled at each end of each
plate-as-rolled.
•
Normalized plates shall be sampled at one end of each
plate-as-heat treated.
•
Quenched and tempered plates shall be sampled at
each end of each plate-as-heat treated.
AASHTO M 270M/M 270 (ASTM A709/A709M)
Grade 36, 50, 50S, 50W, and HPS 50W material for
components designated nonfracture-critical is to be tested
in conformance with AASHTO T 243M/T 243 (ASTM
A673/A673M), Frequency H. AASHTO M 270M/M 270
(ASTM A709/A709M) Grade HPS 70W and HPS 100W
material for components designated nonfracture-critical is
to be tested in conformance with AASHTO T 243M/T 243
(ASTM A673/A673M), Frequency P.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 6: STEEL STRUCTURES
6-55
The criteria for a refined analysis used to
demonstrate that part of a structure is not fracturecritical has not yet been codified. Therefore, the loading
cases to be studied, location of potential cracks, degree
to which the dynamic effects associated with a fracture
are included in the analysis, and fineness of models and
choice of element type should all be agreed upon by the
Owner and the Engineer. The ability of a particular
software product to adequately capture the complexity
of the problem should also be considered and the choice
of software should be mutually agreed upon by the
Owner and the Engineer. Relief from the full factored
loads associated with the Strength I Load Combination
of Table 3.4.1-1 should be considered, as should the
number of loaded design lanes versus the number of
striped traffic lanes.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6-56
Table 6.6.2-2—CVN Impact Energy Requirements
Fracture-Critical
Nonfracture-Critical
Grade
(Y.P./Y.S.)
36
Thickness
(in.)
t≤4
Min. Test
Value
Energy
(ft-lbs.)
20
50/50S/50W
HPS 50W
t≤2
2<t≤4
t≤4
20
24
24
25 @ 70
30 @ 70
30 @ 10
25 @ 40
30 @ 40
30 @ 10
25 @ 10
30 @ 10
30 @ 10
15 @ 70
20 @ 70
20 @ 10
15 @ 40
20 @ 40
20 @ 10
15 @ 10
20 @ 10
20 @ 10
HPS 70W
t≤4
28
35 @ −10
35 @ −10
35 @ −10
25 @ −10
25 @ −10
25 @ −10
HPS 100W
t ≤ 2−1/2
28
35 @ –30
35 @ –30
35 @ −30
25 @ –30
25 @ –30
25 @ −30
2-1/2 < t ≤ 4
36
not permitted
not permitted
not permitted
35 @ –30
35 @ –30
35 @ −30
Zone 1
(ft-lbs. @ °F)
25 @ 70
Zone 2
(ft-lbs. @ °F)
25 @ 40
Zone 3
(ft-lbs. @ °F)
25 @ 10
Zone 1
(ft-lbs. @ °F)
15 @ 70
Zone 2
(ft-lbs. @ °F)
15 @ 40
Zone 3
(ft-lbs. @ °F)
15 @ 10
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 6: STEEL STRUCTURES
6-57
6.7—GENERAL DIMENSION AND DETAIL
REQUIREMENTS
6.7.1—Effective Length of Span
Span lengths shall be taken as the distance between
centers of bearings or other points of support.
6.7.2—Dead Load Camber
C6.7.2
Steel structures should be cambered during fabrication
to compensate for dead load deflection and vertical
alignment.
Deflection due to steel weight and concrete weight
shall be reported separately. Deflections due to future
wearing surfaces or other loads not applied at the time of
construction shall be reported separately.
Vertical camber shall be specified to account for the
computed dead load deflection.
When staged construction is specified, the sequence of
load application should be considered when determining
the cambers.
Selective changes to component length, as
appropriate, may be used for truss, arch, and cable-stayed
systems to:
As specified herein, staged construction refers to the
situation in which superstructures are built in separate
longitudinal units with a longitudinal joint, i.e., it does not
refer to the deck pouring sequence.
The erection and cambering of straight skewed
bridges and horizontally curved bridges with or without
skewed supports is a more complex problem than generally
considered. As of this writing (2005), there has been a
trend toward more complex geometries and more flexible
bridges combined with the use of higher strength steels. In
some cases, failure to engineer the erection to achieve the
intended final position of the girders, or to properly
investigate potential outcomes when detailing to achieve
an intended final position of the girders, has resulted in
construction delays and claims. It is important that
Engineers and Owners recognize the need for an
engineered construction plan and the implied level of
checking of shop drawings of girders and cross-frames or
diaphragms, processing of RFIs or Requests for
Information, and field inspection.
•
Adjust the dead load deflection to comply with the
final geometric position,
•
Reduce or eliminate rib shortening, and
•
Adjust the dead load
indeterminate structures.
moment
diagram
in
For straight skewed I-girder bridges and horizontally
curved I-girder bridges with or without skewed supports,
the contract documents should clearly state an intended
erected position of the girders and the condition under
which that position is to be theoretically achieved. The
provisions of Article 2.5.2.6.1 related to bearing rotations
shall also apply.
Intended erected positions of I-girders in straight
skewed and horizontally curved bridges are defined herein
as either:
•
girder webs theoretically vertical or plumb, or
•
girder webs out-of-plumb.
Three common conditions under which these intended
erected positions can be theoretically achieved are defined
herein as:
•
the no-load condition,
•
the steel dead load condition, or
•
the full dead load condition.
The no-load condition refers to the condition where the
girders are erected under a theoretically zero-stress
condition, i.e., neglecting any stress due to the steel dead
load acting between points of temporary support. The steel
dead load condition refers to the condition after the erection
of the steel is completed. The full dead load condition refers
to the condition after the full noncomposite dead load,
including the concrete deck, is applied.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
6-58
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
In order for the girder webs of straight skewed I-girder
bridges to end up theoretically plumb at the bearings under
either the steel or full dead load condition, the cross-frames
or diaphragms must be detailed for that condition in order to
introduce the necessary twist into the girders during the
erection. Although the cross-frames or diaphragms may have
to be forced into position in this case, this can usually be
accomplished in these types of bridges without inducing
significant additional locked-in stresses in the girder flanges
or the cross-frames or diaphragms. Alternatively, the girders
may be erected plumb in the no-load condition if the
resulting out-of-plumbness at the bearings and any potential
errors in the horizontal roadway alignment under the full
dead load condition are considered. In this case, the crossframes or diaphragms are detailed to fit theoretically stressfree in the no-load condition. In either case, the rotation
capacity of the bearings must either be able to accommodate
the twist or the bearings must be installed in a manner to
ensure that their rotation capacities are not exceeded.
For horizontally curved I-girder bridges with or without
skewed supports, where the girders are erected plumb in the
no-load condition, with the cross-frames or diaphragms
detailed to fit in the no-load condition, the girder webs will
not be plumb in the full dead load condition, except at
supports that do not deflect vertically in bridges for which all
supports are radial. This out-of-plumbness should be
considered in the detailing of the deck and bearings, as
applicable.
In order for the girder webs of horizontally curved
I-girder bridges with or without skewed supports to end up
theoretically plumb under either the steel or full dead load
condition, the cross-frames or diaphragms must again be
detailed for that condition in order to introduce the necessary
twist into the girders. In this case, however, as the crossframes are forced into place and the girders are twisted outof-plumb during the erection, the curved-girder flanges act
to resist the induced change to their radii. Therefore, the
Engineer may need to consider the potential for any
problematic locked-in stresses in the girder flanges or the
cross-frames or diaphragms when this method of detailing is
specified for these types of bridges. The decision as to when
these stresses should be evaluated is currently a matter of
engineering judgment. It is anticipated that these stresses
will be of little consequence in the vast majority of cases and
that the resulting twist of the girders will be small enough
that the cross-frames or diaphragms will easily pull the
girders into their intended position and reverse any locked-in
stresses as the dead load is applied.
For curved I-girder webs to end up theoretically
plumb in the desired final condition without also
theoretically inducing any additional locked-in stresses, the
girders would have to be fabricated for the no-load
position with a twist about the tangential axis of the girder
for that particular condition. In such a case, the girder
flanges would be welded square with respect to the webs
and the cross-frames or diaphragms would be detailed for
the desired final condition to correspond with the twist.
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2012
Edition
SECTION 6: STEEL STRUCTURES
6-59
Such a practice is generally more costly and has found
very limited use as of this writing (2005).
It should be noted that detailing of the cross-frames or
diaphragms for the case where the girder webs are plumb
in the no-load condition can result in the potential for
many different connection-plate configurations. In this
case, the drop of the cross-frames or diaphragms—or
difference in elevation of the girders at the level of the
cross-frames or diaphragms—typically varies causing the
bolt holes in the connection plates to be different distances
from the flanges.
Tub girders should be detailed to be normal to the
crown of the roadway. Although the twist in I-girders is
often greater than in tub girders, twist in tub girders may
also be significant. Almost all horizontally curved tub
girders are fabricated with a twist and are not erected with
the girders plumb in the no-load condition. This is done
because the inherent torsional stiffness of tub sections
makes field adjustments difficult. Particular care must be
taken in analyzing and detailing tub girders; in particular,
tub girders in bridges with skewed supports.
For cases that begin to push the current limits of the
specification or conventional practice, for example, cases
with unusually long spans, tight radii, sharp skews, stiff
and/or slender flanges in the lateral direction, special
attention may be required by the Engineer. In cases where
twist is introduced into the girders during the erection,
slender flanges may be subject to local buckling and
unusually stiff flanges may be difficult to push or pull into
position in a practical manner.
6.7.3—Minimum Thickness of Steel
C6.7.3
Structural steel, including bracing, cross-frames, and
all types of gusset plates, except for webs of rolled shapes,
closed ribs in orthotropic decks, fillers, and in railings,
shall be not less than 0.3125 in. in thickness.
For orthotropic decks, the web thickness of rolled
beams or channels and of closed ribs in orthotropic decks
shall not be less than 0.25 in., the deck plate thickness
shall not be less than 0.625 in. or four percent of the larger
spacing of the ribs, and the thickness of closed ribs shall
not be less than 0.1875.
Where the metal is expected to be exposed to severe
corrosive influences, it shall be specially protected against
corrosion or sacrificial metal thickness shall be specified.
For orthotropic decks, research and development and
general design improvements domestically and abroad
have demonstrated that a minimum deck plate thickness of
5/8 in. has addressed the causes of many problems
resulting from overly flexible decks. Although analysis
may indicate that deck plates less than 5/8 in. thick could
be satisfactory, experience shows that a minimum
thickness of 5/8 in. is advisable both from construction and
long-term performance points of view.
6.7.4—Diaphragms and Cross-Frames
6.7.4.1—General
C6.7.4.1
Diaphragms or cross-frames may be placed at the end
of the structure, across interior supports, and intermittently
along the span.
The need for diaphragms or cross-frames shall be
investigated for all stages of assumed construction
procedures and the final condition.
The arbitrary requirement for diaphragms spaced at
not more than 25.0 ft in the AASHTO Standard
Specifications has been replaced by a requirement for
rational analysis that will often result in the elimination of
fatigue-prone attachment details.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
6-60
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
This investigation should include, but not be limited
to, the following:
•
Transfer of lateral wind loads from the bottom of the
girder to the deck and from the deck to the bearings,
•
Stability of the bottom flange for all loads when it is
in compression,
•
Stability of the top flange in compression prior to
curing of the deck,
•
Consideration of any flange lateral bending effects,
and
•
Distribution of vertical dead and live loads applied to
the structure.
Diaphragms or cross-frames not required for the final
condition may be specified to be temporary bracing. Metal
stay-in-place deck forms should not be assumed to provide
adequate stability to the top flange in compression prior to
curing of the deck.
If permanent cross-frames or diaphragms are included
in the structural model used to determine force effects,
they shall be designed for all applicable limit states for the
calculated force effects. At a minimum, diaphragms and
cross-frames shall be designed to transfer wind loads
according to the provisions of Article 4.6.2.7 and shall
meet all applicable slenderness requirements in
Article 6.8.4 or Article 6.9.3. Diaphragm and cross-frame
members in horizontally curved bridges shall be
considered to be primary members.
Connection plates for diaphragms and cross-frames
shall satisfy the requirements specified in Article 6.6.1.3.1.
Where the diaphragm flanges or cross-frame chords are
not attached directly to the girder flanges, provisions shall
be made to transfer the calculated horizontal force in
diaphragms or cross-frames to the flanges through
connection plates, except in cases where less than full-depth
end angles or connection plates are used for connecting
intermediate diaphragms as permitted in Article 6.6.1.3.1.
At the end of the bridge and intermediate points where
the continuity of the slab is broken, the edges of the slab
shall be supported by diaphragms or other suitable means
as specified in Article 9.4.4.
6.7.4.2—I-Section Members
Diaphragms or cross-frames for rolled beams and
plate girders should be as deep as practicable, but as a
minimum should be at least 0.5 of the beam depth for
rolled beams and 0.75 of the girder depth for plate girders.
Cross-frames in horizontally curved bridges should contain
diagonals and top and bottom chords.
Bracing of horizontally curved members is more
critical than for straight members. Diaphragm and crossframe members resist forces that are critical to the proper
functioning of curved-girder bridges. Since they transmit
the forces necessary to provide equilibrium, they are
considered primary members. Therefore, forces in the
bracing members must be computed and considered in the
design of these members. When I-section members have
been analyzed neglecting the effects of curvature
according to the provisions of Article 4.6.1.2.4, the
diaphragms or cross-frames may be analyzed by the Vload method (United States Steel, 1984) or other rational
means.
If the diaphragm flanges or cross-frame chords are not
attached directly to the girder flanges, forces from these
elements are transferred through the connection plates. The
eccentricity between the diaphragm flanges or cross-frame
chords and the girder flanges should be recognized in the
design of the connection plates and their connection to the
web and flange.
The term connection plate as used herein refers to a
transverse stiffener attached to the girder to which a crossframe or diaphragm is connected.
C6.7.4.2
For the purpose of this Article, as it applies to
horizontally curved girders, the term “normal” shall be
taken to mean normal to a local tangent.
Intermediate diaphragms or cross-frames should be
provided at nearly uniform spacing in most cases, for
efficiency of the structural design, for constructibility,
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 6: STEEL STRUCTURES
End diaphragms shall be designed for forces and
distortion transmitted by the deck and deck joint. End
moments in diaphragms shall be considered in the design
of the connection between the longitudinal component and
the diaphragm. Diaphragms with span-to-depth ratios
greater than or equal to 4.0 may be designed as beams.
Where supports are not skewed, intermediate
diaphragms or cross-frames should be placed in contiguous
lines normal to the girders.
Where support lines are not skewed more than 20
degrees from normal, intermediate diaphragms or crossframes may be placed in contiguous skewed lines parallel
to the skewed support lines.
Where support lines are skewed more than 20 degrees
from normal, intermediate diaphragms or cross-frames
shall be normal to the girders and may be placed in
contiguous or discontinuous lines.
Where a support line at an interior pier is skewed
more than 20 degrees from normal, elimination of the
diaphragms or cross-frames along the skewed interior
support line may be considered at the discretion of the
Owner. Where discontinuous intermediate diaphragm or
cross-frame lines are employed normal to the girders in the
vicinity of that support line, a skewed or normal diaphragm
or cross-frame should be matched with each bearing that
resists lateral force.
If the end diaphragm or cross-frame is skewed, the
effect of the tangential component of force transmitted by
the skewed unit on the girder shall be considered.
Diaphragms or cross-frames at supports shall be
proportioned to transmit all lateral components of force
from the superstructure to the bearings that provide lateral
restraint.
6-61
and/or to allow the use of simplified methods of analysis
for calculation of flange lateral bending stresses, such as
those discussed in Articles C4.6.1.2.4b, C4.6.2.7.1 and
C6.10.3.4. Closer spacings may be necessary adjacent to
interior piers, in the vicinity of skewed supports, and in
some cases, near midspan.
Diaphragms with span-to-depth ratios less than 4.0 act
as deep beams and should be evaluated by considering
principal stresses rather than by beam theory.
Allowance of skewed intermediate diaphragms or
cross-frames where support lines are not skewed more than
20 degrees from normal is consistent with past practice.
Where support lines are skewed more than 20 degrees
from normal, it may be advantageous to place the
intermediate diaphragms or cross-frames oriented normal
to the girders in discontinuous lines in such a manner that
the transverse stiffness of the bridge is reduced,
particularly in the vicinity of the supports. Placing the
cross-frames in discontinuous lines has the effect of
decreasing the cross-frame forces and increasing flange
lateral bending. The actual flange lateral moments with
discontinuous cross-frame lines may differ from those
estimated using Eq. C4.6.1.2.4b-1, or equivalent, so a
special investigation of flange lateral moments and crossframe forces is advisable. Removal of highly stressed
diaphragms or cross-frames, particularly near obtuse
corners, releases the girders torsionally and is often
beneficial as long as girder rotation is not excessive.
At severely skewed support lines at interior piers,
detailing of the intersections of diaphragms or crossframes along the skewed support line with intermediate
diaphragms or cross-frames oriented normal to the girders
is complex and, in many cases, the normal diaphragms or
cross-frames alone should be sufficient to resist any lateral
components of force that develop at the bearings. Where
discontinuous intermediate diaphragm or cross-frame lines
are employed normal to the girders in the vicinity of
interior supports, care should be taken to match a
diaphragm or cross-frame with each bearing that resists
lateral force. Otherwise, the effect of the lateral moment
induced in the bottom flange due the eccentricity between
the intermediate diaphragm or cross-frame and the bearing
should be considered. Also, whenever any bearing along
that support line is not matched with a diaphragm or crossframe, care should be taken to ensure that the bottom
flange of the girder is adequately braced. For such cases,
the provision of diaphragms or cross-frames along the
skewed support line may be necessary. Refined analysis is
recommended to allow for a more detailed examination of
cross-frame forces, lateral bearing reactions, and lateral
flange bending whenever removal of diaphragms or crossframes along and/or in the vicinity of severely skewed
interior support lines is considered. For skews not
exceeding 20 degrees from normal, diaphragms or crossframes along the skewed support line alone may be
sufficient. In this case, intermediate diaphragms or crossframes placed normal to the girders would likely be too
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
6-62
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The spacing, Lb, of intermediate diaphragms or crossframes in horizontally curved I-girder bridges shall not
exceed the following in the erected condition:
Lb ≤ Lr ≤ R / 10
(6.7.4.2-1)
where:
Lr =
R
=
limiting unbraced length determined from
Eq. 6.10.8.2.3-5 (ft)
minimum girder radius within the panel (ft)
In no case shall Lb exceed 30.0 ft.
close together, introducing significant lateral bending into
the girder flanges. For skewed diaphragms or cross-frames,
connection plates should be oriented in the plane of the
transverse bracing. The connection plate must be able to
transfer force between the girder and the bracing without
undue distortion. Welding of skewed connection plates to
the girder may be problematic where the plate forms an
acute angle with the girder.
The spacing of intermediate diaphragms and crossframes in horizontally curved I-girder bridges in the
erected condition is limited to R/10, which is consistent
with past practice. The spacing is also limited to Lr from
Eq. 6.10.8.2.3-5, where Lr is a limiting unbraced length to
achieve the onset of nominal yielding in either flange
under uniform bending with consideration of compressionflange residual stress effects prior to lateral torsional
buckling of the compression flange. Limiting the unbraced
length to Lr theoretically precludes elastic lateral torsional
buckling of the compression flange. At unbraced lengths
beyond Lr, significant flange lateral bending is likely to
occur and the amplification factor for flange lateral
bending specified in Article 6.10.1.6 will tend to become
large even when an effective length factor for lateral
torsional buckling and/or a moment gradient factor, Cb, is
considered.
Eq. C6.7.4.2-1 may be used as a guide for preliminary
framing in horizontally curved I-girder bridges:
5
Lb =
3
rσ Rb f
(C6.7.4.2-1)
where:
bf
Lb
rσ
R
=
=
=
=
flange width (ft)
diaphragm or cross-frame spacing (ft)
desired bending stress ratio equal to f fbu
girder radius (ft)
A maximum value of 0.3 may be used for the bending
stress ratio, rσ. Eq. C6.7.4.2-1 was derived from the V-load
concept (Richardson, Gordon and Associates, 1976) and
has been shown to yield a good correlation with threedimensional finite-element analysis results if the crossframe spacing is relatively uniform (Davidson et al., 1996).
6.7.4.3—Box Section Members
Diaphragms shall be provided within box sections at
each support to resist cross-section distortion of the box
and shall be designed to resist torsional moments in the
box and transmit vertical and lateral forces from the box to
the bearings.
For cross-sections consisting of two or more boxes,
external cross-frames or diaphragms shall be used between
the boxes at end supports. External cross-frames or
diaphragms shall be provided between girder lines at
interior supports, unless analysis indicates that the boxes
C6.7.4.3
Refined analysis of internal diaphragms at supports is
desirable because these primary members are necessary for
the integrity of the bridge. External diaphragms with
aspect ratios, or ratios of length to depth, less than 4.0 and
internal diaphragms act as deep beams and should be
evaluated by considering principal stresses rather than by
simple beam theory. Fatigue-sensitive details on these
diaphragms and at the connection of the diaphragms to the
flanges should be investigated considering the principal
tensile stresses.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
SECTION 6: STEEL STRUCTURES
are torsionally stable without these members, particularly
during erection. Internal cross-frames or diaphragms shall
be provided at locations of external cross-frames or
diaphragms.
If an internal plate diaphragm is provided for
continuity or to resist torsional forces generated by
structural members, it shall be connected to the webs and
flanges of the box section. An access hole at least 18.0 in.
wide and 24.0 in. high should be provided within each
internal intermediate diaphragm. Design of the diaphragm
shall consider the effect of the access hole on the stresses.
Reinforcement around the hole may be required.
Intermediate internal diaphragms or cross-frames shall
be provided. For all single box sections, horizontally
curved sections, and multiple box sections in crosssections of bridges not satisfying the requirements of
Article 6.11.2.3 or with box flanges that are not fully
effective according to the provisions of Article 6.11.1.1,
the spacing of the internal diaphragms or cross-frames
shall not exceed 40.0 ft.
Webs of internal and external diaphragms shall satisfy
Eq. 6.10.1.10.2-2. The nominal shear resistance of internal
and external diaphragm webs shall be determined from
Eq. 6.10.9.3.3-1.
6-63
Boxes may undergo excessive rotation in some cases
when the concrete deck is placed if intermediate
diaphragms or cross-frames are not provided between
boxes. If analysis shows that such rotations are anticipated,
temporary cross-frames may be employed. Removal of
such temporary members may lead to failure of remaining
bolts, creating a safety concern. The effect of the release of
bracing forces on the bridge can be investigated by
considering the effect of reversal of member loads.
Removal of temporary cross-frames having large forces
may cause increased deck stresses.
Until the deck on a tub section hardens, internal crossframes or diaphragms and lateral top flange bracing are
required to stabilize the tub section. For straight boxes
without skew satisfying the requirements of
Article 6.11.2.3 and with fully effective box flanges,
transverse bending stresses and longitudinal warping
stresses due to cross-section distortion have often been
shown to be small (Johnston and Mattock, 1967) and may
be neglected. Torsion may be significant, however, if the
deck weight acting on the box is unsymmetrical. A
reduction in the number of permanent internal crossframes or diaphragms and/or top lateral bracing members
in such boxes is permitted when checked by proper
analysis. Internal cross-frames or diaphragms should be
placed at or near points of maximum moment and near
both sides of field splices. The Engineer should also
consider the need for additional temporary or permanent
internal cross-frames or diaphragms, which may be
required for transportation, construction, and at the lifting
points of each shipping piece.
Cross-sectional distortion stresses are typically
controlled by the internal cross-frames or diaphragms, with
the spacing of these members not to exceed 40.0 ft for the
cases specified herein. For the specific cases listed in
Article 6.11.1.1, transverse bending stresses due to crosssection distortion are explicitly limited to 20.0 ksi at the
strength limit state. Adequate internal cross-frames or
diaphragms must be introduced to meet this limit, and
should also be designed to control the longitudinal warping
stresses due to the critical factored torsional loads. Such
stresses should not exceed approximately ten percent of
the longitudinal stresses due to major-axis bending at the
strength limit state.
In cases with widely spaced internal cross-frames or
diaphragms, additional struts between the top flanges of tub
sections may be necessary in order to satisfy the
constructibility provisions of Article 6.11.3.2. As indicated
in Article C6.11.3.2, struts that are part of top lateral bracing
systems attached to the flanges at points where internal
cross-frames or diaphragms do not exist may be considered
to act as brace points at the discretion of the Engineer.
Where distortion of the section is adequately
controlled by the internal cross-frames or diaphragms,
acting in conjunction with a top lateral bracing system in
the case of tub sections, the St. Venant torsional inertia, J,
for a box section may be determined as:
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
J =4
Ao2
b
t
(C6.7.4.3-1)
where:
Ao =
b =
t
=
area enclosed by the box section (in.2)
width of rectangular plate element (in.)
thickness of plate (in.)
In tub sections with inclined webs with a slope
exceeding 1 to 4 and/or where the unbraced length of the
top flanges exceeds 30.0 ft, additional intermediate internal
cross-frames, diaphragms, or struts may be required to
increase the resistance of discretely braced top flanges of
tub sections to lateral bending resulting from a uniformly
distributed transverse load acting on the flanges. This
lateral load results from the change in the horizontal
component of the web dead load shear plus the change in
the St. Venant torsional dead load shear per unit length
along the member, and is discussed further in
Article C6.11.3.2.
Because of the critical nature of internal and external
diaphragms, particularly at supports, any reliance on postbuckling resistance is not advisable. Satisfaction of
Eq. 6.10.1.10.2-2 ensures that theoretical bend buckling of
internal and external diaphragm webs will not occur for
elastic stress levels at or below the yield stress.
Limiting the nominal shear resistance of diaphragm
webs to the shear buckling or shear yield resistance
according to Eq. 6.10.9.3.3-1 prevents any reliance on
post-buckling shear resistance. Bearing stiffeners on
internal diaphragms act as transverse stiffeners in
computing the nominal shear resistance.
A portion of the box flange width equal to six times its
thickness may be considered effective with an internal
diaphragm.
The attachment of internal cross-frame connection
plates to box flanges is discussed further in
Article C6.6.1.3.1.
6.7.4.4—Trusses and Arches
Diaphragms shall be provided at the connections to
floorbeams and at other connections or points of
application of concentrated loads. Internal diaphragms may
also be provided to maintain member alignment.
Gusset plates engaging a pedestal pin at the end of a
truss shall be connected by a diaphragm. The webs of the
pedestal should be connected by a diaphragm wherever
practical.
If the end of the web plate or cover plate is 4.0 ft or
more from the point of intersection of the members, a
diaphragm shall be provided between gusset plates
engaging main members.
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SECTION 6: STEEL STRUCTURES
6-65
6.7.5—Lateral Bracing
6.7.5.1—General
C6.7.5.1
The need for lateral bracing shall be investigated for
all stages of assumed construction procedures and the final
condition.
Where required, lateral bracing should be placed
either in or near the plane of a flange or chord being
braced. Investigation of the requirement for lateral bracing
shall include, but not be limited to:
•
Transfer of lateral wind loads to the bearings as
specified in Article 4.6.2.7,
•
Transfer of lateral loads as specified in Article 4.6.2.8,
and
•
Control of deformations and cross-section geometry
during fabrication, erection, and placement of the
deck.
Lateral bracing members not required for the final
condition should not be considered to be primary
members, and may be removed at the Owner’s discretion.
If permanent lateral bracing members are included in
the structural model used to determine live load force
effects, they shall be designed for all applicable limit states
and shall be considered to be primary members. The
provisions of Articles 6.8.4 and 6.9.3 shall apply.
Connection plates for lateral bracing shall satisfy the
requirements specified in Article 6.6.1.3.2.
When lateral bracing is designed for seismic loading,
the provisions of Article 4.6.2.8 shall apply.
In I-girder bridges, bottom flange lateral bracing
creates a pseudo-closed section formed by the I-girders
connected with the bracing and the hardened deck, and
therefore becomes load carrying. Cross-frame forces
increase with the addition of bottom flange bracing
because the cross-frames act to retain the shape of the
pseudo-box section. In addition, moments in the braced
girders become more equalized and the bracing members
are also subject to significant live load forces.
6.7.5.2—I-Section Members
Continuously braced flanges should not require lateral
bracing.
The need for lateral bracing adjacent to supports of
I-girder bridges to provide rigidity during construction
should be considered.
C6.7.5.2
Wind-load stresses in I-sections may be reduced by:
•
Changing the flange size,
•
Reducing the diaphragm or cross-frame spacing, or
•
Adding lateral bracing.
The relative economy of these methods should be
investigated.
To help prevent significant relative horizontal movement
of the girders in spans greater than 200 ft during construction,
it may be desirable to consider providing either temporary or
permanent lateral bracing in one or more panels adjacent to
the supports of I-girder bridges. For continuous-span bridges,
such bracing would only be necessary adjacent to interior
supports and should be considered at the free ends of
continuous units. Such a system of lateral bracing can also
provide a stiffer load path for wind loads acting on the
noncomposite structure during construction to help reduce the
lateral deflections and flange lateral bending stresses. Top
lateral bracing is preferred. Bottom lateral bracing can
provide a similar function, but unlike top bracing, would be
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
subject to significant live load forces in the finished structure
that would have to be considered.
For horizontally curved bridges, when the curvature is
sharp and temporary supports are not practical, it may be
desirable to consider providing both top and bottom lateral
bracing to ensure pseudo-box action while the bridge is under
construction. Top and bottom lateral bracing provides
stability to a pair of I-girders.
If temporary lateral bracing is used, the analysis method
used must be able to recognize influence of the lateral
bracing.
6.7.5.3—Tub Section Members
Top lateral bracing shall be provided between common
flanges of individual tub sections. For straight girders, the
need for a full-length lateral bracing system shall be
investigated to ensure that deformations of the tub section are
adequately controlled and that stability of the tub section
members is provided during erection and placement of the
concrete deck. During deck casting, the stability of the
compression flanges between panel points of the lateral
bracing system shall be investigated. If a full-length lateral
bracing system is not provided, the local stability of the top
flanges and global stability of the individual tub sections shall
be investigated for the Engineer’s assumed construction
sequence. For horizontally curved girders, a full-length lateral
bracing system shall be provided and the stability of
compression flanges between panel points of the lateral
bracing system shall be investigated during deck casting.
Top lateral bracing shall be designed to resist shear
flow in the pseudo-box section due to the factored loads
before the concrete deck has hardened or is made
composite. Forces in the bracing due to flexure of the tub
shall also be considered during construction based on the
Engineer’s assumed construction sequence.
If the bracing is attached to the webs, the crosssectional area of the tub for shear flow shall be reduced to
reflect the actual location of the bracing, and a means of
transferring the forces from the bracing to the top flange
shall be provided.
C6.7.5.3
Investigation will generally show that a lateral bracing
system is not required between multiple tub sections.
The shear center of an open tub section is located
below the bottom flange (Heins, 1975). The addition of top
lateral bracing raises the shear center closer to the center of
the resulting pseudo-box section, significantly improving
the torsional stiffness.
In addition to resisting the shear flow before the
concrete deck has hardened or is made composite, top
lateral bracing members are also subject to significant
forces due to flexure of the noncomposite tub. In the
absence of a more refined analysis, Fan and Helwig (1999)
provide an approach for estimating these forces.
Top lateral bracing members are also subject to forces
due to wind loads acting on the noncomposite pseudo-box
section during construction.
For straight tub sections with spans less than about
150 ft, as a minimum, at least one panel of horizontal
lateral bracing should be provided within the tub on each
side of a lifting point. The need for additional lateral
bracing to resist the shear flow resulting from any net
torque on the steel section due to unequal factored deck
weight loads acting on each side of the top flanges, or any
other known eccentric loads acting on the steel section
during construction, should be considered. Cross-section
distortion and top-flange lateral bending stresses may need
to be considered when a tub with a partial-length bracing
system is subjected to a net torque. A full-length lateral
bracing system should be considered for cases where the
torques acting on the steel section are deemed particularly
significant, e.g. tub-section members resting on skewed
supports and/or tub-section members on which the deck
is unsymmetrically placed. If a full-length system is not
provided in a straight tub-section member, the Engineer
must ensure the local and global stability of the top
flanges and the tub-section member, respectively, during
the assumed construction sequence. For straight tub
sections with spans greater than about 150 ft, a fulllength lateral bracing system should be provided within
the tub.
For both straight and horizontally curved tub
sections, a full-length lateral bracing system forms a
pseudo-box to help limit distortions brought about by
temperature changes occurring prior to concrete deck
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2012
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SECTION 6: STEEL STRUCTURES
6-67
placement, and to resist the torsion and twist caused by
any eccentric loads acting on the steel section during
construction. AASHTO (1993) specified that diagonal
members of the top lateral bracing for tub sections satisfy
the following criterion:
Ad ≥ 0.03w
(C6.7.5.3-1)
where:
Ad =
w
=
minimum required cross-sectional area of one
diagonal (in.2)
center-to-center distance between the top flanges
(in.)
Satisfaction of this criterion was intended to ensure that
the top lateral bracing would be sized so that the tub
would act as a pseudo-box section with minimal warping
torsional displacement and normal stresses due to
warping torsion less than or equal to ten percent of the
major-axis bending stresses. This criterion was
developed assuming tub sections with vertical webs and
ratios of section width-to-depth between 0.5 and 2.0, and
an X-type top lateral bracing system with the diagonals
placed at an angle of 45 degrees relative to the
longitudinal centerline of the tub-girder flanges (Heins,
1978). Although this criterion may not necessarily be
directly applicable to other bracing configurations and
cross-section geometries, it is recommended that
Eq. C6.7.5.3-1 still be used as a guideline to ensure that a
reasonable minimum area is provided for the diagonal
bracing members.
Single-diagonal top lateral bracing systems are
preferred over X-type systems because there are fewer
pieces to fabricate and erect and fewer connections.
However, forces in alternating Warren-type single-diagonal
top lateral bracing members, as shown in Figure C6.7.5.3-1,
due to flexure of the tub section can sometimes result in the
development of significant lateral bending stresses in the top
flanges. In lieu of a refined analysis, Fan and Helwig (1999)
provide an approach for estimating the top-flange lateral
bending stresses due to these forces. If necessary, the flange
lateral bending stresses and forces in the bracing members in
this case can often be effectively mitigated by the judicious
placement of parallel single-diagonal members, or a Pratttype configuration, in each bay in lieu of a Warren-type
configuration as shown in Figure C6.7.5.3-2. In this
configuration, the members should be oriented based on the
sign of the torque so that the forces induced in these
members due to torsion offset the compressive or tensile
forces induced in the same members due to flexure of the tub
section. The forces in the lateral bracing system are very
sensitive to the casting sequence. If the member sizes have
been optimized based upon an assumed casting sequence, it
is imperative that the assumed casting sequence be shown in
the contract documents. Field tests have shown that forces in
the top lateral system after the deck has been cast are
negligible.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
CL
.
Abut
C
L
Abu
t.
Figure C6.7.5.3-1—Warren-Type Single-Diagonal Top
Lateral Bracing System for Tub Section Member: Plan View
CL
.
Abut
C
L
Abu
t.
Figure C6.7.5.3-2—Pratt-Type Single-Diagonal Top
Lateral Bracing System for Tub Section Member: Plan
View
Where the forces in the bracing members are not
available from a refined analysis, the shear flow across the
top of the pseudo-box section can be computed from
Eq. C6.11.1.1-1 assuming the top lateral bracing acts as an
equivalent plate. The resulting shear can then be computed
by multiplying the resulting shear flow by the width w, and
the shear can then be resolved into the diagonal bracing
member(s). Should it become necessary for any reason to
compute the St. Venant torsional stiffness of the pseudobox section according to Eq. C6.7.4.3-1, formulas are
available (Kollbrunner and Basler, 1966; Dabrowski,
1968) to calculate the thickness of the equivalent plate for
different possible configurations of top lateral bracing.
Top lateral bracing should be continuous across field
splice locations.
6.7.5.4—Trusses
Through-truss spans and deck truss spans shall have
top and bottom lateral bracing. If an x-system of bracing is
used, each member may be considered effective
simultaneously if the members meet the slenderness
requirements for both tension and compression members.
The members should be connected at their intersections.
The member providing lateral bracing to compression
chords should be as deep as practical and connected to
both flanges.
Floorbeam connections should be located so that the
lateral bracing system will engage both the floorbeam and
the main supporting members. Where the lateral bracing
system intersects a joint formed by a floorbeam and a main
longitudinal member, the lateral member shall be
connected to both members.
6.7.6—Pins
6.7.6.1—Location
Pins should be located so as to minimize the force
effects due to eccentricity.
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SECTION 6: STEEL STRUCTURES
6-69
6.7.6.2—Resistance
6.7.6.2.1—Combined Flexure and Shear
C6.7.6.2.1
Pins subjected to combined flexure and shear shall be
proportioned to satisfy:
2.2 Vu
6.0 M u
+
3
2
φ f D Fy
φv D Fy
The development of Eq. 6.7.6.2.1-1 is discussed in
Kulicki (1983).
3
≤ 0.95
(6.7.6.2.1-1)
where:
D
Mu
Vu
Fy
φf
=
=
=
=
=
φv
=
diameter of pin (in.)
moment due to the factored loads (kip-in.)
shear due to the factored loads (kip)
specified minimum yield strength of the pin (ksi)
resistance factor for flexure as specified in
Article 6.5.4.2
resistance factor for shear as specified in
Article 6.5.4.2
The moment, Mu, and shear, Vu, should be taken at the
same design section along the pin.
6.7.6.2.2—Bearing
as:
C6.7.6.2.2
The factored bearing resistance on pins shall be taken
(R )
pB r
= φb ( R pB )
n
(6.7.6.2.2-1)
in which:
(R )
pB n
= 1.5tDFy
(6.7.6.2.2-2)
where:
t
=
D =
φb =
For the design of new pins subjected to significant
rotations, such as for rocker bearings or hinges, the
coefficient 1.5 in Eq. 6.7.6.2.2-2 may be halved to 0.75 at
the discretion of the Engineer. This accounts for increased
wear over the life of pins used for applications with
significant rotations. An equivalent approach to that
suggested above was used for allowable stress design in
the AASHTO Standard Specifications. For the evaluation
of existing pins subjected to significant rotations, the 1.5
coefficient in Eq. 6.7.6.2.2-2 should not be halved.
thickness of plate (in.)
diameter of pin (in.)
resistance factor for bearing as specified in
Article 6.5.4.2
6.7.6.3—Minimum Size Pin for Eyebars
The diameter of the pin, D, shall satisfy:
3 Fy
D≥ +
b
4 400
(6.7.6.3-1)
where:
Fy =
b
=
specified minimum yield strength of the eyebar
(ksi)
width of the body of the eyebar (in.)
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6.7.6.4—Pins and Pin Nuts
Pins shall be of sufficient length to secure a full
bearing of all parts connected upon the turned body of the
pin. The pin shall be secured in position by:
•
Hexagonal recessed nuts,
•
Hexagonal solid nuts with washers, or
•
If the pins are bored through, a pin cap restrained by
pin rod assemblies.
Pin or rod nuts shall be malleable castings or steel and
shall be secured in position by cotter pins through the
threads or by burring the threads. Commercially available
lock nuts may be used as an alternate to burring the threads
or use of cotter pins.
6.7.7—Heat-Curved Rolled Beams and Welded Plate
Girders
6.7.7.1—Scope
This section pertains to rolled beams and welded
I-section plate girders heat-curved to obtain a horizontal
curvature. Structural steels conforming to AASHTO
M 270M/M 270 (ASTM A709/A709M), Grades 36, 50,
50S, 50W, HPS 50W, HPS 70W or HPS 100W (Grades
250, 345, 345S, 345W, HPS 345W, HPS 485W or
HPS 690W) may be heat-curved.
6.7.7.2—Minimum Radius of Curvature
For heat-curved beams and girders, the horizontal
radius of curvature measured to the centerline of the girder
web shall not be less than 150 ft and shall not be less than
the larger of the values calculated from the following two
equations:
14bD
Fyw ψtw
R=
R=
7,500b
Fywψ
(6.7.7.2-1)
(6.7.7.2-2)
where:
ψ
=
b
D
Fyw
R
=
=
=
=
ratio of the total cross-sectional area to the crosssectional area of both flanges
widest flange width (in.)
clear distance between flanges (in.)
specified minimum yield strength of a web (ksi)
radius of curvature (in.)
In addition to the above requirements, the radius shall
not be less than 1,000 ft when the flange thickness exceeds
3.0 in. or the flange width exceeds 30.0 in.
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SECTION 6: STEEL STRUCTURES
6-71
6.7.7.3—Camber
C6.7.7.3
Where additional camber is specified in the contract
documents to compensate for possible loss of camber of
heat-curved girders in service as residual stresses dissipate,
the amount of camber in inches, Δ, at any section along the
length L of the girder shall be equal to:
Δ=
Δ DL
( ΔM + ΔR )
ΔM
(6.7.7.3-1)
in which:
0.02 L2 Fyf 1,000 − R
EYo 850
where:
ΔR =
(6.7.7.3-2)
ΔDL =
camber at any point along the length L calculated
by usual procedures to compensate for deflection
due to dead loads or any other specified
loads (in.)
maximum value of ΔDL within the length L (in.)
specified minimum yield strength of a flange
(ksi)
distance from the neutral axis to the extreme
outer fiber of the cross-section (in.)
radius of curvature (ft)
span length for simple spans or for continuous
spans, the distance between a simple end support
and the permanent load contraflexure point, or
the distance between points of permanent load
contraflexure (in.)
ΔM =
Fyf =
Yo =
R
L
=
=
Part of the camber loss is attributable to construction
loads and will occur during construction of the bridge;
total camber loss will be complete after several months of
in-service loads. Therefore, a portion of the camber
increase should be included in the bridge profile. In lieu of
other guidelines, camber may be adjusted by one-half of
the camber increase. Camber losses of this nature, but
generally smaller in magnitude, are also known to occur in
straight beams and girders.
For radii greater than 1,000 ft, ΔR should be taken
equal to zero.
See also Article 11.8.3.3.1 of the AASHTO LRFD
Bridge Construction Specifications.
Camber loss between permanent load contraflexure
points adjacent to piers is small and may be neglected.
6.8—TENSION MEMBERS
6.8.1—General
C6.8.1
Members and splices subjected to axial tension shall
be investigated for:
Holes typically deducted where determining the gross
section include pin holes, access holes, and perforations.
•
Yield on the gross section using Eq. 6.8.2.1-1 and
•
Fracture on the net section using Eq. 6.8.2.1-2.
Holes larger than those typically considered for
connectors such as bolts shall be deducted in determining
the gross section area.
The determination of the net section shall require
consideration of:
•
The gross area from which deductions will be made or
reduction factors applied, as appropriate;
•
Deductions for all holes in the design cross-section;
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
•
Correction of the bolt hole deductions for the stagger
rule specified in Article 6.8.3;
•
Application of the reduction factor U specified in
Article 6.8.2.2 for members and Article 6.13.5.2 for
splice plates and other splicing elements to account
for shear lag; and
•
Application of the 85-percent maximum area
efficiency factor for splice plates and other splicing
elements specified in Article 6.13.5.2.
Tension members shall satisfy the slenderness
requirements specified in Article 6.8.4 and the fatigue
requirements of Article 6.6.1. Block shear strength shall be
investigated at end connections as specified in
Article 6.13.4.
6.8.2—Tensile Resistance
6.8.2.1—General
C6.8.2.1
The factored tensile resistance, Pr, shall be taken as
the lesser of the values given by Eqs. 6.8.2.1-1 and
6.8.2.1-2.
Pr = φ y Pny = φ y Fy Ag
(6.8.2.1-1)
Pr = φu Pnu = φu Fu An R pU
(6.8.2.1-2)
where:
Pny =
Fy
Ag
Fu
An
=
=
=
=
Rp =
U
=
φy
=
φu =
nominal tensile resistance for yielding in gross
section (kip)
specified minimum yield strength (ksi)
gross cross-sectional area of the member (in.2)
tensile strength (ksi)
net area of the member as specified in
Article 6.8.3 (in.2)
reduction factor for holes taken equal to 0.90 for
bolt holes punched full size and 1.0 for bolt holes
drilled full size or subpunched and reamed to size
reduction factor to account for shear lag; 1.0 for
components in which force effects are transmitted
to all elements, and as specified in Article 6.8.2.2
for other cases
resistance factor for yielding of tension members
as specified in Article 6.5.4.2
resistance factor for fracture of tension members
as specified in Article 6.5.4.2
The reduction factor, U, does not apply when
checking yielding on the gross section because yielding
tends to equalize the nonuniform tensile stresses caused
over the cross-section by shear lag. The reduction factor,
Rp, conservatively accounts for the reduced fracture
resistance in the vicinity of bolt holes that are punched full
size (Brown et al., 2007). No reduction in the net section
fracture resistance is required for holes that are drilled full
size or subpunched and reamed to size. The reduction in
the factored resistance for punched holes was previously
accounted for by increasing the hole size for design by
1
/16 in., which penalized drilled and subpunched and
reamed holes and did not provide a uniform reduction for
punched holes since the reduction varied with the hole
size.
Due to strain hardening, a ductile steel loaded in axial
tension can resist a force greater than the product of its
gross area and its yield strength prior to fracture. However,
excessive elongation due to uncontrolled yielding of gross
area not only marks the limit of usefulness but it can
precipitate failure of the structural system of which it is a
part. Depending on the ratio of net area to gross area and
the mechanical properties of the steel, the component can
fracture by failure of the net area at a load smaller than that
required to yield the gross area. General yielding of the
gross area and fracture of the net area both constitute
measures of component strength. The relative values of the
resistance factors for yielding and fracture reflect the
different reliability indices deemed proper for the two
modes.
The part of the component occupied by the net area at
fastener holes generally has a negligible length relative to
the total length of the member. As a result, the strain
hardening is quickly reached and, therefore, yielding of the
net area at fastener holes does not constitute a strength
limit of practical significance, except perhaps for some
builtup members of unusual proportions.
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SECTION 6: STEEL STRUCTURES
6-73
For welded connections, An is the gross section less
any access holes in the connection region.
6.8.2.2—Reduction Factor, U
The shear lag reduction factor, U, shall be used when
investigating the tension fracture check specified in
Article 6.8.1 at the strength limit state.
In the absence of more refined analysis or tests, the
reduction factors specified herein may be used to account
for shear lag in connections.
The shear lag reduction factor, U, may be calculated as
specified in Table 6.8.2.2-1. For members composed of
more than one element, the calculated value of U should not
be taken to be less than the ratio of the gross area of the
connected element or elements to the member gross area.
C6.8.2.2
The provisions of Article 6.8.2.2 are adapted from the
2005 AISC Specification Section D3.3, Effective Net Area
for design of tension members. The 2005 AISC provisions
are adapted such that they are consistent with updated draft
2010 AISC provisions. These updated provisions specify
that, for members composed of more than one element, the
calculated value of U should not be taken to be less than
the ratio of the gross area of the connected element or
elements to the member gross area.
Examples of the distances x and L used in the
calculation of the reduction factor U for all types of tension
members, except plates and Hollow Structural Section
(HSS) members, are illustrated in Figure C6.8.2.2-1.
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 6.8.2.2-1—Shear Lag Factors for Connections to Tension Members
Case
1
2
3
4
Description of Element
All tension members where the tension load is
transmitted directly to each of cross-sectional elements
by fasteners or welds (except as in Cases 3, 4, 5, and
6).
All tension members, except plates and HSS, where
the tension load is transmitted to some but not all of
the cross-sectional elements by fasteners or
longitudinal welds. (Alternatively, for W, M, S, and
HP, Case 7 may be used.)
All tension members where the tension load is
transmitted by transverse welds to some but not all of
the cross-sectional elements.
Plates where the tension load is transmitted by
longitudinal welds only.
Shear Lag Factor, U
U = 1.0
U =1−
Example
—
x
L
U = 1.0
and
A = area of the directly
connected elements
L ≥ 2wU = 1.0
2 w > L ≥ 1.5wU = 0.87
—
1.5w > L ≥ wU = 0.75
5
Round HSS with a single concentric gusset plate.
L ≥ 1.3DU = 1.0
D ≤ L < 1.3DU = 1 −
x=
6
Rectangular HSS
with a single concentric
gusset plate
with 2 side gusset plates
8
W, M, S, or HP Shapes or
Tees cut from these
shapes (If U is calculated
per Case 2, the larger
value is permitted to be
used.)
Single angles (If U is
calculated per Case 2, the
larger value is permitted
to be used.)
with flange connected
with 3 or more fasteners
per line in direction of
loading
with web connected with
4 or more fasteners in
direction of loading
with 4 or more fasteners
per line in direction of
loading
with 2 or 3 fasteners per
line in direction of
loading
x
L
B 2 + 2 BH
4( B + H )
L ≥ H U = 1 −
x=
7
D
π
L ≥ H U = 1 −
x=
x
L
x
L
B2
4( B + H )
—
2
d U = 0.90
3
2
b f < d U = 0.85
3
U = 0.70
—
U = 0.80
—
U = 0.60
—
bf ≥
where:
L
w
x
B
H
d
bf
=
=
=
=
=
=
=
length of connection (in.)
plate width (in.)
connection eccentricity (in.)
overall width of rectangular HSS member, measured 90 degrees to the plane of the connection (in.)
overall height of rectangular HSS member, measured in the plane of the connection (in.)
full nominal depth of section (in.)
flange width (in.)
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SECTION 6: STEEL STRUCTURES
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Figure C6.8.2.2-1—Determination of x or L in the Calculation of
the Shear Lag Reduction Factor, U
For members with combinations of longitudinal and
transverse welds, L is the maximum length of the
longitudinal welds. The transverse weld does not
significantly affect the fracture resistance based on shear
lag. The presence of the transverse weld does little to
influence the transfer of the load into the unattached
elements of the member cross-section. The connection
length L is defined for general cases as the maximum
length of the longitudinal welds or the out-to-out distance
between the bolts in the connection parallel to the line of
force (in.).
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6.8.2.3—Combined Tension and Flexure
A component subjected to tension and flexure shall
satisfy Eq. 6.8.2.3-1 or 6.8.2.3-2.
If
Pu
< 0.2, then
Pr
M
M uy
Pu
+ ux +
≤ 1.0
2.0 Pr
M ry
M rx
If
(6.8.2.3-1)
Pu
≥ 0.2, then
Pr
M uy
Pu
8.0 M ux
+
+
≤ 1.0
Pr
M ry
9.0 M rx
(6.8.2.3-2)
C6.8.2.3
Interaction equations in tension and compression
members are a design simplification. Such equations
involving exponents of 1.0 on the moment ratios are
usually conservative. More exact, nonlinear interaction
curves are also available and are discussed in Galambos
(1998). If these interaction equations are used, additional
investigation of service limit state stresses is necessary to
avoid premature yielding.
For sections where the nominal flexural resistance
about the x-axis is expressed in terms of stress, the
factored flexural resistance about the x-axis in
Eqs. 6.8.2.3-1 and 6.8.2.3-2 should be taken as:
M rx = the smaller of φ f Fnc S xc and φ f Fnt S xt (C6.8.2.3-1)
where:
where:
Pr
=
Mrx
=
Mry
=
Mux, Muy =
Pu
=
φf
=
factored tensile resistance as specified in
Article 6.8.2.1 (kip)
factored flexural resistance about the x-axis
taken as φf times the nominal flexural
resistance about the x-axis determined as
specified in Article 6.10, 6.11 or 6.12, as
applicable (kip-in.)
factored flexural resistance about the y-axis
taken as φf times the nominal flexural
resistance about the y-axis determined as
specified in Article 6.12, as applicable
(kip-in.)
moments about the x- and y-axes,
respectively, resulting from factored loads
(kip-in.)
axial force effect resulting from factored
loads (kip)
resistance factor for flexure specified in
Article 6.5.4.2
The stability of a flange subjected to a net
compressive stress due to the tension and flexure shall be
investigated for local buckling.
Fnc =
Fnt =
Myc =
Myt =
Sxc =
Sxt =
nominal flexural resistance of the compression
flange (ksi)
nominal flexural resistance of the tension flange
(ksi)
yield moment with respect to the compression
flange determined as specified in Article D6.2
(kip-in.)
yield moment with respect to the tension flange
determined as specified in Article D6.2 (kip-in.)
elastic section modulus about the major axis of
the section to the compression flange taken as
Myc/Fyc (in.3)
elastic section modulus about the major axis of
the section to the tension flange taken as
Myt/Fyt (in.3)
Sxc and Sxt are defined in this fashion as equivalent
values that account for the combined effects of the loads
acting on different sections in composite members.
For sections where the nominal flexural resistance
about the x-axis is determined according to the provisions
of Appendix A6, the factored flexural resistance about the
x-axis should be taken as:
M rx = the smaller of φ f M nc and φ f M nt
(C6.8.2.3-2)
where:
Mnc =
Mnt =
nominal flexural resistance based on the
compression flange (kip-in.)
nominal flexural resistance based on the tension
flange (kip-in.)
For I- and H-shaped sections, the nominal flexural
resistance about the y-axis is determined according to the
provisions of Article 6.12.2.2.1.
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SECTION 6: STEEL STRUCTURES
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For tees and double angles subject to combined axial
tension and flexure in which the axial and flexural stresses
in the flange of the tee or the connected legs of the angles
are additive in tension, e.g., when a tee is used as a bracing
member and the connection of this member is made to the
flange, a bulge in the interaction curve occurs. As a result,
Eqs. 6.8.2.3-1 and 6.8.2.3-2 may significantly
underestimate the resistance in such cases. Alternative
approaches attempting to capture this bulge have proven to
be generally inconclusive or incomplete as of this writing
(2009). In the interim, it is recommended that
Eqs. 6.8.2.3-1 and 6.8.2.3-2 be conservatively applied to
these cases. Should significant additional resistance be
required, the use of one or more of these alternative
approaches, as described in White (2006), may be
considered.
6.8.3—Net Area
C6.8.3
The net area, An, of an element is the product of the
thickness of the element and its smallest net width. The
width of each standard bolt hole shall be taken as the
nominal diameter of the hole. The width of oversize and
slotted holes, where permitted for use in Article 6.13.2.4.1,
shall be taken as the nominal diameter or width of the hole,
as applicable, specified in Article 6.13.2.4.2. The net width
shall be determined for each chain of holes extending
across the member or element along any transverse,
diagonal, or zigzag line.
The net width for each chain shall be determined by
subtracting from the width of the element the sum of the
widths of all holes in the chain and adding the quantity
s2/4g for each space between consecutive holes in the
chain, where:
s
g
=
=
pitch of any two consecutive holes (in.)
gage of the same two holes (in.)
For angles, the gage for holes in opposite adjacent
legs shall be the sum of the gages from the back of the
angles less the thickness.
The development of the “s2/4g” rule for estimating the
effect of a chain of holes on the tensile resistance of a
section is described in McGuire (1968). Although it has
theoretical shortcomings, it has been used for a long time
and has been found to be adequate for ordinary
connections.
In designing a tension member, it is conservative and
convenient to use the least net width for any chain together
with the full tensile force in the member. It is sometimes
possible to achieve an acceptable, slightly less
conservative design by checking each possible chain with
a tensile force obtained by subtracting the force removed
by each bolt ahead of that chain, i.e., closer to midlength
of the member from the full tensile force in the member.
This approach assumes that the full force is transferred
equally by all bolts at one end.
6.8.4—Limiting Slenderness Ratio
Tension members other than rods, eyebars, cables, and
plates shall satisfy the slenderness requirements specified
below:
•
For
primary
members
subject
to
stress
reversals ....................................................... ≤ 140
r
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
•
For primary members not subject to stress
reversals ..................................................... ≤ 200
r
•
For secondary members .................................
≤ 240
r
where:
ℓ
r
=
=
unbraced length (in.)
radius of gyration (in.)
6.8.5—Builtup Members
6.8.5.1—General
C6.8.5.1
The main elements of tension members built up from
rolled or welded shapes shall be connected by continuous
plates with or without perforations or by tie plates with or
without lacing. Welded connections between shapes and
plates shall be continuous. Bolted connections between
shapes and plates shall conform to the provisions of
Article 6.13.2.
Perforated plates, rather than tie plates and/or lacing,
are now used almost exclusively in builtup members.
However, tie plates with or without lacing may be used
where special circumstances warrant. Limiting design
proportions are given in AASHTO (2002) and AISC
(2005).
6.8.5.2—Perforated Plates
The ratio of length in the direction of stress to width
of holes shall not exceed 2.0.
The clear distance between holes in the direction of
stress shall not be less than the transverse distance between
the nearest line of connection bolts or welds. The clear
distance between the end of the plate and the first hole
shall not be less than 1.25 times the transverse distance
between bolts or welds.
The periphery of the holes shall have a minimum
radius of 1.5 in.
The unsupported widths at the edges of the holes may
be assumed to contribute to the net area of the member.
Where holes are staggered in opposite perforated plates the
net area of the member shall be considered the same as for
a section having holes in the same transverse plane.
6.8.6—Eyebars
6.8.6.1—Factored Resistance
The factored resistance of the body of the eyebar shall
be taken as specified in Eq. 6.8.2.1-1.
6.8.6.2—Proportions
C6.8.6.1
Eq. 6.8.2.1-2 does not control because the net section
in the head is at least 1.35 greater than the section in the
body.
C6.8.6.2
Eyebars shall have a uniform thickness not less than
0.5 in. or more than 2.0 in.
The transition radius between the head and the body
of an eyebar shall not be less than the width of the head at
the centerline of the pin hole.
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SECTION 6: STEEL STRUCTURES
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The net width of the head at the centerline of the pin
hole shall not be less than 135 percent the required width
of the body.
The net dimension of the head beyond the pin hole
taken in the longitudinal direction shall not be less than
75 percent of the width of the body.
The width of the body shall not exceed eight times its
thickness.
The center of the pin hole shall be located on the
longitudinal axis of the body of the eyebar. The pin-hole
diameter shall not be more than 0.03125 in. greater than
the pin diameter.
For steels having a specified minimum yield strength
greater than 70 ksi, the hole diameter shall not exceed
five times the eyebar thickness.
6.8.6.3—Packing
The limitation on the hole diameter for steel with
specified minimum yield strengths above 70 ksi, which is
not included in the AASHTO Standard Specifications, is
intended to prevent dishing beyond the pin hole (AISC,
2005).
C6.8.6.3
The eyebars of a set shall be symmetrical about the
central plane of the member and as parallel as practicable.
They shall be restrained against lateral movement on the
pins and against lateral distortion due to the skew of the
bridge.
The eyebars shall be so arranged that adjacent bars in
the same panel will be separated by at least 0.5 in. Ringshaped spacers shall be provided to fill any gaps between
adjacent eyebars on a pin. Intersecting diagonal bars that
are not sufficiently spaced to clear each other at all times
shall be clamped together at the intersection.
The eyebar assembly should be detailed to prevent
corrosion-causing elements from entering the joints.
Eyebars sometimes vibrate perpendicular to their
plane. The intent of this provision is to prevent repeated
eyebar contact by providing adequate spacing or by
clamping.
6.8.7—Pin-Connected Plates
6.8.7.1—General
Pin-connected plates should be avoided wherever
possible.
The provisions of Article 6.8.2.1 shall be satisfied.
6.8.7.2—Pin Plates
The factored bearing resistance on pin plates, Pr, shall
be taken as:
Pr = φb Pn = φb Ab Fy
(6.8.7.2-1)
where:
Pn =
Ab =
Fy =
φb =
nominal bearing resistance (kip)
projected bearing area on the plate (in.2)
specified minimum yield strength of the plate
(ksi)
resistance factor for bearing specified in
Article 6.5.4.2
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The main plate may be strengthened in the region of
the hole by attaching pin plates to increase the thickness of
the main plate.
If pin plates are used, they shall be arranged to
minimize load eccentricity and shall be attached to the
main plate by sufficient welds or bolts to transmit the
bearing forces from the pin plates into the main plate.
6.8.7.3—Proportions
The combined net area of the main plate and pin plates
on a transverse cross-section through the centerline of the
pin hole shall not be less than 1.4 times the required net
area of the main plate away from the hole.
The combined net area of the main plate and pin plates
beyond the pin hole taken in a longitudinal direction shall
not be less than the required net area of the main plate
away from the pin hole.
The center of the pin hole shall be located on the
longitudinal axis of the main plate. The pin hole diameter
shall not be more than 0.03125 in. greater than the pin
diameter.
For steels having a specified minimum yield strength
greater than 70.0 ksi, the hole diameter shall not exceed
five times the combined thickness of the main plate and
pin plates.
The combined thickness of the main plate and pin
plates shall not be less than 12 percent of the net width
from the edge of the hole to the edge of the plate or plates.
The thickness of the main plate shall not be less than
12 percent of the required width away from the hole.
6.8.7.4—Packing
C6.8.7.3
The proportions specified in this Article assure that
the member will not fail in the region of the hole if the
strength limit state is satisfied in the main plate away from
the hole.
C6.8.7.4
Pin-connected members shall be restrained against
lateral movement on the pin and against lateral distortion
due to the skew of the bridge.
The pin-connected assembly should be detailed to
prevent corrosion-causing elements from entering the
joints.
6.9—COMPRESSION MEMBERS
6.9.1—General
C6.9.1
The provisions of this Article shall apply to prismatic
noncomposite and composite steel members subjected to
either axial compression or combined axial compression
and flexure.
Arches shall also satisfy the requirements of
Article 6.14.4.
Compression chords of half-through trusses shall also
satisfy the requirements of Article 6.14.2.9.
Conventional column design formulas contain
allowances for imperfections and eccentricities permissible
in normal fabrication and erection. The effect of any
significant additional eccentricity should be accounted for
in bridge design.
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SECTION 6: STEEL STRUCTURES
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6.9.2—Compressive Resistance
6.9.2.1—Axial Compression
The factored resistance of
compression, Pr, shall be taken as:
components
in
(6.9.2.1-1)
Pr = φc Pn
where:
Pn =
φc
=
nominal compressive resistance as specified in
Articles 6.9.4 or 6.9.5, as applicable (kip)
resistance factor for compression as specified in
Article 6.5.4.2
6.9.2.2—Combined Axial Compression and
Flexure
Except as permitted otherwise in Article 6.9.4.4, the
axial compressive load, Pu, and concurrent moments, Mux
and Muy, calculated for the factored loadings by elastic
analytical procedures shall satisfy the following relationship:
•
If
Pu
< 0.2, then
Pr
M
M
Pu
+ ux + uy ≤ 1.0
M ry
2.0 Pr
M rx
•
If
(6.9.2.2-1)
Pu
≥ 0.2, then
Pr
M
Pu
8.0 M ux
+
+ uy ≤ 1.0
Pr
M ry
9.0 M rx
(6.9.2.2-2)
where:
Pr =
Mrx =
Mry =
Mux =
Muy =
φf
=
factored compressive resistance as specified in
Article 6.9.2.1 (kip)
factored flexural resistance about the x-axis taken
equal to φf times the nominal flexural resistance
about the x-axis determined as specified in
Article 6.10, 6.11 or 6.12, as applicable (kip-in.)
factored flexural resistance about the y-axis taken
equal to φf times the nominal flexural resistance
about the y-axis determined as specified in
Article 6.12, as applicable (kip-in.)
factored flexural moment about the x-axis
calculated as specified below (kip-in.)
factored flexural moment about the y-axis
calculated as specified below (kip-in.)
resistance factor for flexure specified in
Article 6.5.4.2
C6.9.2.2
These equations are identical to Eqs. (H1-1a) and
(H1-1b) of AISC (2005). They were selected for use in that
Specification after being compared with a number of
alternative formulations with the results of refined inelastic
analyses of 82 frame sidesway cases (Kanchanalai, 1977).
Pu, Mux, and Muy are simultaneous axial and flexural forces
on cross-sections determined by analysis under factored
loads. The maximum calculated moment in the member in
each direction including the second-order effects, should
be considered. Where maxima occur on different crosssections, each should be checked.
For further information on computing the factored
flexural resistances about the x- and y-axes, refer to
Article C6.8.2.3.
For tees and double angles subject to combined axial
compression and flexure in which the axial and flexural
stresses in the flange of the tee or the connected legs of the
angles are additive in compression, e.g., when a tee is used
as a bracing member and the connection of this member is
made to the flange, a bulge in the interaction curve occurs.
As a result, Eqs. 6.9.2.2-1 and 6.9.2.2-2 may significantly
underestimate the resistance in such cases. Alternative
approaches attempting to capture this bulge have proven to
be generally inconclusive or incomplete as of this writing
(2009). In the interim, it is recommended that
Eqs. 6.9.2.2-1 and 6.9.2.2-2 be conservatively applied to
these cases. Should significant additional resistance be
required, the use of one or more of these alternative
approaches, as described in White (2006), may be
considered.
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Mux and Muy, moments about axes of symmetry, may
be determined by:
•
A second-order elastic analysis that accounts for the
magnification of moment caused by the factored axial
load, or
•
The approximate single step adjustment specified in
Article 4.5.3.2.2b.
6.9.3—Limiting Slenderness Ratio
Compression members shall satisfy the slenderness
requirements specified herein.
•
For primary members: .............................
K
≤ 120
r
•
For secondary members: .........................
K
≤ 140
r
where:
K
=
effective length factor specified in Article 4.6.2.5
ℓ
=
unbraced length (in.)
r
=
radius of gyration (in.)
For the purpose of this Article only, the radius of
gyration may be computed on a notional section that
neglects part of the area of a component, provided that:
•
The capacity of the component based on the actual
area and radius of gyration exceeds the factored loads,
and
•
The capacity of the notional component based on a
reduced area and corresponding radius of gyration
also exceeds the factored loads.
6.9.4—Noncomposite Members
6.9.4.1—Nominal Compressive Resistance
C6.9.4.1
6.9.4.1.1—General
C6.9.4.1.1
The nominal compressive resistance, Pn, shall be
taken as the smallest value based on the applicable modes
of flexural buckling, torsional buckling, and flexuraltorsional buckling as follows:
•
Applicable buckling modes for doubly symmetric
members:
o
Flexural buckling shall be applicable. Torsional
buckling shall also be applicable for opensection members in which the effective
torsional unbraced length is larger than the
effective lateral unbraced length.
Eqs. 6.9.4.1.1-1 and 6.9.4.1.1-2 are equivalent to the
equations given in AISC (2005) for computing the nominal
compressive resistance. The equations are written in a
different format in terms of the critical elastic buckling
resistance, Pe, and the equivalent nominal yield resistance,
Po, to allow for more convenient calculation of the nominal
resistance for members subject to buckling modes in
addition to, or other than, flexural buckling, and to allow
for the consideration of compression members with slender
elements, as defined below. Also, this form of the
resistance equations may be used to conveniently calculate
Pn when a refined buckling analysis is employed to assess
the stability of trusses, frames or arches in lieu of utilizing
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SECTION 6: STEEL STRUCTURES
•
•
6-83
Applicable buckling modes for singly symmetric
members:
o
Flexural buckling shall be applicable.
o
Flexural-torsional buckling shall also be
applicable for open-section members.
Applicable
members:
buckling
modes
for
unsymmetric
o
Only flexural-torsional buckling shall be
applicable for open-section members, except
that for single-angle members designed
according to the provisions of Article 6.9.4.4,
only flexural buckling shall be applicable.
o
Only flexural buckling shall be applicable for
closed-section members.
Torsional buckling and flexural-torsional buckling
shall not be applicable for bearing stiffeners.
Pn shall be determined as follows:
•
If
Pe
≥ 0.44 , then:
Po
Po
P
Pn = 0.658 e Po
•
If
(6.9.4.1.1-1)
Pe
< 0.44 , then:
Po
Pn = 0.877 Pe
an effective length factor approach (White, 2006). In such
cases, Pe in Eqs. 6.9.4.1.1-1 and 6.9.4.1.1-2 would be
taken as the axial load in a given member taken from the
analysis at incipient elastic buckling of the structure or
subassemblage.
Eqs. 6.9.4.1.1-1 and 6.9.4.1.1-2 represent a curve that
is essentially the same as column strength curve 2P of
Galambos (1998). The equations incorporate an out-ofstraightness criterion of L/1500. The development of the
mathematical form of these equations is described in Tide
(1985), and the structural reliability they are intended to
provide is discussed in Galambos (1998) and Galambos
(2006).
For the member under consideration, Table 6.9.4.1.1-1
may be used as a guideline for selecting the appropriate
potential buckling mode(s) to be considered in the
determination of Pn, and the equations to use for the
calculation of the corresponding critical elastic buckling
resistance, Pe, and slender element reduction factor, Q, as
applicable. For compression members with cross-sections
composed of one or more slender elements, or elements
not meeting the corresponding width-to-thickness ratio
limits specified in Article 6.9.4.2.1, the slender element
reduction factor Q accounts for the effect of potential local
buckling of those elements on the overall buckling
resistance of the member and has a value less than 1.0. The
value of Q in this instance is determined according to the
provisions of Article 6.9.4.2.2. For compression member
cross-sections without any slender elements, that is,
composed entirely of nonslender elements, Q is taken
equal to 1.0 as specified in Article 6.9.4.2.1. Q is always to
be taken equal to 1.0 for bearing stiffeners.
(6.9.4.1.1-2)
where:
Ag =
Fy =
Pe =
Po =
Q
=
gross cross-sectional area of the member (in.2)
specified minimum yield strength (ksi)
elastic critical buckling resistance determined as
specified in Article 6.9.4.1.2 for flexural
buckling, and as specified in Article 6.9.4.1.3 for
torsional bucking or flexural-torsional buckling,
as applicable (kips)
equivalent nominal yield resistance = QFyAg
(kips)
slender element reduction factor determined as
specified in Article 6.9.4.2. Q shall be taken
equal to 1.0 for bearing stiffeners.
Table 6.9.4.1.1-1 may be used for guidance in
selecting the appropriate potential buckling mode(s) to be
considered in the determination of Pn, and the equations to
use for the calculation of Pe and Q, as applicable.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
6-84
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 6.9.4.1.1-1—Selection Table for Determination of Nominal Compressive Resistance, Pn
Cross-Section
Without Slender
Elements (Q = 1.0)
Potential Buckling
Mode
Applicable
Equation for Pe
FB
and if Kzℓz > Kyℓy:
TB
(6.9.4.1.2-1)
(6.9.4.1.3-1)
Note: see also
Article C6.9.4.1.3
FB
and:
FTB
(6.9.4.1.2-1)
(6.9.4.1.3-2)
Note: see also
Article C6.9.4.1.3
With Slender
Elements (Q < 1.0)
Applicable
Potential Buckling
Equations for Pe and
Mode
Q
FB
(6.9.4.1.2-1)
(6.9.4.1.3-1)
and if Kzℓz > Kyℓy:
Note: see also
TB
Article C6.9.4.1.3
and:
(6.9.4.2.2-1) or
FLB
(6.9.4.2.2-2) or
(6.9.4.2.2-7) or
(6.9.4.2.2-8)
and/or:
(6.9.4.2.2-11)
WLB
FB
(6.9.4.1.2-1)
and:
(6.9.4.1.3-2)
FTB
Note: see also
Article C6.9.4.1.3
and:
(6.9.4.2.2-1) or
FLB
(6.9.4.2.2-2) or
(6.9.4.2.2-7) or
(6.9.4.2.2-8)
and/or:
WLB
(6.9.4.2.2-11)
FB
(6.9.4.1.2-1)
Note: for built-up
sections, see also
Article 6.9.4.3
FB
(6.9.4.1.2-1)
FB
and:
FTB
(6.9.4.1.2-1)
(6.9.4.1.3-2)
Note: see also
Article C6.9.4.1.3
FB
and:
FLB
(6.9.4.1.2-1)
Note: for built-up
sections, see also
Article 6.9.4.3
(6.9.4.2.2-10) or
(6.9.4.2.2-11)
and/or:
WLB
FB
and:
LB
(6.9.4.2.2-11)
FB
and:
FTB
(6.9.4.1.2-1)
(6.9.4.1.3-2)
Note: see also
Article C6.9.4.1.3
Tees
and:
FLB
and/or:
SLB
(6.9.4.1.2-1)
(6.9.4.2.2-12)
(6.9.4.2.2-1) or
(6.9.4.2.2-2) or
(6.9.4.2.2-7) or
(6.9.4.2.2-8)
(6.9.4.2.2-3) or
(6.4.4.2.2-4)
continued on next page
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2012
Edition
SECTION 6: STEEL STRUCTURES
6-85
Table 6.9.4.1.1-1 (continued)—Selection Table for Determination of Nominal Compressive Resistance, Pn
Cross-Section
Without Slender
Elements (Q = 1.0)
Potential Buckling
Mode
FB
Bearing Stiffeners
(6.9.4.1.2-1)
Note: see also
Articles 6.9.4.4 and
C6.9.4.4
FB
(6.9.4.1.2-1)
Note: see also
Article 6.9.4.3
and:
FTB
(6.9.4.1.3-2)
Note: see also
Article C6.9.4.1.3
and:
LLB
FB
and:
LLB
Double Angles with
Separators
FB
and:
FTB
(6.9.4.1.2-1)
Note: see also
Articles 6.9.4.4 and
C6.9.4.4
(6.9.4.2.2-5) or
(6.9.4.2.2-6)
(6.9.4.1.2-1)
Note: see also
Article 6.9.4.3
and:
LLB
(6.9.4.1.3-2)
Note: see also
Article C6.9.4.1.3
(6.9.4.2.2-5) or
(6.9.4.2.2-6)
FB
(6.9.4.1.2-1)
NA
NA
FTB
(6.9.4.1.3-3)
Note: see also
Article C6.9.4.1.3
FTB
and:
LB
(6.9.4.1.3-3)
Note: see also
Article C6.9.4.1.3
See Article
6.9.4.2.2
FB
(6.9.4.1.2-1)
FB
(6.9.4.1.2-1)
Note: See also
Article 6.10.11.2.4
FB
and:
LB
NA
(6.9.4.1.2-1)
See Article
6.9.4.2.2
NA
Unsymmetric
Open-Sections
Unsymmetric
Closed-Sections
Applicable
Equation for Pe
With Slender
Elements (Q < 1.0)
Applicable
Potential Buckling
Equations for Pe and
Mode
Q
(6.9.4.2.2-1)
or
Double Angles in
(6.4.4.2.2-2)
Continuous Contact
where:
FB = flexural buckling
TB = torsional buckling
FTB = flexural-torsional buckling
FLB = flange local buckling
WLB = web local buckling
SLB = stem local buckling
LLB = outstanding leg local buckling
LB = local buckling
NA = not applicable
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6.9.4.1.2—Elastic Flexural Buckling Resistance
The elastic critical buckling resistance, Pe, based on
flexural buckling shall be taken as:
Pe =
π2 E
K
r
2
(6.9.4.1.2-1)
Ag
s
where:
Ag =
K =
rs
=
=
gross cross-sectional area of the member (in.2)
effective length factor in the plane of buckling
determined as specified in Article 4.6.2.5
unbraced length in the plane of buckling (in.)
radius of gyration about the axis normal to the
plane of buckling (in.)
6.9.4.1.3—Elastic Torsional Buckling and FlexuralTorsional Buckling Resistance
For open-section doubly symmetric members, the
elastic critical buckling resistance, Pe, based on torsional
buckling shall be taken as:
π 2 EC
Ag
w
+ GJ
Pe =
2
( K z z )
I x + I y
(6.9.4.1.3-1)
where:
Ag
=
Cw
G
=
=
Ix, Iy
=
J
Kzℓz
=
=
gross cross-sectional area of the member
(in.2)
warping torsional constant (in.6)
shear modulus of elasticity for steel =
0.385E (ksi)
moments of inertia about the major and
minor principal axes of the cross-section,
respectively (in.4)
St. Venant torsional constant (in.4)
effective length for torsional buckling (in.)
For open-section singly symmetric members where y
is the axis of symmetry of the cross-section, the elastic
critical buckling resistance, Pe, based on flexural-torsional
buckling shall be taken as:
4 Pey Pez H
Pey + Pez
Pe =
1− 1−
2
2H
Pey + Pez
(
in which:
)
(6.9.4.1.3-2)
C6.9.4.1.2
Flexural buckling of concentrically loaded
compression members refers to a buckling mode in which
the member deflects laterally without twist or a change in
the cross-sectional shape. Flexural buckling involves
lateral displacements of the member cross-sections in the
direction of the x- or y-axes that are resisted by the
respective flexural rigidities, EIx or EIy, of the member.
Eq. 6.9.4.1.2-1 should be used to calculate the critical
flexural buckling resistances about the x- and y-axes, with
the smaller value taken as Pe for use in Eq. 6.9.4.1.1-1 or
6.9.4.1.1-2, as applicable.
C6.9.4.1.3
2013 Revision
Torsional buckling of concentrically loaded
compression members refers to a buckling mode in which
the member twists about its shear center. Torsional
buckling applies only for open-section doubly symmetric
compression members for which the locations of the
centroid and shear center coincide. Torsional buckling will
rarely control and need not be considered for doubly
symmetric I-section members satisfying the cross-section
proportion limits specified in Article 6.10.2, unless the
effective length for torsional buckling is significantly
larger than the effective length for y-axis flexural buckling.
The effective length for torsional buckling, Kzℓz, is
typically taken as the length between locations where the
member is prevented from twisting. That is, in many cases,
Kzℓz can be taken conservatively as 1.0ℓz. For a cantilever
member fully restrained against twisting and warping at
one end with the other end free, Kzℓz should be taken as 2ℓ
where ℓ is the length of the member (White, 2006). For a
member with twisting and warping restrained at both ends,
Kzℓz may be taken as 0.5ℓ. For a doubly symmetric
I-section, Cw may be taken as Iyh2/4, where h is the
distance between flange centroids, in lieu of a more precise
analysis. For closed sections, Cw may be taken equal to
zero and GJ is relatively large. Because of the large GJ,
torsional buckling and flexural-torsional buckling need not
be considered for built-up members composed of closed
sections.
Flexural-torsional buckling of concentrically loaded
compression members refers to a buckling mode in which
the member twists and bends simultaneously without a
change in the cross-sectional shape. Compression members
composed of open singly symmetric cross-sections, where
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2012
Edition
SECTION 6: STEEL STRUCTURES
H
=
1−
y o2
(6.9.4.1.3-3)
ro2
π 2E
Pey =
6-87
K y y
ry
2
(6.9.4.1.3-4)
Ag
Pez =
π 2 EC w
1
+ GJ 2
(K )2
r
z z
o
ro2 =
yo2 +
(6.9.4.1.3-5)
Ix + Iy
(6.9.4.1.3-6)
Ag
where:
Kyy
=
ro
=
ry
yo
=
=
effective length for flexural buckling about
the y-axis (in.)
polar radius of gyration about the shear
center (in.)
radius of gyration about the y-axis (in.)
distance along the y-axis between the shear
center and centroid of the cross-section (in.)
For open-section unsymmetric members, the elastic
critical buckling resistance, Pe, based on flexural-torsional
buckling shall be taken as the lowest root of the following
cubic equation:
( Pe − Pex ) ( Pe − Pey ) ( Pe − Pez ) −
Pe2
(P − P )
e
ey
xo
ro
2
2
y
− Pe2 ( Pe − Pex ) o = 0
ro
(6.9.4.1.3-7)
in which:
Pex =
ro2 =
π 2E
K x x
rx
2
xo2 + yo2 +
(6.9.4.1.3-8)
Ag
Ix + Iy
Ag
(6.9.4.1.3-9)
where:
Kxℓx
=
effective length for flexural buckling about
the x-axis (in.)
the y-axis is defined as the axis of symmetry of the crosssection, can fail either by flexural buckling about the x-axis or
by torsion combined with flexure about the y-axis.
Compression members composed of open unsymmetric
cross-sections, or members with no cross-section axis of
symmetry, fail by torsion combined with flexure about the xand y-axes. In both of the preceding cases, the centroid and
shear center of the cross-section do not coincide. As buckling
occurs, the axial load has a lateral component resulting from
the lateral deflection of the member. This lateral component,
acting about the shear center of the cross-section, causes
simultaneous twisting of the member. The degree of
interaction between the torsional and flexural deformations
determines the reduction of this buckling load in comparison
to the flexural buckling load (Galambos, 1998). As the
distance between the centroid and shear center increases, the
twisting tendency increases and the flexural-torsional
buckling load decreases. Flexural-torsional buckling may be a
critical mode of failure for thin-walled open-section singly
symmetric compression members, e.g. tees, double angles,
and channels, and for open-section unsymmetric compression
members due to their relatively low torsional rigidity. For
open-section singly symmetric members, the critical flexuraltorsional buckling resistance is always smaller than the
critical flexural buckling resistance about the y-axis, Pey.
Therefore, in such cases, only flexural buckling about the xaxis need be considered along with flexural-torsional
buckling. For open-section unsymmetric members, except for
single-angle members designed according to the provisions of
Article 6.9.4.4, only flexural-torsional buckling is considered;
flexural buckling about the x- and y-axes need not be
checked. Single-angle members designed according to the
provisions of Article 6.9.4.4 need only be checked for
flexural buckling; flexural-torsional buckling need not be
considered (AISC, 2005).
Eqs. 6.9.4.1.3-2 through 6.9.4.1.3-6 assume that the yaxis is defined as the axis of symmetry of the cross-section.
Therefore, for a channel, the y-axis should actually be taken
as the x-axis of the cross-section, or the axis of symmetry for
the channel section, when applying these equations. Cw
should conservatively be taken equal to zero for tees and
double angles in the application of these equations. Refer to
Article C6.12.2.2.4 for additional information on the
calculation of the St. Venant torsional constant J for tees and
double angles. For channels, refer to Article C6.12.2.2.5 for
additional information on the calculation of Cw and J.
For singly symmetric I-section compression members
with equal flange widths and differing flange thicknesses,
flexural-torsional buckling need not be considered as long
as 0.67 ≤ tf1/tf2 ≤ 1.5 and Kzℓz ≤ Kyℓy, where tf1 and tf2 are
the flange thicknesses and Kz and Ky are the effective
length factors for torsional buckling and for flexural
buckling about the y-axis, respectively (White, 2006).
However, flexural-torsional buckling should always be
checked for singly symmetric I-sections that are loaded in
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
=
=
rx
xo
radius of gyration about the x-axis (in.)
distance along the x-axis between the shear
center and centroid of the cross-section (in.)
axial compression when the flange widths are different. Cw
may be computed as follows for such sections in lieu of a
more precise analysis (Salmon and Johnson, 1996):
t f h 2 b13b23
Cw =
12 b13 + b23
(C6.9.4.1.3-1)
where:
b1, b2
h
tf
=
=
=
individual flange widths (in.)
distance between flange centroids (in.)
flange thickness (in.) Use an average
thickness if the flange thicknesses differ.
6.9.4.2—Nonslender and Slender Member
Elements
C6.9.4.2
6.9.4.2.1—Nonslender Member Elements
C6.9.4.2.1
Nonslender member elements shall satisfy the
slenderness limits specified herein. The slender element
reduction factor, Q, specified in Article 6.9.4.1.1 shall be
taken as 1.0 for compression member cross-sections
composed entirely of nonslender elements.
Unless otherwise specified herein, the slenderness of
plates shall satisfy:
b
≤k
t
E
Fy
(6.9.4.2.1-1)
where:
k
=
b
=
t
=
plate buckling coefficient as specified in
Table 6.9.4.2.1-1
width of plate as specified in Table 6.9.4.2.1-1
(in.)
plate thickness (in.). For flanges of rolled
channels, use the average thickness.
Flanges of built-up I-sections, and plates or angle legs
projecting from built-up I-sections, shall satisfy:
k E
b
≤ 0.64 c
t
Fy
(6.9.4.2.1-2)
and:
0.35 ≤ kc ≤ 0.76
in which:
(6.9.4.2.1-3)
Nonslender member elements satisfying the width-tothickness ratio limits specified herein are able to develop
their full nominal yield strength under uniform axial
compression before the onset of local buckling. For
compression member cross-sections composed entirely of
nonslender elements, local buckling does not adversely
affect the nominal compressive resistance; therefore, a
reduction in the resistance is not necessary and the slender
element reduction factor, Q, in Article 6.9.4.1.1 is taken
equal to 1.0. These limits do not apply when determining
the nominal resistance of flexural members for which
compression flange and web elements may need to
withstand larger inelastic strains in order to ensure that
local buckling does not adversely affect the calculated
resistance. For such cases, the more stringent width-tothickness requirements of the applicable portions of
Articles 6.10, 6.11 and 6.12 apply.
In Table 6.9.4.2.1-1, plates supported along one edge
parallel to the direction of the compression force are
identified as unstiffened elements, and plates supported
along two edges parallel to the direction of the force are
identified as stiffened elements.
The form of the width-to-thickness equations derives
from the classical elastic critical stress formula for plates:
Fcr = [π2kE]/[12(1–μ2)(b/t)2], in which the buckling
coefficient, k, is a function of loading and support
conditions. For a long, uniformly compressed plate with
one longitudinal edge simply-supported against rotation
and the other free, k = 0.425, and for both edges simplysupported, k = 4.00 (Timoshenko and Gere, 1961). For
these conditions, the coefficients of the b/t equation
become 0.620 and 1.901, respectively. The coefficients
specified herein are the result of further analyses and
numerous tests and reflect the effect of residual stresses,
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2012
Edition
SECTION 6: STEEL STRUCTURES
4
D
tw
kc =
6-89
(6.9.4.2.1-4)
where:
b
D
=
=
half-width of flange (in.)
web depth (in.)
Wall thickness of circular tubes, including round HSS,
shall satisfy:
D
E
≤ 0.11
t
Fy
(6.9.4.2.1-5)
where:
D
=
outside diameter of tube (in.)
t
=
thickness of tube (in.)
For members designed for combined axial
compression and flexure, Fy, as used herein, may be
replaced with the maximum calculated compressive stress
due to the factored axial load and concurrent bending
moment provided that the interaction relationships of
Article 6.9.2.2 are replaced by the following linear
relationship:
Pu M ux M uy
+
+
≤ 1.0
Pr M rx M ry
(6.9.4.2.1-6)
where:
Pr =
Pu =
Mrx =
Mry =
Mux =
Muy =
factored compressive resistance determined as
specified in Article 6.9.2.1 (kip)
axial compressive force effect resulting from
factored loads (kip)
factored flexural resistance about the x-axis taken
equal to φf times the nominal flexural resistance
about the x-axis determined as specified in
Article 6.10, 6.11 or 6.12, as applicable (kip-in.)
factored flexural resistance about the y-axis taken
equal to φf times the nominal flexural resistance
about the y-axis determined as specified in
Article 6.12, as applicable (kip-in.)
flexural moment about the x-axis resulting from
factored loads (kip-in.)
flexural moment about the y-axis resulting from
factored loads (kip-in.)
initial imperfections, and actual (as opposed to ideal)
support conditions.
For projecting flanges of built-up I-sections under
axial compression, web-flange interaction is considered.
Theory indicates that the web-flange interaction for builtup I-sections under axial compression is at least as severe
as for flexure. The kc factor accounts for the interaction of
flange and web local buckling demonstrated in
experiments conducted by Johnson (1985). For built-up
sections with D/tw ≥ 130.6, kc may be taken equal to 0.35.
For smaller values of D/tw, kc increases from 0.35 up to a
maximum value of 0.76 as a function of the web
slenderness D/tw. A kc value of 0.76 yields a k value of
0.56. Rolled I-sections are excluded from this criteria
because web-flange interaction effects are considered
negligible for these sections.
The local buckling resistance of circular tubes,
including round Hollow Structural Sections (HSS), is
significantly overestimated by the classical theory for
longitudinally compressed cylinders due to imperfections
of shape and eccentricities of the load. Therefore, the limit
given by Eq. 6.9.4.2.1-5 to prevent local buckling of
circular tubes is based on test results (Sherman, 1976)
rather than theoretical calculations. When D/t exceeds the
value given by Eq. 6.9.4.2.1-5, Eq. 6.9.4.2.2-12 should be
used to compute the local buckling reduction factor, Qa.
This equation is valid up to a D/t limit of 0.45E/Fy.
Circular tubes with D/t values greater than this limit are
not recommended for use as compression members.
Circular tubes or pipes may be designed using the
provisions specified herein for round Hollow Structural
Sections (HSS) provided that they conform to ASTM A53,
Class B and the appropriate parameters are used in the
design. Additional information on connection design for
round, square, and rectangular HSS may be found in
Chapter K of AISC (2005).
Eq. 6.9.4.2.1-6 is used if Fy is replaced with the
maximum calculated compressive stress due to the
factored axial load and concurrent bending moment in
checking the slenderness limits for nonslender member
elements since the bilinear interaction relationships of
Article 6.9.2.2 are not valid if the nonslender member
element limits are modified in this fashion.
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2012
Edition
6-90
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6.9.4.2.1-1—Plate Buckling Coefficients and Width of Plates for Axial Compression
Plates Supported along One Edge (Unstiffened Elements)
Flanges of Rolled I-, Tee, and Channel Sections;
Plates Projecting from Rolled I-Sections; and
Outstanding Legs of Double Angles in Continuous
Contact
Stems of Rolled Tees
Outstanding Legs of Single Angles;
Outstanding Legs of Double Angles with Separators; and
All Other Unstiffened Elements
Plates Supported Along Two Edges (Stiffened Elements)
Flanges and Webs of Square and Rectangular Built-Up
Box Sections and HSS; and
Nonperforated Flange Cover Plates
k
0.56
0.75
0.45
k
b
• Half-flange width of rolled I- and tee
sections
• Full-flange width of channel sections
• Distance between free edge and first line
of bolts or welds in plates
• Full width of an outstanding leg for
double angles in continuous contact
• Full depth of tee
• Full width of outstanding leg for single
angle or double angles with separators
• Full projecting width for all others
b
• Distance between adjacent lines of bolts
or welds in flanges of built-up box
sections
• Distance between adjacent lines of bolts
or clear distance between flanges when
welds are used in webs of built-up box
sections
1.40
• Clear distance between webs or flanges
minus inside corner radius on each side
for HSS. Use the outside dimension minus
three times the appropriate design wall
thickness specified in Article 6.12.2.2.2 if
the corner radius is not known
• Distance between lines of welds or bolts
for flange cover plates
Webs of I- and Channel Sections; and
All Other Stiffened Elements
1.49
Perforated Cover Plates
1.86
• Clear distance between flanges minus
the fillet or corner radius at each flange
for webs of rolled I- and channel
sections
• Distance between adjacent lines of bolts
or clear distance between flanges when
welds are used for webs of built-up Iand channel sections
• Clear distance between edge supports for
all others
• Clear distance between edge supports;
see also the paragraph at the end of
Article 6.9.4.3.2
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2012
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SECTION 6: STEEL STRUCTURES
6-91
6.9.4.2.2—Slender Member Elements
C6.9.4.2.2
Member elements not satisfying the slenderness limits
specified in Article 6.9.4.2.1 shall be classified as slender
elements and shall be subject to the requirements specified
herein.
For compression member cross-sections composed of
only unstiffened slender elements, the slender element
reduction factor, Q, specified in Article 6.9.4.1.1 shall be
taken equal to the factor for unstiffened elements, Qs. Qs
shall be taken as the smallest value for all the unstiffened
slender elements in the cross-section. For compression
member cross-sections composed of only stiffened slender
elements, Q shall be taken equal to the factor for stiffened
elements, Qa. For compression member cross-sections
composed of both unstiffened and stiffened slender
elements, Q shall be taken equal to the product of Qs and
Qa.
For unstiffened slender elements, Qs shall be taken as:
•
For flanges of rolled I-, tee and channel sections;
plates projecting from rolled I-sections; and
outstanding legs of pairs of angles in continuous
contact:
o
If 0.56
E
E
b
, then:
< ≤ 1.03
Fy
t
Fy
b Fy
Qs = 1.415 − 0.74
t E
o
If
b
E
, then:
> 1.03
t
Fy
Qs =
•
(6.9.4.2.2-1)
0.69 E
b
Fy
t
2
(6.9.4.2.2-2)
For stems of rolled tees:
o
If 0.75
E
E
b
, then:
< ≤ 1.03
Fy
Fy
t
b Fy
Qs = 1.908 − 1.22
t E
(6.9.4.2.2-3)
For compression members with cross-sections
composed of one or more slender elements, or elements
not meeting the corresponding width-to-thickness ratio
limits specified in Article 6.9.4.2.1, potential local
buckling of those elements may adversely affect the
overall buckling resistance of the member. Hence, the
nominal compressive resistance, Pn, based on flexural,
torsional or flexural-torsional buckling, as applicable, must
be reduced. Rolled wide-flange sections with ratios of d/bf
≥ 1.7, where d is the section depth and bf is the flange
width, typically have slender webs for uniform axial
compression. Webs of welded I- and box sections also
typically classify as slender elements for axial compression
according to these criteria. The stems of a significant
number of rolled tee sections and one or both legs of many
rolled angle sections must be classified as slender
elements.
For compression members containing slender
elements, Pn in Article 6.9.4.1.1 is calculated using a
reduced equivalent nominal yield resistance, Po = QFyAg,
where Ag is the gross cross-sectional area of the member
and the slender element reduction factor, Q, is less than
1.0. An equivalent approach is followed in AISC (2005).
These procedures emulate the approach originally
specified in AISI (1969). In calculating Q as specified
herein, a distinction is made between unstiffened and
stiffened elements as defined in Article C6.9.4.2.1.
Unstiffened slender elements are assumed to reach
their limit of resistance when they attain their theoretical
local buckling resistance. The slender element reduction
factor, Qs, for slender unstiffened elements is equal to the
ratio of the smallest local buckling resistance of all the
unstiffened elements in the cross-section divided by Fy.
That is, for a compression member composed entirely of
unstiffened elements, the reduced equivalent nominal yield
strength of the member is taken as the average axial stress
at which the most critical unstiffened element reaches its
local buckling resistance.
Stiffened slender elements utilize the post-buckling
resistance that is available to a plate supported along two
longitudinal edges. An effective width approach is used to
determine the available post-buckling resistance. The
slender element reduction factor, Qa, for slender stiffened
elements given by Eq. 6.9.4.2.2-9 is based on an effective
cross-sectional area, which is calculated based on the
effective widths, be, for all the stiffened slender elements
within the cross-section. be represents the total width of the
two rectangular stress blocks at each longitudinal edge
over which the maximum stress, f, at each edge can be
assumed to act uniformly to produce the same force as the
actual stresses acting over the full width of the plate. The
actual average stresses in the middle of the plate, averaged
through the thickness, are smaller due to the post-buckling
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
o
If
E
b
, then:
> 1.03
Fy
t
Qs =
•
0.69 E
b
Fy
t
2
For outstanding legs of single angles; outstanding legs
of double angles with separators; and all other
unstiffened elements:
o
If 0.45
E
E
b
, then:
< ≤ 0.91
Fy
Fy
t
b Fy
Qs = 1.34 − 0.76
t E
o
If
(6.9.4.2.2-5)
E
b
, then:
> 0.91
Fy
t
Qs =
•
(6.9.4.2.2-4)
deformations. The stress, f, is simply taken as QsFy in
Eqs. 6.9.4.2.2-10 and 6.9.4.2.2-11, in lieu of the values
specified in AISC (2005), as this is felt to be a more
representative calculation of the true resistance in all cases
(White et al., 2006).
Additional information of the development of the
equations for Qs and Qa may be found in the Commentary
to Section E7 of AISC (2005) and in White (2006). White
(2006) also provides recommendations for the application
of the equations contained herein to hybrid I-sections with
slender web elements subject to axial compression.
0.53E
b
Fy
t
2
(6.9.4.2.2-6)
For flanges of built-up I-sections; and plates or angle
legs projecting from built-up I-sections:
o
If 0.64
k E
kc E b
< ≤ 1.17 c , then:
Fy
Fy
t
b Fy
Qs = 1.415 − 0.65
t kc E
(6.9.4.2.2-7)
o
If
k E
b
> 1.17 c , then:
Fy
t
Qs =
0.90k c E
b
Fy
t
2
(6.9.4.2.2-8)
For stiffened slender elements, except circular tubes
and round HSS, Qa shall be taken as:
Qa =
Aeff
A
(6.9.4.2.2-9)
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SECTION 6: STEEL STRUCTURES
6-93
where:
A
=
Aeff =
total gross cross-sectional area of the member
(in.2)
summation of the effective areas of the crosssection based on a reduced effective width for
each slender stiffened element in the crosssection = A − ¦ ( b − be ) t (in.2)
The effective width, be, shall be determined as
follows:
•
For flanges of square and rectangular box sections and
HSS of uniform thickness; and nonperforated cover
plates:
be = 1.92t
E ª 0.38 E º
«1 −
»≤b
f ¬« (b t ) f ¼»
(6.9.4.2.2-10)
•
For webs; perforated cover plates; and all other
stiffened elements:
be = 1.92t
E ª 0.34 E º
«1 −
»≤b
f ¬« (b t ) f ¼»
(6.9.4.2.2-11)
where:
f
=
QsFy (ksi)
Where all unstiffened elements, if any, in the cross-section
are classified as nonslender, Qs = 1.0.
For circular tubes, including round HSS, with D/t not
exceeding 0.45 E F y , Qa shall be taken as:
Qa =
0.038E
2
+
F y (D / t ) 3
(6.9.4.2.2-12)
In the above, b, D, t, and kc shall be taken as defined
in Article 6.9.4.2.1 for the member element under
consideration.
6.9.4.3—Built-up Members
C6.9.4.3.1
6.9.4.3.1—General
The provisions of Article 6.9.4.2 shall apply. For
built-up members composed of two or more shapes, the
slenderness ratio of each component shape between
connecting fasteners or welds shall not be more than
75 percent of the governing slenderness ratio of the builtup member. The least radius of gyration shall be used in
computing the slenderness ratio of each component shape
between the connectors.
Two types of built-up members are commonly used for
steel bridge construction: closely spaced steel shapes
interconnected at intervals using welds or fasteners, and laced
or battened members with widely spaced flange components.
The compressive resistance of built-up members is
affected by the interaction between the global buckling
mode of the member and the localized component buckling
mode between lacing points or intermediate connectors.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Lacing, including flat bars, angles, channels, or other
shapes employed as lacing, or batten plates shall be spaced
so that the slenderness ratio of each component shape
between the connectors shall not be more than 75 percent
of the governing slenderness ratio of the built-up member.
The nominal compressive resistance of built-up
members composed of two or more shapes shall be
determined as specified in Article 6.9.4.1 subject to the
following modification. If the buckling mode involves
relative deformations that produce shear forces in the
connectors between individual shapes, KƐ/r shall be
replaced by (KƐ/r)m determined as follows for intermediate
connectors that are welded or fully-tensioned bolted:
2
§ α2
§ KA ·
§ KA ·
=
+
.
0
82
¨
¨
¸
¨
¸
2
© r ¹m
© r ¹o
©1+ α
·§ a ·
¸¨ ¸
¹ © rib ¹
2
(6.9.4.3.1-1)
where:
§ KA ·
¨
¸ =
© r ¹m
modified slenderness ratio of the built-up
member
§ KA ·
¨
¸ =
© r ¹o
a
rib
=
=
=
h
=
Duan, Reno, and Uang (2002) refer to this type of buckling
as compound buckling. For both types of built-up
members, limiting the slenderness ratio of each component
shape between connection fasteners or welds or between
lacing points, as applicable, to 75 percent of the governing
global slenderness ratio of the built-up member effectively
mitigates the effect of compound buckling (Duan, Reno,
and Uang, 2002).
The compressive resistance of both types of members
is also affected by any relative deformation that produces
shear forces in the connectors between the individual
shapes. Eq. 6.9.4.3.1-1 is adopted from AISC (2005) and
provides a modified slenderness ratio taking into account
the effect of the shear forces. Eq. 6.9.4.3.1-1 applies for
intermediate connectors that are welded or fully-tensioned
bolted and was derived from theory and verified by test
data (Aslani and Goel, 1991). For other types of
intermediate connectors on built-up members, including
riveted connectors on existing bridges, Eq. C6.9.4.3.1-1 as
follows should instead be applied:
2
§ KA ·
§ KA · § a ·
¨
¸ = ¨
¸ +¨ ¸
© r ¹m
© r ¹o © ri ¹
slenderness ratio of the built-up member
where:
acting as a unit in the buckling direction
being considered
separation ratio = h/2rib
distance between connectors (in.)
radius of gyration of an individual
component shape relative to its centroidal
axis parallel to the member axis of
buckling (in.)
distance between centroids of individual
component shapes perpendicular to the
member axis of buckling (in.)
ri
=
2
(C6.9.4.3.1-1)
minimum radius of gyration of an individual
component shape (in.)
Eq. C6.9.4.3.1-1 is based empirically on test results
(Zandonini, 1985). In all cases, the connectors must be
designed to resist the shear forces that develop in the
buckled member.
Duan, Reno, and Lynch (2000) give an approach for
determining the section properties of latticed built-up
members, such as the moment of inertia and torsional
constant.
6.9.4.3.2—Perforated Plates
Perforated plates shall satisfy the requirements of
Articles 6.9.4.2 and 6.8.5.2 and shall be designed for the
sum of the shear force due to the factored loads and an
additional shear force taken as:
V =
8.8 (A / r ) Fy ·
Pr §
100
+
¨
¸
100 © (A / r ) + 10
E
¹
(6.9.4.3.2-1)
where:
V =
Pr =
Ɛ
r
=
=
additional shear force (kip)
factored compressive resistance specified in
Articles 6.9.2.1 or 6.9.2.2 (kip)
member length (in.)
radius of gyration about an axis perpendicular to
the perforated plate (in.)
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
SECTION 6: STEEL STRUCTURES
Fy =
6-95
specified minimum yield strength (ksi)
In addition to checking the requirements of
Article 6.9.4.2.1 for the clear distance between the two
edge supports of the perforated cover plate utilizing a plate
buckling coefficient k of 1.86, the requirements of
Article 6.9.4.2.1 shall also separately be checked for the
projecting width from the edge of the perforation to a
single edge support utilizing a plate buckling coefficient k
of 0.45.
C6.9.4.4
6.9.4.4—Single-Angle Members
Single angles subject to combined axial compression
and flexure about one or both principal axes and satisfying
all of the following conditions, as applicable:
•
End connections are to a single leg of the angle, and
are welded or use a minimum of two bolts;
•
The angle is loaded at the ends in compression
through the same leg;
•
The angle is not subjected to any intermediate
transverse loads; and
•
If used as web members in trusses, all adjacent web
members are attached to the same side of the gusset
plate or chord;
may be designed as axially loaded compression members
for flexural buckling only according to the provisions of
Articles 6.9.2.1, 6.9.4.1.1, and 6.9.4.1.2 provided the
following effective slenderness ratio, (KƐ/r)eff, is utilized in
determining the nominal compressive resistance, Pn:
•
For equal-leg angles and unequal-leg angles
connected through the longer leg:
o
If A ≤ 80 , then:
rx
A
§ KA·
¨©
¸¹ = 72 + 0.75
r eff
rx
o
If
(6.9.4.4-1)
A
> 80 , then:
rx
A
§ KA·
¨©
¸ = 32 + 1.25
r ¹ eff
rx
(6.9.4.4-2)
Single angles are commonly used as compression
members in cross-frames and lateral bracing for steel
bridges. Since the angle is typically connected through one
leg only, the member is subject to combined axial
compression and flexure, or moments about both principal
axes due to the eccentricities of the applied axial load. The
angle is also usually restrained by differing amounts about
its geometric x- and y-axes. As a result, the prediction of
the nominal compressive resistance of these members
under these conditions is difficult. The provisions
contained herein provide significantly simplified
provisions for the design of single-angle members
satisfying certain conditions that are subject to combined
axial compression and flexure. These provisions are based
on the provisions for the design of single-angle members
used in latticed transmission towers (ASCE, 2000). Similar
provisions are also employed in Section E5 of AISC
(2005).
In essence, these provisions permit the effect of the
eccentricities to be neglected when these members are
evaluated as axially loaded compression members for
flexural buckling only using an appropriate specified
effective slenderness ratio, (KƐ/r)eff, in place of (KƐ/rs) in
Eq. 6.9.4.1.2-1. The effective slenderness ratio indirectly
accounts for the bending in the angles due to the
eccentricity of the loading allowing the member to be
proportioned according to the provisions of Article 6.9.2.1
as if it were a pinned-end concentrically loaded
compression member. Furthermore, when the effective
slenderness ratio is used, single angles need not be
checked for flexural-torsional buckling. The actual
maximum slenderness ratio of the angle, as opposed to
(KƐ/r)eff, is not to exceed the applicable limiting
slenderness ratio specified in Article 6.9.3. Thus, if the
actual maximum slenderness ratio of the angle exceeds the
limiting ratio, a larger angle section must be selected until
the ratio is satisfied. If (KƐ/r)eff exceeds the limiting ratio,
but the actual maximum slenderness ratio of the angle does
not, the design is satisfactory. The limiting ratios specified
in Article 6.9.3 are well below the limiting ratio of 200
specified in AISC (2005).
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6-96
•
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
For unequal-leg angles that are connected through the
shorter leg with the ratio of the leg lengths less than
1.7:
o
If
The expressions for the effective slenderness ratio
presume significant end rotational restraint about the
y-axis, or the axis perpendicular to the connected leg and
gusset plate, as shown in Figure C6.9.4.4-1.
A
≤ 80 , then:
rx
ª§ b · 2 º
A
A
§ KA·
A
¨©
¸¹ = 72 + 0.75 + 4 «¨ ¸ − 1» ≥ 0.95
r eff
rx
rz
«© bs ¹
»
¬
¼
(6.9.4.4-3)
o
If
A
> 80 , then:
rx
ª§ b · 2 º
A
A
§ KA·
« ¨ A ¸ − 1» ≥ 0.95
=
32
+
1.25
+
4
¨©
¸
r ¹ eff
rx
rz
« © bs ¹
»
¬
¼
(6.9.4.4-4)
where:
bA
=
bs
=
A
=
rx
=
rz
=
length of the longer leg of an unequal-leg angle
(in.)
length of the shorter leg of an unequal-leg angle
(in.)
distance between the work points of the joints
measured along the length of the angle (in.)
radius of gyration about the geometric axis of the
angle parallel to the connected leg (in.)
radius of gyration about the minor principal axis
of the angle (in.)
The actual maximum slenderness ratio of the angle
shall not exceed the applicable limiting slenderness ratio
specified in Article 6.9.3. Single angles designed using
(KƐ/r)eff shall not be checked for flexural-torsional
buckling.
Figure C6.9.4.4-1—Single-Angle Geometric Axes Utilized
in the Effective Slenderness Ratio Expressions
As a result, the angle tends to buckle primarily about
the x-axis due to the eccentricity of the load about the
x-axis coupled with the high degree of restraint about the
y-axis (Usami and Galambos, 1971; Woolcock and
Kitipornchai, 1986; Mengelkoch and Yura, 2002).
Therefore, the radius of gyration in the effective
slenderness ratio expressions is to be taken as rx, or the
radius of gyration about the geometric axis parallel to the
connected leg, and not the minimum radius of gyration rz
about the minor principal axis of the angle. When an angle
has significant rotational restraint about the y-axis, the
stress along the connected leg will be approximately
uniform (Lutz, 1996). Lutz (2006) compared the results
from the effective slenderness ratio equations contained
herein to test results for single-angle members in
compression with essentially pinned-end conditions
(Foehl, 1948; Trahair et al., 1969) and found an average
value of Pn /Ptest of 0.998 with a coefficient of variation of
0.109. A separate set of equations provided in AISC
(2005), which assume a higher degree of x-axis rotational
restraint and are thus intended for application only to
single angles used as web members in box or space
trusses, are not provided herein.
For the case of unequal-leg angles connected through
the shorter leg, the limited available test data for this case
gives lower capacities for comparable Ɛ/rx values than
equal-leg angles (Lutz, 2006). Stiffening the shorter leg
rotationally tends to force the buckling axis of the angle
away from the x-axis and closer to the z-axis. Thus,
(KƐ/r)eff for this case is modified by adding an additional
term in Eqs. 6.9.4.4-3 and 6.9.4.4-4 along with a governing
slenderness limit based on Ɛ/rz for slender unequal-leg
angles. The upper limit on bƐ /bs of 1.7 is based on the
limits of the available physical tests. For an unequal-leg
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SECTION 6: STEEL STRUCTURES
6-97
angle connected through the longer leg, note that rx should
be taken as the smaller value about the angle geometric
axes, which is typically listed as ry in AISC (2005a).
Single-angle compression members not meeting one
or more of the conditions required in this Article, or with
leg length ratios bℓ /bs greater than 1.7, should instead be
evaluated for combined axial load and flexure as beamcolumns according to Section H2 of AISC (2005). In
computing Pn for these cases, the end restraint conditions
should be evaluated in calculating the effective length Kℓ,
with the in-plane effective length factor K taken equal to
1.0. When the effective length factors about both
geometric axes have been computed, the procedures given
in Lutz (1992) can be used to obtain a minimum effective
radius of gyration for the angle. In determining whether
the flexural-torsional buckling resistance of the angle
needs to be considered in computing Pn, it is recommended
that AISC (2000) be consulted. Also, it has been observed
that the actual eccentricity in the angle is less than the
distance from the centerline of the gusset if there is any
restraint present about the x-axis (Lutz, 1998). In this
instance, the eccentricity y may be reduced by t/2, where t
is the thickness of the angle, as long the angle is on one
side of the chord or gusset plate (Woolcock and
Kitipornchai, 1986). The nominal flexural resistance of the
angle Mn for these cases should be determined according to
the procedures given in Section F10 of AISC (2005).
Single-angle members are often employed in X-type
configurations in cross-frames. It has been suggested
(ASCE, 2000) that for cases in such configurations, where
one diagonal is in tension with a force not less than
20 percent of the force in the diagonal compression
member, that the crossover or intersection point may be
considered as a brace point for out-of-plane buckling. A
different approach has been suggested for equally loaded
compression and tension diagonals in X-type
configurations in which all connections are welded
(El-Tayem and Goel, 1986), which also assumes a
significant level of restraint at the crossover point. While
such approaches could potentially be utilized in
determining the effective slenderness ratio, they have not
yet received extensive validation and the assumed level of
restraint may not actually be present in certain instances.
For example, should the members be connected with only
a single bolt at the crossover point, the necessary rotational
restraint about the y-axis assumed in the effective
slenderness ratio equations may not be present at that
point. Thus, it is recommended herein in the interim that
the effective slenderness ratio equations be conservatively
applied to single-angle compression members used in
X-type bracing configurations by using the full length of
the diagonal between the connection work points for ℓ.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6.9.5—Composite Members
6.9.5.1—Nominal Compressive Resistance
C6.9.5.1
The provisions of this Article shall apply to composite
columns without flexure. The provisions of Article 6.12.2.3
shall apply to composite columns in flexure.
The nominal compressive resistance of a composite
column satisfying the provisions of Article 6.9.5.2 shall be
taken as:
•
If λ ≤ 2.25, then:
Pn = 0.66λ Fe As
•
(6.9.5.1-1)
The procedure for the design of composite columns is
the same as that for the design of steel columns, except
that the specified minimum yield strength of structural
steel, the modulus of elasticity of steel, and the radius of
gyration of the steel section are modified to account for the
effect of concrete and of longitudinal reinforcing bars.
Explanation of the origin of these modifications and
comparison of the design procedure, with the results of
numerous tests, may be found in SSRC Task Group 20
(1979) and Galambos and Chapuis (1980).
If λ > 2.25, then:
Pn =
0.88 Fe As
λ
(6.9.5.1-2)
in which:
2
K Fe
λ =
rs π Ee
(6.9.5.1-3)
A
A
Fe = Fy + C1Fyr r + C2 f c′ c
As
As
(6.9.5.1-4)
C A
Ee = E 1 + 3 c
n As
(6.9.5.1-5)
where:
As =
Ac =
Ar =
Fy =
Fyr =
f′c =
E
ℓ
K
=
=
=
n
=
rs
=
cross-sectional area of the steel section (in.2)
cross-sectional area of the concrete (in.2)
total cross-sectional area of the longitudinal
reinforcement (in.2)
specified minimum yield strength of the steel
section (ksi)
specified minimum yield strength of the
longitudinal reinforcement (ksi)
specified minimum 28-day compressive strength
of the concrete (ksi)
modulus of elasticity of the steel (ksi)
unbraced length of the column (in.)
effective length factor as specified in
Article 4.6.2.5
modular ratio of the concrete as specified in
Article 6.10.1.1.1b
radius of gyration of the steel section in the plane
of bending but not less than 0.3 times the width
of the composite member in the plane of bending
for composite concrete-encased shapes (in.)
C1, C2,
C3 = composite column
Table 6.9.5.1-1
constant
specified
in
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SECTION 6: STEEL STRUCTURES
6-99
Table 6.9.5.1-1—Composite Column Constants
Filled Tubes
1.00
0.85
0.40
C1
C2
C3
Encased Shapes
0.70
0.60
0.20
In determining the moment magnification for
composite members subject to combined axial
compression and flexure according to the approximate
single step adjustment specified in Article 4.5.3.2.2b, the
following shall apply:
Pe =
As Fe
λ
(6.9.5.1-6)
6.9.5.2—Limitations
6.9.5.2.1—General
C6.9.5.2.1
The compressive resistance shall be calculated in
accordance with Article 6.9.5.1 if the cross-sectional area
of the steel section comprises at least four percent of the
total cross-sectional area of the member.
The compressive resistance shall be calculated as a
reinforced concrete column under Section 5 if the crosssectional area of the shape or tube is less than four percent
of the total cross-sectional area.
The compressive strength of the concrete shall be
between 3.0 ksi and 8.0 ksi.
The specified minimum yield strength of the steel
section and the longitudinal reinforcement used to
calculate the nominal compressive resistance shall not
exceed 60.0 ksi.
The transfer of all load in the composite column shall
be considered in the design of supporting components.
The cross-section shall have at least one axis of
symmetry.
Little of the test data supporting the development of
the present provisions for design of composite columns
involved concrete strengths in excess of 6.0 ksi. Normal
weight concrete was believed to have been used in all
tests. A lower limit of 3.0 ksi is specified to encourage the
use of good-quality concrete.
6.9.5.2.2—Concrete-Filled Tubes
The wall thickness requirements for unfilled tubes
specified in Article 6.9.4.2 shall apply to filled composite
tubes.
6.9.5.2.3—Concrete-Encased Shapes
Concrete-encased steel shapes shall be reinforced with
longitudinal and lateral reinforcement. The reinforcement
shall conform to the provisions of Article 5.7.4.6, except
that the vertical spacing of lateral ties shall not exceed the
least of:
C6.9.5.2.3
Concrete-encased shapes are not subject to the
width/thickness limitations specified in Article 6.9.4.2
because it has been shown that the concrete provides
adequate support against local buckling.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
•
16 longitudinal bar diameters,
•
48 tie bar diameters, or
•
0.5 of the least side dimension of the composite
member.
Multiple steel shapes in the same cross-section of a
composite column shall be connected to one another with
lacing and tie plates to prevent buckling of individual
shapes before hardening of the concrete.
6.10—I-SECTION FLEXURAL MEMBERS
2013 Revision
6.10.1—General
C6.10.1
The provisions of this Article apply to flexure of
rolled or fabricated straight, kinked (chorded)
continuous, or horizontally curved steel I-section
members symmetrical about the vertical axis in the
plane of the web. These provisions cover the design of
composite and noncomposite sections, hybrid and
nonhybrid sections, and constant and variable web depth
members as defined by and subject to the requirements
of Articles 6.10.1.1 through 6.10.1.8. The provisions
also cover the combined effects of major-axis bending
and flange lateral bending from any source.
All types of I-section flexural members shall be
designed as a minimum to satisfy:
This Article addresses general topics that apply to all
types of steel I-sections in either straight bridges,
horizontally curved bridges, or bridges containing both
straight and curved segments. For the application of the
provisions of Article 6.10, bridges containing both straight
and curved segments are to be treated as horizontally
curved bridges since the effects of curvature on the support
reactions and girder deflections, as well as the effects of
flange lateral bending, usually extend beyond the curved
segments. Note that kinked (chorded) girders exhibit the
same actions as curved girders, except that the effect of the
noncollinearity of the flanges is concentrated at the kinks.
Continuous kinked (chorded) girders should be treated as
horizontally curved girders with respect to these
Specifications.
The five bullet items in this Article indicate the
overarching organization of the subsequent provisions for
the design of straight I-section flexural members. Each of
the subarticles throughout Article 6.10 are written such
that they are largely self-contained, thus minimizing the
need for reference to multiple Articles to address any one
of the essential design considerations. For the strength
limit state, Article 6.10.6 directs the Engineer to the
subsequent Articles 6.10.7 through 6.10.12, and optionally
for sections in straight I-girder bridges only, to
Appendices A6 and B6, for the appropriate design
requirements based on the type of I-section. The specific
provisions of these Articles and Appendices are discussed
in the corresponding Articles of the Commentary.
The provisions of Article 6.10 and the optional
Appendices A6 and B6 provide a unified approach for
consideration of combined major-axis bending and flange
lateral bending from any source. For the majority of straight
non-skewed bridges, flange lateral bending effects tend to be
most significant during construction and tend to be
insignificant in the final constructed condition. Significant
flange lateral bending may be caused by wind, by torsion
from eccentric concrete deck overhang loads acting on
cantilever forming brackets placed along exterior girders,
and by the use of discontinuous cross-frames, i.e., not
forming a continuous line between multiple girders, in
conjunction with skews exceeding 20 degrees. In these
•
The cross-section proportion limits specified in
Article 6.10.2;
•
The constructibility requirements specified in
Article 6.10.3;
•
The service limit state requirements specified in
Article 6.10.4;
•
The fatigue and fracture limit state requirements
specified in Article 6.10.5;
•
The strength limit state requirements specified in
Article 6.10.6.
The web bend-buckling resistance in slender web
members shall be determined as specified in
Article 6.10.1.9. Flange-strength reduction factors in
hybrid and/or slender web members shall be determined as
specified in Article 6.10.1.10.
Cross-frames and diaphragms for I-sections shall
satisfy the provisions of Article 6.7.4. Where required,
lateral bracing for I-sections shall satisfy the provisions of
Article 6.7.5.
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2012
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SECTION 6: STEEL STRUCTURES
6-101
cases, the flange lateral bending may be considered at the
discretion of the Engineer. Although the use of refined
analysis methods is not required in order to fulfill the
requirements of these provisions, these methods, when
utilized, do allow for consideration of these effects. Some of
these effects have not been addressed explicitly in previous
Specifications. The intent of the Article 6.10 provisions is to
permit the Engineer to consider flange lateral bending effects
in the design in a direct and rational manner should they be
judged to be significant. In the absence of calculated values
of fℓ from a refined analysis, a suggested estimate for the
total unfactored fℓ in a flange at a cross-frame or diaphragm
due to the use of discontinuous cross-frame or diaphragm
lines is 10.0 ksi for interior girders and 7.5 ksi for exterior
girders. These estimates are based on a limited examination
of refined analysis results for bridges with skews
approaching 60 degrees from normal and an average D/bf
ratio of approximately 4.0. In regions of the girders with
contiguous cross-frames or diaphragms, these values need
not be considered. Lateral flange bending in the exterior
girders is substantially reduced when cross-frames or
diaphragms are placed in discontinuous lines over the entire
bridge due to the reduced cross-frame or diaphragm forces.
A value of 2.0 ksi is suggested for fℓ for the exterior girders
in such cases, with the suggested value of 10 ksi retained for
the interior girders. In all cases, it is suggested that the
recommended values of fℓ be proportioned to dead and live
load in the same proportion as the unfactored major-axis
dead and live load stresses at the section under
consideration. An examination of cross-frame or diaphragm
forces is also considered prudent in all bridges with skew
angles exceeding 20 degrees. When all the above lateral
bending effects are judged to be insignificant or incidental,
the flange lateral bending term, fℓ, is simply set equal to zero
in the appropriate equations. The format of the equations
then reduces simply to the more conventional and familiar
format for checking the nominal flexural resistance of
I-sections in the absence of flange lateral bending.
For horizontally curved bridges, in addition to the
potential sources of flange lateral bending discussed in the
preceding paragraph, flange lateral bending effects due to
curvature must always be considered at all limit states and
also during construction.
The fact that new design equations and provisions are
provided herein does not imply that existing bridges are
unsafe or structurally deficient. It also does not mandate
the need to rehabilitate or perform a new load rating of
existing structures to satisfy these provisions.
Flowcharts for flexural design of I-section members
are provided in Appendix C6. Fundamental calculations
for flexural members previously found in Article 6.10.3 of
AASHTO (2004) have been placed in Appendix D6.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6.10.1.1—Composite Sections
Sections consisting of a concrete deck that provides
proven composite action and lateral support connected to a
steel section by shear connectors designed according to the
provisions of Article 6.10.10 shall be considered
composite sections.
6.10.1.1.1—Stresses
6.10.1.1.1a—Sequence of Loading
The elastic stress at any location on the composite
section due to the applied loads shall be the sum of the
stresses caused by the loads applied separately to the:
•
Steel section,
•
Short-term composite section, and
•
Long-term composite section.
For unshored construction, permanent load applied
before the concrete deck has hardened or is made
composite shall be assumed carried by the steel section
alone; permanent load and live load applied after this stage
shall be assumed carried by the composite section. For
shored construction, all permanent load shall be assumed
applied after the concrete deck has hardened or has been
made composite and the contract documents shall so
indicate.
6.10.1.1.1b—Stresses for Sections in Positive
Flexure
For calculating flexural stresses within sections
subjected to positive flexure, the composite section shall
consist of the steel section and the transformed area of the
effective width of the concrete deck. Concrete on the
tension side of the neutral axis shall not be considered
effective at the strength limit state.
For transient loads assumed applied to the short-term
composite section, the concrete deck area shall be
transformed by using the short-term modular ratio, n. For
permanent loads assumed applied to the long-term
composite section, the concrete deck area shall be
transformed by using the long-term modular ratio, 3n.
Where moments due to the transient and permanent loads
are of opposite sign at the strength limit state, the
associated composite section may be used with each of
these moments if the resulting net stress in the concrete
deck due to the sum of the unfactored moments is
compressive.
Otherwise,
the
provisions
of
Article 6.10.1.1.1c shall be used to determine the stresses
in the steel section. Stresses in the concrete deck shall be
determined as specified in Article 6.10.1.1.1d.
C6.10.1.1.1a
2013 Revision
Previous Specifications indicated that a concrete slab
may be considered sufficiently hardened after the concrete
attains 75 percent of its specified 28-day compressive
strength f ′c. Other indicators may be used based on the
judgment of the Engineer.
While shored construction is permitted according to
these provisions, its use is not recommended. Unshored
construction generally is expected to be more economical.
Also, these provisions may not be sufficient for shored
construction where close tolerances on the girder cambers
are important. There has been limited research on the
effects of concrete creep on composite steel girders under
large dead loads. There have been no known significant
demonstration bridges built with shored construction in the
U.S. Shored composite bridges that are known to have
been constructed in Germany did not retain composite
action. Furthermore, there is an increased likelihood of
significant tensile stresses occurring in the concrete deck at
permanent support points when shored construction is
used.
C6.10.1.1.1b
For normal-weight concrete, the modular ratio may be
taken as:
2.4 ≤ f c′ < 2.9
2.9 ≤ f c′ < 3.6
3.6 ≤ f c′ < 4.6
n = 10
4.6 ≤ f c′ < 6.0
6.0 ≤ f c′
n=7
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n=9
n=8
n=6
2012
Edition
SECTION 6: STEEL STRUCTURES
6-103
The modular ratio should be taken as:
n=
E
Ec
(6.10.1.1.1b-1)
where:
Ec =
modulus of elasticity of the concrete determined
as specified in Article 5.4.2.4 (ksi)
6.10.1.1.1c—Stresses for Sections in Negative
Flexure
For calculating flexural stresses in sections subjected
to negative flexure, the composite section for both shortterm and long-term moments shall consist of the steel
section and the longitudinal reinforcement within the
effective width of the concrete deck, except as specified
otherwise in Article 6.6.1.2.1, Article 6.10.1.1.1d or
Article 6.10.4.2.1.
6.10.1.1.1d—Concrete Deck Stresses
For calculating longitudinal flexural stresses in the
concrete deck due to all permanent and transient loads, the
short-term modular ratio, n, shall be used.
C6.10.1.1.1d
Previous Specifications required that the longitudinal
flexural stresses in the concrete deck due to permanent load
be calculated using the n or the 3n section, whichever gives
the more critical stress within the deck. When the deck
stresses due to short-term and permanent loads are of the
same sign, the n section generally governs the deck stress
calculation. Also, the maximum combined compression in the
deck typically occurs at a section where the permanent and
short-term stresses are additive. However, when considering
the length of the deck over which the provisions of
Article 6.10.1.7 are to be applied, smaller compressive
permanent load stresses can result in larger net tensile stresses
in the deck in the vicinity of inflection point locations. In
these situations, use of the 3n section for the permanent load
stresses produces the more critical tension stress in the deck.
This level of refinement in the calculation of the deck
longitudinal tension stresses is considered unjustified.
6.10.1.1.1e—Effective Width of Concrete Deck
The effective width of the concrete deck shall be
determined as specified in Article 4.6.2.6.
6.10.1.2—Noncomposite Sections
Sections where the concrete deck is not connected to
the steel section by shear connectors designed in
accordance with the provisions of Article 6.10.10 shall be
considered noncomposite sections.
C6.10.1.2
Noncomposite sections are not recommended, but are
permitted.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6.10.1.3—Hybrid Sections
The specified minimum yield strength of the web
should not be less than the larger of 70 percent of the
specified minimum yield strength of the higher strength
flange and 36.0 ksi.
For members with a higher-strength steel in the web
than in one or both flanges, the yield strength of the web
shall not be taken greater than 120 percent of the specified
minimum yield strength of the lower strength flange in
determining the flexural and shear resistance. Composite
girders in positive flexure with a higher strength steel in
the web than in the compression flange may use the full
web strength in determining their flexural and shear
resistance.
C6.10.1.3
Hybrid sections consisting of a web with a specified
minimum yield strength lower than that of one or both of
the flanges may be designed with these Specifications.
Although these provisions can be safely applied to all
types of hybrid sections (ASCE, 1968), it is recommended
that the difference in the specified minimum yield
strengths of the web and the higher strength flange
preferably be limited to one steel grade. Such sections
generally are believed to have greater design efficiency.
For these types of sections, the upper limit of Fyw on the
value of Fyr, determined in Article 6.10.8.2.2, 6.10.8.2.3,
A6.3.2 or A6.3.3 as applicable, does not govern.
Furthermore, as discussed in Article C6.10.1.9.1, this
minimum limit on the web yield strength guards against
early inelastic web bend-buckling of slender hybrid webs.
A number of the curved noncomposite I-girders tested
by Mozer and Culver (1970) and Mozer et al. (1971) had
Fyw/Fyf between 0.72 and 0.76. The flexural and shear
strengths of these hybrid I-girders are predicted adequately
by these Specifications, including the development of
shear strengths associated with tension field action. The
major-axis bending stresses tend to be smaller in curved
I-girder webs compared to straight I-girder webs, since
part of the flexural resistance is taken up by flange lateral
bending. The provisions of Articles 6.10.2 and 6.10.5.3
prevent significant out-of-plane flexing of the web in
straight and curved hybrid I-girders (Yen and Mueller,
1966; ASCE, 1968).
Test data for sections with nominally larger yield
strengths in the web than in one or both flanges are
limited. Nevertheless, in many experimental tests, the
actual yield strength of the thinner web is larger than that
of the flanges. The nominal yield strength that may be used
for the web in determining the flexural and shear resistance
for such cases is limited within these Specifications to a
range supported by the available test data.
C6.10.1.4
6.10.1.4—Variable Web Depth Members
The effect of bottom flange inclination shall be
considered in determining the bottom flange stress caused
by bending about the major-axis of the cross-section.
Where permitted by static equilibrium, the web dead-load
shear may be reduced by the vertical component of the
bottom flange force.
At points where the bottom flange becomes
horizontal, the transfer of the vertical component of the
flange force back into the web shall be considered.
If the normal stress in an inclined bottom flange,
calculated without consideration of flange lateral bending,
is determined by simply dividing the bending moment
about the major-axis of the cross-section by the elastic
section modulus, this stress is generally underestimated.
The normal stress within an inclined bottom flange may be
determined by first calculating the horizontal component
of the flange force required to develop this bending
moment as:
Ph = MAf S x
(C6.10.1.4-1)
where:
Af
=
area of the inclined bottom flange (in.2)
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SECTION 6: STEEL STRUCTURES
6-105
M =
Sx
=
bending moment about the major-axis of the
cross-section at the section under consideration
(kip-in.)
elastic section modulus to the inclined bottom
flange (in.3)
For composite sections, the provisions of
Article 6.10.1.1.1a are to be applied in computing Ph. The
normal stress in the inclined flange, fn, may then be
determined as (Blodgett, 1982):
f n = Ph Af cos θ
(C6.10.1.4-2)
where:
θ
=
angle of inclination of the bottom flange
(degrees)
The corresponding vertical component of the flange
force, Pv, may be determined as:
Pv = Ph tan θ
(C6.10.1.4-3)
This component of the flange force affects the vertical web
shear. In regions of positive flexure with tapered or
parabolic haunches sloping downward toward the supports,
the vertical web shear is increased by Pv. For fish belly
haunches, Pv = 0 near the supports. For all other cases, the
vertical web shear is reduced by Pv. The Specifications
permit the Engineer to reduce the web dead-load shear
accordingly in these cases. Calculation of the reduced liveload shear is problematic because numerous sets of
concurrent moments and shears must be evaluated in order
to determine the critical or smallest shear reduction, and
thus is not likely worth the effort. Also, variable depth
webs are used most often on longer-span girders where
dead load is more predominant.
In parabolic haunches, where the downward slope of the
bottom flange is larger at positions closer to the interior
support, the change in the bottom-flange inclination in
combination with compressive stress in the bottom flange
induces a compressive distributed transverse force on the
web (Blodgett, 1982). If the girder web is unstiffened or
transversely-stiffened with a stiffener spacing do greater than
approximately 1.5D within this type of haunch, the Engineer
should check the stability of the web under this force.
At points where an inclined flange becomes
horizontal, the vertical component of the inclined flange
force is transferred back into the web as a concentrated
load. This concentrated load causes additional stress in the
web and web-to-bottom flange welds, and will often
require additional local stiffening. At these locations, the
web is sufficient without additional stiffening if the
requirement of Article D6.5.2 is satisfied using a length of
bearing N equal to zero. At locations where the
concentrated load is compressive and N is equal to zero,
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
the provisions of Article D6.5.2 generally govern relative
to those of Article D6.5.3; therefore, satisfaction of the
requirement of Article D6.5.2 using a length of bearing N
equal to zero ensures that the web is adequate without
additional stiffening for locations subjected to compressive
or tensile concentrated transverse loads.
C6.10.1.5
6.10.1.5—Stiffness
The following stiffness properties shall be used in the
analysis of flexural members:
•
For loads applied to noncomposite sections: the
stiffness properties of the steel section alone.
•
For permanent loads applied to composite
sections: the stiffness properties of the long-term
composite section, assuming the concrete deck to be
effective over the entire span length.
•
For transient loads applied to composite sections: the
stiffness properties of the short-term composite
section, assuming the concrete deck to be effective
over the entire span length.
6.10.1.6—Flange Stresses and Member Bending
Moments
In line with common practice, it is specified that the
stiffness of the steel section alone be used for
noncomposite sections, although numerous field tests have
shown that considerable unintended composite action
occurs in such sections.
Field tests of composite continuous bridges have shown
that there is considerable composite action in negative
bending regions (Baldwin et al., 1978; Roeder and Eltvik,
1985; Yen et al., 1995). Therefore, the stiffness of the full
composite section is to be used over the entire bridge length
for the analysis of composite flexural members.
C6.10.1.6
2013 Revision
•
The stress fbu shall be determined as the largest value
of the compressive stress throughout the unbraced
length in the flange under consideration, calculated
without consideration of flange lateral bending.
•
The moment Mu shall be determined as the largest
value of the major-axis bending moment throughout
the unbraced length causing compression in the flange
under consideration.
•
The stress fℓ shall be determined as the largest value
of the stress due to lateral bending throughout the
unbraced length in the flange under consideration.
For checking of lateral torsional buckling resistance,
the correct value of the stress fbu or moment Mu is
generally the largest value causing compression in the
flange under consideration throughout the unbraced length.
For a discretely braced compression flange also
subject to lateral bending, the largest lateral bending stress
throughout the unbraced length of the flange under
consideration must be used in combination with fbu or Mu
when the resistance is based on lateral torsional buckling.
Combined vertical and flange lateral bending is addressed
in these Specifications by effectively handling the flanges
as equivalent beam-columns. The use of the maximum fℓ
and fbu or Mu values within the unbraced length, when the
resistance is governed by member stability, i.e., lateral
torsional buckling, is consistent with established practice
in the proper application of beam-column interaction
equations.
For design checks where the flexural resistance is
based on yielding, flange local buckling or web bendbuckling, fbu, Mu and fℓ may be determined as the
corresponding values at the section under consideration.
The values of fbu, Mu and fℓ shall be determined based
on factored loads, and shall be taken as positive in sign in
all resistance equations.
Lateral bending stresses in continuously braced
flanges shall be taken equal to zero. Lateral bending
stresses in discretely braced flanges shall be determined by
structural analysis. All discretely braced flanges shall
satisfy:
Yielding, flange local buckling and web bendbuckling are considered as cross-section limit states.
Hence, the Engineer is allowed to use coincident crosssection values of fℓ and fbu or Mu when checking these limit
states. Generally, this approach necessitates checking of
the limit states at various cross-sections along the unbraced
length. When the maximum values of fℓ and fbu or Mu occur
at different locations within the unbraced length, it is
conservative to use the maximum values in a single
application of the yielding and flange local buckling
equations. Flange lateral bending does not enter into the
web bend-buckling resistance equations.
For design checks where the flexural resistance is
based on lateral torsional buckling:
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
SECTION 6: STEEL STRUCTURES
f A ≤ 0.6 Fyf
6-107
(6.10.1.6-1)
The flange lateral bending stress, fƐ, may be
determined directly from first-order elastic analysis in
discretely braced compression flanges for which:
Lb ≤ 1.2 L p
Cb Rb
f bu / Fyc
(6.10.1.6-2)
or equivalently:
Lb ≤ 1.2 L p
Cb Rb
M u / M yc
(6.10.1.6-3)
where:
Cb =
fbu =
Lb =
Lp =
Mu =
Myc =
Rb =
moment gradient modifier specified in
Article 6.10.8.2.3 or Article A6.3.3, as
applicable.
largest value of the compressive stress throughout
the unbraced length in the flange under
consideration, calculated without consideration of
flange lateral bending (ksi)
unbraced length (in.)
limiting unbraced length specified in
Article 6.10.8.2.3 (in.)
largest value of the major-axis bending moment
throughout the unbraced length causing
compression in the flange under consideration
(kip-in.)
yield moment with respect to the compression
flange determined as specified in Article D6.2
(kip-in.)
web load-shedding factor determined as specified
in Article 6.10.1.10.2
If Eq. 6.10.1.6-2, or Eq. 6.10.1.6-3 as applicable, is not
satisfied, second-order elastic compression-flange lateral
bending stresses shall be determined.
Second-order compression-flange lateral bending
stresses may be approximated by amplifying first-order
values as follows:
§
¨ 0.85
fA = ¨
fbu
¨
¨1− F
cr
©
·
¸
¸ fA 1 ≥ fA 1
¸
¸
¹
or equivalently:
(6.10.1.6-4)
In lieu of a more refined analysis, Article C6.10.3.4
gives approximate equations for calculation of the maximum
flange lateral bending moments due to eccentric concrete
deck overhang loads acting on cantilever forming brackets
placed along exterior members. Determination of flange
wind moments is addressed in Article 4.6.2.7. The
determination of flange lateral bending moments due to the
effect of discontinuous cross-frames and/or support skew is
best handled by a direct structural analysis of the bridge
superstructure. The determination of flange lateral bending
moments due to curvature is addressed in Article 4.6.1.2.4b.
In all resistance equations, fbu, Mu, and fƐ are to be
taken as positive in sign. However, for service and strength
limit state checks at locations where the dead and live load
contributions to fbu, Mu or fƐ are of opposite sign, the signs
of each contribution must be initially taken into account. In
such cases, for both dead and live load, the appropriate net
sum of the major-axis and lateral bending actions due to
the factored loads must be computed, taking the signs into
consideration that will result in the most critical response
for the limit state under consideration.
The top flange may be considered continuously braced
where it is encased in concrete or anchored to the deck by
shear connectors satisfying the provisions of Article 6.10.10.
For a continuously braced flange in tension or compression,
flange lateral bending effects need not be considered.
Additional lateral bending stresses are small once the
concrete deck has been placed. Lateral bending stresses
induced in a continuously braced flange prior to this stage
need not be considered after the deck has been placed. The
resistance of the composite concrete deck is generally
adequate to compensate for the neglect of these initial lateral
bending stresses. The Engineer should consider the noncomposite lateral bending stresses in the top flange if the
flange is not continuously supported by the deck.
The provisions of Article 6.10 for handling of
combined vertical and flange lateral bending are limited to
I-sections that are loaded predominantly in major-axis
bending. For cases in which the elastically computed
flange lateral bending stress is larger than approximately
0.6Fyf, the reduction in the major-axis bending resistance
due to flange lateral bending tends to be greater than that
determined based on these provisions. The service and
strength limit state provisions of these Specifications are
sufficient to ensure acceptable performance of I-girders
with elastically computed fƐ values somewhat larger than
this limit.
Eq. 6.10.1.6-2, or equivalently Eq. 6.10.1.6-3 as
applicable, simply gives a maximum value of Lb for which
fƐ = fƐ1 in Eq. 6.10.1.6-4 or 6.10.1.6-5. Eq. 6.10.1.6-4, or
equivalently Eq. 6.10.1.6-5 as applicable, is an approximate
formula that accounts for the amplification of the first-order
compression-flange lateral bending stresses due to secondorder effects. This equation, which is an established form for
estimating the maximum second-order elastic moments in
braced beam-column members whose ends are restrained by
other framing, tends to be significantly conservative for
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
§
¨ 0.85
fA = ¨
Mu
¨
¨1− F S
cr xc
©
·
¸
¸ fA 1 ≥ fA 1
¸
¸
¹
(6.10.1.6-5)
where:
fbu =
fƐ1 =
Fcr =
Mu =
Sxc =
largest value of the compressive stress throughout
the unbraced length in the flange under
consideration, calculated without consideration of
flange lateral bending (ksi)
first-order compression-flange lateral bending
stress at the section under consideration, or the
maximum first-order lateral bending stress in the
compression flange under consideration
throughout the unbraced length, as applicable
(ksi)
elastic lateral torsional buckling stress for the
flange under consideration determined from
Eq. 6.10.8.2.3-8 or Eq. A6.3.3-8. Eq. A6.3.3-8
may only be applied for unbraced lengths in
straight I-girder bridges in which the web is
compact or noncompact.
largest value of the major-axis bending moment
throughout the unbraced length causing
compression in the flange under consideration
(kip-in.)
elastic section modulus about the major axis of
the section to the compression flange taken as
Myc/Fyc (in.3)
6.10.1.7—Minimum Negative Flexure Concrete
Deck Reinforcement
Wherever the longitudinal tensile stress in the
concrete deck due to either the factored construction loads
or Load Combination Service II in Table 3.4.1-1 exceeds
φfr, the total cross-sectional area of the longitudinal
reinforcement shall not be less than one percent of the total
cross-sectional area of the concrete deck. φ shall be taken
as 0.9 and fr shall be taken as the modulus of rupture of the
concrete determined as follows:
•
For normal-weight concrete: f r = 0.24 f c'
•
For lightweight concrete: fr is calculated as specified
in Article 5.4.2.6,
The longitudinal stresses in the concrete deck shall be
determined as specified in Article 6.10.1.1.1d. The
reinforcement used to satisfy this requirement shall have a
specified minimum yield strength not less than 60.0 ksi; the
size of the reinforcement should not exceed No. 6 bars.
The required reinforcement should be placed in two
layers uniformly distributed across the deck width, and
larger unsupported lengths associated with fbu approaching
Fcr (White et al., 2001). This conservatism exists even when
an effective length factor for lateral torsional buckling and/or
a moment gradient factor Cb is considered in the calculation
of Fcr, and even when one end of the unbraced segment
under consideration is not restrained by an adjacent segment.
Although Eqs. 6.10.1.6-4 and 6.10.1.6-5 are directed at
estimating the maximum second-order lateral bending stress
within the unbraced length, by use of the maximum firstorder lateral bending stress for fƐ1, they may be applied for
estimating the second-order lateral bending stresses at any
cross-section within the unbraced length under consideration
by use of the corresponding value of fƐ1 at that location.
The purpose of Eqs. 6.10.1.6-4 and 6.10.1.6-5 is to guard
conservatively against large unbraced lengths in which the
flange second-order lateral bending effects are significant. In
construction situations where the amplification within these
equations is large, the Engineer may wish to consider a direct
geometric nonlinear analysis to more accurately determine
the second-order effects within the superstructure, or using a
lower value of the effective length factor for lateral torsional
buckling to appropriately increase Fcr according to the
procedure suggested in Article C6.10.8.2.3.
Note that the calculated value of Fcr for use in
Eq. 6.10.1.6-4 is not limited to RbRhFyc as specified in
Article 6.10.8.2.3, and that the calculated value of FcrSxc for
use in Eq. 6.10.1.6-5 is not limited to RpcMyc as specified in
Article A6.3.3. The elastic buckling stress is the appropriate
stress for use in Eqs. 6.10.1.6-4 and 6.10.1.6-5 to estimate
the elastic second-order amplification of the flange lateral
bending stresses.
The definitions of a compact web and of a noncompact
web are discussed in Article C6.10.6.2.3.
C6.10.1.7
The use of one percent reinforcement with a size not
exceeding No. 6 bars, a yield strength greater than or equal
to 60.0 ksi, and spacing at intervals not exceeding 12.0 in.
is intended to control concrete deck cracking. Pertinent
criteria for concrete crack control are discussed in more
detail in AASHTO (1991) and in Haaijer et al. (1987).
Previously, the requirement for one percent
longitudinal reinforcement was limited to negative flexure
regions of continuous spans, which are often implicitly
taken as the regions between points of dead load
contraflexure. Under moving live loads, the deck can
experience significant tensile stresses outside the points of
dead load contraflexure. Placement of the concrete deck in
stages can also produce negative flexure during
construction in regions where the deck already has been
placed, although these regions may be subjected primarily
to positive flexure in the final condition. Thermal and
shrinkage strains can also cause tensile stresses in the deck
in regions where such stresses otherwise might not be
anticipated. To address these issues, the one percent
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
SECTION 6: STEEL STRUCTURES
two-thirds should be placed in the top layer. The individual
bars should be spaced at intervals not exceeding 12.0 in.
Where shear connectors are omitted from the negative
flexure region, all longitudinal reinforcement shall be
extended into the positive flexure region beyond the
additional shear connectors specified in Article 6.10.10.3 a
distance not less than the development length specified in
Section 5.
6-109
longitudinal reinforcement is to be placed wherever the
tensile stress in the deck due to either the factored
construction loads, including loads during the various
phases of the deck placement sequence, or due to Load
Combination Service II in Table 3.4.1-1, exceeds φfr. By
satisfying the provisions of this Article to control the crack
size in regions where adequate shear connection is also
provided, the concrete deck may be considered to be
effective in tension for computing fatigue stress ranges, as
permitted in Article 6.6.1.2.1, and in determining flexural
stresses on the composite section due to Load Combination
Service II, as permitted in Article 6.10.4.2.1.
In addition to providing one percent longitudinal deck
reinforcement, nominal yielding of this reinforcement
should be prevented at Load Combination Service II
(Carskaddan, 1980; AASHTO, 1991; Grubb, 1993) to
control concrete deck cracking. The use of longitudinal
deck reinforcement with a specified minimum yield
strength not less than 60.0 ksi may be taken to preclude
nominal yielding of the longitudinal reinforcement under
this load combination in the following cases:
•
Unshored construction where the steel section utilizes
steel with a specified minimum yield strength less
than or equal to 70.0 ksi in either flange, or
•
Shored construction where the steel section utilizes
steel with a specified minimum yield strength less
than or equal to 50.0 ksi in either flange.
In these cases, the effects of any nominal yielding within
the longitudinal reinforcing steel are judged to be
insignificant. Otherwise, the Engineer should check to
ensure that nominal yielding of the longitudinal
reinforcement does not occur under the applicable
Service II loads. The above rules are based on Carskaddan
(1980) and apply for members that are designed by the
provisions of Article 6.10 or Appendix A6, as well as for
members that are designed for redistribution of the pier
section moments at the Service II Load Combination using
the provisions of Appendix B6.
Where feasible, approximately two-thirds of the
required reinforcement should be placed in the top layer.
When precast deck panels are used as deck forms, it may
not be possible to place the longitudinal reinforcement in
two layers. In such cases, the placement requirements may
be waived at the discretion of the Engineer.
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
6-110
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6.10.1.8—Net Section Fracture
C6.10.1.8
When checking flexural members at the strength limit
state or for constructibility, the following additional
requirement shall be satisfied at all cross-sections
containing holes in the tension flange:
§A
f t ≤ 0.84 ¨ n
¨A
© g
·
¸¸ Fu ≤ Fyt
¹
(6.10.1.8-1)
where:
An =
Ag =
ft =
Fu =
net area of the tension flange determined as
specified in Article 6.8.3 (in.2)
gross area of the tension flange (in.2)
stress on the gross area of the tension flange due
to the factored loads calculated without
consideration of flange lateral bending (ksi)
specified minimum tensile strength of the tension
flange determined as specified in Table 6.4.1-1
(ksi)
If Eq. 6.10.1.8-1 is satisfied under the stated
conditions at a cross-section containing holes in the
tension flange, fracture on the net section of the flange is
prevented. For holes larger than those typically used for
connectors such as bolts, refer to Article 6.8.1.
At compact composite sections in positive flexure and
at sections designed according to the optional provisions of
Appendix A6 with no holes in the tension flange, the
nominal flexural resistance is permitted to exceed the
moment at first yield at the strength limit state. Pending the
results from further research, it is conservatively required
that Eq. 6.10.1.8-1 also be satisfied at the strength limit
state at any such cross-sections containing holes in the
tension flange. It has not yet been fully documented that
complete plastification of the cross-section can occur at
these sections prior to fracture on the net section of the
tension flange. Furthermore, the splice design provisions
of Article 6.13.6.1.4 do not consider the contribution of
substantial web yielding to the flexural resistance of these
sections. Eq. 6.10.1.8-1 will likely prevent holes from
being located in the tension flange at or near points of
maximum applied moment where significant yielding of
the web, beyond the localized yielding permitted in hybrid
sections, may occur.
The factor 0.84 in Eq. 6.10.1.8-1 is approximately
equivalent to the ratio of the resistance factor for fracture
of tension members, φu, to the resistance factor for yielding
of tension members, φy, specified in Article 6.5.4.2.
6.10.1.9—Web Bend-Buckling Resistance
6.10.1.9.1—Webs without Longitudinal Stiffeners
The nominal bend-buckling resistance shall be taken as:
Fcrw =
0.9 Ek
§D·
¨ ¸
© tw ¹
(6.10.1.9.1-1)
2
but not to exceed the smaller of RhFyc and Fyw /0.7
in which:
k
=
=
bend-buckling coefficient
9
( Dc / D )
2
(6.10.1.9.1-2)
where:
Dc =
Rh =
depth of the web in compression in the elastic
range (in.). For composite sections, Dc shall be
determined as specified in Article D6.3.1.
hybrid factor specified in Article 6.10.1.10.1
C6.10.1.9.1
In subsequent Articles, the web theoretical bendbuckling resistance is checked generally against the
maximum compression-flange stress due to the factored
loads, calculated without consideration of flange lateral
bending. The precision associated with making a distinction
between the stress in the compression flange and the
maximum compressive stress in the web is not warranted.
The potential use of a value of Fcrw greater than the specified
minimum yield strength of the web, Fyw, in hybrid sections is
justified since the flange tends to restrain the longitudinal
strains associated with web bend-buckling for nominal
compression-flange stresses up to RhFyc. A stable nominally
elastic compression flange constrains the longitudinal and
plate bending strains in the inelastic web at the web-flange
juncture (ASCE, 1968). ASCE (1968) recommends that web
bend-buckling does not need to be considered in hybrid
sections with Fyc up to 100 ksi as long as the web
slenderness does not exceed 5.87¥E/Fyc. Eq. 6.10.1.9.1-1
predicts Fcrw = Fyc at 2Dc/tw = 5.7¥E/Fyc. For hybrid sections
with Fyw/Fyc < 0.7, these provisions adopt a more
conservative approach than recommended by ASCE (1968)
by limiting Fcrw to the smaller of RhFyc and Fyw/0.7. The
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2012
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SECTION 6: STEEL STRUCTURES
When both edges of the web are in compression, k
shall be taken as 7.2.
6-111
flexural resistance equations of these Specifications give
somewhat conservative predictions for the strengths of
hybrid members without longitudinal stiffeners tested by
Lew and Toprac (1968) that had D/tw and 2Dc/tw values as
high as 305 and Fyw/Fyc = 0.32. Therefore, no additional
requirements are necessary at the strength limit state for all
potential values of Fyw/Fyc associated with the steels
specified in Article 6.4.1.
In many experimental tests, noticeable web plate
bending deformations and associated transverse
displacements occur from the onset of load application due
to initial web out-of-flatness. Because of the stable
postbuckling behavior of the web, there is no significant
change in the rate of increase of the web transverse
displacements as a function of the applied loads as the
theoretical web bend-buckling stress is exceeded (Basler et
al., 1960). Due to unavoidable geometric imperfections, the
web bend-buckling behavior is a load-deflection rather than
a bifurcation problem. The theoretical web-buckling load is
used in these Specifications as a simple index for controlling
the web plate bending strains and transverse displacements.
For a doubly-symmetric I-section without longitudinal
web stiffeners, Eq. 6.10.1.9.1-2 gives k = 36.0, which is
approximately equal to kss + 0.8(ksf – kss), where kss = 23.9
and ksf = 39.6 are the bend-buckling coefficients for
simply-supported and fully restrained longitudinal edge
conditions, respectively (Timoshenko and Gere, 1961). For
I-sections in which Dc ≠ 0.5D, Eq. 6.10.1.9.1-2 provides a
reasonable approximation of theoretical bend-buckling
resistance (Galambos, 1998) consistent with the above.
For composite sections subjected to positive flexure,
these Specifications do not require the use of
Eq. 6.10.1.9.1-1 after the section is in its final composite
condition for webs that do not require longitudinal
stiffeners based on Article 6.10.2.1.1. The section must be
checked for web bend-buckling during construction while
in the noncomposite condition. For loads applied at the
fatigue and service limit states after the deck has hardened
or is made composite, the increased compressive stresses
in the web tend to be compensated for by the increase in
Fcrw resulting from the corresponding decrease in Dc. At
the strength limit state, these compensating effects
continue. Based on the section proportioning limits
specified in Article 6.10.2 and the ductility requirement
specified in Article 6.10.7.3, Fcrw for these sections is
generally close to or larger than Fyc at the strength limit
state.
For composite sections in positive flexure in which
longitudinal web stiffeners are required based on
Article 6.10.2.1.1, the web slenderness requirement of
Article 6.10.2.1.2 is not sufficient in general to ensure that
theoretical bend-buckling of the web will not occur.
Therefore, the Specifications require the calculation of Rb
for these types of sections, as discussed further in
Article C6.10.1.10.2.
For composite sections in negative flexure, Dc is to be
computed using the section consisting of the steel girder
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6-112
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
plus the longitudinal deck reinforcement, with the one
possible exception noted at the service limit state in
Article D6.3.1. This approach limits the potential
complications in subsequent load rating resulting from the
flexural resistance being a function of Dc and Dc being
taken as a function of the applied load. This approach
leads to a more conservative calculation of the flexural
resistance, but the influence on the resistance is typically
inconsequential.
Near points of permanent-load contraflexure, both
edges of the web may be in compression when stresses in
the steel and composite sections due to moments of
opposite sign are accumulated. In this case, the neutral axis
lies outside the web. Thus, the specification states that k be
taken equal to 7.2 when both edges of the web are in
compression, which is approximately equal to the
theoretical bend-buckling coefficient for a web plate under
uniform compression assuming fully restrained
longitudinal edge conditions (Timoshenko and Gere,
1961). Such a case is relatively rare and the accumulated
web compressive stresses are typically small when it
occurs; however, this case may need to be considered in
computer software.
6.10.1.9.2—Webs with Longitudinal Stiffeners
In lieu of an alternative rational analysis, the nominal
bend-buckling resistance may be determined as specified
in Eq. 6.10.1.9.1-1, with the bend-buckling coefficient
taken as follows:
•
If
k=
•
If
k=
ds
≥ 0.4 , then:
Dc
5.17
( ds / D )
2
≥
9
( Dc / D )
2
(6.10.1.9.2-1)
ds
< 0.4 , then:
Dc
11.64
Dc − d s
D
2
(6.10.1.9.2-2)
where:
ds
=
distance from the centerline of the closest plate
longitudinal stiffener or from the gage line of the
closest angle longitudinal stiffener to the inner
surface or leg of the compression-flange element
(in.)
When both edges of the web are in compression, k
shall be taken as 7.2.
C6.10.1.9.2
Eqs. 6.10.1.9.2-1 and 6.10.1.9.2-2 give an accurate
approximation of the bend-buckling coefficient k for webs
with a single longitudinal stiffener in any vertical location
(Frank and Helwig, 1995). The resulting k depends on the
location of the closest longitudinal web stiffener to the
compression flange with respect to its optimum location at
ds/Dc = 0.4 (Vincent, 1969) and is used to determine the
bend-buckling resistance from Eq. 6.10.1.9.1-1.
Changes in flange size cause Dc to vary along the
length of a girder. In a composite girder, Dc is also a
function of the applied load. If the longitudinal stiffener is
located a fixed distance from the compression flange,
which is normally the case, the stiffener cannot be at its
optimum location throughout the girder length. In
composite girders with longitudinally-stiffened webs
subjected to positive flexure, Dc tends to be large for
noncomposite loadings during construction and therefore
web bend-buckling must be checked. Furthermore, Dc can
be sufficiently large for the composite girder at the service
limit state such that web bend-buckling may still be a
concern. Therefore, the value of Dc for checking web
bend-buckling of these sections in regions of positive
flexure at the service limit state is to be determined based
on the accumulated flexural stresses due to the factored
loads, as specified in Article D6.3.1.
For composite sections in negative flexure, Dc is to be
computed in the same manner as discussed in
Article C6.10.1.9.1.
Eqs. 6.10.1.9.2-1 and 6.10.1.9.2-2 and the associated
optimum stiffener location assume simply-supported
boundary conditions at the flanges. These equations for k
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SECTION 6: STEEL STRUCTURES
6-113
allow the Engineer to compute the web bend-buckling
resistance for any position of the longitudinal stiffener
with respect to Dc. When the distance from the closest
longitudinal stiffener to the compression flange, ds, is less
than 0.4Dc, the stiffener is above its optimum location and
web bend-buckling occurs in the panel between the
stiffener and the tension flange. When ds is greater than
0.4Dc, web bend-buckling occurs in the panel between the
stiffener and the compression flange. When ds is equal to
0.4Dc, the stiffener is at its optimum location and bendbuckling occurs in both panels. For this case, both
equations yield a k value equal to 129.3 for a symmetrical
girder (Dubas, 1948). Further information on locating
longitudinal stiffeners on the web may be found in
Article C6.10.11.3.1.
Since bend-buckling of a longitudinally-stiffened web
must be investigated for both noncomposite and composite
stress conditions and at various locations along the girder,
it is possible that the stiffener might be located at an
inefficient position for a particular condition, resulting in a
small bend-buckling coefficient. Because simplysupported boundary conditions were assumed in the
development of Eqs. 6.10.1.9.2-1 and 6.10.1.9.2-2, the
computed web bend-buckling resistance for the
longitudinally-stiffened web may be less than that
computed for a web of the same dimensions without
longitudinal stiffeners where some rotational restraint from
the flanges has been assumed. To prevent this anomaly, the
Specifications state that the k value for a longitudinallystiffened web from Eq. 6.10.1.9.2-1 must equal or exceed a
value of 9.0/(Dc/D)2, which is the k value for a web
without longitudinal stiffeners from Eq. 6.10.1.9.1-2
computed assuming partial rotational restraint from the
flanges. Note this limit only need be checked when
Eq. 6.10.1.9.2-1 controls.
As discussed further in Article C6.10.1.9.1, when both
edges of the web are in compression, the bend-buckling
coefficient is taken equal to 7.2.
Eqs. 6.10.1.9.2-1 and 6.10.1.9.2-2 neglect the benefit
of placing more than one longitudinal stiffener on the web.
Therefore, they may be used conservatively for webs with
multiple longitudinal stiffeners. Alternatively, the Engineer
is permitted to determine Fcrw of Eq. 6.10.1.9.1-1 or the
corresponding k value for use within this equation by a
direct buckling analysis of the web panel. The boundary
conditions at the flanges and at the stiffener locations
should be assumed as simply-supported in this analysis.
6.10.1.10—Flange-Strength Reduction Factors
6.10.1.10.1—Hybrid Factor, Rh
For rolled shapes, homogenous built-up sections and
built-up sections with a higher-strength steel in the web
than in both flanges, Rh shall be taken as 1.0. Otherwise,
in lieu of an alternative rational analysis, the hybrid
factor shall be taken as:
C6.10.1.10.1
The Rh factor accounts for the reduced contribution of
the web to the nominal flexural resistance at first yield in any
flange element, due to earlier yielding of the lower strength
steel in the web of a hybrid section. As used herein, the term
flange element is defined as a flange or cover plate or the
longitudinal reinforcement.
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6-114
Rh =
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
12 + β ( 3ρ − ρ3 )
(6.10.1.10.1-1)
12 + 2β
in which:
β=
2 Dn tw
Afn
ρ
=
(6.10.1.10.1-2)
the smaller of Fyw/fn and 1.0
where:
Afn =
Dn =
fn
=
sum of the flange area and the area of any cover
plates on the side of the neutral axis
corresponding to Dn (in.2). For composite
sections in negative flexure, the area of the
longitudinal reinforcement may be included in
calculating Afn for the top flange.
larger of the distances from the elastic neutral
axis of the cross-section to the inside face of
either flange (in.). For sections where the neutral
axis is at the mid-depth of the web, the distance
from the neutral axis to the inside face of the
flange on the side of the neutral axis where
yielding occurs first.
for sections where yielding occurs first in the
flange, a cover plate or the longitudinal
reinforcement on the side of the neutral axis
corresponding to Dn, the largest of the specified
minimum yield strengths of each component
included in the calculation of Afn (ksi). Otherwise,
the largest of the elastic stresses in the flange,
cover plate or longitudinal reinforcement on the
side of the neutral axis corresponding to Dn at
first yield on the opposite side of the neutral axis.
6.10.1.10.2—Web Load-Shedding Factor, Rb
When checking constructibility according to the
provisions of Article 6.10.3.2, or when:
•
the section is composite and is in positive flexure and
the web satisfies the requirement of Article 6.10.2.1.1
or 6.11.2.1.2, as applicable,
or:
•
one or more longitudinal stiffeners are provided and
D
Ek
≤ 0.95
tw
Fyc
or:
(6.10.1.10.2-1)
Eq. 6.10.1.10.1-1 represents a condensation of the
formulas for Rh in previous AASHTO Specifications and
considers all possible combinations associated with
different positions of the elastic neutral axis and different
yield strengths of the top and bottom flange elements.
The fundamental equation, originally derived for a
doubly-symmetric I-section (ASCE, 1968; Schilling, 1968;
and Frost and Schilling, 1964), is adapted in these
provisions to handle singly-symmetric and composite
sections by focusing on the side of the neutral axis where
yielding occurs first. This side of the neutral axis has the
most extensive web yielding prior to first yielding of any
flange element. All flange elements on this side of the
neutral axis are conservatively assumed to be located at the
edge of the web. The equation is also adapted by assuming
that the shift in the neutral axis due to the onset of web
yielding is negligible. These assumptions are similar to
those used in the development of a separate Rh equation for
composite sections in prior AASHTO Specifications. In
lieu of the approximate Eq. 6.10.1.10.1-1, the Engineer
may determine Rh based on a direct iterative straincompatibility analysis. Since the computed Rh values by
any approach are typically close to 1.0, the conservative
assumptions made in the derivation of the simplified single
noniterative Eq. 6.10.1.10.1-1 should not result in a
significant economic penalty.
For composite sections in positive flexure, Dn may be
taken conservatively as the distance from the neutral axis
of the short-term composite section to the inside face of
the bottom flange. This approach is strongly recommended
to prevent possible complications in subsequent load rating
resulting from the flexural resistance being a function of
Dn and Dn being a function of the applied load.
For composite sections where the neutral axis is at the
mid-depth of the web and where first yield occurs
simultaneously in both flange elements, Dn should be taken
as the distance to the flange element with the smaller Afn.
C6.10.1.10.2
The term Rb is a postbuckling strength reduction factor
that accounts for the nonlinear variation of stresses
subsequent to local bend-buckling of slender webs. This
factor accounts for the reduction in the section flexural
resistance caused by the shedding of compressive stresses
from a slender web and the corresponding increase in the
flexural stress within the compression flange. The Rb factor
given by Eq. 6.10.1.10.2-3 is based on extensive
experimental and theoretical studies (Galambos, 1998) and
is the more refined of two equations developed by Basler
and Thurlimann (1961). The Rb factor is not applied in
determining the nominal flexural resistance of the tension
flange since the tension flange stress is not increased
significantly by the shedding of the web compressive
stresses (Basler and Thurlimann, 1961).
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SECTION 6: STEEL STRUCTURES
•
6-115
the webs satisfy:
2 Dc
≤ λ rw
tw
(6.10.1.10.2-2)
Then, Rb shall be taken as 1.0.
Otherwise:
2 Dc
awc
− λ rw ≤ 1.0
+
1200
300
a
t
wc
w
Rb = 1 −
(6.10.1.10.2-3)
in which:
λrw =
limiting slenderness ratio for a noncompact web
= 5.7
awc =
=
E
Fyc
(6.10.1.10.2-4)
for all sections except as noted below, ratio of
two times the web area in compression to the area
of the compression flange
2 Dc tw
b fc t fc
(6.10.1.10.2-5)
for composite longitudinally-stiffened sections in
positive flexure
=
2 Dc tw
b fc t fc + bs ts (1 − f DC1 / Fyc ) / 3n
(6.10.1.10.2-6)
where:
bs =
fDC1 =
k
=
n
=
ts =
Dc =
effective width of concrete deck (in.)
compression flange stress at the section under
consideration, calculated without consideration of
flange lateral bending and caused by the factored
permanent load applied before the concrete deck
has hardened or is made composite (ksi)
bend-buckling coefficient for webs with
longitudinal stiffeners determined as specified in
Article 6.10.1.9.2
modular ratio determined as specified in
Article 6.10.1.1.1b
thickness of concrete deck (in.)
depth of the web in compression in the elastic
range (in.). For composite sections, Dc shall be
determined as specified in Article D6.3.1.
When computing the nominal flexural resistance of
the compression flange for checking constructibility
according to the provisions of Article 6.10.3.2, Rb is
always to be taken equal to 1.0. This condition is ensured
in these Specifications for all slender-web sections by
limiting the compression-flange flexural stresses under the
factored loads during construction to the elastic bendbuckling resistance of the web, Fcrw.
For composite sections in positive flexure at the
strength limit state, Rb is generally equal to or close to 1.0
for sections that satisfy the requirements of
Articles 6.10.2.2 and 6.10.7.3, as long as the requirement
of Article 6.10.2.1.1 is also met such that longitudinal
stiffeners are not required. This is particularly true when a
transformed area of the concrete deck is taken as part of
the compression flange area as implemented in
Eq. 6.10.1.10.2-6. Therefore, the reduction in the flexural
resistance due to web bend-buckling is zero or negligible
and Rb is simply taken equal to 1.0 for these sections.
For sections in positive or negative flexure with one or
more longitudinal web stiffeners that satisfy
Eq. 6.10.1.10.2-1, Rb is taken equal to 1.0. For these
sections, the web slenderness, D/tw, is at or below the
value at which the theoretical bend-buckling stress at the
strength limit state is equal to Fyc. For a doubly-symmetric
girder, i.e., Dc = 0.5D, with a single longitudinal stiffener
located at the optimum position on the web, this limit is as
follows for different grades of steel:
Table C6.10.1.10.2-1—Limiting Slenderness Ratio for
Rb = 1.0 in a Longitudinally-Stiffened Girder with the
Stiffener at the Optimum Location and Dc /D = 0.5
Fyc (ksi)
36.0
50.0
70.0
90.0
100.0
0.95
Ek
Fyc
300
260
220
194
184
For monosymmetric girders with Dc /D > 0.5 and/or
where a single longitudinal stiffener is not located at its
optimum position, the limiting D/tw from Eq. 6.10.1.10.2-1
generally will be less than the value shown in
Table C6.10.1.10.2-1.
For composite sections in regions of positive flexure,
the concrete deck typically contributes a large fraction of
the flexural resistance as a compression-flange element.
For longitudinally-stiffened sections of this type,
Eq. 6.10.1.10.2-6 accounts for this contribution
conservatively in the calculation of Rb by including a
fraction of the transformed deck area based on the 3n
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
section with the steel compression-flange area in
computing the awc term. Dc in Eq. 6.10.1.10.2-6 is to be
computed as specified for composite sections in positive
flexure in Article D6.3.1 and is a function of the applied
loads. The relationship of the position of the longitudinal
stiffener to Dc and the resulting effect on the web bendbuckling coefficient, k, is discussed further in
Articles C6.10.1.9.2 and C6.10.11.3.1. For the preliminary
design of longitudinally-stiffened sections of this type in
which Rb is anticipated to be less than 1.0, a value of Rb
typically between 0.85 and 0.95 can be assumed. Members
with larger dead-to-live load ratios will tend to fall on the
lower end of this range. This preliminary value of Rb can
then be refined later in the design using Eq. 6.10.1.10.2-3.
In cases where Rb is equal to 1.0 for these sections,
potential difficulties during load rating associated with the
dependency of the flexural resistance on Dc and the
dependency of Dc on the applied loading are avoided.
Eq. 6.10.1.10.2-1 ignores the beneficial effect of
placing more than one longitudinal stiffener on the web.
For webs with more than one longitudinal stiffener, the
girder may be proportioned for Rb = 1.0 if Fcrw, determined
by an alternative rational analysis conducted as specified
in Article C6.10.1.9.2, is greater than or equal to Fyc.
The requirements for proportioning of longitudinal
stiffeners in Article 6.10.11.3 ensure the development of
the web bend-buckling resistance specified in
Article 6.10.1.9. Bend buckling of longitudinally-stiffened
webs is prevented up through the service limit state in
these Specifications, but is permitted at the strength limit
state. The stiffener proportioning requirements do not
ensure that a horizontal line of near zero lateral deflection
will be maintained for the subsequent post-bend-buckling
response of the web (Galambos, 1998). Therefore, the
presence of the longitudinal stiffeners is ignored when
computing the Rb factor for longitudinally-stiffened webs
in regions of positive or negative flexure at the strength
limit state.
For composite sections in negative flexure and
noncomposite sections that satisfy Eq. 6.10.1.10.2-2, Rb is
also taken equal to 1.0 since the web slenderness, 2Dc/tw, is
at or below the value at which the theoretical elastic bendbuckling stress is equal to Fyc at the strength limit state.
Eq. 6.10.1.10.2-2 also defines the slenderness limit for a
noncompact web. Webs with slenderness ratios exceeding
Eq. 6.10.1.10.2-2 are termed slender. For different grades
of steel, this slenderness limit is as follows:
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Table C6.10.1.10.2-2—Limiting Slenderness Ratio for a
Noncompact Web and Rb = 1.0 in Girders without Web
Longitudinal Stiffeners
Fyc (ksi)
36.0
50.0
70.0
90.0
100.0
λrw
162
137
116
102
97
The previous Specifications defined sections as
compact or noncompact and did not explicitly distinguish
between a noncompact and a slender web. The
classification of webs as compact, noncompact, or slender
in these Specifications apply to composite sections in
negative flexure and noncomposite sections. These
classifications are consistent with those in AISC (2005).
For composite sections in positive flexure, these
Specifications still classify the entire cross-section as
compact or noncompact based on the criteria in
Article 6.10.6.2.2. The Article 6.10.6.2.2 classification
includes consideration of the web slenderness as well as
other cross-section characteristics.
For the preliminary design of slender-web sections
without longitudinal stiffeners, a value of Rb typically
between 0.9 and 1.0 can be assumed, depending on an
estimated 2Dc/tw relative to the appropriate limiting
valuegiven in Table C6.10.1.10.2-2. A value typically
between 0.85 and 0.95 should be assumed for
longitudinally-stiffened slender-web sections anticipated
to have D/tw values that will not satisfy
Eq. 6.10.1.10.2-1. This preliminary value of Rb can be
refined later in the design using Eq. 6.10.1.10.2-3.
For composite sections in negative flexure, Dc is to be
computed for the section consisting of the steel girder plus
the longitudinal deck reinforcement when determining Rb
for reasons discussed in Article C6.10.1.9.1.
The factor 5.7 in Eq. 6.10.1.10.2-4 is based on a
bend-buckling coefficient k = 36.0, which is
approximately equal to kss + 0.8(ksf – kss), where kss =
23.9 and ksf = 39.6 are the bend-buckling coefficients for
simply-supported and fully restrained longitudinal edge
conditions, respectively, in webs without longitudinal
stiffeners (Timoshenko and Gere, 1961).
For compression flanges with cover plates, the
cover plate area may be added to the flange area bfctfc in
the denominator of Eq. 6.10.1.10.2-5.
While it is possible to substitute the actual
compression-flange stress due to the factored loads, fbu,
calculated without consideration of flange lateral bending,
for Fyc in Eqs. 6.10.1.10.2-1, 6.10.1.10.2-4, and
6.10.1.10.2-6, such a refinement is not likely to lead to a
significant increase in the value of Rb. Use of the actual
flange stress to compute the flexural resistance can also
lead to subsequent difficulties in load rating since the
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
flexural resistance then becomes a function of the applied
load. Should a larger value of Rb be desired for a section in
which the nominal flexural resistance of the compression
flange is significantly less than Fyc, a preferred alternative
is to substitute the smaller of the following values for Fyc
in Eqs. 6.10.1.10.2-1, 6.10.1.10.2-4, and 6.10.1.10.2-6, as
applicable: (1) the nominal flexural resistance of the
compression flange, Fnc, computed assuming Rb and Rh are
equal to 1.0, or (2) the nominal elastic stress in the
compression flange when the tension flange reaches a
nominal elastic stress of RhFyt. This is similar to the
approach taken in AISC (1999).
6.10.2—Cross-Section Proportion Limits
6.10.2.1—Web Proportions
6.10.2.1.1—Webs without Longitudinal Stiffeners
Webs shall be proportioned such that:
D
≤ 150
tw
(6.10.2.1.1-1)
C6.10.2.1.1
Eq. 6.10.2.1.1-1 is a practical upper limit on the
slenderness of webs without longitudinal stiffeners
expressed in terms of the web depth, D. This equation
allows for easier proportioning of the web in
preliminary design relative to previous Specifications.
In previous Specifications, Eq. 6.10.2.1.1-1 was the
upper limit for unstiffened webs. By also limiting the
slenderness of transversely-stiffened webs to this value,
maximum transverse stiffener spacings up to 3D are
permitted; the requirement in previous Specifications to
provide additional transverse stiffeners for handling in
girders with more slender webs, beyond those required
for shear, is eliminated. Furthermore, satisfaction of
Eq. 6.10.2.1.1-1 allows web bend-buckling to be
disregarded in the design of composite sections in
positive
flexure,
as
discussed
further
in
Article C6.10.1.9.1. The limit in Eq. 6.10.2.1.1-1 is valid
for sections with specified minimum yield strengths up
to and including 100.0 ksi designed according to these
Specifications.
The vertical flange buckling limit-state equations in
AISC (2005), which are based in large part on ASCE
(1968), are not considered in these Specifications. These
equations specify a limit on the web slenderness to prevent
theoretical elastic buckling of the web as a column
subjected to a radial transverse compression due to the
curvature of the flanges. For girders that satisfy
Eq. 6.10.2.1.1-1, these equations do not govern the web
slenderness unless Fyc is greater than 85.0 ksi.
Furthermore, tests conducted by Lew and Toprac (1968),
Cooper (1967), and others, in which the final failure mode
involved vertical flange buckling, or a folding of the
compression flange vertically into the web, indicate that
the influence of this failure mode on the predicted girder
flexural resistances is small. This is the case even for
girders with parameters that significantly violate the
vertical flange buckling limit-state equations.
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SECTION 6: STEEL STRUCTURES
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C6.10.2.1.2
6.10.2.1.2—Webs with Longitudinal Stiffeners
Webs shall be proportioned such that:
D
≤ 300
tw
(6.10.2.1.2-1)
6.10.2.2—Flange Proportions
Compression and
proportioned such that:
bf
2t f
≤ 12.0,
tension
C6.10.2.2
flanges
shall
be
(6.10.2.2-1)
b f ≥ D 6,
(6.10.2.2-2)
t f ≥ 1.1tw ,
(6.10.2.2-3)
and:
0.1 ≤
I yc
I yt
≤ 10
(6.10.2.2-4)
where:
Iyc =
Eq. 6.10.2.1.2-1 is a practical upper limit on the
slenderness of webs with longitudinal stiffeners expressed
in terms of the web depth, D. This limit allows for easier
proportioning of the web for preliminary design than
comparable limits in previous Specifications. The limit in
Eq. 6.10.2.1.2-1 is valid for sections with specified
minimum yield strengths up to and including 100.0 ksi
designed according to these Specifications.
Cooper (1967) discusses the conservatism of vertical
flange buckling limit-state equations and the justification
for not considering this limit state in longitudinallystiffened I-girders. Tests by Cooper (1967), Owen et al.
(1970) and others have demonstrated that the flexural
resistance is not adversely affected by final failure modes
involving vertical flange buckling, even for longitudinallystiffened girders that significantly exceed the limit of
Eq. 6.10.2.1.2-1. In all cases involving a vertical flange
buckling type of failure, extensive flexural yielding of the
compression flange preceded the failure. However, webs
that have larger D/tw values than specified by
Eq. 6.10.2.1.2-1 are relatively inefficient, are likely to be
more susceptible to distortion-induced fatigue, and are
more susceptible to the limit states of web crippling and
web yielding of Article D6.5.
moment of inertia of the compression flange of
the steel section about the vertical axis in the
plane of the web (in.4)
Eq. 6.10.2.2-1 is a practical upper limit to ensure the
flange will not distort excessively when welded to the web.
White and Barth (1998) observe that the cross-section
aspect ratio D/bf is a significant parameter affecting the
strength and moment-rotation characteristics of I-sections.
Eq. 6.10.2.2-2 limits this ratio to a maximum value of 6.
Experimental test data are limited for sections with very
narrow flanges. A significant number of the limited tests
that have been conducted have indicated relatively low
nominal flexural and shear resistances relative to the
values determined using these and previous Specifications.
Limiting this ratio to a maximum value of 6 for both the
compression and tension flanges ensures that stiffened
interior web panels, with the section along the entire panel
proportioned to satisfy Eq. 6.10.9.3.2-1, can develop
postbuckling shear resistance due to tension-field action
(White et al., 2004). Eq. 6.10.2.2-2 provides a lower limit
on the flange width. In most practical cases, a wider flange
will be required, particularly for horizontally curved girders.
Note that Eq. C6.10.3.4-1 should be also considered, as
applicable, in conjunction with these flange proportion
limits to establish appropriate minimum flange widths.
Eq. 6.10.2.2-3 ensures that some restraint will be
provided by the flanges against web shear buckling, and also
that the boundary conditions assumed at the web-flange
juncture in the web bend-buckling and compression-flange
local buckling formulations within these Specifications are
sufficiently accurate. The ratio of the web area to the
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Iyt
=
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
moment of inertia of the tension flange of the
steel section about the vertical axis in the plane of
the web (in.4)
compression flange area is always less than or equal to 5.45
for members that satisfy Eqs. 6.10.2.2-2 and 6.10.2.2-3.
Therefore, the AISC (2005) limit of 10 on this ratio is not
required.
An I-section with a ratio of Iyc/Iyt outside the limits
specified in Eq. 6.10.2.2-4 is more like a tee-section with the
shear center located at the intersection of the larger flange and
the web. The limits of Eq. 6.10.2.2-4 are similar to the limits
specified in previous Specifications, but are easier to apply
since they are based on the ratio of Iyc to Iyt rather than to Iy of
the entire steel section. Eq. 6.10.2.2-4 ensures more efficient
flange proportions and prevents the use of sections that may
be particularly difficult to handle during construction. Also,
Eq. 6.10.2.2-4 ensures the validity of the equations for Cb > 1
in cases involving moment gradients. Furthermore, these
limits tend to prevent the use of extremely monosymmetric
sections for which the larger of the yield moments, Myc or Myt,
may be greater than the plastic moment, Mp. If the flanges are
composed of plates of equal thickness, these limits are
equivalent to bfc ≥ 0.46bft and bfc ≤ 2.15 bft.
The advent of composite design has led to a
significant reduction in the size of compression flanges in
regions of positive flexure. In addition to satisfying the
proportion limits given in this Article, the minimum
compression-flange width in these regions for preliminary
design should also be established based on the L/bfc
guideline suggested in Eq. C6.10.3.4-1.
6.10.3—Constructibility
6.10.3.1—General
C6.10.3.1
The provisions of Article 2.5.3 shall apply. In addition
to providing adequate strength, nominal yielding or reliance
on post-buckling resistance shall not be permitted for main
load-carrying members during critical stages of construction,
except for yielding of the web in hybrid sections. This shall
be accomplished by satisfying the requirements of
Articles 6.10.3.2 and 6.10.3.3 at each critical construction
stage. For sections in positive flexure that are composite in
the final condition, but are noncomposite during
construction, the provisions of Article 6.10.3.4 shall apply.
For investigating the constructibility of flexural members, all
loads shall be factored as specified in Article 3.4.2. For the
calculation of deflections, the load factors shall be taken
as 1.0.
Potential uplift at bearings shall be investigated at
each critical construction stage.
Webs without bearing stiffeners at locations subjected to
concentrated loads not transmitted through a deck or deck
system shall satisfy the provisions of Article D6.5.
If there are holes in the tension flange at the section
under consideration, the tension flange shall also satisfy
the requirement specified in Article 6.10.1.8.
Load-resisting bolted connections either in or to
flexural members shall be proportioned to prevent slip
under the factored loads at each critical construction stage.
If uplift is indicated at any critical stage of
construction, temporary load may be placed to prevent liftoff. The magnitude and position of any required temporary
load should be provided in the contract documents.
Factored forces at high-strength bolted joints of load
carrying members are limited to the slip resistance of the
connection during each critical construction state to ensure
that the correct geometry of the structure is maintained.
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SECTION 6: STEEL STRUCTURES
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The provisions of Article 6.13.2.8 shall apply for
investigation of connection slip.
6.10.3.2—Flexure
6.10.3.2.1—Discretely Braced Flanges in
Compression
For critical stages of construction, each of the
following requirements shall be satisfied. For sections with
slender webs, Eq. 6.10.3.2.1-1 shall not be checked when
fℓ is equal to zero. For sections with compact or
noncompact webs, Eq. 6.10.3.2.1-3 shall not be checked.
f bu + f ≤ φ f Rh Fyc ,
(6.10.3.2.1-1)
1
f ≤ φ f Fnc ,
3
(6.10.3.2.1-2)
f bu +
and
f bu ≤ φ f Fcrw
(6.10.3.2.1-3)
where:
φf
=
fbu =
fℓ
=
Fcrw =
Fnc =
Myc =
Rh =
Sxc =
resistance factor for flexure specified in
Article 6.5.4.2.
flange stress calculated without consideration of
flange lateral bending determined as specified in
Article 6.10.1.6 (ksi)
flange lateral bending stress determined as
specified in Article 6.10.1.6 (ksi)
nominal bend-buckling resistance for webs
specified in Article 6.10.1.9 (ksi)
nominal flexural resistance of the flange (ksi). Fnc
shall be determined as specified in
Article 6.10.8.2. For sections in straight I-girder
bridges with compact or noncompact webs, the
lateral torsional buckling resistance may be taken
as Mnc determined as specified in Article A6.3.3
divided by Sxc. In computing Fnc for
constructibility, the web load-shedding factor, Rb,
shall be taken as 1.0.
yield moment with respect to the compression
flange determined as specified in Article D6.2
(kip-in.)
hybrid factor specified in Article 6.10.1.10.1. For
hybrid sections in which fbu does not exceed the
specified minimum yield strength of the web, the
hybrid factor shall be taken equal to 1.0.
elastic section modulus about the major axis of
the section to the compression flange taken as
Myc/Fyc (in.3)
C6.10.3.2.1
A distinction is made between discretely and
continuously braced compression and tension flanges
because for a continuously braced flange, flange lateral
bending need not be considered.
This Article gives constructibility requirements for
discretely braced compression flanges, expressed by
Eqs. 6.10.3.2.1-1, 6.10.3.2.1-2, and 6.10.3.2.1-3 in terms of
the combined factored vertical and flange lateral bending
stresses during construction. In making these checks, the
stresses fbu and fℓ must be determined according to the
procedures specified in Article 6.10.1.6.
Eq. 6.10.3.2.1-1 ensures that the maximum combined
stress in the compression flange will not exceed the
specified minimum yield strength of the flange times the
hybrid factor; that is, it is a yielding limit state check.
Eq. 6.10.3.2.1-2 ensures that the member has
sufficient strength with respect to lateral torsional and
flange local buckling based limit states, including the
consideration of flange lateral bending where these effects
are judged to be significant. For horizontally curved
bridges, flange lateral bending effects due to curvature
must always be considered in discretely braced flanges
during construction.
Eq. 6.10.3.2.1-3 ensures that theoretical web bendbuckling will not occur during construction.
Eq. 6.10.3.2.1-2 addresses the resistance of the
compression
flange by considering this element as an equivalent beamcolumn. This equation is effectively a beam-column
interaction equation, expressed in terms of the flange
stresses computed from elastic analysis (White and Grubb,
2005). The fbu term is analogous to the axial load and the fℓ
term is analogous to the bending moment within the
equivalent beam-column member. The factor of 1/3 in
front of the fℓ term in Eq. 6.10.3.2.1-2 gives an accurate
linear approximation of the equivalent beam-column
resistance within the limits on fℓ specified in
Article 6.10.1.6 (White and Grubb, 2005).
Eq. 6.10.3.2.1-1 often controls relative to
Eq. 6.10.3.2.1-2, particularly for girders with large fℓ and for
members with compact or noncompact webs. However, for
members with noncompact flanges or large unsupported
lengths during construction combined with small or zero
values for fℓ, Eq. 6.10.3.2.1-2 will typically control. During
construction before the hardening of the deck, most flanges
are discretely braced. The compact, noncompact and slender
web definitions are discussed in Article C6.10.6.2.3. For
making these checks with the section in its noncomposite
condition, the categorization of the web is to be based on the
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properties of the noncomposite section. The meanings
assigned to the compact and noncompact flange
categorizations are discussed in Article C6.10.8.2.2. When
fℓ = 0, Eq. 6.10.3.2.1-1 will not control and need not be
checked for sections with slender webs. For sections with
compact or noncompact webs, Eq. 6.10.3.2.1-1 should still
be checked. However, web bend-buckling is not a
consideration for these types of members, and therefore,
Eq. 6.10.3.2.1-3 need not be checked for these sections.
In checking Eq. 6.10.3.2.1-2 for sections in straight Igirder bridges with compact or noncompact webs, the
lateral torsional buckling resistance of the flange may be
determined from the provisions of Article A6.3.3, which
include the beneficial contribution of the St. Venant
torsional constant J. This may be useful for sections in
such bridges with compact or noncompact webs having
larger unbraced lengths, if additional lateral torsional
buckling resistance is required beyond that calculated
based on the provisions of Article 6.10.8.2. The resulting
lateral torsional buckling resistance, Mnc, is then divided
by Sxc to express the resistance in terms of stress for direct
application in Eq. 6.10.3.2.1-2. In some cases, the
calculated resistance will exceed Fyc since Appendix A6
accounts in general for flexural resistances greater than the
yield moment resistance, Myc or Myt. However,
Eq. 6.10.3.2.1-1 will control in these cases, thus ensuring
that the combined factored stress in the flange will not
exceed Fyc times the hybrid factor during construction.
The rationale for calculation of Sxc, as defined in this
Article for use in determining Fnc for sections with
noncompact or compact webs, is discussed in
Article CA6.1.1.
For sections that are composite in the final condition,
but are noncomposite during construction, different values
of the hybrid factor, Rh, must be calculated for checks in
which the member is noncomposite and for checks in
which the member is composite.
Because the flange stress is limited to the web bendbuckling stress according to Eq. 6.10.3.2.1-3, the Rb factor
is always to be taken equal to 1.0 in computing the
nominal flexural resistance of the compression flange for
constructibility.
Should the web bend-buckling resistance be exceeded
for the construction condition, the Engineer has several
options to consider. These options include providing a
larger compression flange or a smaller tension flange to
decrease the depth of the web in compression, adjusting
the deck-placement sequence to reduce the compressive
stress in the web, or providing a thicker web. Should these
options not prove to be practical or cost-effective, a
longitudinal web stiffener can be provided. As specified in
Article 6.10.11.3.1, the longitudinal stiffener must be
located vertically on the web to satisfy Eq. 6.10.3.2.1-3 for
the construction condition, Eq. 6.10.4.2.2-4 at the service
limit state and all the appropriate design requirements at
the strength limit state. Further discussions of procedures
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SECTION 6: STEEL STRUCTURES
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for locating a longitudinal stiffener are provided in
Article C6.10.11.3.1.
6.10.3.2.2—Discretely Braced Flanges in Tension
For critical stages of construction, the following
requirement shall be satisfied:
(6.10.3.2.2-1)
f bu + f ≤ φ f Rh Fyt
6.10.3.2.3 Continuously Braced Flanges in Tension
or Compression
For critical stages of construction, the following
requirement shall be satisfied:
(6.10.3.2.3-1)
f bu ≤ φ f Rh Fyf
For noncomposite sections with slender webs, flanges
in compression shall also satisfy Eq. 6.10.3.2.1-3.
6.10.3.2.4—Concrete Deck
The longitudinal tensile stress in a composite concrete
deck due to the factored loads shall not exceed φfr during
critical stages of construction, unless longitudinal
reinforcement is provided according to the provisions of
Article 6.10.1.7. The concrete stress shall be determined as
specified in Article 6.10.1.1.1d. φ and fr shall be taken as
specified in Article 6.10.1.7.
C6.10.3.2.2
For a discretely braced flange in tension,
Eq. 6.10.3.2.2-1 ensures that the stress in the flange will
not exceed the specified minimum yield strength of the
flange times the hybrid factor during construction under
the combination of the major-axis bending and lateral
bending stresses due to the factored loads.
C6.10.3.2.3
This Article assumes that a continuously braced
flange in compression is not subject to local or lateral
torsional buckling. Article C6.10.1.6 states the conditions
for which a flange may be considered to be continuously
braced. By encasing the flange in concrete or by attaching
the flange to the concrete deck by shear connectors that
satisfy the requirements of Article 6.10.10, one side of the
flange is effectively prevented from local buckling, or both
sides of the flange must buckle in the direction away from
the concrete deck. Therefore, highly restrained boundary
conditions are provided in effect at the web-flange
juncture. Also, the flange lateral bending deflections,
required to obtain a significant reduction in strength
associated with flange local buckling, are effectively
prevented by the concrete deck. Therefore, neither flange
local nor lateral torsional buckling need to be checked for
compression flanges that satisfy the proportioning limits of
Article 6.10.2.2 and are continuously braced according to
the conditions stated in Article C6.10.1.6.
C6.10.3.2.4
This Article is intended to address primarily the
situation when the concrete deck is placed in a span
adjacent to a span where the concrete has already been
placed. Negative moment in the adjacent span causes
tensile stresses in the previously placed concrete. Also, if
long placements are made such that a negative flexure
region is included in the first placement, it is possible that
the concrete in this region will be stressed in tension
during the remainder of the deck placement, which may
lead to early cracking of the deck. When the longitudinal
tensile stress in the deck exceeds the factored modulus of
rupture of the concrete, longitudinal reinforcement is to be
provided according to the provisions of Article 6.10.1.7 to
control the cracking. Stresses in the concrete deck are to be
computed using the short-term modular ratio, n, per
Article 6.10.1.1.1d.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6.10.3.3—Shear
C6.10.3.3
Webs shall satisfy the following requirement during
critical stages of construction:
(6.10.3.3-1)
Vu ≤ φvVcr
where:
φv
=
Vu =
Vcr =
resistance factor for shear specified in
Article 6.5.4.2
shear in the web at the section under
consideration due to the factored permanent loads
and factored construction loads applied to the
noncomposite section (kip)
shear-buckling resistance determined from
Eq. 6.10.9.3.3-1 (kip)
The web is to be investigated for the sum of the
factored permanent loads and factored construction loads
applied to the noncomposite section during construction.
The nominal shear resistance for this check is limited to
the shear yielding or shear-buckling resistance per
Eq. 6.10.9.3.3-1. The use of tension-field action per
Eq. 6.10.9.3.2-2 is not permitted under these loads during
construction. Use of tension-field action is permitted after
the deck has hardened or is made composite, if the section
along the entire panel is proportioned to satisfy
Eq. 6.10.9.3.2-1.
6.10.3.4—Deck Placement
Sections in positive flexure that are composite in the
final condition, but are noncomposite during construction,
shall be investigated for flexure according to the
provisions of Article 6.10.3.2 during the various stages of
the deck placement.
Geometric properties, bracing lengths and stresses
used in calculating the nominal flexural resistance shall be
for the steel section only. Changes in load, stiffness and
bracing during the various stages of the deck placement
shall be considered.
The effects of forces from deck overhang brackets
acting on the fascia girders shall be considered.
C6.10.3.4
The entire concrete deck may not be placed in one
stage; thus, parts of the girders may become composite in
sequential stages. If certain deck placement sequences are
followed, the temporary moments induced in the girders
during the deck placement can be considerably higher than
the final noncomposite dead load moments after the
sequential placement is complete.
Economical composite girders normally have smaller
top flanges than bottom flanges. Thus, more than half the
web depth is typically in compression in regions of
positive flexure during deck placement. If the maximum
moments generated during the deck placement sequence
are not considered in the design, these conditions, coupled
with narrow top compression flanges, can lead to problems
during construction, such as out-of-plane distortions of the
girder compression flanges and web. By satisfying the
following guideline:
b fc ≥
L
85
(C6.10.3.4-1)
where:
L
=
length of the girder shipping piece (in.),
potential problems can be minimized in these cases.
Therefore, Eq. C6.10.3.4-1 should be used, in conjunction
with the flange proportion limits specified in
Article 6.10.2.2, to establish a minimum required topflange width in positive-flexure regions of composite
girders. It should be emphasized that Eq. C6.10.3.4-1 is
provided merely as a guideline and is not an absolute
requirement.
Ensuring that the flanges of all anticipated lifting
pieces generally satisfy the preceding guideline over the
majority of the length of each piece can also help provide
more stable pieces that are easier to handle during erection
without the need for special stiffening trusses or falsework.
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SECTION 6: STEEL STRUCTURES
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Sequentially staged concrete placement can also result
in significant tensile strains in the previously placed deck
in adjacent spans. When cracking is predicted, longitudinal
deck reinforcement as specified in Article 6.10.3.2.4 is
required to control the cracking. Temporary dead load
deflections during sequential deck placement can also be
different from final noncomposite dead load deflections. If
the differences are deemed significant, this should be
considered when establishing camber and screed
requirements. These constructibility concerns apply to
deck replacement as well as initial construction.
During construction of steel girder bridges, concrete
deck overhang loads are typically supported by cantilever
forming brackets typically placed at 3.0 to 4.0 ft spacings
along the exterior members. The eccentricity of the deck
weight and other loads acting on the overhang brackets
creates applied torsional moments on the exterior
members. As a result, the following issues must be
considered in the design of the exterior members:
•
The applied torsional moments bend the exterior
girder top flanges outward. The resulting flange lateral
bending stresses tend to be largest at the brace points
at one or both ends of the unbraced length. The lateral
bending stress in the top flange is tensile at the brace
points on the side of the flange opposite from the
brackets. These lateral bending stresses should be
considered in the design of the flanges.
•
The horizontal components of the reactions on the
cantilever-forming brackets are often transmitted
directly onto the exterior girder web. The girder web
may exhibit significant plate bending deformations
due to these loads. The effect of these deformations
on the vertical deflections at the outside edge of the
deck should be considered. The effect of the reactions
from the brackets on the cross-frame forces should
also be considered.
•
Excessive deformation of the web or top flange may
lead to excessive deflection of the bracket supports
causing the deck finish to be problematic.
Where practical, forming brackets should be carried to
the intersection of the bottom flange and the web.
Alternatively, the brackets may bear on the girder webs if
means are provided to ensure that the web is not damaged
and that the associated deformations permit proper
placement of the concrete deck. The provisions of
Article 6.10.3.2 allow for the consideration of the flange
lateral bending stresses in the design of the flanges. In the
absence of a more refined analysis, either of the following
equations may be used to estimate the maximum flange
lateral bending moments due to the eccentric loadings
depending on how the lateral load is assumed applied to
the top flange:
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
M =
F Lb 2
12
(C6.10.3.4-2)
where:
Mℓ =
lateral bending moment in the flanges due to
the eccentric loadings from the forming brackets
(kip-in.)
statically equivalent uniformly distributed lateral
force from the brackets due to the factored loads
(kip/in.)
unbraced length (in.)
Fℓ =
Lb =
M =
P Lb
8
(C6.10.3.4-3)
where:
Pℓ =
statically equivalent concentrated lateral bracket
force placed at the middle of the unbraced length
(kip)
Eqs. C6.10.3.4-2 and C6.10.3.4-3 are both based on the
assumption of interior unbraced lengths in which the
flange is continuous with adjacent unbraced lengths, as
well as equal adjacent unbraced lengths such that due to
approximate symmetry boundary conditions, the ends of
the unbraced length are effectively torsionally fixed. The
Engineer should consider other more appropriate
idealizations when these assumptions do not approximate
the actual conditions.
Construction dead loads, such as those acting on the
deck overhangs, are often applied to the noncomposite
section and removed when the bridge has become
composite. Typically, the major-axis bending moments due
to these loads are small relative to other design loads.
However, the Engineer may find it desirable in some cases
to consider the effect of these moments, particularly in
computing deflections for cambers. The lateral bending
moments due to overhang loads not applied through the
shear center of the girder are often more critical. Refined
analysis of the noncomposite bridge for these loads
provides more accurate lateral moments and may identify
any rotation of the overhang that could potentially affect
the elevation of the screed when finishing the deck.
The magnitude and application of the overhang loads
assumed in the design should be shown in the contract
documents.
6.10.3.5—Dead Load Deflections
The provisions of Article 6.7.2 shall apply, as
applicable.
C6.10.3.5
If staged construction is specified, the sequence of
load application should be recognized in determining the
camber and stresses.
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SECTION 6: STEEL STRUCTURES
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6.10.4—Service Limit State
6.10.4.1—Elastic Deformations
C6.10.4.1
The provisions of Article 2.5.2.6 shall apply, as
applicable.
The provisions of Article 2.5.2.6 contain optional live
load deflection criteria and criteria for span-to-depth ratios.
In the absence of depth restrictions, the span-to-depth
ratios should be used to establish a reasonable minimum
web depth for the design.
6.10.4.2—Permanent Deformations
6.10.4.2.1—General
C6.10.4.2.1
For the purposes of this Article, the Service II load
combination specified in Table 3.4.1-1 shall apply.
The following methods may be used to calculate
stresses in structural steel at the Service II limit state:
•
For members with shear connectors provided
throughout their entire length that also satisfy the
provisions of Article 6.10.1.7, flexural stresses in the
structural steel caused by Service II loads applied to the
composite section may be computed using the shortterm or long-term composite section, as appropriate.
The concrete deck may be assumed to be effective for
both positive and negative flexure, provided that the
maximum longitudinal tensile stresses in the concrete
deck at the section under consideration caused by the
Service II loads are smaller than 2fr, where fr is the
modulus of rupture of the concrete specified in
Article 6.10.1.7.
•
For sections that are composite for negative flexure
with maximum longitudinal tensile stresses in the
concrete deck greater than or equal to 2fr, the flexural
stresses in the structural steel caused by Service II loads
shall be computed using the section consisting of the
steel section and the longitudinal reinforcement within
the effective width of the concrete deck.
•
For sections that are noncomposite for negative
flexure, the properties of the steel section alone shall
be used for calculation of the flexural stresses in the
structural steel.
These provisions are intended to apply to the design
live load specified in Article 3.6.1.1. If this criterion were
to be applied to a design permit load, a reduction in the
load factor for live load should be considered.
Article 6.10.1.7 requires that one percent longitudinal
deck reinforcement be placed wherever the tensile stress in
the concrete deck due to either factored construction loads
or due to Load Combination Service II exceeds the
factored modulus of rupture of the concrete. By controlling
the crack size in regions where adequate shear connection
is also provided, the concrete deck may be considered
effective in tension for computing flexural stresses on the
composite section due to Load Combination Service II.
The cracking behavior and the partial participation of
the physically cracked slab in transferring forces in tension
is very complex. Article 6.10.4.2.1 provides specific
guidance that the concrete slab may be assumed to be
uncracked when the maximum longitudinal concrete
tensile stress is smaller than 2fr. This limit between the use
of an uncracked or cracked section for calculation of
flexural stresses in the structural steel is similar to a limit
suggested in CEN (2004) beyond which the effects of
concrete cracking should be considered.
The longitudinal stresses in the concrete deck shall be
determined as specified in Article 6.10.1.1.1d.
6.10.4.2.2—Flexure
C6.10.4.2.2
Flanges shall satisfy the following requirements:
•
For the top steel flange of composite sections:
f f ≤ 0.95 Rh Fyf
•
(6.10.4.2.2-1)
For the bottom steel flange of composite sections:
2013 Revision
Eqs. 6.10.4.2.2-1 through 6.10.4.2.2-3 are intended to
prevent objectionable permanent deflections due to
expected severe traffic loadings that would impair
rideability. For homogeneous sections with zero flange
lateral bending, they correspond to the overload check in
the 2002 AASHTO Standard Specifications and are based
on successful past practice. Their development is described
in Vincent (1969). A resistance factor is not applied in
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
ff +
•
f
≤ 0.95 Rh Fyf
2
(6.10.4.2.2-2)
For both steel flanges of noncomposite sections:
ff +
f
≤ 0.80 Rh Fyf
2
(6.10.4.2.2-3)
where:
ff
=
fℓ
=
Rh =
flange stress at the section under consideration
due to the Service II loads calculated without
consideration of flange lateral bending (ksi)
flange lateral bending stress at the section under
consideration due to the Service II loads
determined as specified in Article 6.10.1.6 (ksi)
hybrid factor determined as specified in
Article 6.10.1.10.1
For continuous span flexural members in straight
I-girder bridges that satisfy the requirements of
Article B6.2, a calculated percentage of the negative
moment due to the Service II loads at the pier section
under consideration may be redistributed using the
procedures of either Article B6.3 or B6.6.
For compact composite sections in positive flexure
utilized in shored construction, the longitudinal
compressive stress in the concrete deck due to the
Service II loads, determined as specified in
Article 6.10.1.1.1d, shall not exceed 0.6f′c.
Except for composite sections in positive flexure in
which the web satisfies the requirement of
Article 6.10.2.1.1, all sections shall also satisfy the
following requirement:
f c ≤ Fcrw
(6.10.4.2.2-4)
where:
=
compression-flange stress at the section under
consideration due to the Service II loads
calculated without consideration of flange lateral
bending (ksi)
Fcrw =
nominal bend-buckling resistance for webs with
or without longitudinal stiffeners, as applicable,
determined as specified in Article 6.10.1.9 (ksi)
fc
these equations because the specified limits are
serviceability criteria for which the resistance factor is 1.0.
Eqs. 6.10.4.2.2-1 through 6.10.4.2.2-3 address the
increase in flange stresses caused by early web yielding in
hybrid sections by including the hybrid factor Rh.
For continuous-span members in which noncomposite
sections are utilized in negative flexure regions only, it is
recommended that Eqs. 6.10.4.2.2-1 and 6.10.4.2.2-2, as
applicable, be applied in those regions.
Under the load combinations specified in
Table 3.4.1-1, Eqs. 6.10.4.2.2-1 through 6.10.4.2.2-3, as
applicable, do not control and need not be checked for the
following sections:
•
Composite sections in negative flexure for which the
nominal flexural resistance under the Strength load
combinations is determined according to the
provisions of Article 6.10.8;
•
Noncomposite sections with fℓ = 0 and for which the
nominal flexural resistance under the Strength load
combinations is determined according to the
provisions of Article 6.10.8;
•
Noncompact composite sections in positive flexure.
However, Eq. 6.10.4.2.2-4 must still be checked for
these sections where applicable.
The 1/2 factor in Eqs. 6.10.4.2.2-2 and 6.10.4.2.2-3
comes from Schilling (1996) and Yoo and Davidson
(1997). Eqs. 6.10.4.2.2-2 and 6.10.4.2.2-3 with a limit of
Fyf on the right-hand side are a close approximation to
rigorous yield interaction equations for the load level
corresponding to the onset of yielding at the web-flange
juncture, including the effect of flange tip yielding that
occurs prior to this stage, but not considering flange
residual stress effects. If the flanges are nominally elastic
at the web-flange juncture and the elastically computed
flange lateral bending stresses are limited as required by
Eq. 6.10.1.6-1, the permanent deflections will be small.
The 0.95Rh and 0.80Rh factors are included on the right
hand side of Eqs. 6.10.4.2.2-2 and 6.10.4.2.2-3 to make
them compatible with the corresponding equations in the
prior Specifications when fℓ = 0, and to provide some
additional conservatism for control of permanent
deformations when the flange lateral bending is
significant. The sign of ff and fℓ should always be taken as
positive in Eqs. 6.10.4.2.2-2 and 6.10.4.2.2-3.
fℓ is not included in Eq. 6.10.4.2.2-1 because the top
flange is continuously braced by the concrete deck. For
continuously braced top flanges of noncomposite sections,
the fℓ term in Eq. 6.10.4.2.2-3 may be taken equal to zero.
Lateral bending in the bottom flange is only a
consideration at the service limit state for all horizontally
curved I-girder bridges and for straight I-girder bridges with
discontinuous cross-frame or diaphragm lines in conjunction
with skews exceeding 20 degrees. Wind load and deck
overhang effects are not considered at the service limit state.
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SECTION 6: STEEL STRUCTURES
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Localized yielding in negative-flexural sections at
interior piers results in redistribution of the elastic
moments. For continuous-span flexural members in
straight I-girder bridges that satisfy the provisions of
Article B6.2, the procedures of either Article B6.3 or
B6.6 may be used to calculate the redistribution
moments at the service limit state. These procedures
represent an improvement on the former ten-percent
redistribution rule. When the redistribution moments are
calculated
according
to
these
procedures,
Eqs. 6.10.4.2.2-1 through 6.10.4.2.2-3, as applicable,
need not be checked within the regions extending from
the pier section under consideration to the nearest flange
transition or point of permanent-load contraflexure,
whichever is closest, in each adjacent span.
Eq. 6.10.4.2.2-4 must still be considered within these
regions using the elastic moments prior to redistribution.
At all locations outside of these regions,
Eqs. 6.10.4.2.2-1 through 6.10.4.2.2-4, as applicable,
must be satisfied after redistribution. Research has not
yet been conducted to extend the provisions of
Appendix B6 to kinked (chorded) continuous or
horizontally curved steel I-girder bridges.
For compact composite sections utilized in shored
construction, the longitudinal stresses in the concrete
deck are limited to 0.6f′c to ensure linear behavior of the
concrete. In unshored construction, the concrete stress
near first yielding of either steel flange is generally
significantly less than f′c thereby eliminating the need to
check the concrete stress in this case.
With the exception of composite sections in positive
flexure in which the web satisfies the requirement of
Article 6.10.2.1.1 such that longitudinal stiffeners are
not required, and web bend-buckling effects are
negligible, web bend-buckling of all sections must be
checked under the Service II Load Combination
according to Eq. 6.10.4.2.2-4. Article C6.10.1.9.1
explains why web bend-buckling does not need to be
checked for the above exception. Options to consider
should the web bend-buckling resistance be exceeded
are similar to those discussed for the construction
condition at the end of Article C6.10.3.2.1, except of
course for adjusting the deck-placement sequence.
If the concrete deck is assumed effective in tension
in regions of negative flexure, as permitted at the
service limit state for composite sections satisfying the
requirements specified in Article 6.10.4.2.1, more than
half of the web may be in compression thus increasing
the susceptibility to web bend-buckling. As specified in
Article D6.3.1, for composite sections in negative
flexure, the appropriate value of Dc to be used at the
service limit state depends on whether or not the
concrete deck is assumed effective in tension. For
noncomposite sections, Dc of the steel section alone
should always be used.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6.10.5—Fatigue and Fracture Limit State
6.10.5.1—Fatigue
C6.10.5.1
Details shall be investigated for fatigue as specified in
Article 6.6.1. The applicable Fatigue load combination
specified in Table 3.4.1-1 and the fatigue live load
specified in Article 3.6.1.4 shall apply.
For horizontally curved I-girder bridges, the fatigue
stress range due to major-axis bending plus lateral bending
shall be investigated.
The provisions for fatigue in shear connectors
specified in Articles 6.10.10.2 and 6.10.10.3 shall apply.
In horizontally curved I-girder bridges, the base metal
adjacent to butt welds and welded attachments on
discretely braced flanges subject to a net applied tensile
stress must be checked for the fatigue stress range due to
major-axis bending, plus flange lateral bending, at the
critical transverse location on the flange. Examples of
welded attachments for which this requirement applies
include transverse stiffeners and gusset plates receiving
lateral bracing members. The base metal adjacent to
flange-to-web welds need only be checked for the stress
range due to major-axis bending since the welds are
located near the center of the flange. Flange lateral
bending need not be considered for details attached to
continuously braced flanges.
6.10.5.2—Fracture
Fracture toughness requirements specified in the
contract documents shall be in conformance with the
provisions of Article 6.6.2.
6.10.5.3—Special Fatigue Requirement for Webs
For the purposes of this Article, the factored fatigue
load shall be determined using the Fatigue I load
combination specified in Table 3.4.1-1, with the fatigue
live load taken as specified in Article 3.6.1.4.
Interior panels of webs with transverse stiffeners, with
or without longitudinal stiffeners, shall satisfy the
following requirement:
Vu ≤ Vcr
(6.10.5.3-1)
where:
Vu =
Vcr =
shear in the web at the section under
consideration due to the unfactored permanent
load plus the factored fatigue load (kip)
shear-buckling resistance determined from
Eq. 6.10.9.3.3-1 (kip)
C6.10.5.3
If Eq. 6.10.5.3-1 is satisfied, significant elastic
flexing of the web due to shear is not expected to occur,
and the member is assumed able to sustain an infinite
number of smaller loadings without fatigue cracking due
to this effect.
This provision is included here, rather than in
Article 6.6, because it involves a check of the maximum
web shear-buckling stress instead of a check of the stress
ranges caused by cyclic loading.
The live load stress due to the passage of the specified
fatigue live load for this check is that of the heaviest truck
expected to cross the bridge in 75 years.
The check for bend-buckling of webs given in
AASHTO (2004) due to the load combination specified in
this Article is not included in these Specifications. For all
sections, except for composite sections in positive flexure
in which the web satisfies Article 6.10.2.1.1, a web
bend-buckling check is required under the Service II
Load Combination according to the provisions of
Article 6.10.4.2.2.
As
discussed
further
in
Article C6.10.1.9.1, web bend-buckling of composite
sections in positive flexure is not a concern at any limit
state after the section is in its final composite condition for
sections with webs that satisfy Article 6.10.2.1.1. For all
other sections, the web bend-buckling check under the
Service II loads will control over a similar check under the
load combination specified in this Article. For composite
sections in positive flexure with webs that do not satisfy
Article 6.10.2.1.1, the smaller value of Fcrw resulting from
the larger value of Dc at the fatigue limit state tends to be
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SECTION 6: STEEL STRUCTURES
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compensated for by the lower web compressive stress due
to the load combination specified in this Article. Web
bend-buckling of these sections is also checked under the
construction condition according to Eq. 6.10.3.2.1-3.
The shear in unstiffened webs is already limited to
either the shear-yielding or shear-buckling resistance at the
strength limit state according to the provisions of
Article 6.10.9.2. The shear in end panels of stiffened webs
is also limited to the shear-yielding or shear-buckling
resistance at the strength limit state according to the
provisions of Article 6.10.9.3.3. Consequently, the
requirement in this Article need not be checked for
unstiffened webs or the end panels of stiffened webs.
6.10.6—Strength Limit State
C6.10.6.1
6.10.6.1—General
For the purposes of this Article, the applicable
Strength load combinations specified in Table 3.4.1-1 shall
apply.
2013 Revision
At the strength limit state, Article 6.10.6 directs the
Engineer to the appropriate Articles for the design of
composite or noncomposite I-sections in regions of
positive or negative flexure.
For sections in which the flexural resistance is
expressed in terms of stress, the elastically computed
flange stress is strictly not an estimate of the actual flange
stress because of limited partial yielding within the crosssection due to the combination of applied load effects with
initial residual stresses and various other incidental stress
contributions not included within the design analysis
calculations. The effects of partial yielding within the
cross-section on the distribution of internal forces within
the system prior to reaching the maximum resistances as
defined in these Specifications are minor and may be
neglected in the calculation of the applied stresses and/or
moments.
The use of stresses is considered to be more
appropriate in members within which the maximum
resistance is always less than or equal to the yield moment
My in major-axis bending. This is due to the nature of the
different types of loadings that contribute to the member
flexural stresses: noncomposite, long-term composite and
short-term composite. The combined effects of the
loadings on these different states of the member crosssection are better handled by working with flange stresses
rather than moments. Also, if the Engineer uses analysis
software in which the webs of I-section members and/or
the composite deck are represented as plate elements, the
flange stresses are obtained directly from the software,
whereas the total bending moment supported by a given
member requires further processing. Finally, bridge
engineers typically are more accustomed to working with
stresses rather than moments. Therefore, although the
provisions can be written equivalently in terms of bending
moment, the provisions of Article 6.10 are written in terms
of stress whenever the maximum potential resistance in
terms of fbu is less than or equal to Fy.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Conversely, for members in which the resistance is
potentially greater than My, significant yielding within the
cross-section makes the handling of the capacities in terms
of stress awkward. Although the provisions that are written
in terms of moment can be written equivalently in terms of
elastic stress quantities, the corresponding elastic stress
limits will be generally greater than the yield stress since
the moments are greater than the yield moment. Also, the
calculation of the resistance where it is generally greater
than My is fundamentally based on stress resultants. For
example, Mp for a compact composite section in positive
flexure is based on a plastic analysis of the composite
cross-section. Therefore, it is more natural to write the
resistance equations in terms of bending moments for these
types of sections. This is also the practice in AASHTO
(2004).
For sections in which the flexural resistance is
expressed in terms of moment, the moments acting on the
noncomposite, long-term composite and short-term
composite sections may be directly summed for
comparison to the nominal flexural resistance. That is, the
effect of the sequence of application of the different types
of loads on the stress states and of partial yielding within
the cross-section on the maximum resistance need not be
considered.
In subsequent Articles, a continuously braced flange
in compression is assumed not to be subject to local or
lateral torsional buckling. The rationale for excluding these
limit state checks is discussed in Article C6.10.3.2.3.
These provisions assume low or zero levels of axial
force in the member. At sections that are also subject to a
concentrically-applied axial force, Pu, due to the factored
loads in excess of ten percent of the factored axial
resistance of the member, Pr, at the strength limit state, the
section should instead be checked according to the
provisions of Article 6.8.2.3 or 6.9.2.2, as applicable.
According to the equations given in these Articles, when
Pu is ten percent of Pr, the flexural resistance of the
member is reduced by five percent. Below this level, it is
reasonable to ignore the effect of the axial force in the
design of the member.
6.10.6.2—Flexure
6.10.6.2.1—General
C6.10.6.2.1
If there are holes in the tension flange at the section
under consideration, the tension flange shall satisfy the
requirement specified in Article 6.10.1.8.
6.10.6.2.2—Composite Sections in Positive Flexure
Composite sections in kinked (chorded) continuous or
horizontally curved steel girder bridges shall be considered
as noncompact sections and shall satisfy the requirements
of Article 6.10.7.2.
The requirement of Article 6.10.1.8 is intended to
prevent net section fracture at a cross-section with holes in
the tension flange subject to either positive or negative
flexure.
C6.10.6.2.2
The nominal flexural resistance of composite sections
in positive flexure in straight bridges satisfying specific
steel grade, web slenderness and ductility requirements is
permitted to exceed the moment at first yield according to
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6-133
Composite sections in straight bridges that satisfy the
following requirements shall qualify as compact composite
sections:
•
The specified minimum yield strengths of the flanges
do not exceed 70.0 ksi,
•
The
web
satisfies
Article 6.10.2.1.1, and
•
The section satisfies the web slenderness limit:
2 Dcp
tw
≤ 3.76
E
Fyc
the
requirement
of
(6.10.6.2.2-1)
where:
Dcp =
depth of the web in compression at the plastic
moment determined as specified in Article D6.3.2
(in.)
Compact sections shall satisfy the requirements of
Article 6.10.7.1. Otherwise, the section shall be
considered noncompact and shall satisfy the requirements
of Article 6.10.7.2.
Compact and noncompact sections shall satisfy the
ductility requirement specified in Article 6.10.7.3.
the provisions of Article 6.10.7. The nominal flexural
resistance of these sections, termed compact sections, is
therefore more appropriately expressed in terms of
moment. For composite sections in positive flexure in
straight bridges not satisfying one or more of these
requirements, or for composite sections in positive flexure
in horizontally curved bridges, termed noncompact
sections, the nominal flexural resistance is not permitted to
exceed the moment at first yield. The nominal flexural
resistance in these cases is therefore more appropriately
expressed in terms of the elastically computed flange
stress.
Composite sections in positive flexure in straight
bridges with flange yield strengths greater than 70.0 ksi or
with webs that do not satisfy Article 6.10.2.1.1 are to be
designed at the strength limit state as noncompact sections
as specified in Article 6.10.7.2. For concrete compressive
strengths typically employed for deck construction, the use
of larger steel yield strengths may result in significant
nonlinearity and potential crushing of the deck concrete
prior to reaching the flexural resistance specified for
compact sections in Article 6.10.7.1. Longitudinal
stiffeners generally must be provided in sections with webs
that do not satisfy Article 6.10.2.1.1. Since composite
longitudinally-stiffened sections tend to be deeper and
used in longer spans with corresponding larger
noncomposite dead load stresses, they tend to have Dc/tw
values that would preclude the development of substantial
inelastic flexural strains within the web prior to bendbuckling at moment levels close to RhMy. Therefore,
although the depth of the web in compression typically
reduces as plastic strains associated with moments larger
than RhMy are incurred, and Dcp may indeed satisfy
Eq. 6.10.6.2.2-1 at the plastic moment resistance, sufficient
test data do not exist to support the design of these types of
sections for Mp. Furthermore, because of the relative size of
the steel section to the concrete deck typical for these types
of sections, Mp often is not substantially larger than RhMy.
Due to these factors, composite sections in positive flexure
in which the web does not satisfy Article 6.10.2.1.1 are
categorized as noncompact sections. Composite sections in
positive flexure in kinked (chorded) continuous or
horizontally curved steel bridges are also to be designed at
the strength limit state as noncompact sections as specified
in Article 6.10.7.2. Research has not yet been conducted to
support the design of these sections for a nominal flexural
resistance exceeding the moment at first yield.
The web slenderness requirement of this Article is
adopted from AISC (2005) and gives approximately the
same allowable web slenderness as specified for compact
sections in AASHTO (2002). Most composite sections in
positive flexure without longitudinal web stiffeners will
qualify as compact according to this criterion since the
concrete deck causes an upward shift in the neutral axis,
which reduces the depth of the web in compression. Also,
D/tw for these sections is limited to a maximum value of
150 based on the requirement of Article 6.10.2.1.1. The
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
location of the neutral axis of the composite section at the
plastic moment may be determined using the equations
listed in Table D6.1-1.
Compact composite sections in positive flexure must
also satisfy the provisions of Article 6.10.7.3 to ensure a
ductile mode of failure. Noncompact sections must also
satisfy the ductility requirement specified in
Article 6.10.7.3 to ensure a ductile failure. Satisfaction of
this requirement ensures an adequate margin of safety
against premature crushing of the concrete deck for
sections utilizing up to 100-ksi steels and/or for sections
utilized in shored construction. This requirement is also a
key limit in allowing web bend-buckling to be disregarded
in the design of composite sections in positive flexure
when the web also satisfies Article 6.10.2.1.1, as discussed
in Article C6.10.1.9.1.
6.10.6.2.3—Composite Sections in Negative Flexure
and Noncomposite Sections
Sections in all kinked (chorded) continuous or
horizontally curved steel girder bridges shall be
proportioned according to the provisions specified in
Article 6.10.8.
Sections in straight bridges whose supports are normal
or skewed not more than 20° from normal, and with
intermediate diaphragms or cross-frames placed in
contiguous lines parallel to the supports, for which:
•
The specified minimum yield strengths of the flanges
do not exceed 70.0 ksi,
•
The web satisfies the noncompact slenderness limit:
2 Dc
E
< 5.7
tw
Fyc
(6.10.6.2.3-1)
and:
•
The flanges satisfy the following ratio:
I yc
I yt
≥ 0.3
(6.10.6.2.3-2)
where:
Dc =
Iyc
Iyt
depth of the web in compression in the elastic
range (in.). For composite sections, Dc shall be
determined as specified in Article D6.3.1.
= moment of inertia of the compression flange of
the steel section about the vertical axis in the
plane of the web (in.4)
= moment of inertia of the tension flange of the
steel section about the vertical axis in the plane of
the web (in.4)
C6.10.6.2.3
For composite sections in negative flexure and
noncomposite sections, the provisions of Article 6.10.8
limit the nominal flexural resistance to be less than or
equal to the moment at first yield. As a result, the nominal
flexural resistance for these sections is conveniently
expressed in terms of the elastically computed flange stress.
For composite sections in negative flexure or
noncomposite sections in straight bridges without skewed
supports or with limited skews that satisfy the specified steel
grade requirements and with webs that satisfy Eq. 6.10.6.2.31 and flanges that satisfy Eq. 6.10.6.2.3-2, the optional
provisions of Appendix A6 may be applied to determine the
nominal flexural resistance, which may exceed the moment at
first yield. Therefore, the nominal flexural resistance
determined from the provisions of Appendix A6 is expressed
in terms of moment. Because these types of sections are less
commonly used, the provisions for their design have been
placed in an appendix in order to simplify and streamline the
main design provisions. The provisions of Article 6.10.8 may
be used for these types of sections to obtain an accurate to
somewhat conservative determination of the nominal flexural
resistance than would be obtained using Appendix A6.
For composite sections in negative flexure or
noncomposite sections in straight bridges not satisfying one
or more of these requirements, or for these sections in
horizontally curved bridges, the provisions of Article 6.10.8
must be used. Research has not yet been conducted to extend
the provisions of Appendix A6 either to sections in kinked
(chorded) continuous or horizontally curved steel bridges or
to bridges with supports skewed more than 20 degrees from
normal. Severely skewed bridges with contiguous crossframes have significant transverse stiffness and thus already
have large cross-frame forces in the elastic range. As
interior-pier sections yield and begin to lose stiffness and
shed their load, the forces in the adjacent cross-frames will
increase. There is currently no established procedure to
predict the resulting increase in the forces without
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SECTION 6: STEEL STRUCTURES
may be proportioned according to the provisions for
compact or noncompact web sections specified in
Appendix A6. Otherwise, the section shall be
proportioned according to provisions specified in
Article 6.10.8.
For continuous span flexural members in straight
bridges that satisfy the requirements of Article B6.2, a
calculated percentage of the negative moments due to
the factored loads at the pier section under consideration
may be redistributed using the procedures of either
Article B6.4 or B6.6.
6-135
performing a refined nonlinear analysis. With discontinuous
cross-frames, significant lateral flange bending effects can
occur. The resulting lateral bending moments and stresses
are amplified in the bottom compression flange adjacent to
the pier as the flange deflects laterally. There is currently no
means to accurately predict these amplification effects as the
flange is also yielding. Skewed supports also result in
twisting of the girders, which is not recognized in plasticdesign theory. The relative vertical deflections of the girders
create eccentricities that are also not recognized in the
theory. Thus, until further research is done to examine these
effects in greater detail, a conservative approach has been
taken in the specification.
Eq. 6.10.6.2.3-1 defines the slenderness limit for a
noncompact web. A web with a slenderness ratio
exceeding this limit is termed slender. The previous
Specifications defined sections as compact or
noncompact and did not explicitly distinguish between a
noncompact and a slender web. For noncompact webs,
theoretical web bend-buckling does not occur for elastic
stress values, computed according to beam theory,
smaller than the limit of the flexural resistance. Sections
with slender webs rely upon the significant web post
bend-buckling resistance under Strength Load
Combinations. Specific values for the noncompact web
slenderness limit for different grades of steel are listed in
Table C6.10.1.10.2-2.
A compact web is one that satisfies the slenderness limit
given by Eq. A6.2.1-1. Sections with compact webs and
Iyc/Iyt ≥ 0.3 are able to develop their full plastic moment
capacity Mp provided that other steel grade, ductility, flange
slenderness and/or lateral bracing requirements are satisfied.
The web-slenderness limit given by Eq. A6.2.1-1 is
significantly smaller than the limit shown in
Table C6.10.1.10.2-2. It is generally satisfied by rolled Ishapes, but typically not by the most efficient built-up section
proportions.
The flange yield stress, Fyc, is more relevant to the
web buckling behavior and its influence on the flexural
resistance than Fyw. For a section that has a web
proportioned at the noncompact limit, a stable nominally
elastic compression flange tends to constrain a lowerstrength hybrid web at stress levels less than or equal to
RhFyc. For a section that has a compact web, the inelastic
strains associated with development of the plastic flexural
resistance are more closely related to the flange rather than
the web yield strength.
The majority of steel-bridge I-sections utilize either
slender webs or noncompact webs that approach the
slenderness limit of Eq. 6.10.6.2.3-1 represented by the
values listed in Table C6.10.1.10.2-2. For these sections, the
simpler and more streamlined provisions of Article 6.10.8
are the most appropriate for determining the nominal
flexural resistance of composite sections in negative flexure
and noncomposite sections. These provisions may also be
applied to sections with compact webs or to sections with
noncompact webs that are nearly compact, but at the
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
expense of some economy. Such sections are typically used
in bridges with shorter spans. The potential loss in economy
increases with decreasing web slenderness. The Engineer
should give strong consideration to utilizing the provisions
of Appendix A6 to compute the nominal flexural resistance
of these sections in straight bridges, in particular, sections
with compact webs.
Eq. 6.10.6.2.3-2 is specified to guard against extremely
monosymmetric noncomposite I-sections, in which
analytical studies indicate a significant loss in the influence
of the St. Venant torsional rigidity GJ on the lateral-torsional
buckling resistance due to cross-section distortion. The
influence of web distortion on the lateral torsional buckling
resistance is larger for such members. If the flanges are of
equal thickness, this limit is equivalent to bfc ≥ 0.67bft.
Yielding in negative-flexural sections at interior piers at
the strength limit state results in redistribution of the elastic
moments. For continuous-span flexural members in straight
bridges that satisfy the provisions of Article B6.2, the
procedures of either Article B6.4 or B6.6 may be used to
calculate redistribution moments at the strength limit state.
These provisions replace the former ten-percent redistribution
allowance and provide a more rational approach for
calculating the percentage redistribution from interior-pier
sections. When the redistribution moments are calculated
according to these procedures, the flexural resistances at the
strength limit state within the unbraced lengths immediately
adjacent to interior-pier sections satisfying the requirements
of Article B6.2 need not be checked. At all other locations,
the provisions of Articles 6.10.7, 6.10.8.1 or A6.1, as
applicable, must be satisfied after redistribution. The
provisions of Article B6.2 are often satisfied by compactflange unstiffened or transversely-stiffened pier sections that
are otherwise designed by Article 6.10.8 or Appendix A6
using Cb = 1.0. Research has not yet been conducted to
extend the provisions of Appendix B6 to kinked (chorded)
continuous or horizontally curved steel bridges.
6.10.6.3—Shear
The provisions of Article 6.10.9 shall apply.
6.10.6.4—Shear Connectors
The provisions of Article 6.10.10.4 shall apply.
6.10.7—Flexural Resistance—Composite Sections in
Positive Flexure
6.10.7.1—Compact Sections
6.10.7.1.1—General
C6.10.7.1.1
At the strength limit state, the section shall satisfy:
Mu +
1
fA S xt ≤ φ f M n
3
(6.10.7.1.1-1)
For composite sections in positive flexure, lateral
bending does not need to be considered in the compression
flange at the strength limit state because the flange is
continuously supported by the concrete deck.
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SECTION 6: STEEL STRUCTURES
6-137
where:
φf
=
fƐ
=
Mn =
Mu =
Myt =
Sxt =
resistance factor for flexure specified in
Article 6.5.4.2
flange lateral bending stress determined as
specified in Article 6.10.1.6 (ksi)
nominal flexural resistance of the section
determined as specified in Article 6.10.7.1.2
(kip-in.)
bending moment about the major-axis of the
cross-section determined as specified in
Article 6.10.1.6 (kip-in.)
yield moment with respect to the tension flange
determined as specified in Article D6.2 (kip-in.)
elastic section modulus about the major axis of
the section to the tension flange taken as Myt/Fyt
(in.3)
6.10.7.1.2—Nominal Flexural Resistance
The nominal flexural resistance of the section shall be
taken as:
If D p ≤ 0.1 Dt , then:
Mn = Mp
(6.10.7.1.2-1)
Otherwise:
Dp ·
§
M n = M p ¨1.07 − 0.7
¸
Dt ¹
©
where:
Dp =
Dt =
Mp =
(6.10.7.1.2-2)
distance from the top of the concrete deck to the
neutral axis of the composite section at the plastic
moment (in.)
total depth of the composite section (in.)
plastic moment of the composite section
determined as specified in Article D6.1 (kip-in.)
In a continuous span, the nominal flexural resistance
of the section shall satisfy:
Eq. 6.10.7.1.1-1 is an interaction equation that
addresses the influence of lateral bending within the
tension flange, represented by the elastically computed
flange lateral bending stress, fƐ, combined with the majoraxis bending moment, Mu. This equation is similar to the
subsequent Eqs. 6.10.7.2.1-2 and 6.10.8.1.2-1, the basis of
which is explained in Article C6.10.8.1.2. However, these
other equations are expressed in an elastically computed
stress format, and the resistance term on their right-hand
side is generally equal to φfRhFyt. Eq. 6.10.7.1.1-1 is
expressed in a bending moment format, but alternatively
can be considered in a stress format by dividing both sides
of the equation by the elastic section modulus, Sxt.
The term Mn on the right-hand side of Eq. 6.10.7.1.1-1
is generally greater than the yield moment capacity, Myt.
Therefore, the corresponding resistance, written in the format
of an elastically computed stress, is generally greater than Fyt.
These Specifications use a moment format for all resistance
equations which, if written in terms of an elastically
computed stress, can potentially assume resistance values
greater than the specified minimum yield strength of the steel.
In these types of sections, the major-axis bending moment is
physically a more meaningful quantity than the corresponding
elastically computed bending stress.
Eq. 6.10.7.1.1-1 gives a reasonably accurate but
conservative representation of the results from an elasticplastic section analysis in which a fraction of the width
from the tips of the tension flange is deducted to
accommodate flange lateral bending. The rationale for
calculation of Sxt, as defined in this Article for use in
Eq. 6.10.7.1.1-1, is discussed in Article CA6.1.1.
C6.10.7.1.2
Eq. 6.10.7.1.2-2 implements the philosophy introduced
by Wittry (1993) that an additional margin of safety should
be applied to the theoretical nominal flexural resistance of
compact composite sections in positive flexure when the
depth of the plastic neutral axis below the top of the deck,
Dp, exceeds a certain value. This additional margin of safety,
which increases approximately as a linear function of Dp/Dt,
is intended to protect the concrete deck from premature
crushing, thereby ensuring adequate ductility of the
composite section. Sections with Dp/Dt less than or equal to
0.1 can reach as a minimum the plastic moment, Mp, of the
composite section without any ductility concerns.
Eq. 6.10.7.1.2-2 gives approximately the same results as
the comparable equation in previous Specifications, but is a
simpler form that depends only on the plastic moment
resistance Mp and on the ratio Dp/Dt, as also suggested in
Yakel and Azizinamini (2005). Both equations implement
the above philosophy justified by Wittry (1993).
Eq. 6.10.7.1.2-2 is somewhat more restrictive than the
equation in previous Specifications for sections with small
values of Mp/My, such as sections with hybrid webs, a
relatively small deck area and a high-strength tension flange.
It is somewhat less restrictive for sections with large values
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
M n ≤ 1.3 Rh M y
(6.10.7.1.2-3)
where:
Mn =
My =
Rh =
nominal flexural resistance determined from
Eq. 6.10.7.1.2-1 or 6.10.7.1.2-2, as applicable
(kip-in.)
yield moment determined as specified in
Article D6.2 (kip-in.)
hybrid factor determined as specified in
Article 6.10.1.10.1
unless:
•
the span under consideration and all adjacent interiorpier sections satisfy the requirements of Article B6.2,
and:
•
the appropriate value of θRL from Article B6.6.2
exceeds 0.009 radians at all adjacent interior-pier
sections,
•
in which case the nominal flexural resistance of the
section is not subject to the limitation of
Eq. 6.10.7.1.2-3.
of Mp/My. Wittry (1993) considered various experimental
test results and performed a large number of parametric
cross-section analyses. The smallest experimental or
theoretical resistance of all the cross-sections considered in
this research and in other subsequent studies is 0.96Mp. Eq.
6.10.7.1.2-2 is based on the target additional margin of
safety of 1.28 specified by Wittry at the maximum allowed
value of Dp combined with an assumed theoretical resistance
of 0.96Mp at this limit. At the maximum allowed value of Dp
specified by Eq. 6.10.7.3-1, the resulting nominal design
flexural resistance is 0.78Mp.
The limit of Dp < 0.1Dt for the use of Eq. 6.10.7.1.2-1
is obtained by use of a single implicit β value of 0.75 in
the comparable equations from AASHTO (2004).
AASHTO (2004) specifies β = 0.7 for Fy = 50 and 70.0 ksi
and β = 0.9 for Fy = 36.0 ksi. The value of β = 0.75 is
justifiable for all cases based on the scatter in strainhardening data. The derived β values are sensitive to the
assumed strain-hardening characteristics.
The shape factor, Mp/My, for composite sections in
positive flexure can be somewhat larger than 1.5 in certain
cases. Therefore, a considerable amount of yielding and
resulting inelastic curvature is required to reach Mp in
these situations. This yielding reduces the effective
stiffness of the positive flexural section. In continuous
spans, the reduction in stiffness can shift moment from the
positive to the negative flexural regions. If the interior-pier
sections in these regions do not have additional capacity to
sustain these larger moments and are not designed to have
ductile moment-rotation characteristics according to the
provisions of Appendix B6, the shedding of moment to
these sections could result in incremental collapse under
repeated live load applications. Therefore, for cases where
the span or either of the adjacent interior-pier sections do
not satisfy the provisions of Article B6.2, or where the
appropriate value of θRL from Article B6.6.2 at either
adjacent pier section is less than or equal to 0.009 radians,
the positive flexural sections must satisfy Eq. 6.10.7.1.2-3.
It is possible to satisfy the above concerns by ensuring
that the pier section flexural resistances are not exceeded if
the positive flexural section moments above RhMy are
redistributed and combined with the concurrent negative
moments at the pier sections determined from an elastic
analysis. This approach is termed the Refined Method in
AASHTO (2004). However, concurrent moments are not
typically tracked in the analysis and so this method is not
included in these Specifications.
Eq. 6.10.7.1.2-3 is provided to limit the amount of
additional moment allowed above RhMy at composite
sections in positive flexure to 30 percent of RhMy in
continuous spans where the span or either of the adjacent
pier sections do not satisfy the requirements of
Article B6.2. The 1.3RhMy limit is the same as the limit
specified for the Approximate Method in AASHTO
(2004). The nominal flexural resistance determined from
Eq. 6.10.7.1.2-3 is not to exceed the resistance determined
from either Eq. 6.10.7.1.2-1 or 6.10.7.1.2-2, as applicable,
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SECTION 6: STEEL STRUCTURES
6-139
to ensure adequate strength and ductility of the composite
section. In cases where Dp/Dt is relatively large and Mp/My
is relatively small, Eq. 6.10.7.1.2-2 may govern relative to
Eq. 6.10.7.1.2-3. However, for most practical cases,
Eq. 6.10.7.1.2-3 will control.
Interior-pier sections satisfying the requirements of
Article B6.2 and for which the appropriate value of θRL
from Article B6.6.2 exceeds 0.009 radians have sufficient
ductility and robustness such that the redistribution of
moments caused by partial yielding within the positive
flexural regions is inconsequential. The value of
0.009 radians is taken as an upper bound for the potential
increase in the inelastic rotations at the interior-pier
sections due to positive-moment yielding. Thus, the
nominal flexural resistance of positive flexural sections in
continuous spans that meet these requirements is not
limited due to the effect of potential moment shifting.
These restrictions are often satisfied by compact-flange
unstiffened or transversely-stiffened pier sections designed
by Article 6.10.8 or Appendix A6 using Cb = 1.0. All
current ASTM A6 rolled I-shapes satisfying Eqs. B6.2.1-3,
B6.2.2-1, and B6.2.4-1 meet these restrictions. All built-up
sections satisfying Article B6.2 that also either have
D/bfc < 3.14 or satisfy the additional requirements of
Article B6.5.1 meet these restrictions.
The Engineer is not required to redistribute moments
from the pier sections in order to utilize the additional
resistance in positive flexure, but only to satisfy the stated
restrictions from Appendix B6 that ensure significant
ductility and robustness of the adjacent pier sections.
Redistribution of the pier moments is permitted in these
cases, if desired, according to the provisions of Appendix B6.
Assuming the fatigue and fracture limit state does not
control, under the load combinations specified in
Table 3.4.1-1 and in the absence of flange lateral bending,
the permanent deflection service limit state criterion given
by Eq. 6.10.4.2.2-2 will often govern the design of the
bottom flange of compact composite sections in positive
flexure wherever the nominal flexural resistance at the
strength limit state is based on either Eq. 6.10.7.1.2-1,
6.10.7.1.2-2, or 6.10.7.1.2-3. Thus, it is prudent and
expedient to initially design these types of sections to satisfy
this permanent deflection service limit state criterion and
then to subsequently check the nominal flexural resistance at
the strength limit state according to the applicable
Eq. 6.10.7.1.2-1, 6.10.7.1.2-2, or 6.10.7.1.2-3.
6.10.7.2—Noncompact Sections
6.10.7.2.1—General
C6.10.7.2.1
At the strength limit state, the compression flange
shall satisfy:
f bu ≤ φ f Fnc
where:
(6.10.7.2.1-1)
For noncompact sections, the compression flange must
satisfy Eq. 6.10.7.2.1-1 and the tension flange must satisfy
Eq. 6.10.7.2.1-2 at the strength limit state. The basis for
Eq. 6.10.7.2.1-2 is explained in Article C6.10.8.1.2. For
composite sections in positive flexure, lateral bending does
not need to be considered in the compression flange at the
strength limit state because the flange is continuously
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2012
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
6-140
φf
fbu
Fnc
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
=
resistance factor for flexure specified in
Article 6.5.4.2
= flange stress calculated without consideration of
flange lateral bending determined as specified in
Article 6.10.1.6 (ksi)
= nominal flexural resistance of the compression
flange
determined
as
specified
in
Article 6.10.7.2.2 (ksi)
The tension flange shall satisfy:
f bu +
1
fA ≤ φ f Fnt
3
(6.10.7.2.1-2)
supported by the concrete deck.
For noncompact sections, the longitudinal stress in the
concrete deck is limited to 0.6f′c to ensure linear behavior
of the concrete, which is assumed in the calculation of the
steel flange stresses. This condition is unlikely to govern
except in cases involving: (1) shored construction, or
unshored construction where the noncomposite steel dead
load stresses are low, combined with (2) geometries
causing the neutral axis of the short-term and long-term
composite section to be significantly below the bottom of
the concrete deck.
where:
fƐ
=
Fnt =
flange lateral bending stress determined as
specified in Article 6.10.1.6 (ksi)
nominal flexural resistance of the tension flange
determined as specified in Article 6.10.7.2.2 (ksi)
The maximum longitudinal compressive stress in the
concrete deck at the strength limit state, determined as
specified in Article 6.10.1.1.1d, shall not exceed 0.6f′c.
6.10.7.2.2—Nominal Flexural Resistance
The nominal flexural resistance of the compression
flange shall be taken as:
Fnc = Rb Rh Fyc
(6.10.7.2.2-1)
where:
Rb =
Rh =
web load-shedding factor determined as specified
in Article 6.10.1.10.2
hybrid factor determined as specified in
Article 6.10.1.10.1
C6.10.7.2.2
The nominal flexural resistance of noncompact
composite sections in positive flexure is limited to the
moment at first yield. Thus, the nominal flexural resistance
is expressed simply in terms of the flange stress. For
noncompact sections, the elastically computed stress in
each flange due to the factored loads, determined in
accordance with Article 6.10.1.1.1a, is compared with the
yield stress of the flange times the appropriate flangestrength reduction factors.
The nominal flexural resistance of the tension flange
shall be taken as:
Fnt = Rh Fyt
(6.10.7.2.2-2)
6.10.7.3—Ductility Requirement
C6.10.7.3
Compact and noncompact sections shall satisfy:
D p ≤ 0.42 Dt
(6.10.7.3-1)
where:
Dp =
Dt =
distance from the top of the concrete deck to the
neutral axis of the composite section at the plastic
moment (in.)
total depth of the composite section (in.)
The ductility requirement specified in this Article is
intended to protect the concrete deck from premature
crushing. The limit of Dp < 5D' in AASHTO (2004)
corresponds to Dp /Dt < 0.5 for β = 0.75. The Dp /Dt ratio
is lowered to 0.42 in Eq. 6.10.7.3-1 to ensure significant
yielding of the bottom flange when the crushing strain is
reached at the top of concrete deck for all potential cases.
In checking this requirement, Dt should be computed using
a lower bound estimate of the actual thickness of the
concrete haunch, or may be determined conservatively by
neglecting the thickness of the haunch.
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2012
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SECTION 6: STEEL STRUCTURES
6-141
6.10.8—Flexural Resistance—Composite Sections in
Negative Flexure and Noncomposite Sections
6.10.8.1—General
6.10.8.1.1—Discretely Braced Flanges in
Compression
At the strength limit state, the following requirement
shall be satisfied:
f bu +
1
f ≤ φ f Fnc
3
(6.10.8.1.1-1)
where:
φf
=
fbu =
fℓ
=
Fnc =
resistance factor for flexure specified in
Article 6.5.4.2
flange stress calculated without consideration of
flange lateral bending determined as specified in
Article 6.10.1.6 (ksi)
flange lateral bending stress determined as
specified in Article 6.10.1.6 (ksi)
nominal flexural resistance of the flange
determined as specified in Article 6.10.8.2 (ksi)
6.10.8.1.2—Discretely Braced Flanges in Tension
At the strength limit state, the following requirement
shall be satisfied:
f bu +
1
f ≤ φ f Fnt
3
(6.10.8.1.2-1)
C6.10.8.1.1
Eq. 6.10.8.1.1-1 addresses the resistance of the
compression flange by considering this element as an
equivalent beam-column. This equation is effectively a
beam-column interaction equation, expressed in terms of
the flange stresses computed from elastic analysis (White
and Grubb, 2004). The fbu term is analogous to the axial
load and the fℓ term is analogous to the bending moment
within the equivalent beam-column member. The factor of
one-third in front of the fℓ term in Eq. 6.10.8.1.1-1 gives an
accurate linear approximation of the equivalent beamcolumn resistance within the limits on fℓ specified in
Article 6.10.1.6 (White and Grubb, 2005).
Eqs. 6.10.8.1.1-1, 6.10.8.1.2-1, and 6.10.8.1.3-1 are
developed specifically for checking of slender-web
noncomposite sections and slender-web composite sections in
negative flexure. These equations may be used as a simple
conservative resistance check for other types of composite
sections in negative flexure and noncomposite sections. The
provisions specified in Appendix A6 may be used for
composite sections in negative flexure and for noncomposite
sections with compact or noncompact webs in straight
bridges for which the specified minimum yield strengths of
the flanges and web do not exceed 70 ksi and for which the
flanges satisfy Eq. 6.10.6.2.3-2. The Engineer should give
consideration to utilizing the provisions of Appendix A6 for
such sections in straight bridges with compact webs;
however, Appendix A6 provides only minor increases in the
nominal resistance for sections in which the web slenderness
approaches the noncompact web limit of Eq. 6.10.6.2.3-1.
C6.10.8.1.2
Eq. 6.10.8.1.2-1 is an accurate approximation of the
full plastic strength of a rectangular flange cross-section
subjected to combined vertical and lateral bending within
the limit of Eq. 6.10.1.6-1, originally proposed by Hall and
Yoo (1996).
where:
Fnt =
nominal flexural resistance of the flange
determined as specified in Article 6.10.8.3 (ksi)
6.10.8.1.3—Continuously Braced Flanges in
Tension or Compression
At the strength limit state, the following requirement
shall be satisfied:
f bu ≤ φ f Rh Fyf
(6.10.8.1.3-1)
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2012
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6-142
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
6.10.8.2 Compression-Flange Flexural Resistance
6.10.8.2.1—General
C6.10.8.2.1
Eq. 6.10.8.1.1-1 shall be satisfied for both local
buckling and lateral torsional buckling using the
appropriate value of Fnc determined for each case as
specified in Articles 6.10.8.2.2 and 6.10.8.2.3,
respectively.
All of the I-section compression-flange flexural
resistance equations of these Specifications are based
consistently on the logic of identifying the two anchor
points shown in Figure C6.10.8.2.1-1 for the case of
uniform major-axis bending. Anchor point 1 is located at
the length Lb = Lp for lateral-torsional buckling (LTB) or
flange slenderness bfc/2tfc = λpf for flange local buckling
(FLB) corresponding to development of the maximum
potential flexural resistance, labeled as Fmax or Mmax in the
figure, as applicable. Anchor point 2 is located at the
length Lr or flange slenderness λrf for which the inelastic
and elastic LTB or FLB resistances are the same. In
Article 6.10.8, this resistance is taken as RbFyr, where Fyr is
taken as the smaller of 0.7Fyc and Fyw, but not less than
0.5Fyc. With the exception of hybrid sections with Fyw
significantly smaller than Fyc, Fyr = 0.7Fyc. This limit
corresponds to a nominal compression flange residual
stress effect of 0.3Fyc. The 0.5Fyc limit on Fyr avoids
anomalous situations for some types of cross-sections in
which the inelastic buckling equation gives a larger
resistance than the corresponding elastic buckling curve.
Also, the 0.5Fyc limit is equivalent to the implicit value of
Fyr used in AASHTO (2004). For Lb > Lr or bfc/2tfc > λrf,
the LTB and FLB resistances are governed by elastic
buckling. However, the elastic FLB resistance equations
are not specified explicitly in these provisions since the
limits of Article 6.10.2.2 preclude elastic FLB for specified
minimum yield strengths up to and including Fyc = 90 ksi.
Use of the inelastic FLB Eq. 6.10.8.2.2-2 is permitted for
rare cases in which bfc/2tfc can potentially exceed λrf for
Fyc > 90 ksi.
For unbraced lengths subjected to moment gradient,
the LTB resistances for the case of uniform major-axis
bending are simply scaled by the moment gradient
modifier Cb, with the exception that the LTB resistance is
capped at Fmax or Mmax, as illustrated by the dashed line in
Figure C6.10.8.2.1-1. The maximum unbraced length at
which the LTB resistance is equal to Fmax or Mmax under a
moment gradient may be determined from Article D6.4.1
or D6.4.2, as applicable. The FLB resistance for moment
gradient cases is the same as that for the case of uniform
major-axis bending, neglecting the relatively minor
influence of moment gradient effects.
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2012
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SECTION 6: STEEL STRUCTURES
6-143
See Art. D6.4.1
or D6.4.2
Fnc or Mnc
FLB resistance; LTB
resistance in uniform bending
Anchor Point 1
LTB resistance under
moment gradient
Fmax or MMmax
max
Anchor Point 2
RbFyr or
RbFyrSxc
noncompact
(inelastic buckling)
nonslender
nonslender
slender
(elastic buckling)
λp λpf
Lp or
r λrf
Lrλor
Uniform Bending
Resistance
compact
C b x Uniform Bending
Resistance
r
L b or bfc/2tfc
Figure C6.10.8.2.1-1—Basic Form of All I-section
Compression-Flange Flexural Resistance Equations
C6.10.8.2.2
6.10.8.2.2—Local Buckling Resistance
The local buckling resistance of the compression
flange shall be taken as:
•
If λ f ≤ λ pf , then:
(6.10.8.2.2-1)
Fnc = Rb Rh Fyc
•
Otherwise:
Fyr
Fnc = 1 − 1 −
Rh Fyc
λ f − λ pf
λ rf − λ pf
Rb Rh Fyc
(6.10.8.2.2-2)
in which:
λf
=
=
λrf =
Table C6.10.8.2.2-1—Limiting Slenderness Ratio for a
Compact Flange
slenderness ratio for the compression flange
b fc
(6.10.8.2.2-3)
2t fc
λpf = 0.38
E
Fyc
(6.10.8.2.2-4)
limiting slenderness ratio for a noncompact
flange
= 0.56
Eq. 6.10.8.2.2-4 defines the slenderness limit for a
compact flange whereas Eq. 6.10.8.2.2-5 gives the
slenderness limit for a noncompact flange. The nominal
flexural resistance of a section with a compact flange is
independent of the flange slenderness, whereas the flexural
resistance of a section with a noncompact flange is
expressed as a linear function of the flange slenderness as
illustrated in Figure C6.10.8.2.1-1. The compact flange
slenderness limit is the same as specified in AISC (2005)
and in AASHTO (1996, 2004). For different grades of
steel, this slenderness limit is as follows:
E
Fyr
Fyc (ksi)
λpf
36.0
50.0
70.0
10.8
9.2
7.7
90.0
100.0
6.8
6.5
Eq. 6.10.8.2.2-5 is based conservatively on the more
general limit given by Eq. A6.3.2-5, but with a flange local
buckling coefficient of kc = 0.35. With the exception of
hybrid sections with Fyw < 0.7Fyc, the term Fyr in
Eq. 6.10.8.2.2-5 is always equal to 0.7Fyc.
(6.10.8.2.2-5)
where:
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2012
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6-144
Fyr =
Rb =
Rh =
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
compression-flange stress at the onset of nominal
yielding within the cross-section, including
residual stress effects, but not including
compression-flange lateral bending, taken as the
smaller of 0.7Fyc and Fyw, but not less than 0.5Fyc
web load-shedding factor determined as specified
in Article 6.10.1.10.2
hybrid factor determined as specified in
Article 6.10.1.10.1
C6.10.8.2.3
6.10.8.2.3—Lateral Torsional Buckling Resistance
For unbraced lengths in which the member is
prismatic, the lateral torsional buckling resistance of the
compression flange shall be taken as:
•
If Lb ≤ L p , then:
(6.10.8.2.3-1)
Fnc = Rb Rh Fyc
•
If L p < Lb ≤ Lr , then:
Fyr
Fnc = Cb 1 − 1 −
R
h Fyc
•
Lb − L p
L − L
p
r
Rb Rh Fyc ≤ Rb Rh Fyc
(6.10.8.2.3-2)
If Lb > Lr , then:
Fnc = Fcr ≤ Rb Rh Fyc
(6.10.8.2.3-3)
in which:
Lb =
Lp =
unbraced length (in.)
limiting unbraced length to achieve the nominal
flexural resistance of RbRhFyc under uniform
bending (in.)
= 1.0 rt
Lr =
(6.10.8.2.3-4)
limiting unbraced length to achieve the onset of
nominal yielding in either flange under uniform
bending with consideration of compressionflange residual stress effects (in.)
= π rt
Cb =
E
Fyc
E
Fyr
(6.10.8.2.3-5)
moment gradient modifier. In lieu of an
alternative rational analysis, Cb may be calculated
as follows:
Eq. 6.10.8.2.3-4 defines the compact unbraced length
limit for a member subjected to uniform major-axis bending,
whereas Eq. 6.10.8.2.3-5 gives the corresponding
noncompact unbraced length limit. The nominal flexural
resistance of a member braced at or below the compact limit
is independent of the unbraced length, whereas the flexural
resistance of a member braced at or below the noncompact
limit is expressed as a linear function of the unbraced length
as illustrated in Figure C6.10.8.2.1-1. The compact bracing
limit of Eq. 6.10.8.2.3-4 is similar to the bracing
requirement for use of the general compact-section flexural
resistance equations and/or the Q formula equations in
AASHTO (2004) for Fyc = 50 ksi. For larger Fyc values, it is
somewhat less restrictive than the previous requirement. The
limit given by Eq. 6.10.8.2.3-4 is generally somewhat more
restrictive than the limit given by the corresponding Lp
equation in AASHTO (2004) and AISC (2005). The limit
given by Eq. 6.10.8.2.3-4 is based on linear regression
analysis within the region corresponding to the inelastic
lateral torsional buckling equation, shown qualitatively in
Figure C6.10.8.2.1-1, for a wide range of data from
experimental flexural tests involving uniform major-axis
bending and in which the physical effective length for lateral
torsional buckling is effectively 1.0.
Note that the most economical solution is not
necessarily achieved by limiting the unbraced length to Lp
in order to reach the maximum flexural resistance, Fmax,
particularly if the moment gradient modifier, Cb, is taken
equal to 1.0.
Eq. 6.10.8.2.3-8 is a conservative simplification of
Eq. A6.3.3-8, which gives the exact beam-theory based
solution for the elastic lateral torsional buckling resistance
of a doubly-symmetric I-section (Timoshenko and Gere,
1961) for the case of uniform major-axis bending when Cb
is equal to 1.0 and when rt is defined as:
rt =
b fc
h 1 Dc tw D 2
12 +
d 3 b t hd
fc fc
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(C6.10.8.2.3-1)
2012
Edition
SECTION 6: STEEL STRUCTURES
•
6-145
For unbraced cantilevers and for members where
fmid/f2 > 1 or f2 = 0
Cb = 1.0
•
(6.10.8.2.3-6)
For all other cases:
2
f
f
Cb = 1.75 − 1.05 1 + 0.3 1 ≤ 2.3 (6.10.8.2.3-7)
f2
f2
Fcr =
=
rt
=
=
elastic lateral torsional buckling stress (ksi)
Cb Rb π2 E
Lb
rt
(6.10.8.2.3-8)
2
effective radius of gyration for lateral torsional
buckling (in.)
b fc
1 Dc tw
12 1 +
3b t
fc fc
(6.10.8.2.3-9)
where:
Fyr =
Dc =
fmid =
f0
=
f1
=
compression-flange stress at the onset of nominal
yielding within the cross-section, including
residual stress effects, but not including
compression-flange lateral bending, taken as the
smaller of 0.7Fyc and Fyw, but not less than 0.5Fyc
depth of the web in compression in the elastic
range (in.). For composite sections, Dc shall be
determined as specified in Article D6.3.1.
stress without consideration of lateral bending at
the middle of the unbraced length of the flange
under consideration, calculated from the moment
envelope value that produces the largest
compression at this point, or the smallest tension
if this point is never in compression (ksi). fmid
shall be due to the factored loads and shall be
taken as positive in compression and negative in
tension.
stress without consideration of lateral bending at
the brace point opposite to the one corresponding
to f2, calculated from the moment envelope value
that produces the largest compression at this
point in the flange under consideration, or the
smallest tension if this point is never in
compression (ksi). f0 shall be due to the factored
loads and shall be taken as positive in
compression and negative in tension.
stress without consideration of lateral bending at
the brace point opposite to the one corresponding
to f2, calculated as the intercept of the most
critical assumed linear stress variation passing
Eq. 6.10.8.2.3-8 provides an accurate to conservative
estimate of the compression flange elastic lateral torsional
buckling resistance, including the effect of the distortional
flexibility of the web (White, 2004). Eq. 6.10.8.2.3-9 is a
simplification of the above rt equation obtained by assuming
D = h = d. For sections with thick flanges, Eq. 6.10.8.2.3-9
gives an rt value that can be as much as three to four percent
conservative relative to the exact equation. Use of
Eq. C6.10.8.2.3-1 is permitted for software calculations or if
the Engineer requires a more precise calculation of the elastic
LTB resistance. The other key simplification in
Eq. 6.10.8.2.3-8 is that the St. Venant torsional constant J is
assumed equal to zero. This simplification is prudent for
cases such as longitudinally-stiffened girders with web
slenderness values approaching the maximum limit of
Eq. 6.10.2.1.2-1. For these types of sections, the contribution
of J to the elastic lateral torsional buckling resistance is
generally small and is likely to be reduced due to distortion of
the web into an S shape and the corresponding raking of the
compression flange relative to the tension flange. However,
for sections that have web slenderness values approaching the
noncompact limit given by Eq. 6.10.6.2.3-1 and listed for
different yield strengths in Table C6.10.1.10.2-2, the
assumption of J = 0 is convenient but tends to be
conservative. For typical flexural I-sections with D/bfc > 2
and Iyc/Iyt ≥ 0.3, the effect of this assumption on the
magnitude of the noncompact bracing limit Lr is usually
smaller than ten percent (White, 2001).
Eqs. 6.10.8.2.3-8 and A6.3.3-8 provide one single
consistent representation of the elastic LTB resistance for all
types of I-section members. These equations give a
conservative representation of the elastic LTB resistance of
composite I-section members in negative flexure since they
neglect the restraint provided to the bottom compression
flange by the lateral and torsional stiffness of the deck. The
effects of this restraint are reduced in general by web
distortion. The benefits of this restraint are judged to not be
worth the additional complexity associated with a general
distortional buckling solution, particularly if it is suspected
that less than effectively fixed torsional restraint is provided
to a relatively large bridge I-girder by the deck.
The Engineer should note the importance of the web
term Dctw within Eq. 6.10.8.2.3-9. Prior Specifications have
often used the radius of gyration of only the compression
flange, ryc = bfc / √12, within the design equations for LTB.
This approximation can lead to significant unconservative
predictions relative to experimental and refined finiteelement results. The web term in Eq. 6.10.8.2.3-9 accounts
for the destabilizing effects of the flexural compression
within the web.
If Dctw/bfctfc in Eq. 6.10.8.2.3-9 is taken as a
representative value of 2.0, this equation reduces to 0.22bfc.
Based on this assumption and Fyc = 50 ksi, the compact
bracing limit is Lp = 5.4bfc and the noncompact bracing limit
given by Eq. 6.10.8.2.3-5 simplifies to Lr = 20bfc. Based on
these same assumptions, the equations of Articles B6.2.4 and
D6.4 give corresponding limits on Lb that are generally larger
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
through f2 and either fmid or f0, whichever
produces the smaller value of Cb (ksi). f1 may be
determined as follows:
•
When the variation in the moment along the entire
length between the brace points is concave in shape:
(6.10.8.2.3-10)
f1 = f 0
•
Otherwise:
f1 = 2 f mid − f 2 ≥ f0
f2
=
Rb =
Rh =
(6.10.8.2.3-11)
except as noted below, largest compressive stress
without consideration of lateral bending at either
end of the unbraced length of the flange under
consideration, calculated from the critical
moment envelope value (ksi). f2 shall be due to
the factored loads and shall be taken as positive.
If the stress is zero or tensile in the flange under
consideration at both ends of the unbraced length,
f2 shall be taken as zero.
web load-shedding factor determined as specified
in Article 6.10.1.10.2
hybrid factor determined as specified in
Article 6.10.1.10.1
For unbraced lengths where the member consists of
noncomposite monosymmetric sections and is subject to
reverse curvature bending, the lateral torsional buckling
resistance shall be checked for both flanges, unless the top
flange is considered to be continuously braced.
For unbraced lengths in which the member is
nonprismatic, the lateral torsional buckling resistance of
the compression flange Fnc at each section within the
unbraced length may be taken as the smallest resistance
within the unbraced length under consideration determined
from Eq. 6.10.8.2.3-1, 6.10.8.2.3-2, or 6.10.8.2.3-3, as
applicable, assuming the unbraced length is prismatic. The
moment gradient modifier, Cb, shall be taken equal to 1.0
in this case and Lb shall not be modified by an effective
length factor.
For unbraced lengths containing a transition to a
smaller section at a distance less than or equal to
20 percent of the unbraced length from the brace point
with the smaller moment, the lateral torsional buckling
resistance may be determined assuming the transition to
the smaller section does not exist provided the lateral
moment of inertia of the flange or flanges of the smaller
section is equal to or larger than one-half the
corresponding value in the larger section.
than 5.4 bfc. The limit given in Article B6.2.4 is sufficient to
permit moment redistribution at interior-pier sections of
continuous-span members. The limit given in Article D6.4 is
sufficient to develop Fmax or Mmax shown in
Figure C6.10.8.2.1-1 in cases involving a moment gradient
along the unbraced length for which Cb > 1.0.
The effect of the variation in the moment along the
length between brace points is accounted for by the
moment gradient modifier, Cb. Cb has a base value of 1.0
when the moment and the corresponding flange
compressive major-axis bending stress are constant over
the unbraced length. Cb may be conservatively taken equal
to 1.0 for all cases, with the exception of some unusual
circumstances involving no cross-bracing within the span
or cantilever beams with significant top-flange loading as
discussed below.
The procedure for calculation of Cb retains
Eq. 6.10.8.2.3-7 from the previous Specifications;
however, the definition of when Cb is to be taken equal to
1.0 and the specific calculation of the terms f1 and f2 in
Eq. 6.10.8.2.3-7 have been modified to remove ambiguities
and to address a number of potentially important cases
where the prior Cb calculations are significantly
unconservative relative to more refined solutions. One
specific example is a simply-supported member supporting
its own weight as well as a uniform transverse load, but
braced only at its ends and its mid-span. This ideal case is
representative of potential erection conditions in which the
number of cross-frames within the superstructure is
minimal and the superstructure is being considered in its
noncomposite condition prior to hardening of a cast-inplace concrete slab. For this case, the prior Specifications
give a Cb value of 1.75 whereas the more accurate
equations from AISC (1999) give a Cb value of 1.30. The
smaller Cb value of 1.30 is due to the parabolic shape of
the moment diagram, and the fact that the flange
compression is significantly larger within the unbraced
lengths than the linear variation implicitly assumed in the
prior application of Eq. 6.10.8.2.3-7.
The procedure for calculation of Cb in these provisions
addresses the above issues by utilizing the stress due to the
factored loads at the middle of the unbraced length of the
flange under consideration, fmid. If fmid is greater than or
equal to the largest compressive stress in the flange due to
the factored loads at either end of the unbraced length, f2,
Cb is taken equal to 1.0. Also, in rare situations where the
flange stress is zero or tensile at both ends of its unbraced
length, for which f2 is defined as zero, Cb is taken equal to
1.0. This type of situation occurs only for members with
very large unbraced lengths such as simply-supported or
continuous spans with no cross-bracing within the span.
For unbraced cantilevers, Cb is also taken equal to 1.0,
consistent with AASHTO (2004) and AISC (2005).
For all other cases, significant beneficial and calculable
moment gradient effects exist. In these cases,
Eq. 6.10.8.2.3-7 requires the approximation of the stress
variation along the unbraced length as the most critical of:
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SECTION 6: STEEL STRUCTURES
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(1) a line that passes through f2 and fmid or (2) a line that
passes between f2 and the calculated stress in the flange
under consideration at the opposite end of the unbraced
length, f0, whichever produces the smaller value of Cb. The
intercept of this most critical assumed linear stress variation
at the opposite end from f2 is denoted as f1. For the specific
example cited above, this procedure gives a Cb value of 1.30,
which is identical to the Cb value predicted by the more
refined AISC (2005) equation. In all cases where fmid is
smaller in magnitude than the average of f0 and f2, or when
the moment diagram or envelope along the entire length
between brace points is concave in shape, f1 and f2 in
Eq. 6.10.8.2.3-7 are always equal to the stresses at the ends
of the unbraced length in the flange under consideration; that
is, f1 = f0. Sample illustrations of the calculation of the Cb
factor for various cases are provided at the end of
Appendix C6.
For unbraced lengths where the member consists of
monosymmetric noncomposite I-sections and is subject to
reverse curvature bending, the lateral torsional buckling
resistance must be checked in general for both flanges,
unless the top flange is considered to be continuously
braced. Since the flanges are of different sizes in these
types of sections, the lateral torsional buckling resistance
may be governed by compression in the smaller flange,
even though this compressive stress may be smaller than
the maximum compression in the larger flange. The
specified approach generally produces accurate to
conservative values of Cb for these cases. For highly
monosymmetric sections and reverse curvature bending,
the values of Cb between 1.75 and 2.3 obtained using these
provisions are often significantly conservative relative to
refined calculations of the lateral torsional buckling
resistance, such as those provided by Kitipornchai and
Trahair (1986). However, these provisions are less
conservative than the resistances estimated by a refinement
of the AISC (2005) Cb equation given by Helwig et al.
(1997) when the transverse loading effects are small and
the variation of the moment along the unbraced length is
approximately linear. For other cases involving significant
transverse loading effects, the refined AISC equation
recommended by Helwig et al. (1997) gives more accurate
and less conservative results for unbraced lengths where
the member is subjected to reverse curvature bending. The
top flange of composite I-sections in unbraced lengths
where the member is subject to reverse curvature bending
need not be checked for lateral torsional buckling since the
flange is continuously braced.
Strict application of the Cb provisions would require
the consideration of the concurrent moments along the
unbraced length. This would necessitate the calculation of:
(1) the maximum possible value of f2 at the brace point
with the higher compressive stress using the critical
moment envelope value, along with calculation of fmid and
f0 using the concurrent moments, and (2) the maximum
possible compressive value of fmid using the critical
moment envelope value, along with the calculation of f0
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
and f2 using the concurrent moments. However, since
concurrent moments are normally not tracked in the
analysis, it is convenient and always conservative to use
the worst-case moment values to compute the above
stresses. The worst-case moment for calculation of f2 is the
critical envelope value, or the moment causing the largest
value of f2 in the flange under consideration. The worstcase moments used to compute f0 and fmid are the values
obtained from the moment envelopes that produce the
largest compressive stress, or the smallest tensile stress if
the point is never in compression, within the flange
under consideration at each of these locations. The
use of the worst-case moments to compute f2, fmid and f0 is
always conservative since it can be shown that a more
critical stress distribution along the unbraced length can
never exist for all possible concurrent loadings. This
includes any potential condition in which the stress is
smaller at the f2 or fmid locations, but in which the moment
gradient is also smaller thus producing a smaller value of
Cb. Furthermore, the use of the concurrent moments to
compute f0 and fmid for the loading that gives the largest
value of f2 always would result in a larger value of Cb for
this specific loading. Similarly, the use of the concurrent
moments to compute f2 and f0 for the loading that produces
the largest compressive value of fmid always would result in
a larger value of Cb for this specific loading.
The preceding guidelines are also applicable when
calculating Cb for compact and noncompact web sections
designed by Article A6.3.3. The use of the compressionflange major-axis bending stresses for calculating Cb is
strongly recommended for sections designed by
Article 6.10.8 since this practice better reflects the fact that
the dead and live load bending moments due to the
factored loads are applied to different sections in
composite girders. However, for convenience, the ratio of
the major-axis bending moments at the brace points may
be used in lieu of the ratio of the compression-flange
stresses if it is felt in the judgment of the Engineer that the
use of these alternative ratios does not have a significant
effect on the final calculated value of Cb. For compact and
noncompact web sections designed by Article A6.3.3, it is
specified that the major-axis bending moments be used
when computing Cb. Moments are used in Eq. A6.3.3-7
because the overall effect of applying the moments to the
different sections is less critical for these types of sections.
Where Cb is greater than 1.0, indicating the presence
of a significant beneficial moment gradient effect, the
lateral torsional buckling resistances may alternatively be
calculated by the equivalent procedures specified in
Article D6.4.1. Both the equations in this Article and in
Article D6.4.1 permit Fmax in Figure C6.10.8.2.1-1 to be
reached at larger unbraced lengths when Cb is greater than
1.0. The procedures in Article D6.4.1 allow the Engineer
to focus directly on the maximum unbraced length at
which the flexural resistance is equal to Fmax. The use of
these equivalent procedures is strongly recommended
when Cb values greater than 1.0 are utilized in the design.
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SECTION 6: STEEL STRUCTURES
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Although the calculation of Cb greater than 1.0 in
general can result in a dependency of the flexural
resistance on the applied loading, and hence subsequent
difficulties in load rating, a Cb value only slightly greater
than 1.0 is sufficient in most cases to develop the
maximum flexural resistance Fmax. As long as the
combination of the brace spacing and Cb > 1.0 is sufficient
to develop Fmax, the flexural resistance is independent of
the applied loading. Therefore, when Cb > 1.0 is used, it is
recommended that the unbraced lengths, Lb, at critical
locations be selected such that this condition is satisfied in
the final constructed condition. The provisions in this
Article tend to give values of Cb that are accurate to
significantly conservative. Therefore, if the above
guidelines are followed in design, it is unlikely that the
flexural resistance would differ from Fmax in any rating
situation, particularly if the Engineer was to use a more
refined calculation of Cb for the rating calculations. Other
more refined formulations for Cb may be found in
Galambos (1998).
The Cb equations in these provisions and in AISC
(2005) both neglect the effect of the location of the applied
load relative to the mid-height of the section. For unusual
situations with no intermediate cross-bracing and for
unbraced cantilevers with significant loading applied at the
level of the top flange, the Engineer should consider
including load-height effects within the calculation of Cb.
In these cases, the associated Cb values can be less than
1.0. Galambos (1998) gives equations for consideration of
load-height effects in simple or continuous spans, and
Dowswell (2002) gives solutions considering these effects
in unbraced cantilevers. When Cb < 1.0, Fn can be smaller
than Fmax in Figure C6.10.8.2.1-1 even when Lb is less than
or equal to Lp. Therefore, for Cb < 1.0, the resistance
should be calculated from Eq. 6.10.8.2.3-2 for Lb less than
or equal to Lr.
For rehabilitation design or in extraordinary
circumstances, the Engineer may consider modifying Lb by
an elastic effective length factor for lateral torsional
buckling. Galambos (1998) and Nethercot and Trahair
(1976) present a simple hand method that may be used for
this calculation.
Galambos (1998) provides general guidelines for
stability design of bracing systems. In past practice, points
of contraflexure sometimes have been considered as brace
points when the influence of moment gradient was not
included in the lateral-torsional buckling resistance
equations. In certain cases, this practice can lead to a
substantially unconservative estimate of the flexural
resistance. These Specifications do not intend for points of
contraflexure to be considered as brace points. The
influence of moment gradient may be accounted for
correctly through the use of Cb and the effect of restraint
from adjacent unbraced segments may be accounted for by
using an effective length factor less than 1.0.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
For the case of uniform bending, the reduction in the
elastic lateral-torsional buckling resistance due to a
transition to a smaller section is approximately five percent
when the transition is placed at 20 percent of the unbraced
length from one of the brace points and the lateral moment
of inertia of the flange in the smaller section is set at onehalf of the corresponding value in the larger section
(Carskaddan and Schilling, 1974). For moment gradient
cases in which the larger bending moment occurs within
the larger section, and/or where the section transition is
placed closer to the brace point, and/or where the lateral
moment of inertia of the flange of the smaller section is
larger than one-half of the corresponding value in the
larger section, the reduction in the lateral-torsional
buckling resistance is less than five percent. Since section
transitions are typically placed within regions having a
significant moment gradient, the effect of the section
transition on the lateral-torsional buckling resistance may
be neglected whenever the stated conditions are satisfied.
For a case with more than one transition, any transition
located within 20 percent of the unbraced length from the
brace point with the smaller moment may be ignored and
the lateral torsional buckling resistance of the remaining
nonprismatic unbraced length may then be computed as the
smallest resistance based on the remaining sections.
For unbraced lengths containing a transition to a
smaller section at a distance greater than 20 percent of the
unbraced length from the brace point with the smaller
moment, the lateral torsional buckling resistance should be
taken as the smallest resistance, Fnc, within the unbraced
length under consideration. This approximation is based on
replacing the nonprismatic member with an equivalent
prismatic member. The cross-section of the equivalent
member that gives the correct lateral torsional buckling
resistance is generally some weighted average of all the
cross-sections along the unbraced length. If the crosssection within the unbraced length that gives the smallest
uniform bending resistance is used, and the calculated
resistance is not exceeded at any section along the
unbraced length, a conservative solution is obtained. A
suggested procedure to provide a more refined estimate of
the lateral torsional buckling resistance for this case is
presented in Grubb and Schmidt (2004).
To avoid a significant reduction in the lateral torsional
buckling resistance, flange transitions can be located
within 20 percent of the unbraced length from the brace
point with the smaller moment, given that the lateral
moment of inertia of the flange or flanges of the smaller
section is equal to or larger than one-half of the
corresponding value in the larger section.
6.10.8.3—Tension-Flange Flexural Resistance
The nominal flexural resistance of the tension flange
shall be taken as:
Fnt = Rh Fyt
(6.10.8.3-1)
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SECTION 6: STEEL STRUCTURES
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where:
Rh =
hybrid factor determined as specified in
Article 6.10.1.10.1
6.10.9—Shear Resistance
6.10.9.1—General
C6.10.9.1
At the strength limit state, straight and curved web
panels shall satisfy:
Vu ≤ φvVn
(6.10.9.1-1)
where:
φv
=
Vn =
Vu =
resistance factor for shear specified in
Article 6.5.4.2
nominal shear resistance determined as specified
in Articles 6.10.9.2 and 6.10.9.3 for unstiffened
and stiffened webs, respectively (kip)
shear in the web at the section under
consideration due to the factored loads (kip)
Transverse intermediate stiffeners shall be designed as
specified in Article 6.10.11.1. Longitudinal stiffeners shall
be designed as specified in Article 6.10.11.3.
Interior web panels of nonhybrid and hybrid I-shaped
members:
•
Without a longitudinal stiffener and with a transverse
stiffener spacing not exceeding 3D, or
•
With one or more longitudinal stiffeners and with a
transverse stiffener spacing not exceeding 1.5D
shall be considered stiffened, and the provisions of
Article 6.10.9.3 shall apply. Otherwise, the panel shall be
considered unstiffened, and the provisions of
Article 6.10.9.2 shall apply.
For stiffened webs, provisions for end panels shall be
as specified in Article 6.10.9.3.3.
This Article applies to:
•
Sections without stiffeners,
•
Sections with transverse stiffeners only, and
•
Sections with both transverse and longitudinal
stiffeners.
A flowchart for determining the shear resistance of
I-sections is shown below.
Shear Resistance of
I-Sections
Hybrid and Non-Hybrid
Unstiffened
Stiffened
6.10.9.2
Shear Yield or
Shear Buckling
6.10.9.3
Interior
Panels
End
Panels
2Dt w
(bfc t fc + b ft t ft )
≤ 2 .5 ?
No
6.10.9.3.3
Shear Yield or
Shear Buckling
Yes
6.10.9.3.2
Eq. 6.10.9.3.2-8
Tension-Field Action
Figure C6.10.9.1-1—Flowchart for Shear Design of
I-Sections
Unstiffened and stiffened interior web panels are
defined according to the maximum transverse stiffener
spacing requirements specified in this Article.
The nominal shear resistance of unstiffened web
panels in both nonhybrid and hybrid members is defined
by either shear yielding or shear buckling, depending on
the web slenderness ratio, as specified in Article 6.10.9.2.
The nominal shear resistance of stiffened interior web
panels of both nonhybrid and hybrid members, where the
section along the entire panel is proportioned to satisfy
Eq. 6.10.9.3.2-1, is defined by the sum of the shearyielding or shear-buckling resistance and the postbuckling
resistance from tension-field action, as specified in
Article 6.10.9.3.2. Otherwise, the shear resistance is taken
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
as the shear resistance given by Eq. 6.10.9.3.2-8. Previous
Specifications did not recognize the potential for web
panels of hybrid members to develop postbuckling
resistance due to tension-field action. The applicability of
these provisions to the shear strength of curved nonhybrid
and hybrid webs is addressed by Zureick et al. (2002),
White et al. (2001), White and Barker (2004), White et al.
(2004), and Jung and White (2006).
For nonhybrid and hybrid members, the nominal shear
resistance of end panels in stiffened webs is defined by
either shear yielding or shear buckling, as specified in
Article 6.10.9.3.3.
6.10.9.2—Nominal Resistance of Unstiffened
Webs
The nominal shear resistance of unstiffened webs shall
be taken as:
Vn = Vcr = CV p
(6.10.9.2-1)
in which:
V p = 0.58 Fyw Dtw
(6.10.9.2-2)
where:
C
=
Vcr =
Vn =
Vp =
ratio of the shear-buckling resistance to the shear
yield strength determined by Eqs. 6.10.9.3.2-4,
6.10.9.3.2-5 or 6.10.9.3.2-6 as applicable, with
the shear-buckling coefficient, k, taken equal to
5.0
shear-buckling resistance (kip)
nominal shear resistance (kip)
plastic shear force (kip)
C6.10.9.2
The consideration of tension-field action (Basler,
1961) is not permitted for unstiffened web panels. The
elastic shear-yielding or shear-buckling resistance is
calculated as the product of the constant C specified in
Article 6.10.9.3.2 times the plastic shear force, Vp, given
by Eq. 6.10.9.2-2. The plastic shear force is equal to the
web area times the assumed shear yield strength of
Fyw 3 . The shear-buckling coefficient, k, to be used in
calculating the constant C is defined as 5.0 for unstiffened
web panels, which is a conservative approximation of the
exact value of 5.35 for an infinitely long strip with simplysupported edges (Timoshenko and Gere, 1961).
6.10.9.3—Nominal Resistance of Stiffened Webs
6.10.9.3.1—General
C6.10.9.3.1
The nominal shear resistance of transversely or
transversely and longitudinally-stiffened interior web
panels shall be as specified in Articles 6.10.9.3.2. The
nominal shear resistance of transversely or transversely
and longitudinally-stiffened end web panels shall be as
specified in Articles 6.10.9.3.3. The total web depth, D,
shall be used in determining the nominal shear resistance
of web panels with longitudinal stiffeners. The required
transverse stiffener spacing shall be calculated using the
maximum shear in a panel.
Stiffeners shall satisfy the requirements specified in
Article 6.10.11.
Longitudinal stiffeners divide a web panel into
subpanels. In Cooper (1967), the shear resistance of the
entire panel is taken as the sum of the shear resistance of
the subpanels. However, the contribution to the shear
resistance of a single longitudinal stiffener located at its
optimum position for flexure is relatively small. Thus, it is
conservatively specified that the influence of the
longitudinal stiffener be neglected in computing the
nominal shear resistance of the web plate.
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SECTION 6: STEEL STRUCTURES
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6.10.9.3.2—Interior Panels
C6.10.9.3.2
The nominal shear resistance of an interior web
panel complying with the provisions of Article 6.10.9.1,
and with the section along the entire panel proportioned
such that:
(b
2 Dtw
t + b ft t ft )
(6.10.9.3.2-1)
≤ 2.5
fc fc
shall be taken as:
0.87 (1 − C )
Vn = V p C +
2
do
+
1
D
(6.10.9.3.2-2)
in which:
V p = 0.58 Fyw Dtw
(6.10.9.3.2-3)
where:
do =
Vn =
Vp =
C =
transverse stiffener spacing (in.)
nominal shear resistance of the web panel
(kip)
plastic shear force (kip)
ratio of the shear-buckling resistance to the shear
yield strength
The ratio, C, shall be determined as specified below:
•
If
D
Ek
≤ 1.12
, then:
tw
Fyw
C = 1.0
•
If 1.12
C=
•
If
(6.10.9.3.2-4)
Ek D
Ek
< ≤ 1.40
, then:
Fyw tw
Fyw
1.12 Ek
D Fyw
tw
(6.10.9.3.2-5)
D
Ek
> 1.40
, then:
tw
Fyw
C=
1.57 Ek
2
D Fyw
tw
(6.10.9.3.2-6)
Stiffened interior web panels of nonhybrid and hybrid
members satisfying Eq. 6.10.9.3.2-1 are capable of
developing postbuckling shear resistance due to tension-field
action (Basler, 1961; White et al., 2004). This action is
analogous to that of the tension diagonals of a Pratt truss.
The nominal shear resistance of these panels can be
computed by summing the contributions of beam action and
post-buckling tension-field action. The resulting expression
is given in Eq. 6.10.9.3.2-2, where the first term in the
bracket relates to either the shear yield or shear-buckling
force and the second term relates to the postbuckling
tension-field force. If Eq. 6.10.9.3.2-1 is not satisfied, the
total area of the flanges within the panel is small relative to
the area of the web and the full postbuckling resistance
generally cannot be developed (White et al., 2004).
However, it is conservative in these cases to use the
postbuckling resistance given by Eq. 6.10.9.3.2-8.
Eq. 6.10.9.3.2-8 gives the solution neglecting the increase in
stress within the wedges of the web panel outside of the
tension band implicitly included within the Basler model
(Gaylord, 1963; Salmon and Johnson, 1996).
Within the restrictions specified by Eqs. 6.10.9.3.2-1
and 6.10.2.2-2 in general, and Article 6.10.9.3.1 for
longitudinally-stiffened I-girders in particular, and provided
that the maximum moment within the panel is utilized in
checking the flexural resistance, White et al. (2004) shows
that the equations of these Specifications sufficiently capture
the resistance of a reasonably comprehensive body of
experimental test results without the need to consider
moment-shear interaction. In addition, the additional shear
resistance and anchorage of tension field action provided by
a composite deck are neglected within the shear resistance
provisions of these Specifications. Also, the maximum
moment and shear envelope values are typically used for
design, whereas the maximum concurrent moment and shear
values tend to be less critical. These factors provide some
additional margin of conservatism beyond the sufficient
level of safety obtained if these factors do not exist.
Therefore, previous provisions related to the effects of
moment-shear interaction are not required in these
Specifications.
The coefficient, C, is equal to the ratio of the elastic
buckling stress of the panel, computed assuming simplysupported boundary conditions, to the shear yield strength
assumed to equal Fyw/√3. Eq. 6.10.9.3.2-6 is applicable
only for C values not exceeding 0.8 (Basler, 1961). Above
0.8, C values are given by Eq. 6.10.9.3.2-5 until a limiting
slenderness ratio is reached where the shear-buckling
stress is equal to the shear yield strength and C = 1.0.
Eq. 6.10.9.3.2-7 for the shear-buckling coefficient is a
simplification of two exact equations for k that depend on
the panel aspect ratio. The coefficients within
Eqs. 6.10.9.3.2-4 through 6.10.9.3.2-6 have been modified
slightly from the values given in previous Specifications to
correct minor round-off errors.
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in which:
k
=
shear-buckling coefficient
= 5+
5
do
D
(6.10.9.3.2-7)
2
Because the slenderness of webs without longitudinal
stiffeners is limited to 150 according to the provisions of
Article 6.10.2.1.1, the separate handling requirement given
in previous Specifications for web panels without
longitudinal stiffeners is not required and is omitted in
these Specifications.
Otherwise, the nominal shear resistance shall be taken
as follows:
0.87(1 − C )
Vn = V p C +
2
d
d
1+ o + o
D
D
(6.10.9.3.2-8)
6.10.9.3.3—End Panels
C6.10.9.3.3
The nominal shear resistance of a web end panel shall
be taken as:
(6.10.9.3.3-1)
Vn = Vcr = CV p
in which:
(6.10.9.3.3-2)
V p = 0.58 Fyw Dtw
The shear in end panels adjacent to simple supports is
limited to either the shear-yielding or shear-buckling
resistance given by Eq. 6.10.9.3.3-1 in order to provide an
anchor for the tension field in adjacent interior panels. The
shear-buckling coefficient, k, to be used in determining the
constant C in Eq. 6.10.9.3.3-1 is to be calculated based on
the spacing from the support to the first stiffener adjacent
to the support, which may not exceed 1.5D.
where:
ratio of the shear-buckling resistance to the shear
yield strength determined by Eqs. 6.10.9.3.2-4,
6.10.9.3.2-5, or 6.10.9.3.2-6 as applicable
Vcr = shear-buckling resistance (kip)
Vp = plastic shear force (kip)
The transverse stiffener spacing for end panels with or
without longitudinal stiffeners shall not exceed 1.5D.
C
=
6.10.10—Shear Connectors
6.10.10.1—General
C6.10.10.1
In composite sections, stud or channel shear connectors
shall be provided at the interface between the concrete deck
and the steel section to resist the interface shear.
Simple span composite bridges shall be provided with
shear connectors throughout the length of the span.
Straight continuous composite bridges should
normally be provided with shear connectors throughout the
length of the bridge. In the negative flexure regions, shear
connectors shall be provided where the longitudinal
reinforcement is considered to be a part of the composite
section. Otherwise, shear connectors need not be provided
in negative flexure regions, but additional connectors shall
be placed in the region of the points of permanent load
contraflexure as specified in Article 6.10.10.3.
Shear connectors help control cracking in regions of
negative flexure where the deck is subject to tensile stress
and has longitudinal reinforcement.
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Where shear connectors are omitted in negative
flexure regions, the longitudinal reinforcement shall be
extended into the positive flexure region as specified in
Article 6.10.1.7.
Curved continuous composite bridges shall be
provided with shear connectors throughout the length of
the bridge.
Shear connectors are to be provided in regions of
negative flexure in curved continuous bridges because
torsional shear exists and is developed in the full
composite section along the entire bridge. For bridges
containing one or more curved segments, the effects of
curvature usually extend beyond the curved segment.
Therefore, it is conservatively specified that shear
connectors be provided along the entire length of the
bridge in this case as well.
6.10.10.1.1—Types
Stud and channel shear connectors shall be designed by
the provisions of this Article.
Shear connectors should be of a type that permits a
thorough compaction of the concrete to ensure that their
entire surfaces are in contact with the concrete. The
connectors shall be capable of resisting both horizontal and
vertical movement between the concrete and the steel.
The ratio of the height to the diameter of a stud shear
connector shall not be less than 4.0.
Channel shear connectors shall have fillet welds not
smaller than 0.1875 in. placed along the heel and toe of the
channel.
6.10.10.1.2—Pitch
C6.10.10.1.2
The pitch of the shear connectors shall be determined
to satisfy the fatigue limit state, as specified in
Article 6.10.10.2 and 6.10.10.3. The resulting number of
shear connectors shall not be less than the number required
to satisfy the strength limit state as specified in
Article 6.10.10.4.
The pitch, p, of shear connectors shall satisfy:
p≤
nZ r
Vsr
(6.10.10.1.2-1)
in which:
Vsr =
=
Vfat =
=
Ffat =
horizontal fatigue shear range per unit length
(kip/in.)
(V ) + ( F )
2
fat
fat
2
(6.10.10.1.2-2)
longitudinal fatigue shear range per unit length
(kip/in.)
Vf Q
(6.10.10.1.2-3)
I
radial fatigue shear range per unit length (kip/in.)
taken as the larger of either:
At the fatigue limit state, shear connectors are designed
for the range of live load shear between the deck and top
flange of the girder. In straight girders, the shear range
normally is due to only major-axis bending if torsion is
ignored. Curvature, skew and other conditions may cause
torsion, which introduces a radial component of the
horizontal shear. These provisions provide for consideration
of both of the components of the shear to be added vectorially
according to Eq. 6.10.10.1.2-2.
The parameters I and Q should be determined using the
deck within the effective flange width. However, in negative
flexure regions of straight girders only, the parameters I and
Q may be determined using the longitudinal reinforcement
within the effective flange width for negative moment, unless
the concrete deck is considered to be effective in tension for
negative moment in computing the range of the longitudinal
stress, as permitted in Article 6.6.1.2.1.
The maximum longitudinal fatigue shear range, Vfat, is
produced by placing the fatigue live load immediately to
the left and to the right of the point under consideration.
For the load in these positions, positive moments are
produced over significant portions of the girder length.Thus,
the use of the full composite section, including the concrete
deck, is reasonable for determining the stiffness used to
determine the shear range along the entire span. Also, the
horizontal shear force in the deck is most often considered to
be effective along the entire span in the analysis. To satisfy
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
6-156
F fat1 =
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Abot σ flg
(6.10.10.1.2-4)
wR
or:
Ffat 2 =
Frc
w
(6.10.10.1.2-5)
where:
σflg =
Abot =
Frc =
I
=
ℓ
n
p
=
=
=
Q
=
R
Vf
=
=
w
=
Zr =
range of longitudinal fatigue stress in the bottom
flange without consideration of flange lateral
bending (ksi)
area of the bottom flange (in.2)
net range of cross-frame or diaphragm force at
the top flange (kip)
moment of inertia of the short-term composite
section (in.4)
distance between brace points (ft)
number of shear connectors in a cross-section
pitch of shear connectors along the longitudinal
axis (in.)
first moment of the transformed short-term area
of the concrete deck about the neutral axis of the
short-term composite section (in.3)
minimum girder radius within the panel (ft)
vertical shear force range under the applicable
fatigue load combination specified in
Table 3.4.1-1 with the fatigue live load taken as
specified in Article 3.6.1.4 (kip)
effective length of deck (in.) taken as 48.0 in.,
except at end supports where w may be taken as
24.0 in.
shear fatigue resistance of an individual shear
connector determined as specified in
Article 6.10.10.2 (kip)
For straight spans or segments, the radial fatigue shear
range from Eq. 6.10.10.1.2-4 may be taken equal to zero.
For straight or horizontally curved bridges with skews not
exceeding 20 degrees, the radial fatigue shear range from
Eq. 6.10.10.1.2-5 may be taken equal to zero.
The center-to-center pitch of shear connectors shall
not exceed 24.0 in. and shall not be less than six stud
diameters.
this assumption, the shear force in the deck should be
developed along the entire span. For straight girders, an
option is permitted to ignore the concrete deck in computing
the shear range in regions of negative flexure, unless the
concrete is considered to be effective in tension in computing
the range of the longitudinal stress, in which case the shear
force in the deck must be developed. If the concrete is
ignored in these regions, the maximum pitch specified at the
end of this Article must not be exceeded.
The radial shear range, Ffat, typically is determined for
the fatigue live load positioned to produce the largest
positive and negative major-axis bending moments in the
span. Therefore, vectorial addition of the longitudinal and
radial components of the shear range is conservative
because the longitudinal and radial shears are not produced
by concurrent loads.
Eq. 6.10.10.1.2-4 may be used to determine the radial
fatigue shear range resulting from the effect of any
curvature between brace points. The shear range is taken
as the radial component of the maximum longitudinal
range of force in the bottom flange between brace points,
which is used as a measure of the major-axis bending
moment. The radial shear range is distributed over an
effective length of girder flange, w. At end supports, w is
halved. Eq. 6.10.10.1.2-4 gives the same units as Vfat.
Eq. 6.10.10.1.2-5 will typically govern the radial
fatigue shear range where torsion is caused by effects other
than curvature, such as skew. Eq. 6.10.10.1.2-5 is most
likely to control when discontinuous cross-frame or
diaphragm lines are used in conjunction with skew angles
exceeding 20 degrees in either a straight or horizontally
curved bridge. For all other cases, Frc can be taken equal to
zero. Eqs. 6.10.10.1.2-4 and 6.10.10.1.2-5 yield
approximately the same value if the span or segment is
curved and there are no other sources of torsion in the
region under consideration. Note that Frc represents the
resultant range of horizontal force from all cross-frames or
diaphragms at the point under consideration due to the
factored fatigue load plus impact that is resisted by the
shear connectors. In lieu of a refined analysis, Frc may be
taken as 25.0 kips for an exterior girder, which is typically
the critical girder. Frc should not be multiplied by the
factor 0.75 discussed in Article C6.6.1.2.1.
Eqs. 6.10.10.1.2-4 and 6.10.10.1.2-5 are provided to
ensure that a load path is provided through the shear
connectors to satisfy equilibrium at a transverse section
through the girders, deck, and cross-frame or diaphragm.
6.10.10.1.3—Transverse Spacing
Shear connectors shall be placed transversely across
the top flange of the steel section and may be spaced at
regular or variable intervals.
Stud shear connectors shall not be closer than 4.0 stud
diameters center-to-center transverse to the longitudinal
axis of the supporting member.
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2012
Edition
Next Page
SECTION 6: STEEL STRUCTURES
6-157
The clear distance between the edge of the top flange
and the edge of the nearest shear connector shall not be
less than 1.0 in.
6.10.10.1.4—Cover and Penetration
C6.10.10.1.4
The clear depth of concrete cover over the tops of the
shear connectors should not be less than 2.0 in. Shear
connectors should penetrate at least 2.0 in. into the
concrete deck.
6.10.10.2—Fatigue Resistance
C6.10.10.2
The fatigue shear resistance of an individual stud
shear connector, Zr, shall be taken as:
For stud type shear connectors:
•
Where the projected 75-year single lane Average
Daily Truck Traffic (ADTT)SL is greater than or equal
to 960 trucks per day, the Fatigue I load combination
shall be used and the fatigue shear resistance for
infinite life shall be taken as:
Z r = 5.5d 2
•
(6.10.10.2-1)
Otherwise, the Fatigue II load combination shall be
used and the fatigue shear resistance for finite life
shall be taken as:
Z r = αd 2
Stud shear connectors should penetrate through the
haunch between the bottom of the deck and the top flange,
if present, and into the deck. Otherwise, the haunch should
be reinforced to contain the stud connector and develop its
load in the deck.
(6.10.10.2-2)
2013 Revision
For the development of this information, see Slutter
and Fisher (1966).
The values of (ADTT)SL specified in this Article were
determined by equating infinite and finite life resistances
with due regard to the difference in load factors used with
the Fatigue I and Fatigue II load combinations. A fatigue
design life of 75 yr and a number of stress range cycles per
truck passage, n, equal to 1.0 were also assumed. For other
values of the fatigue design life, the specified value of
(ADTT)SL for stud shear connectors should be modified by
multiplying the value by the ratio of 71,768 divided by the
fatigue life sought in years; the specified value of
(ADTT)SL for channel shear connectors should be modified
by multiplying the value by the ratio of 138,488 divided by
the fatigue life sought in years. For other values of n, the
values of (ADTT)SL should be modified by dividing by the
appropriate value of n taken from Table 6.6.1.2.5-2.
in which:
α = 34.5 − 4.28 log N
(6.10.10.2-3)
For channel-type shear connectors:
•
Where the projected 75-year single lane Average
Daily Truck Traffic (ADTT)SL is greater than or equal
to 1850 trucks per day, the Fatigue I load combination
shall be used and the fatigue shear resistance for
infinite life shall be taken as:
Z r = 2.1w
•
(6.10.10.2-4)
Otherwise, the Fatigue II load combination shall be
used and the fatigue shear resistance for finite life
shall be taken as:
Z r = Bw
(6.10.10.2-5)
in which:
B = 9.37 − 1.08 log N
(6.10.10.2-6)
where:
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
2013 INTERIM REVISIONS TO THE AASHTO LFRD
BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
SECTION 7
Section 7 Has Been Replaced In Its
Entirety Due to Extreme Revisions
Pages 117–188 have been renumbered as Section 7 to retain the format for the
Table of Contents. (Interim pagination will resume with Section 9)
7-i
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2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2013
Revision
2013 INTERIM REVISIONS TO THE AASHTO LFRD
BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
SECTION 7
SECTION 7: ALUMINUM STRUCTURES
TABLE OF CONTENTS
7.1—SCOPE .................................................................................................................................................................7-1
7.2—DEFINITIONS .....................................................................................................................................................7-1
7.3—NOTATION .........................................................................................................................................................7-1
7.4—MATERIALS .......................................................................................................................................................7-6
7.4.1—Aluminum Alloys .......................................................................................................................................7-6
7.4.2—Pins, Rollers, and Rockers .........................................................................................................................7-7
7.4.3—Bolts, Nuts, and Washers ...........................................................................................................................7-8
7.4.3.1—Bolts .................................................................................................................................................7-8
7.4.3.2—Nuts ..................................................................................................................................................7-8
7.4.3.3—Washers ............................................................................................................................................7-8
7.4.3.4—Alternative Fasteners........................................................................................................................7-8
7.4.3.5—Load Indicator Devices ....................................................................................................................7-8
7.4.4—Shear Connectors .......................................................................................................................................7-8
7.4.5—Weld Metal.................................................................................................................................................7-8
7.5—LIMIT STATES ...................................................................................................................................................7-9
7.5.1—General .......................................................................................................................................................7-9
7.5.2—Service Limit State .....................................................................................................................................7-9
7.5.3—Fatigue Limit State .....................................................................................................................................7-9
7.5.4—Strength Limit State ...................................................................................................................................7-9
7.5.4.1—General .............................................................................................................................................7-9
7.5.4.2—Resistance Factors ............................................................................................................................7-9
7.5.4.3—Buckling Constants ........................................................................................................................ 7-10
7.5.4.4—Nominal Resistance of Elements in Uniform Compression .......................................................... 7-11
7.5.4.4.1—General ................................................................................................................................. 7-11
7.5.4.4.2—Flat Elements Supported on One Edge ................................................................................7-12
7.5.4.4.3—Flat Elements Supported on Both Edges.............................................................................. 7-12
7.5.4.4.4—Flat Elements Supported on One Edge and with a Stiffener on the Other Edge .................. 7-13
7.5.4.4.5—Flat Elements Supported on Both Edges and with an Intermediate Stiffener ...................... 7-14
7.5.4.4.6—Pipes, Tubes, and Curved Elements Supported on Both Edges ........................................... 7-15
7.5.4.4.7—Alternative Method for Flat Elements..................................................................................7-16
7.5.4.5—Nominal Resistance of Elements in Flexural Compression ........................................................... 7-16
7.5.4.5.1—General ................................................................................................................................. 7-17
7.5.4.5.2—Flat Elements Supported on Both Edges.............................................................................. 7-17
7.5.4.5.3—Flat Elements Supported on One Edge, Compression Edge Free ........................................ 7-18
7.5.4.5.4—Flat Elements Supported on Both Edges and with a Longitudinal Stiffener ........................ 7-19
7.5.4.5.5—Alternative Method for Flat Elements..................................................................................7-20
7.5.4.6—Nominal Resistance of Elements in Uniform Tension .................................................................. 7-20
7.5.4.7—Nominal Resistance of Elements in Flexural Tension ................................................................... 7-21
7.5.4.8—Nominal Resistance of Elements in Shear .................................................................................... 7-22
7-ii
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2012 by the American Association of State Highway and Transportation Officials.
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2013
Revision
2013 INTERIM REVISIONS TO THE AASHTO LFRD
BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
SECTION 7
7.5.4.8.1—General ................................................................................................................................ 7-22
7.5.4.8.2—Flat Elements Supported on Both Edges ............................................................................. 7-22
7.5.4.8.3—Flat Elements Supported on One Edge ................................................................................ 7-24
7.5.4.8.4—Round or Oval Tubes ........................................................................................................... 7-25
7.5.4.9—Elastic Buckling Stress of Elements .............................................................................................. 7-25
7.5.5—Extreme Event Limit State ....................................................................................................................... 7-26
7.6—FATIGUE .......................................................................................................................................................... 7-26
7.6.1—General ..................................................................................................................................................... 7-26
7.6.2—Load-Induced Fatigue .............................................................................................................................. 7-26
7.6.2.1—Application .................................................................................................................................... 7-26
7.6.2.2—Design Criteria ............................................................................................................................... 7-27
7.6.2.3—Detail Categories ........................................................................................................................... 7-27
7.6.2.4—Detailing to Reduce Constraint ...................................................................................................... 7-33
7.6.2.5—Fatigue Resistance ......................................................................................................................... 7-33
7.6.3—Distortion-Induced Fatigue ...................................................................................................................... 7-34
7.6.3.1—Transverse Connection Plates ........................................................................................................ 7-34
7.6.3.2—Lateral Connection Plates .............................................................................................................. 7-34
7.7—GENERAL DIMENSION AND DETAIL REQUIREMENTS ......................................................................... 7-34
7.7.1—Effective Length of Span ......................................................................................................................... 7-34
7.7.2—Dead Load Camber .................................................................................................................................. 7-34
7.7.3—Minimum Thickness ................................................................................................................................ 7-34
7.7.4—Diaphragms and Cross-Frames ................................................................................................................ 7-34
7.7.5—Lateral Bracing ........................................................................................................................................ 7-34
7.7.6—Pins .......................................................................................................................................................... 7-35
7.7.6.1—Location ......................................................................................................................................... 7-35
7.7.6.2—Strength Limit State ....................................................................................................................... 7-35
7.7.6.2.1—Combined Flexure and Shear............................................................................................... 7-35
7.7.6.2.2—Bearing ................................................................................................................................ 7-35
7.7.6.3—Pins and Pin Nuts ........................................................................................................................... 7-36
7.8—TENSION MEMBERS ...................................................................................................................................... 7-36
7.8.1—General ..................................................................................................................................................... 7-36
7.8.2—Tensile Resistance.................................................................................................................................... 7-37
7.8.2.1—General .......................................................................................................................................... 7-37
7.8.2.2—Effective Net Area ......................................................................................................................... 7-37
7.8.2.3—Combined Tension and Flexure ..................................................................................................... 7-38
7.8.3—Net Area ................................................................................................................................................... 7-38
7.8.4—Limiting Slenderness Ratio ...................................................................................................................... 7-39
7.8.5—Built-up Members .................................................................................................................................... 7-39
7.9—COMPRESSION MEMBERS ........................................................................................................................... 7-39
7.9.1—General ..................................................................................................................................................... 7-39
7.9.2—Axial Compression Resistance ................................................................................................................ 7-39
7.9.2.1—Member Buckling .......................................................................................................................... 7-40
7.9.2.1.1—General ................................................................................................................................ 7-40
7-iii
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2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2013
Revision
2013 INTERIM REVISIONS TO THE AASHTO LFRD
BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
SECTION 7
7.9.2.1.2—Flexural Buckling ................................................................................................................ 7-41
7.9.2.1.3—Torsional and Flexural-Torsional Buckling ......................................................................... 7-41
7.9.2.2—Local Buckling ............................................................................................................................... 7-42
7.9.2.2.1—General ................................................................................................................................. 7-42
7.9.2.2.2—Weighted Average Local Buckling Resistance .................................................................... 7-42
7.9.2.2.3—Alternative Local Buckling Resistance ................................................................................7-43
7.9.2.3—Interaction Between Member Buckling and Local Buckling ......................................................... 7-43
7.9.3—Limiting Slenderness Ratio ...................................................................................................................... 7-43
7.9.4—Combined Axial Compression and Flexure ............................................................................................. 7-43
7.10—GENERAL FLEXURAL MEMBERS ............................................................................................................. 7-44
7.10.1—General ................................................................................................................................................... 7-44
7.10.2—Flexural Resistance ................................................................................................................................ 7-44
7.10.2.1—General ......................................................................................................................................... 7-44
7.10.2.2—Lateral-Torsional Buckling .......................................................................................................... 7-45
7.10.2.2.1—Open Shapes ...................................................................................................................... 7-45
7.10.2.2.2—Closed Shapes .................................................................................................................... 7-47
7.10.2.2.3—Moment Gradient Modifier ................................................................................................ 7-47
7.10.2.2.3a—Doubly Symmetric Shapes ........................................................................................ 7-47
7.10.2.2.3b—Singly Symmetric Shapes ......................................................................................... 7-48
7.10.2.2.4—Welded Flexural Members ................................................................................................. 7-48
7.10.2.2.4a—Flexural Members with Transverse Welds................................................................ 7-48
7.10.2.2.4b—Flexural Members with Longitudinal Welds ............................................................ 7-49
7.10.2.3—Elements of Flexural Members .................................................................................................... 7-49
7.10.2.3.1—Tension .............................................................................................................................. 7-49
7.10.2.3.2—Compression ...................................................................................................................... 7-49
7.10.2.3.3—Weighted Average Flexural Resistance ............................................................................. 7-50
7.10.3—Shear Resistance .................................................................................................................................... 7-51
7.10.4—Stiffeners ................................................................................................................................................ 7-51
7.10.4.1—Crippling of Flat Webs ........................................................................................................................ 7-51
7.10.4.2—Bearing Stiffeners ........................................................................................................................ 7-53
7.10.4.3—Combined Crippling and Bending of Flat Webs ..........................................................................7-53
7.11—MISCELLANEOUS FLEXURAL MEMBERS .............................................................................................. 7-53
7.11.1—General ................................................................................................................................................... 7-53
7.11.2—Rectangular Bars .................................................................................................................................... 7-54
7.11.2.1—Yielding and Rupture ................................................................................................................... 7-54
7.11.2.2—Lateral-Torsional Buckling .......................................................................................................... 7-54
7.11.3—Single Angles ......................................................................................................................................... 7-55
7.11.4—Pipes and Round Tubes .......................................................................................................................... 7-55
7.11.4.1—Yielding and Rupture ................................................................................................................... 7-55
7.11.4.2—Local Buckling ............................................................................................................................. 7-55
7.11.5—Rods ....................................................................................................................................................... 7-56
7.12—CONNECTIONS AND SPLICES.................................................................................................................... 7-57
7.12.1—General ................................................................................................................................................... 7-57
7.12.2—Bolted Connections ................................................................................................................................ 7-57
7-iv
© 2013
2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2013
Revision
2013 INTERIM REVISIONS TO THE AASHTO LFRD
BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
SECTION 7
7.12.2.1—General......................................................................................................................................... 7-57
7.12.2.2—Factored Resistance ..................................................................................................................... 7-57
7.12.2.3—Washers ....................................................................................................................................... 7-58
7.12.2.4—Holes ............................................................................................................................................ 7-58
7.12.2.5—Size of Bolts................................................................................................................................. 7-58
7.12.2.6—Spacing of Bolts........................................................................................................................... 7-58
7.12.2.6.1—Minimum Spacing and Clear Distance .............................................................................. 7-58
7.12.2.6.2—Minimum Edge Distance ................................................................................................... 7-58
7.12.2.7—Shear Resistance .......................................................................................................................... 7-59
7.12.2.8—Slip Resistance ............................................................................................................................. 7-59
7.12.2.9—Bearing Resistance at Holes and Slots ......................................................................................... 7-59
7.12.2.10—Tensile Resistance ..................................................................................................................... 7-59
7.12.2.11—Combined Tension and Shear .................................................................................................... 7-60
7.12.2.12—Shear Resistance of Anchor Bolts.............................................................................................. 7-60
7.12.3—Welded Connections .............................................................................................................................. 7-60
7.12.3.1—General......................................................................................................................................... 7-60
7.12.3.2—Factored Resistance ..................................................................................................................... 7-60
7.12.3.2.1—General .............................................................................................................................. 7-60
7.12.3.2.2—Complete Penetration Groove-Welded Connections ......................................................... 7-60
7.12.3.2.2a—Tension and Compression......................................................................................... 7-60
7.12.3.2.2b—Shear ......................................................................................................................... 7-61
7.12.3.2.3—Partial Penetration Groove-Welded Connections .............................................................. 7-61
7.12.3.2.3a—Tension and Compression......................................................................................... 7-61
7.12.3.2.3b—Shear ......................................................................................................................... 7-62
7.12.3.2.4—Fillet-Welded Connections ................................................................................................ 7-62
7.12.3.3—Effective Area .............................................................................................................................. 7-63
7.12.3.4—Size of Fillet Welds ..................................................................................................................... 7-63
7.12.3.5—Fillet Weld End Returns .............................................................................................................. 7-64
7.12.4—Block Shear Rupture Resistance ............................................................................................................ 7-64
7.12.5—Connection Elements ............................................................................................................................. 7-64
7.12.5.1—General......................................................................................................................................... 7-64
7.12.5.2—Tension ........................................................................................................................................ 7-65
7.12.5.3—Shear ............................................................................................................................................ 7-65
7.12.6—Splices .................................................................................................................................................... 7-65
7.13—PROVISIONS FOR STRUCTURE TYPES .................................................................................................... 7-65
7.13.1—Deck Superstructures ............................................................................................................................. 7-65
7.13.1.1—General......................................................................................................................................... 7-66
7.13.1.2—Equivalent Strips.......................................................................................................................... 7-66
7.14—REFERENCES ................................................................................................................................................ 7-66
7-v
© 2013
2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2013
Revision
2013 INTERIM REVISIONS TO THE AASHTO LRFD
BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
SECTION 7
SECTION 7
ALUMINUM STRUCTURES
7.1—SCOPE
C7.1
This Section covers the design of aluminum
components, splices, and connections for beam and
girder structures, and metal deck systems. Horizontally
curved girders and non-redundant structures are not
addressed.
In highway bridges, aluminum is usually used in
conjunction with other materials such as steel or
concrete. This Section addresses the design of the
aluminum components; the Designer should use other
Sections for the design of components of other
materials.
Many of the provisions in this Section are based on
the Specification for Aluminum Structures, published by
the Aluminum Association as Part I of the 2010
Aluminum Design Manual (AA, 2010).
7.2—DEFINITIONS
The provisions of Article 6.2 apply to terms used in this Section that are not defined below.
Beam—A structural member whose primary function is to transmit loads to the support primarily through flexure and
shear.
Clear Distance of Bolts—The distance between the edges of adjacent bolt holes.
Closed Shape—A hollow shape that resists lateral-torsional buckling primarily by torsional resistance rather than
warping resistance.
Column—A structural member that has the primary function of resisting a compressive axial force.
Element—A part of a shape’s cross-section that is rectangular in cross-section or of constant curvature and thickness.
Elements are connected to other elements only along their longitudinal edges. An I-beam, for example, consists of
five elements, which include a web element and two elements in each flange.
Longitudinal Weld—A weld whose axis is parallel to the member’s length axis.
Plate—A flat, rolled product whose thickness equals or exceeds 0.250 in.
Transverse Weld—A weld whose axis is perpendicular to the member’s length axis.
Weld-Affected Zone—Material within 1.0 in. of the centerline of a weld.
7.3—NOTATION
(ADTT)SL=
Ae
=
Af
=
Ag
Agc
Agt
Agv
Ai
AL
=
=
=
=
=
=
single lane ADTT as specified in Article 3.6.1.4.2 (7.6.2.5)
effective net area of the member (in.2) (7.8.2.2)
area of the member farther than 2c/3 from the neutral axis, where c is the distance from the neutral axis
to the extreme compression fiber (in.2) (7.10.2.2.4)
gross cross-sectional area (in.2); gross cross-sectional area of the element (in.2) (7.5.4.4.1) (7.5.4.8)
gross area of the element in compression (in.2) (7.5.4.5.1)
gross area in tension (in.2) (7.5.4.7)
gross area in shear (in.2); gross area of the connection element subject to shear (in.2) (7.12.4) (7.12.5.3)
area of element i (in.2) (7.9.2.2.2)
cross-sectional area of the longitudinal stiffener (in.2) (7.5.4.5.4)
7-1
© 2013
2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2013
Revision
2013 INTERIM REVISIONS TO THE AASHTO LRFD
BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
7-2
An
Ant
Anv
As
Av
Aw
Awz
=
=
=
=
=
=
=
Awzc
Awzt
a1
a2
B
b
=
=
=
=
=
=
C
Cb
Cf
Cw
Cwa
Cwb
c
cc
=
=
=
=
=
=
=
=
ccf
=
ccs
=
ccw
=
co
ctf
ctw
D
D
DS
d
de
=
=
=
=
=
=
=
=
ds
d1
E
Fb
Fc
Fcy
=
=
=
=
=
=
net area of the member at the connection (in.2) (7.8.2.2)
net area in tension (in.2) (7.12.4)
net area in shear (in.2); net area of the connection element subject to shear (in.2) (7.12.4) (7.12.5.3)
area of the stiffener (in.2) (7.5.4.4.5)
shear area (in.2) (7.10.3)
area of the web (in.2) (7.5.4.8.2)
cross-sectional area of the weld-affected zone (in.2); weld-affected area of the member farther than 2c/3
from the neutral axis, where c is the distance from the neutral axis to the extreme compression fiber (in.2)
(7.5.4.4.1) (7.10.2.2.4b)
cross-sectional area of the weld-affected zone in compression (in.2) (7.5.4.5.1)
cross-sectional area of the weld-affected zone in tension (in.2) (7.5.4.7)
the lesser of the clear height of the web and the distance between stiffeners (in.) (7.5.4.8.2)
the greater of the clear height of the web and the distance between stiffeners (in.) (7.5.4.8.2)
buckling constant intercept (ksi) (7.5.4.3)
clear height of web (in.); clear height of the web for webs without transverse stiffeners (in.); distance
from the unsupported edge to the mid-thickness of the supporting element (in.) (7.5.4.5.4) (7.5.4.8.2)
(7.5.4.8.3)
buckling constant intersection (7.5.4.3)
moment gradient modifier (7.10.2.2.1)
constant taken from Table 7.6.2.5-1 (ksi) (7.6.2.5)
warping constant (in.6) (7.9.2.1.3)
web crippling parameter (7.10.4.1)
web crippling parameter (7.10.4.1)
distance from the neutral axis to the extreme compression fiber (in.) (7.10.2.2.4b)
distance from neutral axis to the element extreme fiber with the greatest compressive stress (in.)
(7.5.4.5.2)
distance from the centerline of the compression flange to the cross-section’s neutral axis (in.)
(7.10.2.3.3)
distance from the cross-section’s neutral axis to the extreme fiber of compression flange stiffeners (in.)
(7.10.2.3.3)
distance from the web group’s extreme compression fiber to the cross-section’s neutral axis (in.)
(7.10.2.3.3)
distance from neutral axis to other extreme fiber of the element (in.) (7.5.4.5.2)
distance from the extreme tension fiber to the cross-section’s neutral axis (in.) (7.10.2.3.3)
distance from the web group’s extreme tension fiber to the cross-section’s neutral axis (in.) (7.10.2.3.3)
buckling constant slope (ksi) (7.5.4.3)
diameter of pin (in.); nominal diameter of the bolt (in.) (7.7.6.2.2) (7.12.2.9)
clear length of the stiffener (in.) (7.5.4.4.4)
full depth of the section (in.); depth of beam (in.); member depth (in.) (7.5.4.8.2) (7.10.2.2.1) (7.10.4.1)
distance from the center of the pin to the edge of the part in the direction of force (in.); distance from the
center of the bolt to the edge of the part in the direction of force (in.) (7.7.6.2.2) (7.12.2.9)
the stiffener’s flat width (in.) (7.5.4.4.4)
distance from the neutral axis to the compression flange (in.) (7.5.4.5.4)
modulus of elasticity (ksi) (7.4.1)
lateral torsional buckling stress (ksi) (7.10.2.3.3)
compressive buckling stress (ksi) (7.9.2.1.1)
compressive yield strength (ksi) (7.4.1)
© 2013
2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2013
Revision
SECTION 7: ALUMINUM STRUCTURES
Fe
=
Fnb
Fnbo
=
=
Fnbw
=
Fnc
Fnci
=
=
Fnco
=
Fncw
=
Fns
FnST
Fnt
FnUT
=
=
=
=
Fso
=
Fsu
Fsw
=
=
Fsuw
=
Fsy
Fsyw
Ftu
=
=
=
Ftuw
=
Fty
Ftyw
Ftyw6061
f
G
g
Icy
If
IL
Io
=
=
=
=
=
=
=
=
=
=
Is
Iw
Ix
=
=
=
7-3
elastic local buckling stress of the cross-section determined by rational analysis (ksi); elastic buckling
stress (ksi) (7.5.4.4.7) (7.5.4.9)
stress corresponding to the flexural resistance of elements (ksi) (7.5.4.5.1)
stress corresponding to the flexural compressive resistance calculated using Articles 7.5.4.5.2 through
7.5.4.5.4 for an element if no part of the cross-section is weld-affected (ksi) (7.5.4.5.1)
stress corresponding to the flexural compressive resistance calculated using Articles 7.5.4.5.2 through
7.5.4.5.4 for an element if the entire cross-section is weld-affected (ksi) (7.5.4.5.1)
stress corresponding to the uniform compression resistance of elements (ksi) (7.5.4.4.1)
nominal local buckling resistance of element i computed per Articles 7.5.4.4.1 through 7.5.4.4.6 (ksi)
(7.9.2.2.2)
stress corresponding to the uniform compression resistance calculated using Articles 7.5.4.4.2 through
7.5.4.4.6 for an element if no part of the cross-section is weld-affected (ksi) (7.5.4.4.1)
stress corresponding to the uniform compression resistance calculated using Articles 7.5.4.4.2 through
7.5.4.4.6 for an element if the entire cross-section is weld-affected (ksi) (7.5.4.4.1)
stress corresponding to the shear resistance of an element (ksi) (7.5.4.8.1)
stress corresponding to the uniform compression resistance calculated in Article 7.5.4.4.4 (ksi) (7.5.4.4.4)
stress corresponding to the tensile strength of an element (ksi) (7.5.4.6)
stress corresponding to the uniform compression resistance calculated using Article 7.5.4.4.2 (ksi)
(7.5.4.4.4)
shear stress corresponding to the shear resistance for an element if no part of the cross-section were
weld-affected (ksi) (7.5.4.8.1)
shear ultimate strength (ksi); shear ultimate strength of the connection element (ksi) (7.4.1) (7.12.5.3)
shear stress corresponding to the shear resistance for an element if the entire cross-section were weldaffected (ksi); fillet weld strength (kips/in.) (7.5.4.8.1) (7.12.3.2.4)
shear ultimate strength in the weld-affected zone (ksi); lesser of the welded shear ultimate strengths of
the base metals and the filler (ksi); shear ultimate strength of the filler taken as 0.5Ftuw (ksi); welded
shear ultimate strength of the base metal (ksi) (7.5.4.8) (7.12.3.2.2b) (7.12.3.2.3b)
shear yield strength (ksi); shear yield strength of the connection element (7.4.1) (7.12.5.3)
shear yield strength in the weld-affected zone (ksi) (7.12.5.3)
specified minimum tensile ultimate strength (ksi); ultimate tensile strength of the part (ksi); tensile
ultimate strength of the connected part (ksi) (7.4.1) (7.7.6.2.2) (7.12.2.9)
tensile ultimate strength in the weld-affected zone (ksi); lesser of the welded tensile strengths of the base
metals and the filler (ksi); tensile ultimate strength of the filler (ksi) (7.4.1) (7.12.3.2.2a) (7.12.3.2.3a)
specified minimum tensile yield strength (ksi) (7.4.1)
tensile yield strength in the weld-affected zone (ksi) (7.4.1)
tensile yield strength in the weld-affected zone of 6061 (ksi) (7.4.1)
compressive stress at the toe of the flange (ksi) (7.5.4.5.4)
shear modulus of elasticity (ksi) (7.4.1)
transverse center-to-center distance (gauge) between two holes (in.) (7.8.3)
moment of inertia of the compression flange about the weak axis (in.4) (7.10.2.2.3b)
moment of inertia of the flange group about the cross-section’s neutral axis (in.4) (7.10.2.3.3)
moment of inertia of the longitudinal stiffener about the web of the beam (in.4) (7.5.4.5.4)
moment of inertia of a section comprising the stiffener and one half of the width of the adjacent
subelements and the transition corners between them taken about the centroidal axis of the section
parallel to the stiffened element (in.4) (7.5.4.4.5)
moment of inertia of transverse stiffener (in.4) (7.5.4.8.2)
moment of inertia of the web group about the cross-section’s neutral axis (in.4) (7.10.2.3.3)
moment of inertia about the strong axis (in.4) (7.9.1.2.3)
© 2013
2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2013
Revision
2013 INTERIM REVISIONS TO THE AASHTO LRFD
BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
7-4
Iy
J
K
k1
k2
L
Lb
Lv
l
MA
MB
MC
Mmax
Mn
Mnc
Mno
Mnt
Mnw
Mr
Mrx
Mry
Mu
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
Mux
Muy
m
=
=
=
N
n
Pn
Pno
Pnu
Pnw
Pny
Prc
Prt
Puc
Put
R
Rb
Ri
=
=
=
=
=
=
=
=
=
=
=
=
=
=
Rn
=
(RpB)n
(RpB)r
=
=
moment of inertia about the weak axis (in.4) (7.9.1.2.3)
torsion constant (in.4) (7.10.2.2.1)
effective length factor specified in Article 4.6.2.5 (7.9.2.1.1)
postbuckling constant (7.5.4.3)
postbuckling constant (7.5.4.3)
member length (in.) (7.9.2.1.1)
unbraced length (in.) (7.10.2.2.1)
length of tube from maximum to zero shear force (in.) (7.5.4.8.4)
unbraced length (in.) (7.8.4)
absolute value of the moment at the quarter point of the unbraced segment (kip-in.) (7.10.2.2.3)
absolute value of the moment at the midpoint of the unbraced segment (kip-in.) (7.10.2.2.3)
absolute value of the moment at the three-quarter point of the unbraced segment (kip-in.) (7.10.2.2.3)
absolute value of the maximum moment in the unbraced segment (kip-in.) (7.10.2.2.3)
nominal flexural resistance (kip-in.) (7.11.1)
nominal compressive flexural resistance (kip-in.) (7.10.2.3.3)
lateral-torsional buckling resistance if no part of the cross-section is weld-affected (kip-in.) (7.10.2.2.4b)
nominal tensile flexural resistance (kip-in.) (7.10.2.3.3)
lateral-torsional buckling resistance if the entire cross-section is weld-affected (kip-in.) (7.10.2.2.4b)
factored flexural resistance (kip-in.) (7.7.6.2.1)
factored flexural resistance about the major principal axis (kip-in.) (7.8.2.3)
factored flexural resistance about the minor principal axis (kip-in.) (7.8.2.3)
moment resulting from factored loads (kip-in.); moment in the member at the location of the
concentrated force resulting from factored loads (kip-in.) (7.7.6.2.1) (7.10.4.3)
moment about the major principal axis resulting from the factored loads (kip-in.) (7.8.2.3)
moment about the minor principal axis resulting from the factored loads (kip-in.) (7.8.2.3)
factor for determining the flexural compressive resistance of flat elements; constant taken from Table
7.6.2.5-1 (7.5.4.5.2) (7.6.2.5)
length of the bearing surface at the concentrated force (in.) (7.10.4.1)
number of stress range cycles per truck taken from Table 6.6.1.2.5-2 (7.6.2.5)
nominal axial compressive resistance (kip) (7.9.2)
nominal member buckling resistance if no part of the cross-section is weld-affected (kip) (7.9.2.1.1)
nominal resistance for tensile rupture (kip) (7.8.2.1)
nominal member buckling resistance if the entire cross-section is weld-affected (kip) (7.9.2.1.1)
nominal resistance for tensile yield (kip) (7.8.2.1)
factored axial compression resistance (kip) (7.9.4)
factored axial tension resistance (kip) (7.8.2.1)
axial compression resulting from the factored loads (kip) (7.9.4)
axial tension resulting from the factored loads (kip) (7.8.2.3)
transition radius of an attachment (in.) (7.6.2.3)
mid-thickness radius of a round tube or maximum mid-thickness radius of oval tube (in.) (7.5.4.4.6)
for extruded shapes, Ri = 0; for all other shapes, Ri = inside bend radius at the juncture of the flange and
web (in.) (7.10.4.1)
nominal resistance to a concentrated force (kip); nominal resistance of a bolt, connection, or connected
material (kip) (7.10.4.1) (7.12.2.2)
nominal bearing resistance of parts connected by pins (kip) (7.7.6.2.2)
factored bearing resistance of parts connected by pins (kip) (7.7.6.2.2)
© 2013
2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2013
Revision
SECTION 7: ALUMINUM STRUCTURES
7-5
Rr
=
RS
Ru
r
r0
rs
rx
ry
rye
S
Sc
St
sw
s
=
=
=
=
=
=
=
=
=
=
=
=
=
Tn
Tr
t
=
=
=
U
V
Vn
Vr
Vu
xo
yo
Į
Įs
Ȗ
(ǻF)n
(ǻF)TH
(ǻf)
=
=
=
=
=
=
=
=
=
=
=
=
=
ȣ
=
factored resistance to a concentrated force (kip); factored resistance of a bolt, connection, or connected
material (7.10.4.1) (7.12.3.2.2a)
ratio of minimum stress to maximum stress (7.6.2.3)
concentrated force resulting from factored loads (kip) (7.10.4.3)
radius of gyration (in.) (7.8.4)
polar radius of gyration about the shear center (in.) (7.9.2.1.3)
the stiffener’s radius of gyration about the stiffened element’s mid-thickness (in.) (7.5.4.4.4)
major axis radius of gyration (in.) (7.9.2.1.3)
minor axis radius of gyration (in.) (7.9.2.1.3)
effective minor axis radius of gyration (in.) (7.10.2.2.1)
section modulus (in.3) (7.11.2.1)
section modulus on the compression side of the neutral axis (in.3) (7.10.2.2.1)
section modulus on the tension side of the neutral axis (in.3) (7.10.2.3.1)
fillet weld size (in.) (7.12.3.2.4)
distance between transverse stiffeners (in.); longitudinal center-to-center distance (pitch) between two
holes (in.) (7.5.4.5.4) (7.8.3)
nominal tensile resistance of bolt (kip) (7.12.2.2)
factored tensile resistance of bolt (kip) (7.12.2.2)
thickness of web, tube, or pin-connected part (in.); for plain holes, thickness of the connected part; for
countersunk holes, thickness of the connected part less 1/2 the countersink depth (in.) (7.4.1) (7.12.2.9)
reduction factor to account for shear lag taken as given in Section 6.8.2.1 (7.8.2.2)
shear force on the web at the transverse stiffener (kip) (7.5.4.8.2)
nominal shear resistance (kip) (C7.7.6.2.1)
factored shear resistance (kip) (7.7.6.2.1)
shear resulting from factored loads (kip) (7.7.6.2.1)
x-coordinate of the shear center with respect to the centroid (in.) (7.9.2.1.3)
y-coordinate of the shear center with respect to the centroid (in.) (7.9.2.1.3)
thermal coefficient of expansion (in./in./°F) (7.4.1)
factor for a longitudinal web stiffener (7.5.4.5.4)
load factor specified in Table 3.4.1-1 for the fatigue load combination (7.6.2.2)
nominal fatigue resistance as specified in Article 7.6.2.5 (ksi) (7.6.2.2)
constant amplitude threshold taken from Table 7.6.2.5-1 (ksi) (7.6.2.5)
force effect, live load stress range due to the passage of the fatigue load as specified in Article 3.6.1.4
(ksi) (7.6.2.2)
Poisson’s ratio (7.4.1)
φb
=
resistance factor for pins bearing on connected parts (7.5.4.2)
φbb
=
resistance factor for bolts bearing on connected parts (7.5.4.2)
φbs
=
resistance factor for block shear rupture (7.5.4.2)
φc
=
resistance factor for axial compression (7.5.4.2)
φe
=
resistance factor for weld metal and base metal at welds (7.5.4.2)
φf
=
resistance factor for flexural for limit states other than tensile rupture (7.5.4.2)
φft
=
resistance factor for tensile rupture (7.5.4.2)
φs
=
resistance factor for bolts in shear (6.5.4.2) (7.12.2.2)
φt
=
resistance factor for bolts in tension (7.5.4.2) (7.12.2.2)
φu
=
resistance factor for axial tensile rupture (7.5.4.2)
© 2013
2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2013
Revision
2013 INTERIM REVISIONS TO THE AASHTO LRFD
BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
7-6
φv
=
resistance factor for shear or torsion (7.5.4.2)
φvu
=
resistance factor for shear rupture of a connection element (7.5.4.2)
φw
=
resistance factor for web crippling (7.5.4.2)
φy
șs
șw
Ȝe
Ȝeq
Ȝs
Ȝt
Ȝ1
=
=
=
=
=
=
=
=
resistance factor for axial tensile yield (7.5.4.2)
angle between the stiffener and the stiffened element (7.5.4.4.4)
angle between the plane of web and the plane of the bearing surface (șw < 90°) (7.10.4.1)
slenderness boundary for the effectiveness of edge stiffeners (7.5.4.4.4)
slenderness ratio of a shape corresponding to the elastic local buckling stress (7.5.4.4.7)
slenderness of an element supported on both edges and with an intermediate stiffener (7.5.4.4.5)
slenderness of round or oval tubes (7.5.4.8.4)
slenderness at the intersection of yielding and inelastic buckling (7.5.4.4.1)
ρST
=
stiffener effectiveness ratio (7.5.4.4.4)
7.4—MATERIALS
7.4.1—Aluminum Alloys
Aluminum extrusions shall conform to the
requirements of Table 7.4.1-1. Aluminum sheet and
plate shall conform to the requirements of Table 7.4.1-2.
Design shall be based on the strength and stiffness
properties given in Tables 7.4.1-1, 7.4.1-2, and 7.4.1-3.
For 6061 parts of any thickness welded with 5183, 5356,
or 5556 filler and parts 0.375 in. thick or less when
welded with 4043 filler, Ftyw6061 shall be taken as 15 ksi;
for 6061 parts thicker than 0.375 in. when welded with
4043 filler, Ftyw6061 shall be taken as 11 ksi.
C7.4.1
The strengths given in Tables 7.4.1-1 and 7.4.1-2
are:
•
The specified minimum tensile ultimate strength Ftu
and the tensile yield strength Fty are the minimum
strengths specified in ASTM B209 and B221.
•
The welded minimum tensile ultimate strength Ftuw
is the qualification strength required by AWS
D1.2/D1.2M, Structural Welding Code—Aluminum
(AWS, 2008), hereafter referred to as “AWS D1.2.”
•
The welded tensile yield strength Ftyw is taken from
the Aluminum Design Manual (AA, 2010).
The modulus of elasticity and coefficient of thermal
expansion vary slightly among aluminum alloys; the
values given here are conservative. The relationship
between shear yield strength and tensile yield strength
and between shear ultimate strength and tensile ultimate
strength are based on the von Mises yield criterion.
Some aluminum alloys are notch-sensitive, and in
the Aluminum Design Manual (AA, 2010) their tensile
rupture strengths are divided by a tension coefficient kt,
which is greater than one. The aluminum alloys included
in Tables 7.4.1-1 and 7.4.1-2 are not notch-sensitive, and
therefore, for these alloys, kt is 1, and thus the kt factor is
not included in the expressions for tensile strength given
in this Specification. Aluminum castings are not
included in this Specification because their fatigue
strengths have not been established and their use in
highway bridges is rare.
The properties given in Article 7.4.1 apply to
material held at temperatures of 200°F or less for any
period of time. Aluminum’s strength and modulus of
elasticity decrease at temperatures above 200°F, and the
decrease in strength remains after returning to ambient
temperature after heating above 200°F.
© 2013
2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2013
Revision
SECTION 7: ALUMINUM STRUCTURES
7-7
Table 7.4.1-1—Minimum Mechanical Properties of Aluminum Extrusions
ASTM
Specification
B221
Alloy-Temper
6005A-T61
Thickness
t (in.)
Ftu (ksi)
Fty (ksi)
Ftuw (ksi)
Ftyw (ksi)
Unwelded Ct
Welded Ct
B221
6061-T6,
T6510, T6511
B221
B221
B221
6063-T5
6063-T5
6063-T6
t < 1.000
All
t < 0.500
38
35
24
13
141
446
38
35
24
22
16
17
8
275
715
Ftyw6061
141
389
0.500 < t <
1.000
21
15
17
8
290
715
30
25
17
8
189
715
B221
6082-T6,
T6511
0.200 < t <
6.000
45
38
28
16
131
366
B928
B209
5086-H116
6061-T6, T651
t < 2.000
t < 6.000
40
28
35
14
235
427
42
35
24
All
Table 7.4.1-2—Minimum Mechanical Properties of Aluminum Sheet and Plate
ASTM
Specification
B209
B209
Alloy-Temper
5052-H32
5052-H34
t < 2.000
t < 1.000
t < 1.500
31
23
25
9.5
284
608
34
26
25
9.5
250
608
44
31
40
18
235
336
Thickness
t (in.)
Ftu (ksi)
Fty (ksi)
Ftuw (ksi)
Ftyw (ksi)
Unwelded Ct
Welded Ct
B928
5083-H116,
H321
B928
5083-H116,
H321
1.500 < t <
3.000
41
29
39
17
254
532
Ftyw6061
141
389
Table 7.4.1-3—Aluminum Properties
Modulus of elasticity
Shear modulus of elasticity
Poisson’s ratio
Thermal coefficient of expansion
Compressive yield strength for unwelded tempers
beginning with H
Compressive yield strength for all other material
Shear yield strength
Shear ultimate strength
E
G
ȣ
Į
10,100 ksi
3800 ksi
0.33
13 × 10-6 in./in./°F
Fcy
0.9Fty
Fcy
Fsy
Fsu
Fty
0.6Fty
0.6Ftu
7.4.2—Pins, Rollers, and Rockers
Pins, rollers, and expansion rockers shall conform
to one of the following:
•
Steel pins, rollers, and expansion rockers shall
conform to Article 6.4.2 and shall be galvanized.
•
Aluminum pins, rollers, and expansion rockers shall
conform to Article 7.4.1.
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7-8
7.4.3—Bolts, Nuts, and Washers
7.4.3.1—Bolts
C7.4.3.1
Bolts used as structural fasteners shall be:
•
Steel bolts conforming to Article 6.4.3.1, except
that ASTM A325 Type 3 and A490 bolts shall not
be used, and A325 bolts shall be zinc coated.
•
300 series stainless steel bolts conforming to ASTM
F593.
The specification requires that steel fasteners be
zinc-coated in order to minimize galvanic corrosion
between the connected aluminum parts and the steel
fasteners. A490 bolts are prohibited because they may
become brittle if galvanized. Zinc coating may be hotdip or mechanically deposited.
Anchor bolts shall be galvanized steel and conform
to Article 6.4.3.1.
7.4.3.2—Nuts
Nuts for steel bolts shall be galvanized steel and
conform to Article 6.4.3.2. Nuts for stainless steel bolts
shall conform to ASTM F594.
7.4.3.3—Washers
Washers for steel bolts other than stainless steel
bolts shall be galvanized steel and conform to Article
6.4.3.3. Washers for stainless steel bolts shall be 300
series stainless steel.
7.4.3.4—Alternative Fasteners
Alternative fasteners shall meet the material,
manufacturing, and chemical composition requirements
of ASTM A325, be zinc coated, and conform to Article
6.4.3.4.
7.4.3.5—Load Indicator Devices
Load-indicator devices shall conform to Article
6.4.3.5 and shall be zinc coated.
7.4.4—Shear Connectors
C7.4.4
Shear connectors shall conform to Article 7.4.1 or
7.4.3.
Headed aluminum shear studs are not a standard
commercial product. Extruded shapes or bolts are
typically used to transfer shear instead of studs.
7.4.5—Weld Metal
C7.4.5
Weld metal shall meet the requirements of AWS
D1.2.
The Structural Welding Code—Aluminum (AWS,
2008) requires that weld metal (fillers) meet the
requirements of AWS A5.10, Specification for Bare
Aluminum and Aluminum Alloy Welding Electrodes and
Rods (AWS, 1999).
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2013
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SECTION 7: ALUMINUM STRUCTURES
7-9
7.5—LIMIT STATES
7.5.1—General
The structural behavior of components made of
aluminum, or aluminum in combination with other
materials, shall be investigated for each stage that may
be critical during construction, handling, transportation,
and erection as well as during the service life of the
structure of which they are part.
Structural components shall be proportioned to
satisfy the requirements at strength, extreme event,
service, and fatigue limit states.
7.5.2—Service Limit State
The provisions of Article 2.5.2.6 shall apply.
7.5.3—Fatigue Limit State
Components shall be investigated for fatigue as
specified in Article 7.6.
The fatigue load combinations specified in Table
3.4.1-1 and the fatigue live load specified in Article
3.6.1.4 shall apply.
7.5.4—Strength Limit State
7.5.4.1—General
Strength and stability shall be considered using the
applicable strength load combinations specified in Table
3.4.1-1.
7.5.4.2—Resistance Factors
Resistance factors φ for the strength limit state shall
be taken as follows:
•
For flexure: tensile rupture
φft
= 0.75
•
For flexure: other failure modes
φf
= 0.90
•
For shear or torsion
φv
= 0.90
•
For axial compression
φc
= 0.90
•
For axial tension: rupture
φu
= 0.75
•
For axial tension: yield
φy
= 0.90
•
For pins bearing on connected
parts
φb
= 0.90
•
For bolts bearing on connected
parts
φb
= 0.75
•
For block shear rupture
φbs
= 0.75
•
For shear rupture of a connection
element
φvu
= 0.80
b
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BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
7-10
•
For web crippling
φw
= 0.80
•
For weld metal and base metal at
welds
φe
= 0.75
7.5.4.3—Buckling Constants
C7.5.4.3
Buckling constants B, D, and C shall be determined
from Tables 7.5.4.3-1 and 7.5.4.3-2. Ct shall be
determined using a plot of curves of limit state stress
based on elastic and inelastic buckling or by trial and
error solution. Postbuckling constants k1 and k2 shall be
determined from Table 7.5.4.3-3.
Buckling constants are used to determine inelastic
buckling strengths of aluminum structural components.
Table 7.5.4.3-1 matches Table B.4.1; Table 7.5.4.3-2
matches Table B.4.2; and Table 7.5.4.3-3 matches Table
B.4.3 of the Aluminum Design Manual (AA, 2010).
T5 and T6 are artificially aged tempers.
Table 7.5.4.3-1—Buckling Constants for Tempers Beginning with H and Weld-Affected Zones of All Tempers
Type of Stress
and Member
Compression
in Columns
and Beam
Flanges
Axial
Compression
in Flat
Elements
Axial
Compression
in Curved
Elements
Flexural
Compression
in Flat
Elements
Flexural
Compression
in Curved
Elements
Shear in Flat
Elements
Intercept B (ksi)
§ § F ·
cy
¸
Bc = Fcy ¨1 + ¨¨
¨
1000 ¸¹
©
©
Slope D (ksi)
1/ 2
·
¸
¸
¹
§ § F ·1 / 3 ·
cy
¸ ¸
B p = Fcy ¨1 + ¨¨
¸ ¸
¨
440
¹ ¹
© ©
§ § F ·1 / 5 ·
cy
¸ ¸
Bt = Fcy ¨1 + ¨¨
¸ ¸
¨
6500
¹ ¹
© ©
Intersection C
1/ 2
Dc =
Bc § 6 Bc ·
¨
¸
20 © E ¹
B p § 6B p
¨
Dp =
20 ¨© E
B §B ·
Dt = t ¨ t ¸
3 .7 © E ¹
·
¸
¸
¹
1/ 2
2B p
3D p
Ct, see Tables 7.4.1-1
and 7.4.1-2
Dbr =
Bbr § 6 Bbr ·
¨
¸
20 © E ¹
§ § F ·1 / 5 ·
cy
¸ ¸
Btb = 1.5 Fcy ¨1 + ¨¨
¸ ¸
¨
6500
¹ ¹
© ©
Dtb =
Btb § Btb ·
¨
¸
2.7 © E ¹
§ § F ·1 / 3 ·
sy
¸ ¸
Bs = Fsy ¨1 + ¨¨
¸ ¸
¨
240
¹ ¹
© ©
Cp =
2 Bc
3Dc
1/ 3
§ § F ·1 / 3 ·
cy
¸ ¸
= 1.3 Fcy ¨1 + ¨¨
¨
340 ¸¹ ¸
¹
© ©
Bbr
Cc =
B § 6B ·
Ds = s ¨ s ¸
20 © E ¹
1/ 2
1/ 3
1/ 2
C br =
2 Bbr
3Dbr
§ B − Bt ·
¸¸
C tb = ¨¨ tb
© Dtb − Dt ¹
Cs =
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2
2 Bs
3Ds
2013
Revision
SECTION 7: ALUMINUM STRUCTURES
7-11
Table 7.5.4.3-2—Buckling Constants for Tempers Beginning with T5 or T6
Type of Stress
and Member
Compression
in Columns
and Beam
Flanges
Axial
Compression
in Flat
Elements
Axial
Compression
in Curved
Elements
Flexural
Compression
in Flat
Elements
Flexural
Compression
in Curved
Elements
Shear in Flat
Elements
Intercept B (ksi)
§ § F ·
cy
¸
Bc = Fcy ¨1 + ¨¨
¸
¨
2250
¹
© ©
Slope D (ksi)
1/ 2
·
¸
¸
¹
§ § F ·1 / 3 ·
cy
¸ ¸
B p = Fcy ¨1 + ¨¨
¸ ¸
¨
1500
¹ ¹
© ©
1/ 5
§ § F
· ·¸
cy
¸
Bt = Fcy ¨1 + ¨¨
¨
50,000 ¸¹ ¸
¹
© ©
Bbr
§ § F ·1 / 3 ·
cy
¸ ¸
= 1.3 Fcy ¨1 + ¨¨
¸ ¸
¨
340
¹ ¹
© ©
1/ 5
§ § F
· ·¸
cy
¨
¸
Btb = 1.5 Fcy 1 + ¨¨
¨
50,000 ¸¹ ¸
©
¹
©
§ § F ·1 / 3 ·
sy
¸ ¸
B s = Fsy ¨1 + ¨¨
¨
800 ¸¹ ¸
¹
© ©
Intersection C
1/ 2
Dc =
Bc § Bc ·
¨ ¸
10 © E ¹
Bp § Bp
¨
Dp =
10 ¨© E
1/ 2
·
¸
¸
¹
B §B ·
Dt = t ¨ t ¸
4 .5 © E ¹
Dbr =
Bbr
20
C p = 0.41
Bp
Dp
Ct, see Tables
7.4.1-1 and 7.4.1-2
§ 6 Bbr ·
¨
¸
© E ¹
Bs § Bs ·
¨
¸
10 © E ¹
Bc
Dc
1/ 3
B §B ·
Dtb = tb ¨ tb ¸
2.7 © E ¹
Ds =
C c = 0.41
1/ 2
1/ 3
1/ 2
C br =
2 Bbr
3Dbr
§ B − Bt ·
¸¸
Ctb = ¨¨ tb
© Dtb − Dt ¹
C s = 0.41
2
Bs
Ds
Table 7.5.4.3-3—Postbuckling Constants for Flat Elements
Type of Element
Flat Elements in Compression for Temper Designations
Beginning with H, and Weld-Affected Zones of All
Tempers
Flat Elements in Compression for Temper Designations
Beginning with T5 or T6
Flat Elements in Flexure
k1
0.50
k2
2.04
0.35
2.27
0.50
2.04
7.5.4.4—Nominal Resistance of Elements in
Uniform Compression
7.5.4.4.1—General
C7.5.4.4.1
The nominal resistance of elements in uniform
compression shall be taken as:
•
For unwelded elements:
Fnc = Fnco
•
Articles in Article 7.5.4.4 for elements in uniform
compression match Section B.5.4 of the Aluminum
Design Manual (AA, 2010).
(7.5.4.4.1-1)
For welded elements:
Fnc = Fnco(1 – Awz /Ag) + Fncw Awz /Ag (7.5.4.4.1-2)
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7-12
where:
Fnco =
stress corresponding to the uniform
compression resistance calculated using
Articles 7.5.4.4.2 through 7.5.4.4.6 for an
element if no part of the cross-section is weldaffected using buckling constants for
unwelded metal and unwelded strengths (ksi)
Fncw =
stress corresponding to the uniform
compression resistance calculated using
Articles 7.5.4.4.2 through 7.5.4.4.6 for an
element if the entire cross-section is weldaffected using buckling constants for weldaffected zones and welded strengths (ksi). For
transversely welded elements with b/t < Ȝ1,
Fncw = Fnco
Awz =
cross-sectional area of the weld-affected zone
(in.2)
Ag =
gross cross-sectional area of the element (in.2)
Ȝ1 =
slenderness at the intersection of yielding and
inelastic buckling
7.5.4.4.2—Flat Elements Supported on One Edge
The nominal resistance Fnc of flat elements
supported on one edge shall be taken as:
•
If b t ≤
B p − Fcy
5.0 D p
If
Bp − Fcy
5.0Dp
(7.5.4.4.2-1)
<b t <
Cp
5.0
, then
Fnc = B p − 5.0 D p b t
• If b t ≥
Fnc =
This Article matches Section B.5.4.1 of the
Aluminum Design Manual (AA, 2010).
= λ1 , then
Fnc = Fcy
•
C7.5.4.4.2
Cp
5.0
(7.5.4.4.2-2)
, then
π2 Ε
(7.5.4.4.2-3)
( 5.0 b t )2
where:
Bp, Dp, and Cp = parameters specified
7.5.4.3-1 or 7.5.4.3-2
in
Table
7.5.4.4.3—Flat Elements Supported on Both Edges
The stress Fnc corresponding to the uniform
compression resistance of flat elements supported on
both edges shall be taken as:
C7.5.4.4.3
This Article matches Section B.5.4.2 of the
Aluminum Design Manual (AA, 2010).
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SECTION 7: ALUMINUM STRUCTURES
•
B p − Fcy
If b t ≤
1.6 D p
7-13
= λ1 , then
Fnc = Fcy
•
If
Bp − Fcy
1.6 Dp
(7.5.4.4.3-1)
<b t <
k1 Bp
1.6 Dp
, then
Fnc = B p − 1.6 D p b t
•
If b t ≥
Fnc =
k1 Bp
1.6 Dp
k2
(7.5.4.4.3-2)
, then
Bp E
(7.5.4.4.3-3)
1.6b / t
7.5.4.4.4—Flat Elements Supported on One Edge
and with a Stiffener on the Other Edge
For flat elements satisfying all of the following
criteria:
•
Supported on one edge and with a stiffener on the
other edge,
•
With a stiffener of depth DS < 0.8b, where DS is
the clear length of the stiffener, and
•
With a thickness no greater than the stiffener’s
thickness,
C7.5.4.4.4
This Article matches Section B.5.4.3 of the
Aluminum Design Manual (AA, 2010).
The nominal resistance shall be taken as:
Fnc = FnUT + (FnST –FnUT) ρST
(7.5.4.4.4-1)
where FnUT is Fnc determined using Article 7.5.4.4.2 and
neglecting the stiffener. FnST is Fnc determined using
Article 7.5.4.4.3.
ρST = stiffener effectiveness ratio determined as
follows:
•
If b t < λe 3, then
ρST = 1.0
•
If λ e 3 < b t < λe , then
ρST =
•
(7.5.4.4.4-2)
rs
§b/t 1·
− ¸
9t ¨
© λe 3 ¹
≤ 1.0
(7.5.4.4.4-3)
If λ e < b t < 2λ e , then
ρST =
rs
§b/t
·
+ 3¸
1.5t ¨
© λe
¹
≤ 1.0
(7.5.4.4.4-4)
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7-14
in which:
λe = 1.28 E / Fcy
(7.5.4.4.4-5)
where:
= the stiffener’s radius of gyration about the
stiffened element’s mid-thickness
rs
For straight stiffeners of constant thicknesses, rs
may be taken as:
( d s sin șs )
rs =
(7.5.4.4.4-6)
3
where:
ds
=
the stiffener’s flat width (in.)
șs
=
the angle between the stiffener and the
stiffened element (deg)
Fnc for the stiffened element determined using
Article 7.5.4.4.4 shall not exceed Fnc for the stiffener
alone determined using Article 7.5.4.4.2.
For flat elements:
•
supported on one edge and with a stiffener on the
other edge, and
•
with a stiffener of depth DS > 0.8b, where DS is the
clear length of the stiffener, or
•
with a thickness greater than the stiffener’s
thickness
the nominal resistance shall be taken as:
Fnc = FnUT
(7.5.4.4.4-7)
7.5.4.4.5—Flat Elements Supported on Both Edges
and with an Intermediate Stiffener
The nominal resistance of flat elements supported
on both edges and with an intermediate stiffener shall
be taken as:
•
If λ s ≤
Bc − Fcy
Dc
This Article matches Section B.5.4.4 of the
Aluminum Design Manual (AA, 2010).
= λ1 , then
Fnc = Fcy
• If
C7.5.4.4.5
(7.5.4.4.5-1)
Bc − Fcy
< λs < Cc , then
Dc
Fnc = Bc − Dc λ s
(7.5.4.4.5-2)
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SECTION 7: ALUMINUM STRUCTURES
7-15
• If λ s ≥ Cc , then
π2 E
λs2
Fnc =
(7.5.4.4.5-3)
in which:
§b·
λ s = 4.62 ¨ ¸
©t¹
1 + As / ( bt )
(7.5.4.4.5-4)
10.67 I o
1+ 1+
bt 3
where:
As
=
area of the stiffener (in.2)
Io
=
moment of inertia of a section
comprising the stiffener and one
half of the width of the adjacent
subelements and the transition
corners between them taken about
the centroidal axis of the section
parallel to the stiffened element
(in.4)
Bc, Dc, and Cc =
parameters specified
7.5.4.3-1 or 7.5.4.3-2
in
Table
Fnc shall not exceed Fnc determined using Article
7.5.4.4.3 for the sub-elements of the stiffened element.
Fnc need not be less than Fnc determined using
Article 7.5.4.4.3 and neglecting the stiffener.
7.5.4.4.6—Pipes, Tubes, and Curved Elements
Supported on Both Edges
The nominal resistance of pipes, tubes, and curved
elements supported on both edges shall be taken as:
2
§ Bt − Fcy ·
• If Rb / t < ¨
¸ = λ1 , then
© Dt ¹
Fnc = Fny
C7.5.4.4.6
This Article matches Section B.5.4.5 of the
Aluminum Design Manual (AA, 2010), but also permits
the strength of curved elements to be no less than the
strength of flat elements of the same length.
(7.5.4.4.6-1)
2
§ Bt − Fcy ·
• If ¨
¸ < Rb / t < Ct , then
© Dt ¹
Fnc = Bt − Dt
Rb
t
(7.5.4.4.6-2)
• If Rb / t ≥ Ct , then
2
Fnc =
πE
§R
16 ¨
© t
b
· §1 + R / t ·
¸
¸ ¨¨
35 ¸¹
¹©
2
(7.5.4.4.6-3)
b
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7-16
Fnc need not be less than that determined using
Article 7.5.4.4.3, where b is the length of the curved
element.
For tubes with circumferential welds, use of Article
7.5.4.4.6 shall be limited to tubes with Rb /t 20.
where:
Rb
= mid-thickness radius of a round tube
or maximum mid-thickness radius of
oval tube (in.)
Bt, Dt, and Ct = parameters specified
7.5.4.3-1 or 7.5.4.3-2
in
Table
7.5.4.4.7—Alternative Method for Flat Elements
As an alternative to Articles 7.5.4.4.2 through
7.5.4.4.5, the nominal resistance of flat elements
without welds in uniform compression may be
determined as:
• If λeq ≤
Bp − Fcy
Dp
(7.5.4.4.7-1)
Bp − Fcy
Dp
< λeq <
k1Bp
Dp
Fnc = B p – D p λ eq
• If λ eq ≥
Fnc =
This Article matches Section B.5.4.6 of the
Aluminum Design Manual (AA, 2010).
= λ1 , then
Fnc = Fcy
• If
C7.5.4.4.7
k1 B p
Dp
(7.5.4.4.7-2)
, then
k2 B p E
λ eq
, then
(7.5.4.4.7-3)
in which:
E
Fe
λ eq = π
(7.5.4.4.7-4)
where:
Fe
=
Bp, Dp
=
the elastic local buckling stress of the
cross-section determined by rational
analysis (ksi)
parameters specified in Table 7.5.4.3-1 or
7.5.4.3-2
7.5.4.5—Nominal Resistance of Elements in
Flexural Compression
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SECTION 7: ALUMINUM STRUCTURES
7-17
7.5.4.5.1—General
C7.5.4.5.1
The nominal resistance of elements in flexural
compression shall be taken as:
•
Article 7.5.4.5 matches Section B.5.5 of the
Aluminum Design Manual (AA, 2010).
For unwelded elements:
Fnb = Fnbo
•
(7.5.4.5.1-1)
For welded elements:
Fnb = Fnbo(1 – Awzc /Agc) + Fnbw Awzc /Agc
(7.5.4.5.1-2)
where:
Fnbo
=
stress corresponding to the flexural
compressive resistance calculated using
Articles 7.5.4.5.2 through 7.5.4.5.4 for an
element if no part of the cross-section is
weld-affected using buckling constants for
unwelded metal and unwelded strengths
(ksi)
Fnbw
=
stress corresponding to the flexural
compressive resistance calculated using
Articles 7.5.4.5.2 through 7.5.4.5.4 for an
element if the entire cross-section is weldaffected. Use buckling constants for weldaffected zones and welded strengths (ksi).
For transversely welded elements with
b/t < Ȝ1, Fnbw = Fnbo.
Awzc
=
cross-sectional area of the weld-affected
zone in compression (in.2)
Agc
=
gross cross-sectional area of the element in
compression (in.2)
7.5.4.5.2—Flat Elements Supported on Both Edges
The nominal resistance of flat elements supported
on both edges and flat elements supported on the
compression edge with the tension edge free shall be
taken as:
• If b / t ≤
Bbr − 1.3Fcy
mDbr
C7.5.4.5.2
This Article matches Section B.5.5.1 of the
Aluminum Design Manual (AA, 2010).
= λ1 , then
Fnb = Bbr – mDbr b / t
(7.5.4.5.2-1)
Bbr −1.3Fcy
kB
< b / t < 1 br , then
mDbr
mDbr
Fnb = Bbr – mDbr b / t
(7.5.4.5.2-2)
• If
• If b / t >
k1 Bbr
, then
mDbr
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Fnb =
k2 Bbr E
(7.5.4.5.2-3)
( mb / t )
in which:
m
=
factor
for
determining
the
flexural
compressive resistance of flat elements
m = 1.15 + co /(2cc) for –1 < co /cc < 1
(7.5.4.5.2-4)
m = 1.3/(1 – co /cc) for co /cc < –1
(7.5.4.5.2-5)
m = 0.65 for cc = – co
(7.5.4.5.2-6)
where:
cc
= distance from neutral axis to the element
extreme fiber with the greatest compressive
stress (in.)
co
= distance from neutral axis to other extreme
fiber of the element (in.)
Bbr, Dbr = parameters specified in Table 7.5.4.3-1 or
7.5.4.3-2
Distances to compressive fibers shall be taken as
negative and distances to tensile fibers shall be taken as
positive.
7.5.4.5.3—Flat Elements Supported on One Edge,
Compression Edge Free
The nominal flexural compressive resistance of flat
elements supported on one edge with the compression
edge free shall be taken as:
•
If b/t <
Bbr − 1.3Fcy
3.5Dbr
C7.5.4.5.3
This Article matches Section B.5.5.2 of the
Aluminum Design Manual (AA, 2010).
= λ1, then
Fnb = 1.3Fcy
(7.5.4.5.3-1)
Bbr − 1.3Fcy
C
b / t br < b t <, then
3.5Dbr
3.5
Fnb = Bbr – 3.5Dbr b / t
• If
•
If b t ≥
Fnb =
(7.5.4.5.3-2)
Cbr
, then
3.5
π2 E
( 3.5b / t )2
(7.5.4.5.3-3)
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2013
Revision
SECTION 7: ALUMINUM STRUCTURES
7-19
7.5.4.5.4—Flat Elements Supported on Both Edges
and with a Longitudinal Stiffener
The nominal resistance of flat elements supported
on both edges and with a longitudinal stiffener located
0.4d1 from the supported edge shall be taken as:
• If b/t <
Bbr − 1.3Fcy
0.29 Dbr
This Article matches Section B.5.5.3 of the
Aluminum Design Manual (AA, 2010).
= λ1, then
Fnb = 1.3Fcy
• If
C7.5.4.5.4
(7.5.4.5.4-1)
Bbr −1.3Fcy
kB
< b / t < 1 br , then
0.29Dbr
0.29Dbr
Fnb = Bbr − 0.29 Dbr b t
• If b / t ≥
Fnb =
(7.5.4.5.4-2)
k1 Bbr
, then
0.29 Dbr
k2 Bbr E
(7.5.4.5.4-3)
( 0.29b / t )
The moment of inertia of the longitudinal stiffener
IL about the web of the beam shall satisfy:
IL ≥
0.02α s ftb3
E
ª§ 6 AL ·§ s ·2
º
Ǭ 1 +
¨ ¸ + 0.4»
¸
bt ¹ © b ¹
¬«©
¼»
(7.5.4.5.4-4)
where:
AL =
cross-sectional
stiffener (in.2)
area
of
the
longitudinal
d1
=
distance from the neutral
compression flange (in.)
f
=
compressive stress at the toe of the flange (ksi)
b
=
clear height of the web (in.)
s
=
distance between transverse stiffeners (in.)
t
=
web thickness (in.)
Įs
=
1 for a stiffener consisting of equal members
on both sides of the web
3.5 for a stiffener consisting of a member on
only one side of the web
=
axis
to
the
For a stiffener consisting of equal members on both
sides of the web, the moment of inertia IL shall be the
sum of the moments of inertia about the centerline of
the web.
For a stiffener consisting of a member on one side
of the web only, the moment of inertia IL shall be taken
about the face of the web in contact with the stiffener.
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2013
Revision
2013 INTERIM REVISIONS TO THE AASHTO LRFD
BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
7-20
7.5.4.5.5—Alternative Method for Flat Elements
As an alternative to Articles 7.5.4.5.2 through
7.5.4.5.4 for flat elements in flexure without welds, the
stress Fnb may be determined as:
This Article matches Section B.5.5.4 of the
Aluminum Design Manual (AA, 2010).
Bbr − 1.3Fcy
= λ1 , then
Dbr
• If λ eq ≤
Fnb = 1.3Fcy
• If
C7.5.4.5.5
(7.5.4.5.5-1)
Bbr − 1.3Fcy
kB
< λeq < 1 br , then
Dbr
Dbr
Fnb = Bbr – Dbr λ eq
• If λ eq ≥
(7.5.4.5.5-2)
k1 Bbr
, then
Dbr
k2 Bbr E
Fnb =
λ eq
(7.5.4.5.5-3)
in which:
λ eq = π
E
Fe
(7.5.4.5.5-4)
where:
Fe =
the elastic local buckling stress of the crosssection determined by rational analysis (ksi)
7.5.4.6—Nominal Resistance of Elements in
Uniform Tension
The nominal tensile resistance for yielding shall be
taken as:
•
(7.5.4.6-1)
For transversely welded elements:
Fnt = Ftyw
•
This Article matches Section F.8.1.1 of the Aluminum
Design Manual (AA, 2010).
For unwelded elements:
Fnt = Fty
•
C7.5.4.6
(7.5.4.6-2)
For longitudinally welded elements:
Fnt = Fty(1 – Awz /Ag) + Ftyw Awz /Ag
(7.5.4.6-3)
where:
Ag =
gross cross-sectional area (in.2)
Awz =
cross-sectional area of the weld-affected zone
(in.2)
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2013
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SECTION 7: ALUMINUM STRUCTURES
7-21
The nominal tensile resistance for rupture shall be
taken as:
•
For unwelded elements:
Fnt = Ftu
•
(7.5.4.6-4)
For transversely welded elements:
Fnt = Ftuw
•
(7.5.4.6-5)
For longitudinally welded elements:
Fnt = Ftu(1 – Awz /Ag) + Ftuw Awz /Ag
(7.5.4.6-6)
7.5.4.7—Nominal Resistance of Elements in
Flexural Tension
The nominal resistance for flexural tensile yielding,
shall be taken as:
•
(7.5.4.7-1)
For transversely welded elements:
Fnb = 1.30 Ftyw
•
This Article matches Section F.8.1.2 of the Aluminum
Design Manual (AA, 2010).
For unwelded elements:
Fnb = 1.30 Fty
•
C7.5.4.7
(7.5.4.7-2)
For longitudinally welded elements:
Fnb = 1.30[Fty(1 – Awzt /Agt) + Ftyw Awzt /Agt]
(7.5.4.7-3)
The nominal resistance for flexural tensile rupture
shall be taken as:
•
For unwelded elements:
Fnb = 1.42Ftu
•
(7.5.4.7-4)
For transversely welded elements:
Fnb = 1.42Ftuw
•
(7.5.4.7-5)
For longitudinally welded elements:
Fnb = 1.42[Ftu(1 – Awzt /Agt) + Ftuw Awzt /Agt]
(7.5.4.7-6)
where:
Awzt =
weld affected area in tension (in.2)
Agt =
gross area in tension (in.2)
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BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
7-22
7.5.4.8—Nominal Resistance of Elements in
Shear
7.5.4.8.1—General
C7.5.4.8.1
The nominal shear resistance shall be taken as:
•
For unwelded members:
Fns = Fso
•
This Article matches Section G.1 of the Aluminum
Design Manual (AA, 2010).
(7.5.4.8.1-1)
For welded members:
Fns = Fso(1 – Awz /Ag) + Fsw Awz /Ag
(7.5.4.8.1-2)
where:
Fso =
shear stress corresponding to the shear
resistance for an element if no part of the
cross-section were weld-affected (ksi). Use
buckling constants for unwelded metal and
unwelded strengths.
Fsw =
shear stress corresponding to the shear
resistance for an element if the entire crosssection were weld-affected (ksi). Use buckling
constants for weld-affected zones and welded
strengths. For transversely welded elements
with b/t < Ȝ1, Fsw = Fso.
Awz =
cross-sectional area of the weld-affected zone
(in.2)
Ag =
gross cross-sectional area of the element (in.2)
The nominal shear resistance Fns in weld-affected
zones shall not exceed Fsuw /1.2.
where:
Fsuw =
shear ultimate strength in the weld-affected
zone (ksi)
7.5.4.8.2—Flat Elements Supported on Both Edges
The nominal shear resistance of flat elements
supported on both edges shall be taken as:
•
If b t ≥
If
This Article matches Section G.2 of the Aluminum
Design Manual (AA, 2010).
Bs − Fsy
= λ1 , then
1.25Ds
Fns = Fsy
•
C7.5.4.8.2
(7.5.4.8.2-1)
Bs − Fsy
C
< b / t < s , then
1.25Ds
1.25
(7.5.4.8.2-2)
Fns = Bs – 1.25Ds b / t
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2013
Revision
SECTION 7: ALUMINUM STRUCTURES
•
If b t ≥
Fns =
7-23
Cs
, then
1.25
π2 E
(7.5.4.8.2-3)
(1.25b / t )2
For webs without transverse stiffeners b shall be
taken as the clear height of the web; for webs with
transverse stiffeners b shall be determined as:
b=
a1
§a ·
1 + 0.7 ¨ 1 ¸
© a2 ¹
(7.5.4.8.2-4)
2
where:
a1
= the lesser of the clear height of the web
and the distance between stiffeners (in.)
a2
= the greater of the clear height of the
web and the distance between stiffeners
(in.)
t
= web thickness (in.)
Aw
= area of the web (in.2) = dt
d
= full depth of the section (in.)
Bs, Ds, and Cs = parameters specified in Table 7.5.4.3-1
or 7.5.4.3-2
Transverse stiffeners shall have a moment of
inertia Is not less than the following:
•
If
s
≤ 0.4 , then
b
Is =
•
If
0.55Vb 2 § s ·
¨ ¸
E
©b¹
(7.5.4.8.2-5)
s
> 0.4 , then
b
Is =
0.88Vb 2
E
§b·
¨ ¸
©s¹
(7.5.4.8.2-6)
where:
b
=
clear height of the web regardless of whether
or not a longitudinal stiffener is present (in.)
Is
=
moment of inertia of the transverse stiffener
(in.4). For a stiffener composed of members of
equal size on each side of the web, the moment
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BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
7-24
of inertia of the stiffener shall be computed
about the centerline of the web. For a stiffener
composed of a member on only one side of the
web, the moment of inertia of the stiffener
shall be computed about the face of the web in
contact with the stiffener.
s
=
distance between transverse stiffeners (in.).
For a stiffener composed of a pair of members,
one on each side of the web, the stiffener
spacing s is the clear distance between the
pairs of stiffeners. For a stiffener composed of
a member on only one side of the web, the
stiffener spacing s is the distance between
fastener lines or other connecting lines.
V
=
shear force on the web at the transverse
stiffener (kip)
Transverse stiffeners shall consist of plates or
angles welded or bolted to either one or both sides of
the web. Stiffeners in straight girders not used as
connection plates shall be tight fit or attached at the
compression flange, but need not be in bearing with the
tension flange.
7.5.4.8.3—Flat Elements Supported on One Edge
The nominal shear resistance of flat elements
supported on one edge shall be taken as:
•
If b t ≤
Bs − Fsy
3.0 Ds
= λ1 , then
Fns = Fsy
•
If
(7.5.4.8.3-1)
Bs − Fsy
3.0 Ds
<b t<
Cs
, then
3.0
Fns = Bs – 3.0 Ds b / t
•
If b t ≥
Fns =
(7.5.4.8.3-2)
Cs
, then
3.0
π2 E
(7.5.4.8.3-3)
( 3.0b / t )2
where:
b
=
distance from the unsupported edge to the
mid-thickness of the supporting element (in.)
t
=
web thickness (in.)
Aw =
area of the web (in.2) = bt
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2013
Revision
SECTION 7: ALUMINUM STRUCTURES
7-25
7.5.4.8.4—Round or Oval Tubes
C7.5.4.8.4
The nominal shear resistance of round or oval
tubes shall be taken as:
•
If λt ≤
1.3Bs − Fsy
= λ1 , then
1.63Ds
Fns = Fsy
•
If
(7.5.4.8.4-1)
1.3Bs − Fsy
1.63Ds
< λt <
Cs
, then
1.25
Fns = 1.3Bs – 1.63Ds λt
•
If λ t >
Fns =
This Article matches Section G.3 of the Aluminum
Design Manual (AA, 2010).
(7.5.4.8.4-2)
Cs
, then
1.25
1.3π2 E
(7.5.4.8.4-3)
(1.25λt )2
in which:
§R ·
λ t = 2.9 ¨ b ¸
© t ¹
5/8
1/4
§ Lv ·
¨ ¸
© Rb ¹
(7.5.4.8.4-4)
where:
Rb = mid-thickness radius of a round tube or
maximum mid-thickness radius of an oval tube
(in.)
t
=
Lv =
thickness of tube (in.)
length of tube from maximum to zero shear
force (in.)
7.5.4.9—Elastic Buckling Stress of Elements
The elastic buckling stress, Fe, of elements shall be
determined using Table 7.5.4.9-1.
C7.5.4.9
This Article matches Section B.5.6 of the Aluminum
Design Manual (AA, 2010).
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2013 INTERIM REVISIONS TO THE AASHTO LRFD
BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
7-26
Table 7.5.4.9-1—Elastic Buckling Stress Fe of Elements
Element Type
Element Stress
Element Support
Flat
Uniform
Compression
Supported on both edges
Flat
Uniform
Compression
Supported on one edge
Flat
Uniform
Compression
Supported on one edge and with a
stiffener on the other edge
Flat
Uniform
Compression
Supported on both edges and with
an intermediate stiffener
Fe (ksi)
π2 E
(1.6b / t )2
π2 E
(5.0b / t )2
(
1 − ρST
)
π2 E
( 5.0b / t )2
+ ρST
π2 E
(1.6b / t )2
π2 E
λ2s
π2 E
Curved
Uniform
Compression
Supported on both edges
Flat
Flexural
Compression
Supported on one edge,
compression edge free
§R
16 ¨ b
© t
·§
¸ ¨¨ 1 +
¹©
Rb / t
35
·
¸
¸
¹
2
π2 E
( 3.5b / t )2
7.5.5—Extreme Event Limit State
All applicable extreme event load combinations in
Table 3.4.1-1 shall be investigated. All resistance
factors for the extreme limit state shall be taken as 1.0.
Bolted joints not protected by capacity design or
structural fuses may be assumed to behave as bearingtype connections at the extreme event limit state, and
the resistance factors given in Article 7.5.4.2 shall
apply.
7.6—FATIGUE
7.6.1—General
Fatigue shall be categorized as load- or distortioninduced fatigue.
7.6.2—Load-Induced Fatigue
7.6.2.1—Application
The force effect considered for the fatigue design
of an aluminum bridge detail shall be the live load
stress range. Residual stresses shall not be included in
investigating fatigue.
These provisions shall be applied only to details
subjected to a net applied tensile stress. In regions
where the unfactored permanent loads produce
compression, fatigue shall be considered only if the
compressive stress is less than that resulting from the
Fatigue I load combination specified in Table 3.4.1-1.
2013 by the American Association of State Highway and Transportation Officials.
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2013
Revision
SECTION 7: ALUMINUM STRUCTURES
7-27
7.6.2.2—Design Criteria
For load-induced fatigue considerations, each
detail shall satisfy:
(7.6.2.2-1)
Ȗ(ǻf) < (ǻF)n
where:
Ȗ
=
load factor specified in Table 3.4.1-1 for
the fatigue load combination
(ǻf)
=
force effect, live load stress range due to
the passage of the fatigue load as specified
in Article 3.6.1.4 (ksi)
(ǻF)n
=
nominal fatigue resistance as specified in
Article 7.6.2.5 (ksi)
7.6.2.3—Detail Categories
Components and details shall be designed to satisfy
the requirements of their respective detail categories
summarized in Table 7.6.2.3-1 and illustrated in Figure
7.6.2.3-1 which provides examples as guidelines and is
not intended to exclude other similar details. Tensile
stresses shall be considered to be positive and
compressive stresses shall be considered to be negative.
Bolt fabrication shall conform to the provisions of
Article 11.4.8.5 of the AASHTO LRFD Bridge
Construction Specifications. Where permitted for use,
unless specific information is available to the contrary,
bolt holes in cross-frame, diaphragm, and lateral
bracing members and their connection plates shall be
assumed for design to be punched full size.
Except as specified herein for fracture critical
members, where the projected 75-year single lane
Average Daily Truck Traffic (ADTT)SL is less than or
equal to that specified in Table 7.6.2.3-2 for the
component or detail under consideration, that
component or detail should be designed for finite life
using the Fatigue II load combination specified in Table
3.4.1-1. Otherwise, the component or detail shall be
designed for infinite life using the Fatigue I load
combination. A single-lane Average Daily Truck
Traffic (ADTT)SL shall be computed as specified in
Article 3.6.1.4.2.
C7.6.2.3
Table 7.6.2.3-1 matches Table 3.1 of the Aluminum
Design Manual (AA, 2010).
The values in Table 7.6.2.3-2 were determined by
equating infinite and finite life resistances with due regard
to the difference in load factors used with the infinite (1.5
for Fatigue I) and finite life (0.75 for Fatigue II) load
combinations. The values were computed using the values
for Cf, m, and (ǻF)TH given in Table 7.6.2.5-1 and a
number of stress range cycles per truck passage n equal to
one, and rounded up to the nearest five trucks per day.
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BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
7-28
Table 7.6.2.3-1—Detail Categories for Load-Induced Fatigue
General
Condition
Detail
Detail
Category
Fatigue Design
Details (Note 1)
Plain Material
Base metal with rolled, extruded, drawn,
or cold finished surfaces; cut or sheared
surfaces with ANSI/ASME B46.1
surface roughness < 1000 ȝ in.
A
1, 2
Built-up
Members
Base metal and weld metal in members
without attachments and built up of
plates or shapes connected by continuous
full- or partial-penetration groove welds
or continuous fillet welds parallel to the
direction of applied stress.
B
3, 4, 5
Flexural stress in base metal at the toe of
welds on girder webs or flanges adjacent
to welded transverse stiffeners.
C
6, 21
Base metal at the end of partial-length
welded cover plates with square or
tapered ends, with or without welds
across the ends.
E
5
RS < 0
B
7
0 < RS < 0.5
D
7
RS 0.5
E
7
Base metal at the gross section of slipcritical connections and at the net section
of bearing connections, where the joint
configuration results in out-of-plane
bending in connected material.
E
8
Base metal at intermittent fillet welds
E
Base metal at the junction of axially
loaded members with fillet-welded end
connections. Welds shall be disposed
about the axis of the members so as to
balance weld stresses.
E
15, 17
Shear stress in weld metal of continuous
or intermittent longitudinal or transverse
fillet welds.
F
5, 15, 18
Mechanically
Fastened
Connections
Fillet Welds
Base metal at the gross section of slipcritical connections and at the net section
of bearing connections, where the joint
configuration does not result in out-ofplane bending in the connected material
and the stress ratio (the ratio of
minimum stress to maximum stress) RS
is (Note 2)
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2013
Revision
SECTION 7: ALUMINUM STRUCTURES
Groove Welds
Attachments
7-29
Base metal and weld metal at fullpenetration groove welded splices of
parts of similar cross-section ground
flush, with grinding in the direction of
applied stress and with weld soundness
established by radiographic or ultrasonic
inspection.
B
9, 10
Base metal and weld metal at fullpenetration groove welded splices at
transitions in width or thickness, with
welds ground to slopes < 1: 2.5, with
grinding in the direction of applied
stress, and with weld soundness
established by radiographic or ultrasonic
inspection.
B
11, 12
Base metal and weld metal at fullpenetration groove welded splices with
or without transitions with slopes
< 1: 2.5, when reinforcement is not
removed or weld soundness is not
established by radiographic or ultrasonic
inspection; or both.
C
9, 10, 11, 12
Base metal and weld metal at fullpenetration groove welds with
permanent backing.
E
22
R > 24 in.
B
13
24 in. > R > 6 in.
C
13
6 in. > R > 2 in.
D
13
Base metal at a detail attached by groove
welds or fillet welds with a detail
dimension parallel to the direction of
stress a < 2 in.
C
19
2 in. < a < 12b or 4 in.
D
14
a > 12b or 4 in.
E
14, 19, 20
Base metal detail of any length attached
by groove welds subject to transverse or
longitudinal loading, or both; with a
transition radius R > 2 in., and with the
weld termination ground smooth:
Base metal at a detail attached by groove
welds or fillet welds subject to
longitudinal loading, with a transition
radius, if any, < 2 in.:
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BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
7-30
Base metal at a detail of any length
attached by fillet welds or partialpenetration groove welds in the direction
parallel to the stress, with a transition
radius R > 2 in., and the weld
termination is ground smooth:
R > 24 in.
B
16
24 in. > R > 6 in.
C
16
6 in. > R > 2 in.
D
16
Notes:
1. See Figure 7.6.2.3-1. These examples are provided as guidelines and are not intended to exclude other similar details.
2. Tensile stresses are considered to be positive and compressive stresses are considered to be negative.
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SECTION 7: ALUMINUM STRUCTURES
7-31
Figure 7.6.2.3-1—Illustrative Examples
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7-32
Figure 7.6.2.3-1—Illustrative Examples (continued)
Table 7.6.2.3-2—75-yr (ADTT)SL Equivalent to Infinite
Life
Detail
Category
75-Year (ADTT)SL Equivalent
to Infinite Life (Trucks/Day)
A
B
C
D
E
F
20,410
5,085
2,310
2,465
2,115
2,005
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SECTION 7: ALUMINUM STRUCTURES
7-33
7.6.2.4—Detailing to Reduce Constraint
To the extent practical, welded structures shall be
detailed to avoid conditions that create highly
constrained
joints
and
crack-like
geometric
discontinuities that are susceptible to constraint-induced
fracture. Welds that are parallel to the primary stress but
interrupted by intersecting members shall be detailed to
allow a minimum gap of 1.0 in. between weld toes.
7.6.2.5—Fatigue Resistance
C7.6.2.5
Nominal fatigue resistance (ǻF)n shall be taken as:
•
For the Fatigue I load combination and infinite life:
(ǻF)n = (ǻF)TH
•
(7.6.2.5-1)
For the Fatigue II load combination and finite life:
(ǻF)n = Cf /N 1/m
(7.6.2.5-2)
in which:
(7.6.2.5-3)
N = (365)(75)n (ADTT)SL
where:
Cf
=
constant taken from Table 7.6.2.5-1 (ksi)
m
=
constant taken from Table 7.6.2.5-1
n
=
number of stress range cycles per truck
taken from Table 6.6.1.2.5-2
(ADTT)SL=
single lane ADTT as specified in Article
3.6.1.4
=
constant amplitude threshold taken from
Table 7.6.2.5-1
(ǻF)TH
Table 7.6.2.5-1 matches Table 3.2 of the Aluminum
Design Manual and Eq. 7.6.2.5-2 matches the equation
for fatigue strength given in Section 3.2 (AA, 2010).
While the S-N curves of different fatigue categories for
steel are parallel, the curves for aluminum are not. When
the curves were derived, the best fits were used. The S-N
curves for detail Classes C through F could be made
parallel without significant loss of accuracy. However,
this was not done in part to maintain some consistency
with fatigue provisions developed in conjunction with
European partners. From a fracture mechanics
perspective, the relationship between incremental crack
growth and applied stress intensity factor range is more
complex than for steel, particularly in the slow growth
regime, and is reflective of aluminum’s microstructural
barriers to crack growth extension, like sub-grain
structures. Further, it seems clear that Class A details,
like plain extruded sections, would be expected to have
a different fatigue response than other classes with
residual stresses caused by welds, and perhaps a
significantly different S-N curve slope.
Table 7.6.2.5-1—Detail Category Constant and Constant
Amplitude Fatigue Threshold
Detail
Category
Cf
(ksi)
m
(ǻF)TH
(ksi)
A
B
C
D
E
F
96.5
130
278
157
160
174
6.85
4.84
3.64
3.73
3.45
3.42
10.2
5.4
4.0
2.5
1.8
1.9
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7.6.3—Distortion-Induced Fatigue
Load paths that are sufficient to transmit all
intended and unintended forces shall be provided by
connecting all transverse members to appropriate
components of the cross-section of longitudinal
members. The load paths shall be provided by attaching
the various components by either welding or bolting.
7.6.3.1—Transverse Connection Plates
The provisions of Article 6.6.1.3.1 shall apply.
7.6.3.2—Lateral Connection Plates
The provisions of Article 6.6.1.3.2 shall apply.
7.7—GENERAL DIMENSION AND DETAIL
REQUIREMENTS
7.7.1—Effective Length of Span
Span lengths shall be taken as the distance between
centers of bearings or other points of support.
7.7.2—Dead Load Camber
Aluminum structures should be cambered during
fabrication to compensate for dead load deflection and
vertical alignment.
Deflection due to aluminum weight, steel weight,
concrete weight, wearing surface weight, and loads not
applied at the time of construction shall be reported
separately.
Vertical camber shall be specified to account for the
computed dead load deflection.
When staged construction is specified, the sequence
of load application should be considered when
determining the cambers.
7.7.3—Minimum Thickness
C7.7.3
The nominal thickness of aluminum components
shall not be less than 0.187 in.
The minimum thickness of aluminum components
depends primarily on resistance to damage during
fabrication and handling rather than a need for corrosion
allowance.
7.7.4—Diaphragms and Cross-Frames
Diaphragms and cross-frames shall conform to the
intent of Articles 6.7.4.1, 6.7.4.2, 6.7.4.3, and 6.7.4.4,
except the provisions for horizontally curved girders.
7.7.5—Lateral Bracing
Lateral bracing shall conform to the intent of
Article 6.7.5.
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SECTION 7: ALUMINUM STRUCTURES
7-35
7.7.6—Pins
7.7.6.1—Location
Pins should be located to minimize force effects due
to eccentricity. The distance from the center of a pin to
the edge of a part shall not be less than 1.5D, where D is
the nominal diameter of the pin. The pin hole diameter
shall not exceed the nominal diameter of the pin by
more than 1/32 in.
7.7.6.2—Strength Limit State
7.7.6.2.1—Combined Flexure and Shear
C7.7.6.2.1
Pins subjected to combined flexure and shear shall
be proportioned to satisfy:
3
§ M u · § Vu ·
¨
¸ + ¨ ¸ ≤ 1.0
© M r ¹ © Vr ¹
(7.7.6.2.1-1)
fs =
V
4V
=
A π D2
(C7.7.6.2.1-1)
Setting fs = Fsu, the shear ultimate strength of the pin,
and rearranging:
in which:
Mr = φy(ʌD3Fty /24.6) < φu(ʌD3Ftu /22.5)
(7.7.6.2.1-2)
Vr = φy(ʌD2Fsy /4) < φu(ʌD2Fsu /4)
(7.7.6.2.1-3)
Vu
=
shear resulting from factored loads (kip)
Vr
=
factored shear resistance (kip)
Mu
=
moment
(kip-in.)
Mr
=
factored flexural resistance (kip-in.)
resulting
from
factored
Vn =
Fsu π D 2
4
(C7.7.6.2.1-2)
The flexural resistance of aluminum pins is the
same as the flexural rupture resistance of aluminum rods
given in Article 7.11.5.
where:
φu, φy =
The shear resistance of aluminum pins is based on
the shear stress fs = V/A. For a rod,
loads
Mn =
1.42 Ftu S 1.42 Ftuπ D3 π D3 Ftu
=
=
kt
32kt
22.5kt
(C7.7.6.2.1-3)
The interaction equation for combined shear and
flexure of pins is based on Kulicki (1983).
resistance factors specified in Article 7.5.4.2
7.7.6.2.2—Bearing
C7.7.6.2.2
The factored bearing resistance of parts connected
by pins shall be taken as:
(RpB)r = φb(RpB)n
Article 7.7.6.2.2 matches Section J.7 of the
Aluminum Design Manual (AA, 2010).
(7.7.6.2.2-1)
in which:
(RpB)n = detFtu /1.5 < 1.33DtFtu
(7.7.6.2.2-2)
where:
de
=
distance from the center of the pin to the edge
of the part in the direction of force (in.)
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t
=
thickness of part (in.)
D
=
diameter of pin (in.)
φb =
resistance factor for pin bearing as specified in
Article 7.5.4.2
Ftu =
ultimate tensile strength of the part (ksi)
7.7.6.3—Pins and Pin Nuts
Pins shall be of sufficient lengths to secure a full
bearing of all parts connected upon the turned body of
the pin. The pin shall be secured in position by:
•
Hexagonal recessed nuts, or
•
Hexagonal solid nuts with washers, or
•
If the pins are bored through, a pin cap restrained by
pin rod assemblies.
Pin or rod nuts shall be aluminum or zinc-coated
steel and shall be secured in position by cotter pins
through the threads, lock nuts, or by burring the threads.
7.8—TENSION MEMBERS
7.8.1—General
Members and splices subjected to axial tension shall
be investigated for:
•
Yield on the gross section, and
•
Fracture on the net section
Holes larger than those typically used for
connectors such as bolts shall be deducted in
determining the gross section area, Ag.
The determination of the net section, An, requires
consideration of:
•
The gross area from which deductions will be made
or reduction factors applied, as appropriate;
•
Deductions for all holes in the design cross-section;
•
Correction of the bolt hole deductions for the
stagger rule specified in Article 7.8.3;
•
Application of the reduction factor specified in
Article 7.8.2.2 to account for shear lag.
Tension members shall satisfy the slenderness
requirements specified in Article 7.8.4 and the fatigue
requirements of Article 7.6. Block shear resistance shall
be investigated at end connections as specified in Article
7.12.4.
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SECTION 7: ALUMINUM STRUCTURES
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7.8.2—Tensile Resistance
7.8.2.1—General
C7.8.2.1
The factored tensile resistance Prt shall be taken as
the lesser of the values for tensile yielding on the gross
section and tensile rupture on the net section.
For tensile yielding on the gross section:
Prt = φy Pny
Article 7.8.2.1 matches Section D.2 of the
Aluminum Design Manual (AA, 2010).
(7.8.2.1-1)
in which:
For unwelded
transverse welds
members
and
members
Pny = Fty Ag
•
(7.8.2.1-2)
For members with longitudinal welds
Pny = Fty(Ag – Awz) + Ftyw Awz
•
with
(7.8.2.1-3)
For tensile rupture on the net section:
Prt = φu Pnu
(7.8.2.1-4)
in which:
•
For unwelded members
Pnu = Ftu Ae
•
(7.8.2.1-5)
For welded members
Pnu = Ftu(Ae – Awz) + Ftuw Awz
(7.8.2.1-6)
7.8.2.2—Effective Net Area
C7.8.2.2
The effective net area, Ae for angles, channels, tees,
zees, and I-shaped sections shall be determined as
follows:
•
If tension is transmitted directly to each of the
cross-sectional elements of the member by fasteners
or welds, the effective net area Ae shall be taken as
the net area An.
•
If tension is transmitted by fasteners or welds
through some but not all of the cross-sectional
elements of the member, the effective net area Ae
shall be taken as:
Ae = UAn
Article 7.8.2.2 matches Section D.3.2 of the
Aluminum Design Manual (AA, 2010).
(7.8.2.2-1)
where:
An =
net area of the member at the connection (in.2)
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U
=
reduction factor to account for shear lag taken
as given in Article 6.8.2.1
The net effective area shall not be less than the net
area of the connected elements.
7.8.2.3—Combined Tension and Flexure
A component subjected to tension and flexure shall
satisfy Eq. 7.8.2.3-1.
Put M ux M uy
+
+
≤ 1.0
Prt M rx M ry
C7.8.2.3
Article 7.8.2.3 matches Section H.1 of the
Aluminum Design Manual (AA, 2010).
(7.8.2.3-1)
where:
Put =
axial tension resulting from the factored loads
(kip)
Prt =
factored tensile resistance (kip)
Mux =
moment about the major principal axis
resulting from the factored loads (kip-in.)
Mrx =
factored flexural resistance about the major
principal axis (kip-in.)
Muy =
moment about the minor principal axis
resulting from the factored loads (kip-in.)
Mry =
factored flexural resistance about the minor
principal axis (kip-in.)
7.8.3—Net Area
The net area, An, of an element is the product of the
thickness of the element and its smallest net width. The
width of each drilled hole shall be taken as the nominal
diameter of the hole and the width of each punched hole
shall be taken as the nominal diameter of the hole plus
1
/32 in. The net width shall be determined for each chain
of holes extending across the member or along any
transverse, diagonal, or zigzag line.
The net width for each chain shall be determined by
subtracting from the width of the element the sum of the
widths of all holes in the chain and adding the quantity
s2/4g for each space between consecutive holes in the
chain.
where:
s
=
longitudinal center-to-center distance (pitch)
between two holes (in.)
g
=
transverse center-to-center distance (gauge)
between two holes (in.)
© 2013
the American
Association
of State
Highway
and Transportation
Officials.
© 2012
by thebyAmerican
Association
of State
Highway
and Transportation
Officials.
All rights
reserved.
Duplication
is a violation
of applicable
All rights
reserved.
Duplication
is a violation
of applicable
law. law.
2013
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SECTION 7: ALUMINUM STRUCTURES
7-39
7.8.4—Limiting Slenderness Ratio
C7.8.4
Tension members other than rods, eyebars, and
plates shall satisfy the slenderness requirements
specified below:
The slenderness limits of Article 7.8.4 match
Article 6.8.4.
•
For primary members subject to stress reversals,
l/r < 140
•
For primary members not subject to stress reversals,
l/r < 200
•
For secondary members, l/r < 240
where:
l
=
unbraced length (in.)
r
=
radius of gyration (in.)
7.8.5—Built-up Members
The main elements of built-up tension members
shall be connected by continuous plates with or without
perforations, or by tie plates with or without lacing.
Welded connections between shapes and plates shall be
continuous. Bolted connections between shapes and
plates shall conform to Articles 7.12.2 and 7.12.5.
7.9—COMPRESSION MEMBERS
7.9.1—General
The provisions of this Article shall apply to
prismatic aluminum members subjected to either axial
compression, or combined axial compression and
flexure.
7.9.2—Axial Compression Resistance
C7.9.2
The factored resistance, Prc, of components in axial
compression shall be taken as:
The nominal compressive resistance given in
Article 7.9.2 matches Section E.1 of the Aluminum
Design Manual (AA, 2010).
Prc = φc Pn
(7.9.2-1)
where:
Pn =
least of the nominal compressive resistance
for member buckling specified in Article
7.9.2.1, the nominal compressive resistance for
local buckling specified in Article 7.9.2.2, and
the nominal compressive resistance for
the interaction between member buckling
and local buckling specified in Article 7.9.2.3
(kip)
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φc =
resistance factor for compression specified in
Article 7.5.4.2
7.9.2.1—Member Buckling
7.9.2.1.1—General
C7.9.2.1.1
The nominal compressive resistance Pn for member
buckling is:
Pn = Fc Ag
This Article matches Sections E.3 and E.6 of the
Aluminum Design Manual (AA, 2010).
(7.9.2.1.1-1)
in which the compressive buckling stress Fc shall be
taken as:
•
If Kl/r < Cc, then
Fc = 0.85(Bc – Dc Kl/r) < Fcy
•
(7.9.2.1.1-2)
If Kl/r > Cc then
Fc =
0.85π 2 E
§ Kl ·
¨
¸
© r ¹
(7.9.2.1.1-3)
2
where:
Kl/r
= largest column effective slenderness
determined from Articles 7.9.2.1.2
Bc, Dc, and Cc = parameters
specified
7.5.4.3-1 or 7.5.4.3-2
in
Table
The effective length factor, K, shall be determined
in accordance with Article 4.6.2.5. For members without
welds, Bc, Dc, Cc, and Fcy shall be determined using
unwelded material properties. For members whose
cross-section is fully weld-affected over the entire length
of the member, Bc, Dc, Cc, and Fcy shall be determined
using welded material properties. For other members:
•
For members supported at both ends and with no
transverse weld farther than 0.05L from the member
ends, Bc, Dc, Cc, and Fcy shall be determined using
unwelded material properties.
•
For members supported at both ends with a
transverse weld farther than 0.05L from the member
ends and for members supported at only one end
with a transverse weld, Bc, Dc, Cc, and Fcy shall be
determined using welded material properties.
•
For members with longitudinal welds:
The nominal member buckling resistance Pn is
Pn = Pno(1 – Awz /Ag) + Pnw (Awz /Ag)
(7.9.2.1.1-4)
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2013
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SECTION 7: ALUMINUM STRUCTURES
7-41
where:
Pno =
nominal member buckling resistance if no part
of the cross-section is weld-affected (kip)
Pnw =
nominal member buckling resistance if the
entire cross-section is weld-affected (kip)
7.9.2.1.2—Flexural Buckling
C7.9.2.1.2
For flexural buckling, Kl/r is the largest slenderness
ratio of the column.
7.9.2.1.3—Torsional and Flexural-Torsional
Buckling
For torsional or flexural-torsional buckling, Kl/r
shall be taken as the larger of the slenderness ratio for
flexural buckling and the equivalent slenderness ratio,
which shall be determined as:
E
§ Kl ·
¨ ¸ =π
Fe
© r ¹e
This Article matches Section E.3.1 of the Aluminum
Design Manual (AA, 2010).
C7.9.2.1.3
This Article matches Section E.3.2 of the Aluminum
Design Manual (AA, 2010).
(7.9.2.1.3-1)
The elastic buckling stress, Fe, (ksi) shall be
determined by rational analysis or as follows:
•
For doubly symmetric members:
§ π 2 ECw
· 1
Fe = ¨
+
GJ
¸¸
¨ ( K l )2
© zz
¹ Ix + I y
•
For singly symmetric members where y is the axis
of symmetry:
§ Fey + Fez
Fe = ¨
© 2H
•
(7.9.2.1.3-2)
4 Fey Fez H
·ª
¸ «1 − 1 −
( Fey + Fez )2
¹ «¬
º
»
»
¼
(7.9.2.1.3-3)
For unsymmetric members, Fe is the lowest root of
the cubic equation:
(Fe – Fex)(Fe – Fey)(Fe – Fez) – Fe2(Fe – Fey)(x0 /r0)2
– Fe2(Fe – Fex)(y0 /r0)2 = 0
(7.9.2.1.3-4)
in which:
r02 = x0 2 + y0 2 +
H = 1−
Ix + I y
x02 + y02
r02
Ag
(7.9.2.1.3-5)
(7.9.2.1.3-6)
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Fex =
Fey =
Fez =
π2 E
2
(7.9.2.1.3-7)
2
(7.9.2.1.3-8)
§ K x lx ·
¨
¸
© rx ¹
π2 E
§ K yly
¨¨
© ry
·
¸¸
¹
§
π2 ECw ·
¨¨ GJ +
¸
Ag r0 ©
( K z l z )2 ¸¹
1
(7.9.2.1.3-9)
2
where:
r0
=
polar radius of gyration about the shear
center (in.)
x0, y0
=
coordinates of the shear center with respect
to the centroid (in.)
I x, I y
=
moments of inertia about the principal axes
(in.4)
rx, ry
=
radii of gyration about the centroidal
principal axes (in.)
7.9.2.2—Local Buckling
7.9.2.2.1—General
C7.9.2.2.1
For members without welds, the nominal
compressive resistance, Pn, for local buckling shall be
determined in accordance with either Article 7.9.2.2.2 or
7.9.2.2.3. For members with welds, the local buckling
resistance shall be determined in accordance with
Article 7.9.2.2.2.
7.9.2.2.2—Weighted Average Local Buckling
Resistance
The weighted average local buckling resistance may
be determined as:
n
Pn =
¦
i =1
§
Fnci Ai + Fcy ¨ Ag −
¨
©
·
n
¦ A ¸¸¹
i
This Article matches Section E.4 of the Aluminum
Design Manual (AA, 2010).
C7.9.2.2.2
This Article matches Section E.4.1 of the Aluminum
Design Manual (AA, 2010).
(7.9.2.2.2-1)
i =1
where:
Fnci
=
nominal local buckling resistance of
element i computed per Articles 7.5.4.4.1
through 7.5.4.4.6 (ksi)
Ai
=
area of element i (in.2)
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2013
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SECTION 7: ALUMINUM STRUCTURES
7-43
7.9.2.2.3—Alternative Local Buckling Resistance
As an alternative to Article 7.9.2.2.2, the local
buckling resistance of a shape composed of flat elements
may be determined as:
Pn = Fnc Ag
(7.9.2.2.3-1)
C7.9.2.2.3
This Article matches Section E.4.2 of the Aluminum
Design Manual (AA, 2010). Article 7.9.2.2.3 may be
used for shapes not addressed by Article 7.5.4.4, or for a
more accurate determination of local buckling resistance
of any shape.
where Fnc is determined in accordance with Article
7.5.4.4.7.
7.9.2.3—Interaction Between Member Buckling
and Local Buckling
If the elastic local buckling stress, Fe, is less than
the member buckling stress given by Eq. 7.9.2.1.1-2 or
7.9.2.1.1-3 as appropriate, the nominal compressive
resistance of the member shall not exceed
C7.9.2.3
Article 7.9.2.3 matches Section E.5 of the
Aluminum Design Manual (AA, 2010).
1/3
ª 0.85π2 E º
»
Pn = «
«¬ ( Kl / r )2 »¼
Fe 2/3 Ag
(7.9.2.3 -1)
If the local buckling resistance is determined from
Article 7.9.2.2.2, Fe is the smallest elastic local buckling
stress for all elements of the cross-section determined
from Table 7.5.4.9-1.
If the local buckling resistance is determined from
Article 7.9.2.2.3, Fe is the elastic local buckling stress of
the cross-section determined by rational analysis.
7.9.3—Limiting Slenderness Ratio
C7.9.3
Compression members shall satisfy the slenderness
requirements specified below:
•
For primary members, Kl/r < 120
•
For secondary members, Kl/r < 140
Article 7.9.3 matches Article 6.9.3.
where:
K
=
effective length factor specified in Article
4.6.2.5
l
=
unbraced length (in.)
r
=
radius of gyration (in.)
7.9.4—Combined Axial Compression and Flexure
C7.9.4
A component subjected to axial compression and
flexure shall satisfy:
Article 7.9.4 matches Section H.1 of the Aluminum
Design Manual (AA, 2010).
Puc M ux M uy
+
+
≤ 1.0
Prc M rx M ry
(7.9.4-1)
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2013
Revision
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where:
Puc
=
axial compression resulting from the
factored loads (kip)
Prc
=
factored axial compression resistance (kip)
Mux
=
moment about the major principal axis
resulting from the factored loads
(kip-in.)
Mrx
=
factored flexural resistance about the major
principal axis (kip-in.)
Muy
=
moment about the minor principal axis
resulting from the factored loads
(kip-in.)
Mry
=
factored flexural resistance about the
minor principal axis (kip-in.)
Mux, Muy =
moments about axes of symmetry, may be
determined by:
•
•
A second-order elastic analysis that
accounts for the magnification of
moment caused by the factored axial
load, or
The
approximate
single-step
adjustment in Article 4.5.3.2.2b.
7.10—GENERAL FLEXURAL MEMBERS
7.10.1—General
This Article shall be applied to all structural shapes
except rectangular bars, pipes, round tubes, and rods,
which are addressed in Article 7.11.
7.10.2—Flexural Resistance
7.10.2.1—General
as:
The factored flexural resistance, Mr, shall be taken
Mr = φ Mn
(7.10.2.1-1)
where:
φ
=
resistance factor for flexure specified in Article
7.5.4.2, taken as:
• φft for tensile rupture, or
• φf for all other flexural limit states
Mn =
nominal flexural resistance, which is the lesser
of the nominal flexural resistance for lateraltorsional buckling specified in Article 7.10.2.2
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SECTION 7: ALUMINUM STRUCTURES
7-45
and the nominal flexural resistance of the
elements specified in Article 7.10.2.3 (kip-in.)
7.10.2.2—Lateral-Torsional Buckling
7.10.2.2.1—Open Shapes
C7.10.2.2.1
For open shapes subject to lateral-torsional
buckling, the nominal flexural resistance shall be
determined as follows:
Mn = Fnb Sc
This Article matches Sections F.2.1, F.2.2.1,
F.2.2.2, and F.2.3 of the Aluminum Design Manual (AA,
2010).
(7.10.2.2.1-1)
where:
=
section modulus on the compression side of the
neutral axis (in.3)
Fnb =
lateral-torsional buckling stress (ksi) shall be
taken as:
Sc
•
For
Lb
rye Cb
Dc Lb
Fnb = Bc −
•
For
1.2rye Cb
Lb
rye Cb
Fnb =
< 1.2Cc , then
(7.10.2.2.1-2)
≥ 1.2c , then
π2 E
§
·
Lb
¨
¸
¨ 1.2rye Cb ¸
©
¹
2
(7.10.2.2.1-3)
where:
Lb
=
unbraced length (in.)
Cb
=
moment gradient modifier,
defined in Article 7.10.2.2.3
Bc, Dc, and Cc =
as
parameters given in Table 7.5.4.3-1
or 7.5.4.3-2
rye shall be ry or determined as follows:
For shapes symmetric about the bending axis:
•
Between brace points of beams subjected to
end moment only or to transverse loads applied
at the beam’s neutral axis, or at brace points:
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BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
7-46
rye =
1
I yd
1.7
Sc
1 + 0.152
J § Lb ·
¨ ¸
Iy © d ¹
2
(7.10.2.2.1-4)
•
Between brace points of beams subjected to
transverse loads applied on the top or bottom
flange such that the load is free to move
laterally with the beam if the beam buckles:
2
ª
J L º
« ±0.5 + 1.25 + 0.152 ¨§ b ¸· »
Iy © d ¹ »
«
¬
¼
1 I yd
rye =
1.7 Sc
(7.10.2.2.1-5)
The term 0.5 shall be taken as negative when the
load acts toward the shear center and positive when the
load acts away from the shear center.
where:
The y-axis is the centroidal symmetry or principal axis
that is parallel to the web.
Iy
=
moment of inertia about the weak axis (in.4)
d
=
depth of the beam (in.)
Sc
=
•
whose flanges are flat elements supported on one
edge and
•
for which the flange’s elastic buckling stress, Fe,
given in Article 7.5.4.9 is less than the lateraltorsional buckling stress of the beam Fnb
section modulus on the compression side of the
neutral axis (in.3)
For singly symmetric shapes unsymmetric about the
bending axis, rye shall be determined with Iy, Sc, and J
determined as though both flanges were the same as the
compression flange with the overall depth d remaining
the same. For open shapes:
The lateral-torsional buckling resistance shall not
exceed:
ª
π2 E
Mn = «
Ǥ
Lb
Ǭ
¨
«¬ © 1.2rye Cb
1/3
º
2»
· »
¸ »
¸ »
¹ ¼
Fe 2/3 Sc
(7.10.2.2.1-6)
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SECTION 7: ALUMINUM STRUCTURES
7-47
7.10.2.2.2—Closed Shapes
C7.10.2.2.2
For noncircular closed shapes bent about their
major axis, the nominal flexural resistance for the limit
state of lateral-torsional buckling shall be taken as:
Mn = FnbSc
This Article matches Section F.3.1 of the Aluminum
Design Manual (AA, 2010).
(7.10.2.2.2-1)
where:
=
section modulus on the compression side of the
neutral axis (in.3)
Fnb =
the lateral-torsional buckling stress (ksi) shall
be taken as:
Sc
•
If
2
§C ·
< ¨ c ¸ , then
I y J © 1.6 ¹
2Lb Sc
Cb
Fnb = Bc − 1.6 Dc
•
If
Fnb =
(7.10.2.2.2-2)
2
§C ·
≥ ¨ c ¸ , then
I y J © 1.6 ¹
2Lb Sc
Cb
2 Lb Sc
Cb I y J
π2 E
§ 2L S
b c
2.56 ¨
¨ Cb I y J
©
·
¸
¸
¹
(7.10.2.2.2-3)
where:
Lb
=
unbraced length (in.)
Cb
=
moment gradient modifier, as defined in
Article 7.10.2.2.3
Bc,Dc,Cc
=
parameters given in Table 7.5.4.3-1 or
7.5.4.3-2
7.10.2.2.3—Moment Gradient Modifier
•
Members supported on both ends: For the case of
uniform bending moment, the moment gradient
modifier Cb = 1. For other cases, Cb shall be taken
as 1 or determined in accordance with Article
7.10.2.2.3a or 7.10.2.2.3b.
•
Cantilevers: Cb shall be determined in accordance
with Article 7.10.2.2.3a.
7.10.2.2.3a—Doubly Symmetric Shapes
For doubly symmetric shapes between brace points:
C7.10.2.2.3
This Article matches Section F.1.1 of the Aluminum
Design Manual (AA, 2010).
C7.10.2.2.3a
This Article matches Section F.1.1.1 of the
Aluminum Design Manual (AA, 2010).
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BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
7-48
Cb =
12.5M max
≥ 1.0
2.5M max + 3M A + 4 M B + 3M C
(7.10.2.2.3a-1)
where:
Mmax
=
absolute value of the maximum moment in
the unbraced segment (kip-in.)
MA
=
absolute value of the moment at the quarter
point of the unbraced segment (kip-in.)
MB
=
absolute value of the moment at the
midpoint of the unbraced segment (kip-in.)
MC
=
absolute value of the moment at the threequarter point of the unbraced segment
(kip-in.)
For doubly symmetric shape cantilevers unbraced at
the free end, Cb shall be determined as follows:
Loading
Concentrated load applied at the centroid at the
free end
Uniform transverse load applied at the centroid
Cb
1.3
2.1
7.10.2.2.3b—Singly Symmetric Shapes
For singly symmetric shapes between brace points:
•
If Icy /Iy < 0.1 or Icy /Iy > 0.9, then Cb = 1.0
•
If 0.1 < Icy /Iy < 0.9, then Cb shall be determined
using Eq. 7.10.2.2.3a-1.
C7.10.2.2.3b
This Article matches Section F.1.1.2 of the
Aluminum Design Manual (AA, 2010).
Where Mmax produces compression on the larger
flange and the smaller flange is also subjected to
compression at another location in the unbraced length,
the member shall be investigated at the location of Mmax
using Cb determined using Eq. 7.10.2.2.3a-1 and at the
location where the smaller flange is subjected to its
maximum compression using Cb = 1.67.
7.10.2.2.4—Welded Flexural Members
7.10.2.2.4a—Flexural Members with
Transverse Welds
The lateral-torsional buckling resistance of
members supported at both ends with no transverse weld
farther than 0.05L from the member ends shall be
determined as if there were no welds.
The lateral-torsional buckling resistance of
members supported at both ends with a transverse weld
farther than 0.05L from the member ends and members
C7.10.2.2.4a
This Article matches Section F.9.1 of the Aluminum
Design Manual (AA, 2010).
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2013
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SECTION 7: ALUMINUM STRUCTURES
7-49
supported at only one end with a transverse weld at any
location shall be determined as if the entire crosssectional area were weld-affected.
7.10.2.2.4b—Flexural Members with
Longitudinal Welds
The nominal lateral-torsional buckling resistance
Mn of members with longitudinal welds shall be taken
as:
Mn = Mno(1 – Awz /Af) + Mnw (Awz /Af)
C7.10.2.2.4b
This Article matches Section F.9.2 of the Aluminum
Design Manual (AA, 2010).
(7.10.2.2.4b-1)
where:
Mno =
lateral-torsional buckling resistance if no part
of the cross-section is weld-affected using
buckling constants for unwelded metal and
unwelded strengths (kip-in.)
Awz =
weld-affected area of the member farther than
2c/3 from the neutral axis, where c is the
distance from the neutral axis to the extreme
compression fiber (in.2)
Af
=
area of the member farther than 2c/3 from the
neutral axis, where c is the distance from the
neutral axis to the extreme compression fiber
(in.2)
Mnw =
lateral-torsional buckling resistance if the entire
cross-section is weld-affected using buckling
constants for weld-affected zones and welded
strengths (kip-in.)
7.10.2.3—Elements of Flexural Members
The nominal flexural resistance of the elements of
flexural members shall be taken as the least of the
resistance for tensile yielding, tensile rupture,
compression yielding, and local buckling. Alternately,
the nominal flexural resistance of the elements of
flexural members shall be determined as the weighted
average flexural resistance using Article 7.10.2.3.3.
7.10.2.3.1—Tension
C7.10.2.3
This Article matches Section F.8 of the Aluminum
Design Manual (AA, 2010).
C7.10.2.3.1
For the limit states of yielding and tensile rupture,
the nominal flexural resistance shall be determined as
Mn = FnbSt where Fnb is determined for elements in
uniform tension per Article 7.5.4.6 and for elements in
flexural tension per Article 7.5.4.7, and St = section
modulus on the tension side of the neutral axis (in.3).
7.10.2.3.2—Compression
For the limit state of compression, the nominal
flexural resistance may be determined as Mn = FnbSc
This Article matches Section F.8.1 of the Aluminum
Design Manual (AA, 2010).
C7.10.2.3.2
This Article matches Section F.8.2 of the Aluminum
Design Manual (AA, 2010).
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7-50
where Fnb is determined for elements in uniform
compression per Article 7.5.4.4 and for elements in
flexural compression per Article 7.5.4.5.
7.10.2.3.3—Weighted Average Flexural Resistance
The weighted average nominal flexural resistance,
Mn, shall be taken as the lesser of the compressive
flexural resistance, Mnc, and the tensile flexural
resistance, Mnt. The compressive flexural resistance,
Mnc, shall be taken as:
Mnc = Fnc If /ccf + Fnb Iw /ccw
C7.10.2.3.3
This Article matches Section F.8.3 of the Aluminum
Design Manual (AA, 2010).
(7.10.2.3.3-1)
where:
Fnc =
local buckling stress of the flat elements in
uniform compression determined using Article
7.5.4.4 (ksi). The resistance of stiffened
elements shall not exceed the resistance of an
intermediate stiffener or an edge stiffener.
=
moment of inertia of the flange group about the
cross-section’s neutral axis (in.4). The flange
group consists of the flat elements in uniform
compression and the flat elements in uniform
tension and their edge or intermediate
stiffeners.
ccf =
distance from the centerline of the compression
flange to the cross-section’s neutral axis (in.)
Fnb =
local buckling stress of the flat elements in
flexural compression determined using Article
7.5.4.5 (ksi).
Iw
=
moment of inertia of the web group about the
cross-section’s neutral axis (in.4). The web
group consists of the flat elements in flexure
and their intermediate stiffeners.
ccw =
distance from the web group’s extreme
compression fiber to the cross-section’s neutral
axis (in.)
If
If there are stiffeners located farther than the
compression flange from the cross-section’s neutral axis,
the compressive flexural resistance shall not exceed
Fcy If /ccs + Fb Iw /ccw.
where:
ccs =
distance from the cross-section’s neutral axis to
the extreme fiber of compression flange
stiffeners (in.)
The nominal tensile flexural resistance, Mnt, shall be
taken as:
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SECTION 7: ALUMINUM STRUCTURES
Mnt = Fnt If /ctf + Fnb Iw /ctw
7-51
(7.10.2.3.3-2)
where:
Fnt =
tensile stress for the flat elements in uniform
tension determined using Article 7.5.4.6 (ksi)
ctf =
distance from the extreme tension fiber to the
cross-section’s neutral axis (in.)
Fnb =
tensile stress for the flat elements in flexural
tension determined using Article 7.5.4.7 (ksi)
ctw =
distance from the web group’s extreme tension
fiber to the cross-section’s neutral axis (in.)
7.10.3—Shear Resistance
The factored resistance, Vr, of components in shear
shall be taken as:
Vr = φvVn
(7.10.3-1)
where:
φv Vn = Fns Av
Fns =
Av
(7.10.3-2)
the nominal shear stress specified in Article
7.5.4.8 (ksi)
= shear area (in.2) taken as:
φv =
•
For flat elements supported on both edges,
Av = dt, where d = full depth of the section
(in.)
•
For flat elements supported on one edge,
Av = bt, where b = distance from the
unsupported edge to the mid-thickness of
the supporting element (in.)
•
For round or oval tubes, Av = Ag/2
resistance factor for shear specified in Article
7.5.4.2
7.10.4—Stiffeners
7.10.4.1—Crippling of Flat Webs
C7.10.4.1
The factored resistance of flat webs for the limit
state of web crippling shall be taken as:
This Article matches Section J.8.1 of the Aluminum
Design Manual (AA, 2010).
Rr = φw Rn
(7.10.4.1-1)
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7-52
where:
φw =
resistance factor for web crippling specified in
Article 7.5.4.2
Rn =
the nominal web
determined as follows:
•
resistance
For concentrated forces applied at a
distance from a member support that
equals or exceeds d/2:
Rn =
•
crippling
Cwa ( N + 5.4)
(7.10.4.1-2)
Cwb
For concentrated forces applied at a
distance from a member support that is less
than d/2:
Rn =
1.2C wa ( N + 1.3)
(7.10.4.1-3)
C wb
in which:
(
Cwa = t 2 sin θ w 0.46 Fcy + 0.02 EFcy
Cwb = 0.4 + Ri (1 − cos șw )
)
(7.10.4.1-4)
(7.10.4.1-5)
where:
d
= member depth (in.)
N
=
length of the bearing
concentrated force (in.)
Ri
=
for extruded shapes, Ri = 0; for all other shapes,
Ri inside bend radius at the juncture of the
flange and web (in.)
t
=
web thickness (in.)
șw =
surface
at
the
angle between the plane of web and the plane
of the bearing surface (θ w ≤ 90°)
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2013
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SECTION 7: ALUMINUM STRUCTURES
7-53
7.10.4.2—Bearing Stiffeners
C7.10.4.2
Bearing stiffeners at concentrated forces shall be
sufficiently connected to the web to transmit the
concentrated force. Such stiffeners shall form a tight
and uniform bearing against the flanges unless welds
designed to transmit the full concentrated force are
provided between flange and stiffener. Only the part of a
stiffener cross-section outside the flange-to-web fillet
shall be considered effective in bearing. The bearing
stiffener shall meet the requirements of Article 7.9 with
the length of the stiffener equal to the height of the web.
7.10.4.3—Combined Crippling and Bending of
Flat Webs
Combinations of bending and concentrated forces
applied at a distance of one-half or more of the member
depth from the member support shall satisfy the
following equation:
1.5
This Article matches Section J.8.2 of the Aluminum
Design Manual (AA, 2010).
C7.10.4.3
This Article matches Section J.8.3 of the Aluminum
Design Manual (AA, 2010).
1.5
§ Ru ·
§ Mu ·
¨ ¸ +¨
¸
© Rr ¹
© Mr ¹
≤ 1.0
(7.10.4.3-1)
where:
Ru =
concentrated force resulting from factored
loads (kip)
Rr =
factored
resistance
concentrated
force
determined in accordance with Article 7.10.4.1
(kip)
Mu =
moment in the member at the location of the
concentrated force resulting from factored
loads (kip-in.)
Mr =
factored flexural resistance determined in
accordance with Article 7.10 (kip-in.)
7.11—MISCELLANEOUS FLEXURAL MEMBERS
7.11.1—General
as:
The factored flexural resistance, Mr, shall be taken
Mr = φMn
(7.11.1-1)
where:
Mn =
nominal flexural resistance (kip-in.)
φ
resistance factor for flexure specified in Article
7.5.4.2, taken as φft for tensile rupture, or φf for
all other flexural limit states
=
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BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
7-54
7.11.2—Rectangular Bars
C7.11.2
The nominal flexural resistance of rectangular bars
shall be determined for yielding and rupture in Article
7.11.2.1 and lateral-torsional buckling in Article
7.11.2.2.
This Article matches Section F.4 of the Aluminum
Design Manual (AA, 2010).
7.11.2.1—Yielding and Rupture
C7.11.2.1
For yielding the nominal flexural resistance shall be
taken as:
Mn = 1.3 Fcy S
This Article matches Section F.4.1 of the Aluminum
Design Manual (AA, 2010).
(7.11.2.1-1)
For tensile rupture, the nominal flexural resistance
shall be taken as:
Mn = 1.42 Ftu S
(7.11.2.1-2)
where:
Fcy = compressive yield strength (ksi)
S
= section modulus (in.3)
Ftu = specified minimum tensile ultimate strength (ksi)
7.11.2.2—Lateral-Torsional Buckling
C7.11.2.2
For lateral-torsional buckling, the nominal flexural
resistance shall be taken as:
Mn = Fnb S
This Article matches Section F.4.2 of the Aluminum
Design Manual (AA, 2010).
(7.11.2.2-1)
in which the nominal lateral-torsional buckling stress,
Fnb, shall be taken as: then
• If
d Lb
< Cbr / 2.3, then
t Cb d
Fnb = Bbr − 2.3Dbr
•
If
d
t
Fnb =
d
t
Lb
Cb d
(7.11.2.2-2)
Lb
≥ Cbr 2.3, then
Cb d
π2 E
2
§d · § L ·
5.29 ¨ ¸ ¨ b ¸
© t ¹ © Cb d ¹
(7.11.2.2-3)
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SECTION 7: ALUMINUM STRUCTURES
7-55
where:
Lb
= unbraced length (in.)
Cb
= moment gradient modifier between
brace points, as defined in Article
7.10.2.2.3
Cbr,Bbr, and Dbr = parameters specified
7.5.4.3-1 or 7.5.4.3-2
in
Table
7.11.3—Single Angles
C7.11.3
Single angles should not be used as pure flexural
members.
Single angles are not usually intended to serve as
pure flexural members in bridges. In most practical
applications, single angles are subject to flexure about
both principal axes due to the eccentricity of applied
axial loads. The flexural resistance of single angles can
be determined using Section F.5 of the Aluminum
Design Manual (AA, 2010).
7.11.4—Pipes and Round Tubes
C7.11.4
The nominal flexural resistance of pipes and round
tubes shall be determined for yielding and rupture in
Article 7.11.4.1 and local buckling in Article 7.11.4.2.
This Article matches Section F.6 of the Aluminum
Design Manual (AA, 2010).
7.11.4.1—Yielding and Rupture
C7.11.4.1
For yielding, the nominal flexural resistance shall
be taken as:
Mn = 1.17 Fcy S
This Article matches Section F.6.1 of the Aluminum
Design Manual (AA, 2010).
(7.11.4.1-1)
For rupture, the nominal flexural resistance shall
be taken as:
Mn = 1.24 Ftu S
(7.11.4.1-2)
C7.11.4.2
7.11.4.2—Local Buckling
For local buckling, the nominal flexural resistance
shall be taken as:
Mn = Fnb S
This Article matches Section F.6.2 of the Aluminum
Design Manual (AA, 2010).
(7.11.4.2-1)
in which the nominal local buckling stress Fnb shall be
taken as:
•
2
§ B −B
R
t
If b ≤ ¨ tb
¨D −D
t
t
© tb
·
¸ , then
¸
¹
F = B −D
nb
tb
tb
R
b
t
(7.11.4.2-2)
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BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
7-56
•
§ B −B
t
If ¨ tb
¨D −D
© tb
t
2
R
·
¸ < b < C , then
t
¸
t
¹
F = B −D
nb
t
t
•
R
b
t
(7.11.4.2-3)
R
If b ≥ C , then
t
t
F =
nb
2
ʌ E
§
R ·
b ¸
¨
§ Rb · ¨
t ¸
16 ¨
1+
¨ t ¸¸ ¨
35 ¸
© ¹¨
¸¸
¨
©
¹
2
(7.11.4.2-4)
where:
Rb
= mid-thickness radius (in.)
t
= thickness (in.)
Btb, Bt, Dtb, Dt , and Ct = parameters specified in Table
7.5.4.3-1 or 7.5.4.3-2
7.11.5—Rods
C7.11.5
For rods, the nominal flexural resistance shall be
determined for the limit states of yielding and tensile
rupture.
For yielding, the nominal flexural resistance shall
be taken as:
This Article matches Section F.7 of the Aluminum
Design Manual (AA, 2010).
Mn = 1.3Fcy S
(7.11.5-1)
For tensile rupture, the nominal flexural resistance
shall be taken as:
Mn = 1.42Ftu S
(7.11.5-2)
where:
Fcy = compressive yield strength (ksi)
S
= section modulus (in.3)
Ftu = specified minimum tensile ultimate strength (ksi)
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2013
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SECTION 7: ALUMINUM STRUCTURES
7-57
7.12—CONNECTIONS AND SPLICES
7.12.1—General
Connections shall be designed for the factored
member force effects.
Connections, except for lacing and handrails, shall
not contain less than two bolts.
Members and connections shall be designed for the
effects of any eccentricity in joints.
7.12.2—Bolted Connections
7.12.2.1—General
C7.12.2.1
Contract documents shall specify that all joint
surfaces, including surfaces under bolt heads, nuts, and
washers, shall be free from foreign material.
Articles 6.13.2.1.1 and 6.13.2.1.2 shall be used to
determine whether a connection shall be designed as a
slip-critical connection or a bearing connection. Only
A325 bolts shall be used in slip-critical connections. The
slip resistance of slip-critical connections shall be
determined in accordance with Article 7.12.2.8.
C7.12.2.2
7.12.2.2—Factored Resistance
For slip-critical connections, the factored resistance
Rr, of a bolt at the Service II Load Combination shall be
taken as:
Rr = Rn
Additional requirements related to bolts, nuts, and
washers are provided in Article 7.4.3.
(7.12.2.2-1)
Article 7.12.2.2 is similar to Article 6.13.2.2. The
resistance of steel parts of the connection (the bolts) is
addressed in Section 6, and the resistance of the
aluminum parts of the connection (the connected parts)
is addressed in Section 7.
where:
Rn =
nominal slip resistance specified in Article
7.12.2.8
The factored resistance, Rr or Tr, of a bolted
connection at the strength limit state shall be taken as
either:
Rr = φRn
(7.12.2.2-2)
or:
Tr = φTn
(7.12.2.2-3)
where:
φ
=
resistance factor for bolts taken as
•
•
•
φs for bolts in shear as specified in Article
6.5.4.2
φt for bolts in tension as specified in
Article 6.5.4.2
φbb for bolts in bearing as specified in
Article 7.5.4.2
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2013
Revision
2013 INTERIM REVISIONS TO THE AASHTO LRFD
BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
7-58
•
•
Rn =
nominal shear resistance of the bolt or
connected material taken as follows:
•
•
•
Tn =
φy or φu for connected material in tension
as specified in Article 7.5.4.2
φv for connected material in shear as
specified in Article 7.5.4.2
For bolts in shear, Rn shall be taken
specified in Article 7.12.2.7
For the connected material, Rn shall
taken as specified in Article 7.12.2.9
For the connected material in tension
shear, Rn shall be taken as specified
Article 7.12.5
as
be
or
in
nominal tensile resistance of the bolt taken as
follows:
•
For bolts in tension, Tn shall be taken as specified in
Article 7.12.2.10
•
For bolts in combined tension and shear, Tn shall be
taken as specified in Article 7.12.2.11
7.12.2.3—Washers
Hardened washers shall be provided for A325
bolted connections where required by Article 6.13.2.3.2.
7.12.2.4—Holes
Holes shall comply with Article 6.13.2.4.
7.12.2.5—Size of Bolts
The size of bolts shall comply with Article 6.13.2.5,
except that the minimum nominal diameter shall be
0.5 in.
7.12.2.6—Spacing of Bolts
7.12.2.6.1—Minimum Spacing and Clear Distance
The distance between bolt centers shall not be less
than 2.5 times the nominal diameter of the bolt. For
oversized or slotted holes, the minimum clear distance
between the edges of adjacent bolt holes shall not be less
than twice the nominal diameter of the bolt.
7.12.2.6.2—Minimum Edge Distance
The distance from the center of a bolt to an edge of
a part shall not be less than 1.5 times the nominal
diameter of the bolt. See Article 7.12.2.9 for the effect
of edge distance on bearing strength.
C7.12.2.6.1
The requirement for the distance between hole
centers matches Section J.3.3 of the Aluminum Design
Manual (AA, 2010). The requirement for the clear
distance between the edges of adjacent holes matches
Article 6.13.2.6.1.
C7.12.2.6.2
This Article matches Section J.3.4 of the Aluminum
Design Manual (AA, 2010). Bearing strength is reduced
when the hole is less than two bolt diameters from an
edge.
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2013
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SECTION 7: ALUMINUM STRUCTURES
7-59
7.12.2.7—Shear Resistance
The nominal shear resistance of bolts shall be
determined in accordance with Article 6.13.2.7.
7.12.2.8—Slip Resistance
C7.12.2.8
The nominal slip resistance of a bolt in a slipcritical connection shall be determined in accordance
with Article 6.13.2.8. Aluminum members in slipcritical connections shall have tensile yield strength of at
least 15 ksi. Aluminum surfaces abrasion blasted with
coal slag to SSPC SP-5 (SSPC, 2007) to an average
substrate profile of 2.0 mils in contact with similar
aluminum surfaces or zinc painted steel surfaces with a
maximum dry film thickness of 4 mils shall be
considered to be Class B surface conditions. Slip
coefficients for other surfaces shall be determined in
accordance with the Research Council on Structural
Connection’s Specification for Structural Joints Using
High Strength Bolts (RCSC, 2009).
7.12.2.9—Bearing Resistance at Holes and Slots
The nominal bearing resistance of a connected part
shall be determined as follows:
• For a bolt in a hole,
Rn = de tFtu < 2 DtFtu
•
This Article matches Section J.3.8 of the Aluminum
Design Manual (AA, 2010).
C7.12.2.9
This Article matches Section J.3.7 of the Aluminum
Design Manual (AA, 2010).
(7.12.2.9-1)
For a bolt in a slot with the slot perpendicular to the
direction of force:
Rn = 1.33DtFtu
(7.12.2.9-2)
The edge distance perpendicular to the slot length
and slot length shall be sized to avoid overstressing the
material between the slot and the edge of the part.
where:
de
=
distance from the center of the bolt to the edge
of the part in the direction of force (in.)
t
=
for plain holes, thickness of the connected part;
for countersunk holes, thickness of the
connected part less 1/2 the countersink depth
(in.)
Ftu =
tensile ultimate strength of the connected part
(ksi)
D
nominal diameter of the bolt (in.)
=
7.12.2.10—Tensile Resistance
The nominal tensile resistance of bolts shall be
determined as specified in Article 6.13.2.10.
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2012 by the American Association of State Highway and Transportation Officials.
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2013
Revision
2013 INTERIM REVISIONS TO THE AASHTO LRFD
BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
7-60
7.12.2.11—Combined Tension and Shear
The nominal tensile resistance of bolts subjected to
combined shear and axial tension shall be determined in
accordance with Article 6.13.2.11.
7.12.2.12—Shear Resistance of Anchor Bolts
The nominal shear resistance of anchor bolts shall
be determined in accordance with Article 6.13.2.12.
7.12.3—Welded Connections
7.12.3.1—General
Welding shall comply with AWS D1.2/D1.2M
Structural Welding Code—Aluminum.
7.12.3.2—Factored Resistance
7.12.3.2.1—General
C7.12.3.2.1
The factored resistance of welded connections, Rr,
at the strength limit state shall be taken as given in
Articles 7.12.3.2.2 through 7.12.3.2.4. Filler strengths
shall be taken from Table 7.12.3.2.1-1.
Filler strengths given in Table 7.12.3.2.1-1 match
those in Table J.2.1 in the Aluminum Design Manual
(AA, 2010).
Table 7.12.3.2.1-1—Filler Strengths
Tensile Ultimate
Strength Ftuw (ksi)
Filler
4043
24
5183
40
5356
35
5556
42
7.12.3.2.2—Complete Penetration Groove-Welded
Connections
7.12.3.2.2a—Tension and Compression
The factored resistance of complete penetration
groove-welded connections subjected to tension or
compression normal to the effective area of the weld
shall be taken as:
Rr = φe Ftuw
(7.12.3.2.2a-1)
C7.12.3.2.2a
The strength of complete penetration groove welds
may be governed by the welded strength of either of the
base metals joined or by the strength of the filler metal.
Usually, the filler metal is selected so that its strength
equals or exceeds the strength of the welded base
metals, but this is not required.
where:
φe
=
resistance factor for weld metal specified in
Article 7.5.4.2
Ftuw
=
least of the welded tensile ultimate strengths
of the base metals and the filler (ksi).
Welded tensile ultimate strengths of base
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2013
Revision
SECTION 7: ALUMINUM STRUCTURES
7-61
metals shall be determined from Article 7.4.1
and tensile ultimate strengths of fillers from
Table 7.12.3.2.1-1.
The factored resistance of complete penetration
groove-welded connections subjected to tension or
compression parallel to the axis of the weld shall be
taken as the factored resistance of the base metal.
7.12.3.2.2b—Shear
The factored resistance of complete penetration
groove-welded connections subjected to shear on the
effective area of the weld shall be taken as:
Rr = φe Fsuw
(7.12.3.2.2b-1)
where:
φe =
resistance factor for weld metal specified in
Article 7.5.4.2
Fsuw =
least of the welded shear ultimate strengths of
the base metals and the filler (ksi)
Welded shear ultimate strengths of base metals shall
be determined from Article 7.4.1 and shear ultimate
strengths of fillers shall be taken as 0.5Ftuw where Ftuw is
determined from Table 7.12.3.2.1-1.
7.12.3.2.3—Partial Penetration Groove-Welded
Connections
Where practical, partial penetration groove welds
should be avoided.
7.12.3.2.3a—Tension and Compression
The factored resistance of partial penetration
groove-welded connections subjected to tension normal
to the effective area of the weld shall be taken as the
lesser of:
Rr = 0.6φe Ftuw
C7.12.3.2.3
Partial penetration groove welds may be used if
necessary, but where practical should be avoided.
C7.12.3.2.3a
The strength of partial penetration groove weld
metal is factored by 0.6 to account for the notch effect
that may occur due to incomplete penetration at the root
of the weld.
(7.12.3.2.3a-1)
where:
Ftuw =
tensile ultimate strength of the filler (ksi) from
Table 7.12.3.2.1-1
φe =
resistance factor for weld metal specified in
Article 7.5.4.2
or:
Rr = φe Ftuw
(7.12.3.2.3a-2)
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2012 by the American Association of State Highway and Transportation Officials.
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2013
Revision
2013 INTERIM REVISIONS TO THE AASHTO LRFD
BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
7-62
where:
Ftuw =
welded tensile ultimate strength of the base
metal from Article 7.4.1 (ksi)
φe =
resistance factor for base metal at welds
specified in Article 7.5.4.2
The factored resistance of partial penetration
groove-welded connections subjected to tension or
compression parallel to the axis of the weld or
compression normal to the effective area shall be taken
as the factored resistance of the base metal.
7.12.3.2.3b—Shear
The factored resistance of partial penetration
groove-welded connections subjected to shear on the
effective area of the weld shall be taken as the lesser of:
Rr = 0.6φe Fsuw
(7.12.3.2.3b-1)
where:
Fsuw =
shear ultimate strength of the filler taken as
0.5Ftuw where Ftuw is determined from Table
7.12.3.2.1-1 (ksi)
φe =
resistance factor for weld metal specified in
Article 7.5.4.2
or:
Rr = φe Fsuw
(7.12.3.2.3b-2)
where:
φe =
resistance factor for base metal at welds
specified in Article 7.5.4.2
Fsuw =
welded shear ultimate strength of the base
metal from Article 7.4.1 (ksi)
7.12.3.2.4—Fillet-Welded Connections
The factored resistance of fillet-welded connections
subjected to tension or compression parallel to the axis
of the weld or compression normal to the axis of the
weld shall be taken as the factored resistance of the base
metal.
The factored resistance of fillet-welded connections
subjected to tension perpendicular to the axis of the weld
or shear shall be taken as:
Rr = φe Fsw
C7.12.3.2.4
The strength of fillet welds may be governed by
either the base metals welded strength or by the filler
metal strength. Usually (but not always), the strength of
the filler metal governs the strength of the joint because
the area of the weld is based on the weld throat, which is
less than the area of the base metal which is based on the
weld size.
(7.12.3.2.4-1)
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2013
Revision
SECTION 7: ALUMINUM STRUCTURES
7-63
where:
φe =
resistance factor for weld metal specified in
Article 7.5.4.2
Fsw =
least of (kips/in.):
•
the product of the weld filler’s shear
ultimate strength, 0.5Fsuw (ksi), and the
weld’s effective throat (in.)
•
for base metal in shear at the weld-base
metal joint, the product of the base metal’s
welded shear ultimate strength, 0.6Fsuw
(ksi), and the fillet size Sw (in.)
•
for base metal in tension at the weld-base
metal joint, the product of the base metal’s
welded tensile ultimate strength, Ftuw (ksi),
and the fillet size Sw (in.)
Welded tensile ultimate strengths of base metals
shall be determined from Article 7.4.1 and tensile
ultimate strengths of weld fillers from Table 7.12.3.2-1.
7.12.3.3—Effective Area
C7.12.3.3
The effective area shall be determined as defined in
AWS D1.2.
7.12.3.4—Size of Fillet Welds
Weld effective areas given in the Aluminum Design
Manual (AA, 2010) match those given in AWS D1.2.
C7.12.3.4
The size used in design of a fillet weld along edges
of connected parts shall not exceed:
•
For material less than 0.25 in. thick, the thickness of
the material;
•
For material 0.25 in. or more in thickness, 1/16 in.
less than the material thickness, unless the weld is
designated on the contract documents to be built out
to obtain full throat thickness.
Maximum fillet weld size requirements match those
given in Article 6.13.3.4 for steel welds. Minimum fillet
weld size requirements match those given in AWS D1.2,
Table 2.2. If fillet welds are too small they may crack
upon cooling or when stressed by unanticipated loads.
The minimum size of a fillet weld shall be as given
in Table 7.12.3.4-1, except that the weld size shall not
exceed the thickness of the thinner part joined.
Table 7.12.3.4-1—Minimum Size of Fillet Welds
Base Metal Thickness (t) of
Thicker Part Joined (in.)
t < 1/16
1
¼ < t < /2
1
t > /2
Minimum Size of
Fillet Weld (in.)
1
/8
3
/16
1
/4
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BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
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7.12.3.5—Fillet Weld End Returns
Fillet weld end returns shall comply with Article
6.13.3.6.
7.12.4—Block Shear Rupture Resistance
C7.12.4
The block shear factored resistance shall be taken
as:
Rr = φbs Rn
This Article matches Section J.6.3 of the Aluminum
Design Manual (AA, 2010).
(7.12.4-1)
where:
φbs =
resistance factor for block shear specified in
Article 7.5.4.2
For connections on a failure path with shear on
some segments and tension on the other segments:
If Ftu Ant > Fsu Anv, then
Rn = Fsy Agv + Ftu Ant
(7.12.4-2)
otherwise:
Rn = Fsu Anv + Fty Agt
(7.12.4-3)
where for bolted connections:
Ftu =
specified minimum tensile ultimate strength
(ksi)
Ant =
net area in tension (in.2)
Fsu =
shear ultimate strength (ksi)
Anv =
net area in shear (in.2)
Fsy =
shear yield strength (ksi)
Agv =
gross area in shear (in.2)
Fty =
specified minimum tensile yield strength (ksi)
Agt =
gross area in tension (in.2)
Fsu.
For weld affected zones, use Ftuw for Ftu and Fsuw for
7.12.5—Connection Elements
7.12.5.1—General
This Article applies to the design of connection
elements such as plates, gussets, angles, and brackets.
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2013
Revision
SECTION 7: ALUMINUM STRUCTURES
7-65
7.12.5.2—Tension
The factored tensile resistance, Rr, of connection
elements is the lesser of the resistances for tensile
yielding and tensile rupture given in Article 7.8.2.1.
7.12.5.3—Shear
C7.12.5.3
The factored shear resistance, Rr, of connection
elements is the lesser of the resistances for shear
yielding and shear rupture. The factored shear yielding
resistance of connection elements shall be taken as:
Rr = φv FsyAgv
This Article is similar to Article 6.13.5.3.
(7.12.5.3-1)
where:
φv =
resistance factor for shear specified in Article
7.5.4.2
Fsy =
shear yield strength of the connection element
(ksi)
Agv =
gross area of the connection element subject to
shear (in.2)
The factored shear rupture resistance of connection
elements shall be taken as:
Rr = φvu FsuAv
(7.12.5.3-2)
where:
φvu =
resistance factor for shear rupture of connection
elements specified in Article 7.5.4.2
Fsu =
shear ultimate strength of the connection
element (ksi)
Anv =
net area of the connection element subject to
shear (in.2)
For welded connection elements, Fsy = Fsyw and
Fsu = Fsuw.
where:
Fsyw =
shear yield strength in the weld-affected zone
(ksi)
7.12.6—Splices
Splices shall be designed at the strength limit state
to satisfy the connection requirements of Article 7.12.1.
7.13—PROVISIONS FOR STRUCTURE TYPES
7.13.1—Deck Superstructures
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2013
Revision
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BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
7-66
7.13.1.1—General
C7.13.1.1
The provisions of this Article shall apply to the
design of bridges that use an aluminum deck that is
connected to the superstructure with slip-critical
connections. The aluminum deck shall be considered an
integral part of the bridge superstructure and shall
participate in resisting global force effects on the bridge.
Connections between the deck and the main structural
members shall be designed for interaction effects
specified in Article 9.4.1.
Aluminum decks transfer the load from vehicles’
tires to the bridge superstructure.
For decks that act compositely with the bridge
girders, this load transfer can be thought of as three
systems:
•
System 3 transfers the load from the tire patch on
the top flange of the deck to the ribs that support the
top flange. This load causes bending in the top
flange.
•
System 2 transfers the load transverse to traffic to
the bridge girders. This load creates transverse
forces in the top and bottom flanges and ribs of the
deck.
•
System 1 transfers the load in the direction of traffic
in participation with the bridge girders to the bridge
supports. This load causes longitudinal axial force
in the deck.
7.13.1.2—Equivalent Strips
For decks with continuous top and bottom flanges,
the equivalent strip used for analysis in accordance with
Article 4.6.2.1 shall be as determined for cast-in-place
concrete decks.
7.14—REFERENCES
AA. 2010. Aluminum Design Manual 2010. Aluminum Association, Arlington, VA.
AASHTO. 2010. AASHTO LRFD Bridge Construction Specifications, Third Edition with 2011 and 2012 Interim
Revisions, LRFDCONS-3-M. American Association of State Highway and Transportation Officials, Washington, DC.
AWS. 2008. Structural Welding Code—Aluminum, D1.2/D.1.2M. American Welding Society, Miami, FL.
AWS. 1999. Specification for Bare Aluminum and Aluminum Alloy Welding Electrodes and Rods, A5.10-99.
American Welding Society, Miami, FL.
Kulicki, J. 1983. “Load Factor Design of Truss Bridges with Applications to Greater New Orleans Bridge No. 2.” In
Transportation Research Record 903, National Transportation Research Board, Washington, DC.
Research Council on Structural Connections. 2009. Specification for Structural Joints Using High-Strength Bolts.
Research Council on Structural Connections, Chicago, IL.
SSPC. 2007. White Metal Blast Cleaning, SSPC SP 5/Nace No. 1. Society for Protective Coatings, Pittsburgh, PA.
© 2013
2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2013
Revision
SECTION 8: WOOD STRUCTURES
TABLE OF CONTENTS
8.1—SCOPE ................................................................................................................................................................. 8-1
8.2—DEFINITIONS ..................................................................................................................................................... 8-1
8.3—NOTATION ......................................................................................................................................................... 8-4
8.4—MATERIALS ....................................................................................................................................................... 8-5
8.4.1—Wood Products ........................................................................................................................................... 8-5
8.4.1.1—Sawn Lumber ................................................................................................................................... 8-5
8.4.1.1.1—General .................................................................................................................................. 8-5
8.4.1.1.2—Dimensions ............................................................................................................................ 8-6
8.4.1.1.3—Moisture Content ................................................................................................................... 8-6
8.4.1.1.4—Reference Design Values ....................................................................................................... 8-6
8.4.1.2—Structural Glued Laminated Timber (Glulam) ............................................................................... 8-12
8.4.1.2.1—General ................................................................................................................................ 8-12
8.4.1.2.2—Dimensions .......................................................................................................................... 8-13
8.4.1.2.3—Reference Design Values ..................................................................................................... 8-14
8.4.1.3—Tension-Reinforced Glulams ......................................................................................................... 8-18
8.4.1.3.1—General ................................................................................................................................ 8-18
8.4.1.3.2—Dimensions .......................................................................................................................... 8-18
8.4.1.3.3—Fatigue ................................................................................................................................. 8-19
8.4.1.3.4—Reference Design Values for Tension-Reinforced Glulams ................................................ 8-19
8.4.1.3.5—Volume Effect ...................................................................................................................... 8-20
8.4.1.3.6—Preservative Treatment ........................................................................................................ 8-21
8.4.1.4—Piles ............................................................................................................................................... 8-21
8.4.2—Metal Fasteners and Hardware ................................................................................................................. 8-21
8.4.2.1—General........................................................................................................................................... 8-21
8.4.2.2—Minimum Requirements ................................................................................................................ 8-21
8.4.2.2.1—Fasteners .............................................................................................................................. 8-21
8.4.2.2.2—Prestressing Bars.................................................................................................................. 8-21
8.4.2.2.3—Split Ring Connectors .......................................................................................................... 8-22
8.4.2.2.4—Shear Plate Connectors ........................................................................................................ 8-22
8.4.2.2.5—Nails and Spikes .................................................................................................................. 8-22
8.4.2.2.6—Drift Pins and Bolts ............................................................................................................. 8-22
8.4.2.2.7—Spike Grids .......................................................................................................................... 8-22
8.4.2.2.8—Toothed Metal Plate Connectors .......................................................................................... 8-22
8.4.2.3—Corrosion Protection ...................................................................................................................... 8-23
8.4.2.3.1—Metallic Coating .................................................................................................................. 8-23
8.4.2.3.2—Alternative Coating .............................................................................................................. 8-23
8.4.3—Preservative Treatment ............................................................................................................................ 8-23
8.4.3.1—Requirement for Treatment ............................................................................................................ 8-23
8.4.3.2—Treatment Chemicals ..................................................................................................................... 8-23
8.4.3.3—Inspection and Marking ................................................................................................................. 8-24
8.4.3.4—Fire Retardant Treatment ............................................................................................................... 8-24
8.4.4—Adjustment Factors for Reference Design Values ................................................................................... 8-24
8-i
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
8-ii
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
8.4.4.1—General ........................................................................................................................................... 8-24
8.4.4.2—Format Conversion Factor, CKF ...................................................................................................... 8-25
8.4.4.3—Wet Service Factor, CM .................................................................................................................. 8-26
8.4.4.4—Size Factor, CF, for Sawn Lumber ................................................................................................. 8-26
8.4.4.5—Volume Factor, CV, (Glulam) ......................................................................................................... 8-27
8.4.4.6—Flat-Use Factor, Cfu ........................................................................................................................ 8-28
8.4.4.7—Incising Factor, Ci .......................................................................................................................... 8-29
8.4.4.8—Deck Factor, Cd .............................................................................................................................. 8-29
8.4.4.9—Time Effect Factor, Cλ ................................................................................................................... 8-30
8.5—LIMIT STATES ................................................................................................................................................. 8-30
8.5.1—Service Limit State ................................................................................................................................... 8-30
8.5.2—Strength Limit State ................................................................................................................................. 8-30
8.5.2.1—General ........................................................................................................................................... 8-30
8.5.2.2—Resistance Factors .......................................................................................................................... 8-31
8.5.2.3—Stability .......................................................................................................................................... 8-31
8.5.3—Extreme Event Limit State ....................................................................................................................... 8-31
8.6—COMPONENTS IN FLEXURE ......................................................................................................................... 8-31
8.6.1—General ..................................................................................................................................................... 8-31
8.6.2—Rectangular Section.................................................................................................................................. 8-31
8.6.3—Circular Section ........................................................................................................................................ 8-33
8.7—COMPONENTS UNDER SHEAR .................................................................................................................... 8-33
8.8—COMPONENTS IN COMPRESSION ............................................................................................................... 8-33
8.8.1—General ..................................................................................................................................................... 8-33
8.8.2—Compression Parallel to Grain.................................................................................................................. 8-33
8.8.3—Compression Perpendicular to Grain ........................................................................................................ 8-34
8.9—COMPONENTS IN TENSION PARALLEL TO GRAIN ................................................................................. 8-35
8.10—COMPONENTS IN COMBINED FLEXURE AND AXIAL LOADING ....................................................... 8-35
8.10.1—Components in Combined Flexure and Tension..................................................................................... 8-35
8.10.2—Components in Combined Flexure and Compression Parallel to Grain ................................................. 8-36
8.11—BRACING REQUIREMENTS ........................................................................................................................ 8-36
8.11.1—General ................................................................................................................................................... 8-36
8.11.2—Sawn Wood Beams ................................................................................................................................ 8-36
8.11.3—Glued Laminated Timber Girders........................................................................................................... 8-37
8.11.4—Bracing of Trusses.................................................................................................................................. 8-37
8.12—CAMBER REQUIREMENTS ......................................................................................................................... 8-37
8.12.1—Glued Laminated Timber Girders........................................................................................................... 8-37
8.12.2—Trusses ................................................................................................................................................... 8-37
8.12.3—Stress Laminated Timber Deck Bridge................................................................................................... 8-37
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 8: WOOD STRUCTURES
8-iii
8.13—CONNECTION DESIGN ................................................................................................................................ 8-37
8.14—REFERENCES................................................................................................................................................. 8-37
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 8
WOOD STRUCTURES
Chapter 8
8.1—SCOPE
This Section specifies design requirements for
structural components made of sawn lumber products,
stressed wood, glued laminated timber, wood piles, and
mechanical connections.
8.2—DEFINITIONS
Adjusted Design Value—Reference design value multiplied by applicable adjustment factors.
Beams and Stringers (B&S)—Beams and stringers are rectangular pieces that are 5.0 or more in. thick (nominal), with a
depth more than 2.0 in. (nominal) greater than the thickness. B&S are graded primarily for use as beams, with loads
applied to the narrow face.
Bent—A type of pier consisting of two or more columns or column-like components connected at their top ends by a cap,
strut, or other component holding them in their correct positions.
Bonded Reinforcement—A reinforcing material that is continuously attached to a glulam beam through adhesive bonding.
Bumper Lamination—A sacrificial wood lamination continuously bonded to the outer face of reinforcement to protect the
reinforcement from damage, fire, or for visual appearance. The bumper lam is an option, not a requirement.
Cap—A sawn lumber or glulam component placed horizontally on an abutment or pier to distribute the live load and dead
load of the superstructure. Also, a metal, wood, or mastic cover to protect exposed wood end grain from wetting.
Combination Symbol—A product designation used by the structural glued laminated timber industry; see AITC 117-2004.
Conventional Lamstock—Solid sawn wood laminations with a net thickness of 2.0 in. or less, graded either visually or
through mechanical means, finger-jointed and face-bonded to form a glulam per ASTM D7199.
Crib—A structure consisting of a foundation grillage and a framework providing compartments that are filled with gravel,
stones, or other material satisfactory for supporting the structure to be placed thereon.
Decking—A subcategory of dimension lumber, graded primarily for use with the wide face placed flatwise.
Delamination—Adhesive failure causing the separation of laminations.
Development Length—The length of the bond line along the axis of the beam required to develop the design tensile
strength of the reinforcement.
Diaphragm—Blocking between two main longitudinal beams consisting of solid lumber, glued laminated timber, or steel
cross bracing.
Dimension Lumber—Lumber with a nominal thickness of from 2.0 up to but not including 5.0 in. and having a nominal
width of 2.0 in. or more.
Dowel—A relatively short length of round metal bar used to interconnect or attach two wood components in a manner to
minimize movement and displacement.
Dressed Lumber—Lumber that has been surfaced by a planing machine on one or more sides or edges.
Dry—The condition of having a relatively low moisture content, i.e., not more than 19 percent for sawn lumber and
16 percent for glued laminated timber.
8-1
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
8-2
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
E-Glass—A low alkali (borosilicate glass) electrical grade glass fiber commonly used by the composite industry for the
manufacture of FRP composites.
Fiber-Reinforced Polymer (FRP)—Any material consisting of at least two distinct components: reinforcing fibers and a
binder matrix (a polymer). The reinforcing fibers are permitted to be either synthetic (e.g. glass), metallic, or natural (e.g.
bamboo), and are permitted to be long and continuously-oriented or short and randomly oriented. The binder matrix is
permitted to be either thermoplastic (e.g. polypropylene or nylon) or thermosetting (e.g. epoxy or vinyl-ester).
Frame Bent—A type of framed timber substructure.
Grade—The designation of the material quality of a manufactured piece of wood.
Grade Mark—The identification of lumber with symbols or lettering to certify its quality or grade.
Grain—The direction, size, arrangement, appearance, or quality of the fibers in wood or lumber.
Green Wood—A freshly sawn or undried wood. Wood that has become completely wet after immersion in water would not
be considered green but may be said to be in the green condition.
Hardwood—Generally one of the botanical groups of trees that have broad leaves or the wood produced by such trees. The
term has no reference to the actual hardness of the wood.
Horizontally Laminated Timber—Laminated wood in which the laminations are arranged with their wider dimension
approximately perpendicular to the direction of applied transverse loads.
Laminate—A product made by bonding together two or more layers (laminations) of material or materials.
Laminated Wood—An assembly made by bonding layers of veneer or lumber with an adhesive, nails, or stressing to
provide a structural continuum so that the grain of all laminations is essentially parallel.
Laminating—The process of bonding laminations together with adhesive, including the preparation of the laminations,
preparation and spreading of adhesive, assembly of laminations in packages, application of pressure, and curing.
Lamination—A full width and full length layer contained in a component bonded together with adhesive. The layer itself
may be composed of one or several wood pieces in width or length.
Machine Evaluated Lumber (MEL)—Mechanically graded lumber certified as meeting the criteria of a specific commercial
grading system.
Machine Stress Rated (MSR) Lumber—Mechanically graded lumber certified as meeting the criteria of a specific
commercial grading system.
Mechanically Graded Lumber—Solid sawn lumber graded by mechanical evaluation in addition to visual examination.
Modulus of Rupture (MOR)—The maximum stress at the extreme fiber in bending, calculated from the maximum bending
moment on the basis of an assumed stress distribution.
Moisture Content—An indication of the amount of water contained in the wood, usually expressed as a percentage of the
weight of the oven dry wood.
NDS®—National Design Specification® for Wood Construction by the American Forest and Paper Association.
NELMA—Grading rules by Northeastern Lumber Manufacturers Association.
NLGA—Grading rules by National Lumber Grades Authority.
Net Size—The size used in design to calculate the resistance of a component. Net size is close to the actual dry size.
Nominal Size—As applied to timber or lumber, the size by which it is specified and sold; often differs from the actual size.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 8: WOOD STRUCTURES
8-3
NSLB—Grading rules by Northern Softwood Lumber Bureau.
Oil-Borne Preservative—A preservative that is introduced into wood in the form of an oil-based solution.
Plank—A broad board, usually more than 1.0 in. thick, laid with its wide dimension horizontal and used as a bearing
surface or riding surface.
Posts and Timber (P&T)—Posts and timbers pieces with a square or nearly square cross-section, 5.0 by 5.0 in. (nominal)
and larger, with the width not more than 2.0 in. (nominal) greater than the thickness. Lumber in the P&T size classification
is graded primarily for resisting axial loads.
Preservative—Any substance that is effective in preventing the development and action of wood-decaying fungi, borers of
various kinds, and harmful insects.
Reinforcement (for Glulam)—Any material that is not a conventional lamstock lumber whose mean (ultimate) longitudinal
unit strength exceeds 20 ksi for tension and compression, and whose mean tension and compression modulus of elasticity
exceeds 3,000 ksi. Acceptable reinforcing materials include but are not restricted to: Fiber-Reinforced Polymer (FRP)
plates and bars, and metallic plates and bars.
Reference Design Value—The allowable stress value or modulus of elasticity specified in the NDS®.
Rough Sawn Lumber—Lumber that has not been dressed but that has been sawn, edged, and trimmed.
Sawn Lumber—The product of a sawmill not further manufactured other than by sawing, resawing, passing lengthwise
through a standard planing mill, drying, and cross-cutting to length.
Sawn Timbers—Lumber that is nominally 5.0 in. or more in least dimension.
Softwood—Generally, one of the conifers or the wood produced by such trees. The term has no reference to the actual
hardness of the wood.
SPIB—Grading rules by Southern Pine Inspection Bureau.
Stress Grades—Lumber grades having assigned working stress and modulus of elasticity in accordance with accepted
principles of resistance grading.
Structural Glued Laminated Timber (glulam)—An engineered, stress-rated product of a timber laminating plant comprised
of assemblies of specially selected and prepared wood laminations securely bonded together with adhesives. The grain of
all laminations is approximately parallel longitudinally. Glued laminated timber is permitted to be comprised of pieces end
joined to form any length, of pieces placed or bonded edge to edge to make any width, or of pieces bent to curbed form
during bonding.
Structural Lumber—Lumber that has been graded and assigned design values based on standardized procedures to ensure
acceptable reliability.
Tension Reinforcement—Reinforcement placed on the tension side of a flexural member on the first glueline or on the face
of the beam.
Vertically Laminated Timber—Laminated wood in which the laminations are arranged with their wider dimension
approximately parallel to the direction of load.
Visually Graded Lumber—Structural lumber graded solely by visual examination.
Waterborne Preservative—A preservative that is introduced into wood in the form of a water-based solution.
WCLIB—Grading rules by West Coast Lumber Inspection Bureau.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
8-4
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Wet-Use—Use conditions where the moisture content of the wood in service exceeds 16 percent for glulam and 19 percent
for sawn lumber.
WWPA—Grading rules by Western Wood Products Association.
8.3—NOTATION
A
Ab
Ag
An
a
B
b
=
=
=
=
=
=
=
Cb
Cc
Cd
CF
Cfu
Ci
CKF
CL
CM
CP
CV
Cλ
d
=
=
=
=
=
=
=
=
=
=
=
=
=
E
Eo
F
Fb
Fbo
Fc
Fco
Fcp
Fcpo
Fo
Ft
Fto
Fv
Fvo
G
K
L
Le
Lu
Mn
Mr
Mu
Pn
Pr
Pu
S
Vn
Vr
φ
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
parameter for beam stability (8.6.2)
bearing area (in.2) (8.8.3)
gross cross-sectional area of the component (in.2) (8.8.2)
net cross-sectional area of the component (in.2) (8.9)
coefficient (8.4.4.5)
parameter for compression (8.8.2)
width of the glued laminated timber component; thickness of lumber component (see Figure 8.3-1) (in.)
(8.4.4.5)
bearing factor (8.8.3)
curvature factor (8.4.1.2)
deck factor (8.4.4.8)
size factor (8.4.4.4)
flat use factor (8.4.4.6)
incising factor (8.4.4.7)
format conversion factor (8.4.4.2)
beam stability factor (8.6.2)
wet service factor (8.4.4.3)
column stability factor (8.8.2)
volume factor (8.4.4.5)
time effect factor (8.4.4.9)
depth of the beams or stringers or width of the dimension lumber component (8.4.4.4) or glulam depth
(8.4.4.5) as shown in Figure 8.3-1 (in.)
adjusted modulus of elasticity (ksi) (8.4.4.1)
reference modulus of elasticity (ksi) (8.4.1.1.4)
adjusted design value (ksi) (8.4.4.1)
adjusted design value in flexure (ksi) (8.4.4.1)
reference design value of wood in flexure (ksi) (8.4.1.1.4)
adjusted design value of wood in compression parallel to grain (ksi) (8.4.4.1)
reference design value of wood in compression parallel to grain (ksi) (8.4.1.1.4)
adjusted design value of wood in compression perpendicular to grain (ksi) (8.4.4.1)
reference design value of wood in compression perpendicular to grain (ksi) (8.4.1.1.4)
reference design value (ksi) (8.4.4.1)
adjusted design value of wood in tension (ksi) (8.4.4.1)
reference design value of wood in tension (ksi) (8.4.1.1.4)
adjusted design value of wood in shear (ksi) (8.4.4.1)
reference design value of wood in shear (ksi) (8.4.1.1.4)
specific gravity (8.4.1.1.4)
effective buckling length factor (8.8.2)
length (ft) (8.4.4.5)
effective length (in.) (8.6.2)
laterally unsupported length of the component (in.) (8.6.2)
nominal flexural resistance (kip-in.) (8.6)
factored flexural resistance, φ Mn (kip-in.) (8.6)
factored moment (kip-in.) (8.10)
nominal compression or tension resistance (kips) (8.8) (8.9)
factored axial resistance (kips) (8.8) (8.9)
factored axial load (kips) (8.10)
section modulus (in.3) (8.6.2)
nominal shear resistance (kips) (8.7)
factored shear resistance, φ Vn (kips) (8.7)
resistance factor (8.5.2.2)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 8: WOOD STRUCTURES
8-5
Figure 8.3-1—Dimensions as Defined for Various Types of Wood Products
8.4—MATERIALS
8.4.1—Wood Products
C8.4.1
Nominal resistance for wood products shall be based
on specified size and conditions of use with respect to
moisture content and time effect. To obtain nominal
resistance and stiffness values for design, the reference
design values specified in Tables 8.4.1.1.4-1, 8.4.1.1.4-2
8.4.1.1.4-3, 8.4.1.2.3-1, 8.4.1.2.3-2, 8.4.1.3.4-1, and
8.4.1.4-1 shall be adjusted for actual conditions of use in
accordance with Article 8.4.4.
Reference design values are based on dry-use
conditions, with the wood moisture content not exceeding
19 percent for sawn lumber and 16 percent for structural
glued laminated timber. Reference design values are
applied to material preservatively treated in accordance
with AASHTO M 133.
Reference design values have been taken from the
National Design Specification® (NDS®) for Wood
Construction. The NDS® publishes reference values for
allowable stress design (ASD) and provides format
conversion factors for use of these values with the load and
resistance factor design (LRFD) methodology. To facilitate
the direct use of the values developed by the wood
products industry and included in the NDS®, the same
format has been adopted for AASHTO LRFD design.
Reference design values for tension-reinforced
glulams have been developed following procedures in
ASTM D7199 and AC 280 (ICC-ES).
8.4.1.1—Sawn Lumber
8.4.1.1.1—General
Sawn lumber shall comply with the requirements of
AASHTO M 168.
When solid sawn beams and stringers are used as
continuous or cantilevered beams, the grading provisions
applicable to the middle third of the length shall be applied
to at least the middle two-thirds of the length of pieces to
be used as two-span continuous beams and to the entire
length of pieces to be used over three or more spans or as
cantilevered beams.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
8-6
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
8.4.1.1.2—Dimensions
Structural calculations shall be based on the actual net
dimensions for the anticipated use conditions.
Dimensions stated for dressed lumber shall be the
nominal dimensions. Net dimensions for dressed lumber
shall be taken as 0.5 in. less than nominal, except that the
net width of dimension lumber exceeding 6.0 in. shall be
taken as 0.75 in. less than nominal.
For rough-sawn, full-sawn, or special sizes, the actual
dimensions and moisture content used in design shall be
indicated in the contract documents.
C8.4.1.1.2
These net dimensions depend on the type of surfacing,
whether dressed, rough-sawn, or full-sawn.
The designer should specify surface requirements on
the plans. Rough-sawn lumber is typically 0.125 in. larger
than standard dry dressed sizes, associated with the Fbo
value in Table 8.4.1.1.4-2 and full-sawn lumber, which is
not widely used, is cut to the same dimensions as the
nominal size. In both of the latter cases, thickness and
width dimensions are variable, depending on the sawmill
equipment. Therefore, it is impractical to use rough-sawn
or full-sawn lumber in a structure that requires close
dimensional tolerances.
For more accurate dimensions, surfacing can be
specified on one side (S1S), two sides (S2S), one edge
(S1E), two edge (S2E), combinations of sides and edges
(S1S1E, S2S1E, S1S2E) or all sides (S4S).
8.4.1.1.3—Moisture Content
The moisture content of dimension lumber shall not be
greater than 19 percent at the time of installation.
8.4.1.1.4—Reference Design Values
Reference design values for visually graded sawn
lumber shall be as specified in Table 8.1.1.4-1.
Reference design values for mechanically graded
dimension lumber shall be as specified in Table 8.1.1.4-2.
Unless otherwise indicated, reference design value in
flexure for dimension lumber and posts and timbers shall
apply to material where the load is applied to either the
narrow or wide face. Reference design value in flexure for
decking grades shall apply only with the load applied to
the wide face.
Values for specific gravity, G, shear parallel to grain,
Fv, and compression perpendicular to grain, Fcpo, for
mechanically graded dimension lumber shall be taken as
specified in Table 8.1.1.4-3. For species or species groups
not given in Table 8.1.1.4-3, the G, Fvo, and Fcpo values for
visually graded lumber may be used.
Reference design values for lumber grades not given
in Table 8.1.1.4-1 and Table 8.1.1.4-2 shall be obtained
from the National Design Specification® (NDS®) for
Wood Construction.
Where the Eo or Fto values shown on a grade stamp
differ from Table 8.1.1.4-2 values associated with the Fbo
on the grade stamp, the values on the stamp shall be used
in design, and the Fco value associated with the Fbo value
in Table 8.1.1.4-2 shall be used.
For machine evaluated lumber (MEL) commercial
grades M-17, M-20 and M-27, Fco, requires qualification
and quality control shall be required.
C8.4.1.1.4
In calculating design values in Table 8.1.1.4-2, the
natural gain in strength and stiffness that occurs as lumber
dries has been taken into consideration as well as the
reduction in size that occurs when unseasoned lumber
shrinks. The gain in load carrying capacity due to
increased strength and stiffness resulting from drying more
than offsets the design effect of size reductions due to
shrinkage.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 8: WOOD STRUCTURES
Reference design values specified in Table 8.1.1.4-2
shall be taken as applicable to lumber that will be used
under dry conditions. For 2.0-in. to 4.0-in. thick lumber,
the dry dressed sizes shall be used regardless of the
moisture content at the time of manufacture or use.
8-7
For any given bending design value, Fbo, the modulus
of elasticity, Eo, and tension parallel to grain, Fto, design
value may vary depending upon species, timber source or
other variables. The Eo and Fto values included in the
Fbo-Eo grade designations in Table 8.1.1.4-2 are those
usually associated with each Fbo level. Grade stamps may
show higher or lower values if machine rating indicates the
assignment is appropriate.
Higher G values may be claimed when (a) specifically
assigned by the rules writing agency or (b) when qualified
by test, quality controlled for G and provided for on the
grade stamp. When a different G value is provided on the
grade stamp, higher Fvo and Fcpo design values may be
calculated in accordance with the grading rule
requirements.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
8-8
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 8.4.1.1.4-1—Reference Design Values for Visually Graded Sawn Lumber
Species and
Commercial Grade
Douglas Fir-Larch
Select Structural
No. 1 & Btr
No. 1
No. 2
Dense Select Structural
Select Structural
Dense No. 1
No. 1
No. 2
Dense Select Structural
Select Structural
Dense No. 1
No. 1
No. 2
Dense Select Structural
Select Structural
Dense No. 1
No. 1
No. 2 Dense
No. 2
Dense Select Structural
Select Structural
Dense No. 1
No. 1
No. 2 Dense
No. 2
Eastern Softwoods
Select Structural
No. 1
No. 2
Hem-Fir
Select Structural
No. 1 & Btr
No. 1
No. 2
Select Structural
No.1
No.2
Select Structural
No.1
No.2
Mixed Southern Pine
Select Structural
No.1
No.2
Select Structural
No.1
No.2
Select Structural
No.1
No.2
Size
Classificatio
n
Dimension
≥2 in. Wide
Beams and
Stringers
Posts and
Timbers
Beams and
Stringers
Posts and
Timbers
Dimension
≥2 in. Wide
Dimension
≥2 in. Wide
Beams and
Stringers
Posts and
Timbers
Dimension
2 in.–4 in.
Wide
Dimension 5
in.–6 in.
Wide
Dimension
8 in. Wide
Design Values (ksi)
Shear
Compression
parallel to
perpendicula
grain
r to grain
Bending
Tension
parallel
to grain
Compression
parallel to
grain
Modulus of
Elasticity
Fbo
Fto
Fvo
Fcpo
Fco
Eo
1.50
1.20
1.00
0.90
1.90
1.60
1.55
1.35
0.875
1.75
1.50
1.40
1.20
0.75
1.90
1.60
1.55
1.35
1.00
0.875
1.75
1,50
1.40
1.20
0.85
0.75
1.00
0.80
0.675
0.575
1.10
0.95
0.775
0.675
0.425
1.15
1.00
0.95
0.825
0.475
1.10
0.95
0.775
0.675
0.50
0.425
1.15
1.00
0.95
0.825
0.55
0.475
0.18
0.18
0.18
0.18
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.625
0.625
0.625
0.625
0.73
0.625
0.73
0.625
0.625
0.73
0.625
0.73
0.625
0.625
0.73
0.625
0.73
0.625
0.73
0.625
0.73
0.625
0.73
0.625
0.73
0.625
1.70
1.55
1.50
1.35
1.30
1.10
1.10
0.92
0.60
1.35
1.15
1,20
1.00
0.70
1.30
1.10
1.10
0.925
0.70
0.60
1.35
1.15
1.20
1.00
0.825
0.70
1,900
1,800
1,700
1,600
1,700
1,600
1,700
1,600
1,300
1,700
1,600
1,700
1,600
1,300
1,700
1,600
1,700
1,600
1,400
1,300
1,700
1,600
1,700
1,600
1,400
1,300
1.25
0.775
0.575
0.575
0.35
0.275
0.14
0.14
0.14
0.335
0.335
0.335
1.20
1.00
0.825
1,200
1,100
1,100
NELMA
NSLB
1.40
1.10
0.975
0.85
1.30
1.05
0.675
1.20
0.975
0.575
0.925
0.725
0.625
0.525
0.75
0.525
0.35
0.80
0.65
0.375
0.15
0.15
0.15
0.15
0.14
0.14
0.14
0.14
0.14
0.14
0.405
0.405
0.405
0.405
0.405
0.405
0.405
0.405
0.405
0.405
1.50
1.35
1.35
1.30
0.925
0.75
0.50
0.975
0.85
0.575
1,600
1,500
1,500
1,300
1,300
1,300
1,100
1,300
1,300
1,100
WCLIB
WWPA
2.05
1.45
1.30
1.85
1.30
1.15
1.75
1.20
1.05
1.20
0.875
0.775
1.10
0.75
0.675
1.00
0.70
0.625
0.175
0.175
0.175
0.175
0.175
0.175
0.175
0.175
0.175
0.565
0.565
0.565
0.565
0.565
0.565
0.565
0.565
0.565
1.80
1.65
1.65
1.70
1.55
1.55
1.60
1.45
1.45
1,600
1,500
1,400
1,600
1,500
1,400
1,600
1,500
1,400
SPIB
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
Grading
Rules
Agency
WCLIB
WWPA
WCLIB
WWPA
2012
Edition
SECTION 8: WOOD STRUCTURES
8-9
Table 8.4.1.1.4-1 (continued)—Reference Design Values for Visually Graded Sawn Lumber
Species and
Commercial Grade
Size
Classification
Design Values (ksi)
Shear
Compression
parallel to
perpendicular
grain
to grain
Bending
Tension
parallel to
grain
Fbo
Fto
Fvo
Fcpo
Fco
Eo
Compression
parallel to
grain
Modulus of
Elasticity
Grading
Rules
Agency
Mixed Southern Pine (continued)
No.2
Select Structural
Dimension
No.1
10 in. Wide
No.2
Select Structural
Dimension
No.1
12 in. Wide
No.2
Select Structural
5 in.× 5 in.
No.1
and Larger
No.2
Northern Red Oak
Select Structural
Dimension
No. 1
≥2 in. Wide
No. 2
Select Structural
Beams and
No.1
Stringers
No.2
Select Structural
Posts and
No.1
Timbers
No.2
1.05
1.50
1.05
0.925
1.40
0.975
0.875
1.50
1.35
0.85
0.625
0.875
0.60
0.55
0.825
0.575
0.525
1.00
0.90
0.55
0.175
0.175
0.175
0.175
0.175
0.175
0.175
0.165
0.165
0.165
0.565
0.565
0.565
0.565
0.565
0.565
0.565
0.375
0.375
0.375
1.45
1.60
1.45
1.45
1.55
1.40
1.40
0.90
0.80
0.525
1,400
1,600
1,500
1,400
1,600
1,500
1,400
1,300
1,300
1,000
SPIB
1.40
1.00
0.975
1.60
1.35
0.875
1.50
1.20
0.70
0.80
0.575
0.575
0.95
0.675
0.425
1.00
0.80
0.475
0.22
0.22
0.22
0.205
0.205
0.205
0.205
0.205
0.205
0.885
0.885
0.885
0.885
0.885
0.885
0.885
0.885
0.885
1.15
0.925
0.725
0.95
0.80
0.50
1.00
0.875
0.40
1,400,
1,400
1,300
1,300
1,300
1,000
1,300
1,300
1,000
NELMA
Red Maple
Select Structural
No. 1
No. 2
Select Structural
No.1
No.2
Select Structural
No.1
No.2
1.30
0.925
0.90
1.50
1.25
0.80
1.40
1.15
0.65
0.75
0.55
0.525
0.875
0.625
0.40
0.925
0.75
0.425
0.21
0.21
0.21
0.195
0.195
0.195
0.195
0.195
0.195
0.615
0.615
0.615
0.615
0.615
0.615
0.615
0.615
0.615
1.10
0.90
0.70
0.90
0.75
0.475
0.95
0.825
0.375
1,700
1,600
1,500
1,500
1,500
1,200
1,500
1,500
1,200
NELMA
1.15
0.825
0.80
1.35
1.15
0.725
1.25
1.00
0.575
0.675
0.50
0.475
0.80
0.55
0.375
0.85
0.675
0.40
0.17
0.17
0.17
0.155
0.155
0.155
0.155
0.155
0.155
0.82
0.82
0.82
0.82
0.82
0.82
0.82
0.82
0.82
1.00
0.825
0.625
0.825
0.70
0.45
0.875
0.775
0.35
1,400
1,300
1,200
1,200
1,200
1,000
1,200
1,200
1,000
NELMA
Red Oak
Select Structural
No. 1
No. 2
Select Structural
No.1
No.2
Select Structural
No.1
No.2
Dimension
≥2 in. Wide
Beams and
Stringers
Posts and
Timbers
Dimension
≥2 in. Wide
Beams and
Stringers
Posts and
Timbers
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
8-10
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 8.4.1.1.4-1 (continued)—Reference Design Values for Visually Graded Sawn Lumber
Species and
Commercial
Grade
Size
Classificatio
n
Southern Pine
Select Structural
Dimension
No.1
2 in.–4 in.
Wide
No.2
Select Structural
Dimension
No.1
5 in.–6 in.
Wide
No.2
Select Structural
Dimension
No.1
8 in. wide
No.2
Select Structural
Dimension
No.1
10 in. Wide
No.2
Select Structural
Dimension
No.1
12 in. Wide
No.2
Select Structural
5 in. × 5 in.
No. 1
and Larger
No. 2
Spruce-Pine-Fir
Select Structural
Dimension
≥2 in. Wide
No. 1/ No. 2
Select Structural
Beams and
No.1
Stringers
No.2
Select Structural
Posts and
No.1
Timbers
No.2
Spruce-Pine-Fir (South)
Select Structural
Dimension
No. 1
≥2 in. Wide
No. 2
Select Structural
Beams and
No.1
Stringers
No.2
Select Structural
Posts and
No.1
Timbers
No.2
Yellow Poplar
Select Structural
Dimension
No. 1
≥2 in. Wide
No. 2
Design Values (ksi)
Compression
Shear Parallel to
Perpendicular
Grain
to Grain
Fvo
Fcpo
Bending
Fbo
Tension
Parallel to
Grain
Fto
2.85
1.85
1.50
2.55
1.65
1.25
2.30
1.50
1.20
2.05
1.30
1.05
1.90
1.25
0.975
1.50
1.35
0.85
1.60
1.05
0.825
1.40
0.90
0.725
1.30
0.825
0.65
1.10
0.725
0.575
1.05
0.675
0.55
1.00
0.90
0.55
0.175
0.175
0.175
0.175
0.175
0.175
0.175
0.175
0.175
0.175
0.175
0.175
0.175
0.175
0.175
0.165
0.165
0.165
0.565
0.565
0.565
0.565
0.565
0.565
0.565
0.565
0.565
0.565
0.565
0.565
0.565
0.565
0.565
0.375
0.375
0.375
2.10
1.85
1.65
2.00
1.75
1.60
1.90
1.65
1.55
1.85
1.60
1.50
1.80
1.60
1.45
0.95
0.825
0.525
1,800
1,700
1,600
1,800
1,700
1,600
1,800
1,700
1,600
1,800
1,700
1,600
1,800
1,700
1,600
1,500
1,500
1,200
SPIB
1.25
0.875
1.10
0.90
0.60
1.05
0.85
0.50
0.70
0.45
0.65
0.45
0.30
0.70
0.55
0.325
0.135
0.135
0.125
0.125
0.125
0.125
0.125
0.125
0.425
0.425
0.425
0.425
0.425
0.425
0.425
0.425
1.40
1.15
0.775
0.625
0.425
0.80
0.70
0.50
1,500
1,400
1,300
1,300
1,000
1,300
1,300
1,000
NLGA
1.30
0.875
0.775
1.05
0.90
0.575
1.00
0.80
0.475
0.575
0.40
0.35
0.625
0.45
0.30
0.675
0.55
0.325
0.135
0.135
0.135
0.125
0.125
0.125
0.125
0.125
0.125
0.335
0.335
0.335
0.335
0.335
0.335
0.335
0.335
0.335
1.20
1.05
1.00
0.675
0.55
0.375
0.70
0.625
0.425
1,300
1,200
1,100
1,200
1,200
1,000
1,200
1,200
1,000
NELMA
NSLB
WCLIB
WWPA
1.00
0.725
0.70
0.575
0.425
0.40
0.145
0.145
0.145
0.42
0.42
0.42
0.90
0.725
0.575
1,500
1,400
1,300
NSLB
Compression
Parallel
to Grain
Fco
Modulus
of
Elasticity
Eo
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
Grading
Rules
Agency
2012
Edition
SECTION 8: WOOD STRUCTURES
8-11
Table 8.4.1.1.4-2—Reference Design Values for Mechanically Graded Dimension Lumber
Commercial Grade
Size
Classification
Bending
Fbo
Design Values (ksi)
Tension
Compression
Parallel to
Parallel to
Grain
Grain
Fto
Fco
Modulus of
Elasticity
Eo
Grading Rules Agency
Machine Stress Rated (MSR) Lumber
900f-1.0E
0.90
0.35
1.05
1,000
WCLIB, WWPA, NELMA, NSLB
1200f-1.2E
1.20
0.60
1.40
1,200
NLGA, WCLIB, WWPA, NELMA, NSLB
1250f-1.4E
1.25
0.80
1.475
1,400
WCLIB, WWPA
1350f-1.3E
1.35
0.75
1.60
1,300
NLGA, WCLIB, WWPA, NELMA, NSLB
1400f-1.2E
1.40
0.80
1.60
1,200
NLGA, WWPA
1450f-1.3E
1.45
0.80
1.625
1,300
NLGA, WCLIB, WWPA, NELMA, NSLB
1450f-1.5E
1.45
0.875
1.625
1,500
WCLIB, WWPA
1500f-1.4E
1.50
0.90
1.65
1,400
NLGA, WCLIB, WWPA, NELMA, NSLB
1600f-1.4E
1.60
0.95
1.675
1,400
NLGA, WWPA
1650f-1.3E
1.65
1.02
1.70
1,300
NLGA, WWPA
1650f-1.5E
1.65
1.02
1.70
1,500
1.65
1.65
1.075
1.175
1.70
1.70
1,600
1,600
NLGA,SPIB,WCLIB,WWPA,NELMA,NS
LB
WCLIB, WWPA
WCLIB, WWPA
≤2 in. Thick
1650f-1.6E-1075 ft
1650f-1.6E
1650f-1.8E
1.65
1.02
1.75
1,800
WCLIB, WWPA
1700f-1.6E
1.70
1.175
1.725
1,600
WCLIB, WWPA
1750f-2.0E
1.75
1.125
1.725
2,000
WCLIB, WWPA
1800f-1.5E
1.80
1.30
1.75
1,500
NLGA, WWPA
1800f-1.6E
1.80
1.175
1.75
1,600
1800f-1.8E
1.80
1.20
1.75
1,800
NLGA,SPIB,WCLIB,WWPA,NELMA,NS
LB
WCLIB, WWPA
1950f-1.5E
1.95
1.375
1.80
1,500
SPIB, WWPA
1950f-1.7E
1.95
1.375
1.80
1,700
2000f-1.6E
2.00
1.30
1.825
1,600
NLGA,SPIB,WCLIB,WWPA,NELMA,NS
LB
NLGA, WWPA
2100f-1.8E
2.10
1.575
1.875
1,800
2250f-1.7E
2.25
1.75
1.925
1,700
2250f-1.8E
2.25
1.75
1.925
1,800
NLGA, WCLIB, WWPA
2250f-1.9E
2.25
1.75
1.925
1,900
2250f-2.0E-1600ft
2.25
1.60
1.925
2,000
NLGA,SPIB,WCLIB,WWPA,NELMA,NS
LB
WCLIB, WWPA
2250f-2.0E
2.25
1.75
1.925
2,000
WCLIB, WWPA
2400f-1.8E
2.40
1.925
1.975
1,800
NLGA, WWPA
2400f-2.0E
2.40
1.925
1.975
2,000
2500f-2.2E
2.50
1.75
2.00
2,200
NLGA,SPIB,WCLIB,WWPA,NELMA,NS
LB
WCLIB, WWPA
2500f-2.2E-1925ft
2.50
1.925
2.00
2,200
WCLIB, WWPA
2550f-2.1E
2.55
2.05
2.025
2,100
2700f-2.0E
2.70
1.80
2.10
2,000
NLGA,SPIB,WCLIB,WWPA,NELMA,NS
LB
WCLIB, WWPA
2700f-2.2E
2.70
2.15
2.10
2,200
2850f-2.3E
2.85
2.30
2.150
2,300
3000f-2.4E
3.00
2.40
2.20
2,400
NLGA,SPIB,WCLIB,WWPA,NELMA,NS
LB
NLGA,SPIB,WCLIB,WWPA,NELMA,NS
LB
NLGA, SPIB
Machine Evaluated Lumber (MEL)
M-5
≤2 in. Thick
M-6
0.90
0.500
1.05
1.100
SPIB
1.10
0.600
1.30
1.000
SPIB
M-7
1.20
0.650
1.40
1.100
SPIB
≥2 in. Wide
≥2 in. Wide
NLGA,SPIB,WCLIB,WWPA,NELMA,NS
LB
NLGA, WWPA
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
8-12
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 8.4.1.1.4-3—Reference Design Values of Specific Gravity, G, Shear, Fvo, and Compression Perpendicular to Grain,
Fcpo, for Mechanically Graded Dimension Lumber
Species
Douglas Fir-Larch
Hem-Fir
Southern Pine
Spruce-Pine-Fir
Spruce-Pine-Fir (S)
Modulus of
Elasticity E (ksi)
≥1,000
2,000
2,100
2,200
2,300
2,400
≥1,000
1,600
1,700
1,800
1,900
2,000
2,100
2,200
2,300
2,400
≥1,000
≥1,800
≥1,200
1,800–1,900
≥2,000
≥1,000
1,200–1,900
1,200–1,700
1,800–1,900
≥2,000
Specific
Gravity
Design Values (ksi)
Compression
Shear
Perpendicular
Parallel to
to Grain
Grain
G
0.50
0.51
0.52
0.53
0.54
0.55
0.43
0.44
0.45
0.46
0.47
0.48
0.49
0.50
0.51
0.52
0.55
0.57
0.42
0.46
0.50
0.36
0.42
0.42
0.46
0.50
Fvo
0.180
0.180
0.180
0.180
0.185
0.185
0.150
0.155
0.160
0.160
0.165
0.170
0.170
0.175
0.190
0.190
0.175
0.190
0.135
0.160
0.170
0.135
0.150
0.150
0.160
0.175
Fcpo
Grading Rules Agency
0.625
0.670
0.690
0.715
0.735
0.760
0.405
0.510
0.535
0.555
0.580
0.600
0.625
0.645
0.670
0.690
0.565
0.805
0.425
0.525
0.615
0.335
0.465
0.465
0.555
0.645
WCLIB, WWPA
WCLIB, WWPA
WCLIB, WWPA
WCLIB, WWPA
SPIB
SPIB
NLGA
NLGA
NELMA, NSLB, WCLIB, WWPA
NELMA, NSLB
WWPA
NELMA, NSLB, WWPA
8.4.1.2—Structural Glued Laminated Timber
(Glulam)
C8.4.1.2.1
8.4.1.2.1—General
Structural glued laminated timber shall be
manufactured using wet-use adhesives and shall comply
with the requirements of ANSI/AITC A190.1-2002. Glued
laminated timber may be manufactured from any lumber
species, provided that it meets the requirements of
ANSI/AITC A190.1 and is treatable with wood
preservatives in accordance with the requirements of
Article 8.4.3.
The contract documents shall require that each piece
of glued laminated timber be distinctively marked and
provided with a Certificate of Conformance by an
accredited inspection and testing agency, indicating that
the requirements of ANSI/AITC A190.1 have been met
and that straight or slightly cambered bending members
have been stamped TOP on the top at both ends so that the
natural camber, if any, shall be positioned opposite to the
direction of applied loads.
When wet-use adhesives are used, the bond between
the laminations, which is stronger than the wood, will be
maintained under all exposure conditions. Dry-use
adhesives will deteriorate under wet conditions. For bridge
applications, it is not possible to ensure that all areas of the
components will remain dry. ANSI/AITC A190.1-2002
requires the use of wet-use adhesives for the manufacture
of structural glued laminated timber.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 8: WOOD STRUCTURES
8-13
Industrial appearance grade, as defined in
AITC 110-2001, Standard Appearance Grades for
Structural Glued Laminated Timber, shall be used, unless
otherwise specified.
8.4.1.2.2—Dimensions
Structural glued laminated timber is available in four
standard appearance grades: framing, industrial,
architectural, and premium. Architectural and premium
grades are typically planed or sanded, and exposed
irregularities are filled with a wood filler that may crack
and dislodge under exterior exposure conditions. Framing
grade is surfaced hit-or-miss to produce a timber with the
same net width as standard lumber for concealed
applications where matching the width of framing lumber
is important. Framing grade is not typically used for bridge
applications. In addition to the four standard appearance
grades, certain manufacturers will use special surfacing
techniques to achieve a desired look, such as a rough sawn
look. Individual manufacturers should be contacted for
details.
C8.4.1.2.2
Dimensions stated for glued laminated timber shall be
taken as the actual net dimensions.
In design, structural calculations shall be based on the
actual net dimensions. Net width of structural glued
laminated timber shall be as specified in Table 8.4.1.2.2-1
or other dimensions as agreed upon by buyer and seller.
Structural glued laminated timber can be
manufactured to virtually any shape or size. The most
efficient and economical design generally results when
standard sizes are used. Acceptable manufacturing
tolerances are given in ANSI/AITC A190.1-2002.
The use of standard sizes constitutes good practice
and is recommended whenever possible. Nonstandard sizes
should only be specified after consultation with the
laminator.
Southern Pine timbers are typically manufactured
from 1.375-in. thick laminations, while timbers made from
Western Species and Hardwoods are commonly
manufactured from 1.5-in. thick laminations. Curved
members may be manufactured from thinner laminations
depending on the radius of curvature. Radii of curvature of
less than 27.0 ft, 6.0 in. normally require the use of thinner
laminations.
Table 8.4.1.2.2-1—Net Dimensions of Glued Laminated Timber
Nominal
Width of
Laminations
(in.)
3
4
6
8
10
12
14
16
Western Species
Net Finished
Dimension
(in.)
2 1/8 or 2 1/2
3 1/8
5 1/8
6 3/4
8 3/4
10 3/4
12 1/4
14 1/4
Southern Pine
Net Finished
Dimension
(in.)
2 1/8 or 2 1/2
3.0 or 3 1/8
5.0 or 5 1/8
6 3/4
8 1/2
10 1/2
12.0
14.0
The total glulam net depth shall be taken as the
product of the thickness of the laminations and the number
of laminations.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
8-14
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
8.4.1.2.3—Reference Design Values
Grade combinations for structural glued laminated
timber shall be as provided in AITC 117-2004, Standard
Specifications for Structural Glued Laminated Timber of
Softwood Species, or AITC 119-96, Standard
Specifications for Structural Glued Laminated Timber of
Hardwood Species.
Reference Design Values for structural glued
laminated timber shall be as specified in Tables 8.4.1.2.3-1
and 8.4.1.2.3-2:
•
Table 8.4.1.2.3-1 contains design values for
timbers with layups optimized to resist bending
loads applied perpendicular to the wide face of
the laminations (bending about the x-x axis).
Design values are also included, however, for
axial loads and bending loads applied parallel to
the wide faces of the laminations. The design
values in Table 8.4.1.2.3-1 are applicable to
timbers with four or more laminations.
•
Table 8.4.1.2.3-2 contains design values for
timbers with uniform-grade layups. These layups
are intended primarily for timbers loaded axially
or in bending due to loads applied parallel to the
wide faces of the laminations (bending about the
y-y axis). Design values are also included,
however, for bending due to loads applied
perpendicular to the wide faces of the laminations.
The design values in Table 8.4.1.2.3-2 are
applicable to timbers with two or more
laminations.
C8.4.1.2.3
The combinations in Table 8.4.1.2.3-1 are applicable
to members consisting of four or more laminations and are
intended primarily for members stressed in bending due to
loads applied perpendicular to the wide faces of the
laminations. However, design values are tabulated for
loading both perpendicular and parallel to the wide faces
of the laminations. The combinations and design values
applicable to members loaded primarily axially or parallel
to the wide faces of the laminations, are specified in
Table 8.4.1.2.3-2. Design values for members of two or
three laminations, are specified in Table 8.4.1.2.3-2.
In Table 8.4.1.2.3-1, the tabulated design values, Fbx,
for bending about the x-x axis (Fbx), require the use of
special tension laminations. If these special tension
laminations are omitted, value shall be multiplied by 0.75 for
members greater than or equal to 15 in. in depth or by 0.85
for members less than 15 in. in depth.
In Table 8.4.1.2.3-1, the design value for shear, Fvx,
shall be decreased by multiplying by a factor of 0.72 for
nonprismatic members, notched members, and for all
members subject to impact or cyclic loading. The reduced
design value shall be used for design of members at
connections that transfer shear by mechanical fasteners. The
reduced design value shall also be used for determination of
design values for radial tension and torsion. Design values,
Fvy, shall be used for timbers with laminations made from a
single piece of lumber across the width or multiple pieces
that have been edge bonded. For timber manufactured from
multiple-piece laminations (across width) that are not edgebonded, in addition to other reduction, design value shall be
multiplied by 0.4 for members with five, seven, or nine
laminations or by 0.5 for all other members. If combination
24F-V4 contain lumber with wane, then, in addition, the
design value for shear parallel to grain, Fvx, shall be
multiplied by 0.67 if wane is allowed on both sides. If wane
is limited to one side, Fvx, shall be multiplied by 0.83.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 8: WOOD STRUCTURES
8-15
In Table 8.4.1.2.3-2, for members with two or three
laminations, the shear design value for transverse loads
parallel to the wide faces of the laminations, Fvy, shall be
reduced by multiplying by a factor of 0.84 or 0.95,
respectively. For members with five, seven, or nine
laminations, in addition, Fvy, shall be multiplied by 0.4 for
members manufactured from multiple-piece laminations
(across width) that are not edge bonded. The shear design
value, Fvy, shall be multiplied by 0.5 for all other members
manufactured from multiple-piece laminations with
unbonded edge joints.
In Table 8.4.1.2.3-2, the design value for shear, Fvx,
shall be decreased by multiplying by a factor of 0.72 for
nonprismatic members, notched members, and for all
members subject to impact or cyclic loading. The reduced
design value shall be used for design of members at
connections that transfer shear by mechanical fasteners.
The reduced design value shall also be used for
determination of design values for radial tension and
torsion.
In Table 8.4.1.2.3-2, the tabulated design values shall
apply to timbers without special tension laminations. If
special tension laminations are used, for members to 15 in.
deep the design value for bending, Fbx, may be increased
by multiplying by 1.18. For members greater than 15 in.
deep and without special tension laminations, the bending
design value, Fbx, shall be reduced by multiplying by a
factor of 0.88.
Reference design values for combinations not given in
Table 8.4.1.2.3-1 or Table 8.4.1.2.3-2 shall be obtained
from AITC 117-2004.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
8-16
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 8.4.1.2.3-1—Reference Design Values, ksi, for Structural Glued Laminated Softwood Timber Combinations (Members stressed primarily in bending)
Bending About X-X Axis
Bending About Y-Y Axis
(Loaded Perpendicular to Wide Faces
of Laminations)
(Loaded Parallel to Wide Faces
of Laminations)
Extreme Fiber in
Bending
Combination
Symbol
Species
Tension
Zone
Stressed
in
Compression
Zone
Stressed
in
Tension
Tension
Fbxo
Fbxo
+
Compression
Perpendicular
to Grain
Tension
Compression
Face
Face
-
Fcpo
Shear Parallel
to Grain
(Horizontal)
Extreme
Fiber in
Bending
Compression
Perpendicular
to Grain
Shear Parallel
to Grain
(Horizontal)
Fvxo
Exo
Fbyo
Fcpo
Fvyo
(103)
0.425
Modulus
of
Elasticity
Tension
Parallel to
Grain
Compression
Parallel to
Grain
Fasteners
Modulus
of
Elasticity
Specific Gravity
for
Fastener Design
Top or
Bottom Face
Outer/ Core
20F-1.5E
Modulus
of
Elasticity
Axially Loaded
Eyo
Fto
Fco
(103)
Eo axial
Side Face
Go
(103)
0.42
20F-V3
20F-V7
20F-V9
20F-V12
20F-V13
DF/DF
DF/DF
HF/HF
AC/AC
AC/AC
2
2.000
2.000
2.000
2.000
2.000
1.1
1.450
2.000
2.000
1.400
2.000
0.650
0.650
0.500
0.560
0.560
0.560
0.650
0.500
0.560
0.560
0.21
0.265
0.265
0.215
0.265
0.265
1.5
1.6
1.6
1.5
1.5
1.5
0.8
1.45
1.45
1.35
1.25
1.25
0.315
0.56
0.56
0.38
0.47
0.47
0.185
0.23
0.23
0.19
0.23
0.23
1.2
1.5
1.6
1.4
1.4
1.4
0.725
0.975
1.000
0.975
0.900
0.925
0.925
1.550
1.600
1.400
1.500
1.550
1.3
1.6
1.6
1.5
1.4
1.5
0.5
0.5
0.43
0.46
0.46
0.5
0.5
0.43
0.46
0.46
20F-V2
20F-V3
20F-V5
SP/SP
SP/SP
SP/SP
2.000
2.000
2.000
1.550
1.450
2.000
0.740
0.650
0.740
0.650
0.650
0.740
0.300
0.300
0.300
1.5
1.5
1.6
1.45
1.75
1.45
0.65
0.65
0.65
0.26
0.26
0.26
1.4
1.4
1.4
0.975
1.050
1.050
1.350
1.400
1.500
1.5
1.5
1.5
0.55
0.55
0.55
0.55
0.55
0.55
24F-1.7E
0.5
0.42
24F-V5
24F-V10
DF/HF
DF/HF
2.4
2.400
2.400
1.45
1.600
2.400
0.650
0.650
0.650
0.650
0.21
0.215
0.215
1.7
1.7
1.8
1.05
1.20
1.45
0.315
0.38
0.38
0.185
0.19
0.19
1.2
1.5
1.5
0.775
1.150
1.100
1
1.450
1.550
1.4
1.6
1.6
0.5
0.5
0.43
0.43
24F-V1
SP/SP
2.400
1.750
0.740
0.650
0.300
1.7
1.45
0.65
0.26
1.5
1.100
1.550
1.6
0.55
0.55
24F-V4
24F-V5
SP/SP
SP/SP
2.400
2.400
1.450
2.400
0.740
0.740
0.650
0.740
0.210
0.300
1.7
1.7
1.05
1.75
0.47
0.65
0.19
0.26
1.3
1.5
0.875
1.150
1.000
1.650
1.5
1.6
0.55
0.55
0.43
0.55
DF/DF
DF/DF
2.4
2.400
2.400
1.45
1.850
2.400
0.650
0.650
0.650
0.650
0.265
0.265
0.265
1.8
1.8
1.8
1.45
1.45
1.45
0.56
0.56
0.56
0.23
0.23
0.23
1.6
1.6
1.6
1.1
1.100
1.100
1.6
1.650
1.650
1.7
1.7
1.7
0.5
0.5
SP/SP
2.400
1.950
0.740
0.740
0.300
1.8
1.75
0.65
0.26
1.6
1.150
1.650
1.7
0.55
2.6
1.95
0.265
1.9
1.6
0.56
0.23
1.6
1.15
1.6
1.7
24F-1.8E
24F-V4
24F-V8
24F-V3
26F-1.9E
0.65
0.65
0.5
0.5
0.5
0.55
0.5
26F-V1
26F-V2
DF/DF
DF/DF
2.600
2.600
1.950
2.600
0.650
0.650
0.650
0.650
0.265
0.265
2.0
2.0
1.750
1.750
0.560
0.560
0.230
0.230
1.8
1.8
1.300
1.300
1.850
1.850
1.9
1.9
0.5
0.5
0.5
0.5
26F-V2
26F-V4
SP/SP
SP/SP
2.600
2.600
2.100
2.600
0.740
0.740
0.740
0.740
0.300
0.300
1.9
1.9
2.200
2.100
0.740
0.650
0.260
0.260
1.8
1.8
1.250
1.200
1.650
1.600
1.9
1.9
0.55
0.55
0.55
0.55
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
8-17
SECTION 8: WOOD STRUCTURES
Table 8.4.1.2.3-2—Reference Design Values, ksi, for Structural Glued Laminated Softwood Timber (Members stressed primarily in axial tension and compression)
All Loading
Axially Loaded
Tension
Parallel
to Grain
Identification Species
Number
Grade
Modulus
of
Elasticity
Eo
Bending about Y-Y Axis
Bending About X-X Axis
Loaded Parallel to Wide
Faces of Laminations
Shear Parallel
Bending
to Grain
Compression
Parallel
to Grain
Compression
Perpendicular
to Grain
Fcpo
2 or More
Laminations
Fto
4 or More
Laminations
Fcpo
2 or 3
Laminations
Fcpo
4 or More
Laminations
Fbyo
3
Laminations
Fbyo
2
Laminations
Fbyo
1.5
1.6
1.9
2.0
1.3
1.4
1.6
1.7
1.2
1.3
1.6
0.560
0.560
0.650
0.650
0.375
0.375
0.375
0.500
0.470
0.470
0.560
0.900
1.250
1.450
1.600
0.800
1.050
1.200
1.400
0.725
0.975
1.250
1.550
1.950
2.300
2.400
1.100
1.350
1.500
1.750
1.150
1.450
1.900
1.200
1.600
1.850
2.100
0.975
1.300
1.450
1.700
1.100
1.450
1.900
1.450
1.800
2.100
2.400
1.200
1.500
1.750
2.000
1.100
1.400
1.850
1.250
1.600
1.850
2.100
1.050
1.350
1.550
1.850
0.975
1.250
1.650
1.4
1.7
1.7
1.9
0.650
0.740
0.650
0.740
1.200
1.400
1.350
1.550
1.900
2.200
2.100
2.300
1.150
1.350
1.450
1.700
1.750
2.000
1.950
2.300
1.550
1.800
1.750
2.100
Loaded Perpendicular to Wide
Faces of Laminations
Bending
Shear Parallel
to Grain
Fvyo
2 Laminations to
15 in. Deep
Fbxo
Fvxo
1.000
1.300
1.550
1.800
0.850
1.100
1.300
1.550
0.775
1.000
1.400
0.230
0.230
0.230
0.230
0.190
0.190
0.190
0.190
0.230
0.230
0.230
1.250
1.700
2.000
2.200
1.100
1.450
1.600
1.900
1.000
1.350
1.700
0.265
0.265
0.265
0.265
0.215
0.215
0.215
0.215
0.265
0.265
0.265
1.300
1.500
1.500
1.750
0.260
0.260
0.260
0.260
1.400
1.600
1.800
2.100
0.300
0.300
0.300
0.300
(103)
Visually Graded Western Species
1
DF
L3
2
DF
L2
3
DF
L2D
5
DF
L1
14
HF
L3
15
HF
L2
16
HF
L1
17
HF
L1D
69
AC
L3
70
AC
L2
71
AC
L1D
Visually Graded Southern Pine
47
48
49
50
SP
SP
SP
SP
N2M14
N2D14
N1M16
N1D14
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
8-18
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
8.4.1.3—Tension-Reinforced Glulams
C8.4.1.3.1
8.4.1.3.1—General
Tension–reinforced glulams shall incorporate a
continuous reinforcement material placed on the tension
side of a flexural member to increase its flexural bending
strength and stiffness. Reinforcement may be any material
that is not a conventional lamstock whose mean
longitudinal unit strength exceeds 20 ksi for tension and
compression mean ultimate strength, and whose mean
tension and compression modulus of elasticity exceeds
3,000 ksi, when placed into a glulam timber. Acceptable
reinforcing materials include but are not restricted to:
Fiber-Reinforced Polymer (FRP) plates and bars using Eglass fibers (GFRP) or carbon fibers (CFRP), and metallic
plates and bars.
The reinforced ratio, ρ, shall be determined as the
cross-sectional area of tension reinforcement divided by
cross-sectional area of beam above the center of gravity of
tension reinforcement, expressed in percent. Typical
reinforcement ratios and modulus of elasticity values for
various types of reinforcement given in Table 8.4.1.3.1-1
shall apply.
Table 8.4.1.3.1-1—Typical Reinforcement Ratios
MOE (ksi)
Min. ρ %
Typical ρ %
Max. ρ %
E-Glass
FRP
6,000
1
2
3
Reinforcement Material
Aramid
Carbon
FRP
FRP
10,000
20,000
0.6
0.3
1.2
0.6
1.8
0.9
Steel
Plate
30,000
0.2
0.4
0.6
Tension-reinforced glued laminated timber shall be
manufactured using wet-use adhesives in accordance with
applicable provisions of ANSI/AITC 190.1, and shall
comply with the requirements listed in Article 8.4.1.2,
except as described in detail in ASTM D7199. The
additional requirements cited in ASTM D7199 to be
investigated shall include bond strength and durability
requirements for the tension reinforcement, preservative
treatment, volume factor, and fatigue considerations.
The determination of reinforcement ratio, ρ, is
analogous to that used for reinforced concrete.
The scope of ASTM D7199 pertains to the analysis of
FRP-glulams in bending.
The addition of FRP
reinforcement in the tension region of the glulam does not
require new test or analytical methods to determine the
secondary design properties (shear, compression
perpendicular to grain, tension parallel to grain,
compression parallel to grain, etc.). These properties are
determined for glulam layups following ASTM D3737.
Tension-reinforced glulam beams subject to axial
compression loads are outside the scope of this
Specification. This Specification does not cover unbonded
reinforcement (i.e. material not continuously bonded to the
beam), prestressed reinforcement (i.e. material pretensioned
before being bonded or anchored to the beam), nor shear
reinforcement (i.e. material intended to increase the shear
strength of the beam).
ASTM D7199 also provides a mechanics-based
approach for predicting the mechanical properties of
tension-reinforced glulams, and may be used by engineers
who have applications with unique reinforcement
requirements. ASTM D7199 addresses methods to obtain
bending properties parallel to grain about the x-x axis
(MOR5% and MOE) for horizontally-laminated reinforced
glulam beams. Secondary properties such as bending
about the y-y axis (Fby-y), shear parallel to grain (Fv),
tension parallel to grain (Ft), compression parallel to grain
(Fc), and compression perpendicular to grain (Fc┴) are
determined following methods described in ASTM D3737
or testing according to other applicable methods such as
ASTM D198 or ASTM D143.
8.4.1.3.2—Dimensions
Dimensions stated for tension-reinforced glued
laminated timber shall be taken as the actual net dimensions.
In design, structural calculations shall be based on the
actual net dimensions. Net width of tension-reinforced
structural glued laminated timber shall be as specified in
Table 8.4.1.2.2-1 or other dimensions as agreed upon by
buyer and seller. The total reinforced glulam net depth
shall be the sum of the thicknesses of all laminations
including the thickness of the tension reinforcement
lamination(s). The gross section properties shall be
calculated using the net depth and the net width.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 8: WOOD STRUCTURES
8-19
C8.4.1.3.3
8.4.1.3.3—Fatigue
Except as noted herein, tension reinforcement shall
extend the full length of the beam or girder and be
confined by the supports.
For E-glass FRP reinforcement produced using the
pultrusion process, beams which satisfy the requirements
for design for static loads specified herein may be
considered to have adequate fatigue design capacity. For
reinforcements
other
than
pultruded
E-glass
reinforcements, coupon level fatigue testing of the
reinforcing material per ASTM D3479 or a similar
procedure shall be required to develop the strength-load
cycle relationship for the reinforcing material. A minimum
of three representative FRP samples shall be tested to
establish the strength-load cycle relationship. This
strength-load cycle relationship shall be the basis for
checking fatigue capacity of the FRP under specific enduse environment.
Full-scale fatigue testing shall be required where
partial-length reinforcement is used to evaluate the
effectiveness of reinforcement end-confinement detail. The
reinforcement termination for partial-length FRP
reinforcement shall be confined over the length at least
equal to the width of the reinforcing material. Unconfined,
partial-length reinforcement shall not be permitted in
bridge applications where fatigue loading exists.
Full-scale fatigue testing shall be required on FRPglulam beams where the allowable stress is more than
75 percent greater than conventional glulam (Fb > 4000 psi).
Where fatigue is a design consideration, the
reinforcement used shall not increase the MOR5% of the
beam by more than 75 percent relative to the strength of
the unreinforced beam.
8.4.1.3.4—Reference Design Values for TensionReinforced Glulams
Reference design values for tension-reinforced glulams
shall be taken as specified in Table 8.4.1.3.4-1 for beams
with no bumper-lams. For the beam lay-ups given in
Table 8.4.1.3.4-1, the volume factor shall be taken equal to
one. The values are for dry use, with adjustment factors
given in Article 8.4.4.3 and shall be used in the same manner
as conventional glulam design values except as specified in
Article 8.4.1.3. These design values shall be used with the
overall gross section properties of the beam, including the
reinforcement.
The research that was performed utilized confinement
achieved by end-bearing support. Confinement proposed
by alternative methods may require full-scale testing.
Under the specified conditions, testing has shown that
the fatigue resistance of tension-reinforced glulam beams
is similar to that of conventional glulam beams. These tests
have included both fatigue and hygrothermal cyclic tests
(Davids et al., 2005 and 2008).
For pultruded E-glass FRP reinforcement, full-scale
tension-reinforced glulam beam flexural fatigue tests,
where the reinforcement extends the full-length of the
beam, have shown that the reinforced beams properly
designed for static loads will have fatigue design capacity
in excess of two million constant-amplitude sinusoidal
cycles. Each of these cycles applied an extreme fiber stress
range starting from the dead load bending stress to a
bending stress equivalent to the full allowable design
stress. Under these conditions, no degradation in bending
strength or stiffness has been observed.
Full-scale fatigue testing has been performed on FRPreinforced glulam beams, considering both full-length and
partial-length reinforced glulams. These tests were
conducted for tension-reinforced beams where the
allowable design stresses were up to 75 percent greater
than the conventional unreinforced glulam. This testing
has shown that premature failure due to fatigue in FRPglulams is not a concern if (1) the FRP reinforcement has
been fatigue-tested at the coupon level and (2) the FRP
tension reinforcement runs for the full length of the glulam
over the supports. For partial-length reinforcement (where
the FRP is terminated before the supports) and for FRPglulams where the allowable stress is more than 75 percent
greater than conventional glulam (Fb > 4000 psi), full-scale
fatigue testing is required. Guidance on performing such
tests can be found in Davids et al. (2005 and 2008).
Fatigue tests where MOR5% has been increased by more
than 75 percent, flexural compression and shear failures
have been observed in addition to flexural tension failures.
FRP coupon fatigue design data should be available
from reinforced beam manufacturers or FRP suppliers. The
vast majority of applications will not require full-scale
fatigue testing of beams.
C8.4.1.3.4
Axial compression is outside the scope of this
Specification. For tension- reinforced glulam subjected to
axial compression, ASTM D3737 provides a method to
account for the Neutral Axis (NA) change in unbalanced
layups. FRP stiffness and shift in the neutral axis shall be
accounted for when developing axial compression design
values. Bending properties about the y-y axis may be
conservatively taken as those of the wood-portion of the
beam, neglecting the reinforcement.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
8-20
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Analysis has shown that with the level of FRP extreme
fiber tension reinforcement typically envisioned (up to three
percent GFRP or one percent CFRP), the maximum shear
stress at the reinforced beam neutral axis is very similar to
that of an unreinforced rectangular section. In addition,
under the same conditions, the shear stress at the FRP-wood
interface is always significantly smaller than the shear
stress at the reinforced beam neutral axis.
Table 8.4.1.3.4-1—Reference Design Values for Tension-Reinforced Structural Glued Laminated Douglas Fir
Combinations (ksi)1
Extreme Fiber in Bending
Combination
Species
Symbol
(Outer/Core)
30F-1.9E
30F-V1R
DF/DF
30F-2.0E
30F-V4R
DF/DF
30F-2.1E
30F-V7R
DF/DF
32F-2.1E
32F-V1R
DF/DF
34F-2.2E
34F-V1R
DF/DF
1
Tension
Zone
Stressed in
Tension
Fbxo +
Compression
Zone
Stressed in
Tension
Fbxo –
3.000
Bending about x-x Axis
Compression
Perpendicular to Grain
Tension
Compression
Face
Face
Shear
Fcpo
Fcpo
Fvxo
Modulus
of
Elasticity
Exo ×103
1.900
0.56
0.56
0.265
1.9
3.000
1.900
0.56
0.56
0.265
2.0
3.000
2.100
0.56
0.56
0.265
2.1
3.200
2.100
0.56
0.56
0.265
2.2
3.400
2.100
0.56
0.56
0.265
2.2
Species other than Douglas Fir may be used if evaluated in accordance with ASTM D7199.
8.4.1.3.5—Volume Effect
Volume factors for the tension-reinforced glulams
listed in Table 8.4.1.3.4-1 shall be taken equal to one
except where the unreinforced compression zone is
stressed in tension. In this latter case, the volume factor
used in conventional glulams shall apply for the
determination of this value.
C8.4.1.3.5
The addition of tension reinforcement diminishes the
volume effect in glulams, and with enough reinforcement
in tension, the volume effect disappears (Lindyberg, 2000).
The tension reinforcement that is necessary to eliminate
the volume effect varies with the wood species and grade,
as well as the type of reinforcement used (e.g. E-glass,
carbon, or Aramid FRP). For example, western species
glulam reinforced with E-glass FRP in tension,
approximately 1.5–3 percent FRP by volume will eliminate
the volume effect (Lindyberg, 2000). For the particular
glulams listed in Table 8.4.1.3.4-1, the E-glass tension
reinforcement ratio is over three percent, and the
corresponding volume factor is equal to one. If the tension
reinforcement ratio is reduced the actual volume factor is a
function of the reinforcement ratio and the reinforcement
longitudinal stiffness. A numerical model that predicts the
volume factor for reinforced glulams for any layup and
type of reinforcement is available (Lindyberg, 2000).
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 8: WOOD STRUCTURES
8-21
8.4.1.3.6—Preservative Treatment
C8.4.1.3.6
Designers shall specify that the effect of preservative
treatment on the properties of the FRP reinforcement and
on the strength and durability of the FRP-wood bond shall
be evaluated as described in ASTM D7199. Preservative
treatment shall be applied after bonding of the
reinforcement. GFRP reinforced beams shall not be posttreated with CCA preservatives.
CCA preservative has been shown to cause severe
cracking in the E-glass reinforcement.
C8.4.1.4
8.4.1.4—Piles
Wood piles shall comply with the requirements of
AASHTO M 168.
Reference design values for round wood piles shall be
as specified in Table 8.4.1.4-1.
The reference design values for wood piles are based
on wet-use conditions.
Table 8.4.1.4-1—Reference Design Values for Piles, ksi
Species
Pacific Coast Douglas-Fir1
Red Oak2
Red Pine3
Southern Pine4
1
2
3
4
Fco
1.25
1.10
0.90
1.20
Fbo
2.45
2.45
1.90
2.40
Fcpo
0.23
0.35
1.55
0.25
Fvo
0.115
0.135
0.085
0.11
Eo
1500
1250
1280
1500
For connection design, use Douglas Fir-Larch reference design values.
Red Oak reference strengths apply to Northern and Southern Red Oak.
Red Pine reference strengths apply to Red Pine grown in the U.S. For connection design, use Northern Pine reference design values.
Southern Pine reference strengths apply to Loblolly, Longleaf, Shortleaf, and Slash Pine.
8.4.2—Metal Fasteners and Hardware
8.4.2.1—General
Structural metal, including shapes, plates, bars, and
welded assemblies, shall comply with the applicable
material requirements of Section 6.
8.4.2.2—Minimum Requirements
8.4.2.2.1—Fasteners
Bolts and lag screws shall comply with the
dimensional and material quality requirements of
ANSI/ASME B18.2.1, Square and Hex Bolts and
Screws—Inch Series. Strengths for low-carbon steel bolts,
Grade 1 through Grade 8, shall be as specified in Society
of Automotive Engineers Specification SAE-429,
Mechanical and Material Requirements for Externally
Threaded Fasteners. Bolt and lag screw grades not given
in SAE-429 shall have a minimum tensile yield strength of
33.0 ksi.
8.4.2.2.2—Prestressing Bars
Prestressing bars shall comply with the requirements
of AASHTO M 275M/M 275 (ASTM A722/A722M) and
the applicable provisions of Section 5.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
8-22
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
8.4.2.2.3—Split Ring Connectors
Split ring connectors shall be manufactured from
hot-rolled carbon steel complying with the requirements of
Society of Automotive Engineers Specification SAE-1010.
Each circular ring shall be cut through in one place in its
circumference to form a tongue and slot.
8.4.2.2.4—Shear Plate Connectors
Shear plate connectors shall be manufactured from
pressed steel, light gage steel, or malleable iron. Pressed
steel connectors shall be manufactured from hot-rolled
carbon steel meeting Society of Automotive Engineers
Specification SAE-1010. Malleable iron connectors shall
be manufactured in accordance with ASTM A47,
Grade 32510.
Each shear plate shall be a circle with a flange around
the edge, extending at right angles to the plate face from
one face only.
8.4.2.2.5—Nails and Spikes
Nails and spikes shall be manufactured from common
steel wire or high-carbon steel wire that is heat-treated and
tempered. When used in withdrawal-type connections, the
shank of the nail or spike shall be annularly or helically
threaded.
8.4.2.2.6—Drift Pins and Bolts
Drift pins and drift bolts shall have a minimum
flexural yield strength of 30.0 ksi.
8.4.2.2.7—Spike Grids
Spike grids shall conform to the requirements of
ASTM A47, Grade 32510, for malleable iron casting.
8.4.2.2.8—Toothed Metal Plate Connectors
Metal plate connectors shall be manufactured from
galvanized sheet steel that complies with the requirements
of ASTM A653, Grade A, or better, with the following
minimum mechanical properties:
Yield Point .......................................................... 33.0 ksi
Ultimate Strength ................................................ 45.0 ksi
Elongation in 2.0 in. ........................................ 20 percent
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
SECTION 8: WOOD STRUCTURES
8-23
8.4.2.3—Corrosion Protection
8.4.2.3.1—Metallic Coating
Except as permitted by this Section, all steel hardware
for wood components shall be galvanized in accordance
with AASHTO M 232M/M 232 (ASTM A153/A153M) or
cadmium plated in accordance with AASHTO M 299
(ASTM B696).
Except as otherwise permitted, all steel components,
timber connectors, and castings other than malleable iron
shall be galvanized in accordance with AASHTO
M 111M/M 111 (ASTM A123/A123M).
C8.4.2.3.1
Galvanized nuts should be retapped to allow for the
increased diameter of the bolt due to galvanizing.
Protection for the high-strength bars used in
stress-laminated decks should be clearly specified.
Standard hot-dip galvanizing can adversely affect the
properties of high-strength post-tensioning materials. A
lower temperature galvanizing is possible with some highstrength bars. The manufacturer of the bars should be
consulted on this issue.
8.4.2.3.2—Alternative Coating
Alternative corrosion protection coatings may be
used when the demonstrated performance of the coating
is sufficient to provide adequate protection for the
intended exposure condition during the design life of the
bridge. When epoxy coatings are used, minimum
coating requirements shall comply with AASHTO
M 284M/M 284.
Heat-treated alloy components and fastenings shall
be protected by an approved alternative protective
treatment that does not adversely affect the mechanical
properties of the material.
8.4.3—Preservative Treatment
8.4.3.1—Requirement for Treatment
All wood used for permanent applications shall be
pressure impregnated with wood preservative in
accordance with the requirements of AASHTO M 133.
Insofar as is practicable, all wood components should
be designed and detailed to be cut, drilled, and otherwise
fabricated prior to pressure treatment with wood
preservatives. When cutting, boring, or other fabrication is
necessary after preservative treatment, exposed, untreated
wood shall be specified to be treated in accordance with
the requirements of AASHTO M 133.
8.4.3.2—Treatment Chemicals
Unless otherwise approved, all structural components
that are not subject to direct pedestrian contact shall be
treated with oil-borne preservatives. Pedestrian railings
and nonstructural components that are subject to direct
pedestrian contact shall be treated with water-borne
preservatives or oil-borne preservatives in light petroleum
solvent.
C8.4.3.2
The oil-borne preservative treatments have proven to
provide adequate protection against wood attacking
organisms. In addition, the oil provides a water repellant
coating that reduces surface effects caused by cyclic
moisture conditions. Water-borne preservative treatments
do not provide the water repellency of the oil-borne
treatment, and components frequently split and check,
leading to poor field performance and reduced service life.
Direct pedestrian contact is considered to be contact
that can be made while the pedestrian is situated anywhere
in the access route provided for pedestrian traffic.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
8-24
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Treating of glued laminated timbers with water-borne
preservatives after gluing is not recommended. Use of
water-borne treatments for glued laminated timber after
gluing may result in excessive warping, checking, or
splitting of the components due to post-treatment re-drying.
8.4.3.3—Inspection and Marking
Preservative treated wood shall be tested and
inspected in accordance with the requirements of
AASHTO M 133. Where size permits, each piece of
treated wood that meets treatment requirements shall be
legibly stamped, branded, or tagged to indicate the name of
the treater and the specification symbol or specification
requirements to which the treatment conforms.
When requested, a certification indicating test results and
the identification of the inspection agency shall be provided.
8.4.3.4—Fire Retardant Treatment
C8.4.3.4
Fire retardant treatments shall not be applied unless it
is demonstrated that they are compatible with the
preservative treatment used, and the usable resistance and
stiffness are reduced as recommended by the product
manufacturer and applicator.
Use of fire retardant treatments is not recommended
because the large sizes of timber components typically used
in bridge construction have inherent fire resistance
characteristics. The pressure impregnation of wood products
with fire retardant chemicals is known to cause certain
resistance and stiffness losses in the wood. These resistance
and stiffness losses vary with specific resistance
characteristic, i.e., bending resistance, tension parallel to grain
resistance, etc., treatment process, wood species and type of
wood product, i.e., solid sawn, glued laminated, or other.
8.4.4—Adjustment Factors for Reference Design
Values
8.4.4.1—General
Adjusted design values shall be obtained by adjusting
reference design values by applicable adjustment factors in
accordance with the following equations:
Fb = Fbo CKF CM (CF or Cv) Cfu Ci Cd Cλ
(8.4.4.1-1)
Fv = Fvo CKF CM Ci Cλ
(8.4.4.1-2)
Ft = Fto CKF CM CF Ci Cλ
(8.4.4.1-3)
Fc = Fco CKF CM CF Ci Cλ
(8.4.4.1-4)
Fcp =
(8.4.4.1-5)
Fcpo CKF CM Ci Cλ
E = Eo CM Ci
(8.4.4.1-6)
where:
F
=
applicable adjusted design values Fb, Fv, Ft, Fc, or
Fcp (ksi)
Fo =
reference design values Fbo, Fvo, Fto, Fco, or Fcpo
specified in Article 8.4 (ksi)
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2012
Edition
SECTION 8: WOOD STRUCTURES
E
=
8-25
adjusted modulus of elasticity (ksi)
Eo =
reference modulus of elasticity specified in
Article 8.4. (ksi)
CKF =
format conversion
Article 8.4.4.2
CM =
wet service factor specified in Article 8.4.4.3
CF =
size factor for visually-graded dimension lumber
and sawn timbers specified in Article 8.4.4.4
CV =
volume factor for structural glued laminated
timber specified in Article 8.4.4.5
Cfu =
flat-use factor specified in Article 8.4.4.6
Ci =
incising factor specified in Article 8.4.4.7
Cd =
deck factor specified in Article 8.4.4.8
Cλ =
time effect factor specified in Article 8.4.4.9
factor
specified
in
C8.4.4.2
8.4.4.2—Format Conversion Factor, CKF
The reference design values in Tables 8.4.1.1.4-1,
8.4.1.1.4-2,
8.4.1.1.4-3,
8.4.1.2.3-1,
8.4.1.2.3-2,
8.4.1.3.4-1, and 8.4.1.4-1 and reference design values
specified in the NDS® shall be multiplied by a format
conversion factor, CKF, for use with load and resistance
factor design (LRFD). CKF = 2.5/φ, except for compression
perpendicular to grain which shall be obtained by
multiplying the allowable stress by a format conversion
factor of CKF = 2.1/φ.
The conversion factors were derived so that LRFD
design will result in same size member as the allowable
stress design (ASD) specified in NDS®. For example, a
rectangular component in flexure has to satisfy:
1.25 MDL + 1.75 MLL ≤ φ S Fbo CKF CM (CF or Cv) Cfu Ci
(C8.4.4.2-1)
Cd Cλ CL
or:
(1.25 MDL + 1.75 MLL) / (φCKF Cλ) ≤ S Fbo CM (CF or Cv)
(C8.4.4.2-2)
Cfu Ci Cd CL
where:
MDL =
moment due to dead load
MLL =
moment due to live load
On the other hand, the allowable stress design (ASD) has
to satisfy:
MDL + MLL ≤ S Fbo CM (CF or Cv) Cfu Ci Cd CD CL or
(MDL + MLL) / (CD) ≤ S Fbo CM (CF or Cv) Cfu Ci Cd CL
(C8.4.4.2-3)
Therefore:
(1.25 MDL + 1.75 MLL) / (φCKF Cλ) = (MDL + MLL) / (CD)
(C8.4.4.2-4)
CKF = [(1.25 MDL + 1.75 MLL)(CD)] / [(MDL + MLL)(φCλ)]
(C8.4.4.2-5)
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2012
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8-26
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The format conversion factor is calculated assuming the
ratio of MDL and MLL is 1:10, φ = 0.85, Cλ = 0.8, and
CD = 1.15.
C8.4.4.3
8.4.4.3—Wet Service Factor, CM
The reference design values specified in
Tables 8.4.1.1.4-1, 8.4.1.1.4-2, 8.4.1.1.4-3, 8.4.1.2.3-1,
8.4.1.2.3-2, 8.4.1.3.4-1, and 8.4.1.4-1 are for dry use
conditions and shall be adjusted for moisture content
using the wet service factor, CM, specified below:
•
For sawn lumber with an in-service moisture
content of 19 percent or less, CM shall be taken
as 1.0.
•
For glued laminated and tension-reinforced glued
laminated (reinforced and unreinforced) timber
with an in-service moisture content of 16 percent
or less, CM shall be taken as 1.0.
•
Otherwise, CM shall be taken as specified in
Tables 8.4.4.3-1 for sawn lumber and
Table 8.4.4.3-2 for reinforced and unreinforced
glued laminated timber, respectively.
Reference design values for Southern Pine and Mixed
Southern Pine sawn timbers 5 in. × 5 in. and larger shall be
taken to apply to wet or dry use.
The wet service factors for reinforced and
unreinforced glued laminated timber shall be the same.
An analysis of in-service moisture content should be
based on regional, geographic, and climatological
conditions. In the absence of such analysis, wet-use
conditions should be assumed.
Reduction for wet-use is not required for Southern
Pine and Mixed Southern Pine sawn timbers 5 in. × 5 in.
and larger.
Table 8.4.4.3-1—Wet Service Factor for Sawn Lumber, CM
Nominal
Thickness
FboCF ≤ 1.15
ksi
FboCF > 1.15
ksi
Fto
FcoCF≤0.75
ksi
FcoCF > 0.75
ksi
Fvo
Fcpo
Eo
≤4 in.
>4.0 in.
1.00
1.00
0.85
1.00
1.00
1.00
1.00
0.91
0.80
0.91
0.97
1.00
0.67
0.67
0.90
1.00
Table 8.4.4.3-2—Wet Service Factor for Glued Laminated Timber and Tension-Reinforced Glued Laminated Timber, CM
Fbo
Fvo
Fto
Fco
Fcpo
Eo
0.80
0.875
0.80
0.73
0.53
0.833
8.4.4.4—Size Factor, CF, for Sawn Lumber
The size factor, CF, shall be 1.0 unless specified
otherwise herein.
For visually-graded dimension lumber of all species
except Southern Pine and Mixed Southern Pine, CF shall
be as specified in Table 8.4.4.4-1.
Reference design values for Southern Pine and Mixed
Southern Pine dimension lumber have been size-adjusted;
no further adjustment for size shall be applied.
For Southern Pine and Mixed Southern Pine
dimension lumber wider than 12.0 in., the tabulated
bending, compression, and tension parallel to grain design
values, for the 12.0 in. depth, shall be multiplied by the
size factor, CF = 0.9.
C8.4.4.4
CF does not apply to mechanically-graded lumber
(MSR, MEL) or to structural glued laminated timber.
Tabulated design values for visually-graded lumber of
Southern Pine and Mixed Southern Pine species groups
have already been adjusted for size. Further adjustment by
the size factor is not permitted.
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2012
Edition
SECTION 8: WOOD STRUCTURES
8-27
Table 8.4.4.4-1—Size Effect Factor, CF, for Sawn Dimension Lumber
Fbo
Grade
Width (in.)
≤4
5
6
8
10
12
≥14
Sel. Str.
No. 1
No. 2
Fto
Thickness
Fco
2.0 in. and
3.0 in.
4.0 in.
All
All
Structural Light Framing: 2.0 in × 2.0 in. through 4.0 in. × 4.0 in.
Structural Joists and Planks: 2.0 in × 5.0 in. through 4.0 in. × 16.0 in.
1.5
1.54
1.5
1.15
1.4
1.4
1.4
1.1
1.3
1.3
1.3
1.1
1.2
1.3
1.2
1.05
1.1
1.2
1.1
1.0
1.0
1.1
1.0
1.0
0.9
1.0
0.9
0.9
All Other
Properties
All
1.00
For sawn beams and stringers with loads applied to
the narrow face and posts and timbers with loads applied
to either face, Fbo shall be adjusted by CF determined as:
•
If d ≤ 12.0 in., then
CF = 1.0
•
(8.4.4.4-1)
If d > 12.0 in., then
1
12 9
CF =
d
(8.4.4.4-2)
where:
d
= net width as shown in Figure 8.3-1
For beams and stringers with loads applied to the wide
face, Fbo shall be adjusted by CF as specified in
Table 8.4.4.4-2.
Table 8.4.4.4-2—Size Factor, CF, for Beams and Stringers
with Loads Applied to the Wide Face
Grade
SS
No. 1
No. 2
Fbo
0.86
0.74
1.00
Eo
1.00
0.90
1.00
Other Properties
1.00
1.00
1.00
8.4.4.5—Volume Factor, CV, (Glulam)
For horizontally laminated glulam, with loads applied
perpendicular to the wide face of the laminations, Fbo shall
be reduced by CV, given below, when the depth, width, or
length of a glued laminated timber exceeds 12.0 in.,
5.125 in., or 21.0 ft, respectively:
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8-28
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
a
12.0 5.125 21
CV =
≤ 1.0
d b L
(8.4.4.5-1)
where:
d
=
depth of the component (in.)
b
=
width of the component (in.) For layups with
multiple piece laminations (across the width)
b = width of widest piece. Therefore: b ≤ 10.75 in.
L
=
length of the component measured between
points of contraflexure (ft)
a
=
0.05 for Southern Pine and 0.10 for all other
species.
The volume factor, CV, shall not be applied
simultaneously with the beam stability factor, CL,
therefore, the lesser of these factors shall apply.
The conventional glulam volume factor shall not be
applied to tension-reinforced glulams except when
unreinforced compression zone is stressed in tension (see
Article C8.4.1.3.5). For tension-reinforced glulam beams
where unreinforced compression zone is stressed in tension
the volume factor, Cv, the same as for conventional glulam,
shall be used.
C8.4.4.6
8.4.4.6—Flat-Use Factor, Cfu
When dimension lumber graded as Structural Light
Framing or Structural Joists and Planks is used flatwise
(load applied to the wide face), the bending reference
design value shall be multiplied by the flat use factor
specified in Table 8.4.4.6-1.
The flat-use factor shall not apply to dimension
lumber graded as Decking.
Table 8.4.4.6-1—Flat-Use Factor, Cfu, for Dimension
Lumber
Width (in.)
2 and 3
4
5
6
8
≥10
Thickness (in.)
2 and 3
1.0
1.1
1.1
1.15
1.15
1.2
Design values for flexure of dimension lumber
adjusted by the size factor, CF, are based on edgewise use
(load applied to the narrow face). When dimension lumber
is used flatwise (load applied to the wide face), the
bending reference design value should also be multiplied
by the flat use factor specified in Table 8.4.4.6-1.
Design values for dimension lumber graded as
Decking are based on flatwise use. Further adjustment by
the flat-use factor is not permitted.
4
—
1.0
1.05
1.05
1.05
1.1
Reference design values for flexure of vertically
laminated glulam (loads applied parallel to wide faces of
laminations) shall be multiplied by the flat use factors
specified in Table 8.4.4.6-2 when the member dimension
parallel to wide faces of laminations is less than 12.0 in.
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2012
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SECTION 8: WOOD STRUCTURES
8-29
Table 8.4.4.6-2—Flat-Use Factor, Cfu, for Glulam
Member dimension parallel to wide
faces of laminations (in.)
10 3/4 or 10 1/2
8 3/4 or 8 1/2
6 3/4
5 1/8 or 5
3 1/8 or 3
2 1/2 or 2 1/8
Cfu
1.01
1.04
1.07
1.10
1.16
1.19
8.4.4.7—Incising Factor, Ci
Reference design values for dimension lumber shall
be multiplied by the incising factor specified in
Table 8.4.4.7-1 when members are incised parallel to grain
a maximum depth of 0.4 in., a maximum length of 3/8 in.,
and a density of incisions up to 1100/ft2. Incising factors
shall be determined by test or by calculation using reduced
section properties for incising patterns exceeding these
limits.
Table 8.4.4.7-1—Incising Factor for Dimension Lumber
Design Value
Eo
Fbo, Fto, Fco, Fvo
Fcpo
Ci
0.95
0.80
1.00
8.4.4.8—Deck Factor, Cd
C8.4.4.8
Unless specified otherwise in this Article, the deck
factor, Cd, shall be equal to 1.0.
For stressed wood, nail-laminated, and spikelaminated decks constructed of solid sawn lumber 2.0 in.
to 4.0 in. thick, Fbo may be adjusted by Cd as specified in
Table 8.4.4.8-1.
Table 8.4.4.8-1—Deck Factor for Stressed Wood and
Laminated Decks
Deck Type
Stressed Wood
Spike-Laminated or
Nail-Laminated
Lumber Grade
Select Structural
No. 1 or No. 2
All
Mechanically laminated decks made of stressed wood,
spike laminated, or nail-laminated solid sawn lumber
exhibit an increased resistance in bending. The resistance
of mechanically laminated solid sawn lumber decks is
calculated by multiplying Fbo in Table 8.4.1.1.4-1 by the
deck factor.
Deck factor is used instead of the repetitive member
factor that is used in NDS®.
1.30
1.50
1.15
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2012
Edition
8-30
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
For planks 4 × 6 in., 4 × 8 in., 4 × 10 in. and
4 × 12 in., used in plank decks with the load applied to the
wide face of planks, Fbo may be adjusted by Cd as
specified in Table 8.4.4.8-2.
Table 8.4.4.8-2—Deck Factor for Plank Decks
Size (in.)
The specified deck factors for planks in plank decks
are based test results comparing the modulus of rupture
(MOR) for plank specimens with load applied in narrow
face and wide face (Stankiewicz and Nowak, 1997). These
deck factors can be applied cumulatively with the size
factor, CF, specified in Article 8.4.4.4.
Cd
1.10
1.15
1.25
1.50
4×6
4×8
4 × 10
4 × 12
The deck factors for planks in plank decks shall not be
applied cumulatively with the flat use factor, Cfu, specified
in Article 8.4.4.6.
C8.4.4.9
8.4.4.9—Time Effect Factor, Cλ
The time effect factor, Cλ shall be chosen to
correspond to the appropriate strength limit state as
specified in Table 8.4.4.9-1.
Table 8.4.4.9-1—Time Effect Factor
Limit State
Strength I
Strength II
Strength III
Strength IV
Extreme Event I
Cλ
0.8
1.0
1.0
0.6
1.0
NDS® and AITC 117-2004 reference design values
(based on 10-yr loading) multiplied by the format
conversion factors specified in Article 8.4.4.2, transform
allowable stress values to strength level stress values based
on 10-min. loading. It is assumed that a cumulative
duration of bridge live load is two months and the
corresponding time effect factor for Strength I is 0.8. A
cumulative duration of live load in Strength II is shorter
and the corresponding time effect factor for Strength II is
1.0. Resistance of wood subjected to long-duration loads is
reduced. Load combination IV consists of permanent
loads, including dead load and earth pressure.
8.5—LIMIT STATES
8.5.1—Service Limit State
The provisions of Article 2.5.2.6.2 should be
considered.
8.5.2—Strength Limit State
8.5.2.1—General
Factored resistance shall be the product of nominal
resistance determined in accordance with Article 8.6, 8.7,
8.8, and 8.9 and the resistance factor as specified in
Article 8.5.2.2.
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2012
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SECTION 8: WOOD STRUCTURES
8-31
8.5.2.2—Resistance Factors
C8.5.2.2
Resistance factors, φ, shall be as given below:
Flexure ................................................................ φ = 0.85
Shear ................................................................... φ = 0.75
Compression Parallel to Grain ............................ φ = 0.90
Compression Perpendicular to Grain .................. φ = 0.90
Tension Parallel to Grain .................................... φ = 0.80
Resistance During Pile Driving ........................... φ = 1.15
Connections ........................................................ φ = 0.65
In the case of timber pile foundations, the resistance
factor may be raised to 1.0 when, in the judgment of the
Engineer, a sufficient number of piles is used in a
foundation element to consider it to be highly redundant.
This is indicated to be a judgment issue because there are
no generally accepted quantitative guidelines at this
writing.
For timber piles, the resistance factor to be applied
when determining the maximum allowable driving
resistance accounts for the short duration of the load
induced by the pile driving hammer.
8.5.2.3—Stability
The structure as a whole or its components shall be
proportioned to resist sliding, overturning, uplift, and
buckling.
8.5.3—Extreme Event Limit State
For extreme event limit state, the resistance factor
shall be taken as 1.0.
8.6—COMPONENTS IN FLEXURE
8.6.1—General
The factored resistance, Mr, shall be taken as:
M r = φM n
(8.6.1-1)
where:
Mn =
nominal resistance specified herein (kip-in.)
φ
resistance factor specified in Article 8.5.2
=
8.6.2—Rectangular Section
C8.6.2
The nominal resistance, Mn, of a rectangular
component in flexure shall be determined from:
If lateral support is provided to prevent rotation at the
points of bearing, but no other lateral support is provided
throughout the bending component length, the unsupported
length, Lu, is the distance between such points of
intermediate lateral support.
The volume factor for the tension-reinforced glulams
listed in Table 8.4.1.3.4-1 is equal to one; therefore, for
these beams, CL will always be less or equal to CV, and CL
will control the modification factor for the allowable
bending strength Fb.
Mn = Fb SCL
(8.6.2-1)
in which:
CL =
A=
1+ A
1.9
F bE
Fb
−
(1 + A )
3.61
2
−
A
0.95
(8.6.2-2)
(8.6.2-3)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
8-32
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
FbE =
K bE E
Rb =
RB
(8.6.2-4)
2
Le d
b2
≤ 50
(8.6.2-5)
where:
KbE =
0.76 for visually graded lumber
KbE =
0.98 for MEL lumber
KbE =
1.06 for MSR lumber
KbE =
1.10 for glulam and tension-reinforced glulam
Fb =
adjusted design value in flexure specified in
Article 8.4.4 (ksi)
E
=
adjusted modulus of elasticity specified in
Article 8.4.4 (ksi)
CL =
beam stability factor for both conventional
glulam and tension-reinforced glulam
d
=
net depth specified in Article 8.4.1.1.2 (in.)
b
=
net width, as specified in Article 8.4.1.1.2 (in.)
Le =
effective unbraced length (in.)
S
section modulus (in.3)
=
Where the depth of a flexural component does not
exceed its width, or where lateral movement of the
compression zone is prevented by continuous support and
where points of bearing have lateral support to prevent
rotation, the stability factor, CL = 1.0. For other conditions,
the beam stability factor shall be determined in accordance
with the provisions specified herein.
The beam stability factor shall not be applied
simultaneous with the volume factor for structural glued
laminated timber, therefore, the lesser of these factors shall
apply.
The effective unbraced length, Le, may be determined
as:
•
If Lu/d < 7, then Le = 2.06 Lu
•
If 7 ≤ Lu/d ≤ 14.3, then Le = 1.63 Lu + 3d
•
If Lu/d > 14.3, then Le = 1.84 Lu
where:
Lu =
distance between point of lateral and rotational
support (in.)
d
net depth specified in Article 8.4.1.1.2 (in.)
=
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 8: WOOD STRUCTURES
8-33
8.6.3—Circular Section
The nominal resistance, Mn, of a circular component
in flexure shall be taken as:
M n = Fb S
(8.6.3-1)
8.7—COMPONENTS UNDER SHEAR
C8.7
Shear shall be investigated at a distance away from the
face of support equal to the depth of the component. When
calculating the maximum design shear, the live load shall
be placed so as to produce the maximum shear at a
distance from the support equal to the lesser of either three
times the depth, d, of the component or one-quarter of the
span L.
The factored shear resistance, Vr, of a component of
rectangular cross-section shall be calculated from:
The critical section is between one and three depths
from the support.
The critical shear in flexural components is horizontal
shear acting parallel to the grain of the component. The
resistance of bending components in shear perpendicular to
grain need not be investigated.
Note that Eq. 4.6.2.2.2a-1 requires a special
distribution factor in the calculation of the live load force
effect when investigating shear parallel to the grain.
Vr = φVn
(8.7-1)
in which:
Vn =
Fv bd
1.5
(8.7-2)
where:
φ
=
Fv =
resistance factor specified in Article 8.5.2
adjusted design value of wood in shear, specified
in Article 8.4.1 (ksi)
8.8—COMPONENTS IN COMPRESSION
8.8.1—General
The factored resistance in compression, Pr, shall be
taken as:
Pr = φPn
(8.8.1-1)
where:
Pn =
nominal resistance as specified in Article 8.8.2
and 8.8.3 (kips)
φ
resistance factor specified in Article 8.5.2
=
8.8.2—Compression Parallel to Grain
C8.8.2
Where components are not adequately braced, the
nominal stress shall be modified by the column stability
factor, Cp. If the component is adequately braced, Cp shall
be taken as 1.0.
The nominal resistance, Pn, of a component in the
compression parallel to grain shall be taken as:
The coefficient of variation of the bending Modulus of
Rupture (MOR) of tension-reinforced glulams has been
shown through extensive testing to be less than or equal to
that of conventional unreinforced glulams. Therefore, it is
conservative to use KcE = 0.76 for tension-reinforced
glulams.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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8-34
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Pn = Fc Ag C p
(8.8.2-1)
in which:
2
1+ B
1+ B B
−
− ≤ 1.0
2c
c
2c
(8.8.2-2)
FcE
≤ 1.0
Fc
(8.8.2-3)
Cp =
B=
FcE =
K cE Ed 2
(8.8.2-4)
L2e
where:
c
=
0.8 for sawn lumber
c
=
0.85 for round timber piles
c
=
0.9 for glulam
KcE =
0.52 for visually graded lumber
KcE =
0.67 for MEL lumber
KcE =
0.73 for MSR lumber
KcE =
0.76 for glulam, tension-reinforced glulam, and
round piles
Fc =
adjusted design value in compression parallel to
the grain specified in Article 8.4.4 (ksi)
Le =
effective length taken as KL (in.)
Ag =
gross cross-sectional area of the component (in.2)
8.8.3—Compression Perpendicular to Grain
The nominal resistance, Pn, of a component in
compression perpendicular to the grain shall be taken as:
Pn = Fcp Ab Cb
(8.8.3-1)
where:
Fcp =
adjusted design
perpendicular to
Article 8.4.4 (ksi)
Ab =
bearing area (in.2)
Cb =
bearing adjustment
Table 8.8.3-1
value
grain,
in compression
as specified in
factor
specified
in
When the bearing area is in a location of high flexural
stress or is closer than 3.0 in. from the end of the
component, Cb shall be taken as 1.0. In all other cases, Cb
shall be as specified in Table 8.8.3-1.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 8: WOOD STRUCTURES
8-35
Table 8.8.3-1—Adjustment Factors for Bearing
0.5
1.75
Cb
1.0
1.38
Length of bearing measured along the grain, in.
1.5
2.0
3.0
1.25
1.19
1.13
4.0
1.10
6.0
1.00
8.9—COMPONENTS IN TENSION PARALLEL
TO GRAIN
The factored resistance, Pr, of a component in tension
shall be taken as:
Pr Pn
(8.9-1)
in which:
Pn Ft An
(8.9-2)
where:
Ft
=
adjusted design value of wood in tension
specified in Article 8.4.4 (ksi)
An =
smallest net cross-sectional
component (in.2)
resistance factor specified in Article 8.5.2
=
area
of
the
8.10—COMPONENTS IN COMBINED FLEXURE
AND AXIAL LOADING
8.10.1—Components in Combined Flexure and
Tension
C8.10.1
Components subjected to flexure and tension shall
satisfy:
Satisfying Eq. 8.10.1-1 ensures that stress interaction
on the tension face of the bending member does not cause
beam rupture. Mr* in this formula does not include
modification by the beam stability factor, CL.
Eq. 8.10.1-2 is applied to ensure that the
bending/tension member does not fail due to lateral
buckling of the compression face.
Pu
Mu
Pr
*
1.0
(8.10.1-1)
Mr
and
Mu
d
6
**
Pu
1.0
(8.10.1-2)
Mr
where:
Pu =
factored tensile load (kips)
Pr =
factored tensile resistance calculated as specified
in Article 8.9 (kips)
Mu =
factored flexural moment (kip-in.)
Mr* =
FbS
Mr**= factored flexural resistance adjusted by all
applicable adjustment factors except CV
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
8-36
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
8.10.2—Components in Combined Flexure and
Compression Parallel to Grain
Components subjected to flexure and compression
parallel to grain shall satisfy:
2
Pu
P +
r
Mu
Pu
M r 1 −
FcE Ag
≤ 1.0
(8.10.2-1)
where:
Pu =
factored compression load (kips)
Pr =
factored compressive resistance calculated as
specified in Article 8.8 (kips)
Mu =
factored flexural moment (kip-in.)
Mr =
factored flexural resistance calculated
specified in Article 8.6 (kip-in.)
FcE =
Euler buckling stress as defined in Eq. 8.8.2-4
Ag =
gross cross-sectional area
as
8.11—BRACING REQUIREMENTS
8.11.1—General
C8.11.1
Where bracing is required, it shall prevent both lateral
and rotational deformation.
In detailing of the diaphragms, the potential for
shrinkage and expansion of the beam and the diaphragm
should be considered. Rigidly connected steel angle
framing may cause splitting of the beam and diaphragm as
the wood attempts to swell and shrink under the effects of
cyclic moisture.
8.11.2—Sawn Wood Beams
C8.11.2
Beams shall be transversely braced to prevent lateral
displacement and rotation of the beams and to transmit
lateral forces to the bearings. Transverse bracing shall be
provided at the supports for all span lengths and at
intermediate locations for spans longer than 20.0 ft. The
spacing of intermediate bracing shall be based on lateral
stability and load transfer requirements but shall not
exceed 25.0 ft. The depth of transverse bracing shall not be
less than three-fourths the depth of the stringers or girders.
Transverse bracing should consist of solid wood
blocking or fabricated steel shapes. Wood blocking shall
be bolted to stringers with steel angles or suspended in
steel saddles that are nailed to the blocks and stringer
sides. Blocking shall be positively connected to the beams.
Transverse bracing at supports may be placed within a
distance from the center of bearing equal to the stringer or
girder depth.
The effectiveness of the transverse bracing directly
affects the long-term durability of the system. The bracing
facilitates erection, improves load distribution, and reduces
relative movements of the stringers and girders, thereby
reducing deck deformations. Excessive deformation can
lead to mechanical deterioration of the system.
Bracing should be accurately framed to provide full
bearing against stringer sides. Wood cross-frames or
blocking that are toe-nailed to stringers have been found to
be ineffective and should not be used.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 8: WOOD STRUCTURES
8-37
8.11.3—Glued Laminated Timber Girders
C8.11.3
Transverse bracing should consist of fabricated steel
shapes or solid wood diaphragms.
Girders shall be attached to supports with steel shoes
or angles that are bolted through the girder and into or
through the support.
Bracing should be placed tight against the girders and
perpendicular to the longitudinal girder axis.
8.11.4—Bracing of Trusses
C8.11.4
Wood trusses shall be provided with a rigid system of
lateral bracing in the plane of the loaded chord. Lateral
bracing in the plane of the unloaded chord and rigid portal
and sway bracing shall be provided in all trusses having
sufficient headroom. Outrigger bracing connected to
extensions of the floorbeams shall be used for bracing
through-trusses having insufficient headroom for a top
chord lateral bracing system.
Bracing is used to provide resistance to lateral forces,
to hold the trusses plumb and true, and to hold
compression elements in line.
8.12—CAMBER REQUIREMENTS
8.12.1—Glued Laminated Timber Girders
C8.12.1
Glued laminated timber girders shall be cambered a
minimum of two times the dead load deflection at the
service limit state.
The initial camber offsets the effects of dead load
deflection and long-term creep deflection.
8.12.2—Trusses
C8.12.2
Trusses shall be cambered to sufficiently offset the
deflection due to dead load, shrinkage, and creep.
Camber should be determined by considering both
elastic deformations due to applied loads and inelastic
deformations such as those caused by joint slippage, creep
of the timber components, or shrinkage due to moisture
changes in the wood components.
8.12.3—Stress Laminated Timber Deck Bridge
Deck bridges shall be cambered for three times the
dead load deflection at the service limit state.
8.13—CONNECTION DESIGN
The design of timber connections using mechanical
fasteners including, wood screws, nails, bolts, lag screws,
drift bolts, drift pins, shear plates, split rings, and timber
rivets shall be in accordance with the 2005 NDS®.
8.14—REFERENCES
AF&PA. 2005. National Design Specification® (NDS®) for Wood Construction. American Forest and Paper Association,
Washington, DC.
AITC. 1996. Standard Specifications for Structural Glued Laminated Timber of Hardwood Species, AITC 119-96.
American Institute of Timber Construction, Centennial, CO.
AITC. 2001. Standard Appearance Grades for Structural Glued Laminated Timber, AITC 110-2001. American Institute of
Timber Construction, Centennial, CO.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
8-38
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
AITC. 2002. Structural Glued Laminated Timber, ANSI/AITC A190.1. American Institute of Timber Construction,
Centennial, CO.
AITC. 2004. Standard Specifications for Structural Glued Laminated Timber of Softwood Species, AITC 117-2004.
American Institute of Timber Construction, Centennial, CO.
Davids, W. G., M. Richie, and C. Gamache. 2005. “Fatigue of Glulam Beams with Fiber-Reinforced Polymer Tension
Reinforcing,” Forest Products Journal. Forest Products Society, Madison, WI, Vol. 55, No. 1.
Davids, W. G, E. Nagy, and M. Richie. 2008. “Fatigue Behavior of Composite-Reinforced Glulam Bridge Girders,”
Journal of Bridge Engineering. American Society of Civil Engineers, Reston, VA, March/April 2008.
ICC-ES. 2005. Acceptance Criteria for Fiber-Reinforced-Polymer Glue-Laminated Timber Using Mechanics Based
Models, AC280. ICC Evaluation Service, Inc., Whittier, CA.
Lindyberg, R. L. 2000. ReLAM: A Nonlinear Probablistic Model for the Analysis of Reinforced Glulam Beams in Bending,
Document ID CIE2000-001. Dissertation. University of Maine, Orono, ME.
Nowak, A. S. 1997. Load Distribution for Plank Decks, UMCEE 97-11. Report submitted to U.S. Forest Service, U.S.
Department of Agriculture, Washington, DC, April 1997.
Nowak, A. S. 1999. Calibration of LRFD Bridge Design Code, NCHRP Report 368. Transportation Research Board,
National Research Council, Washington, DC.
Nowak, A. S., C. Eamon, M. A. Ritter, and J. Murphy. 2001. LRFD Calibration for Wood Bridges, UMCEE 01-01. Report
submitted to U.S. Forest Service, U.S. Department of Agriculture, Washington, DC, April 2001.
Nowak, A. S., P. R. Stankiewicz, and M. A. Ritter. 1999. “Bending Tests of Bridge Deck Planks.” Construction and
Building Materials Journal, Vol. 13, No. 4, pp. 221–228.
Ritter, M. A. 1990. Timber Bridges, Design, Construction, Inspection, and Maintenance, EM7700-B. U.S. Forest Service,
U.S. Department of Agriculture, Washington, DC.
Stankiewicz, P. R., and A. S. Nowak. 1997. Material Testing for Wood Plank Decks, UMCEE 97-10. Report submitted to
U.S. Forest Service, U.S. Department of Agriculture, Washington, DC, April 1997.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 9: DECKS AND DECK SYSTEMS
TABLE OF CONTENTS
9
9.1—SCOPE ................................................................................................................................................................. 9-1
9.2—DEFINITIONS ..................................................................................................................................................... 9-1
9.3—NOTATION ......................................................................................................................................................... 9-4
9.4—GENERAL DESIGN REQUIREMENTS ............................................................................................................ 9-4
9.4.1—Interface Action ......................................................................................................................................... 9-4
9.4.2—Deck Drainage ........................................................................................................................................... 9-4
9.4.3—Concrete Appurtenances ............................................................................................................................ 9-5
9.4.4—Edge Supports ............................................................................................................................................ 9-5
9.4.5—Stay-in-Place Formwork for Overhangs..................................................................................................... 9-5
9.5—LIMIT STATES ................................................................................................................................................... 9-5
9.5.1—General ....................................................................................................................................................... 9-5
9.5.2—Service Limit States ................................................................................................................................... 9-5
9.5.3—Fatigue and Fracture Limit State ................................................................................................................ 9-6
9.5.4—Strength Limit States .................................................................................................................................. 9-6
9.5.5—Extreme Event Limit States ....................................................................................................................... 9-6
9.6—ANALYSIS .......................................................................................................................................................... 9-6
9.6.1—Methods of Analysis .................................................................................................................................. 9-6
9.6.2—Loading ...................................................................................................................................................... 9-6
9.7—CONCRETE DECK SLABS ............................................................................................................................... 9-7
9.7.1—General ....................................................................................................................................................... 9-7
9.7.1.1—Minimum Depth and Cover ............................................................................................................. 9-7
9.7.1.2—Composite Action ............................................................................................................................ 9-7
9.7.1.3—Skewed Decks .................................................................................................................................. 9-7
9.7.1.4—Edge Support ................................................................................................................................... 9-8
9.7.1.5—Design of Cantilever Slabs............................................................................................................... 9-8
9.7.2—Empirical Design ....................................................................................................................................... 9-8
9.7.2.1—General............................................................................................................................................. 9-8
9.7.2.2—Application ...................................................................................................................................... 9-9
9.7.2.3—Effective Length .............................................................................................................................. 9-9
9.7.2.4—Design Conditions.......................................................................................................................... 9-10
9.7.2.5—Reinforcement Requirements ......................................................................................................... 9-11
9.7.2.6—Deck with Stay-in-Place Formwork ............................................................................................... 9-12
9.7.3—Traditional Design ................................................................................................................................... 9-12
9.7.3.1—General........................................................................................................................................... 9-12
9.7.3.2—Distribution Reinforcement............................................................................................................ 9-12
9.7.4—Stay-in-Place Formwork .......................................................................................................................... 9-13
9.7.4.1—General........................................................................................................................................... 9-13
9.7.4.2—Steel Formwork.............................................................................................................................. 9-13
9.7.4.3—Concrete Formwork ....................................................................................................................... 9-13
9.7.4.3.1—Depth ................................................................................................................................... 9-13
9-i
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
9-ii
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
9.7.4.3.2—Reinforcement ...................................................................................................................... 9-13
9.7.4.3.3—Creep and Shrinkage Control ............................................................................................... 9-14
9.7.4.3.4—Bedding of Panels ................................................................................................................ 9-14
9.7.5—Precast Deck Slabs on Girders ................................................................................................................. 9-14
9.7.5.1—General ........................................................................................................................................... 9-14
9.7.5.2—Transversely Joined Precast Decks ................................................................................................ 9-14
9.7.5.3—Longitudinally Post-Tensioned Precast Decks ............................................................................... 9-15
9.7.6—Deck Slabs in Segmental Construction .................................................................................................... 9-15
9.7.6.1—General ........................................................................................................................................... 9-15
9.7.6.2—Joints in Decks ............................................................................................................................... 9-15
9.8—METAL DECKS ................................................................................................................................................ 9-15
9.8.1—General ..................................................................................................................................................... 9-15
9.8.2—Metal Grid Decks ..................................................................................................................................... 9-16
9.8.2.1—General ........................................................................................................................................... 9-16
9.8.2.2—Open Grid Floors ........................................................................................................................... 9-16
9.8.2.3—Filled and Partially Filled Grid Decks ............................................................................................ 9-17
9.8.2.3.1—General ................................................................................................................................. 9-17
9.8.2.3.2—Design Requirements ........................................................................................................... 9-17
9.8.2.3.3—Fatigue and Fracture Limit State .......................................................................................... 9-18
9.8.2.4—Unfilled Grid Decks Composite with Reinforced Concrete Slabs.................................................. 9-18
9.8.2.4.1—General ................................................................................................................................. 9-18
9.8.2.4.2—Design .................................................................................................................................. 9-19
9.8.2.4.3—Fatigue Limit State ............................................................................................................... 9-19
9.8.3—Orthotropic Steel Decks ........................................................................................................................... 9-20
9.8.3.1—General ........................................................................................................................................... 9-20
9.8.3.2—Wheel Load Distribution ................................................................................................................ 9-20
9.8.3.3—Wearing Surface ............................................................................................................................. 9-20
9.8.3.4—Analysis of Orthotropic Decks ....................................................................................................... 9-21
9.8.3.4.1—General ................................................................................................................................. 9-21
9.8.3.4.2—Level 1 Design ..................................................................................................................... 9-23
9.8.3.4.3—Level 2 Design ..................................................................................................................... 9-23
9.8.3.4.3a—General ........................................................................................................................ 9-23
9.8.3.4.3b—Decks with Open Ribs ................................................................................................ 9-24
9.8.3.4.3c—Decks with Closed Ribs .............................................................................................. 9-24
9.8.3.4.4—Level 3 Design ..................................................................................................................... 9-24
9.8.3.5—Design ............................................................................................................................................ 9-25
9.8.3.5.1—Superposition of Local and Global Effects .......................................................................... 9-25
9.8.3.5.2—Limit States .......................................................................................................................... 9-25
9.8.3.5.2a—General ........................................................................................................................ 9-25
9.8.3.5.2b—Service Limit State ...................................................................................................... 9-26
9.8.3.5.2c—Strength Limit State .................................................................................................... 9-26
9.8.3.5.2d—Fatigue Limit State ...................................................................................................... 9-26
9.8.3.6—Detailing Requirements .................................................................................................................. 9-26
9.8.3.6.1—Minimum Plate Thickness.................................................................................................... 9-26
9.8.3.6.2—Limit States .......................................................................................................................... 9-27
9.8.3.6.2a—General ........................................................................................................................ 9-27
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
TABLE OF CONTENTS
9-iii
9.8.3.6.2b—Service Limit State ..................................................................................................... 9-27
9.8.3.6.2c—Strength Limit State .................................................................................................... 9-27
9.8.3.6.2d—Fatigue Limit State ..................................................................................................... 9-27
9.8.3.6.3—Welding to Orthotropic Decks ............................................................................................. 9-28
9.8.3.6.4—Deck and Rib Details ........................................................................................................... 9-28
9.8.3.7—Detailing Requirements ................................................................................................................. 9-29
9.8.3.7.1—Minimum Plate Thickness ................................................................................................... 9-29
9.8.3.7.2—Closed Ribs .......................................................................................................................... 9-29
9.8.3.7.3—Welding to Orthotropic Decks ............................................................................................. 9-30
9.8.3.7.4—Deck and Rib Details ........................................................................................................... 9-30
9.8.4—Orthotropic Aluminum Decks .................................................................................................................. 9-31
9.8.4.1—General........................................................................................................................................... 9-31
9.8.4.2—Approximate Analysis ................................................................................................................... 9-31
9.8.4.3—Limit States .................................................................................................................................... 9-31
9.8.5—Corrugated Metal Decks .......................................................................................................................... 9-32
9.8.5.1—General........................................................................................................................................... 9-32
9.8.5.2—Distribution of Wheel Loads .......................................................................................................... 9-32
9.8.5.3—Composite Action .......................................................................................................................... 9-32
9.9—WOOD DECKS AND DECK SYSTEMS ......................................................................................................... 9-32
9.9.1—Scope........................................................................................................................................................ 9-32
9.9.2—General ..................................................................................................................................................... 9-32
9.9.3—Design Requirements ............................................................................................................................... 9-32
9.9.3.1—Load Distribution ........................................................................................................................... 9-32
9.9.3.2—Shear Design .................................................................................................................................. 9-33
9.9.3.3—Deformation ................................................................................................................................... 9-33
9.9.3.4—Thermal Expansion ........................................................................................................................ 9-33
9.9.3.5—Wearing Surfaces ........................................................................................................................... 9-33
9.9.3.6—Skewed Decks ................................................................................................................................ 9-33
9.9.4—Glued Laminated Decks ........................................................................................................................... 9-34
9.9.4.1—General........................................................................................................................................... 9-34
9.9.4.2—Deck Tie-Downs ............................................................................................................................ 9-34
9.9.4.3—Interconnected Decks ..................................................................................................................... 9-34
9.9.4.3.1—Panels Parallel to Traffic...................................................................................................... 9-34
9.9.4.3.2—Panels Perpendicular to Traffic ............................................................................................ 9-34
9.9.4.4—Noninterconnected Decks .............................................................................................................. 9-35
9.9.5—Stress Laminated Decks ........................................................................................................................... 9-35
9.9.5.1—General........................................................................................................................................... 9-35
9.9.5.2—Nailing ........................................................................................................................................... 9-35
9.9.5.3—Staggered Butt Joints ..................................................................................................................... 9-36
9.9.5.4—Holes in Laminations ..................................................................................................................... 9-36
9.9.5.5—Deck Tie-Downs ............................................................................................................................ 9-36
9.9.5.6—Stressing......................................................................................................................................... 9-36
9.9.5.6.1—Prestressing System ............................................................................................................. 9-36
9.9.5.6.2—Prestressing Materials .......................................................................................................... 9-38
9.9.5.6.3—Design Requirements ........................................................................................................... 9-39
9.9.5.6.4—Corrosion Protection ............................................................................................................ 9-40
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9-iv
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
9.9.5.6.5—Railings ................................................................................................................................ 9-40
9.9.6—Spike Laminated Decks ............................................................................................................................ 9-40
9.9.6.1—General ........................................................................................................................................... 9-40
9.9.6.2—Deck Tie-Downs ............................................................................................................................ 9-41
9.9.6.3—Panel Decks .................................................................................................................................... 9-41
9.9.7—Plank Decks.............................................................................................................................................. 9-42
9.9.7.1—General ........................................................................................................................................... 9-42
9.9.7.2—Deck Tie-Downs ............................................................................................................................ 9-42
9.9.8—Wearing Surfaces for Wood Decks .......................................................................................................... 9-42
9.9.8.1—General ........................................................................................................................................... 9-42
9.9.8.2—Plant Mix Asphalt .......................................................................................................................... 9-42
9.9.8.3—Chip Seal ........................................................................................................................................ 9-43
9.10—REFERENCES ................................................................................................................................................. 9-43
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SECTION 9
DECKS AND DECK SYSTEMS
9.1—SCOPE
C9.1
This Section contains provisions for the analysis and
design of bridge decks and deck systems of concrete,
metal, and wood or combinations thereof subjected to
gravity loads.
For monolithic concrete bridge decks satisfying
specific conditions, an empirical design, requiring no
analysis, is permitted.
Continuity in the deck and its supporting components
is encouraged.
Composite action between the deck and its supporting
components is required where technically feasible.
9
9.2—DEFINITIONS
Implicit in this Section is a design philosophy that
prefers jointless, continuous bridge decks and deck
systems to improve the weather and corrosion-resisting
effects of the whole bridge, reduce inspection efforts and
maintenance costs, and increase structural effectiveness
and redundancy.
Appurtenance—Curbs, parapets, railings, barriers, dividers, and sign and lighting posts attached to the deck.
Arching Action—A structural phenomenon in which wheel loads are transmitted primarily by compressive struts formed in
the slab.
Band—A strip of laminated wood deck within which the pattern of butt joints is not repeated.
Bolster—A spacer between a metal deck and a beam.
Bulkhead—A steel element attached to the side of stress laminated timber decks to distribute the prestressing force and
reduce the tendency to crush the wood.
Cellular Deck—A concrete deck with void-ratio in excess of 40 percent.
Clear Span—The face-to-face distance between supporting components.
Closed Rib—A rib in an orthotropic deck consisting of a plate forming a trough, welded to the deck plate along both sides
of the rib.
Closure Joint—A cast-in-place concrete fill between precast components to provide continuity.
Compatibility—The equality of deformation at the interface of elements and/or components joined together.
Component—A structural element or combination of elements requiring individual design consideration.
Composite Action—A condition in which two or more elements or components are made to act together by preventing
relative movement at their interface.
Continuity—In decks, both structural continuity and the ability to prevent water penetration without the assistance of
nonstructural elements.
Core Depth—The distance between the top of top reinforcement and the bottom of bottom reinforcement in a concrete
slab.
Deck—A component, with or without wearing surface, that supports wheel loads directly and is supported by other
components.
Deck Joint—A complete or partial interruption of the deck to accommodate relative movement between portions of a
structure.
9-1
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9-2
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Deck System—A superstructure, in which the deck is integral with its supporting components, or in which the effects or
deformation of supporting components on the behavior of the deck is significant.
Design Span—For decks, the center-to-center distance between the adjacent supporting components, taken in the primary
direction.
Effective Length—The span length used in the empirical design of concrete slabs defined in Article 9.7.2.3.
Elastic—A structural response in which stress is directly proportional to strain and no deformation remains upon removal
of loading.
Equilibrium—A state where the sum of forces parallel to any axis and the sum of moments about any axis in space are 0.0.
Equivalent Strip—An artificial linear element, isolated from a deck for the purpose of analysis, in which extreme force
effects calculated for a line of wheel loads, transverse or longitudinal, will approximate those actually taking place in the
deck.
Extreme—Maximum or minimum.
Flexural Continuity—The ability to transmit moment and rotation between components or within a component.
Floorbeam—The traditional name for a cross-beam.
Footprint—The specified contact area between wheel and roadway surface.
Frame Action—Transverse continuity between the deck and the webs of cellular cross-section or between the deck and
primary components in large bridges.
Glued Laminated Deck Panel—A deck panel made from wood laminations connected by adhesives.
Governing Position—The location and orientation of a transient load to cause extreme force effects.
Inelastic—The structural response in which stress is not directly proportional to strain and deformation may remain upon
removal of loading.
Interface—The location where two elements and/or components are in contact.
Internal Composite Action—The interaction between a deck and a structural overlay.
Isotropic Plate—A plate having essentially identical structural properties in the two principal directions.
Isotropic Reinforcement—Two identical layers of reinforcement, perpendicular to and in touch with each other.
Lateral—Any horizontal or close to horizontal direction.
Laminated Deck—A deck consisting of a series of laminated wood elements that are tightly abutted along their edges to
form a continuous surface.
Local Analysis—An in-depth study of strains and stresses in or among components using force effects obtained from global
analysis.
Net Depth—The depth of concrete, excluding the concrete placed in the corrugations of a metal formwork.
Open Grid Floor—A metal grid floor not filled or covered with concrete.
Open Rib—A rib in an orthotropic deck consisting of a single plate or rolled section welded to the deck plate.
Orthotropic—A plate having significantly different structural properties in the two principal directions.
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SECTION 9: DECKS AND DECK SYSTEMS
9-3
Overfill—The concrete above the top of the steel grid of filled or partially filled steel grid deck systems.
Partial Composite Action—A condition in which two or more elements or components are made to act together by
decreasing, but not eliminating, relative movement at their interface, or where the connecting elements are too flexible to
fully develop the deck in composite action.
Primary Direction—In isotropic decks: direction of the shorter span; in orthotropic decks: direction of the main loadcarrying elements.
Secondary Direction—The direction normal to the primary direction.
Segmental Construction—A method of building a bridge utilizing match-cast, prefabricated, or cast-in-place concrete
segments joined together by longitudinal post-tensioning.
Shear Connector—A mechanical device that prevents relative movements both normal and parallel to an interface.
Shear Continuity—A condition where shear and displacement are transmitted between components or within a component.
Shear Key—A preformed hollow in the side of a precast component filled with grout or a system of match-cast depressions
and protrusions in the face of segments that is intended to provide shear continuity between components.
Skew Angle—The angle between the axis of support relative to a line normal to the longitudinal axis of the bridge, i.e., a
zero-degree skew denotes a rectangular bridge.
Spacing—Center-to-center distance of elements or components, such as reinforcing bars, girders, bearings, etc.
Stay-in-Place Formwork—Permanent metal or precast concrete forms that remain in place after construction is finished.
Stiffener Beam—An unsupported beam attached to the underside of a wood deck to enhance lateral continuity.
Stress Range—The algebraic difference between extreme stresses.
Structural Overlay—An overlay bonded to the deck that consists of concretes other than asphaltic concretes.
Tandem—Two closely spaced and mechanically interconnected axles of equal weight.
Tie-Down—A mechanical device that prevents relative movement normal to an interface.
Void—An internal discontinuity of the deck by which its self-weight is reduced.
Voided Deck—Concrete deck in which the area of the voids does not constitute more than 40 percent of the gross area.
Wheel—One tire or a pair of tires at one end of an axle.
Wheel Load—One-half of a specified design axle load.
Wearing Surface—An overlay or sacrificial layer of the structural deck to protect the structural deck against wear, road
salts, and environmental effects. The overlay may include waterproofing.
Yield Line—A plastic hinge line.
Yield Line Analysis—A method of determining the load-carrying capacity of a component on the basis of the formation of a
mechanism.
Yield Line Method—A method of analysis in which a number of possible yield line patterns of concrete slabs are examined
in order to determine minimum load-carrying capacity.
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9-4
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
9.3—NOTATION
AB
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2013 Revision
effective bearing area of anchorage bulkhead (in.2) (9.9.5.6.3)
area of steel bar or strand (in.2) (9.9.5.6.3)
larger of the spacing of the rib webs (in.) (9.8.3.6.2)
depth of the bottom cutout to accommodate a rib in an orthotropic deck (in.) (9.8.3.6.4)
effective depth: distance between the outside compressive fiber and the center of gravity of the tensile
reinforcement (in.) (C9.7.2.5)
clear spacing between closed ribs in orthotropic steel decks (in.) (9.8.3.6.4)
nominal bearing resistance of wood across the grain (ksi) (9.9.5.6.3)
the out-of-plane flexural stresses in rib webs (ksi) (C9.8.3.6.2)
depth of deck (in.) (9.9.5.6.3)
length of the inclined portion of the rib web (in.) (9.8.3.6.2)
factor representing a distribution of bending moment along a rib (C9.8.3.6.2)
span length from center-to-center of supports (9.5.2)
factored compressive resistance of the wood under the bulkhead (kip) (9.9.5.6.3)
prestressing force per prestressing element (kip) (9.9.5.6.3)
load intensity (ksi) (C9.8.3.6.2)
steel-wood ratio (9.9.5.6.3)
effective span length (ft) (9.7.3.2)
spacing of prestressing bars (in.) (9.9.5.6.3)
thickness of slab or plate (in.) (9.8.3.6.1)
effective depth of deck plate, including the stiffening effect of surfacing (in.) (9.8.3.6.2)
thickness of rib web (in.) (9.8.3.6.2)
resistance factor (9.9.5.6.3)
9.4—GENERAL DESIGN REQUIREMENTS
9.4.1—Interface Action
C9.4.1
Decks other than wood and open grid floors shall be
made composite with their supporting components, unless
there are compelling reasons to the contrary.
Noncomposite decks shall be connected to their supporting
components to prevent vertical separation.
Composite action is recommended to enhance the
stiffness and economy of structures.
Some decks without shear connectors have historically
demonstrated a degree of composite action due to chemical
bond and/or friction that cannot be accounted for in
structural design.
It is difficult to design and detail a tie-down device
that does not attract shear forces due to transient loads,
temperature changes, and fluctuation in moisture content.
These forces may loosen and/or break such devices, and
cause fatigue damage in other parts of the floor system and
its connections to main members, and to floorbeams in
particular.
Shear connectors and other connections between
decks, other than open grid floors and wood decks, and
their supporting members shall be designed for force
effects calculated on the basis of full composite action,
whether or not that composite action is considered in
proportioning the primary members. The details for
transmitting shear across the interface to metal supporting
components shall satisfy the applicable provisions of
Article 6.6 or Article 7.6.
Force effects between the deck and appurtenances or
other components shall be accommodated.
9.4.2—Deck Drainage
With the exception of unfilled steel grid decks, cross
and longitudinal slopes of the deck surface shall be
provided as specified in Article 2.6.6.
Structural effects of drainage openings shall be
considered in the design of decks.
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SECTION 9: DECKS AND DECK SYSTEMS
9-5
9.4.3—Concrete Appurtenances
C9.4.3
Unless otherwise specified by the Owner, concrete
curbs, parapets, barriers, and dividers should be made
structurally continuous. Consideration of their structural
contribution to the deck should be limited in accordance
with the provisions of Article 9.5.1.
Experience indicates that the interruption of concrete
appurtenances at locations other than deck joints does not
serve the intended purpose of stress relief. Large cracks,
only a foot or so away from open joints, have been
observed in concrete parapets. The structural participation
of these components is usually but not always beneficial.
One possible negative aspect of continuity is increased
cracking in the appurtenance.
9.4.4—Edge Supports
C9.4.4
Unless the deck is designed to support wheel loads in
extreme positions with respect to its edges, edge supports
shall be provided. Nonintegral edge beams shall conform
to the provisions of Article 9.7.1.4.
If the deck joint hardware is integrated with the deck,
it may be utilized as a structural element of the edge beam.
9.4.5—Stay-in-Place Formwork for Overhangs
Stay-in-place formwork, other than that in filled steel
decks, shall not be used in the overhang of concrete decks.
9.5—LIMIT STATES
9.5.1—General
C9.5.1
The structural contribution of a concrete appurtenance
to the deck may be considered for service and fatigue but
not for strength or extreme event limit states.
Exclusion of contribution of an appurtenance at
strength limit state is a safety measure in that advantage is
not taken of a component that may be damaged,
disconnected, or destroyed by a collision.
Article 9.7.2.2 states that the empirical design method
does not apply to overhangs.
For other than the deck overhang, where the
conditions specified in Article 9.7.2 are met, a concrete
deck may be assumed to satisfy service, fatigue, and
fracture and strength limit state requirements and need not
meet the other provisions of Article 9.5.
9.5.2—Service Limit States
At service limit states, decks and deck systems shall
be analyzed as fully elastic structures and shall be
designed and detailed to satisfy the provisions of
Sections 5, 6, 7, and 8.
The effects of excessive deck deformation, including
deflection, shall be considered for metal grid decks and
other lightweight metal and concrete bridge decks. For
these deck systems, the deflection caused by live load plus
dynamic load allowance shall not exceed the following
criteria:
•
L/800 for decks with no pedestrian traffic,
•
L/1000 for decks with limited pedestrian traffic, and
•
L/1200 for decks with significant pedestrian traffic
where:
L
=
span length from center-to-center of supports.
C9.5.2
Deck deformation refers to local dishing at wheel
loads, not to overall superstructure deformation.
The primary objective of curtailing excessive deck
deformation is to prevent breakup and loss of the wearing
surface. No overall limit can be specified because such
limit is a function of the composition of the wearing
surface and the adhesion between the deck and the wearing
surface. The limits should be established by testing.
Substantial work has been done relating accelerations
to user comfort. Acceleration is a function of the
fundamental frequency of vibration of the deck on a
particular span, and the magnitude of dynamic deflection
due to live load. Dynamic deflections are typically
15 percent to 20 percent of static deflections. Analysis
shows that static deflections serve well as a proxy for
acceleration levels for deck systems.
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9-6
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
9.5.3—Fatigue and Fracture Limit State
Fatigue need not be investigated for:
•
Concrete decks, and
•
Wood decks as listed in Article 9.9.
Open grid, filled grid, partially filled grid, and unfilled
grid decks composite with reinforced concrete slabs shall
comply with the provisions of Articles 4.6.2.1, 6.5.3, and
9.8.2.
Steel orthotropic decks shall comply with the
provisions of Article 6.5.3. Aluminum decks shall comply
with the provisions of Article 7.6.
Concrete decks, other than those in multigirder
application, shall be investigated for the fatigue limit states
as specified in Article 5.5.3.
C9.5.3
The provisions that do not require fatigue
investigation of certain types of decks are based
exclusively on observed performance and laboratory
testing.
A series of 35 pulsating load fatigue tests of model
slabs indicate that the fatigue limit for the slabs designed
by the conventional AASHTO moment methods was
approximately three times the service level. Decks based
on the isotropic reinforcement method specified in
Article 9.7.2 had fatigue limits of approximately twice the
service level (deV Batchelor et al., 1978).
9.5.4—Strength Limit States
C9.5.4
At strength limit states, decks and deck systems may
be analyzed as either elastic or inelastic structures and
shall be designed and detailed to satisfy the provisions of
Sections 5, 6, 7, and 8.
These Specifications do not permit an unlimited
application of inelastic methods of analysis due to the lack
of adequate background research. There are, however,
well-established inelastic plate analyses whose use is
allowed.
9.5.5—Extreme Event Limit States
Decks shall be designed for force effects transmitted
by traffic and combination railings using loads, analysis
procedures, and limit states specified in Section 13.
Acceptance testing, complying with Section 13, may be
used to satisfy this requirement.
9.6—ANALYSIS
9.6.1—Methods of Analysis
C9.6.1
Approximate elastic methods of analysis specified in
Article 4.6.2.1, refined methods specified in
Article 4.6.3.2, or the empirical design of concrete slabs
specified in Article 9.7 may be used for various limit states
as permitted in Article 9.5.
Analytical methods presented herein should not be
construed as excluding other analytical approaches,
provided that they are approved by the Owner.
9.6.2—Loading
Loads, load positions, tire contact area, and load
combinations shall be in accordance with the provisions of
Section 3.
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SECTION 9: DECKS AND DECK SYSTEMS
9-7
9.7—CONCRETE DECK SLABS
9.7.1—General
9.7.1.1—Minimum Depth and Cover
Unless approved by the Owner, the depth of a
concrete deck, excluding any provision for grinding,
grooving, and sacrificial surface, should not be less than
7.0 in.
Minimum cover shall be in accordance with the
provisions of Article 5.12.3.
9.7.1.2—Composite Action
Shear connectors shall be designed in accordance with
the provisions of Section 5 for concrete beams and
Sections 6 and 7 for metal beams.
9.7.1.3—Skewed Decks
If the skew angle of the deck does not exceed
25 degrees, the primary reinforcement may be placed in
the direction of the skew; otherwise, it shall be placed
perpendicular to the main supporting components.
C9.7.1.1
For slabs of depth less than 1/20 of the design span,
consideration should be given to prestressing in the
direction of that span in order to control cracking.
Construction tolerances become a concern for thin
decks.
Minimum cover requirements are based on traditional
concrete mixes and on the absence of protective coating on
either the concrete or the steel inside. A combination of
special mix design, protective coatings, dry or moderate
climate, and the absence of corrosion chemicals may
justify a reduction of these requirements provided that the
Owner approves.
C9.7.1.2
Some research efforts have dealt with wood beams
composite with concrete decks and steel beams with
stressed wood decks, but progress is not advanced to a
point which permits codification.
C9.7.1.3
The intent of this provision is to prevent extensive
cracking of the deck, which may result from the absence of
appreciable reinforcement acting in the direction of
principal flexural stresses due to a heavily skewed
reinforcement, as shown in Figure C9.7.1.3-1. The
somewhat arbitrary 25-degree limit could affect the area of
steel as much as ten percent. This was not taken into
account because the analysis procedure and the use of
bending moment as a basis of design were not believed to
be sufficiently accurate to warrant such an adjustment.
Owners interested in making this refinement should also
consider one of the refined methods of analysis identified
in Article 4.6.3.2.
Figure C9.7.1.3-1—Reinforcement Layout
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9-8
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
9.7.1.4—Edge Support
Unless otherwise specified, at lines of discontinuity,
the edge of the deck shall either be strengthened or be
supported by a beam or other line component. The beam or
component shall be integrated in or made composite with
the deck. The edge beams may be designed as beams
whose width may be taken as the effective width of the
deck specified in Article 4.6.2.1.4.
Where the primary direction of the deck is transverse,
and/or the deck is composite with a structurally continuous
concrete barrier, no additional edge beam need be
provided.
9.7.1.5—Design of Cantilever Slabs
The overhanging portion of the deck shall be designed
for railing impact loads and in accordance with the
provisions of Article 3.6.1.3.4.
Punching shear effects at the outside toe of a railing
post or barrier due to vehicle collision loads shall be
investigated.
C9.7.1.5
An acceptable method of analyzing deck overhangs
for railing impact loads is presented in the appendix to
Section 13.
Any combination of increasing the depth of the slab,
employing special reinforcement extending the slab width
beyond the railing, and enlarging base plates under railing
posts may be utilized to prevent failure due to punching
shear.
9.7.2—Empirical Design
9.7.2.1—General
C9.7.2.1
The provisions of Article 9.7.2 relate exclusively to
the empirical design process for concrete deck slabs
supported by longitudinal components and shall not be
applied to any other Article in this Section, unless
specifically permitted.
Extensive research into the behavior of concrete deck
slabs discovered that the primary structural action by
which these slabs resist concentrated wheel loads is not
flexure, as traditionally believed, but a complex internal
membrane stress state referred to as internal arching. This
action is made possible by the cracking of the concrete in
the positive moment region of the design slab and the
resulting upward shift of the neutral axis in that portion of
the slab. The action is sustained by in-plane membrane
forces that develop as a result of lateral confinement
provided by the surrounding concrete slab, rigid
appurtenances, and supporting components acting
compositely with the slab.
The arching creates what can best be described as an
internal compressive dome, the failure of which usually
occurs as a result of overstraining around the perimeter of
the wheel footprint. The resulting failure mode is that of
punching shear, although the inclination of the fracture
surface is much less than 45 degrees due to the presence of
large in-plane compressive forces associated with arching.
The arching action, however, cannot resist the full wheel
load. There remains a small flexural component for which
the specified minimum amount of isotropic reinforcement
is more than adequate. The steel has a dual purpose: it
provides for both local flexural resistance and global
confinement required to develop arching effects (Fang,
1985; Holowka et al., 1980).
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SECTION 9: DECKS AND DECK SYSTEMS
The longitudinal bars of the isotropic reinforcement
may participate in resisting negative moments at an
internal support in continuous structures.
9.7.2.2—Application
Empirical design of reinforced concrete decks may be
used if the conditions set forth in Article 9.7.2.4 are
satisfied.
The provisions of this Article shall not be applied to
overhangs.
The overhang should be designed for:
•
Wheel loads for decks with discontinuous railings and
barriers using the equivalent strip method,
•
Equivalent line load for decks with continuous
barriers specified in Article 3.6.1.3.4, and
•
Collision loads using a failure mechanism as specified
in Article A13.2.
9.7.2.3—Effective Length
For the purpose of the empirical design method, the
effective length of slab shall be taken as:
•
For slabs monolithic with walls or beams: the face-toface distance, and
•
For slabs supported on steel or concrete girders: the
distance between flange tips, plus the flange
overhang, taken as the distance from the extreme
flange tip to the face of the web, disregarding any
fillets.
9-9
All available test data indicate that the factor of safety
of a deck designed by the flexural method specified in the
16th edition of the AASHTO Standard Specifications,
working stress design, is at least 10.0. Tests indicate a
comparable factor of safety of about 8.0 for an empirical
design. Therefore, even the empirical design possesses an
extraordinary reserve strength.
The design of reinforced concrete decks using the
concept of internal arching action within the limits
specified herein has been verified by extensive nonlinear
finite element analysis (Hewitt and deV Batchelor, 1975;
Fang et al. 1990). These analyses are accepted in lieu of
project-specific design calculation as a preapproved basis
of design.
Slabs with the minimum specified reinforcement have
demonstrated nearly complete insensitivity to differential
displacement among their supports.
The additional longitudinal reinforcement provided for
the slab in the negative moment region of continuous
beams and girder-type bridges beyond that required for
isotropic reinforcement according to the provisions of
Article 9.7.2.5 need not be matched in the perpendicular
direction. Theoretically, this portion of the deck will be
orthotropically reinforced, but this does not weaken the
deck.
C9.7.2.2
Although current tests indicated that arching action
may exist in the cantilevered overhang of the slab, the
available evidence is not sufficient to formulate code
provisions for it (Hays et al., 1989).
As indicated in Article 9.5.5, acceptance testing
complying with Section 13 may be used to satisfy design
requirements for deck overhangs.
C9.7.2.3
Physical tests and analytical investigations indicate
that the most important parameter concerning the
resistance of concrete slabs to wheel loads is the ratio
between the effective length and the depth of the slab.
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9-10
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
In case of nonuniform spacing of supporting
components, the effective length, Seffective, shall be taken as
the larger of the deck lengths at the two locations shown in
Figure 9.7.2.3-1.
Figure 9.7.2.3-1—Effective Length for Nonuniform
Spacing of Beams
9.7.2.4—Design Conditions
For the purpose of this Article, the design depth of the
slab shall exclude the loss that is expected to occur as a
result of grinding, grooving, or wear.
The empirical design may be used only if the
following conditions are satisfied:
•
Cross-frames or diaphragms are used throughout the
cross-section at lines of support;
•
For cross-section involving torsionally stiff units,
such as individual separated box beams, either
intermediate diaphragms between the boxes are
provided at a spacing not to exceed 25.0 ft, or the
need for supplemental reinforcement over the webs to
accommodate transverse bending between the box
units is investigated and reinforcement is provided if
necessary;
•
The supporting components are made of steel and/or
concrete;
•
The deck is fully cast-in-place and water cured;
•
The deck is of uniform depth, except for haunches at
girder flanges and other local thickening;
•
The ratio of effective length to design depth does not
exceed 18.0 and is not less than 6.0;
C9.7.2.4
Intermediate cross-frames are not needed in order to
use the empirical deck design method for cross-sections
involving torsionally weak open shapes, such as T- or Ishaped girders.
Use of separated, torsionally stiff beams without
intermediate diaphragms can give rise to the situation,
shown in Figure C9.7.2.4-1, in which there is a relative
displacement between beams and in which the beams do
not rotate sufficiently to relieve the moment over the webs.
This moment may or may not require more reinforcing
than is provided by the empirical deck design.
Figure C9.7.2.4-1—Schematic of Effect of Relative
Displacements in Torsionally Stiff Cross-Section
All the tests carried out so far were restricted to
specimens of uniform depth. Slabs supported by wood
beams are not qualified for the empirical design due to the
lack of experimental evidence regarding adequate lateral
shear transfer between the slab and the relatively soft
timber beams.
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2012
Edition
SECTION 9: DECKS AND DECK SYSTEMS
•
Core depth of the slab is not less than 4.0 in.;
•
The effective length, as specified in Article 9.7.2.3,
does not exceed 13.5 ft;
•
The minimum depth of the slab is not less than 7.0 in.,
excluding a sacrificial wearing surface where
applicable;
•
There is an overhang beyond the centerline of the
outside girder of at least 5.0 times the depth of the
slab; this condition is satisfied if the overhang is at
least 3.0 times the depth of the slab and a structurally
continuous concrete barrier is made composite with
the overhang;
•
The specified 28-day strength of the deck concrete is
not less than 4.0 ksi; and
•
The deck is made composite with the supporting
structural components.
For the purpose of this Article, a minimum of two
shear connectors at 24.0-in. centers shall be provided in
the negative moment region of continuous steel
superstructures. The provisions of Article 6.10.1.1 shall
also be satisfied. For concrete girders, the use of stirrups
extending into the deck shall be taken as sufficient to
satisfy this requirement.
9.7.2.5—Reinforcement Requirements
Four layers of isotropic reinforcement shall be
provided in empirically designed slabs. Reinforcement
shall be located as close to the outside surfaces as
permitted by cover requirements. Reinforcement shall be
provided in each face of the slab with the outermost layers
placed in the direction of the effective length. The
minimum amount of reinforcement shall be 0.27 in.2/ft of
steel for each bottom layer and 0.18 in.2/ft of steel for each
top layer. Spacing of steel shall not exceed 18.0 in.
Reinforcing steel shall be Grade 60 or better. All
reinforcement shall be straight bars, except that hooks may
be provided where required.
Both lap splices and mechanical splices shall be
allowed. Mechanical splices shall be tested and approved
to conform to the limits for slip in Article 5.11.5.2.2,
Mechanical Couplers, and for fatigue in Article 5.5.3.4,
Welded or Mechanical Splices of Reinforcement. Sleeve
wedge-type couplers shall not be permitted on coated
reinforcing.
9-11
No experience exists for effective lengths exceeding
13.5 ft. The 7.0-in. depth is considered an absolute
minimum with 2.0-in. cover on top and 1.0-in. cover on the
bottom, providing for a reinforced core of 4.0 in., as
indicated in Figure C9.7.2.4-2.
Figure C9.7.2.4-2—Core of a Concrete Slab
The provisions of the Ontario Highway Bridge Design
Code (1991), based on model test results, do not permit
length-to-depth ratios in excess of 15.0. The larger value of
18.0 is based on recent experiments (Hays et al., 1989).
The intention of the overhang provision is to ensure
confinement of the slab between the first and the second
beam.
The 4.0-ksi limit is based on the fact that none of the
tests included concrete with less than 4.0-ksi strength at
28 days. Many jurisdictions specify 4.5-ksi concrete for
ensuring reduced permeability of the deck. On the other
hand, tests indicate that resistance is not sensitive to the
compressive strength, and 3.5 ksi may be accepted with the
approval of the Owner.
C9.7.2.5
Prototype tests indicated that 0.2 percent
reinforcement in each of four layers based on the effective
depth d satisfies strength requirements. However, the
conservative value of 0.3 percent of the gross area, which
corresponds to about 0.27 in.2/ft in a 7.5-in. slab, is
specified for better crack control in the positive moment
area. Field measurements show very low stresses in
negative moment steel; this is reflected by the 0.18-in.2/ft
requirement, which is about 0.2 percent reinforcement
steel. The additional intent of this low amount of steel is to
prevent spalling of the deck due to corrosion of the bars or
wires.
Welded splices are not permitted due to fatigue
considerations. Tested and preapproved mechanical splices
may be permitted when lapping of reinforcing is not
possible or desirable, as often occurs in staged
construction and widenings. Sleeve wedge-type couplers
will not be permitted on coated reinforcing due to stripping
of the coating.
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All rights reserved. Duplication is a violation of applicable law.
2012
Edition
9-12
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
If the skew exceeds 25 degrees, the specified
reinforcement in both directions shall be doubled in the
end zones of the deck. Each end zone shall be taken as a
longitudinal distance equal to the effective length of the
slab specified in Article 9.7.2.3.
9.7.2.6—Deck with Stay-in-Place Formwork
For decks made with corrugated metal formwork, the
design depth of the slab shall be assumed to be the
minimum concrete depth.
Stay-in-place concrete formwork shall not be
permitted in conjunction with empirical design of concrete
slabs.
The intent of this provision is crack control. Beam
slab bridges with a skew exceeding 25 degrees have shown
a tendency to develop torsional cracks due to differential
deflections in the end zone (OHBDC, 1991). The extent of
cracking is usually limited to a width that approximates the
effective length.
C9.7.2.6
Concrete in the troughs of the corrugated metal deck
is ignored due to lack of evidence that it consistently
contributes to the strength of the deck. Reinforcement
should not be placed directly on corrugated metal
formwork.
The empirical design is based on a radial confinement
around the wheel load, which may be weakened by the
inherent discontinuity of the bottom reinforcement at the
boundaries between formwork panels. Limited tests carried
out on flexurally designed slabs with stay-in-place
concrete formwork indicate a punching shear failure mode,
but somewhat less resistance than that provided by fully
cast-in-place slabs. The reason for this decrease is that the
discontinuity between the panels intercepts, and thus
prevents, the undisturbed formation of the frustum of a
cone where punching shear occurs (Buth et al., 1992).
9.7.3—Traditional Design
9.7.3.1—General
C9.7.3.1
The provisions of this Article shall apply to concrete
slabs that have four layers of reinforcement, two in each
direction, and that comply with Article 9.7.1.1.
The traditional design is based on flexure. The live
load force effect in the slab may be determined using the
approximate methods of Article 4.6.2.1 or the refined
methods of Article 4.6.3.2.
9.7.3.2—Distribution Reinforcement
Reinforcement shall be placed in the secondary
direction in the bottom of slabs as a percentage of the
primary reinforcement for positive moment as follows:
•
For primary reinforcement parallel to traffic:
100 / S ≤ 50 percent
•
For primary reinforcement perpendicular to traffic:
220 / S ≤ 67 percent
where:
S
=
the effective span length taken as equal to the
effective length specified in Article 9.7.2.3 (ft)
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2012
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SECTION 9: DECKS AND DECK SYSTEMS
9-13
9.7.4—Stay-in-Place Formwork
9.7.4.1—General
C9.7.4.1
Stay-in-place formwork shall be designed to be elastic
under construction loads. The construction load shall not
be taken to be less than the weight of the form and the
concrete slab plus 0.050 ksf.
Flexural stresses due to unfactored construction loads
shall not exceed:
•
75 percent of the yield strength of steel, or
•
65 percent of the 28-day compressive strength for
concrete in compression or the modulus of rupture in
tension for prestressed concrete form panels.
The intent of this Article is to prevent excessive
sagging of the formwork during construction, which would
result in an unanticipated increase in the weight of the
concrete slab.
Deflection limits are specified to ensure adequate
cover for reinforcing steel and to account for all dead load
in the design.
The elastic deformation caused by the dead load of the
forms, plastic concrete, and reinforcement shall not
exceed:
•
For form span lengths of 10.0 ft or less, the form span
length divided by 180 but not exceeding 0.50 in.; or
•
For form span lengths greater than 10.0 ft, the form
span length divided by 240 but not exceeding 0.75 in.
9.7.4.2—Steel Formwork
Panels shall be specified to be tied together
mechanically at their common edges and fastened to their
support. No welding of the steel formwork to the
supporting components shall be permitted, unless
otherwise shown in the contract documents.
Steel formwork shall not be considered to be
composite with a concrete slab.
C9.7.4.2
For steel stay-in-place formwork, it has been common
to provide an allowance for the weight of the form and
additional concrete, with the provision added to the
contract documents that if the allowance is exceeded by
the Contractor's choice, the Contractor is responsible for
showing that the effects on the rest of the bridge are
acceptable or providing additional strengthening as needed
at no cost to the Owner. The customary allowance has
been 0.015 ksf, but this should be reviewed if form spans
exceed about 10.0 ft.
9.7.4.3—Concrete Formwork
9.7.4.3.1—Depth
C9.7.4.3.1
The depth of stay-in-place concrete should neither
exceed 55 percent of the depth of the finished deck slab
nor be less than 3.5 in.
9.7.4.3.2—Reinforcement
Concrete formwork panels may be prestressed in the
direction of the design span.
If the precast formwork is prestressed, the strands may
be considered as primary reinforcement in the deck slab.
Transfer and development lengths of the strands shall
be investigated for conditions during construction and in
service.
Thousands of bridges have successfully been built
with a depth ratio of 43 percent or somewhat higher;
55 percent is believed to be a practical limit, beyond which
cracking of the cast-in-place concrete at the panel interface
may be expected.
C9.7.4.3.2
The transfer and development lengths for epoxycoated strands with alkali-resistant hard particles
embedded in the coating may be less than that for uncoated
strands. Where epoxy-coated strands are used, this value
should be determined by testing.
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2012
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9-14
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Prestressing strands and/or reinforcing bars in the
precast panel need not be extended into the cast-in-place
concrete above the beams.
Tests indicate no difference between constructions
with and without reinforcement extended into the cast-inplace concrete over the beams (Bieschke and Klingner,
1982). The absence of extended reinforcement, however,
may affect transverse load distribution due to a lack of
positive moment continuity over the beams or may result
in reflective cracking at the ends of the panel. In addition
to transverse cracking, which usually occurs at the panel
joints due to creep and shrinkage, the latter may appear
unseemly and/or make the construction of this type of deck
questionable where deicing salts are used.
If used, bottom distribution reinforcement may be
placed directly on the top of the panels. Splices in the top
primary reinforcement in deck slab shall not be located
over the panel joints.
The concrete cover below the strands should not be
less than 0.75 in.
9.7.4.3.3—Creep and Shrinkage Control
The age of the panel concrete at the time of placing
the cast-in-place concrete shall be such that the difference
between the combined shrinkage and creep of the precast
panel and the shrinkage of the cast-in-place concrete is
minimized.
The upper surface of the panels shall be specified to
be roughened in such a manner as to ensure composite
action with the cast-in-place concrete.
9.7.4.3.4—Bedding of Panels
The ends of the formwork panels shall be supported
on a continuous mortar bed or shall be supported during
construction in such a manner that the cast-in-place
concrete flows into the space between the panel and the
supporting component to form a concrete bedding.
C9.7.4.3.3
The objective of this Article is to minimize interface
shear stresses between the precast panel and the cast-inplace concrete and to promote good bond. Normally, no
bonding agents and/or mechanical connectors are needed
for composite action.
C9.7.4.3.4
Setting screws, bituminous fiber boards, neoprene
glands, etc., may be appropriate as temporary supports. In
the past, some jurisdictions have had bad experience where
prestressed concrete panels were supported only by
flexible materials. Creep due to prestress had apparently
pulled the panel ends away from cast-in-place concrete.
Load was transferred to the flexible panel supports, which
compressed, resulting in excessive reflective cracking in
the cast-in-place concrete.
9.7.5—Precast Deck Slabs on Girders
9.7.5.1—General
Both reinforced and prestressed precast concrete slab
panels may be used. The depth of the slab, excluding any
provision for grinding, grooving, and sacrificial surface,
shall not be less than 7.0 in.
9.7.5.2—Transversely Joined Precast Decks
Flexurally discontinuous decks made from precast
panels and joined together by shear keys may be used. The
design of the shear key and the grout used in the key shall
be approved by the Owner. The provisions of
Article 9.7.4.3.4 may be applicable for the design of
bedding.
C9.7.5.2
The shear keys tend to crack due to wheel loads,
warping, and environmental effects, leading to leaking of the
keys and decreased shear transfer. The relative movement
between adjacent panels tends to crack the overlay, if
present. Therefore, this construction is not recommended for
the regions where the deck may be exposed to salts.
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2012
Edition
SECTION 9: DECKS AND DECK SYSTEMS
9.7.5.3—Longitudinally Post-Tensioned Precast
Decks
The precast components may be placed on beams and
joined together by longitudinal post-tensioning. The
minimum average effective prestress shall not be less than
0.25 ksi.
The transverse joint between the components and the
block-outs at the coupling of post-tensioning ducts shall be
specified to be filled with a nonshrink grout having a
minimum compressive strength of 5.0 ksi at 24 hours.
Block-outs shall be provided in the slab around the
shear connectors and shall be filled with the same grout
upon completion of post-tensioning.
9-15
C9.7.5.3
Decks made flexurally continuous by longitudinal
post-tensioning are the more preferred solution because
they behave monolithically and are expected to require less
maintenance on the long-term basis.
The post-tensioning ducts should be located at the
center of the slab cross-section. Block-outs should be
provided in the joints to permit the splicing of posttensioning ducts.
Panels should be placed on the girders without mortar
or adhesives to permit their movement relative to the
girders during prestressing. Panels can be placed directly
on the girders or located with the help of shims of
inorganic material or other leveling devices. If the panels
are not laid directly on the beams, the space therein should
be grouted at the same time as the shear connector blockouts.
A variety of shear key formations has been used in the
past. Recent prototype tests indicate that a “V” joint may
be the easiest to form and to fill.
9.7.6—Deck Slabs in Segmental Construction
9.7.6.1—General
The provisions of this Article shall apply to the top
slabs of post-tensioned girders whose cross-sections
consist of single or multicell boxes. The slab shall be
analyzed in accordance with the provisions of
Article 4.6.2.1.6.
9.7.6.2—Joints in Decks
Joints in the decks of precast segmental bridges may
be dry joints, epoxied match-cast surfaces, or cast-in-place
concrete.
Dry joints should be used only in regions where
deicing salts are not applied.
The strength of cast-in-place concrete joints shall not
be less than that of the precast concrete. The width of the
concrete joint shall permit the development of
reinforcement in the joint or coupling of ducts if used, but
in no case shall it be less than 12.0 in.
C9.7.6.2
Dry joints in the deck, with or without a nonstructural
sealant, have been observed to permit percolation of water
due to shrinkage as well as creep and temperature-induced
warping of segments. Both epoxied match-cast and cast-inplace concrete joints permitted herein should produce
water-tight joints. The 12.0-in. cast-in-place closure joint
is believed to provide a better riding profile if the deck is
not overlaid.
A combination joint in which only the deck part of a
match-cast joint is epoxied should be avoided.
9.8—METAL DECKS
9.8.1—General
Metal decks shall be designed to satisfy the
requirements of Sections 6 and 7. The tire contact area
shall be determined as specified in Article 3.6.1.2.5.
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2012
Edition
9-16
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
9.8.2—Metal Grid Decks
9.8.2.1—General
C9.8.2.1
Grid deck shall be composed of main elements that
span between beams, stringers, or cross-beams and
secondary members that interconnect and span between the
main elements. The main and secondary elements may
form a rectangular or diagonal pattern and shall be
securely joined together. All intersections of elements in
open grid floors, partially filled grid decks, and unfilled
grid decks composite with reinforced concrete slabs shall
be welded.
Force effects may be determined using one of the
following methods:
•
The approximate methods specified in Article 4.6.2.1,
as applicable;
•
Orthotropic plate theory;
•
Equivalent grillage; or
•
Design aids provided by the manufacturers, if the
performance of the deck is documented and supported
by sufficient technical evidence.
One of the accepted approximate methods is based on
transformed cross-section area. Mechanical shear transfer
devices, including indentations, embossment, sand coating
of surface, and other appropriate means may be used to
enhance the composite action between elements of the grid
and the concrete fill.
If a filled or partially filled grid deck, or an unfilled
grid deck composite with reinforced concrete slab is
considered to be composite with its supporting members
for the purpose of designing those members, the effective
width of slab in composite section shall be as specified in
Article 4.6.2.6.1.
9.8.2.2—Open Grid Floors
Open grid floors shall be connected to the supporting
components by welding or by mechanically fastening at
each main element. Where welding is used to make this
connection, a single-sided 3.0-in. long weld or a 1.5-in.
weld on each side of the main element may be used.
Research has shown that welds between elements in
partially filled grids “may be very important to the survival
of the cross bar” (Gangarao et al., 1992).
Laboratory tests have shown that section properties of
filled and partially filled grids, computed by the
transformed area method, are conservative (Gangarao et
al., 1992). Tests have also demonstrated that a monolithic
concrete overpour may be considered fully effective in
determining section properties.
Filled and partially filled grid decks and unfilled grid
decks composite with reinforced concrete slabs have better
potential for composite action with the supporting
components due to their considerable in-plane rigidity.
In computing section properties, omit any effect of
concrete in tension (i.e., below the neutral axis in positive
bending, and above the neutral axis in negative bending).
The modular ratios may be applied to the composite
action of concrete fill with grid deck in flexure and to the
composite action between the deck and its supporting beams.
Field tests of systems consisting of unfilled grid decks
composite with reinforced concrete slabs and stringers or
floorbeams demonstrate significant levels of composite
action, with the effective width being at least 12.0 times
the overall thickness of the deck, including the grid portion
and the structural reinforced concrete slab.
C9.8.2.2
Long-term experience indicates that even where there
is an apparently insignificant degree of composite action
between the deck and its supporting components, high
stresses may develop at their interface, resulting in local
failures and separation of the deck. Therefore, the
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2012
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SECTION 9: DECKS AND DECK SYSTEMS
Unless evidence is provided to the contrary, welding
within open grid floors should be considered as a Category
E detail, and the provisions of Article 6.6 shall apply.
Ends and edges of open grid floors that may be
exposed to vehicular traffic shall be supported by closure
bars or other effective means.
9-17
requirement to connect at each intersection of a main bar,
as indicated, applies even to open grid floors.
9.8.2.3—Filled and Partially Filled Grid Decks
C9.8.2.3.1
9.8.2.3.1—General
These decks shall consist of a metal grid or other
metal structural system filled either completely or partially
with concrete.
The provisions of Article 9.8.2.1 shall apply to filled
and partially filled grid decks.
Where possible, a 1.75-in. thick structural overfill
should be provided.
Filled and partially filled grids shall be attached to
supporting components by welding or shear studs to
transfer shear between the two surfaces.
Full-scale tests on systems consisting of partially
filled grid decks and stringers demonstrated significant
levels of composite action, with the effective width being
at least 12.0 times the depth of the deck. Under load, the
deck strain readings across the width of the deck were
nearly uniform, with extremely small slip recorded at the
deck-stringer interface.
In order to activate the deck in composite action, large
shear forces need be resisted at the interface. A preferred
method of shear transfer is by welded studs encased in a
concrete haunch, similar to that illustrated in
Figure C9.8.2.3.1-1.
Figure C9.8.2.3.1-1—An Acceptable Shear Connection of
Partially and Fully Filled Grid Decks to Beams
9.8.2.3.2—Design Requirements
Design of filled and partially filled grid decks shall be
in accordance with the provisions of Article 9.8.2.1 and
Article 4.6.2.1.8.
C9.8.2.3.2
The presence of a composite structural overlay
improves both the structural performance and riding
quality of the deck.
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2012
Edition
9-18
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The concrete portion of filled and partially filled grid
decks shall be in accordance with the general provisions of
Section 5 relating to long-term durability and integrity.
For cast-in-place applications, weight of concrete fill
shall be assumed to be carried solely by the metal portion
of the deck. The transient loads and superimposed
permanent loads may be assumed to be supported by the
grid bars and concrete fill acting compositely. A structural
overfill may be considered as part of the composite
structural deck. Where a structural overfill is provided, the
design depth of the deck shall be reduced by a provision
for loss that is expected as a result of grinding, grooving,
or wear of the concrete.
9.8.2.3.3—Fatigue and Fracture Limit State
All connections among the elements of the steel grid
in a fully filled grid deck or the connections within the
concrete fill of a partially filled grid deck need not be
investigated for fatigue in the local negative moment
region of the deck (e.g., negative moment in the deck over
a longitudinal stringer or floorbeam) when the deck is
designed with a continuity factor of 1.0.
C9.8.2.3.3
Fully filled and partially filled steel grid decks must
be checked for fatigue only in the positive moment region
(mid span of the deck). However, the deck fatigue moment
should be calculated for a simple span configuration
(C = 1.0) regardless of the actual span configuration.
The fatigue category to be used for fatigue
investigation should be determined by appropriate
laboratory testing in positive and negative bending. The
fatigue category for welds and punchouts shall not be
taken as better than Category C, which has been shown by
testing to be appropriate for most details of grid decks
constructed with concrete.
The small fillet welds used in the fabrication of grid
decks are generally less than 1.5 in. long, but are not
considered “tack welds.” In grid decks, “tack welds” refers
only to small welds used to attach sheet metal pans that
serve only as forms for concrete poured onto or into the
grid.
Where possible, form pans should be attached by
means other than tack welding.
9.8.2.4—Unfilled Grid Decks Composite with
Reinforced Concrete Slabs
C9.8.2.4.1
9.8.2.4.1—General
An unfilled grid deck composite with reinforced
concrete slab consists of a reinforced concrete slab that is
cast on top of and is composite with an unfilled steel grid.
Composite action between the concrete slab and the grid
deck shall be ensured by providing shear connectors or
other means capable of resisting horizontal and vertical
components of interface shears.
Composite action between the grid deck and the
supporting components should be ensured by mechanical
shear connectors.
Unless otherwise specified, provisions of
Article 9.8.2.1 shall apply.
Discontinuities and cold joints in such decks should
be kept to a minimum.
This bridge deck combines the attributes of a concrete
deck and a steel grid deck.
An acceptable way of providing composite action
between the deck and the supporting components is shown
in Figure C9.8.2.4.1-1.
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All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 9: DECKS AND DECK SYSTEMS
9-19
Figure C9.8.2.4.1-1—An Acceptable Shear Connection of
Unfilled Grid Decks Composite with Reinforced Concrete
Slabs to Beams
9.8.2.4.2—Design
C9.8.2.4.2
Design of unfilled grid decks composite with
reinforced concrete slabs shall be in accordance with the
provisions of Article 9.8.2.1 and Article 4.6.2.1.8. The
design depth of the deck shall be reduced by a provision
for loss that is expected as a result of grinding, grooving,
or wear of the concrete.
The reinforced concrete portion of unfilled grid decks
composite with reinforced concrete slabs shall be in
accordance with the general provisions of Section 5
relating to long-term durability and integrity.
In the concrete slab, one layer of reinforcement in
each principal direction may be used.
For cast-in-place applications, weight of concrete slab
shall be assumed to be carried solely by the grid portion of
the deck. The transient loads and superimposed permanent
loads may be assumed to be supported by the composite
section.
The interface between the concrete slab and
the metal system shall satisfy the provisions of
Article 6.10.10. Acceptable methods of shear connection
shall include tertiary bars to which 0.5-in. diameter rebar
or round studs have been welded, or the punching of holes
at least 0.75 in. in size in the top portion of the main bars
of the grid which are embedded in the reinforced concrete
slab by a minimum of 1.0 in.
9.8.2.4.3—Fatigue Limit State
The internal connection between the elements of the
steel grid in unfilled grid decks composite with reinforced
concrete slabs shall be investigated for fatigue.
For the purpose of design, the deck can be
subdivided into intersecting sets of composite
concrete/steel beams.
C9.8.2.4.3
The fatigue category to be used for fatigue
investigation should be determined by appropriate
laboratory testing in positive and negative bending. The
fatigue category for welds and punchouts shall not be
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2012
Edition
9-20
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Unless evidence is provided to the contrary, tack
welds attaching horizontal form pans to metal grids shall
be considered Category E′ details.
The composite reinforced concrete slab shall be
included in the calculation of stress range.
better than Category C, which has been shown by testing
to be appropriate for most details of grid decks constructed
with concrete.
The small fillet welds used in the fabrication of grid
decks are generally less than 1.5 in. long, but are not
considered “tack welds.” In grid decks, “tack welds”
refers only to small welds used to attach sheet metal pans
that serve only as forms for concrete poured onto or into
the grid.
Where possible, form pans should be attached by
means other than tack welding.
9.8.3—Orthotropic Steel Decks
C9.8.3.1
9.8.3.1—General
Orthotropic steel decks shall consist of a deck plate
stiffened and supported by longitudinal ribs and transverse
floorbeams. The deck plate shall act as a common flange
of the ribs, the floorbeams, and the main longitudinal
components of the bridge.
In rehabilitation, if the orthotropic deck is supported
by existing floorbeams, the connection between the deck
and the floorbeam should be designed for full composite
action, even if the effect of composite action is neglected
in the design of floorbeams. Where practical, connections
suitable to develop composite action between the deck and
the main longitudinal components should be provided.
9.8.3.2—Wheel Load Distribution
A 45-degree distribution of the tire pressure may be
assumed to occur in all directions from the surface contact
area to the middle of the deck plate. The tire footprint shall
be as specified in Article 3.6.1.2.5.
9.8.3.3—Wearing Surface
The wearing surface should be regarded as an integral
part of the total orthotropic deck system and shall be
specified to be bonded to the top of the deck plate.
The contribution of a wearing surface to the stiffness
of the members of an orthotropic deck may be considered
if structural and bonding properties are satisfactorily
demonstrated over the temperature range of −20° to
+120°F. If the contribution of the wearing surface to
stiffness is considered in the design, the required
engineering properties of the wearing surface shall be
indicated in the contract documents.
Force effects in the wearing surface and at the
interface with the deck plate shall be investigated with
consideration of engineering properties of the wearing
surface at anticipated extreme service temperatures.
The long-term composite action between deck plate
and wearing surface shall be documented by both static
and cyclic load tests.
The intent of this Article is to ensure the structural
integrity of the deck and its structural participation with
the cross-beams and the primary longitudinal components,
as appropriate. Any structural arrangement in which the
orthotropic deck is made to act independently from the
main components is undesirable.
C9.8.3.2
The 45-degree distribution is the traditional,
conservative assumption.
C9.8.3.3
Wearing surfaces acting compositely with the deck
plate may reduce deformations and stresses in orthotropic
decks.
The deck stiffening effect of the wearing surface is
dependent upon its thickness, the elastic modulus which is
dependent on temperature and the load application, i.e.,
static or dynamic, and bond characteristics.
The combination of temperature and live load effects
has resulted in debonding of some wearing surfaces in the
field, which should be regarded as failure of the wearing
surface. The Designer should consider past experience in
selection of a wearing surface and in determination of its
long-term contribution to the structural system.
Wearing surface cracking is related to stresses
exceeding tensile strength of surfacing material. Flexural
stresses in surfacing may be reduced by limiting local deck
flexibility, as indicated in Article 2.5.2.6.2. Safety against
surfacing cracking may be best assured by using surfacing
materials with semiplastic properties or with low elastic
modulus not subject to much variation with temperature.
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2012
Edition
SECTION 9: DECKS AND DECK SYSTEMS
For the purpose of designing the wearing surface and
its adhesion to the deck plate, the wearing surface shall be
assumed to be composite with the deck plate, regardless of
whether the deck plate is designed on that basis.
9-21
The wearing surface plays an important role in
improving skid resistance, distributing wheel loads, and
protecting the deck against corrosion and abuse.
Selection or design of a wearing surface should
include evaluation of the following functional
requirements:
•
Sufficient ductility and strength to accommodate
expansion, contraction, and imposed deformation
without cracking or debonding;
•
Sufficient fatigue strength to withstand flexural
stresses due to composite action of the wearing
surface with the deck plate resulting from local
flexure;
•
Sufficient durability to resist rutting, shoving, and
wearing;
•
Imperviousness to water and motor vehicle fuels and
oils;
•
Resistance to deterioration from deicing salts; and
•
Resistance to aging and deterioration due to solar
radiation.
9.8.3.4—Analysis of Orthotropic Decks
9.8.3.4.1—General
C9.8.3.4.1
2013 Revision
Design of orthotropic decks shall be based on
appropriate use of the three levels of analysis specified
herein. The fatigue limit state shall be investigated using at
least one of the three levels of design specified in
Articles 9.8.3.4.2 through 9.8.3.4.4. Strength service and
extreme event limit states, as appropriate, and
constructability criteria shall be investigated using Level 2
design.
2013 Revision
The updated design approach for orthotropic deck
bridges is based on the following considerations:
•
Simplified methods do not currently exist which can
evaluate the fatigue limit state at all fatigue-sensitive
details,
•
Design cannot be accomplished by detailing
requirements alone due to a lack of tested and
established standard deck panel details,
•
Refined analysis for new designs will add engineering
cost and potentially limit use for routine span
arrangements, and
•
Verification testing of every design adds unnecessary
cost and has the potential to delay construction.
Hence, design verification of orthotropic steel bridge
decks requires a new approach. Since many of the
controlling aspects of orthotropic deck panel design are
local rather than global demands, a well-designed and
detailed panel has the potential to be reused in future
applications and become a standardized modular
component. Therefore, the required effort for design can
vary depending on the application and available test data.
These different levels of required effort for design or
design levels are summarized as follows:
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
•
Level 1 design is based on little or no structural
analysis but is done by selection of details that are
verified to have adequate resistance by experimental
testing (new or previous). When appropriate
laboratory tests have been conducted for previous
projects or on specimens similar in design and details
to those proposed for a new project, the previous tests
may be used as the basis for the design on the new
project. All details must provide a level of safety
consistent with the AASHTO specifications.
•
Level 2 design is based on simplified one-dimensional
or two-dimensional analysis of certain panel details
where such analysis is sufficiently accurate or for
certain details that are similar to previous tested
details as described in Level 1. Calculations consider
only nominal stresses and not local stress
concentrations. This is primarily intended to allow
incremental improvement of previously tested details
as verified by Level 1. Approximate analysis of both
open rib and closed rib decks may be based on the
Pelikan-Esslinger method presented by Wolchuck
(1963) and Troitsky (1987). This method gives
conservative values of global force effects in the
orthotropic deck supported on longitudinal edge
girders. Load distribution of adjacent transversely
located wheel loads on decks with closed ribs is
discussed in Wolchuck (1963).
•
Level 3 design is based on refined three-dimensional
analysis of the panel to quantify the local stresses to
the most accurate extent reasonably expected from a
qualified design engineer experienced in refined
analysis. Level 3 designs will be dictated by the
requirements to provide safety against fatigue failure.
If no test data is available for a panel, design Level 3
is required unless it can be proven that the local
distortional mechanisms (floorbeam distortion and rib
distortion) will not lead to fatigue cracking. For
design of panels for bridge redecking applications,
design Level 3 should always be used unless an
exception is approved by the Owner.
Level 3 design is an extension of current AASHTO
methodology for fatigue evaluation by nominal
stresses. The proposed Level 3 design method is also
a similar methodology applied by the American
Petroleum Institute (API) and American Welding
Society (AWS, 2004) and is well documented by the
International Institute of Welding (IIW, 2007). It is
used extensively for the fatigue evaluation of tubular
structures and plate-type structures with complex
geometries by various industries, where there is no
clearly defined nominal stress due to complicated
geometric effects, conditions very similar to
orthotropic deck details. This approach recognizes
that fatigue damage is caused by stress raisers that
exist at details and attempts to quantify them by
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2012
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SECTION 9: DECKS AND DECK SYSTEMS
9-23
refined analysis rather than accounting for the stresses
risers using classification into general categories.
Research has demonstrated that evaluating the local
structural stress and evaluating the stress range with
AASHTO Category C provides a reliably conservative
assessment of the weld toe cracks at orthotropic deck panel
welded joints subjected to distortional stresses. The
AASHTO Category C curve is similar to the curves
provided in the Eurocode (ECS, 1992) and IIW (2007) for
evaluation of welded details. Furthermore, research by
Dexter et al. (1994) found that the AASHTO Category C
curve provides the 97.5 percent survival lower bound for
welded details on flexible plates subjected to combined inplane and out-of-plane stresses in all cases where local
stress measured 5 mm from weld toe was used for the
fatigue life stress range. The work by Connor and Fisher
(2006) also found similar results. This approach is
predicated on the modeling and stress analysis being
conducted by the method prescribed by Level 3 design.
The procedures for calculating local structural stress
for welded connections are representative of a mesh sizing
where the length and width of each individual shell or
solid element is equivalent to the thickness (t) of the
connected component. For modeling with other mesh
spacing, different procedures are required for extrapolation
of the local structural stress and are presented in more
detail in Recommendations for Fatigue Design of Welded
Joints and Components (IIW, 2007) and Manual for
Design, Construction, and Maintenance of Orthotropic
Steel Bridges (in development).
9.8.3.4.2—Level 1 Design
Orthotropic deck panels and details verified by
appropriate full-scale laboratory testing may be used
without consideration of design Levels 2 and 3 provided
the testing protocol envelopes the structural design loads
and stresses for the new application. Test loading should
be equivalent to the maximum truck load; stress ranges at
details should accurately simulate expected in service
demands and should have accurate boundary conditions.
For finite fatigue life design, the resistance shall provide
97.5 percent confidence of survival. For infinite fatigue
life design, the constant amplitude fatigue limit (CAFL)
should be exceeded no more than one in 10,000 cycles
(0.01 percent). Full-scale test should include a minimum of
two rib-spans with three floorbeams.
Previously verified Level 1 designs that have been
verified by laboratory testing may be used as the basis for
design on new projects without additional testing, subject
to approval by the Owner.
9.8.3.4.3—Level 2 Design
9.8.3.4.3a—General
Details not subjected to local distortional mechanisms
similar to those previously proven by appropriate
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
laboratory testing or those that have been proven effective
by Level 3 designs and long term observation while
subjected to the appropriate loads may be verified
considering only nominal stresses determined from
simplified analysis.
9.8.3.4.3b—Decks with Open Ribs
The rib may be analyzed as a continuous beam
supported by the floorbeams.
For rib spans not exceeding 15.0 ft, the load on the
one rib due to wheel loads may be determined as the
reaction of transversely continuous deck plate supported
by rigid ribs. For rib spans with greater than 15.0 ft, the
effect of rib flexibility on the lateral distribution of wheel
loads may be determined by elastic analysis.
For rib spans less than 10.0 ft or for decks with
shallow floorbeams, the flexibility of the floorbeams shall
be considered in calculating force effects in the ribs.
9.8.3.4.3c—Decks with Closed Ribs
For the global analysis of decks with closed ribs, the
semi-empirical Pelikan-Esslinger method may be used.
The load effects on a closed rib with a span not greater
than 20.0 ft may be calculated from wheel loads placed
over one rib only, without regard for the effects of adjacent
transversely located wheel loads.
For longer rib spans, appropriate corrections of load
effects on ribs shall be calculated.
9.8.3.4.4—Level 3 Design
2013 Revision
New orthotropic details may be designed using refined
three-dimensional analysis as defined in Article 4.6.3.2.3
and as specified below. For fatigue analysis, the structural
modeling techniques shall include:
•
Use of shell or solid elements with acceptable
formulation to accommodate steep stress gradients,
•
Mesh density of t × t, where t is the thickness of the
plate component, and
•
Local structural stresses shall be determined as
specified below
For fatigue design, the local structural stress shall be
used for comparison to the nominal fatigue resistance.
Local structural stress at welded connections shall be
measured perpendicular to the weld toe and is determined
using reference points in the finite element model and
extrapolation as shown in Figure 9.8.3.4.4-1. The reference
points shall be located at the surface of elements at a
distance of 0.5 t and 1.5 t measured perpendicular from the
weld toe, respectively, with the local structural stress flss
determined as:
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2012
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
SECTION 9: DECKS AND DECK SYSTEMS
flss = 1.5 f 0.5 − 0.50 f1.5
9-25
(9.8.3.4.4-1)
where:
f0.5 = the surface stress at a distance of 0.5t from the weld
toe (ksi)
f1.5 = the surface stress at a distance of 1.5t from the weld
toe (ksi)
Design Level 3 shall be required for all bridge
redecking applications unless the redecking procedure can
be demonstrated as meeting the requirements of
Article 9.8.3.4.1 and is approved by the Owner.
Local Total Stress
Reference Points
Local Structural Stress
Stress on Surface
Fillet Weld
(Typically not modeled)
Nominal Stress
t
0.5 t
1.5 t
Nominal Stress
Figure 9.8.3.4.4-1—Local Structural Stress
9.8.3.5—Design
9.8.3.5.1—Superposition of Local and Global
Effects
In calculating extreme force effects in the deck, the
combination of local and global effects should be
determined as specified in Article 6.14.3.
C9.8.3.5.1
The orthotropic deck is part of the global structural
system, and, therefore, participates in distributing global
stresses. These stresses may be additive to those generated
in the deck locally. The axles of the design truck or the
design tandem is used for the design of decks, whereas the
rest of the bridge is proportioned for combinations of the
design truck, the design tandem, and the design lane load.
The governing positions of the same load for local and
global effects could be quite different. Therefore, the
Designer should analyze the bridge for both load regimes
separately, apply the appropriate dynamic load allowance
factor, and use the one that governs.
9.8.3.5.2—Limit States
9.8.3.5.2a—General
Orthotropic decks shall be designed to meet the
requirements of Section 6 at all applicable limit states
unless otherwise specified herein.
C9.8.3.5.2a
Tests indicate a large degree of redundancy and load
redistribution between first yield and failure of the deck.
The large reduction in combined force effects is a
reflection of this performance.
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9-26
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
9.8.3.5.2b—Service Limit State
At the service limit state, the deck shall satisfy the
requirements as specified in Article 2.5.2.6.
9.8.3.5.2c—Strength Limit State
At the strength limit state for the combination of local
and global force effects, the provisions of Article 6.14.3
shall apply.
The effects of compressive instability shall be
investigated at the strength limit state. If instability does
not control, the resistance of orthotropic plate deck shall be
based on the attainment of yield strength at any point in the
cross-section.
9.8.3.5.2d—Fatigue Limit State
Structural components shall be checked for fatigue in
accordance with the appropriate design level as specified
in Article 9.8.3.4. The provisions of Article 6.6.1.2 shall
apply for load-induced fatigue.
With the Owner’s approval, application of less
stringent fatigue design rules for interior traffic lanes of
multilane decks subjected to infrequent traffic may be
considered.
C9.8.3.5.2b
Service Limit State I must be satisfied of overall
deflection limits and is intended to prevent premature
deterioration of the wearing surface.
Service Limit State II is for the design of bolted
connections against slip for overload and should be
considered for the design of the rib and floorbeam splices.
The remaining limit states are for tensile stresses in
concrete structures and can be ignored.
C9.8.3.5.2c
The deck, because it acts as part of the global
structural system, is exposed to in-plane axial tension or
compression. Consequently, buckling should be
investigated.
Strength design must consider the following demands:
rib flexure and shear, floorbeam flexure and shear, and
panel buckling. The rib, including the effective portion of
deck plate, must be evaluated for flexural and shear
strength for its span between the floorbeams. The
floorbeam, including the effective portion of the deck
plate, must be evaluated for flexural and shear strength for
its span between primary girders or webs. The reduction in
floorbeam cross-section due to rib cutouts must be
considered. When the panel is part of a primary girder
flange, the panel must be evaluated for axial strength based
on stability considerations.
Strength Limit IV condition is only expected to
control where the orthotropic deck is integral with a longspan bridge superstructure.
C9.8.3.5.2d
Experience has shown that fatigue damage on
orthotropic decks occurs mainly at the ribs under the truck
wheel paths in the exterior lanes.
For Level 1 design, test loads should be representative
of the fatigue truck factored for the Fatigue I load
combination and the critical details of the test specimen(s)
should simulate both the expected service conditions and
the appropriate boundary conditions; verification of these
details is sufficient in lieu of a detailed refined fatigue
analysis.
9.8.3.6—Detailing Requirements
9.8.3.6.1—Minimum Plate Thickness
Minimum plate thickness shall be determined as
specified in Article 6.7.3.
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
SECTION 9: DECKS AND DECK SYSTEMS
9.8.3.6.2—Closed Ribs
The one-sided weld between the web of a closed rib
and the deck plate shall have a target penetration of
80 percent, with 70 percent minimum and no blowthrough, and shall be placed with a tight fit of less than
0.02 in. gap prior to welding.
9-27
C9.8.3.6.2
Historically, the rib-to-deck plate weld has been
specified as a one-sided partial penetration weld with
minimum 80 percent penetration. Achieving a minimum of
80 percent penetration without blow-through is very
difficult and fabricators have often failed to consistently
satisfy this requirement. A review of the literature suggests
that it is the maximum penetration that could be achieved
without regularly resulting in weld blow-through. It has
been suggested that the weld throat should, at a minimum,
be of the same size as the rib wall and that the penetration
be between 50 and 80 percent (Kolstein, 2007). However,
a lower penetration limit of only 50 percent results in a
rather large lack of fusion plane and increases the risk of
cracks initiating from the root. Levels between 75 and
95 percent, with a target of 80 percent, are achievable and
the lower bound of 70 percent is supported by research
(Xiao, 2008).
The root gap is also a parameter that may influence
performance. Research has shown that fatigue resistance of
the weld is clearly improved when the root gap is closed in
the final condition. When there is full contact, it appears
that the root is protected and cracking is prevented. Shop
experience indicates that using a tight fit prior to welding
will also help prevent weld blow-through. Kolstein (2007)
suggests the limit of 0.02 in. and this is adopted in these
Specifications.
Additionally, melt-through of the weld is a quality
issue that must be controlled. Fatigue tests on a limited
number of samples (Sim and Uang, 2007) indicate that the
performance of locations of melt-through is greater than or
equal to those created by the notch condition of the
80 percent penetration. However, there are legitimate
concerns that excessive melt-through may provide
potential fatigue initiation sites and as such it should be
avoided if possible. As such, the proposed detailing criteria
is that the rib to deck shall be one-sided nominal
80 percent penetration, with 70 percent minimum and no
blow-through, and with a tight fit less than 0.02 in. prior to
welding. Additional details of the weld joint should be left
for the fabricator to develop.
9.8.3.6.3—Welding to Orthotropic Decks
Welding of attachments, utility supports, lifting lugs,
or shear connectors to the deck plate or ribs shall require
approval by an Engineer.
9.8.3.6.4—Deck and Rib Details
Deck and rib splices shall either be welded or
mechanically fastened by high-strength bolts. Ribs shall
be run continuously through cutouts in the webs of
floorbeams, as shown in Figure 9.8.3.6.4-1. The following
fabrication details shall be required by the contract
documents as identified in Figure 9.8.3.6.4-1:
C9.8.3.6.4
Closed ribs may be trapezoidal, U-shaped, or
V-shaped; the latter two are most efficient.
The floorbeam web cutouts at the intersections with
the ribs may be with or without an additional free cutout at
the bottom of the ribs. The former detail is generally
preferable since it minimizes the rib restraint against
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9-28
a)
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
No snipes (cutouts) in floorbeam web
b) Welds to be wrapped around
c)
Grind smooth
d) Combined fillet-groove welds may have to be used 1)
in cases where the required size of fillet welds to
satisfy the fatigue resistance requirements would be
excessive if used alone or 2) to accomplish a ground
termination.
rotation in its plane and associated stresses in the welds
and in the floorbeam web.
If the bottom cutout depth c is small enough, the
rotation of the rib is restrained and considerable out-ofplane stresses are introduced in the floorbeam web when
the floorbeam is shallow. Local secondary stresses are
also introduced in the rib walls by the interaction forces
between the floorbeam webs and the rib walls and by
secondary effects due to the small depth of cutout c
(Wolchuk and Ostapenko, 1992).
If the floorbeam web is deep and flexible, or where
additional depth of the cutout would unduly reduce the
shear strength of the floorbeam, welding all around the rib
periphery may be appropriate (ECSC Report on Fatigue,
1995, Wolchuk, 1999).
Fatigue test suggested that open snipes in the
floorbeam webs at the junctions of the rib walls with the
deck plate may cause cracks in the rib walls. Therefore, a
tight-fitting snipe and a continuous weld between the
floorbeam web and the deck and rib wall plates appear to
be preferable.
Open ribs may be flat bars, angles, tees or bulb bars.
Open-rib decks are less efficient and require more welding
but are generally considered less risky to fabricate.
Figure 9.8.3.6.4-1—Detailing Requirements for
Orthotropic Decks
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SECTION 9: DECKS AND DECK SYSTEMS
9-29
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
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SECTION 9: DECKS AND DECK SYSTEMS
9-31
9.8.4—Orthotropic Aluminum Decks
9.8.4.1—General
C9.8.4.1
Orthotropic aluminum decks shall consist of a deck
plate stiffened and supported by rib extrusions. The ribs
may be parallel or perpendicular to the direction of traffic.
The provisions of Article 9.8.3.2 through
Article 9.8.3.3 shall apply, except that the wearing surface
shall not be regarded as an integral part of the orthotropic
deck for analysis and design of the deck or rib.
When an aluminum orthotropic deck is supported by
components of another material, the differences in thermal
expansion of the two materials and the potential for
accelerated corrosion due to dissimilar metals shall be
considered.
The structural interaction of an aluminum orthotropic
deck with the existing structure shall be investigated.
9.8.4.2—Approximate Analysis
In lieu of more precise information, the effective
width of deck plate acting with a rib shall not exceed the
rib spacing or one-third of the span.
The flexibility of the supports shall be considered in
determining the longitudinal moments in continuous decks.
In determining the transverse moments, the effects of
the torsional rigidity of the ribs shall be included when the
ribs are torsionally stiff and may be disregarded if the ribs
are torsionally flexible.
For the analysis of decks with closed ribs, the
provisions of Article 9.8.3.4.3c may be applied.
9.8.4.3—Limit States
Orthotropic decks shall be designed to meet the
requirements of Section 7 at all applicable limit states.
At the service limit state, the deck shall satisfy the
requirement of Article 2.5.2.6.
The longitudinal ribs, including an effective width of
deck plate, shall be investigated for stability as individual
beam-columns assumed as simply supported at transverse
beams.
At the fatigue limit state, the deck shall satisfy the
provisions of Article 7.6.
Regardless of whether the stress range is tensile,
compressive, or reversal, maximum stress range shall be
investigated for:
•
Transverse direction at the rib-to-plate connection;
•
Longitudinal direction;
•
All bolted, welded end, and edge details; and
•
Transverse direction at the rib-to-plate connection
when the adjacent rib is loaded.
Only one application of ribs placed perpendicular to
traffic was known as of 1997. Therefore, little or no
experience of in-service fatigue behavior exists, and
complete investigation of load-induced and distortioninduced fatigue should be required for this application.
C9.8.4.2
The transverse moments should be calculated in two
stages: those due to the direct loading of the deck plate,
assuming nondeflecting ribs, and those due to the
transverse shear transfer resulting from the rib
displacements. Stresses from these moments are then
combined.
C9.8.4.3
This condition has been shown to control the design
under certain geometrical conditions.
The maximum stress range is used for design because
significant tensile residual stresses exist adjacent to most
weldments, and gross compressive stresses may result in a
net tensile stress range.
See Menzemer et al. (1987) for additional discussion.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
9.8.5—Corrugated Metal Decks
9.8.5.1—General
C9.8.5.1
Corrugated metal decks should be used only on
secondary and rural roads.
Corrugated metal decks shall consist of corrugated
metal pans filled with bituminous asphalt or another
approved surfacing material. The metal pans shall be
positively fastened to the supporting components.
9.8.5.2—Distribution of Wheel Loads
A 45-degree distribution of the tire load from the
contact area to the neutral axis of the corrugated metal
pans may be assumed.
9.8.5.3—Composite Action
For contribution of the fill to composite action with
the deck plate, the provisions of Article 9.8.3.3 shall apply.
Composite action of the corrugated metal deck pan
with the supporting components may be considered only if
the interface connections are designed for full composite
action, and the deck is shown to resist the compressive
forces associated with the composite action.
The intent of fastening the corrugated metal pans to
the supporting components is to ensure the stability of both
under transient loads.
C9.8.5.2
The 45-degree distribution is a traditional approach
for most nonmetallic structural materials.
C9.8.5.3
Due to the sensitivity of the plate to temperature,
corrosion, and structural instability, composite action
should be utilized only if physical evidence is sufficient to
prove that its functionality can be counted on for the
specified design life.
9.9—WOOD DECKS AND DECK SYSTEMS
9.9.1—Scope
C9.9.1
This Article shall apply to the design of wood decks
supported by beams, stringers, or floorbeams or used as a
deck system.
This Article applies to wood decks and deck systems
that are currently being designed and built in the United
States and that have demonstrated acceptable performance.
The supporting components may be metal, concrete, or
wood.
9.9.2—General
C9.9.2
The provisions of Section 8 shall apply.
Materials used in wood decks and their preservative
treatment shall meet the requirements of Sections 2, 5, 6,
and 8.
The nominal thickness of plank decks shall not be less
than 4.0 in. for roadways and 2.0 in. for sidewalks. The
nominal thickness of wood decks other than plank decks
shall not be less than 6.0 in.
In laminated decks, large deviations in the thickness
or extensive warping of the laminations may be
detrimental regarding both strength and long-term
performance. Although rough or full sawn material can be
more economical than planed, the variations in dimensions
can be quite large. If appropriate dimensional tolerances
are not likely to be obtained, dressing of the components
should be recommended.
9.9.3—Design Requirements
9.9.3.1—Load Distribution
C9.9.3.1
Force effects may be determined by using one of the
following methods:
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 9: DECKS AND DECK SYSTEMS
•
The approximate method specified in Article 4.6.2.1,
•
Orthotropic plate theory, or
•
Equivalent grillage model.
If the spacing of the supporting components is less
than either 36.0 in. or 6.0 times the nominal depth of the
deck, the deck system, including the supporting
components, shall be modeled as an orthotropic plate or an
equivalent grid.
In stress laminated decks, satisfying the butt stagger
requirements specified in Article 9.9.5.3, rigidity may be
determined without deduction for the butt joints.
9.9.3.2—Shear Design
Shear effects may be neglected in the design of stress
laminated decks.
In longitudinal decks, maximum shear shall be
computed in accordance with the provisions of Article 8.7.
In transverse decks, maximum shear shall be computed
at a distance from the support equal to the depth of the deck.
For both longitudinal and transverse decks, the tire
footprint shall be located adjacent to, and on the span side
of, the point of the span where maximum force effect is
sought.
9-33
In wood decks with closely spaced supporting
components, the assumption of infinitely rigid supports
upon which approximate methods of analysis are based, is
not valid. Two-dimensional methods of analysis are,
therefore, recommended to obtain force effects with
reasonable accuracy.
C9.9.3.2
Shear problems in laminated wood decks are rare, as
the inherent load sharing benefits of the multiple member
system are believed to be quite significant. The probability
of simultaneous occurrence of potentially weak shear
zones in adjacent laminates is low. Therefore, a multiple
member shear failure, which would be necessary to
propagate shear splits in any one lamination, would be
difficult to achieve.
With little test data available, no changes to the shear
design for spike laminated decks is being introduced.
9.9.3.3—Deformation
At the service limit state, wood decks shall satisfy the
requirements as specified in Article 2.5.2.6.
9.9.3.4—Thermal Expansion
The coefficient of thermal expansion of wood parallel
to its fibers shall be taken as 0.000002 per °F.
Thermal effects may be neglected in plank decks and
spike laminated decks.
For stress laminated and glued laminated panel decks
made continuous over more than 400 ft, relative
movements due to thermal expansion with respect to
substructures and abutments shall be investigated.
9.9.3.5—Wearing Surfaces
Wood decks shall be provided with a wearing surface
conforming to the provisions of Article 9.9.8.
9.9.3.6—Skewed Decks
Where the skew of the deck is less than 25 degrees,
transverse laminations may be placed on the skew angle.
Otherwise, the transverse laminations shall be placed
normal to the supporting components, and the free ends of
the laminations at the ends of the deck shall be supported
by a diagonal beam or other suitable means.
C9.9.3.4
Generally, thermal expansion has not presented
problems in wood deck systems. Except for the stress
laminated deck and tightly placed glued laminated panels,
most wood decks inherently contain gaps at the butt joints
that can absorb thermal movements.
C9.9.3.5
Experience has shown that unprotected wood deck
surfaces are vulnerable to wear and abrasion and/or may
become slippery when wet.
C9.9.3.6
With transverse decks, placement of the laminations
on the skew is the easiest and most practical method for
small skew angles, and cutting the ends of the laminations
on the skew provides a continuous straight edge.
In longitudinal decks, except for stress laminated
wood, any skew angle can generally be accommodated by
offsetting each adjacent lamination on the skew.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
9-34
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
9.9.4—Glued Laminated Decks
9.9.4.1—General
C9.9.4.1
Glued laminated timber panel decks shall consist of a
series of panels, prefabricated with water-resistant
adhesives, that are tightly abutted along their edges.
Transverse deck panels shall be continuous across the
bridge width.
If the span in the primary direction exceeds 8.0 ft, the
panels shall be interconnected with stiffener beams as
specified in Article 9.9.4.3.
9.9.4.2—Deck Tie-Downs
Where panels are attached to wood supports, the tiedowns shall consist of metal brackets that are bolted
through the deck and attached to the sides of the
supporting component. Lag screws or deformed shank
spikes may be used to tie panels down to wood support.
Where panels are attached to steel beams, they shall
be tied down with metal clips that extend over the beam
flange and that are bolted through the deck.
In glued laminated decks built to date, transverse deck
panels have been 3.0 to 6.0 ft wide, and longitudinal deck
panels have been 3.5 to 4.5 ft wide. The design provisions
are considered applicable only to the range of panel sizes
given herein.
These design provisions are based upon development
work carried out at the USDA Forest Products Laboratory
in the late 1970s.
This form of deck is appropriate only for roads having
low to medium volumes of commercial vehicles.
C9.9.4.2
The methods of tie-down specified herein are based
upon current practices that have proven to be adequate.
Use of other methods require approval by Owner.
9.9.4.3—Interconnected Decks
9.9.4.3.1—Panels Parallel to Traffic
Interconnection of panels shall be made with
transverse stiffener beams attached to the underside of the
deck. The distance between stiffener beams shall not
exceed 8.0 ft, and the rigidity, EI, of each stiffener beam
shall not be less than 80,000 kip-in.2. The beams shall be
attached to each deck panel near the panel edges and at
intervals not exceeding 15.0 in.
9.9.4.3.2—Panels Perpendicular to Traffic
Interconnection of panels may be made with
mechanical fasteners, splines, dowels, or stiffener beams.
Where used, the stiffener beams should be continuous over
the full length of the span and should be secured through
the deck within 6.0 in. of the edges of each panel and as
required between edges.
When panels are interconnected with stiffener beams,
the beams shall be placed longitudinally along the
centerspan of each deck span. Provisions of
Article 9.9.4.3.1 shall apply for the design of the stiffener
beams.
The live load bending moment per unit width shall be
determined in accordance with the provisions of
Article 4.6.2.1.3.
C9.9.4.3.1
Although the transverse stiffener beam ensures
interpanel shear transfer of loads, some relative deflection
will take place. Under frequent heavy loads, this relative
deflection will cause reflective cracking of bituminous
wearing surfaces.
C9.9.4.3.2
The doweling of the deck system is intended to
prevent relative displacement of the glued laminated deck
panels. A design procedure for dowels can be found in
Ritter (1990). With proper prefabrication and construction,
this doweled system has proven to be effective in
preventing relative displacement between panels.
However, in practice, problems with hole alignment and
the necessity for field modifications may reduce their
efficiency.
Using one longitudinal stiffener beam in each space
between girders has proven to be both a practical and
effective method of reducing relative displacements
between transverse panels.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 9: DECKS AND DECK SYSTEMS
9.9.4.4—Noninterconnected Decks
Decks not interconnected at their edges shall only be
employed on secondary, rural roads. No transfer of force
effects at the panel edges shall be assumed in the analysis.
9-35
C9.9.4.4
The noninterconnected panel deck will likely cause
reflective cracking in the wearing surface at the butt joints,
even under relatively low levels of loading. It is
appropriate only for roads having low volumes of
commercial vehicles in order to avoid the extensive
maintenance that the wearing surface may require.
9.9.5—Stress Laminated Decks
9.9.5.1—General
C9.9.5.1
Stress laminated decks shall consist of a series of
wood laminations that are placed edgewise and posttensioned together, normal to the direction of the
lamination.
Stress laminated decks shall not be used where the
skew exceeds 45 degrees.
The contract documents shall require that the material
be subjected to expansion baths to remove excess oils.
9.9.5.2—Nailing
The majority of decks of this type include laminations
which are 2.0 to 3.0 in. in thickness.
The increased load distribution and load sharing
qualities of this deck, coupled with its improved durability
under the effects of repeated heavy vehicles, make it the
best choice among the several wood decks for high volume
road application (Csagoly and Taylor, 1979; Sexsmith et
al., 1979).
The structural performance of these decks relies on
friction, due to transverse prestress, between the surfaces
of the laminations to transfer force effects. Unlike spiked
or bolted connections in wood, the friction-based
performance of stress laminated decks does not deteriorate
with time under the action of repeated heavy loads.
Experience seems to indicate that the use of
waterborne preservatives can negatively affect the
performance of stress laminated decks. Wood treated with
waterborne preservatives responds rapidly to the shortterm changes in moisture conditions to which bridges are
subjected frequently in most areas of North America. The
attendant dimensional changes in the wood can result in
substantial changes in the prestressing forces. Wood
treated with oil-borne preservatives does not respond so
readily to short-term changes in moisture conditions.
The preservative treatment for wood to be used in
stress laminated decks should be kept to the minimum
specified in the standards given in Article 8.4.3. Excessive
oils in the wood may be expelled after the deck is stressed
and can contribute to higher prestress losses over a short
period after construction.
C9.9.5.2
Each lamination shall be specified to be fastened to
the preceding one by common or spiral nails at intervals
not exceeding 4.0 ft. The nails shall be driven alternately
near the top and bottom edges of the laminations. One nail
shall be located near both the top and bottom at butt joints.
The nails should be of sufficient length to pass through
two laminations.
Nailing is only a temporary construction convenience
in stress laminated decks, and it should be kept as close to
minimum requirements as possible. Excessive nailing may
inhibit the build up of elastic strains during transverse
stressing, which could subsequently contribute to
decreasing its effectiveness.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
9-36
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
9.9.5.3—Staggered Butt Joints
Where butt joints are used, not more than one butt
joint shall occur in any four adjacent laminations within a
4.0 ft distance, as shown in Figure 9.9.5.3-1.
C9.9.5.3
Butt joint requirements are extreme values and are
intended to allow for lamination lengths that are less than
the deck length. Uniformly reducing or eliminating the
occurrence of butt joints and/or distributing butt joints will
improve performance.
The implication of this provision is that laminations
shorter than 16.0 ft cannot be used. If laminations longer
than 16.0 ft are used, the spacing of butt joint is onequarter of the length.
Figure 9.9.5.3-1—Minimum Spacing of Lines of Butt Joints
9.9.5.4—Holes in Laminations
The diameter of holes in laminations for the
prestressing unit shall not be greater than 20 percent of the
lamination depth. Spacing of the holes along the
laminations shall be neither less than 15.0 times the hole
diameter nor less than 2.5 times the depth of the laminate.
Only drilled holes shall be permitted.
9.9.5.5—Deck Tie-Downs
Decks shall be tied down at every support, and the
spacing of the tie-downs along each support shall not
exceed 3.0 ft. Each tie-down shall consist of a minimum of
two 0.75-in. diameter bolts for decks up to and including
12.0 in. deep and two 1.0-in. diameter bolts for decks more
than 12.0 in. deep.
C9.9.5.4
These empirical limitations are intended to minimize
the negative effects of hole size and spacing on the
performance of the deck.
Punched holes can seriously affect the performance of
the laminates by breaking the wood fibers in the vicinity of
the holes.
C9.9.5.5
The stress laminated deck requires a more effective
tie-down than toe-nailing or drift pins. It has a tendency to
develop curvature perpendicular to the laminates when
transversely stressed. Tie-downs using bolts or lag screws
ensure proper contact of the deck with the supporting
members.
9.9.5.6—Stressing
9.9.5.6.1—Prestressing System
New stressed wood decks shall be designed using
internal prestressing. External prestressing may be used to
rehabilitate existing nail laminated decks and shall utilize
continuous steel bulkheads.
In stress laminated decks, with skew angles less than
25 degrees, stressing bars may be parallel to the skew. For
skew angles between 25 degrees and 45 degrees, the bars
should be placed perpendicular to the laminations, and in
the end zones, the transverse prestressing bars should be
fanned in plan as shown in Figure 9.9.5.6.1-1 or arranged
in a step pattern as shown in Figure 9.9.5.6.1-2.
Dimensional changes in the deck due to prestressing
shall be considered in the design.
Anchorage hardware for the prestressing rods should
be arranged in one of the three ways shown in
Figure 9.9.5.6.1-3.
C9.9.5.6.1
External and internal prestressing systems are shown
in Figure 9.9.5.6.1-3. The internal system provides better
protection to the prestressing element and lessens
restriction to the application of wearing surfaces.
Generally, it is not necessary to secure timber decks to
the supports until all the transverse stressing has been
completed. There is the potential for extensive deformation
when a deck is stressed over a very long length due to
unintentional eccentricity of prestressing. It is recommended
that restraints during stressing be provided when the width
of the deck, perpendicular to the laminations, exceeds
50.0 times the depth of the deck for longitudinal decks and
40.0 times the depth of the deck for transverse decks. These
restraints should not inhibit the lateral movement of the deck
over its width during the stressing procedure.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 9: DECKS AND DECK SYSTEMS
9-37
Potential concentration of bearing stresses and sliding
of the common bearing plate should be considered in
conjunction with the fanned arrangement of prestressing
elements shown in Figure 9.9.5.6.1-1.
Figure 9.9.5.6.1-1—Fanned Layout of Prestressing Bars in
End Zones of Skewed Decks—Illustrative Only
Figure 9.9.5.6.1-2—Staggered Layout of Prestressing Bars
in End Zones of Skewed Decks—Illustrative Only
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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9-38
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure 9.9.5.6.1-3—Types of Prestressing Configurations
The isolated steel bearing plates should be used only
on hardwood decks, or, where a minimum of two
hardwood laminations are provided, on the outside edges
of the deck.
9.9.5.6.2—Prestressing Materials
Prestressing materials shall comply with the
provisions of Article 5.4.
Continuous steel bulkheads or hardwood laminations
are required because they improve field performance.
Isolated steel bearing plates on softwood decks have
caused crushing of the wood, substantially increased stress
losses and resulted in poor aesthetics.
C9.9.5.6.2
All prestressed wood decks built to date have utilized
high-strength bars as the stressing elements. Theoretically,
any prestressing system that can be adequately protected
against corrosion is acceptable.
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2012
Edition
SECTION 9: DECKS AND DECK SYSTEMS
9-39
C9.9.5.6.3
9.9.5.6.3—Design Requirements
The steel-wood ratio, Rsw, shall satisfy:
Rsw =
As
≤ 0.0016
sh
(9.9.5.6.3-1)
where:
s
=
spacing of the prestressing elements (in.)
h
=
depth of deck (in.)
As =
area of steel bar or strand (in.2)
The prestressing force per prestressing element (kip)
shall be determined as:
Ppt = 0.1hs
(9.9.5.6.3-2)
The effective bearing area, AB, on the wood directly
under the anchorage bulkhead due to prestress shall be
determined by considering the relative stiffness of the
wood deck and the steel bulkhead. The bulkhead shall
satisfy:
PBU = φFAB ≥ Ppt
(9.9.5.6.3-3)
where:
PBU =
φ
=
F
=
factored compressive resistance of the wood
under the bulkhead (kip)
resistance factor for compression perpendicular
to grain as specified in Article 8.5.2.2
as specified in Table 9.9.5.6.3-1
The limitation on the steel-wood area ratio is intended
to decrease prestress losses due to relaxation caused by
wood and steel creep as well as deck dimensional changes
due to variations in wood moisture content. Prestress losses
are very sensitive to this ratio, and most existing structures
have values less than 0.0016. A small area ratio of 0.0012 to
0.0014, coupled with an initial moisture content of less than
19 percent and proper preservative treatment, will ensure the
highest long-term prestress levels in the deck.
The average compressive design stress represents the
uniform pressure that is achieved away from the anchorage
bulkhead. Limitation on compressive stress at maximum
prestress minimizes permanent deformation in the wood.
Increasing the initial compressive stress beyond these
levels does not significantly increase the final compressive
stress after all losses have occurred.
Eq. 9.9.5.6.3-2 is based on a uniform compressive
stress of 0.1 ksi between the laminations due to
prestressing. For structural analysis, a net compressive
stress of 0.04 ksi, after losses, may be assumed.
Relaxation of the prestressing system is timedependent, and the extensive research work, along with the
experience obtained on the numerous field structures, have
shown that it is necessary to restress the system after the
initial stressing to offset long-term relaxation effects. The
optimum stressing sequence is as follows:
•
Stress to full design level at time of construction,
•
Restress to full design level not less than one week
after the initial stressing, and
•
Restress to full design level not less than four weeks
after the second stressing.
After the first restressing, increasing the time period to
the second restressing improves long-term stress retention.
Subsequent restressings will further decrease the effects of
long-term creep losses and improve stress retention.
Table 9.9.5.6.3-1—F Values for Prestressed Wood Decks
Species
Douglas Fir Larch
Hemlock Fir
Spruce-Pine Fir
Eastern Softwoods
Mixed Southern Pine
Southern Pine
Spruce-Pine Fir-South
Northern Red Oak
Red Maple
Red Oak
Yellow Poplar
F (ksi)
0.425
0.275
0.275
0.225
0.375
0.375
0.225
0.600
0.400
0.550
0.275
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2012
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9-40
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
9.9.5.6.4—Corrosion Protection
Elements of the prestressing system shall be protected
by encapsulation and/or surface coatings. The protective
tubing shall be capable of adjusting at least ten percent of
its length during stressing without damage.
C9.9.5.6.4
Elements of a suitable protection system are shown in
Figure C9.9.5.6.4-1.
Figure C9.9.5.6.4-1—Elements of Corrosion Protection
9.9.5.6.5—Railings
C9.9.5.6.5
Railings shall not be attached directly either to any
prestressing element or to bulkhead systems. The deck
shall not be penetrated within 6.0 in. of a prestressing
element.
Curb and rail attachment directly to any component of
the stressing system increases the risk of failure in the
event of vehicle impact.
9.9.6—Spike Laminated Decks
9.9.6.1—General
C9.9.6.1
Spike laminated decks shall consist of a series of
lumber laminations that are placed edgewise between
supports and spiked together on their wide face with
deformed spikes of sufficient length to fully penetrate four
laminations. The spikes shall be placed in lead holes that
are bored through pairs of laminations at each end and at
intervals not greater than 12.0 in. in an alternating pattern
near the top and bottom of the laminations, as shown in
Figure 9.9.6.1-1.
Laminations shall not be butt spliced within their
unsupported length.
The use of spike laminated decks should be limited to
secondary roads with low truck volumes, i.e., ADTT
significantly less than 100 trucks per day.
The majority of decks of this type have used
laminations of 3.0 to 4.0 in. in thickness. The laminates are
either assembled on site or are prefabricated into panels in
preparation for such assembly.
The specified design details for lamination
arrangement and spiking are based upon current practice. It
is important that the spike lead holes provide a tight fit to
ensure proper load transfer between laminations and to
minimize mechanical movements.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 9: DECKS AND DECK SYSTEMS
9-41
Figure 9.9.6.1-1—Spike Layout for Spike Laminated Decks
9.9.6.2—Deck Tie-Downs
Deck tie-downs shall be as specified in Article 9.9.4.2.
9.9.6.3—Panel Decks
The distribution widths for interconnected spike
laminated panels may be assumed to be the same as those
for continuous decks, as specified in Section 4.
The panels may be interconnected with mechanical
fasteners, splines, dowels, or stiffener beams to transfer
shear between the panels. If stiffener beams are used, the
provisions of Article 9.9.4.3 shall apply.
C9.9.6.3
The use of noninterconnected decks should be limited
to secondary and rural roads.
It is important to provide an effective interconnection
between panels to ensure proper load transfer. Stiffener
beams, comparable to those specified for glued laminated
timber panels, are recommended. Use of an adequate
stiffener beam enables the spike laminated deck to
approach the serviceability of glue laminated panel
construction.
With time, the deck may begin to delaminate in the
vicinity of the edge-to-edge panel joints. The load
distribution provisions given for the noninterconnected
panels are intended for use in the evaluation of existing
noninterconnected panel decks and interconnected panel
decks in which the interconnection is no longer effective.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
9-42
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
9.9.7—Plank Decks
9.9.7.1—General
C9.9.7.1
Wood plank decks shall consist of a series of lumber
planks placed flatwise on supports. Butt joints shall be
placed over supports and shall be staggered a minimum of
3.0 ft for adjacent planks.
This type of deck has been used on low volume roads
with little or no heavy vehicles, and it is usually
economical. However, these decks provide no protection
against moisture to the supporting members; they will not
readily accept and/or retain a bituminous wearing surface
and usually require continuous maintenance if used by
heavy vehicles.
These decks should be limited to roads that carry little
or no heavy vehicles or where the running surface is
constantly monitored and maintained.
9.9.7.2—Deck Tie-Downs
On wood beams, each plank shall be nailed to each
support with two nails of minimum length equal to twice
the plank thickness.
On steel beams, planks shall be bolted to the beams or
nailed to wood nailing strips. The strips should be at least
4.0 in. thick, and their width should exceed that of the
beam flange. The strips should be secured with A 307 bolts
at least 0.625 in. in diameter and placed through the
flanges, spaced not more than 4.0 ft apart and no more than
1.5 ft from the ends of the strips.
9.9.8—Wearing Surfaces for Wood Decks
9.9.8.1—General
C9.9.8.1
Wearing surfaces shall be of continuous nature and no
nails, except in wood planks, shall be used to fasten them
to the deck.
9.9.8.2—Plant Mix Asphalt
An approved tack coat shall be applied to wood decks
prior to the application of an asphalt wearing surface. The
tack coat may be omitted when a geotextile fabric is used,
subject to the recommendations of the manufacturer.
When possible, a positive connection between the
wood deck and the wearing surface shall be provided. This
connection may be provided mechanically or with a
geotextile fabric.
The asphalt should have a minimum compacted depth
of 2.0 in. Where cross slope is not provided by the wood
deck, a minimum of one percent shall be provided by the
wearing surface.
Bituminous wearing surfaces are recommended for
wood decks.
The surface of wood deck should be free of surface
oils to encourage adhesion and prevent bleeding of the
preservative treatment through the wearing surface.
Excessive bleeding of the treatment can seriously reduce
the adhesion. The plans and specifications should clearly
state that the deck material be treated using the empty cell
process, followed by an expansion bath or steaming.
C9.9.8.2
The application of a tack coat greatly improves the
adhesion of asphalt wearing surfaces.
Due to the smooth surface of individual laminations
and glued laminated decks, it is beneficial to provide a
positive connection in order to ensure proper performance.
The use of asphalt impregnated geotextile fabric, when
installed properly, has proven to be effective.
Asphalt wearing surfaces on stress laminated wood
decks have proven to perform well with only a tack coat
and no reinforcement between the deck and the asphalt.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
SECTION 9: DECKS AND DECK SYSTEMS
9.9.8.3—Chip Seal
C9.9.8.3
When a chip seal wearing surface is used on wood
decks, a minimum of two layers should be provided.
9.10—REFERENCES
9-43
Laminated decks may have offset laminations creating
irregularities on the surface, and it is necessary to provide
an adequate depth of wearing surface to provide proper
protection to the wood deck. Chip seal wearing surfaces
have a good record as applied to stress laminated decks
due to their behavior approaching that of solid slabs.
2013 Revision
Ahlskog, J. 2000. “Vibration and Deflection Criteria for Lightweight Decks Designed Using the LRFD Code.” Being
submitted for publication.
AISC. 1963. Design Manual for Orthotropic Steel Plate Deck Bridges. American Institute of Steel Construction,
Chicago, IL.
Baker, T. H. 1991. Volume I, Plate Stiffness Constants for Concrete Filled Steel Grid Decks, Static and Fatigue Strength
Determination of Design Properties for Grid Bridge Decks, Research Report ST-9, Department of Civil Engineering,
University of Pittsburgh, Pittsburgh, PA.
Bieschke, L. A., and R. E. Klingner. 1982. The Effect of Transverse Strand Extensions on the Behavior of Precast
Prestressed Panel Bridges, FHWA/TX-82/18-303-1F. Federal Highway Administration, Washington, DC, University of
Texas, Austin, TX.
Buth, E., H. L. Furr, and H. L. Jones. 1992. Evaluation of a Prestressed Panel, Cast-in-Place Bridge, TTI-2-5-70-145-3.
Texas Transportation Institute, College Station, TX.
Connor, R. J. 2002. “A Comparison of the In-service Response of an Orthotropic Steel Deck with Laboratory Studies and
Design Assumptions.” Ph.D. dissertation, Department of Civil Engineering, Lehigh University, Bethlehem, PA,
May 2002.
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Connor, R. J., and J. W. Fisher. 2006. “Consistent Approach to Calculating Stresses for Fatigue Design of Welded Rib-toWeb Connections in Steel Orthotropic Bridge Decks,” Journal of Bridge Engineering. American Society of Civil
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Csagoly, P. F. 1979. Design of Thin Concrete Deck Slabs by the Ontario Highway Bridge Design Code. Ministry of
Transportation of Ontario, Downsville, Ontario, Canada.
Csagoly, P. F., and J. M. Lybas. 1989. “Advanced Design Method for Concrete Bridge Deck Slabs,” Concrete
International. American Concrete Institute, Farmington Hills, MI, Vol. 11, No. 5, May 1989, pp. 53–64.
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
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No. 200.84.795.1, Lehigh University, Bethlehem, PA, January 1985.
Darlow, M., and N. Bettigole. 1989. “Instrumentation and Testing of Bridge Rehabilitated with Exodermic Deck,” Journal
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deV Batchelor, B., K. V. Dalen, T. Morrison, and R. J. Taylor. 1981. Structural Characteristics of Red-Pine and Hem-Fir
in Prestressed Laminated Wood Bridge Decks. Queens University, Ontario, Canada.
deV Batchelor, B., B . E. Hewitt, and P. F. Csagoly. 1978. “Investigation of the Fatigue Strength of Deck Slabs of
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Flexible Plate. In Proc., 13th International Conference on Offshore Mechanics and Arctic Engineering, ASME, Vol. III,
Material Engineering, pp. 85–92.
DiCesare, A., and J. Pensiero. 1992. Bridge Analysis Report: High Street Bridge over Metro-North Railroad, Dobbs Ferry.
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Composite Steel Grid Bridge Decks, Report CFC92-150. West Virginia University, Constructed Facilities Center,
Morgantown, WV, December 1993, Volume III.
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Transportation Research Record 1371. Transportation Research Board, National Research Council, Washington, DC.
Hays, C. O., J. M. Lybas, and J. O. Guevara. 1989. Test of Punching Shear Strength of Lightly Reinforced Orthotropic
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Higgins, C. 2003. “LRFD Orthotropic Plate Model for Determining Live Load Moments in Concrete Filled Grid Bridge
Decks,” Journal of Bridge Engineering. American Society of Civil Engineers, Reston, VA, January/February 2003,
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Edition
SECTION 9: DECKS AND DECK SYSTEMS
9-45
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Girders. University of Texas, Austin, TX.
Klippstein, Karl H. 1993. Fatigue Tests and Stain Measurements on Grid Decks. University of Pittsburgh and Western
Pennsylvania Advanced Technology Center and IKG Industries, Volume III.
Kolstein, M. H. 2007. Fatigue Classification of Welded Joints in Orthotropic Steel Bridge Decks, Ph.D. Dissertation. Delft
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Wolchuk, R. 1999. “Steel Orthotropic Decks—Developments in the 1990's.” In Transportation Research Record 1688.
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SECTION 10: FOUNDATIONS
TABLE OF CONTENTS
10
10.1—SCOPE ............................................................................................................................................................. 10-1
10.2—DEFINITIONS................................................................................................................................................. 10-1
10.3—NOTATION ..................................................................................................................................................... 10-3
10.4—SOIL AND ROCK PROPERTIES................................................................................................................... 10-7
10.4.1—Informational Needs .............................................................................................................................. 10-7
10.4.2—Subsurface Exploration .......................................................................................................................... 10-8
10.4.3—Laboratory Tests .................................................................................................................................. 10-11
10.4.3.1—Soil Tests ................................................................................................................................... 10-11
10.4.3.2—Rock Tests ................................................................................................................................. 10-11
10.4.4—In-Situ Tests ......................................................................................................................................... 10-11
10.4.5—Geophysical Tests ................................................................................................................................ 10-12
10.4.6—Selection of Design Properties ............................................................................................................. 10-13
10.4.6.1—General....................................................................................................................................... 10-13
10.4.6.2—Soil Strength .............................................................................................................................. 10-15
10.4.6.2.1—General ............................................................................................................................ 10-15
10.4.6.2.2—Undrained Strength of Cohesive Soils ............................................................................. 10-15
10.4.6.2.3—Drained Strength of Cohesive Soils ................................................................................. 10-16
10.4.6.2.4—Drained Strength of Granular Soils ................................................................................. 10-16
10.4.6.3—Soil Deformation ....................................................................................................................... 10-18
10.4.6.4—Rock Mass Strength ................................................................................................................... 10-21
10.4.6.5—Rock Mass Deformation ............................................................................................................ 10-25
10.4.6.6—Erodibility of Rock .................................................................................................................... 10-27
10.5—LIMIT STATES AND RESISTANCE FACTORS ....................................................................................... 10-27
10.5.1—General ................................................................................................................................................. 10-27
10.5.2—Service Limit States ............................................................................................................................. 10-27
10.5.2.1—General....................................................................................................................................... 10-27
10.5.2.2—Tolerable Movements and Movement Criteria .......................................................................... 10-28
10.5.2.3—Overall Stability ......................................................................................................................... 10-28
10.5.2.4—Abutment Transitions ................................................................................................................ 10-29
10.5.3—Strength Limit States ........................................................................................................................... 10-29
10.5.3.1—General....................................................................................................................................... 10-29
10.5.3.2—Spread Footings ......................................................................................................................... 10-29
10.5.3.3—Driven Piles ............................................................................................................................... 10-30
10.5.3.4—Drilled Shafts ............................................................................................................................. 10-30
10.5.3.5—Micropiles .................................................................................................................................. 10-30
10.5.4—Extreme Events Limit States ................................................................................................................ 10-31
10.5.4.1—Extreme Events Design.............................................................................................................. 10-31
10.5.4.2—Liquefaction Design Requirements............................................................................................ 10-31
10.5.5—Resistance Factors................................................................................................................................ 10-38
10.5.5.1—Service Limit States ................................................................................................................... 10-38
10.5.5.2—Strength Limit States ................................................................................................................. 10-38
10-i
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
10.5.5.2.1—General ............................................................................................................................. 10-38
10.5.5.2.2—Spread Footings ............................................................................................................... 10-39
10.5.5.2.3—Driven Piles...................................................................................................................... 10-40
10.5.5.2.4—Drilled Shafts ................................................................................................................... 10-47
10.5.5.2.5—Micropiles ........................................................................................................................ 10-49
10.5.5.3—Extreme Limit States .................................................................................................................. 10-50
10.5.5.3.1—General ............................................................................................................................. 10-50
10.5.5.3.2—Scour ................................................................................................................................ 10-50
10.5.5.3.3—Other Extreme Limit States ............................................................................................. 10-51
10.6—SPREAD FOOTINGS .................................................................................................................................... 10-51
10.6.1—General Considerations ........................................................................................................................ 10-51
10.6.1.1—General ....................................................................................................................................... 10-51
10.6.1.2—Bearing Depth ............................................................................................................................ 10-51
10.6.1.3—Effective Footing Dimensions.................................................................................................... 10-52
10.6.1.4—Bearing Stress Distributions....................................................................................................... 10-52
10.6.1.5—Anchorage of Inclined Footings ................................................................................................. 10-53
10.6.1.6—Groundwater .............................................................................................................................. 10-53
10.6.1.7—Uplift .......................................................................................................................................... 10-53
10.6.1.8—Nearby Structures....................................................................................................................... 10-53
10.6.2—Service Limit State Design................................................................................................................... 10-53
10.6.2.1—General ....................................................................................................................................... 10-53
10.6.2.2—Tolerable Movements ................................................................................................................ 10-53
10.6.2.3—Loads .......................................................................................................................................... 10-54
10.6.2.4—Settlement Analyses ................................................................................................................... 10-54
10.6.2.4.1—General ............................................................................................................................. 10-54
10.6.2.4.2—Settlement of Footings on Cohesionless Soils ................................................................. 10-55
10.6.2.4.3—Settlement of Footings on Cohesive Soils ....................................................................... 10-58
10.6.2.4.4—Settlement of Footings on Rock ....................................................................................... 10-63
10.6.2.5—Overall Stability ......................................................................................................................... 10-64
10.6.2.6—Bearing Resistance at the Service Limit State............................................................................ 10-64
10.6.2.6.1—Presumptive Values for Bearing Resistance .................................................................... 10-64
10.6.2.6.2—Semiempirical Procedures for Bearing Resistance .......................................................... 10-65
10.6.3—Strength Limit State Design ................................................................................................................. 10-66
10.6.3.1—Bearing Resistance of Soil ......................................................................................................... 10-66
10.6.3.1.1—General ............................................................................................................................. 10-66
10.6.3.1.2—Theoretical Estimation ..................................................................................................... 10-67
10.6.3.1.2a—Basic Formulation ................................................................................................... 10-67
10.6.3.1.2b—Considerations for Punching Shear ......................................................................... 10-70
10.6.3.1.2c—Considerations for Footings on Slopes.................................................................... 10-71
10.6.3.1.2d—Considerations for Two-Layer Soil Systems—Critical Depth ................................ 10-73
10.6.3.1.2e—Two-Layered Soil System in Undrained Loading ................................................... 10-74
10.6.3.1.2f—Two-Layered Soil System in Drained Loading ....................................................... 10-76
10.6.3.1.3—Semiempirical Procedures ............................................................................................... 10-76
10.6.3.1.4—Plate Load Tests ............................................................................................................... 10-77
10.6.3.2—Bearing Resistance of Rock ....................................................................................................... 10-77
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TABLE OF CONTENTS
10-iii
10.6.3.2.1—General ............................................................................................................................ 10-77
10.6.3.2.2—Semiempirical Procedures ............................................................................................... 10-78
10.6.3.2.3—Analytic Method .............................................................................................................. 10-78
10.6.3.2.4—Load Test ......................................................................................................................... 10-78
10.6.3.3—Eccentric Load Limitations ........................................................................................................ 10-78
10.6.3.4—Failure by Sliding ...................................................................................................................... 10-79
10.6.4—Extreme Event Limit State Design....................................................................................................... 10-80
10.6.4.1—General....................................................................................................................................... 10-80
10.6.4.2—Eccentric Load Limitations ........................................................................................................ 10-81
10.6.5—Structural Design ................................................................................................................................. 10-81
10.7—DRIVEN PILES ............................................................................................................................................. 10-81
10.7.1—General ................................................................................................................................................. 10-81
10.7.1.1—Application ................................................................................................................................ 10-81
10.7.1.2—Minimum Pile Spacing, Clearance, and Embedment into Cap .................................................. 10-81
10.7.1.3—Piles through Embankment Fill ................................................................................................. 10-82
10.7.1.4—Batter Piles ................................................................................................................................. 10-82
10.7.1.5—Pile Design Requirements .......................................................................................................... 10-82
10.7.1.6—Determination of Pile Loads ...................................................................................................... 10-83
10.7.1.6.1—General ............................................................................................................................ 10-83
10.7.1.6.2—Downdrag ........................................................................................................................ 10-83
10.7.1.6.3—Uplift Due to Expansive Soils ......................................................................................... 10-83
10.7.1.6.4—Nearby Structures ............................................................................................................ 10-84
10.7.2—Service Limit State Design .................................................................................................................. 10-84
10.7.2.1—General....................................................................................................................................... 10-84
10.7.2.2—Tolerable Movements ................................................................................................................ 10-84
10.7.2.3—Settlement .................................................................................................................................. 10-84
10.7.2.3.1—Equivalent Footing Analogy ............................................................................................ 10-84
10.7.2.3.2—Pile Groups in Cohesive Soil ........................................................................................... 10-86
10.7.2.4—Horizontal Pile Foundation Movement ...................................................................................... 10-87
10.7.2.5—Settlement Due to Downdrag ..................................................................................................... 10-89
10.7.2.6—Lateral Squeeze.......................................................................................................................... 10-89
10.7.3—Strength Limit State Design ................................................................................................................. 10-89
10.7.3.1—General....................................................................................................................................... 10-89
10.7.3.2—Point Bearing Piles on Rock ...................................................................................................... 10-90
10.7.3.2.1—General ............................................................................................................................ 10-90
10.7.3.2.2—Piles Driven to Soft Rock ................................................................................................ 10-90
10.7.3.2.3—Piles Driven to Hard Rock ............................................................................................... 10-90
10.7.3.3—Pile Length Estimates for Contract Documents ......................................................................... 10-91
10.7.3.4—Nominal Axial Resistance Change after Pile Driving................................................................ 10-93
10.7.3.4.1—General ............................................................................................................................ 10-93
10.7.3.4.2—Relaxation ........................................................................................................................ 10-93
10.7.3.4.3—Setup ................................................................................................................................ 10-93
10.7.3.5—Groundwater Effects and Buoyancy .......................................................................................... 10-94
10.7.3.6—Scour .......................................................................................................................................... 10-94
10.7.3.7—Downdrag .................................................................................................................................. 10-95
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
10.7.3.8—Determination of Nominal Bearing Resistance for Piles ........................................................... 10-96
10.7.3.8.1—General ............................................................................................................................. 10-96
10.7.3.8.2—Static Load Test ............................................................................................................... 10-97
10.7.3.8.3—Dynamic Testing .............................................................................................................. 10-97
10.7.3.8.4—Wave Equation Analysis .................................................................................................. 10-98
10.7.3.8.5—Dynamic Formula ............................................................................................................ 10-99
10.7.3.8.6—Static Analysis ............................................................................................................... 10-100
10.7.3.8.6a—General .................................................................................................................. 10-100
10.7.3.8.6b—α-Method .............................................................................................................. 10-101
10.7.3.8.6c—β-Method .............................................................................................................. 10-102
10.7.3.8.6d—λ-Method .............................................................................................................. 10-102
10.7.3.8.6e—Tip Resistance in Cohesive Soils .......................................................................... 10-103
10.7.3.8.6f—Nordlund/Thurman Method in Cohesionless Soils ................................................ 10-103
10.7.3.8.6g—Using SPT or CPT in Cohesionless Soils ............................................................. 10-108
10.7.3.9—Resistance of Pile Groups in Compression .............................................................................. 10-112
10.7.3.10—Uplift Resistance of Single Piles ............................................................................................ 10-114
10.7.3.11—Uplift Resistance of Pile Groups ............................................................................................ 10-114
10.7.3.12—Nominal Lateral Resistance of Pile Foundations ................................................................... 10-116
10.7.3.13—Pile Structural Resistance....................................................................................................... 10-117
10.7.3.13.1—Steel Piles ..................................................................................................................... 10-117
10.7.3.13.2—Concrete Piles .............................................................................................................. 10-117
10.7.3.13.3—Timber Piles ................................................................................................................. 10-118
10.7.3.13.4—Buckling and Lateral Stability ..................................................................................... 10-118
10.7.4—Extreme Event Limit State ................................................................................................................. 10-118
10.7.5—Corrosion and Deterioration ............................................................................................................... 10-119
10.7.6—Determination of Minimum Pile Penetration ..................................................................................... 10-120
10.7.7—Determination of Rndr Used to Establish Contract Driving Criteria for Nominal
Bearing Resistance ........................................................................................................................................... 10-121
10.7.8—Drivability Analysis ........................................................................................................................... 10-121
10.7.9—Probe Piles.......................................................................................................................................... 10-123
10.8—DRILLED SHAFTS ..................................................................................................................................... 10-123
10.8.1—General ............................................................................................................................................... 10-123
10.8.1.1—Scope ........................................................................................................................................ 10-123
10.8.1.2—Shaft Spacing, Clearance, and Embedment into Cap ............................................................... 10-124
10.8.1.3—Shaft Diameter and Enlarged Bases ......................................................................................... 10-124
10.8.1.4—Battered Shafts ......................................................................................................................... 10-124
10.8.1.5—Drilled Shaft Resistance ........................................................................................................... 10-125
10.8.1.6—Determination of Shaft Loads .................................................................................................. 10-126
10.8.1.6.1—General ........................................................................................................................... 10-126
10.8.1.6.2—Downdrag ...................................................................................................................... 10-126
10.8.1.6.3—Uplift .............................................................................................................................. 10-126
10.8.2—Service Limit State Design................................................................................................................. 10-126
10.8.2.1—Tolerable Movements .............................................................................................................. 10-126
10.8.2.2—Settlement ................................................................................................................................ 10-126
10.8.2.2.1—General ........................................................................................................................... 10-126
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TABLE OF CONTENTS
10-v
10.8.2.2.2—Settlement of Single-Drilled Shaft................................................................................. 10-127
10.8.2.2.3—Intermediate Geo Materials (IGMs) .............................................................................. 10-129
10.8.2.2.4—Group Settlement ........................................................................................................... 10-130
10.8.2.3—Horizontal Movement of Shafts and Shaft Groups .................................................................. 10-130
10.8.2.4—Settlement Due to Downdrag ................................................................................................... 10-130
10.8.2.5—Lateral Squeeze........................................................................................................................ 10-130
10.8.3—Strength Limit State Design ............................................................................................................... 10-130
10.8.3.1—General..................................................................................................................................... 10-130
10.8.3.2—Groundwater Table and Buoyancy .......................................................................................... 10-130
10.8.3.3—Scour ........................................................................................................................................ 10-130
10.8.3.4—Downdrag ................................................................................................................................ 10-130
10.8.3.5—Nominal Axial Compression Resistance of Single Drilled Shafts ........................................... 10-131
10.8.3.5.1—Estimation of Drilled Shaft Resistance in Cohesive Soils ............................................. 10-131
10.8.3.5.1a—General.................................................................................................................. 10-131
10.8.3.5.1b—Side Resistance ..................................................................................................... 10-132
10.8.3.5.1c—Tip Resistance....................................................................................................... 10-133
10.8.3.5.2—Estimation of Drilled Shaft Resistance in Cohesionless Soils ....................................... 10-134
10.8.3.5.2a—General.................................................................................................................. 10-134
10.8.3.5.2b—Side Resistance ..................................................................................................... 10-134
10.8.3.5.2c—Tip Resistance....................................................................................................... 10-135
10.8.3.5.3—Shafts in Strong Soil Overlying Weaker Compressible Soil ......................................... 10-136
10.8.3.5.4—Estimation of Drilled Shaft Resistance in Rock ............................................................ 10-136
10.8.3.5.4a—General.................................................................................................................. 10-136
10.8.3.5.4b—Side Resistance ..................................................................................................... 10-137
10.8.3.5.4c—Tip Resistance....................................................................................................... 10-138
10.8.3.5.4d—Combined Side and Tip Resistance ...................................................................... 10-138
10.8.3.5.5—Estimation of Drilled Shaft Resistance in Intermediate Geo Materials (IGMs) ............ 10-139
10.8.3.5.6—Shaft Load Test.............................................................................................................. 10-139
10.8.3.6—Shaft Group Resistance............................................................................................................ 10-140
10.8.3.6.1—General .......................................................................................................................... 10-140
10.8.3.6.2—Cohesive Soil ................................................................................................................. 10-140
10.8.3.6.3—Cohesionless Soil ........................................................................................................... 10-141
10.8.3.6.4—Shaft Groups in Strong Soil Overlying Weak Soil ........................................................ 10-141
10.8.3.7—Uplift Resistance...................................................................................................................... 10-142
10.8.3.7.1—General .......................................................................................................................... 10-142
10.8.3.7.2—Uplift Resistance of Single Drilled Shaft ...................................................................... 10-142
10.8.3.7.3—Group Uplift Resistance ................................................................................................ 10-143
10.8.3.7.4—Uplift Load Test............................................................................................................. 10-143
10.8.3.8—Nominal Horizontal Resistance of Shaft and Shaft Groups ..................................................... 10-143
10.8.3.9—Shaft Structural Resistance ...................................................................................................... 10-143
10.8.3.9.1—General .......................................................................................................................... 10-143
10.8.3.9.2—Buckling and Lateral Stability ....................................................................................... 10-143
10.8.3.9.3—Reinforcement ............................................................................................................... 10-143
10.8.3.9.4—Transverse Reinforcement ............................................................................................. 10-144
10.8.3.9.5—Concrete......................................................................................................................... 10-144
10.8.3.9.6—Reinforcement into Superstructure ................................................................................ 10-144
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
10-vi
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
10.8.3.9.7—Enlarged Bases ............................................................................................................... 10-144
10.8.4—Extreme Event Limit State ................................................................................................................. 10-144
10.9—MICROPILES .............................................................................................................................................. 10-145
10.9.1—General ............................................................................................................................................... 10-145
10.9.1.1—Scope ........................................................................................................................................ 10-146
10.9.1.2—Minimum Micropile Spacing, Clearance, and Embedment into Cap ....................................... 10-146
10.9.1.3—Micropiles through Embankment Fill ...................................................................................... 10-146
10.9.1.4—Battered Micropiles .................................................................................................................. 10-146
10.9.1.5—Micropile Design Requirements .............................................................................................. 10-146
10.9.1.6—Determination of Micropile Loads ........................................................................................... 10-147
10.9.1.6.1—Downdrag ...................................................................................................................... 10-147
10.9.1.6.2—Uplift Due to Expansive Soils........................................................................................ 10-147
10.9.1.6.3—Nearby Structures .......................................................................................................... 10-147
10.9.2—Service Limit State Design................................................................................................................. 10-147
10.9.2.1—General ..................................................................................................................................... 10-147
10.9.2.2—Tolerable Movements .............................................................................................................. 10-147
10.9.2.3—Settlement ................................................................................................................................ 10-147
10.9.2.3.1—Micropile Groups in Cohesive Soil ................................................................................ 10-147
10.9.2.3.2—Micropile Groups in Cohesionless Soil.......................................................................... 10-147
10.9.2.4—Horizontal Micropile Foundation Movement .......................................................................... 10-147
10.9.2.5—Settlement Due to Downdrag ................................................................................................... 10-147
10.9.2.6—Lateral Squeeze ........................................................................................................................ 10-147
10.9.3—Strength Limit State Design ............................................................................................................... 10-148
10.9.3.1—General ..................................................................................................................................... 10-148
10.9.3.2—Ground Water Table and Bouyancy ......................................................................................... 10-148
10.9.3.3—Scour ........................................................................................................................................ 10-148
10.9.3.4—Downdrag................................................................................................................................. 10-148
10.9.3.5—Nominal Axial Compression Resistance of a Single Micropile ............................................... 10-148
10.9.3.5.1—General ........................................................................................................................... 10-148
10.9.3.5.2—Estimation of Grout-to-Ground Bond Resistance .......................................................... 10-149
10.9.3.5.3—Estimation of Micropile Tip Resistance in Rock ........................................................... 10-150
10.9.3.5.4—Micropile Load Test ....................................................................................................... 10-151
10.9.3.6—Resistance of Micropile Groups in Compression ..................................................................... 10-151
10.9.3.7—Nominal Uplift Resistance of a Single Micropile .................................................................... 10-151
10.9.3.8—Nominal Uplift Resistance of Micropile Groups ..................................................................... 10-151
10.9.3.9—Nominal Horizontal Resistance of Micropiles and Micropile Groups ..................................... 10-152
10.9.3.10—Structural Resistance .............................................................................................................. 10-152
10.9.3.10.1—General ......................................................................................................................... 10-152
10.9.3.10.2—Axial Compressive Resistance ..................................................................................... 10-152
10.9.3.10.2a—Cased Length ...................................................................................................... 10-153
10.9.3.10.2b—Uncased Length .................................................................................................. 10-153
10.9.3.10.3—Axial Tension Resistance ............................................................................................. 10-154
10.9.3.10.3a—Cased Length ...................................................................................................... 10-154
10.9.3.10.3b—Uncased Length .................................................................................................. 10-155
10.9.3.10.4—Plunge Length Transfer Load ...................................................................................... 10-155
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
TABLE OF CONTENTS
10-vii
10.9.3.10.5—Grout-to-Steel Bond .................................................................................................... 10-156
10.9.3.10.6—Buckling and Lateral Stability ..................................................................................... 10-156
10.9.3.10.7—Reinforcement into Superstructure .............................................................................. 10-156
10.9.4—Extreme Event Limit State ................................................................................................................. 10-156
10.9.5—Corrosion and Deterioration .............................................................................................................. 10-156
10.10—REFERENCES .......................................................................................................................................... 10-156
APPENDIX A10—SEISMIC ANALYSIS AND DESIGN OF FOUNDATIONS ................................................ 10-163
A10.1—INVESTIGATION .................................................................................................................................... 10-163
A10.2—FOUNDATION DESIGN ......................................................................................................................... 10-163
A10.3—SPECIAL PILE REQUIREMENTS ......................................................................................................... 10-167
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 10
FOUNDATIONS
10.1—SCOPE
C10.1
Provisions of this Section shall apply for the design
of spread footings, driven piles, drilled shaft, and
micropile foundations.
The probabilistic LRFD basis of these
Specifications, which produces an interrelated
combination of load, load factor resistance, resistance
factor, and statistical reliability, shall be considered
when selecting procedures for calculating resistance
other than that specified herein. Other methods,
especially when locally recognized and considered
suitable for regional conditions, may be used if
resistance factors are developed in a manner that is
consistent with the development of the resistance factors
for the method(s) provided in these Specifications, and
are approved by the Owner.
The development of the resistance factors provided
in this Section are summarized in Allen (2005), with
additional details provided in Appendix A of Barker et
al. (1991), in Paikowsky et al. (2004), in Allen (2005),
and in D’Appolonia (2006).
The specification of methods of analysis and
calculation of resistance for foundations herein is not
intended to imply that field verification and/or reaction
to conditions actually encountered in the field are no
longer needed. These traditional features of foundation
design and construction are still practical considerations
when designing in accordance with these Specifications.
10.2—DEFINITIONS
Battered Pile—A pile or micropile installed at an angle inclined to the vertical to provide higher resistance to lateral loads.
Bearing Pile—A pile or micropile whose purpose is to carry axial load through friction or point bearing.
Bent—A type of pier comprised of multiple columns or piles supporting a single cap and in some cases connected
with bracing.
Bent Cap—A flexural substructure element supported by columns or piles that receives loads from the superstructure.
Bond Length—The length of a micropile that is bonded to the ground and which is conceptually used to transfer the
applied axial loads to the surrounding soil or rock. Also known as the load transfer length.
Casing—Steel pipe introduced during the drilling process to temporarily stabilize the drill hole. Depending on the
details of micropile construction and composition, this casing may be fully extracted during or after grouting, or may
remain partially or completely in place as part of the final micropile pile configuration.
Centralizer—A device to centrally locate the core steel within a borehole.
Column Bent—A type of bent that uses two or more columns to support a cap. Columns may be drilled shafts or other
independent units supported by individual footings or a combined footing; and may employ bracing or struts for
lateral support above ground level.
Combination Point Bearing and Friction Pile—Pile that derives its capacity from contributions of both point bearing
developed at the pile tip and resistance mobilized along the embedded shaft.
Combined Footing—A footing that supports more than one column.
Core Steel—Reinforcing bars or pipes used to strengthen or stiffen a micropile, excluding any left-in casing.
CPT—Cone Penetration Test.
CU—Consolidated Undrained.
Deep Foundation—A foundation that derives its support by transferring loads to soil or rock at some depth below the
structure by end bearing, adhesion or friction, or both.
DMT—Flat Plate Dilatometer Test.
10-1
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
10-2
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Drilled Shaft—A deep foundation unit, wholly or partly embedded in the ground, constructed by placing fresh
concrete in a drilled hole with or without steel reinforcement. Drilled shafts derive their capacity from the surrounding
soil and/or from the soil or rock strata below its tip. Drilled shafts are also commonly referred to as caissons, drilled
caissons, bored piles, or drilled piers.
Effective Stress—The net stress across points of contact of soil particles, generally considered as equivalent to the
total stress minus the pore water pressure.
ER—Hammer efficiency expressed as percent of theoretical free fall energy delivered by the hammer system actually
used in a Standard Penetration Test.
Free (Unbonded) Length—The designed length of a micropile that is not bonded to the surrounding ground or grout.
Friction Pile—A pile whose support capacity is derived principally from soil resistance mobilized along the side of
the embedded pile.
Geomechanics Rock Mass Rating System—Rating system developed to characterize the engineering behavior of rock
masses (Bieniawski, 1984).
Geotechnical Bond Strength—The nominal grout-to-ground bond strength.
IGM—Intermediate Geomaterial, a material that is transitional between soil and rock in terms of strength and
compressibility, such as residual soils, glacial tills, or very weak rock.
Isolated Footing—Individual support for the various parts of a substructure unit; the foundation is called a footing
foundation.
Length of Foundation—Maximum plan dimension of a foundation element.
Load Test—Incremental loading of a foundation element, recording the total movement at each increment.
Micropile—A small-diameter drilled and grouted non-displacement pile (normally less than 12 in.) that is typically
reinforced.
OCR—Over Consolidation Ratio, the ratio of the preconsolidation pressure to the current vertical effective stress.
Pile—A slender deep foundation unit, wholly or partly embedded in the ground, that is installed by driving, drilling,
auguring, jetting, or otherwise and that derives its capacity from the surrounding soil and/or from the soil or rock
strata below its tip.
Pile Bent—A type of bent using pile units, driven or placed, as the column members supporting a cap.
Pile Cap—A flexural substructure element located above or below the finished ground line that receives loads from
substructure columns and is supported by shafts or piles.
Pile Shoe—A metal piece fixed to the penetration end of a pile to protect it from damage during driving and to
facilitate penetration through very dense material.
Piping—Progressive erosion of soil by seeping water that produces an open pipe through the soil through which water
flows in an uncontrolled and dangerous manner.
Plunge Length—The length of casing inserted into the bond zone to effect a transition between the upper cased
portion to the lower uncased portion of a micropile.
Plunging—A mode of behavior observed in some pile load tests, wherein the settlement of the pile continues to
increase with no increase in load.
PMT—Pressuremeter Test.
Point-Bearing Pile—A pile whose support capacity is derived principally from the resistance of the foundation
material on which the pile tip bears.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
SECTION 10: FOUNDATIONS
10-3
Post Grouting—The injection of additional grout into the load bond length of a micropile after the primary grout has
set. Also known as regrouting or secondary grouting.
Primary Grout—Portland cement-based grout that is injected into a micropile hole, prior to or after the installation of
the reinforcement to provide the load transfer to the surrounding ground along the micropile and afford a degree of
corrosion protection for a micropile loaded in compression.
Reinforcement—The steel component of a micropile which accepts and/or resists applied loadings.
RMR—Rock Mass Rating.
RQD—Rock Quality Designation.
Shallow Foundation—A foundation that derives its support by transferring load directly to the soil or rock at shallow
depth.
Slickensides—Polished and grooved surfaces in clayey soils or rocks resulting from shearing displacements along
planes.
SPT—Standard Penetration Test.
Total Stress—Total pressure exerted in any direction by both soil and water.
UU—Unconsolidated Undrained.
VST—Vane Shear Test (performed in the field).
Width of Foundation—Minimum plan dimension of a foundation element.
10.3—NOTATION
A
Ab
Ac
Act
Ag
Ap
As
=
=
=
=
=
=
=
Au
A′
=
=
asi
B
B′
Cα
Cαε
Cc
Ccε
CF
CN
Cr
Crε
Cwq, Cwγ
C′
c
cv
c1
c2
c′1
c*
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
steel pile cross-sectional area (ft2) (10.7.3.8.2)
cross-sectional area of steel reinforcing bar (in.2) (10.9.3.10.2a)
cross-sectional area of steel casing (in.2) (10.9.3.10.2a)
cross-sectional area of steel casing considering reduction for threads (in.2) (10.9.3.10.3a)
cross-sectional area of grout within micropile (in.2) (10.9.3.10.3a)
area of pile or micropile tip or base of drilled shaft (ft2) (10.7.3.8.6a) (10.8.3.5) (10.9.3.5.1)
surface area of pile shaft; area of grout to ground bond surface of micropile through bond length (ft2)
(10.7.3.8.6a) (10.9.3.5.1)
uplift area of a belled drilled shaft (ft2) (10.8.3.7.2)
effective footing area for determination of elastic settlement of footing subjected to eccentric loads (ft2)
(10.6.2.4.2)
pile perimeter at the point considered (ft) (10.7.3.8.6g)
footing width; pile group width; pile diameter (ft) (10.6.1.3) (10.7.2.3.2) (10.7.2.4)
effective footing width (ft) (10.6.1.3)
secondary compression index, void ratio definition (dim) (10.4.6.3)
secondary compression index, strain definition (dim) (10.6.2.4.3)
compression index, void ratio definition (dim) (10.4.6.3)
compression index, strain definition (dim) (10.6.2.4.3)
correction factor for Kδ when δ is not equal to φf (dim) (10.7.3.8.6f)
overburden stress correction factor for N (dim) (10.4.6.2.4)
recompression index, void ratio definition (dim) (10.4.6.3)
recompression index, strain definition (dim) (10.6.2.4.3)
correction factors for groundwater effect (dim) (10.6.3.1.2a)
bearing capacity index (dim) (10.6.2.4.2)
cohesion of soil taken as undrained shear strength (ksf) (10.6.3.1.2a)
coefficient of consolidation (ft2/yr) (10.4.6.3)
undrained shear strength of the top layer of soil as depicted in Figure 10.6.3.1.2e-1 (ksf) (10.6.3.1.2e)
undrained shear strength of the lower layer of soil as depicted in Figure 10.6.3.1.2e-1 (ksf) (10.6.3.1.2e)
drained shear strength of the top layer of soil (ksf) (10.6.3.1.2f)
reduced effective stress soil cohesion for punching shear (ksf) (10.6.3.1.2b)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
10-4
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
c′
c′i
D
=
=
=
DD
D′
Db
Dest
Df
Di
Dp
Dr
Dw
db
dq
=
=
=
=
=
=
=
=
=
=
=
E
Ed
Ei
Em
Ep
ER
=
=
=
=
=
=
Es
e
eB
eL
eo
FCO
f ′c
=
=
=
=
=
=
=
fpe
fs
=
=
fsi
fy
H
Hc
Hcrit
=
=
=
=
=
Hd
Hs
Hs2
hi
I
Ip
Iw
ic, iq, iγ
j
Kc
Ks
Kδ
L
Lb
Li
Lp
L′
LL
N
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
effective stress cohesion intercept (ksf) (10.4.6.2.3)
instantaneous cohesion at a discrete value of normal stress (ksf) (C10.4.6.4)
depth of pile embedment; pile width or diameter; diameter of drilled shaft (ft) (10.7.2.3) (10.7.3.8.6g)
(10.8.3.5.1c)
downdrag load per pile (kips) (C10.7.3.7)
effective depth of pile or micropile group (ft) (10.7.2.3.2) (10.9.2.3.2)
depth of embedment of pile into a bearing stratum (ft) (10.7.2.3.2)
estimated pile length needed to obtain desired nominal resistance per pile (ft) (C10.7.3.7)
foundation embedment depth taken from ground surface to bottom of footing (ft) (10.6.3.1.2a)
pile width or diameter at the point considered (ft) (10.7.3.8.6g)
diameter of the bell on a belled drilled shaft (ft) (10.8.3.7.2)
relative density (percent) (C10.6.3.1.2b)
depth to water surface taken from the ground surface (ft) (10.6.3.1.2a)
grouted bond zone diameter (ft) (10.9.3.5.2)
correction factor to account for the shearing resistance along the failure surface passing through
cohesionless material above the bearing elevation (dim) (10.6.3.1.2a)
modulus of elasticity of pile material (ksi) (10.7.3.8.2)
developed hammer energy (ft-lb) (10.7.3.8.5)
modulus of elasticity of intact rock (ksi) (10.4.6.5)
rock mass modulus (ksi) (10.4.6.5)
modulus of elasticity of pile (ksi) (10.7.3.13.4)
hammer efficiency expressed as percent of theoretical free fall energy delivered by the hammer system
actually used (dim) (10.4.6.2.4)
soil (Young’s) modulus (ksi) (C10.4.6.3)
void ratio (dim) (10.6.2.4.3)
eccentricity of load parallel to the width of the footing (ft) (10.6.1.3)
eccentricity of load parallel to the length of the footing (ft) (10.6.1.3)
void ratio at initial vertical effective stress (dim) (10.6.2.4.3)
base resistance of wood in compression parallel to the grain (ksi) (10.7.8)
28-day compressive strength of concrete or grout, unless another age is specified (ksi) (10.6.2.6.2)
(10.9.3.10.2a)
effective stress in the prestressing steel after losses (ksi) (10.7.8)
approximate constant sleeve friction resistance measured from a CPT at depths below 8D (ksf)
(C10.7.3.8.6g)
unit local sleeve friction resistance from CPT at the point considered (ksf) (10.7.3.8.6g)
specified minimum yield strength of steel (ksi) (10.7.8) (10.9.3.10.2a)
horizontal component of inclined loads (kips) (10.6.3.1.2a)
height of compressible soil layer (ft) (10.6.2.4.2)
minimum distance below a spread footing to a second separate layer of soil with different properties that
will affect shear strength of the foundation (ft) (10.6.3.1.2d)
length of longest drainage path in compressible soil layer (ft) (10.6.2.4.3)
height of sloping ground mass (ft) (10.6.3.1.2c)
distance from bottom of footing to top of the second soil layer (ft) (10.6.3.1.2e)
length interval at the point considered (ft) (10.7.3.8.6g)
influence factor of the effective group embedment (dim) (10.7.2.3.2)
influence coefficient to account for rigidity and dimensions of footing (dim) (10.6.2.4.4)
weak axis moment of inertia for a pile (ft4) (10.7.3.13.4)
load inclination factors (dim) (10.6.3.1.2a)
damping constant (dim) (10.7.3.8.3)
correction factor for side friction in clay (dim) (10.7.3.8.6g)
correction factor for side friction in sand (dim) (10.7.3.8.6g)
coefficient of lateral earth pressure at midpoint of soil layer under consideration (dim) (10.7.3.8.6f)
length of foundation; pile length (ft) (10.6.1.3) (10.7.3.8.2)
micropile bonded length (ft) (10.9.3.5.2)
depth to middle of length interval at the point considered (ft) (10.7.3.8.6g)
micropile casing plunge length (ft) (10.9.3.10.4)
effective footing length (ft) (10.6.1.3)
liquid limit of soil (percent) (10.4.6.3)
uncorrected Standard Penetration Test (SPT) blow count (blows/ft) (10.4.6.2.4)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 10: FOUNDATIONS
N 160
N1
N160
=
=
=
=
Nb
=
Nc
Ncm, Nqm,
Nγm
=
=
Ncq
=
Nm
=
Ns
=
Nq
=
Nu
=
N′
=
N ′q
Nγ
=
=
N1
N2
N60
n
=
=
=
nh
PL
Pf
Pm
Pt
Pu
pa
Q
=
=
=
=
=
=
=
=
Qf
Qg
Qp
QT1
q
=
=
=
=
=
qc
qc
qc1
qc2
qL
qℓ
qn
qo
qp
qR
qs
qsbell
qu
qult
q1
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
q2
=
10-5
average corrected SPT blow count along pile side (blows/ft) (10.7.3.8.6g)
SPT blow count corrected for overburden pressure σ′v (blows/ft) (10.4.6.2.4)
SPT blow count corrected for both overburden and hammer efficiency effects (blows/ft) (10.4.6.2.4)
(10.7.2.3.2)
number of hammer blows for 1 in. of pile permanent set (blows/in.) (10.7.3.8.5)
cohesion term (undrained loading) bearing capacity factor (dim) (10.6.3.1.2a)
modified bearing capacity factors (dim) (10.6.3.1.2a)
modified bearing capacity factor (dim) (10.6.3.1.2e)
modified bearing capacity factor (dim) (10.6.3.1.2e)
slope stability factor (dim) (10.6.3.1.2c)
surcharge (embedment) term (drained or undrained loading) bearing capacity factor (dim) (10.6.3.1.2a)
uplift adhesion factor for bell (dim) (10.8.3.7.2)
alternate notation for N1 (blows/ft) (10.6.2.4.2)
pile bearing capacity factor from Figure 10.7.3.8.6f-8 (dim) (10.7.3.8.6f)
unit weight (footing width) term (drained loading) bearing capacity factor (dim) (10.6.3.1.2a)
number of intervals between the ground surface and a point 8D below the ground surface (dim)
(10.7.3.8.6g)
number of intervals between 8D below the ground surface and the tip of the pile (dim) (10.7.3.8.6g)
SPT blow count corrected for hammer efficiency (blows/ft) (10.4.6.2.4)
porosity (dim); number of soil layers within zone of stress influence of the footing (dim) (10.4.6.2.4)
(10.6.2.4.2)
rate of increase of soil modulus with depth (ksi/ft) (10.4.6.3)
plastic limit of soil (percent) (10.4.6.3)
probability of failure (dim) (C10.5.5.2.1)
p-multiplier from Table 10.7.2.4-1 (dim) (10.7.2.4)
factored axial load transferred to ground along micropile plunge length (kips) (10.9.3.10.4)
factored axial load on uncased micropile segment adjusted for plunge length load transfer (10.9.3.10.4)
atmospheric pressure (ksf) ( Sea level value equivalent to 2.12 ksf or 1 atm or 14.7 psi) (10.8.3.5.1b)
load applied to top of footing, shaft, or micropile (kips); load test load (kips) (C10.6.3.1.2b) (10.7.3.8.2)
(10.9.3.10.4)
load at failure during load test (kips) (10.7.3.8.2)
bearing capacity for block failure (kips) (C10.7.3.9)
factored load per pile, excluding downdrag load (kips) (C10.7.3.7)
total load acting at the head of the drilled shaft (kips) (C10.8.3.5.4d)
net foundation pressure applied at 2Db/3; this pressure is equal to applied load at top of the group divided
by the area of the equivalent footing and does not include the weight of the piles or the soil between the
piles (ksf) (10.7.2.3.2)
static cone tip resistance (ksf) (C10.4.6.3)
average static cone tip resistance over a depth B below the equivalent footing (ksf) (10.6.3.1.3)
average qc over a distance of yD below the pile tip (path a-b-c) (ksf) (10.7.3.8.6g)
average qc over a distance of 8D above the pile tip (path c-e) (ksf) (10.7.3.8.6g)
limiting unit tip resistance of a single pile from Figure 10.7.3.8.6f-9 (ksf) (10.7.3.8.6f)
limiting tip resistance of a single pile (ksf) (10.7.3.8.6g)
nominal bearing resistance (ksf) (10.6.3.1.1)
applied vertical stress at base of loaded area (ksf) (10.6.2.4.2)
nominal unit tip resistance of pile or micropile (ksf) (10.7.3.8.6a) (10.9.3.5.1)
factored bearing resistance (ksf) (10.6.3.1.1)
unit shear resistance (ksf); unit side resistance of pile or micropile (ksf) (10.6.3.4) (10.7.3.8.6a) (10.9.3.5.1)
nominal unit uplift resistance of a belled drilled shaft (ksf) (10.8.3.7.2)
uniaxial compression strength of rock (ksf) (10.4.6.4)
nominal bearing resistance (ksf) (10.6.3.1.2e)
nominal bearing resistance of footing supported in the upper layer of a two-layer system, assuming the
upper layer is infinitely thick (ksf) (10.6.3.1.2d)
nominal bearing resistance of a fictitious footing of the same size and shape as the actual footing but
supported on surface of the second (lower) layer of a two-layer system (ksf) (10.6.3.1.2d)
2012
Edition
10-6
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
RC
RCC
RCU
Rep
Rn
Rndr
Rnstat
Rp
RR
Rs
=
=
=
=
=
=
=
=
=
=
Rsbell
Rsdd
RT
RTC
RTU
Rug
Rτ
r
Sc
Sc(1-D)
Se
Ss
St
Su
Su
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
s
s, m
s c , s q, s γ
sf
T
t
t1, t2
U
V
=
=
=
=
=
=
=
=
=
Wg
WT1
X
Y
Z
z
α
αb
αE
αt
β
=
=
=
=
=
=
=
=
=
=
=
βm
βz
γ
γp
ΔHi
δ
=
=
=
=
=
=
εv
=
factored micropile structural axial compression resistance (kips) (10.9.3.10.2)
factored structural axial compression resistance of cased micropile segments (kips) (10.9.3.10.2a)
factored structural axial compression resistance of uncased micropile segments (kips) (10.9.3.10.2b)
nominal passive resistance of soil available throughout the design life of the structure (kips) (10.6.3.4)
nominal resistance of footing, pile, shaft, or micropile (kips) (10.6.3.4)
nominal pile driving resistance including downdrag (kips) (C10.7.3.3)
nominal resistance of pile from static analysis method (kips) (C10.7.3.3)
nominal pile or micropile tip resistance (kips) (10.7.3.8.6a) (10.9.3.5.1)
factored nominal resistance of a footing, pile, micropile, or shaft (kips) (10.6.3.4) (10.9.3.5.1)
pile side resistance (kips); nominal uplift resistance due to side resistance (kips); nominal micropile
grout-to-ground bond resistance (kips) (10.7.3.8.6a) (10.7.3.10) (C10.9.3.5.1)
nominal uplift resistance of a belled drilled shaft (kips) (10.8.3.5.2)
skin friction which must be overcome during driving (kips) (C10.7.3.7)
factored structural axial tension resistance (kips) (10.9.3.10.3)
factored structural axial tension resistance of cased micropile segments (kips) (10.9.3.10.3a)
factored structural axial tension resistance of uncased micropile segments (kips) (10.9.3.10.3b)
nominal uplift resistance of a pile group (kips) (10.7.3.11)
nominal sliding resistance between the footing and the soil (kips) (10.6.3.4)
radius of circular footing or B/2 for square footing (ft) (10.6.2.4.4)
primary consolidation settlement (ft) (10.6.2.4.1)
single dimensional consolidation settlement (ft) (10.6.2.4.3)
elastic settlement (ft) (10.6.2.4.1)
secondary settlement (ft) (10.6.2.4.1)
total settlement (ft) (10.6.2.4.1)
undrained shear strength (ksf) (10.4.6.2.2)
average undrained shear strength along pile side (ksf) (10.7.3.9)
pile permanent set (in.) (10.7.3.8.5)
fractured rock mass parameters (10.4.6.4)
shape factors (dim) (10.6.3.1.2a)
pile top movement during load test (in.) (10.7.3.8.2)
time factor (dim) (10.6.2.4.3)
time for a given percentage of one-dimensional consolidation settlement to occur (yr) (10.6.2.4.3)
arbitrary time intervals for determination of secondary settlement, Ss (yr) (10.6.2.4.3)
percentage of consolidation (10.6.2.4.3)
total vertical force applied by a footing (kips); pile displacement volume (ft3/ft) (10.6.3.1.2a)
(10.7.3.8.6f)
weight of block of soil, piles and pile cap (kips) (10.7.3.11)
vertical movement at the head of the drilled shaft (in.) (C10.8.3.5.4d)
width or smallest dimension of pile group (ft) (10.7.3.9)
length of pile group (ft) (10.7.3.9)
total embedded pile length; penetration of shaft (ft) (10.7.3.8.6g)
depth below ground surface (ft) (C10.4.6.3)
adhesion factor applied to su (dim) (10.7.3.8.6b)
nominal micropile grout-to-ground bond stress (ksf) (10.9.3.5.2)
reduction factor to account for jointing in rock (dim) (10.8.3.5.4b)
coefficient from Figure 10.7.3.8.6f-7 (dim) (10.7.3.8.6f)
reliability index; coefficient relating the vertical effective stress and the unit skin friction of a pile or
drilled shaft (dim) (C10.5.5.2.1) (10.7.3.8.6c)
punching index (dim) (10.6.3.1.2e)
factor to account for footing shape and rigidity (dim) (10.6.2.4.2)
unit density of soil (kcf) (10.6.3.1.2a)
load factor for downdrag (C10.7.3.7)
elastic settlement of layer i (ft) (10.6.2.4.2)
elastic deformation of pile (in.); friction angle between foundation and soil (degrees) (C10.7.3.8.2)
(10.7.3.8.6f)
vertical strain of over consolidated soil (in./in.) (10.6.2.4.3)
2012
Edition
SECTION 10: FOUNDATIONS
η
λ
=
=
μc
φf
φ′f
φ′i
φ′1
φ′s
φ*
ϕ
ϕb
ϕbl
ϕC
ϕCC
ϕCU
ϕda
ϕdyn
ϕep
ϕload
ϕqp
ϕqs
ϕstat
ϕT
ϕTC
ϕTU
ϕug
ϕup
ϕupload
ϕτ
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
10-7
shaft efficiency reduction factor for axial resistance of a drilled shaft or micropile group (dim) (10.7.3.9)
empirical coefficient relating the passive lateral earth pressure and the unit skin friction of a pile (dim)
(10.7.3.8.6d)
reduction factor for consolidation settlements to account for three-dimensional effects (dim) (10.6.2.4.3)
angle of internal friction of drained soil (degrees) (10.4.6.2.4)
drained (long term) effective angle of internal friction of clays (degrees) (10.4.6.2.3)
instantaneous friction angle of the rock mass (degrees) (10.4.6.4)
effective stress angle of internal friction of the top layer of soil (degrees) (10.6.3.1.2f)
secant friction angle (degrees) (10.4.6.2.4)
reduced effective stress soil friction angle for punching shear (degrees) (10.6.3.1.2b)
resistance factor (dim) (10.5.5.2.3)
resistance factor for bearing of shallow foundations (dim) (10.5.5.2.2)
resistance factor for driven piles or shafts, block failure in clay (dim) (10.5.5.2.3)
structural resistance factor for micropiles in axial compression (dim) (10.9.3.10.2)
structural resistance factor for cased micropiles segments in axial compression (dim) (10.9.3.10.2a)
structural resistance factor for uncased micropiles segments in axial compression (dim) (10.9.3.10.2b)
resistance factor for driven piles, drivability analysis (dim) (10.5.5.2.3)
resistance factor for driven piles, dynamic analysis and static load test methods (dim) (10.5.5.2.3)
resistance factor for passive soil resistance (dim) (10.5.5.2.2)
resistance factor for shafts, static load test (dim) (10.5.5.2.4)
resistance factor for tip resistance (dim) (10.8.3.5) (10.9.3.5.1)
resistance factor for shaft side resistance (dim) (10.8.3.5)
resistance factor for driven piles or shafts, static analysis methods (dim) (10.5.5.2.3)
structural resistance factor for micropiles in axial tension (dim) (10.9.3.10.3)
structural resistance factor for cased micropiles segments in axial tension (dim) (10.9.3.10.3a)
structural resistance factor for uncased micropiles segments in axial tension (dim) (10.9.3.10.3b)
resistance factor for group uplift (dim) (10.5.5.2.3)
resistance factor for uplift resistance of a single pile or drilled shaft (dim) (10.5.5.2.3)
resistance factor for shafts, static uplift load test (dim) (10.5.5.2.4) (10.9.3.5.1)
resistance factor for sliding resistance between soil and footing (dim) (10.5.5.2.2)
10.4—SOIL AND ROCK PROPERTIES
10.4.1—Informational Needs
The expected project
analyzed to determine the
information to be developed
exploration. This analysis
following:
C10.4.1
requirements shall be
type and quantity of
during the geotechnical
should consist of the
•
Identify design and constructability requirements,
e.g., provide grade separation, support loads from
bridge superstructure, provide for dry excavation,
and their effect on the geotechnical information
needed.
•
Identify performance criteria, e.g., limiting
settlements, right of way restrictions, proximity of
adjacent structures, and schedule constraints.
•
Identify areas of geologic concern on the site and
potential variability of local geology.
•
Identify areas of hydrologic concern on the site,
e.g., potential erosion or scour locations.
The first phase of an exploration and testing
program requires that the Engineer understand the
project requirements and the site conditions and/or
restrictions. The ultimate goal of this phase is to identify
geotechnical data needs for the project and potential
methods available to assess these needs.
Geotechnical Engineering Circular #5—Evaluation
of Soil and Rock Properties (Sabatini et al., 2002)
provides a summary of information needs and testing
considerations for various geotechnical applications.
2012
Edition
10-8
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
•
Develop likely sequence and phases of construction
and their effect on the geotechnical information
needed.
•
Identify engineering analyses to be performed, e.g.,
bearing capacity, settlement, global stability.
•
Identify engineering properties and parameters
required for these analyses.
•
Determine methods to obtain parameters and assess
the validity of such methods for the material type
and construction methods.
•
Determine the number of tests/samples needed and
appropriate locations for them.
10.4.2—Subsurface Exploration
C10.4.2
Subsurface explorations shall be performed to
provide the information needed for the design and
construction of foundations. The extent of exploration
shall be based on variability in the subsurface
conditions, structure type, and any project
requirements that may affect the foundation design or
construction. The exploration program should be
extensive enough to reveal the nature and types of soil
deposits and/or rock formations encountered, the
engineering properties of the soils and/or rocks, the
potential for liquefaction, and the groundwater
conditions. The exploration program should be
sufficient to identify and delineate problematic
subsurface conditions such as karstic formations,
mined out areas, swelling/collapsing soils, existing fill
or waste areas, etc.
Borings should be sufficient in number and depth to
establish a reliable longitudinal and transverse substrata
profile at areas of concern such as at structure
foundation locations and adjacent earthwork locations,
and to investigate any adjacent geologic hazards that
could affect the structure performance.
As a minimum, the subsurface exploration and testing
program shall obtain information adequate to analyze
foundation stability and settlement with respect to:
The performance of a subsurface exploration program
is part of the process of obtaining information relevant for
the design and construction of substructure elements. The
elements of the process that should precede the actual
exploration program include a search and review of
published and unpublished information at and near the site,
a visual site inspection, and design of the subsurface
exploration program. Refer to Mayne et al. (2001) and
Sabatini et al. (2002) for guidance regarding the planning
and conduct of subsurface exploration programs.
The suggested minimum number and depth of borings
are provided in Table 10.4.2-1. While engineering
judgment will need to be applied by a licensed and
experienced geotechnical professional to adapt the
exploration program to the foundation types and depths
needed and to the variability in the subsurface conditions
observed, the intent of Table 10.4.2-1 regarding the
minimum level of exploration needed should be carried
out. The depth of borings indicated in Table 10.4.2-1
performed before or during design should take into account
the potential for changes in the type, size and depth of the
planned foundation elements.
This Table should be used only as a first step in
estimating the number of borings for a particular
design, as actual boring spacings will depend upon the
project type and geologic environment. In areas
underlain by heterogeneous soil deposits and/or rock
formations, it will probably be necessary to drill more
frequently and/or deeper than the minimum guidelines
in Table 10.4.2-1 to capture variations in soil and/or
rock type and to assess consistency across the site area.
For situations where large diameter rock socketed
shafts will be used or where drilled shafts are being
installed in formations known to have large boulders,
or voids such as in karstic or mined areas, it may be
necessary to advance a boring at the location of each
shaft. Even the best and most detailed subsurface
exploration programs may not identify every important
subsurface problem condition if conditions are highly
variable. The goal of the subsurface exploration
program, however, is to reduce the risk of such
problems to an acceptable minimum.
•
Geological formation(s) present,
•
Location and thickness of soil and rock units,
•
Engineering properties of soil and rock units, such
as unit weight, shear strength and compressibility,
•
Groundwater conditions,
•
Ground surface topography, and
•
Local considerations, e.g., liquefiable, expansive or
dispersive soil deposits, underground voids from
solution weathering or mining activity, or slope
instability potential.
2012
Edition
SECTION 10: FOUNDATIONS
Table 10.4.2-1 shall be used as a starting point for
determining the locations of borings. The final
exploration program should be adjusted based on the
variability of the anticipated subsurface conditions as
well as the variability observed during the exploration
program. If conditions are determined to be variable, the
exploration program should be increased relative to the
requirements in Table 10.4.2-1 such that the objective of
establishing a reliable longitudinal and transverse
substrata profile is achieved. If conditions are observed
to be homogeneous or otherwise are likely to have
minimal impact on the foundation performance, and
previous local geotechnical and construction experience
has indicated that subsurface conditions are
homogeneous or otherwise are likely to have minimal
impact on the foundation performance, a reduced
exploration program relative to what is specified in
Table 10.4.2-1 may be considered.
If requested by the Owner or as required by law,
boring and penetration test holes shall be plugged.
Laboratory and/or in-situ tests shall be performed to
determine the strength, deformation, and permeability
characteristics of soils and/or rocks and their suitability
for the foundation proposed.
10-9
In a laterally homogeneous area, drilling or
advancing a large number of borings may be redundant,
since each sample tested would exhibit similar
engineering properties. Furthermore, in areas where soil
or rock conditions are known to be very favorable to the
construction and performance of the foundation type
likely to be used, e.g., footings on very dense soil, and
groundwater is deep enough to not be a factor, obtaining
fewer borings than provided in Table 10.4.2-1 may be
justified. In all cases, it is necessary to understand how
the design and construction of the geotechnical feature
will be affected by the soil and/or rock mass conditions
in order to optimize the exploration.
Borings may need to be plugged due to
requirements by regulatory agencies having jurisdiction
and/or to prevent water contamination and/or surface
hazards.
Parameters derived from field tests, e.g., driven pile
resistance based on cone penetrometer testing, may also
be used directly in design calculations based on
empirical relationships. These are sometimes found to
be more reliable than analytical calculations, especially
in familiar ground conditions for which the empirical
relationships are well established.
2012
Edition
10-10
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 10.4.2-1—Minimum Number of Exploration Points and Depth of Exploration (modified after Sabatini et al., 2002)
Application
Retaining Walls
Shallow
Foundations
Deep
Foundations
Minimum Number of Exploration Points and
Location of Exploration Points
A minimum of one exploration point for each
retaining wall. For retaining walls more than
100 ft in length, exploration points spaced every
100 to 200 ft with locations alternating from in
front of the wall to behind the wall. For
anchored walls, additional exploration points in
the anchorage zone spaced at 100 to 200 ft. For
soil-nailed walls, additional exploration points
at a distance of 1.0 to 1.5 times the height of the
wall behind the wall spaced at 100 to 200 ft.
For substructure, e.g., piers or abutments,
widths less than or equal to 100 ft, a minimum
of one exploration point per substructure. For
substructure widths greater than 100 ft, a
minimum of two exploration points per
substructure. Additional exploration points
should be provided if erratic subsurface
conditions are encountered.
For substructure, e.g., bridge piers or
abutments, widths less than or equal to 100 ft, a
minimum of one exploration point per
substructure. For substructure widths greater
than 100 ft, a minimum of two exploration
points per substructure. Additional exploration
points should be provided if erratic subsurface
conditions are encountered, especially for the
case of shafts socketed into bedrock.
Minimum Depth of Exploration
Investigate to a depth below bottom of wall at least to a
depth where stress increase due to estimated foundation
load is less than ten percent of the existing effective
overburden stress at that depth and between one and two
times the wall height. Exploration depth should be great
enough to fully penetrate soft highly compressible soils,
e.g., peat, organic silt, or soft fine grained soils, into
competent material of suitable bearing capacity, e.g.,
stiff to hard cohesive soil, compact dense cohesionless
soil, or bedrock.
Depth of exploration should be:
•
great enough to fully penetrate unsuitable
foundation soils, e.g., peat, organic silt, or soft fine
grained soils, into competent material of suitable
bearing resistance, e.g., stiff to hard cohesive soil,
or compact to dense cohesionless soil or bedrock ;
•
at least to a depth where stress increase due to
estimated foundation load is less than ten percent of
the existing effective overburden stress at that
depth; and
•
if bedrock is encountered before the depth required
by the second criterion above is achieved,
exploration depth should be great enough to
penetrate a minimum of 10 ft into the bedrock, but
rock exploration should be sufficient to characterize
compressibility of infill material of near-horizontal
to horizontal discontinuities.
Note that for highly variable bedrock conditions, or in
areas where very large boulders are likely, more than
10 ft or rock core may be required to verify that adequate
quality bedrock is present.
In soil, depth of exploration should extend below the
anticipated pile or shaft tip elevation a minimum of 20 ft,
or a minimum of two times the maximum pile group
dimension, whichever is deeper. All borings should
extend through unsuitable strata such as unconsolidated
fill, peat, highly organic materials, soft fine-grained
soils, and loose coarse-grained soils to reach hard or
dense materials.
For piles bearing on rock, a minimum of 10 ft of rock
core shall be obtained at each exploration point location
to verify that the boring has not terminated on a boulder.
For shafts supported on or extending into rock, a
minimum of 10 ft of rock core, or a length of rock core
equal to at least three times the shaft diameter for
isolated shafts or two times the maximum shaft group
dimension, whichever is greater, shall be extended below
the anticipated shaft tip elevation to determine the
physical characteristics of rock within the zone of
foundation influence.
Note that for highly variable bedrock conditions, or in
areas where very large boulders are likely, more than
10 ft or rock core may be required to verify that adequate
quality bedrock is present.
2012
Edition
SECTION 10: FOUNDATIONS
10-11
10.4.3—Laboratory Tests
10.4.3.1—Soil Tests
Laboratory testing should be conducted to provide
the basic data with which to classify soils and to
measure their engineering properties.
When performed, laboratory tests shall be
conducted in accordance with the AASHTO, ASTM, or
Owner-supplied procedures applicable to the design
properties needed.
C10.4.3.1
Laboratory tests of soils may be grouped broadly
into two general classes:
•
Classification or index tests. These may be
performed on either disturbed or undisturbed
samples.
•
Quantitative or performance tests for permeability,
compressibility and shear strength. These tests are
generally performed on undisturbed samples, except
for materials to be placed as controlled fill or
materials that do not have a stable soil-structure,
e.g., cohesionless materials. In these cases, tests
should be performed on specimens prepared in the
laboratory.
Detailed information regarding the types of tests
needed for foundation design is provided in
Geotechnical Engineering Circular #5—Evaluation of
Soil and Rock Properties (Sabatini et al., 2002).
10.4.3.2—Rock Tests
C10.4.3.2
If laboratory strength tests are conducted on intact
rock samples for classification purposes, they should be
considered as upper bound values. If laboratory
compressibility tests are conducted, they should be
considered as lower bound values. Additionally,
laboratory tests should be used in conjunction with field
tests and field characterization of the rock mass to give
estimates of rock mass behavioral characteristics. When
performed, laboratory tests shall be conducted in
accordance with the ASTM or Owner-supplied
procedures applicable to the design properties needed.
Rock samples small enough to be tested in the
laboratory are usually not representative of the entire
rock mass. Laboratory testing of rock is used primarily
for classification of intact rock samples, and, if
performed properly, serves a useful function in this
regard.
Detailed information regarding the types of tests
needed and their use for foundation design is provided
in Geotechnical Engineering Circular #5—Evaluation of
Soil and Rock Properties, April 2002 (Sabatini et al.,
2002).
10.4.4—In-Situ Tests
C10.4.4
In-situ tests may be performed to obtain
deformation and strength parameters of foundation soils
or rock for the purposes of design and/or analysis. Insitu tests should be conducted in soils that do not lend
themselves to undisturbed sampling as a means to
estimate soil design parameters. When performed, insitu tests shall be conducted in accordance with the
appropriate ASTM or AASHTO standards.
Where in-situ test results are used to estimate
design properties through correlations, such correlations
should be well established through long-term
widespread use or through detailed measurements that
illustrate the accuracy of the correlation.
Detailed information on in-situ testing of soils and
rock and their application to geotechnical design can be
found in Sabatini et al. (2002) and Wyllie (1999).
Correlations are in some cases specific to a
geological formation. While this fact does not preclude
the correlation from being useful in other geologic
formations, the applicability of the correlation to those
other formations should be evaluated.
For further discussion, see Article 10.4.6.
2012
Edition
10-12
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
10.4.5—Geophysical Tests
C10.4.5
Geophysical testing should be used only in
combination with information from direct methods of
exploration, such as SPT, CPT, etc. to establish
stratification of the subsurface materials, the profile of
the top of bedrock and bedrock quality, depth to
groundwater, limits of types of soil deposits, the
presence of voids, anomalous deposits, buried pipes, and
depths of existing foundations. Geophysical tests shall
be selected and conducted in accordance with available
ASTM standards. For those cases where ASTM
standards are not available, other widely accepted
detailed guidelines, such as Sabatini et al. (2002),
AASHTO Manual on Subsurface Investigations (1988),
Arman et al. (1997) and Campanella (1994), should be
used.
Geophysical testing offers some notable advantages
and some disadvantages that should be considered
before the technique is recommended for a specific
application. The advantages are summarized as follows:
•
Many geophysical tests are noninvasive and thus,
offer, significant benefits in cases where
conventional drilling, testing and sampling are
difficult, e.g., deposits of gravel, talus deposits, or
where potentially contaminated subsurface soils
may occur.
•
In general, geophysical testing covers a relatively
large area, thus providing the opportunity to
generally characterize large areas in order to optimize
the locations and types of in-situ testing and
sampling. Geophysical methods are particularly well
suited to projects that have large longitudinal extent
compared to lateral extent, e.g., new highway
construction.
•
Geophysical
measurement
assesses
the
characteristics of soil and rock at very small strains,
typically on the order of 0.001 percent, thus
providing information on truly elastic properties,
which are used to evaluate service limit states.
•
For the purpose of obtaining subsurface
information, geophysical methods are relatively
inexpensive when considering cost relative to the
large areas over which information can be obtained.
Some of the disadvantages of geophysical methods
include:
•
Most methods work best for situations in which
there is a large difference in stiffness or
conductivity between adjacent subsurface units.
•
It is difficult to develop good stratigraphic profiling
if the general stratigraphy consists of hard material
over soft material or resistive material over
conductive material.
•
Results are generally interpreted qualitatively and,
therefore, only an experienced engineer or geologist
familiar with the particular testing method can
obtain useful results.
•
Specialized equipment is required (compared to more
conventional subsurface exploration tools).
•
Since evaluation is performed at very low strains, or
no strain at all, information regarding ultimate
strength for evaluation of strength limit states is
only obtained by correlation.
2012
Edition
SECTION 10: FOUNDATIONS
10-13
There are a number of different geophysical in-situ
tests that can be used for stratigraphic information and
determination of engineering properties. These methods
can be combined with each other and/or combined with
the in-situ tests presented in Article 10.4.4 to provide
additional resolution and accuracy. ASTM D6429,
Standard Guide for Selecting Surface Geophysical
Methods, provides additional guidance on selection of
suitable methods.
10.4.6—Selection of Design Properties
10.4.6.1—General
Subsurface soil or rock properties shall be
determined using one or more of the following methods:
•
In-situ testing during the field exploration program,
including consideration of any geophysical testing
conducted,
•
Laboratory testing, and
•
Back analysis of design parameters based on site
performance data.
Local experience, local geologic formation specific
property correlations, and knowledge of local geology,
in addition to broader based experience and relevant
published data, should also be considered in the final
selection of design parameters. If published correlations
are used in combination with one of the methods listed
above, the applicability of the correlation to the specific
geologic formation shall be considered through the use
of local experience, local test results, and/or long-term
experience.
The focus of geotechnical design property
assessment and final selection shall be on the individual
geologic strata identified at the project site.
The design values selected for the parameters
should be appropriate to the particular limit state and its
correspondent calculation model under consideration.
The determination of design parameters for rock
shall take into consideration that rock mass properties
are generally controlled by the discontinuities within the
rock mass and not the properties of the intact material.
Therefore, engineering properties for rock should
account for the properties of the intact pieces and for the
properties of the rock mass as a whole, specifically
considering the discontinuities within the rock mass. A
combination of laboratory testing of small samples,
empirical analysis, and field observations should be
employed to determine the engineering properties of
rock masses, with greater emphasis placed on visual
observations and quantitative descriptions of the rock
mass.
C10.4.6.1
A geologic stratum is characterized as having the
same geologic depositional history and stress history, and
generally has similarities throughout the stratum in terms
of density, source material, stress history, and
hydrogeology. The properties of a given geologic stratum
at a project site are likely to vary significantly from point
to point within the stratum. In some cases, a measured
property value may be closer in magnitude to the
measured property value in an adjacent geologic stratum
than to the measured properties at another point within the
same stratum. However, soil and rock properties for
design should not be averaged across multiple strata.
It should also be recognized that some properties,
e.g., undrained shear strength in normally consolidated
clays, may vary as a predictable function of a stratum
dimension, e.g., depth below the top of the stratum.
Where the property within the stratum varies in this
manner, the design parameters should be developed
taking this variation into account, which may result in
multiple values of the property within the stratum as a
function of a stratum dimension such as depth.
The observational method, or use of back analysis, to
determine engineering properties of soil or rock is often
used with slope failures, embankment settlement or
excessive settlement of existing structures. With landslides
or slope failures, the process generally starts with
determining the geometry of the failure and then
determining the soil/rock parameters or subsurface
conditions that result from a combination of load and
resistance factors that approach 1.0. Often the
determination of the properties is aided by correlations with
index tests or experience on other projects. For
embankment settlement, a range of soil properties is
generally determined based on laboratory performance
testing on undisturbed samples. Monitoring of fill
settlement and pore pressure in the soil during construction
allows the soil properties and prediction of the rate of future
settlement to be refined. For structures such as bridges that
experience unacceptable settlement or retaining walls that
have excessive deflection, the engineering properties of the
soils can sometimes be determined if the magnitudes of the
loads are known. As with slope stability analysis, the
subsurface stratigraphy must be adequately known,
including the history of the groundwater level at the site.
2012
Edition
10-14
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Local geologic formation-specific correlations may
be used if well established by data comparing the
prediction from the correlation to measured high quality
laboratory performance data, or back-analysis from full
scale performance of geotechnical elements affected by
the geologic formation in question.
The Engineer should assess the variability of relevant
data to determine if the observed variability is a result of
inherent variability of subsurface materials and testing
methods or if the variability is a result of significant
variations across the site. Methods to compare soil
parameter variability for a particular project to published
values of variability based on database information of
common soil parameters are presented in Sabatini (2002)
and Duncan (2000). Where the variability is deemed to
exceed the inherent variability of the material and testing
methods, or where sufficient relevant data is not available
to determine an average value and variability, the
Engineer may perform a sensitivity analysis using average
parameters and a parameter reduced by one standard
deviation, i.e., “mean minus 1 sigma,” or a lower bound
value. By conducting analyses at these two potential
values, an assessment is made of the sensitivity of the
analysis results to a range of potential design values. If
these analyses indicate that acceptable results are
provided and that the analyses are not particularly
sensitive to the selected parameters, the Engineer may be
comfortable with concluding the analyses. If, on the other
hand, the Engineer determines that the calculation results
are marginal or that the results are sensitive to the selected
parameter, additional data collection/review and
parameter selection are warranted.
When evaluating service limit states, it is often
appropriate to determine both upper and lower bound
values from the relevant data, since the difference in
displacement of substructure units is often more critical
to overall performance than the actual value of the
displacement for the individual substructure unit.
For strength limit states, average measured values
of relevant laboratory test data and/or in-situ test data
were used to calibrate the resistance factors provided in
Article 10.5, at least for those resistance factors
developed using reliability theory, rather than a lower
bound value. It should be recognized that to be
consistent with how the resistance factors presented in
Article 10.5.5.2 were calibrated, i.e., to average property
values, accounting for the typical variability in the
property, average property values for a given geologic
unit should be selected. However, depending on the
availability of soil or rock property data and the
variability of the geologic strata under consideration, it
may not be possible to reliably estimate the average
value of the properties needed for design. In such cases,
the Engineer may have no choice but to use a more
conservative selection of design parameters to
mitigate the additional risks created by potential
variability or the paucity of relevant data.
2012
Edition
SECTION 10: FOUNDATIONS
10-15
Note that for those resistance factors that were
determined based on calibration by fitting to allowable
stress design, this property selection issue is not
relevant, and property selection should be based on past
practice.
10.4.6.2—Soil Strength
C10.4.6.2.1
10.4.6.2.1—General
The selection of soil shear strength for design
should consider, at a minimum, the following:
•
the rate of construction loading relative to the
hydraulic conductivity of the soil, i.e., drained or
undrained strengths;
•
the effect of applied load direction on the measured
shear strengths during testing;
•
the effect of expected levels of deformation for the
geotechnical structure; and
•
the effect of the construction sequence.
Refer to Sabatini et al. (2002) for additional
guidance on determining which soil strength
parameters are appropriate for evaluating a particular
soil type and loading condition. In general, where
loading is rapid enough and/or the hydraulic
conductivity of the soil is low enough such that excess
pore pressure induced by the loading does not
dissipate, undrained (total) stress parameters should be
used. Where loading is slow enough and/or the
hydraulic conductivity of the soil is great enough such
that excess pore pressures induced by the applied load
dissipate as the load is applied, drained (effective) soil
parameters should be used. Drained (effective) soil
parameters should also be used to evaluate long term
conditions where excess pore pressures have been
allowed to dissipate or where the designer has explicit
knowledge of the expected magnitude and distribution
of the excess pore pressure.
C10 .4.6.2.2
10.4.6.2.2—Undrained Strength of Cohesive Soils
Where possible, laboratory consolidated undrained
(CU) and unconsolidated undrained (UU) testing should
be used to estimate the undrained shear strength, Su,
supplemented as needed with values determined from
in-situ testing. Where collection of undisturbed samples
for laboratory testing is difficult, values obtained from
in-situ testing methods may be used. For relatively thick
deposits of cohesive soil, profiles of Su as a function of
depth should be obtained so that the deposit stress
history and properties can be ascertained.
For design analyses of short-term conditions in
normally to lightly overconsolidated cohesive soils, the
undrained shear strength, Su, is commonly evaluated.
Since undrained strength is not a unique property,
profiles of undrained strength developed using different
testing methods will vary. Typical transportation
project practice entails determination of Su based on
laboratory CU and UU testing and, for cases where
undisturbed sampling is very difficult, field vane
testing. Other in-situ methods can also be used to
estimate the value of Su.
Specific issues that should be considered when
estimating the undrained shear strength are described
below:
•
Strength measurements from hand torvanes, pocket
penetrometers, or unconfined compression tests
should not be solely used to evaluate undrained
shear strength for design analyses. Consolidated
undrained (CU) triaxial tests and in-situ tests should
be used.
2012
Edition
10-16
10.4.6.2.3—Drained Strength of Cohesive Soils
Long-term effective stress strength parameters, c′
and φ′f, of clays should be evaluated by slow
consolidated drained direct shear box tests, consolidated
drained (CD) triaxial tests, or consolidated undrained
(CU) triaxial tests with pore pressure measurements. In
laboratory tests, the rate of shearing should be
sufficiently slow to ensure substantially complete
dissipation of excess pore pressure in the drained tests
or, in undrained tests, complete equalization of pore
pressure throughout the specimen.
10.4.6.2.4—Drained Strength of Granular Soils
The drained friction angle of granular deposits
should be evaluated by correlation to the results of SPT
testing, CPT testing, or other relevant in-situ tests.
Laboratory shear strength tests on undisturbed samples,
if feasible to obtain, or reconstituted disturbed samples,
may also be used to determine the shear strength of
granular soils.
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
•
For relatively deep deposits of cohesive soil, e.g.,
approximately 20 ft depth or more, all available
undrained strength data should be plotted with
depth. The type of test used to evaluate each
undrained strength value should be clearly
identified. Known soil layering should be used so
that trends in undrained strength data can be
developed for each soil layer.
•
Review data summaries for each laboratory strength
test method. Moisture contents of specimens for
strength testing should be compared to moisture
contents of other samples at similar depths.
Significant changes in moisture content will affect
measured undrained strengths. Review boring logs,
Atterberg limits, grain size, and unit weight
measurements to confirm soil layering.
•
CU tests on normally to slightly over consolidated
samples that exhibit disturbance should contain at
least one specimen consolidated to at least 4σp′ to
permit extrapolation of the undrained shear strength
at σp′.
•
Undrained strengths from CU tests correspond to
the effective consolidation pressure used in the test.
This effective stress needs to be converted to the
equivalent depth in the ground.
•
A profile of σp′ (or OCR) should be developed and
used in evaluating undrained shear strength.
•
Correlations for Su based on in-situ test
measurements should not be used for final design
unless they have been calibrated to the specific soil
profile under consideration. Correlations for Su
based on SPT tests should be avoided.
C10.4.6.2.3
The selection of peak, fully softened, or residual
strength for design analyses should be based on a review
of the expected or tolerable displacements of the soil
mass.
The use of a nonzero cohesion intercept (c′) for
long-term analyses in natural materials must be
carefully assessed. With continuing displacements, it is
likely that the cohesion intercept value will decrease to
zero for long-term conditions, especially for highly
plastic clays.
C10.4.6.2.4
Because obtaining undisturbed samples of granular
deposits for laboratory testing is extremely difficult, the
results of in-situ tests are commonly used to develop
estimates of the drained friction angle, φf. If
reconstituted disturbed soil samples and laboratory tests
are used to estimate the drained friction angle, the
reconstituted samples should be compacted to the same
2012
Edition
SECTION 10: FOUNDATIONS
10-17
If SPT N values are used, unless otherwise specified
for the design method or correlation being used, they
shall be corrected for the effects of overburden pressure
determined as:
N 1 = CN N
(10.4.6.2.4-1)
N1 =
SPT blow count corrected for overburden
pressure, σ′v (blows/ft)
CN =
[0.77 log10 (40/σ′v)], and CN < 2.0
σ′v =
vertical effective stress (ksf)
N
=
uncorrected SPT blow count (blows/ft)
SPT N values should also be corrected for hammer
efficiency, if applicable to the design method or
correlation being used, determined as:
N 60 = ( ER / 60%) N
(10.4.6.2.4-2)
where:
N60 =
SPT blow count corrected
efficiency (blows/ft)
ER =
hammer efficiency expressed as percent of
theoretical free fall energy delivered by the
hammer system actually used
N
=
relative density estimated from the available in-situ data.
The test specimen should be large enough to allow the
full grain size range of the soil to be included in the
specimen. This may not always be possible, and if not
possible, it should be recognized that the shear strength
measured would likely be conservative.
A method using the results of SPT testing is
presented. Other in-situ tests such as CPT and DMT may
be used. For details on determination of φf from these
tests, refer to Sabatini et al. (2002).
for
hammer
uncorrected SPT blow count (blows/ft)
The use of automatic trip hammers is increasing. In
order to use correlations based on standard rope and
cathead hammers, the SPT N values must be corrected to
reflect the greater energy delivered to the sampler by
these systems.
Hammer efficiency (ER) for specific hammer
systems used in local practice may be used in lieu of the
values provided. If used, specific hammer system
efficiencies shall be developed in general accordance
with ASTM D4945 for dynamic analysis of driven piles
or other accepted procedure.
The following values for ER may be assumed if
hammer specific data are not available, e.g., from older
boring logs:
ER = 60 percent for conventional drop hammer using
rope and cathead
ER = 80 percent for automatic trip hammer
When SPT blow counts have been corrected for
both overburden effects and hammer efficiency effects,
the resulting corrected blow count shall be denoted as
N160, determined as:
N160 = C N N 60
(10.4.6.2.4-3)
The drained friction angle of granular deposits
should be determined based on the following
correlation.
Table 10.4.6.2.4-1—Correlation of SPT N160 Values to
Drained Friction Angle of Granular Soils (modified after
Bowles, 1977)
N160
<4
4
10
30
50
φf
25–30
27–32
30–35
35–40
38–43
Corrections for rod length, hole size, and use of a
liner may also be made if appropriate. In general, these
are only significant in unusual cases or where there is
significant variation from standard procedures. These
corrections may be significant for evaluation of
liquefaction. Information on these additional corrections
may be found in Youd and Idriss (1997).
The N160-φf correlation used is modified after
Bowles (1977). The correlation of Peck, Hanson, and
Thornburn (1974) falls within the ranges specified.
Experience should be used to select specific values
within the ranges. In general, finer materials or materials
with significant silt-sized material will fall in the lower
portion of the range. Coarser materials with less than
five percent fines will fall in the upper portion of the
ranges. The geologic history and angularity of the
particles may also need to be considered when selecting
a value for φf.
Care should be exercised when using other
correlations of SPT results to soil parameters. Some
published correlations are based on corrected values
2012
Edition
10-18
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
For gravels and rock fill materials where SPT
testing is not reliable, Figure 10.4.6.2.4-1 should be used
to estimate the drained friction angle.
Rock Fill Grade
A
B
C
D
E
Particle Unconfined
Compressive Strength
(ksf)
>4610
3460– 4610
2590– 3460
1730– 2590
≤1730
(N160) and some are based on uncorrected values (N).
The designer should ascertain the basis of the correlation
and use either N160 or N as appropriate.
Care should also be exercised when using SPT blow
counts to estimate soil shear strength if in soils with
coarse gravel, cobbles, or boulders. Large gravels,
cobbles, or boulders could cause the SPT blow counts to
be unrealistically high.
The secant friction angle derived from the
procedure to estimate the drained friction angle of
gravels and rock fill materials depicted in
Figure 10.4.6.2.4-1 is based on a straight line from the
origin of a Mohr diagram to the intersection with the
strength envelope at the effective normal stress. Thus
the angle derived is applicable only to analysis of field
conditions subject to similar normal stresses. See
Terzaghi, Peck, and Mesri (1996) for additional details
regarding this procedure.
Figure 10.4.6.2.4-1—Estimation of Drained Friction Angle
of Gravels and Rock Fills (modified after Terzaghi, Peck,
and Mesri, 1996)
10.4.6.3—Soil Deformation
Consolidation parameters Cc, Cr, Cα should be
determined from the results of one-dimensional
consolidation tests. To assess the potential variability in
the settlement estimate, the average, upper and lower
bound values obtained from testing should be
considered.
C10.4.6.3
It is important to understand whether the values
obtained are computed based on a void ratio definition
or a strain definition. Computational methods vary for
each definition.
For preliminary analyses or where accurate
prediction of settlement is not critical, values obtained
2012
Edition
SECTION 10: FOUNDATIONS
Preconsolidation stress may be determined from
one-dimensional consolidation tests and in-situ tests.
Knowledge of the stress history of the soil should be
used to supplement data from laboratory and/or in-situ
tests, if available.
The coefficient of consolidation, cv, should be
determined from the results of one-dimensional
consolidation tests. The variability in laboratory
determination of cv results should be considered in the
final selection of the value of cv to be used for design.
Where evaluation of elastic settlement is critical to
the design of the foundation or selection of the
foundation type, in-situ methods such as PMT or DMT
for evaluating the modulus of the stratum should be
used.
10-19
from correlations to index properties may be used. Refer
to Sabatini et al. (2002) for discussion of the various
correlations available. If correlations for prediction of
settlement are used, their applicability to the specific
geologic formation under consideration should be
evaluated.
A profile of σp′, or OCR = σp′/σo′, with depth
should be developed for the site for design applications
where the stress history could have a significant impact
on the design properties selected and the performance of
the foundation. As with consolidation properties, an
upper and lower bound profile should be developed
based on laboratory tests and plotted with a profile
based on particular in-situ test(s), if used. It is
particularly important to accurately compute
preconsolidation stress values for relatively shallow
depths where in-situ effective stresses are low. An
underestimation of the preconsolidation stress at shallow
depths will result in overly conservative estimates of
settlement for shallow soil layers.
Due to the numerous simplifying assumptions
associated with conventional consolidation theory, on
which the coefficient of consolidation is based, it is
unlikely that even the best estimates of cv from highquality laboratory tests will result in predictions of time
rate of settlement in the field that are significantly better
than a prediction within one order of magnitude. In
general, the in-situ value of cv is larger than the value
measured in the laboratory test. Therefore, a rational
approach is to select average, upper, and lower bound
values for the appropriate stress range of concern for the
design application. These values should be compared to
values obtained from previous work performed in the
same soil deposit. Under the best-case conditions, these
values should be compared to values computed from
measurements of excess pore pressures or settlement
rates during construction of other structures.
CPTu tests in which the pore pressure dissipation
rate is measured may be used to estimate the field
coefficient of consolidation.
For preliminary analyses or where accurate
prediction of settlement is not critical, values obtained
from correlations to index properties presented in
Sabatini et al. (2002) may be used.
For preliminary design or for final design where the
prediction of deformation is not critical to structure
performance, i.e., the structure design can tolerate the
potential inaccuracies inherent in the correlations. The
elastic properties (Es, ν) of a soil may be estimated from
empirical relationships presented in Table C10.4.6.3-1.
The specific definition of Es is not always consistent
for the various correlations and methods of in-situ
measurement. See Sabatini et al. (2002) for additional
details regarding the definition and determination of Es.
An alternative method of evaluating the equivalent
elastic modulus using measured shear wave velocities is
presented in Sabatini et al. (2002).
2012
Edition
10-20
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table C10.4.6.3-1—Elastic Constants of Various Soils
(modified after U.S. Department of the Navy, 1982;
Bowles, 1988)
Soil Type
Clay:
Soft sensitive
Medium stiff
to stiff
Very stiff
Loess
Silt
Fine Sand:
Loose
Medium dense
Dense
Sand:
Loose
Medium dense
Dense
Gravel:
Loose
Medium dense
Dense
Typical Range
of Young’s
Modulus
Values, Es
(ksi)
0.347–2.08
2.08–6.94
6.94–13.89
2.08–8.33
0.278–2.78
1.11–1.67
1.67–2.78
2.78–4.17
Poisson’s
Ratio, ν (dim)
0.4–0.5
(undrained)
0.1–0.3
0.3–0.35
0.25
1.39–4.17
4.17–6.94
6.94–11.11
0.20–0.36
4.17–11.11
11.11–13.89
13.89–27.78
0.20–0.35
0.30–0.40
0.30–0.40
Estimating Es from SPT N Value
Soil Type
Es (ksi)
Silts, sandy silts, slightly cohesive
mixtures
0.056 N160
Clean fine to medium sands and
slightly silty sands
0.097 N160
Coarse sands and sands with little
gravel
0.139 N160
Sandy gravel and gravels
0.167 N160
Estimating Es from qc (static cone resistance)
Sandy soils
0.028qc
2012
Edition
SECTION 10: FOUNDATIONS
10-21
The modulus of elasticity for normally consolidated
granular soils tends to increase with depth. An
alternative method of defining the soil modulus for
granular soils is to assume that it increases linearly with
depth starting at zero at the ground surface in
accordance with the following equation:
Es = nh × z
(C10.4.6.3-1)
where:
Es =
nh =
z
=
the soil modulus at depth z (ksi)
rate of increase of soil modulus with depth as
defined in Table C10.4.6.3-2 (ksi/ft)
depth below the ground surface (ft)
Table C10.4.6.3-2—Rate of Increase of Soil Modulus with
Depth nh (ksi/ft) for Sand
The potential for soil swell that may result in uplift
on deep foundations or heave of shallow foundations
should be evaluated based on Table 10.4.6.3-1.
Consistency
Loose
Medium
Dense
Dry or Moist
0.417
1.11
2.78
Submerged
0.208
0.556
1.39
The formulation provided in Eq. C10.4.6.3-1 is used
primarily for analysis of lateral response or buckling of
deep foundations.
Table 10.4.6.3-1—Method for Identifying Potentially
Expansive Soils (Reese and O'Neill, 1988)
Liquid
Limit
LL
(%)
>60
50–60
<50
Plastic
Limit
PL
(%)
>35
25–35
<25
Soil
Suction
(ksf)
>8
3–8
<3
Potential
Swell
(%)
>1.5
0.5–1.5
<0.5
Potential
Swell
Classification
High
Marginal
Low
10.4.6.4—Rock Mass Strength
The strength of intact rock material should be
determined using the results of unconfined compression
tests on intact rock cores, splitting tensile tests on intact
rock cores, or point load strength tests on intact
specimens of rock.
The rock should be classified using the rock mass
rating system (RMR) as described in Table 10.4.6.4-1.
For each of the five parameters in the Table, the relative
rating based on the ranges of values provided should be
evaluated. The rock mass rating (RMR) should be
determined as the sum of all five relative ratings. The
RMR should be adjusted in accordance with the criteria
in Table 10.4.6.4-2. The rock classification should be
determined in accordance with Table 10.4.6.4-3.
C10.4.6.4
Because of the importance of the discontinuities in
rock, and the fact that most rock is much more
discontinuous than soil, emphasis is placed on visual
assessment of the rock and the rock mass.
Other methods for assessing rock mass strength,
including in-situ tests or other visual systems that have
proven to yield accurate results may be used in lieu of
the specified method.
2012
Edition
10-22
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 10.4.6.4-1—Geomechanics Classification of Rock Masses
Parameter
1
Strength of
intact rock
material
Ranges of Values
Point load
strength index
Uniaxial
compressive
strength
Relative Rating
Drill core quality RQD
Relative Rating
3
Spacing of joints
Relative Rating
45–85
ksf
1080–
2160 ksf
20–45
ksf
520–
1080 ksf
12
7
4
4
Relative Rating
For this low range, uniaxial
compressive test is preferred
215–520
70–215
20–70 ksf
ksf
ksf
2
1
0
90% to 100%
20
75% to 90%
17
50% to 75%
13
25% to 50%
8
<25%
3
>10 ft
30
3–10 ft
25
1–3 ft
20
2 in.–1 ft
10
<2 in.
5
• Very rough
• Slightly rough • Slightly
rough
surfaces
surfaces
surfaces
• Not
• Separation
continuous
<0.05 in.
• Separation
<0.05 in.
• No separation • Hard joint wall
rock
•
Soft
joint
• Hard joint
wall rock
wall rock
Condition of joints
Groundwater
conditions
(use one of the
three evaluation
criteria as
appropriate to
the method of
exploration)
>4320 ksf
85–175
ksf
2160–
4320 ksf
15
2
5
>175 ksf
• Soft gouge
>0.2 in.
thick or
• Joints open
>0.2 in.
• Continuous
joints
25
20
Inflow per
30 ft tunnel
length
None
<400 gal./hr.
400–2000 gal./hr.
>2000 gal./hr.
Ratio = joint
water
pressure/
major
principal
stress
0
0.0–0.2
0.2–0.5
>0.5
Completely Dry
Moist only
(interstitial water)
Water under
moderate pressure
Severe water
problems
10
7
4
0
General
Conditions
Relative Rating
12
• Slicken-sided
surfaces or
• Gouge <0.2 in.
thick or
• Joints open
0.05–0.2 in.
• Continuous
joints
6
0
Table 10.4.6.4-2—Geomechanics Rating Adjustment for Joint Orientations
Strike and Dip Orientations
of Joints
Tunnels
Ratings
Foundations
Slopes
Very
Favorable
0
0
0
Favorable
–2
–2
–5
Fair
–5
–7
–25
Unfavorable
–10
–15
–50
Very Unfavorable
–12
–25
–60
2012
Edition
SECTION 10: FOUNDATIONS
10-23
Table 10.4.6.4-3—Geomechanics Rock Mass Classes Determined from Total Ratings
RMR Rating
Class No.
Description
100–81
I
Very good rock
80–61
II
Good rock
The shear strength of fractured rock masses should
be evaluated using the Hoek and Brown criteria, in
which the shear strength is represented as a curved
envelope that is a function of the uniaxial compressive
strength of the intact rock, qu, and two dimensionless
constants m and s. The values of m and s as defined in
Table 10.4.6.4-4 should be used.
The shear strength of the rock mass should be
determined as:
τ = ( cot φ′i − cos φ′i ) m
qu
8
(10.4.6.4-1)
in which:
−1
−3
2
2
-1
−1
φ′i = tan 4 h cos 30 + 0.33 sin h 2 − 1
h = 1+
16 ( mσ′n + squ )
60–41
III
Fair rock
40–21
IV
Poor rock
<20
V
Very poor rock
This method was developed by Hoek (1983) and
Hoek and Brown (1988, 1997). Note that the
instantaneous cohesion at a discrete value of normal
stress can be taken as:
ci = τ − σ′n tan φ′i
(C10.4.6.4-1)
The instantaneous cohesion and instantaneous
friction angle define a conventional linear Mohr
envelope at the normal stress under consideration. For
normal stresses significantly different than that used to
compute the instantaneous values, the resulting shear
strength will be unconservative. If there is considerable
variation in the effective normal stress in the zone of
concern, consideration should be given to subdividing
the zone into areas where the normal stress is relative
constant and assigning separate strength parameters to
each zone. Alternatively, the methods of Hoek (1983)
may be used to compute average values for the range of
normal stresses expected.
2
(3m qu )
where:
τ
=
the shear strength of the rock mass (ksf)
φ′i
=
the instantaneous friction angle of the rock
mass (degrees)
qu
=
average unconfined compressive strength
of rock core (ksf)
σ′n
=
effective normal stress (ksf)
m, s
=
constants from Table 10.4.6.4-4 (dim)
2012
Edition
10-24
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 10.4.6.4-4—Approximate Relationship between Rock-Mass Quality and Material Constants Used in Defining
Nonlinear Strength (Hoek and Brown, 1988)
Rock Quality
INTACT ROCK SAMPLES
Laboratory size specimens free from
discontinuities.
CSIR rating: RMR = 100
VERY GOOD QUALITY ROCK MASS
Tightly interlocking undisturbed rock
with unweathered joints at 3–10 ft
CSIR rating: RMR = 85
GOOD QUALITY ROCK MASS
Fresh to slightly weathered rock, slightly
disturbed with joints at 3–10 ft
CSIR rating: RMR = 65
FAIR QUALITY ROCK MASS
Several sets of moderately weathered
joints spaced at 1–3 ft
CSIR rating: RMR = 44
POOR QUALITY ROCK MASS
Numerous weathered joints at 2 to 12 in.;
some gouge. Clean compacted waste
rock.
CSIR rating: RMR = 23
VERY POOR QUALITY ROCK MASS
Numerous heavily weathered joints
spaced <2 in. with gouge. Waste rock
with fines.
CSIR rating: RMR = 3
Constants
Rock Type
A = Carbonate rocks with well developed crystal cleavage—
dolomite, limestone and marble
B = Lithified argrillaceous rocks—mudstone, siltstone, shale
and slate (normal to cleavage)
C = Arenaceous rocks with strong crystals and poorly developed
crystal cleavage—sandstone and quartzite
D = Fine grained polyminerallic igneous crystalline rocks—
andesite, dolerite, diabase and rhyolite
E = Coarse grained polyminerallic igneous & metamorphic
crystalline rocks—amphibolite, gabbro gneiss, granite,
norite, quartz-diorite
A
B
C
D
E
m
s
7.00
1.00
10.00
1.00
15.00
1.00
17.00
1.00
25.00
1.00
m
s
2.40
0.082
3.43
0.082
5.14
0.082
5.82
0.082
8.567
0.082
m
s
0.575
0.00293
0.821
0.00293
1.231
0.00293
1.395
0.00293
2.052
0.00293
m
s
0.128
0.00009
0.183
0.00009
0.275
0.00009
0.311
0.00009
0.458
0.00009
m
s
0.029
3 × 10 –6
0.041
3 × 10 –6
0.061
3 × 10 –6
0.069
3 × 10 –6
0.102
3 × 10 –6
m
s
0.007
1 × 10 –7
0.010
1 × 10 –7
0.015
1 × 10 –7
0.017
1 × 10 –7
0.025
1 × 10 –7
Where it is necessary to evaluate the strength of a
single discontinuity or set of discontinuities, the strength
along the discontinuity should be determined as follows:
•
For smooth discontinuities, the shear strength is
represented by a friction angle of the parent rock
material. To evaluate the friction angle of this type
of discontinuity surface for design, direct shear tests
on samples should be performed. Samples should
be formed in the laboratory by cutting samples of
intact core.
•
For rough discontinuities the nonlinear criterion of
Barton (1976) should be applied.
The range of typical friction angles provided in
Table C10.4.6.4-1 may be used in evaluating measured
values of friction angles for smooth joints.
2012
Edition
SECTION 10: FOUNDATIONS
10-25
Table C10.4.6.4-1—Typical Ranges of Friction Angles for
Smooth Joints in a Variety of Rock Types (modified after
Barton, 1976; Jaeger and Cook, 1976)
Rock Class
Low Friction
Friction Angle
Range
20–27°
Medium
Friction
27–34°
High Friction
34–40°
Typical Rock
Types
Schists (high
mica content),
shale, marl
Sandstone,
siltstone, chalk,
gneiss, slate
Basalt, granite,
limestone,
conglomerate
Note: Values assume no infilling and little relative movement
between joint faces.
When a major discontinuity with a significant
thickness of infilling is to be investigated, the shear
strength will be governed by the strength of the infilling
material and the past and expected future displacement
of the discontinuity. Refer to Sabatini et al. (2002) for
detailed procedures to evaluate infilled discontinuities.
C10.4.6.5
10.4.6.5—Rock Mass Deformation
The elastic modulus of a rock mass (Em) shall be
taken as the lesser of the intact modulus of a sample of
rock core (Ei) or the modulus determined from one of
the following equations:
RMR −10
Em = 145 10
40
(10.4.6.5-1)
where:
Em
=
Elastic modulus of the rock mass (ksi)
Em
≤
Ei
Ei
=
Elastic modulus of intact rock (ksi)
RMR
=
Rock
mass
rating
Article 10.4.6.4.
or
Em
Ei
Ei
Em =
specified
Table 10.4.6.5-1 was developed by O’Neill and
Reese (1999) based on a reanalysis of the data presented
by Carter and Kulhawy (1988) for the purposes of
estimating side resistance of shafts in rock.
Preliminary estimates of the elastic modulus of
intact rock may be made from Table C10.4.6.5-1. Note
that some of the rock types identified in the Table are
not present in the U.S.
It is extremely important to use the elastic modulus
of the rock mass for computation of displacements of
rock materials under applied loads. Use of the intact
modulus will result in unrealistic and unconservative
estimates.
in
(10.4.6.5-2)
2012
Edition
10-26
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
where:
Em
=
Elastic
(ksi)
modulus
of
the
rock
mass
Em/Ei
=
Reduction factor determined
Table 10.4.6.5-1 (dim)
Ei
=
Elastic modulus of intact rock from tests
(ksi)
from
For critical or large structures, determination of
rock mass modulus (Em) using in-situ tests may be
warranted. Refer to Sabatini et al. (2002) for
descriptions of suitable in-situ tests.
Table 10.4.6.5-1—Estimation of Em Based on RQD (after O’Neill and Reese, 1999)
RQD
(percent)
100
70
50
20
Closed Joints
1.00
0.70
0.15
0.05
Em/Ei
Open Joints
0.60
0.10
0.10
0.05
Table C10.4.6.5-1—Summary of Elastic Moduli for Intact Rock (modified after Kulhawy, 1978)
Rock Type
Granite
Diorite
Gabbro
Diabase
Basalt
Quartzite
Marble
Gneiss
Slate
Schist
Phyllite
Sandstone
Siltstone
Shale
Limestone
Dolostone
No. of Values
26
3
3
7
12
7
14
13
11
13
3
27
5
30
30
17
No. of Rock
Types
26
3
3
7
12
7
13
13
2
12
3
19
5
14
30
16
Maximum
14.5
16.2
12.2
15.1
12.2
12.8
10.7
11.9
3.79
10.0
2.51
5.68
4.76
5.60
13.0
11.4
Poisson’s ratio for rock should be determined from
tests on intact rock core.
Elastic Modulus, Ei
(ksi ×103)
Minimum
Mean
0.93
7.64
2.48
7.45
9.8
11.0
10.0
12.8
4.20
8.14
5.29
9.59
0.58
6.18
4.13
8.86
0.35
1.39
0.86
4.97
1.25
1.71
0.09
2.13
0.38
2.39
0.001
1.42
0.65
5.7
0.83
4.22
Standard
Deviation
(ksi × 103)
3.55
6.19
0.97
1.78
2.60
2.32
2.49
2.31
0.96
3.18
0.57
1.19
1.65
1.45
3.73
3.44
Where tests on rock core are not practical, Poisson’s
ratio may be estimated from Table C10.4.6.5-2.
2012
Edition
SECTION 10: FOUNDATIONS
10-27
Table C10.4.6.5-2—Summary of Poisson's Ratio for Intact Rock (modified after Kulhawy, 1978)
Rock Type
Granite
Gabbro
Diabase
Basalt
Quartzite
Marble
Gneiss
Schist
Sandstone
Siltstone
Shale
Limestone
Dolostone
No. of Values
22
3
6
11
6
5
11
12
12
3
3
19
5
No. of
Rock Types
22
3
6
11
6
5
11
11
9
3
3
19
5
Maximum
0.39
0.20
0.38
0.32
0.22
0.40
0.40
0.31
0.46
0.23
0.18
0.33
0.35
10.4.6.6—Erodibility of Rock
STATES
AND
Standard
Deviation
0.08
0.02
0.06
0.05
0.05
0.08
0.09
0.08
0.11
0.06
0.06
0.06
0.08
C10.4.6.6
Consideration should be given to the physical
characteristics of the rock and the condition of the rock
mass when determining a rock’s susceptibility to erosion
in the vicinity of bridge foundations. Physical
characteristics that should be considered in the
assessment of erodibility include cementing agents,
mineralogy, joint spacing, and weathering.
10.5—LIMIT
FACTORS
Poisson's Ratio, ν
Minimum
Mean
0.09
0.20
0.16
0.18
0.20
0.29
0.16
0.23
0.08
0.14
0.17
0.28
0.09
0.22
0.02
0.12
0.08
0.20
0.09
0.18
0.03
0.09
0.12
0.23
0.14
0.29
There is no consensus on how to determine
erodibility of rock masses near bridge foundations. Refer
to Richardson and Davis (2001) “Evaluating Scour at
Bridges—Fourth Edition”, Mayne et al. (2001), Appendix
M for guidance on two proposed methods. The first
method was proposed in an FHWA memorandum of July
1991 and consists of evaluating various rock index
properties. The second method is documented in Smith
(1994) “Preliminary Procedure to Evaluate Scour in
Bedrock” which uses the erodibility index proposed by G.
W. Annandale. The Engineer should consider the
appropriateness of these two methods when determining
the potential for a rock mass to scour.
RESISTANCE
10.5.1—General
The limit states shall be as specified
Article 1.3.2; foundation-specific provisions
contained in this Section.
Foundations shall be proportioned so that
factored resistance is not less than the effects of
factored loads specified in Section 3.
in
are
the
the
10.5.2—Service Limit States
10.5.2.1—General
Foundation design at the service limit state shall
include:
•
Settlements,
C10.5.2.1
In bridges where the superstructure and substructure
are not integrated, settlement corrections can be made
by jacking and shimming bearings. Article 2.5.2.3
requires jacking provisions for these bridges.
2012
Edition
10-28
•
Horizontal movements,
•
Overall stability, and
•
Scour at the design flood.
Consideration of foundation movements shall be
based upon structure tolerance to total and differential
movements, rideability and economy. Foundation
movements shall include all movement from settlement,
horizontal movement, and rotation.
Bearing resistance estimated using the presumptive
allowable bearing pressure for spread footings, if used,
shall be applied only to address the service limit state.
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The cost of limiting foundation movements should
be compared with the cost of designing the
superstructure so that it can tolerate larger movements or
of correcting the consequences of movements through
maintenance to determine minimum lifetime cost. The
Owner may establish more stringent criteria.
The design flood for scour is defined in
Article 2.6.4.4.2, and is specified in Article 3.7.5 as
applicable at the service limit state.
Presumptive bearing pressures were developed for
use with working stress design. These values may be
used for preliminary sizing of foundations, but should
generally not be used for final design. If used for final
design, presumptive values are only applicable at service
limit states.
10.5.2.2—Tolerable Movements and Movement
Criteria
Foundation movement criteria shall be consistent
with the function and type of structure, anticipated
service life, and consequences of unacceptable
movements on structure performance. Foundation
movement shall include vertical, horizontal, and
rotational movements. The tolerable movement criteria
shall be established by either empirical procedures or
structural analyses, or by consideration of both.
Foundation settlement shall be investigated using
all applicable loads in the Service I Load Combination
specified in Table 3.4.1-1. Transient loads may be
omitted from settlement analyses for foundations
bearing on or in cohesive soil deposits that are subject to
time-dependant consolidation settlements.
All applicable service limit state load combinations
in Table 3.4.1-1 shall be used for evaluating horizontal
movement and rotation of foundations.
Horizontal movement criteria should be established
at the top of the foundation based on the tolerance of the
structure to lateral movement, with consideration of the
column length and stiffness.
C10.5.2.2
Experience has shown that bridges can and often do
accommodate more movement and/or rotation than
traditionally allowed or anticipated in design. Creep,
relaxation, and redistribution of force effects
accommodate these movements. Some studies have
been made to synthesize apparent response. These
studies indicate that angular distortions between
adjacent foundations greater than 0.008 rad. in simple
spans and 0.004 rad. in continuous spans should not be
permitted in settlement criteria (Moulton et al., 1985;
DiMillio, 1982; Barker et al., 1991). Other angular
distortion limits may be appropriate after consideration
of:
•
cost of mitigation through larger foundations,
realignment or surcharge,
•
rideability,
•
aesthetics, and
•
safety.
Rotation movements should be evaluated at the top
of the substructure unit in plan location and at the deck
elevation.
Tolerance of the superstructure to lateral movement
will depend on bridge seat or joint widths, bearing
type(s), structure type, and load distribution effects.
10.5.2.3—Overall Stability
The evaluation of overall stability of earth slopes
with or without a foundation unit shall be investigated at
the service limit state as specified in Article 11.6.2.3.
2012
Edition
SECTION 10: FOUNDATIONS
10.5.2.4—Abutment Transitions
Vertical and horizontal movements caused by
embankment loads behind bridge abutments shall be
investigated.
10-29
C10.5.2.4
Settlement of foundation soils induced by
embankment loads can result in excessive movements of
substructure elements. Both short and long term
settlement potential should be considered.
Settlement of improperly placed or compacted
backfill behind abutments can cause poor rideability and
a possibly dangerous bump at the end of the bridge.
Guidance for proper detailing and material requirements
for abutment backfill is provided in Cheney and Chassie
(2000).
Lateral earth pressure behind and/or lateral squeeze
below abutments can also contribute to lateral
movement of abutments and should be investigated, if
applicable.
10.5.3—Strength Limit States
10.5.3.1—General
Design of foundations at strength limit states shall
include consideration of the nominal geotechnical and
structural resistances of the foundation elements. Design
at strength limit states shall not consider the
deformations required to mobilize the nominal
resistance, unless a definition of failure based on
deformation is specified.
The design of all foundations at the strength limit
state shall consider:
•
Structural resistance and
•
Loss of lateral and vertical support due to scour at
the design flood event.
10.5.3.2—Spread Footings
The design of spread footings at the strength limit
state shall also consider:
•
Nominal bearing resistance,
•
Overturning or excessive loss of contact,
•
Sliding at the base of footing, and
•
constructability.
C10.5.3.1
For the purpose of design at strength limit states,
the nominal resistance is considered synonymous with
the ultimate capacity of an element as previously
defined under allowable stress design, i.e., AASHTO
(2002).
For design of foundations such as piles or drilled
shafts that may be based directly on static load tests, or
correlation to static load tests, the definition of failure
may include a deflection-limited criteria.
Structural resistance includes checks for axial,
lateral and flexural resistance.
The design event for scour is defined in Section 2
and is specified in Article 3.7.5 as applicable at the
strength limit state.
C10.5.3.2
The designer should consider whether special
construction methods are required to bear a spread
footing at the design depth. Consideration should be
given to the potential need for shoring, cofferdams,
seals, and/or dewatering. Basal stability of excavations
should be evaluated, particularly if dewatering or
cofferdams are required.
Effort should be made to identify the presence of
expansive/collapsible soils in the vicinity of the footing.
If present, the structural design of the footing should be
modified to accommodate the potential impact to the
performance
of
the
structure,
or
the
expansive/collapsible soils should be removed or
otherwise remediated. Special conditions such as the
presence of karstic formations or mines should also be
evaluated, if present.
2012
Edition
10-30
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
10.5.3.3—Driven Piles
The design of pile foundations at the strength limit
state shall also consider:
•
Axial compression resistance for single piles,
•
Pile group compression resistance,
•
Uplift resistance for single piles,
•
Uplift resistance for pile groups,
•
Pile punching failure into a weaker stratum below
the bearing stratum,
•
Single pile and pile group lateral resistance, and
•
Constructability, including pile drivability.
10.5.3.4—Drilled Shafts
The design of drilled shaft foundations at the
strength limit state shall also consider:
•
Axial compression resistance for single drilled
shafts,
•
Shaft group compression resistance,
•
Uplift resistance for single shafts,
•
Uplift resistance for shaft groups,
•
Single shaft and shaft group lateral resistance,
•
Shaft punching failure into a weaker stratum below
the bearing stratum, and
•
Constructability, including method(s) of shaft
construction.
10.5.3.5—Micropiles
The design of micropile foundations at the strength
limit state shall also consider:
•
Axial compression resistance for single micropile,
•
Micropile group compression resistance,
•
Uplift resistance for single micropile,
•
Uplift resistance for micropile groups,
•
Micropile group punching failure into a weaker
stratum below the bearing stratum, and single
micropile punching failure where tip resistance is
considered,
•
Single micropile and micropile group lateral
resistance, and
•
Constructibility, including method(s) of micropile
construction.
C10.5.3.3
The commentary in Article C10.5.3.2 is applicable
if a pile cap is needed.
For pile foundations, as part of the evaluation for
the strength limit states identified herein, the effects of
downdrag, soil setup or relaxation, and buoyancy due to
groundwater should be evaluated.
C10.5.3.4
See commentary in Articles C10.5.3.2 and
C10.5.3.3.
The design of drilled shafts for each of these limit
states should include the effects of the method of
construction, including construction sequencing,
whether the shaft will be excavated in the dry or if wet
methods must be used, as well as the need for temporary
or permanent casing to control caving ground
conditions. The design assumptions regarding
construction methods must carry through to the contract
documents to provide assurance that the geotechnical
and structural resistance used for design will be
provided by the constructed product.
C10.5.3.5
The commentary in Article C10.5.3.2 is applicable
if a pile cap is needed.
The design of micropiles for each of these limit
states should include the effects of the method of
construction for the micropile type to be constructed.
The design assumptions regarding construction methods
must carry through to the contract documents to provide
assurance that the geotechnical and structural resistance
used for design will be provided by the constructed
product.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 10: FOUNDATIONS
10-31
10.5.4—Extreme Events Limit States
10.5.4.1—Extreme Events Design
C10.5.4.1
Foundations shall be designed for extreme events as
applicable.
Extreme events include the check flood for scour,
vessel and vehicle collision, seismic loading, and other
site-specific situations that the Engineer determines
should be included. Appendix A10 gives additional
guidance regarding seismic analysis and design.
C10.5.4.2
10.5.4.2—Liquefaction Design Requirements
A liquefaction assessment shall be conducted for
Seismic Zones 3 and 4 if both of the following
conditions are present:
•
Ground Water Level—The groundwater level
anticipated at the site is within 50 ft of the existing
ground surface or the final ground surface,
whichever is lower.
•
Soil Characteristics—Low plasticity silts and sands
within the upper 75 ft are characterized by one of the
following conditions: (1) the corrected standard
penetration test (SPT) blow count, (N1)60, is less than
or equal to 25 blows/ft in sand and nonplastic silt
layers, (2) the corrected cone penetration test (CPT)
tip resistance, qciN, is less than or equal to 150 in
sand, and nonplastic silt layers, (3) the normalized
shear wave velocity, Vs1, is less than 660 fps, or (4) a
geologic unit is present at the site that has been
observed to liquefy in past earthquakes.
Where loose to very loose saturated sands are
within the subsurface soil profile such that liquefaction
of these soils could impact the stability of the structure,
the potential for liquefaction in Seismic Zone 2 should
also be considered.
For sites that require an assessment of liquefaction,
the potential effects of liquefaction on soils and
foundations shall be evaluated. The assessment shall
consider the following effects of liquefaction:
•
Loss in strength in the liquefied layer or layers,
•
Liquefaction-induced ground settlement,
•
Flow failures,
instability.
lateral
spreading,
and
slope
For sites where liquefaction occurs around bridge
foundations, bridges should be analyzed and designed in
two configurations as follows:
•
Nonliquefied Configuration—The structure should
be analyzed and designed, assuming no liquefaction
occurs, using the ground response spectrum
appropriate for the site soil conditions in a
nonliquefied state.
All of the following general conditions are
necessary for liquefaction to occur:
•
A sustained ground acceleration that is large enough
and acting over a long enough period of time to
develop excess pore-water pressure, thereby
reducing effective stress and soil strength.
•
Predominantly cohesionless soil that has the right
gradation and composition. Liquefaction has occurred
in soils ranging from low plasticity silts to gravels.
Clean or silty sands and nonplastic silts are most
susceptible to liquefaction.
•
The state of the soil is characterized by a density
that is low enough for the soil to exhibit contractive
behavior when sheared undrained under the initial
effective overburden stress.
•
The presence of groundwater, resulting in a
saturated or nearly saturated soil.
Methods used to assess the potential for
liquefaction range from empirically-based design
methods to complex numerical, effective stress
methods that can model the time-dependent generation
of pore-water pressure and its effect on soil strength
and deformation. Furthermore, dynamic performance
soil tests such as cyclic simple shear or cyclic triaxial
tests can be used to assess liquefaction susceptibility
and behavior to be used as input for liquefaction
analysis and design.
The most common method of assessing liquefaction
involves the use of empirical methods (e.g., Youd et al.,
2001). These methods provide an estimate of
liquefaction potential based on SPT blowcounts, CPT
cone tip resistance, or shear wave velocity. This type of
analysis should be conducted as a baseline evaluation,
even when more rigorous methods are used.
Youd et al. (2001) summarizes the consensus of the
profession up to year 2000 regarding the use of the
simplified methods. Since the publication of this
consensus paper, various other modifications to the
consensus approach have been introduced, including
those by Cetin et al. (2004), Moss et al. (2006), and
Boulanger and Idriss (2006). These more recent methods
account for additions to the database on liquefaction, as
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
10-32
•
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Liquefied Configuration—The structure as designed
in nonliquefied configuration above should be
reanalyzed assuming that the layer has liquefied and
the liquefied soil provides the appropriate residual
resistance for lateral and axial deep foundation
response analyses consistent with liquefied soil
conditions (i.e., modified P-y curves, modulus of
subgrade reaction, or t-z curves). The design
spectrum should be the same as that used in the
nonliquefied configuration.
With the Owner’s approval, or as required by the
Owner, a site-specific response spectrum that accounts
for the modifications in spectral content from the
liquefying soil may be developed. Unless approved
otherwise by the Owner, the reduced response spectrum
resulting from the site-specific analyses shall not be less
than two-thirds of the spectrum developed at the ground
surface using the general procedure described in
Article 3.10.4.1 modified by the site factors in
Article 3.10.3.2.
The Designer should provide explicit detailing of
plastic hinging zones for both cases mentioned above
since it is likely that locations of plastic hinges for the
liquefied configuration are different than locations of
plastic hinges for the nonliquefied configuration. Design
requirements including shear reinforcement should be
met for the liquefied and nonliquefied configuration.
Where liquefaction is identified, plastic hinging in the
foundation may be permitted with the Owner’s approval.
For those sites where liquefaction-related
permanent lateral ground displacements (e.g., flow,
lateral spreading, or slope instability) are determined to
occur, the effects of lateral displacements on the bridge
and retaining structures should be evaluated. These
effects can include increased lateral pressure on bridge
foundations and retaining walls.
The effects of liquefaction-related, permanent
lateral ground displacements on bridge and retaining
wall performance should be considered separate from
the inertial evaluation of the bridge structures. However,
if large magnitude earthquakes dominate the seismic
hazards, the bridge response evaluation should consider
the potential simultaneous occurrence of:
•
Inertial response of the bridge, and loss in ground
response from liquefaction around the bridge
foundations, and
•
Predicted
amounts
of
displacement of the soil.
permanent
lateral
well as refinements in the interpretation of case history
data. The newer methods potentially offer improved
estimates of liquefaction potential and can be considered
for use.
The simplified empirical methods are suited for use
to a maximum depth of approximately 75 ft. This depth
limit relates to the database upon which the original
empirical method was developed. Most of the database
was from observations of liquefaction at depths less than
50 to 60 ft. Extrapolation of the simplified method
beyond 75 ft is therefore of uncertain validity. This
limitation should not be interpreted as meaning
liquefaction does not occur beyond 75 ft. Rather,
different methods should be used for greater depths,
including the use of site-specific ground motion
response modeling in combination with liquefaction
testing in the laboratory.
The magnitude for the design earthquake must be
determined when conducting liquefaction assessments
using the simplified empirical procedures. The
earthquake magnitude used to assess liquefaction can be
determined from earthquake deaggregation data for the
site, available through the USGS national seismic hazard
website
http://earthquake.usgs.gov/research/hazmaps/
based on the 975-yr return period (i.e., five percent in
50 yr within the USGS website). If a single or a few
larger
magnitude
earthquakes
dominate
the
deaggregation, the magnitude of the single dominant
earthquake or the mean of the few dominant earthquakes
in the deaggregation should be used.
Liquefaction is generally limited to granular soils,
such as sands and non-plastic silts. Loose gravels also can
liquefy if drainage is prevented such as might occur if a
layer of clay or frozen soil is located over the gravel.
Methods for eliminating sites based on soil type have
been developed, as discussed by Youd et al., (2001), Bray
and Sancio (2006), and Boulanger and Idriss (2006).
These methods can be used to screen the potential for
liquefaction in certain soil types. In the past soil screening
with regard to silts was done using the Chinese criteria
(Kramer, 1996). Recent studies (Bray and Sancio, 2006;
Boulanger and Idriss, 2006) indicate that the Chinese
criteria are unconservative, and therefore their use should
be discontinued.
Two criteria for assessing liquefaction susceptibility
of soils have been recently proposed as replacements to
the Chinese criteria:
•
Boulanger and Idriss (2006) recommend
considering a soil to have clay-like behavior (i.e.,
not susceptible to liquefaction) if the plasticity
index (PI) ≥ 7.
•
Bray and Sancio (2006) suggest that a soil with a PI
< 12 and a ratio of water content to liquid limit
(wc/LL) > 0.85 will be susceptible to liquefaction.
There is no current consensus on the preferred of
the two criteria, and, therefore, either method may be
used, unless the Owner has a specific preference.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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SECTION 10: FOUNDATIONS
10-33
If inelastic deformations are expected in the
foundation due to liquefaction-induced effects, a
quantitative assessment of such effects should be
considered. Such assessment may follow the approach
outlined for SDC D in the AASHTO Guide
Specifications for LRFD Seismic Bridge Design.
To determine the location of soils that are
adequately saturated for liquefaction to occur, the
seasonally averaged groundwater elevation should be
used. Groundwater fluctuations caused by tidal action or
seasonal variations will cause the soil to be saturated
only during a limited period of time, significantly
reducing the risk that liquefaction could occur within the
zone of fluctuation.
Liquefaction evaluation is required only for sites
meeting requirements for Seismic Zones 3 and 4, provided
that the soil is saturated and of a type that is susceptible to
liquefaction. For loose to very loose sand sites (e.g., (N1)60
< 10 bpf or qc1N < 75), a potential exists for liquefaction in
Seismic Zone 2, if the acceleration coefficient, As, is 0.15 or
higher. The potential for and consequences of liquefaction
for these sites will depend on the dominant magnitude for
the seismic hazard. As the magnitude decreases, the
liquefaction resistance of the soil increases due to the
limited number of earthquake loading cycles. Generally, if
the magnitude is 6 or less, even in these very loose soils,
either the potential for liquefaction is very low or the extent
of liquefaction is very limited. Nevertheless, a liquefaction
assessment should be made if loose to very loose sands are
present to a sufficient extent to impact bridge stability and
As is greater than or equal to 0.15. These loose to very loose
sands are likely to be present in hydraulically placed fills
and alluvial or estuarine deposits near rivers and
waterfronts.
During liquefaction, pore-water pressure build-up
occurs, resulting in loss of strength and then settlement
as the excess pore-water pressures dissipate after the
earthquake. The potential effects of strength loss and
settlement include:
•
Slope Failure, Flow Failure, or Lateral Spreading—
The strength loss associated with pore-water pressure
build-up can lead to slope instability. Generally, if
the factor of safety against liquefaction is less than
approximately 1.2 to 1.3, a potential for pore-water
pressure build-up will occur, and the effects of this
build-up should be assessed. If the soil liquefies, the
stability is determined by the residual strength of the
soil. The residual strength of liquefied soils can be
determined using empirical methods developed by
Seed and Harder (1990), Olson and Stark (2002), and
others. Loss of lateral resistance can allow abutment
soils to move laterally, resulting in bridge
substructure
distortion
and
unacceptable
deformations and moments in the superstructure.
•
Reduced Foundation Bearing Resistance—Liquefied
strength is often a fraction of nonliquefied strength.
This loss in strength can result in large displacements
or bearing failure. For this reason, spread footing
foundations are not recommended where liquefiable
soils occur unless the spread footing is located below
the maximum depth of liquefaction or soil
improvement techniques are used to mitigate the
effects of liquefaction.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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10-34
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
•
Reduced Soil Stiffness and Loss of Lateral Support
for Deep Foundations—This loss in strength can
change the lateral response characteristics of piles
and shafts under lateral load.
•
Vertical Ground Settlement as Excess Pore-Water
Pressures Induced by Liquefaction Dissipate,
Resulting in Downdrag Loads on Deep
Foundations—If liquefaction-induced downdrag
loads can occur, the downdrag loads should be
assessed as specified in Article 3.11.8.
Most liquefaction-related damage to bridges during
past earthquakes has been the result of lateral movement
of the soil, causing severe column distortion and potential
structure collapse. Therefore, a thorough analysis of the
effects of lateral soil movement due to liquefaction on the
structure is necessary. If there is potential for significant
soil movement, the structure design should meet the
requirements of Seismic Zone 4.
The effects of liquefaction will depend in large part
on the amount of soil that liquefies and the location of
the liquefied soil with respect to the foundation. On
sloping ground, lateral flow, spreading, and slope
instability can occur on relatively thin layers of
liquefiable soils, whereas the effects of thin liquefied
layer on the lateral response of piles or shafts (without
lateral ground movement) may be negligible. Likewise,
a thin liquefied layer at the ground surface results in
essentially no downdrag loads, whereas the same
liquefied layer deeper in the soil profile could result in
large downdrag loads. Given these potential variations,
site investigation plays a fundamental part of the
liquefaction assessment. Article 10.4 identifies
requirements for site investigations.
When assessing the effects of liquefaction on bridge
response, the recommendations herein require that
structure be designed for two cases, one in which the
full seismic acceleration is applied to the structure
assuming the soil does not liquefy, and one in which the
full seismic acceleration is applied to the structure
assuming the soil does liquefy but the spectrum is
unchanged by liquefaction. This approach should
produce conservative results for bridges with periods
less than 1 sec. However, Youd and Carter (2005)
suggest that at periods greater than 1 second, it is
possible for liquefaction to result in higher spectral
accelerations than occur for equivalent nonliquefied
cases, all other conditions being equal. For Site Class C
or D and bridges with periods greater than 1 sec., the
Designer may consider using a response spectrum
constructed using Site Class E for the liquefied
condition. Alternately, site-specific ground motion
response evaluations may be used to evaluate this
potential.
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2012
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SECTION 10: FOUNDATIONS
10-35
There is currently no consensus on how to address
this issue of timing of seismic acceleration and the
development of full liquefaction and its combined
impact on the structure without resorting to more
rigorous analyses, such as by using nonlinear, effective
stress methods. In general, the larger the earthquake
magnitude (e.g., M > 8), the longer the period of time
over which strong shaking acts, and the more likely the
strong shaking and liquefaction effects will be acting
concurrently. The smaller the earthquake magnitude, the
more likely that these two effects will not be concurrent,
in which case the peak inertial response of the bridge
may occur before much, if any, reduction in soil support
from liquefaction occurs.
Site-specific dynamic ground motion response
analyses offers one method of evaluating the effects of
pore-water pressure increases and timing on the
development of the response spectrum. These analyses
can be conducted using a nonlinear, effective stress
method that accounts for the build-up in pore-water
pressure and stiffness degradation in liquefiable layers.
Use of this approach requires considerable skill in terms
of selecting model parameters, particularly the pore
pressure model. The complexity of this approach is such
that Owner’s approval is mandatory, and it is highly
advisable that an independent peer review panel with
expertise in nonlinear, effective stress modeling be used
to review the methods and the resulting spectrum.
The limit of two-thirds for reduction of the liquefied
response spectrum below the nonliquefied spectrum is
meant to apply to any ordinate of the response spectrum.
Generally, liquefied conditions may produce significant
reductions in the shorter period range, but the reductions
will be smaller or could be increased over nonliquefied
conditions in the longer period range over about 1–2 sec.
The developer of the site response analysis should
capture accurate estimates of response for all periods
that could be of importance in both nonliquefied and
liquefied conditions. This consideration is particularly
important if the conventional spectral shapes of
Article 3.10.4.1 are being used.
The timing of liquefaction relative to the
development of strong shaking also can be an important
consideration for sites where lateral ground movement
occurs. Both the development of liquefaction and the
ground movement are dependent on the size and
magnitude of the earthquake, but they do not necessarily
occur at the same time. This issue is especially
important when determining how to combine the inertial
response of the structure and the response to lateral
movement of the soil against the foundations and other
substructure elements due to lateral spreading, slope
instability, and flow failure. Current practice is to
consider these two mechanisms to be independent, and
therefore, the analyses are decoupled; i.e., the analysis is
first performed to evaluate inertial effects during
liquefaction following the same guidance as for level-
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2012
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10-36
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
ground sites, and then the foundation is evaluated for the
moving ground, but without the inertial effects of the
bridge superimposed. For critical bridges or in areas
where very large magnitude earthquakes could occur,
detailed studies addressing the two mechanisms acting
concurrently may be warranted. This timing issue also
affects liquefaction-induced downdrag, in that
settlement and downdrag generally does not occur until
the pore pressures induced by ground shaking begin to
dissipate after shaking ceases.
For assessment of existing structures, the Designer
should consider using Seismic Zone 4 regardless of the
magnitude of As, even when significant lateral soil
movement is not expected, if the structure is particularly
weak with regard to its ability to resist the forces and
displacements that could be caused by liquefaction.
Examples of weaknesses that could exacerbate the
impact of liquefaction to the structure include presence
of shallow foundations, deep foundations tipped in
liquefiable soil, very limited bridge support lengths that
have little tolerance of lateral movement of the
substructure, deterioration of superstructure or
substructure components due to advanced age of the
structure or severe environmental conditions, and the
absence of substructure redundancy.
The intent of these Specifications is to limit
inelastic deformations under seismic loading to aboveground locations that can be inspected. However, if
liquefaction occurs, it may be difficult or impossible to
restrict inelastic action solely to above-ground locations
without site improvement. If inelastic deformations are
expected in the foundation, then the Owner may
consider installation of devices that permit postearthquake assessment; for example, installation of
inclinometer tubes in drilled shafts permits limited
evaluation of the deformations of the foundation, which
would otherwise be impossible to inspect at any
significant depth. Permitting inelastic behavior below
the ground implies that the shaft or piles will be
damaged, possibly along with other parts of the bridge,
and may need to be replaced.
Design options range from (a) an acceptance of the
movements with significant damage to the piles and
columns if the movements are large (possibly requiring
demolition but still preserving the no-collapse
philosophy) to (b) designing the piles to resist the forces
generated by lateral spreading. Between these options
are a range of mitigation measures to limit the amount of
movement to tolerable levels for the desired
performance objective. However, tolerable structural
movements should be evaluated quantitatively.
Quantitative assessments of liquefaction-induced
deformations on foundations may be accomplished
using the nonlinear static “push over” methodology.
However, such analysis is complicated by the need to
model nonlinear P-y behavior of the liquefied soil along
with the nonlinear behavior of the structure. Analyses
where the liquefied soil is represented by appropriate
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2012
Edition
SECTION 10: FOUNDATIONS
10-37
residual resistance (P-y curves or modulus of subgrade
reaction values) will generally provide conservative
results for the actual inelastic behavior of the foundation
structural elements. The approach for such analyses
should be developed on a case-by-case basis due to the
varied conditions found in liquefiable sites. Careful
coordination between the geotechnical and structural
engineers is essential to estimating the expected
response and to evaluating whether the structure can
tolerate the response. Often mitigation strategies may be
required to reduce structural movements.
Mitigation of the effects of liquefaction-induced
settlement or lateral soil movement may include ground
stabilization to either prevent liquefaction or add strength
to keep soil deformation from occurring, foundation or
superstructure modifications to resist the forces and
accommodate the deformations that may occur, or both.
It is often cost prohibitive to design the bridge
foundation system to resist the loads imposed by
liquefaction-induced lateral loads, especially if the depth
of liquefaction extends more than about 20 ft below the
ground surface and if a nonliquefied crust is part of the
failure surface. Ground improvement to mitigate the
liquefaction hazard is the likely alternative if it is not
practical to design the foundation system to
accommodate the lateral loads.
The primary ground improvement techniques to
mitigate liquefaction fall into five general categories,
namely removal and replacement, densification,
reinforcement, altering the soil composition, and
enhanced drainage. Any one or a combination of methods
can be used. However, drainage improvement is not
currently considered adequately reliable to prevent
liquefaction-induced, excess pore-water pressure build-up
due to (1) the time required for excess pore-water
pressures to dissipate through the drainage paths, and (2)
the potential for drainage materials to become clogged
during installation and in service. In addition, with
drainage enhancements some settlement is still likely.
Therefore, drainage enhancements should not be used as a
means to fully mitigate liquefaction. For further
discussion of ground improvement methods, see
FHWA-SA-98-086, Ground Improvement Technical
Summaries (Elias, et al., 2000); FHWA-SA-95-037;
Geotechnical Engineering Circular No. 1, Dynamic
Compaction (Lukas, 1995); and FHWA/RD-83/O2C,
Design and Construction of Stone Columns (Barkdale and
Bachus, 1983).
The use of large diameter shafts in lieu of the
conventional pile cap foundation type may be
considered in order to achieve the lateral strength and
stiffness required to sustain the column demand while
minimizing the foundation exposed surface area normal
to the lateral flow direction.
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2012
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10-38
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
10.5.5—Resistance Factors
10.5.5.1—Service Limit States
Resistance factors for the service limit states shall
be taken as 1.0, except as provided for overall stability
in Article 11.6.2.3.
A resistance factor of 1.0 shall be used to assess the
ability of the foundation to meet the specified deflection
criteria after scour due to the design flood.
10.5.5.2—Strength Limit States
10.5.5.2.1—General
C10.5.5.2.1
Resistance factors for different types of foundation
systems at the strength limit state shall be taken as
specified in Articles 10.5.5.2.2, 10.5.5.2.3, 10.5.5.2.4,
and 10.5.5.2.5, unless regionally specific values or
substantial successful experience is available to justify
higher values.
Regionally specific values should be determined
based on substantial statistical data combined with
calibration or substantial successful experience to justify
higher values. Smaller resistance factors should be used
if site or material variability is anticipated to be
unusually high or if design assumptions are required that
increase design uncertainty that have not been mitigated
through conservative selection of design parameters.
Certain resistance factors in Articles 10.5.5.2.2,
10.5.5.2.3, 10.5.5.2.4, and 10.5.5.2.5 are presented as a
function of soil type, e.g., sand or clay. Naturally
occurring soils do not fall neatly into these two
classifications. In general, the terms “sand” and
“cohesionless soil” may be connoted to mean drained
conditions during loading, while “clay” or “cohesive
soil” implies undrained conditions. For other or
intermediate soil classifications, such as silts or gravels,
the designer should choose, depending on the load case
under consideration, whether the resistance provided by
the soil will be a drained or undrained strength, and
select the method of computing resistance and
associated resistance factor accordingly.
In general, resistance factors for bridge and other
structure design have been derived to achieve a
reliability index, β, of 3.5, an approximate probability of
failure, Pf, of 1 in 5,000. However, past geotechnical
design practice has resulted in an effective reliability
index, β, of 3.0, or an approximate probability of a
failure of 1 in 1,000, for foundations in general , and for
highly redundant systems, such as pile groups, an
approximate reliability index, β, of 2.3, an approximate
probability of failure of 1 in 100 (Zhang et al., 2001;
Paikowsky et al., 2004; Allen, 2005). If the resistance
factors provided in this Article are adjusted to account
for regional practices using statistical data and
calibration, they should be developed using the β values
provided above, with consideration given to the
redundancy in the foundation system.
For bearing resistance, lateral resistance, and uplift
calculations, the focus of the calculation is on the
individual foundation element, e.g., a single pile or
drilled shaft. Since these foundation elements are
usually part of a foundation unit that contains multiple
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2012
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SECTION 10: FOUNDATIONS
10-39
The foundation resistance after scour due to the
design flood shall provide adequate foundation
resistance using the resistance factors given in this
Article.
10.5.5.2.2—Spread Footings
elements, failure of one of these foundation elements
usually does not cause the entire foundation unit to
reach failure, i.e., due to load sharing and overall
redundancy. Therefore, the reliability of the foundation
unit is usually more, and in many cases considerably
more, than the reliability of the individual foundation
element. Hence, a lower reliability can be successfully
used for redundant foundations than is typically the case
for the superstructure.
Note that not all of the resistance factors provided
in this Article have been derived using statistical data
from which a specific β value can be estimated, since
such data were not always available. In those cases,
where data were not available, resistance factors were
estimated through calibration by fitting to past allowable
stress design safety factors, e.g., the AASHTO Standard
Specifications for Highway Bridges (2002).
Additional discussion regarding the basis for the
resistance factors for each foundation type and limit
state is provided in Articles 10.5.5.2.2, 10.5.5.2.3,
10.5.5.2.4, and 10.5.5.2.5. Additional, more detailed
information on the development of the resistance factors
for foundations provided in this Article, and a
comparison of those resistance factors to previous
Allowable Stress Design practice, e.g., AASHTO
(2002), is provided in Allen (2005).
Scour design for the design flood must satisfy the
requirement that the factored foundation resistance after
scour is greater than the factored load determined with
the scoured soil removed. The resistance factors will be
those used in the Strength Limit State, without scour.
C10.5.5.2.2
The
resistance
factors
provided
in
Table 10.5.5.2.2-1 shall be used for strength limit state
design of spread footings, with the exception of the
deviations allowed for local practices and site specific
considerations in Article 10.5.5.2.
Table 10.5.5.2.2-1—Resistance Factors for Geotechnical Resistance of Shallow Foundations at the Strength Limit State
Bearing Resistance
Sliding
ϕb
ϕτ
ϕep
Method/Soil/Condition
Theoretical method (Munfakh et al., 2001), in clay
Theoretical method (Munfakh et al., 2001), in sand, using CPT
Theoretical method (Munfakh et al., 2001), in sand, using SPT
Semi-empirical methods (Meyerhof, 1957), all soils
Footings on rock
Plate Load Test
Precast concrete placed on sand
Cast-in-Place Concrete on sand
Cast-in-Place or precast Concrete on Clay
Soil on soil
Passive earth pressure component of sliding resistance
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Resistance Factor
0.50
0.50
0.45
0.45
0.45
0.55
0.90
0.80
0.85
0.90
0.50
2012
Edition
10-40
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The resistance factors in Table 10.5.5.2.2-1 were
developed using both reliability theory and calibration by
fitting to Allowable Stress Design (ASD). In general, ASD
safety factors for footing bearing capacity range from 2.5 to
3.0, corresponding to a resistance factor of approximately
0.55 to 0.45, respectively, and for sliding, an ASD safety
factor of 1.5, corresponding to a resistance factor of
approximately 0.9. Calibration by fitting to ASD controlled
the selection of the resistance factor in cases where
statistical data were limited in quality or quantity. The
resistance factor for sliding of cast-in-place concrete on
sand is slightly lower than the other sliding resistance
factors based on reliability theory analysis (Barker et al.,
1991). The higher interface friction coefficient used for
sliding of cast-in-place concrete on sand relative to that
used for precast concrete on sand causes the cast-in-place
concrete sliding analysis to be less conservative, resulting
in the need for the lower resistance factor. A more detailed
explanation of the development of the resistance factors
provided in Table 10.5.5.2.2-1 is provided in Allen (2005).
The resistance factors for plate load tests and
passive resistance were based on engineering judgment
and past ASD practice.
10.5.5.2.3—Driven Piles
Resistance factors shall be selected from
Table 10.5.5.2.3-1 based on the method used for
determining the driving criterion necessary to achieve
the required nominal pile bearing resistance.
Regarding load tests, and dynamic tests with signal
matching, the number of tests to be conducted to justify
the design resistance factors selected should be based on
the variability in the properties and geologic
stratification of the site to which the test results are to be
applied. A site shall be defined as a project site, or a
portion of it, where the subsurface conditions can be
characterized as geologically similar in terms of
subsurface stratification, i.e., sequence, thickness,
and geologic history of strata, the engineering
properties of the strata, and groundwater conditions.
C10.5.5.2.3
Where nominal pile bearing resistance is
determined by static load test, dynamic testing, wave
equation, or dynamic formulas, the uncertainty in the
nominal resistance is strictly due to the reliability of the
resistance determination method used in the field during
pile installation.
In most cases, the nominal bearing resistance of
each production pile is field-verified based on
compliance with a driving criterion developed using a
dynamic method (see Articles 10.7.3.8.2, 10.7.3.8.3,
10.7.3.8.4, or 10.7.3.8.5). The actual penetration depth
where the pile is stopped using the driving criterion
(e.g., a blow count measured during pile driving) will
likely not be the same as the estimated depth from the
static analysis. Hence, the reliability of the nominal pile
bearing resistance is dependent on the reliability of the
method used to verify the nominal resistance during pile
installation (see Allen, 2005, for additional discussion
on this issue). Therefore, the resistance factor for the
field verification method should be used to determine
the number of piles of a given nominal resistance
needed to resist the factored loads in the strength limit
state.
If the resistance factors provided in Table 10.5.5.2.3-1
are to be applied to small pile groups, the resistance factor
values in the table should be reduced by 20 percent to
reflect the reduced ability for overstressing of an individual
foundation element to be carried by adjacent foundation
elements. The minimum size of a pile group necessary to
provide significant opportunity for load sharing ranges
from 2 or 3 (Isenhower and Long, 1997) to 5 (Paikowsky,
et al., 2004).
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2012
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SECTION 10: FOUNDATIONS
10-41
Note that a site as defined herein may be only a
portion of the area in which the structure (or structures)
is located. For sites where conditions are highly
variable, a site could even be limited to a single pier.
The ability to share load between structural
elements should an overstress occur is addressed in
Article 1.3.4 through the use of ηR. The values for ηR
provided in that Article have been developed in general
for the superstructure, and no specific guidance on the
application of ηR to foundations is provided. The ηR
factor values recommended in Article 1.3.4 are not
adequate to address this ability to shed load to other
foundation elements when some of the foundation
elements become overstressed, based on the results
provided by Paikowsky et al. (2004) and others (see
also Allen, 2005). Therefore, the resistance factors
specified in Table 10.5.5.2.3-1 should be reduced based
on the guidance provided in this Article to account for
the lack of load sharing opportunities due to the small
pile group size.
Dynamic methods may underpredict the nominal
axial resistance of piles driven in soft silts or clays
where a large amount of setup is anticipated and it is
not feasible to perform static load or dynamic tests over
a sufficient length of time to assess soil setup.
See Allen (2005) for an explanation on the
development of the resistance factors for pile foundation
design.
For all axial resistance calculation methods, the
resistance factors were, in general, developed from load
test results obtained on piles with diameters of 24 in. or
less. Very little data were available for larger diameter
piles. Therefore, these resistance factors should be used
with caution for design of significantly larger diameter
piles. In general, experience has shown that the static
analysis methods identified in Table 10.5.5.2.3-1 tend to
significantly overestimate the available nominal
resistance for larger diameter piles. A static or dynamic
load test should be considered if piles larger than 24 in.
in diameter are anticipated.
Where driving criteria are established based on a
static load test, the potential for site variability should be
considered. The number of load tests required should be
established based on the characterization of site
subsurface conditions by the field and laboratory
exploration and testing program.
One of the following alternative approaches may
be used to address site variability when extrapolating
pile load test results, and the application of driving
criteria from those load test results, to piles not load
tested:
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
1.
Divide up the site into zones where subsurface
conditions are relatively uniform using engineering
judgment, conducting one static pile load test in
each zone, and dynamic testing with signal
matching on a minimum of two percent of the
production piles, but no less than two production
piles. A resistance factor of 0.80 is recommended if
this approach is used. If production pile dynamic
testing is not conducted, then a resistance factor of
0.75 should be used.
2.
Characterize the site variability and select resistance
factors using the approach described by Paikowsky
et al. (2004).
The dynamic testing with signal matching should be
evenly distributed within a pier and across the entire
structure. However, within a particular footing, an
increase in safety is realized where the most heavily
loaded piles are tested.
The resistance factors in Table 10.5.5.2.3-1 for the
case where dynamic testing is conducted without static
load testing were developed using reliability theory for
beginning of redrive (BOR) conditions. These resistance
factors may be used for end of driving (EOD)
conditions, but it should be recognized that dynamic
testing with signal matching at EOD will likely produce
conservative results because soil set up, which causes
nominal pile bearing resistance to increase, is not taken
into account. If, instead, relaxation is anticipated to
occur, these resistance factors for dynamic testing
should only be used at BOR.
The 0.50 resistance factor in Table 10.5.5.2.3-1 for
use of the wave equation without dynamic measurements
to estimate nominal pile bearing resistance is based on
calibration by fitting to past allowable stress design
practice. Using default wave equation hammer and soil
input values, reliability theory calibrations performed by
Paikowsky et al. (2004) suggest that a resistance factor of
0.40 should be used if the wave equation is used to
estimate nominal pile bearing resistance. Their
recommendation is more conservative than the resistance
factor implied by past allowable stress design practice.
Their
recommendation
should
be
considered
representative of the reliability of the wave equation to
estimate nominal pile bearing resistance by designers
who lack experience with the wave equation and its
application to local or regional subsurface conditions.
Application of default wave equation input parameters
without consideration to local site conditions and
observed hammer performance in combination with this
lower resistance factor is not recommended.
Local experience or site-specific test results should
be used to refine the wave equation soil input values, or to
at least use the input values selected with greater
confidence, and field verification of the hammer
performance should be conducted to justify the use of the
resistance factor of 0.50 provided in Table 10.5.5.2.3-1.
Field verification of hammer performance is considered to
be a direct measurement of either stroke or kinetic energy.
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2012
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SECTION 10: FOUNDATIONS
10-43
See Articles 10.7.3.8.2, 10.7.3.8.3, 10.7.3.8.4, and
10.7.3.8.5 for additional guidance regarding static pile
load testing, dynamic testing and signal matching, wave
equation analysis, and dynamic formulas, respectively,
as they apply to the resistance factors provided in
Table 10.5.5.2.3-1.
The dynamic pile formulas, i.e., FHWA modified
Gates and Engineering News, identified in
Table 10.5.5.2.3-1 require the pile hammer energy as an
input parameter. The developed hammer energy should
be used for this purpose, defined as the product of actual
stroke developed during the driving of the pile (or
equivalent stroke as determined from the bounce
chamber pressure for double acting hammers) and the
hammer ram weight.
The
resistance
factors
provided
in
Table 10.5.5.2.3-1 are specifically applicable to the
dynamic pile formula as provided in Article 10.7.3.8.5.
Note that for the Engineering News (EN) formula, the
built-in safety factor of 6 has been removed so that it
predicts nominal resistance. Therefore, the resistance
factor shown in Table 10.5.5.2.3-1 for EN formula
should not be applied to the traditional “allowable
stress” form of the equation.
The resistance factors for the dynamic pile
formulas, i.e., FHWA modified Gates and EN, in
Table 10.5.5.2.3-1 have been specifically developed for
EOD conditions. Since static pile load test data, which
include the effects of soil setup or relaxation (for the
database used, primarily soil setup), were used to
develop the resistance factors for these formulas, the
resistance factors reflect soil setup occurring after the
pile installation. At BOR, the blow count obtained
already includes the soil setup. Therefore, a lower
resistance factor for the driving formulas should be used
for BOR conditions than the ones shown in
Table 10.5.5.2.3-1 for EOD conditions. In general,
dynamic testing should be conducted to verify nominal
pile resistance at BOR in lieu of the use of driving
formulas.
Paikowsky et al. (2004) indicate that the resistance
factors for static pile resistance analysis methods can
vary significantly for different pile types. The resistance
factors presented are average values for the method. See
Paikowsky et al. (2004) and Allen (2005) for additional
information regarding this issue.
The resistance factor for the Nordlund/Thurman
method was derived primarily using the Peck et al.
(1974) correlation between SPT N160 and the soil
friction angle, using a maximum design soil friction
angle of 36 degrees, assuming the contributing zone for
the bearing resistance is from the tip to two pile
diameters below the tip. These assumptions should be
considered when using the resistance factor specified in
Table 10.5.5.2.3-1 for this static analysis method.
For the clay static pile analysis methods, if the soil
cohesion was not measured in the laboratory, the
correlation between SPT N and Su by Hara et al. (1974)
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
was used for the calibration. Use of other methods to
estimate Su may require the development of resistance
factors based on those methods.
The resistance factors provided for uplift of single
piles are generally less than the resistance factors for
axial side resistance under compressive loading. This is
consistent with past practice that recognizes the side
resistance in uplift is generally less than the side
resistance under compressive loading, and is also
consistent with the statistical calibrations performed in
Paikowsky et al. (2004). Since the reduction in uplift
resistance that occurs in tension relative to the side
resistance in compression is taken into account through
the resistance factor, the calculation of side resistance
using a static pile resistance analysis method should not
be reduced from what is calculated from the methods
provided in Article 10.7.3.8.6.
For uplift, the number of pile load tests required to
justify a specific resistance factor are the same as that
required for determining compression resistance.
Extrapolating the pile load test results to other untested
piles as specified in Article 10.7.3.10 does create some
uncertainty, since there is not a way to directly verify
that the desired uplift resistance has been obtained for
each production pile. This uncertainty has not been
quantified. Therefore, it is recommended that a
resistance factor of not greater than 0.60 be used if an
uplift load test is conducted.
Regarding pile drivability analysis, the only source
of load is from the pile driving hammer. Therefore, the
load factors provided in Section 3 do not apply. In past
practice, e.g., AASHTO (2002), no load factors were
applied to the stresses imparted to the pile top by the
pile hammer. Therefore, a load factor of 1.0 should be
used for this type of analysis. Generally, either a wave
equation analysis or dynamic testing, or both, are used
to determine the stresses in the pile resulting from
hammer impact forces. See Article 10.7.8 for the
specific calculation of the pile structural resistance
available for analysis of pile drivability. The structural
resistance available during driving determined as
specified in Article 10.7.8 considers the ability of the
pile to handle the transient stresses resulting from
hammer impact, considering variations in the
materials, pile/hammer misalignment, and variations in
the pile straightness and uniformity of the pile head
impact surface.
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SECTION 10: FOUNDATIONS
10-45
Table 10.5.5.2.3-1—Resistance Factors for Driven Piles
Condition/Resistance Determination Method
Driving criteria established by successful static load test of at
least one pile per site condition and dynamic testing* of at
least two piles per site condition, but no less than 2% of the
production piles
Driving criteria established by successful static load test of at
least one pile per site condition without dynamic testing
Driving criteria established by dynamic testing* conducted on
100% of production piles
Nominal Bearing Resistance
of Single Pile—Dynamic
Driving criteria established by dynamic testing,* quality
Analysis and Static Load Test control by dynamic testing* of at least two piles per site
Methods, ϕdyn
condition, but no less than 2% of the production piles
Wave equation analysis, without pile dynamic measurements
or load test but with field confirmation of hammer
performance
FHWA-modified Gates dynamic pile formula (End of Drive
condition only)
Engineering News (as defined in Article 10.7.3.8.5) dynamic
pile formula (End of Drive condition only)
Resistance
Factor
0.80
0.75
0.75
0.65
0.50
0.40
0.10
* Dynamic testing requires signal matching, and best estimates of nominal resistance are made from a restrike. Dynamic tests are
calibrated to the static load test, when available.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 10.5.5.2.3-1—Resistance Factors for Driven Piles (continued)
Nominal Bearing
Resistance of
Single Pile—Static
Analysis Methods,
ϕstat
Condition/Resistance Determination Method
Side Resistance and End Bearing: Clay and Mixed Soils
α-method (Tomlinson, 1987; Skempton, 1951)
β-method (Esrig & Kirby, 1979; Skempton, 1951)
λ-method (Vijayvergiya & Focht, 1972; Skempton, 1951)
Side Resistance and End Bearing: Sand
Nordlund/Thurman Method (Hannigan et al., 2005)
SPT-method (Meyerhof)
CPT-method (Schmertmann)
End bearing in rock (Canadian Geotech. Society, 1985)
Block Failure, ϕb1
Uplift Resistance
of Single Piles, ϕup
Group Uplift
Resistance, ϕug
Lateral
Geotechnical
Resistance of
Single Pile or Pile
Group
Structural Limit
State
Pile Drivability
Analysis, ϕda
Resistance Factor
0.35
0.25
0.40
0.45
0.30
Clay
Nordlund Method
α-method
β-method
λ-method
SPT-method
CPT-method
Static load test
Dynamic test with signal matching
All soils
0.50
0.45
0.60
0.35
0.25
0.20
0.30
0.25
0.40
0.60
0.50
0.50
All soils and rock
1.0
Steel piles
Concrete piles
Timber piles
Steel piles
Concrete piles
Timber piles
See the provisions of Article 6.5.4.2
See the provisions of Article 5.5.4.2.1
See the provisions of Article 8.5.2.2 and 8.5.2.3
See the provisions of Article 6.5.4.2
See the provisions of Article 5.5.4.2.1
See the provisions of Article 8.5.2.2
In all three Articles identified above, use ϕ identified as “resistance during pile driving”
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SECTION 10: FOUNDATIONS
10-47
10.5.5.2.4—Drilled Shafts
Resistance factors shall be selected based on the
method used for determining the nominal shaft
resistance. When selecting a resistance factor for shafts
in clays or other easily disturbed formations, local
experience with the geologic formations and with
typical shaft construction practices shall be considered.
Where the resistance factors provided in
Table 10.5.5.2.4-1 are to be applied to a single shaft
supporting a bridge pier, the resistance factor values in
the Table should be reduced by 20 percent. Where the
resistance factor is decreased in this manner, the ηR
factor provided in Article 1.3.4 shall not be increased to
address the lack of foundation redundancy.
The number of static load tests to be conducted to
justify the resistance factors provided in Table 10.5.5.2.4-1
shall be based on the variability in the properties and
geologic stratification of the site to which the test results
are to be applied. A site, for the purpose of assessing
variability, shall be defined in accordance with
Article 10.5.5.2.3.
C10.5.5.2.4
The resistance factors in Table 10.5.5.2.4-1 were
developed using either statistical analysis of shaft load
tests combined with reliability theory (Paikowsky et al.,
2004), fitting to allowable stress design (ASD), or both.
Where the two approaches resulted in a significantly
different resistance factor, engineering judgment was
used to establish the final resistance factor, considering
the quality and quantity of the available data used in the
calibration. The available reliability theory calibrations
were conducted for the Reese and O’Neill (1988)
method, with the exception of shafts in intermediate
geo-materials (IGMs), in which case the O’Neill and
Reese (1999) method was used. In Article 10.8, the
O’Neill and Reese (1999) method is recommended. See
Allen (2005) for a more detailed explanation on the
development of the resistance factors for shaft
foundation design, and the implications of the
differences in these two shaft design methods on the
selection of resistance factors.
The information in the commentary to
Article 10.5.5.2.3 regarding the number of load tests to
conduct considering site variability applies to drilled
shafts as well.
For single shafts, lower resistance factors are
specified to address the lack of redundancy. See
Article C10.5.5.2.3 regarding the use of ηR.
Where installation criteria are established based on
one or more static load tests, the potential for site
variability should be considered. The number of load
tests required should be established based on the
characterization of site subsurface conditions by the
field and laboratory exploration and testing program.
One or more static load tests should be performed per
site to justify the resistance factor selection as discussed
in Article C10.5.5.2.3, applied to drilled shafts installed
within the site. See Article C10.5.5.2.3 for details on
assessing site variability as applied to selection and use
of load tests.
For the specific case of shafts in clay, the resistance
factor recommended by Paikowsky et al. (2004) is much
lower than the recommendation from Barker et al.
(1991). Since the shaft design method for clay is nearly
the same for both the 1988 and 1999 methods, a
resistance factor that represents the average of the two
resistance factor recommendations is provided in
Table 10.5.5.2.4-1. This difference may point to the
differences in local geologic formations and local
construction practices, pointing to the importance of
taking such issues into consideration when selecting
resistance factors, especially for shafts in clay.
IGMs are materials that are transitional between soil
and rock in terms of their strength and compressibility,
such as residual soils, glacial tills, or very weak rock.
See Article C10.8.2.2.3 for a more detailed definition of
an IGM.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Since the mobilization of shaft base resistance is
less certain than side resistance due to the greater
deformation required to mobilize the base resistance, a
lower resistance factor relative to the side resistance is
provided for the base resistance in Table 10.5.5.2.4-1.
O’Neill and Reese (1999) make further comment that
the recommended resistance factor for tip resistance in
sand is applicable for conditions of high quality control
on the properties of drilling slurries and base cleanout
procedures. If high quality control procedures are not
used, the resistance factor for the O’Neill and Reese
(1999) method for tip resistance in sand should be also
be reduced. The amount of reduction should be based on
engineering judgment.
Shaft compression load test data should be
extrapolated to production shafts that are not load tested
as specified in Article 10.8.3.5.6. There is no way to
verify shaft resistance for the untested production shafts,
other than through good construction inspection and
visual observation of the soil or rock encountered in
each shaft. Because of this, extrapolation of the shaft
load test results to the untested production shafts may
introduce some uncertainty. Statistical data are not
available to quantify this at this time. Historically,
resistance factors higher than 0.70, or their equivalent
safety factor in previous practice, have not been used for
shaft foundations. If the recommendations in
Paikowsky, et al. (2004) are used to establish a
resistance factor when shaft static load tests are
conducted, in consideration of site variability, the
resistance factors recommended by Paikowsky, et al. for
this case should be reduced by 0.05, and should be less
than or equal to 0.70 as specified in Table 10.5.5.2.4-1.
This issue of uncertainty in how the load test is
applied to shafts not load tested is even more acute for
shafts subjected to uplift load tests, as failure in uplift
can be more abrupt than failure in compression. Hence,
a resistance factor of 0.60 for the use of uplift load test
results is recommended.
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2012
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SECTION 10: FOUNDATIONS
10-49
Table 10.5.5.2.4-1—Resistance Factors for Geotechnical Resistance of Drilled Shafts
Nominal Axial
Compressive
Resistance of
Single-Drilled
Shafts, ϕstat
Block Failure, ϕb1
Uplift Resistance of
Single-Drilled
Shafts, ϕup
Group Uplift
Resistance, ϕug
Horizontal
Geotechnical
Resistance of Single
Shaft or Shaft
Group
Static Load Test
(compression), ϕload
Static Load Test
(uplift), ϕupload
Method/Soil/Condition
Side resistance in clay
α-method
(O’Neill and Reese, 1999)
Tip resistance in clay
Total Stress
(O’Neill and Reese, 1999)
Side resistance in sand
β-method
(O’Neill and Reese, 1999)
Tip resistance in sand
O’Neill and Reese (1999)
Resistance Factor
0.45
0.40
0.55
0.50
Side resistance in IGMs
O’Neill and Reese (1999)
0.60
Tip resistance in IGMs
Side resistance in rock
O’Neill and Reese (1999)
Horvath and Kenney (1979)
O’Neill and Reese (1999)
0.55
0.55
Side resistance in rock
Tip resistance in rock
Carter and Kulhawy (1988)
Canadian Geotechnical Society
(1985)
Pressuremeter Method (Canadian
Geotechnical Society, 1985)
O’Neill and Reese (1999)
0.50
0.50
Clay
Clay
Sand
Rock
α-method
(O’Neill and Reese, 1999)
β-method
(O’Neill and Reese, 1999)
Horvath and Kenney (1979)
Carter and Kulhawy (1988)
Sand and clay
All materials
0.40
0.45
0.70
All Materials
Resistance factors shall be selected from
Table 10.5.5.2.5-1 based on the method used for
determining the nominal axial pile resistance. If the
resistance factors provided in Table 10.5.5.2.5-1 are to
be applied to piles in potentially creeping soils, highly
plastic soils, weak rock, or other marginal ground type,
the resistance factor values in the Table should be
reduced by 20 percent to reflect greater design
uncertainty.
0.45
1.0
All Materials
10.5.5.2.5—Micropiles
0.55
0.35
0.60
C10.5.5.2.5
The resistance factors in Table 10.5.5.2.5-1 were
calibrated by fitting to ASD procedures tempered with
engineering judgment. The resistance factors in
Table 10.5.5.2.5.-2 for structural resistance were
calibrated by fitting to ASD procedures and are equal to
or slightly more conservative than corresponding
resistance factors from Section 5 of the AASHTO LRFD
Specifications for reinforced concrete column design.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 10.5.5.2.5-1—Resistance Factors for Geotechnical Resistance of Axially Loaded Micropiles
Limit State
Method/ Ground Condition
Side Resistance (Bond Resistance):
Presumptive Values
Tip Resistance on Rock
O’Neill and Reese (1999)
Compression Resistance of
Single Micropile, φstat
Side Resistance and Tip Resistance
Load Test
Resistance Factor
0.55(1)
0.50
Values in
Table 10.5.5.2.3-1, but
no greater than 0.70
Clay
Block Failure, φbl
0.60
0.55(1)
Presumptive Values
Uplift Resistance of Single
Micropile, φup
Sand & Clay
Group Uplift Resistance, φug
(1)
Values in
Table 10.5.5.2.3-1, but
no greater than 0.70
Tension Load Test
0.50
Apply to presumptive grout-to-ground bond values for preliminary design only in Article C10.9.3.5.2.
Table 10.5.5.2.5-2—Resistance Factors for Structural Resistance of Axially Loaded Micropiles
Section / Loading Condition
Pile Cased Length
Pile Uncased Length
Resistance Factor
Tension, ϕTC
0.80
Compression, ϕCC
0.75
Tension, ϕTU
0.80
Compression, ϕCU
0.75
10.5.5.3—Extreme Limit States
10.5.5.3.1—General
Design of foundations at extreme limit states shall
be consistent with the expectation that structure collapse
is prevented and that life safety is protected.
10.5.5.3.2—Scour
C10.5.5.3.2
The provisions of Articles 2.6.4.4.2 and 3.7.5 shall
apply to the changed foundation conditions resulting
from scour. Resistance factors at the strength limit state
shall be taken as specified herein. Resistance factors at
the extreme event shall be taken as 1.0 except that for
uplift resistance of piles and shafts, the resistance factor
shall be taken as 0.80 or less.
The foundation shall resist not only the loads
applied from the structure but also any debris loads
occurring during the flood event.
The specified resistance factors should be used
provided that the method used to compute the nominal
resistance does not exhibit bias that is unconservative.
See Paikowsky et al. (2004) regarding bias values for
pile resistance prediction methods.
Design for scour is discussed in Hannigan et al.
(2005).
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2012
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SECTION 10: FOUNDATIONS
10-51
10.5.5.3.3—Other Extreme Limit States
Resistance factors for extreme limit state, including
the design of foundations to resist earthquake, ice,
vehicle or vessel impact loads, shall be taken as 1.0. For
uplift resistance of piles and shafts, the resistance factor
shall be taken as 0.80 or less.
C10.5.5.3.3
The difference between compression skin friction
and tension skin friction should be taken into account
through the resistance factor, to be consistent with how
this is done for the strength limit state (see
Article 10.5.5.2.3).
10.6—SPREAD FOOTINGS
10.6.1—General Considerations
C10.6.1.1
10.6.1.1—General
Provisions of this Article shall apply to design of
isolated, continuous strip and combined footings for use
in support of columns, walls and other substructure and
superstructure elements. Special attention shall be given
to footings on fill, to make sure that the quality of the
fill placed below the footing is well controlled and of
adequate quality in terms of shear strength and
compressibility to support the footing loads.
Spread footings shall be proportioned and designed
such that the supporting soil or rock provides adequate
nominal resistance, considering both the potential for
adequate bearing strength and the potential for
settlement, under all applicable limit states in
accordance with the provisions of this Section.
Spread footings shall be proportioned and located to
maintain stability under all applicable limit states,
considering the potential for, but not necessarily limited
to, overturning (eccentricity), sliding, uplift, overall
stability and loss of lateral support.
10.6.1.2—Bearing Depth
Where the potential for scour, erosion or
undermining exists, spread footings shall be located to
bear below the maximum anticipated depth of scour,
erosion, or undermining as specified in Article 2.6.4.4.
Problems with insufficient bearing and/or excessive
settlements in fill can be significant, particularly if poor,
e.g., soft, wet, frozen, or nondurable, material is used, or
if the material is not properly compacted.
Spread footings should not be used on soil or rock
conditions that are determined to be too soft or weak to
support the design loads without excessive movement or
loss of stability. Alternatively, the unsuitable material
can be removed and replaced with suitable and properly
compacted engineered fill material, or improved in
place, at reasonable cost as compared to other
foundation support alternatives.
Footings should be proportioned so that the stress
under the footing is as nearly uniform as practicable at
the service limit state. The distribution of soil stress
should be consistent with properties of the soil or rock
and the structure and with established principles of soil
and rock mechanics.
C10.6.1.2
Consideration should be given to the use of either a
geotextile or graded granular filter material to reduce the
susceptibility of fine grained material piping into rip rap
or open-graded granular foundation material.
For spread footings founded on excavated or blasted
rock, attention should be paid to the effect of excavation
and/or blasting. Blasting of highly resistant competent
rock formations may result in overbreak and fracturing
of the rock to some depth below the bearing elevation.
Blasting may reduce the resistance to scour within the
zone of overbreak or fracturing.
Evaluation of seepage forces and hydraulic
gradients should be performed as part of the design of
foundations that will extend below the groundwater
table. Upward seepage forces in the bottom of
excavations can result in piping loss of soil and/or
heaving and loss of stability in the base of foundation
excavations. Dewatering with wells or wellpoints can
control these problems. Dewatering can result in
settlement of adjacent ground or structures. If adjacent
structures may be damaged by settlement induced by
dewatering, seepage cut-off methods such as sheet piling
or slurry walls may be necessary.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Spread footings shall be located below the depth of
frost potential. Depth of frost potential shall be
determined on the basis of local or regional frost
penetration data.
10.6.1.3—Effective Footing Dimensions
For eccentrically loaded footings, a reduced
effective area, B′ × L′, within the confines of the
physical footing shall be used in geotechnical design for
settlement or bearing resistance. The point of load
application shall be at the centroid of the reduced
effective area.
The reduced dimensions for an eccentrically loaded
rectangular footing shall be taken as:
B′ = B − 2eB
Consideration may be given to over-excavation of
frost susceptible material to below the frost depth and
replacement with material that is not frost susceptible.
C10.6.1.3
The reduced dimensions for a rectangular footing
are shown in Figure C10.6.1.3-1.
(10.6.1.3-1)
L′ = L − 2eL
where:
eB = eccentricity parallel to dimension B (ft)
eL = eccentricity parallel to dimension L (ft)
Footings under eccentric loads shall be designed to
ensure that the factored bearing resistance is not less
than the effects of factored loads at all applicable limit
states.
Figure C10.6.1.3-1—Reduced Footing Dimensions
For footings that are not rectangular, similar
procedures should be used based upon the principles
specified above.
For footings that are not rectangular, such as the
circular footing shown in Figure C10.6.1.3-1, the
reduced effective area is always concentrically loaded
and can be estimated by approximation and judgment.
Such an approximation could be made, assuming a
reduced rectangular footing size having the same area
and centroid as the shaded area of the circular footing
shown in Figure C10.6.1.3-1.
10.6.1.4—Bearing Stress Distributions
When proportioning footing dimensions to meet
settlement and bearing resistance requirements at all
applicable limit states, the distribution of bearing stress
on the effective area shall be assumed to be:
•
Uniform for footings on soils, or
•
Linearly varying, i.e., triangular or trapezoidal as
applicable, for footings on rock
The distribution of bearing stress shall be
determined as specified in Article 11.6.3.2.
Bearing stress distributions for structural design of
the footing shall be as specified in Article 10.6.5.
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SECTION 10: FOUNDATIONS
10-53
10.6.1.5—Anchorage of Inclined Footings
Footings that are founded on inclined smooth solid
rock surfaces and that are not restrained by an
overburden of resistant material shall be effectively
anchored by means of rock anchors, rock bolts, dowels,
keys or other suitable means. Shallow keying of large
footings shall be avoided where blasting is required for
rock removal.
C10.6.1.5
Design of anchorages should include consideration
of corrosion potential and protection.
10.6.1.6—Groundwater
Spread footings shall be designed in consideration
of the highest anticipated groundwater table.
The influences of groundwater table on the bearing
resistance of soils or rock and on the settlement of the
structure shall be considered. In cases where seepage
forces are present, they should also be included in the
analyses.
10.6.1.7—Uplift
Where spread footings are subjected to uplift forces,
they shall be investigated both for resistance to uplift
and for structural strength.
10.6.1.8—Nearby Structures
Where foundations are placed adjacent to existing
structures, the influence of the existing structure on the
behavior of the foundation and the effect of the
foundation on the existing structures shall be
investigated.
10.6.2—Service Limit State Design
C10.6.2.1
10.6.2.1—General
Service limit state design of spread footings shall
include evaluation of total and differential settlement
and overall stability. Overall stability of a footing shall
be evaluated where one or more of the following
conditions exist:
•
Horizontal or inclined loads are present,
•
The foundation is placed on embankment,
•
The footing is located on, near or within a slope,
•
The possibility of loss of foundation support
through erosion or scour exists, or
•
Bearing strata are significantly inclined.
The design of spread footings is frequently
controlled by movement at the service limit state. It is
therefore usually advantageous to proportion spread
footings at the service limit state and check for adequate
design at the strength and extreme limit states.
10.6.2.2—Tolerable Movements
The requirements of Article 10.5.2.1 shall apply.
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10-54
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
C10.6.2.3
10.6.2.3—Loads
Immediate settlement shall be determined using
load combination Service I, as specified in
Table 3.4.1-1. Time-dependent settlements in cohesive
soils should be determined using only the permanent
loads, i.e., transient loads should not be considered.
The type of load or the load characteristics may
have a significant effect on spread footing deformation.
The following factors should be considered in the
estimation of footing deformation:
•
The ratio of sustained load to total load,
•
The duration of sustained loads, and
•
The time interval over which settlement or lateral
displacement occurs.
The consolidation settlements in cohesive soils are
time-dependent; consequently, transient loads have
negligible effect. However, in cohesionless soils where
the permeability is sufficiently high, elastic deformation
of the supporting soil due to transient load can take
place. Because deformation in cohesionless soils often
takes place during construction while the loads are being
applied, it can be accommodated by the structure to an
extent, depending on the type of structure and
construction method.
Deformation in cohesionless, or granular, soils
often occurs as soon as loads are applied. As a
consequence, settlements due to transient loads may be
significant in cohesionless soils, and they should be
included in settlement analyses.
10.6.2.4—Settlement Analyses
10.6.2.4.1—General
C10.6.2.4.1
Foundation settlements should be estimated using
computational methods based on the results of
laboratory or insitu testing, or both. The soil parameters
used in the computations should be chosen to reflect the
loading history of the ground, the construction sequence,
and the effects of soil layering.
Both total and differential settlements, including
time dependant effects, shall be considered.
Total settlement, including elastic, consolidation,
and secondary components may be taken as:
St = S e + Sc + S s
(10.6.2.4.1-1)
where:
Se
= elastic settlement (ft)
Sc
= primary consolidation settlement (ft)
Ss
= secondary settlement (ft)
Elastic, or immediate, settlement is the
instantaneous deformation of the soil mass that occurs as
the soil is loaded. The magnitude of elastic settlement is
estimated as a function of the applied stress beneath a
footing or embankment. Elastic settlement is usually
small and neglected in design, but where settlement is
critical, it is the most important deformation
consideration in cohesionless soil deposits and for
footings bearing on rock. For footings located on overconsolidated clays, the magnitude of elastic settlement is
not necessarily small and should be checked.
In a nearly saturated or saturated cohesive soil, the
pore water pressure initially carries the applied stress.
As pore water is forced from the voids in the soil by the
applied load, the load is transferred to the soil skeleton.
Consolidation settlement is the gradual compression of
the soil skeleton as the pore water is forced from the
voids in the soil. Consolidation settlement is the most
important deformation consideration in cohesive soil
deposits that possess sufficient strength to safely support
a spread footing. While consolidation settlement can
occur in saturated cohesionless soils, the consolidation
occurs quickly and is normally not distinguishable from
the elastic settlement.
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SECTION 10: FOUNDATIONS
10-55
The effects of the zone of stress influence, or
vertical stress distribution, beneath a footing shall be
considered in estimating the settlement of the footing.
Spread footings bearing on a layered profile
consisting of a combination of cohesive soil,
cohesionless soil and/or rock shall be evaluated using an
appropriate settlement estimation procedure for each
layer within the zone of influence of induced stress
beneath the footing.
The distribution of vertical stress increase below
circular or square and long rectangular footings, i.e.,
where L > 5B, may be estimated using
Figure 10.6.2.4.1-1.
Secondary settlement, or creep, occurs as a result of
the plastic deformation of the soil skeleton under a
constant effective stress. Secondary settlement is of
principal concern in highly plastic or organic soil
deposits. Such deposits are normally so obviously weak
and soft as to preclude consideration of bearing a spread
footing on such materials.
The principal deformation component for footings
on rock is elastic settlement, unless the rock or included
discontinuities exhibit noticeable time-dependent
behavior.
For guidance on vertical stress distribution for
complex footing geometries, see Poulos and Davis
(1974) or Lambe and Whitman (1969).
Some methods used for estimating settlement of
footings on sand include an integral method to account
for the effects of vertical stress increase variations. For
guidance regarding application of these procedures, see
Gifford et al. (1987).
Figure 10.6.2.4.1-1—Boussinesq Vertical Stress Contours
for Continuous and Square Footings Modified after Sowers
(1979)
10.6.2.4.2—Settlement of Footings on Cohesionless
Soils
The settlement of spread footings bearing on
cohesionless soil deposits shall be estimated as a
function of effective footing width and shall consider the
effects of footing geometry and soil and rock layering
with depth.
C10.6.2.4.2
Although methods are recommended for the
determination of settlement of cohesionless soils,
experience has indicated that settlements can vary
considerably in a construction site, and this variation
may not be predicted by conventional calculations.
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10-56
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Settlements of footings on cohesionless soils shall
be estimated using elastic theory or empirical
procedures.
The elastic half-space method assumes the footing
is flexible and is supported on a homogeneous soil of
infinite depth. The elastic settlement of spread footings,
in feet, by the elastic half-space method shall be
estimated as:
(
)
q 1 −ν 2
A′
o
S =
e
144 E β
s z
(10.6.2.4.2-1)
where:
qo =
applied vertical stress (ksf)
A′ =
effective area of footing (ft2)
Es =
Young’s modulus of soil taken as specified in
Article 10.4.6.3 if direct measurements of Es
are not available from the results of in situ or
laboratory tests (ksi)
Settlements of cohesionless soils occur rapidly,
essentially as soon as the foundation is loaded.
Therefore, the total settlement under the service loads
may not be as important as the incremental settlement
between intermediate load stages. For example, the total
and differential settlement due to loads applied by
columns and cross beams is generally less important
than the total and differential settlements due to girder
placement and casting of continuous concrete decks.
Generally conservative settlement estimates may be
obtained using the elastic half-space procedure or the
empirical method by Hough. Additional information
regarding the accuracy of the methods described herein
is provided in Gifford et al. (1987) and Kimmerling
(2002). This information, in combination with local
experience and engineering judgment, should be used
when determining the estimated settlement for a
structure foundation, as there may be cases, such as
attempting to build a structure grade high to account for
the estimated settlement, when overestimating the
settlement magnitude could be problematic.
Details of other procedures can be found in
textbooks and engineering manuals, including:
•
Terzaghi and Peck (1967)
•
Sowers (1979)
•
U.S. Department of the Navy (1982)
•
D’Appolonia (Gifford et al., 1987)—This method
includes consideration for over-consolidated sands.
•
Tomlinson (1986)
•
Gifford et al. (1987)
For general guidance regarding the estimation of
elastic settlement of footings on sand, see Gifford et al.
(1987) and Kimmerling (2002).
The stress distributions used to calculate elastic
settlement assume the footing is flexible and supported
on a homogeneous soil of infinite depth. The settlement
below a flexible footing varies from a maximum near
the center to a minimum at the edge equal to about
50 percent and 64 percent of the maximum for
rectangular and circular footings, respectively. The
settlement profile for rigid footings is assumed to be
uniform across the width of the footing.
Spread footings of the dimensions normally used
for bridges are generally assumed to be rigid, although
the actual performance will be somewhere between
perfectly rigid and perfectly flexible, even for relatively
thick concrete footings, due to stress redistribution and
concrete creep.
The accuracy of settlement estimates using elastic
theory are strongly affected by the selection of soil
modulus and the inherent assumptions of infinite elastic
half space. Accurate estimates of soil moduli are
difficult to obtain because the analyses are based on
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SECTION 10: FOUNDATIONS
shape factor taken
Table 10.6.2.4.2-1 (dim)
βz =
ν
10-57
=
as
specified
in
Poisson’s Ratio, taken as specified in
Article 10.4.6.3 if direct measurements of ν are
not available from the results of in situ or
laboratory tests (dim)
Unless Es varies significantly with depth, Es should
be determined at a depth of about 1/2 to 2/3 of B below
the footing, where B is the footing width. If the soil
modulus varies significantly with depth, a weighted
average value of Es should be used.
only a single value of soil modulus, and Young’s
modulus varies with depth as a function of overburden
stress. Therefore, in selecting an appropriate value for
soil modulus, consideration should be given to the
influence of soil layering, bedrock at a shallow depth,
and adjacent footings.
For footings with eccentric loads, the area, A′,
should be computed based on reduced footing
dimensions as specified in Article 10.6.1.3.
Table 10.6.2.4.2-1—Elastic Shape and Rigidity Factors,
EPRI (1983)
L/B
Circular
1
2
3
5
10
Flexible, βz
(average)
1.04
1.06
1.09
1.13
1.22
1.41
βz
Rigid
1.13
1.08
1.10
1.15
1.24
1.41
Estimation of spread footing settlement on
cohesionless soils by the empirical Hough method shall
be determined using Eqs. 10.6.2.4.2-2 and 10.6.2.4.2-3.
SPT blow counts shall be corrected as specified in
Article 10.4.6.2.4 for depth, i.e. overburden stress,
before correlating the SPT blow counts to the bearing
capacity index, C ′.
n
S e = ΔH i
(10.6.2.4.2-2)
i =1
in which:
ΔH i = H c
where:
n
=
σ′ + Δσv
1
log o
′
C
σ′o
(10.6.2.4.2-3)
number of soil layers within zone of stress
influence of the footing
ΔHi =
elastic settlement of layer i (ft)
HC =
initial height of layer i (ft)
C′ =
bearing capacity index from Figure 10.6.2.4.2-1
(dim)
The Hough method was developed for normally
consolidated cohesionless soils.
The Hough method has several advantages over
other methods used to estimate settlement in
cohesionless soil deposits, including express
consideration of soil layering and the zone of stress
influence beneath a footing of finite size.
The subsurface soil profile should be subdivided
into layers based on stratigraphy to a depth of about
three times the footing width. The maximum layer
thickness should be about 10 ft.
While Cheney and Chassie (2000), and Hough
(1959), did not specifically state that the SPT N values
should be corrected for hammer energy in addition to
overburden pressure, due to the vintage of the original
work, hammers that typically have an efficiency of
approximately 60 percent were in general used to
develop the empirical correlations contained in the
method. If using SPT hammers with efficiencies that
differ significantly from this 60 percent value, the N
values should also be corrected for hammer energy, in
effect requiring that N160 be used.
In Figure 10.5.2.4.2-1, N′ shall be taken as N160, Standard
Penetration Resistance, N (blows/ft), corrected for
overburden pressure as specified in Article 10.4.6.2.4.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
σ′o =
initial vertical effective stress at the midpoint of
layer i (ksf)
Δσv =
increase in vertical stress at the midpoint of
layer i (ksf)
The Hough method is applicable to cohesionless
soil deposits. The “Inorganic Silt” curve should
generally not be applied to soils that exhibit plasticity.
The settlement characteristics of cohesive soils that
exhibit plasticity should be investigated using
undisturbed samples and laboratory consolidation tests
as prescribed in Article 10.6.2.4.3.
Figure 10.6.2.4.2-1—Bearing Capacity Index versus
Corrected SPT (modified from Cheney and Chassie, 2000,
after Hough, 1959)
10.6.2.4.3—Settlement of Footings on Cohesive
Soils
Spread footings in which cohesive soils are located
within the zone of stress influence shall be investigated
for consolidation settlement. Elastic and secondary
settlement shall also be investigated in consideration of
the timing and sequence of construction loading and the
tolerance of the structure to total and differential
movements.
Where laboratory test results are expressed in terms
of void ratio, e, the consolidation settlement of footings
shall be taken as:
•
For overconsolidated soils where σ′p > σ ′o, see
Figure 10.6.2.4.3-1:
σ ' f
Hc
σ 'p
Sc =
+ C c log
C r log
1 + eo
σ 'o
σ ' p
(10.6.2.4.3-1)
•
For
normally
σ′p = σ′o:
consolidated
soils
where
C10.6.2.4.3
In practice, footings on cohesive soils are most
likely founded on overconsolidated clays, and
settlements can be estimated using elastic theory
(Baguelin et al., 1978), or the tangent modulus method
(Janbu, 1963, 1967). Settlements of footings on
overconsolidated clay usually occur at approximately
one order of magnitude faster than soils without
preconsolidation, and it is reasonable to assume that
they take place as rapidly as the loads are applied.
Infrequently, a layer of cohesive soil may exhibit a
preconsolidation stress less than the calculated existing
overburden stress. The soil is then said to be
underconsolidated because a state of equilibrium has not
yet been reached under the applied overburden stress.
Such a condition may have been caused by a recent
lowering of the groundwater table. In this case,
consolidation settlement will occur due to the additional
load of the structure and the settlement that is occurring
to reach a state of equilibrium. The total consolidation
settlement due to these two components can be
estimated by Eq. 10.6.2.4.3-3 or Eq. 10.6.2.4.3-6.
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SECTION 10: FOUNDATIONS
10-59
σ'f
H
Sc = c Cc log
σ 'p
1 + eo
•
(10.6.2.4.3-2)
For underconsolidated soils where σ′p < σ′o:
σ'
H
Sc = c Cc log f
σ'
1 + eo
pc
(10.6.2.4.3-3)
Where laboratory test results are expressed in terms
of vertical strain, εv, the consolidation settlement of
footings shall be taken as:
•
For overconsolidated soils where σ′p > σ′o, see
Figure 10.6.2.4.3-2:
σ 'f
σ 'p
log
+
C
c
ε
σ 'o
σ ' p
S c = H c C r ε log
•
(10.6.2.4.3-4)
For
normally
where σ ′p = σ ′o:
consolidated
σ 'f
σ 'p
(10.6.2.4.3-5)
S c = H c Ccε log
•
soils
For underconsolidated soils where σ ′p < σ ′o:
σ 'f
σ ' pc
(10.6.2.4.3-6)
S c = H c Ccε log
where:
Hc =
eo
=
initial height of compressible soil layer (ft)
void ratio at initial vertical effective stress
(dim)
Cr =
recompression index (dim)
Cc =
compression index (dim)
Crε =
recompression ratio (dim)
Ccε =
compression ratio (dim)
σ′p =
maximum past vertical effective stress in soil at
midpoint of soil layer under consideration (ksf)
σ′o =
initial vertical effective stress in soil at
midpoint of soil layer under consideration (ksf)
Normally consolidated and underconsolidated soils
should be considered unsuitable for direct support of
spread footings due to the magnitude of potential
settlement, the time required for settlement, for low
shear strength concerns, or any combination of these
design considerations. Preloading or vertical drains may
be considered to mitigate these concerns.
To account for the decreasing stress with increased
depth below a footing and variations in soil
compressibility with depth, the compressible layer
should be divided into vertical increments, i.e., typically
5.0 to 10.0 ft for most normal width footings for
highway applications, and the consolidation settlement
of each increment analyzed separately. The total value
of Sc is the summation of Sc for each increment.
The magnitude of consolidation settlement depends
on the consolidation properties of the soil. These
properties include the compression and recompression
constants, Cc and Cr, or Ccε, and Crε; the
preconsolidation stress, σ′p; the current, initial vertical
effective stress, σ′o; and the final vertical effective stress
after application of additional loading, σ′f. An
overconsolidated soil has been subjected to larger
stresses in the past than at present. This could be a result
of preloading by previously overlying strata,
desiccation, groundwater lowering, glacial overriding or
an engineered preload. If σ′o = σ′p, the soil is normally
consolidated. Because the recompression constant is
typically about an order of magnitude smaller than the
compression constant, an accurate determination of the
preconsolidation stress, σ′p, is needed to make reliable
estimates of consolidation settlement.
The reliability of consolidation settlement estimates
is also affected by the quality of the consolidation test
sample and by the accuracy with which changes in σ′p
with depth are known or estimated. As shown in
Figure C10.6.2.4.3-1, the slope of the e or εv versus log
σ′v curve and the location of σ′p can be strongly affected
by the quality of samples used for the laboratory
consolidation tests. In general, the use of poor quality
samples will result in an overestimate of consolidation
settlement. Typically, the value of σ′p will vary with
depth as shown in Figure C10.6.2.4.3-2. If the variation
of σ′p with depth is unknown, e.g., only one
consolidation test was conducted in the soil profile,
actual settlements could be higher or lower than the
computed value based on a single value of σ′p.
The cone penetrometer test may be used to improve
understanding of both soil layering and variation of σ′p
with depth by correlation to laboratory tests from
discrete locations.
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10-60
σ′f =
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
final vertical effective stress in soil at midpoint
of soil layer under consideration (ksf)
σ′pc = current vertical effective stress in soil, not
including the additional stress due to the
footing loads, at midpoint of soil layer under
consideration (ksf)
Figure C10.6.2.4.3-1—Effects of Sample Quality on
Consolidation Test Results, Holtz and Kovacs (1981)
Figure 10.6.2.4.3-1—Typical Consolidation Compression
Curve for Overconsolidated Soil: Void Ratio versus
Vertical Effective Stress, EPRI (1983)
Figure C10.6.2.4.3-2—Typical Variation of
Preconsolidation Stress with Depth, Holtz and Kovacs
(1981)
Figure 10.6.2.4.3-2—Typical Consolidation Compression
Curve for Overconsolidated Soil: Vertical Strain versus
Vertical Effective Stress, EPRI (1983)
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SECTION 10: FOUNDATIONS
10-61
If the footing width, B, is small relative to the
thickness of the compressible soil, Hc, the effect of
three-dimensional loading shall be considered and shall
be taken as:
S c (3− D ) = μc Sc (1− D )
(10.6.2.4.3-7)
where:
μc
=
reduction factor taken as specified in
Figure 10.6.2.4.3-3 (dim)
Sc(1-D)
=
single
dimensional
settlement (ft)
consolidation
Figure 10.6.2.4.3-3—Reduction Factor to Account for
Effects of Three-Dimensional Consolidation Settlement
(EPRI, 1983)
The time, t, to achieve a given percentage of the
total estimated one-dimensional consolidation settlement
shall be taken as:
t=
TH d 2
cv
(10.6.2.4.3-8)
where:
=
time
factor
taken
as
specified
in
Figure 10.6.2.4.3-4 for the excess pore pressure
distributions shown in the Figure (dim)
Hd =
length of longest drainage path in compressible
layer under consideration (ft)
T
cv
=
coefficient of consolidation (ft2/yr)
Consolidation occurs when a saturated compressible
layer of soil is loaded and water is squeezed out of the
layer. The time required for the (primary) consolidation
process to end will depend on the permeability of the
soil. Because the time factor, T, is defined as
logarithmic, the consolidation process theoretically
never ends. The practical assumption is usually made
that the additional consolidation past 90 percent or
95 percent consolidation is negligible, or is taken into
consideration as part of the total long term settlement.
Refer to Winterkorn and Fang (1975) for values of
T for excess pore pressure distributions other than
indicated in Figure 10.6.2.4.3-4.
The length of the drainage path is the longest
distance from any point in a compressible layer to a
drainage boundary at the top or bottom of the
compressible soil unit. Where a compressible layer is
located between two drainage boundaries, Hd equals
one-half the actual height of the layer. Where a
compressible layer is adjacent to an impermeable
boundary (usually below), Hd equals the full height of
the layer.
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10-62
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Computations to predict the time rate of
consolidation based on the result of laboratory tests
generally tend to over-estimate the actual time required
for consolidation in the field. This over-estimation is
principally due to:
Figure 10.6.2.4.3-4 Percentage of Consolidation as a
Function of Time Factor, T (EPRI, 1983)
Where laboratory test results are expressed in terms
of void ratio, e, the secondary settlement of footings on
cohesive soil shall be taken as:
Ss =
Cα
1 + eo
t2
t1
H c log
(10.6.2.4.3-9)
Where laboratory test results are expressed in terms
of vertical strain, εv, the secondary settlement of
footings on cohesive soils shall be taken as:
t2
t1
S s = Cαε H c log
(10.6.2.4.3-10)
•
The presence of thin drainage layers within the
compressible layer that are not observed from the
subsurface exploration nor considered in the
settlement computations,
•
The effects of three-dimensional dissipation of pore
water pressures in the field, rather than the onedimensional dissipation that is imposed by
laboratory odometer tests and assumed in the
computations, and
•
The effects of sample disturbance, which tend to
reduce the permeability of the laboratory tested
samples.
If the total consolidation settlement is within the
serviceability limits for the structure, the time rate of
consolidation is usually of lesser concern for spread
footings. If the total consolidation settlement exceeds
the serviceability limitations, superstructure damage will
occur unless provisions are made for timing of closure
pours as a function of settlement, simple support of
spans and/or periodic jacking of bearing supports.
Secondary compression component if settlement
results from compression of bonds between individual
clay particles and domains, as well as other effects on
the microscale that are not yet clearly understood (Holtz
and Kovacs, 1981). Secondary settlement is most
important for highly plastic clays and organic and
micaceous soils. Accordingly, secondary settlement
predictions should be considered as approximate
estimates only.
If secondary compression is estimated to exceed
serviceability limitations, either deep foundations or
ground improvement should be considered to mitigate
the effects of secondary compression. Experience
indicates preloading and surcharging may not be
effective in eliminating secondary compression.
where:
Hc =
initial height of compressible soil layer (ft)
eo
=
void ratio at initial vertical effective stress
(dim)
t1
=
time when secondary settlement begins, i.e.,
typically at a time equivalent to 90 percent
average degree of primary consolidation (yr)
t2
=
arbitrary time that could represent the service
life of the structure (yr)
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SECTION 10: FOUNDATIONS
10-63
Cα =
secondary compression index estimated from
the results of laboratory consolidation testing of
undisturbed soil samples (dim)
Cαε =
modified secondary compression index
estimated from the results of laboratory
consolidation testing of undisturbed soil
samples (dim)
10.6.2.4.4—Settlement of Footings on Rock
For footings bearing on fair to very good rock,
according to the Geomechanics Classification system, as
defined in Article 10.4.6.4, and designed in accordance
with the provisions of this Section, elastic settlements
may generally be assumed to be less than 0.5 in. When
elastic settlements of this magnitude are unacceptable or
when the rock is not competent, an analysis of
settlement based on rock mass characteristics shall be
made.
Where rock is broken or jointed (relative rating of
ten or less for RQD and joint spacing), the rock joint
condition is poor (relative rating of ten or less) or the
criteria for fair to very good rock are not met, a
settlement analysis should be conducted, and the
influence of rock type, condition of discontinuities, and
degree of weathering shall be considered in the
settlement analysis.
The elastic settlement of footings on broken or
jointed rock, in feet, should be taken as:
•
C10.6.2.4.4
In most cases, it is sufficient to determine
settlement using the average bearing stress under the
footing.
Where the foundations are subjected to a very large
load or where settlement tolerance may be small,
settlements of footings on rock may be estimated using
elastic theory. The stiffness of the rock mass should be
used in such analyses.
The accuracy with which settlements can be
estimated by using elastic theory is dependent on the
accuracy of the estimated rock mass modulus, Em. In
some cases, the value of Em can be estimated through
empirical correlation with the value of the modulus of
elasticity for the intact rock between joints. For unusual
or poor rock mass conditions, it may be necessary to
determine the modulus from in-situ tests, such as plate
loading and pressuremeter tests.
For circular (or square) footings:
rI p
(
) 144 E
ρ = qo 1 − ν 2
(10.6.2.4.4-1)
m
in which:
Ip =
•
( π)
(10.6.2.4.4-2)
βz
For rectangular footings:
(
ρ = qo 1 − ν 2
BI p
) 144 E
(10.6.2.4.4-3)
m
in which:
( L / B)
1/ 2
Ip =
βz
(10.6.2.4.4-4)
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2012
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10-64
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
where:
qo =
applied vertical stress at base of loaded area
(ksf)
ν
=
Poisson's Ratio (dim)
r
=
radius of circular footing or B/2 for square
footing (ft)
Ip
=
influence coefficient to account for rigidity and
dimensions of footing (dim)
Em =
rock mass modulus (ksi)
βz =
factor to account for footing shape and rigidity
(dim)
Values of Ip should be computed using the βz values
presented in Table 10.6.2.4.2-1 for rigid footings. Where
the results of laboratory testing are not available, values
of Poisson's ratio, ν, for typical rock types may be taken
as specified in Table C10.4.6.5-2. Determination of the
rock mass modulus, Em, should be based on the methods
described in Article 10.4.6.5.
The magnitude of consolidation and secondary
settlements in rock masses containing soft seams or
other material with time-dependent settlement
characteristics should be estimated by applying
procedures specified in Article 10.6.2.4.3.
10.6.2.5—Overall Stability
Overall stability of spread footings shall be
investigated using Service I Load Combination and the
provisions of Articles 3.4.1, 10.5.2.3, and 11.6.3.4.
10.6.2.6—Bearing Resistance at the Service
Limit State
10.6.2.6.1—Presumptive
Resistance
Values
for
Bearing
The use of presumptive values shall be based on
knowledge of geological conditions at or near the
structure site.
C10.6.2.6.1
Unless more appropriate regional data are available,
the presumptive values given in Table C10.6.2.6.1-1
may be used. These bearing resistances are settlement
limited, e.g., 1.0 in., and apply only at the service limit
state.
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2012
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SECTION 10: FOUNDATIONS
10-65
Table C10.6.2.6.1-1—Presumptive Bearing Resistance for Spread Footing Foundations at the Service Limit State Modified
after U.S. Department of the Navy (1982)
Type of Bearing Material
Massive crystalline igneous and metamorphic rock:
granite, diorite, basalt, gneiss, thoroughly cemented
conglomerate (sound condition allows minor cracks)
Foliated metamorphic rock: slate, schist (sound
condition allows minor cracks)
Sedimentary rock: hard cemented shales, siltstone,
sandstone, limestone without cavities
Weathered or broken bedrock of any kind, except
highly argillaceous rock (shale)
Compaction shale or other highly argillaceous rock
in sound condition
Well-graded mixture of fine- and coarse-grained
soil: glacial till, hardpan, boulder clay (GW-GC,
GC, SC)
Gravel, gravel-sand mixture, boulder-gravel
mixtures (GW, GP, SW, SP)
Coarse to medium sand, and with little gravel (SW,
SP)
Fine to medium sand, silty or clayey medium to
coarse sand (SW, SM, SC)
Fine sand, silty or clayey medium to fine sand (SP,
SM, SC)
Homogeneous inorganic clay, sandy or silty clay
(CL, CH)
Inorganic silt, sandy or clayey silt, varved silt-clayfine sand (ML, MH)
Consistency in Place
Very hard, sound rock
Bearing Resistance (ksf)
Recommended
Ordinary Range
Value of Use
120–200
160
Hard sound rock
60–80
70
Hard sound rock
30–50
40
Medium hard rock
16–24
20
Medium hard rock
16–24
20
Very dense
16–24
20
Very dense
Medium dense to dense
Loose
Very dense
Medium dense to dense
Loose
Very dense
Medium dense to dense
Loose
Very dense
Medium dense to dense
Loose
Very dense
Medium dense to dense
Loose
Very stiff to hard
Medium stiff to stiff
Soft
12–20
8–14
4–12
8–12
4–8
2–6
6–10
4–8
2–4
6–10
4–8
2–4
6–12
2–6
1–2
4–8
2–6
1–2
14
10
6
8
6
3
6
5
3
6
5
3
8
4
1
6
3
1
10.6.2.6.2—Semiempirical Procedures for Bearing
Resistance
Bearing resistance on rock shall be determined
using empirical correlation to the Geomechanic Rock
Mass Rating System, RMR, as specified in
Article 10.4.6.4. Local experience should be considered
in the use of these semi-empirical procedures.
If the recommended value of presumptive bearing
resistance exceeds either the unconfined compressive
strength of the rock or the nominal resistance of the
concrete, the presumptive bearing resistance shall be
taken as the lesser of the unconfined compressive
strength of the rock or the nominal resistance of the
concrete. The nominal resistance of concrete shall be
taken as 0.3 f ′c.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
10.6.3—Strength Limit State Design
10.6.3.1—Bearing Resistance of Soil
C10.6.3.1.1
10.6.3.1.1—General
Bearing resistance of spread footings shall be
determined based on the highest anticipated position of
groundwater level at the footing location.
The factored resistance, qR, at the strength limit
state shall be taken as:
q R = ϕ b qn
(10.6.3.1.1-1)
where:
ϕb =
qn =
resistance factor specified in Article 10.5.5.2.2
nominal bearing resistance (ksf)
Where loads are eccentric, the effective footing
dimensions, L′ and B′, as specified in Article 10.6.1.3,
shall be used instead of the overall dimensions L and B
in all equations, tables, and figures pertaining to bearing
resistance.
The bearing resistance of footings on soil should be
evaluated using soil shear strength parameters that are
representative of the soil shear strength under the
loading conditions being analyzed. The bearing
resistance of footings supported on granular soils should
be evaluated for both permanent dead loading conditions
and short-duration live loading conditions using
effective stress methods of analysis and drained soil
shear strength parameters. The bearing resistance of
footings supported on cohesive soils should be evaluated
for short-duration live loading conditions using total
stress methods of analysis and undrained soil shear
strength parameters. In addition, the bearing resistance
of footings supported on cohesive soils, which could
soften and lose strength with time, should be evaluated
for permanent dead loading conditions using effective
stress methods of analysis and drained soil shear
strength parameters.
The position of the groundwater table can
significantly influence the bearing resistance of soils
through its effect on shear strength and unit weight of
the foundation soils. In general, the submergence of
soils will reduce the effective shear strength of
cohesionless (or granular) materials, as well as the longterm (or drained) shear strength of cohesive (clayey)
soils. Moreover, the effective unit weights of submerged
soils are about half of those for the same soils under dry
conditions. Thus, submergence may lead to a significant
reduction in the bearing resistance provided by the
foundation soils, and it is essential that the bearing
resistance analyses be carried out under the assumption
of the highest groundwater table expected within the
service life of the structure.
Footings with inclined bases should be avoided
wherever possible. Where use of an inclined footing
base cannot be avoided, the nominal bearing resistance
determined in accordance with the provisions herein
should be further reduced using accepted corrections for
inclined footing bases in Munfakh, et al. (2001).
Because the effective dimensions will vary slightly
for each limit state under consideration, strict adherence
to this provision will require re-computation of the
nominal bearing resistance at each limit state.
Further, some of the equations for the bearing
resistance modification factors based on L and B were
not necessarily or specifically developed with the
intention that effective dimensions be used. The
designer should ensure that appropriate values of L and
B are used, and that effective footing dimensions L′ and
B′ are used appropriately.
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SECTION 10: FOUNDATIONS
10-67
Consideration should be given to the relative
change in the computed nominal resistance based on
effective versus gross footing dimensions for the size of
footings typically used for bridges. Judgment should be
used in deciding whether the use of gross footing
dimensions for computing nominal bearing resistance at
the strength limit state would result in a conservative
design.
10.6.3.1.2—Theoretical Estimation
10.6.3.1.2a—Basic Formulation
C10.6.3.1.2a
The nominal bearing resistance shall be estimated
using accepted soil mechanics theories and should be
based on measured soil parameters. The soil parameters
used in the analyses shall be representative of the soil
shear strength under the considered loading and
subsurface conditions.
The nominal bearing resistance of spread footings
on cohesionless soils shall be evaluated using effective
stress analyses and drained soil strength parameters.
The nominal bearing resistance of spread footings
on cohesive soils shall be evaluated for total stress
analyses and undrained soil strength parameters. In
cases where the cohesive soils may soften and lose
strength with time, the bearing resistance of these soils
shall also be evaluated for permanent loading conditions
using effective stress analyses and drained soil strength
parameters.
For spread footings bearing on compacted soils, the
nominal bearing resistance shall be evaluated using the
more critical of either total or effective stress analyses.
Except as noted below, the nominal bearing
resistance of a soil layer, in ksf, should be taken as:
qn = cN cm + γD f N qm Cwq + 0.5γ BN γm Cwγ
(10.6.3.1.2a-1)
in which:
N cm = N c sc ic
(10.6.3.1.2a-2)
N qm = N q sq d q iq
(10.6.3.1.2a-3)
N γ m = N γ sγ iγ
(10.6.3.1.2a-4)
The bearing resistance formulation provided in
Eqs. 10.6.3.1.2a-1 though 10.6.3.1.2a-4 is the complete
formulation as described in the Munfakh, et al. (2001).
However, in practice, not all of the factors included in
these equations have been routinely used.
where:
c
=
cohesion, taken as undrained shear strength
(ksf)
Nc
=
cohesion term (undrained loading) bearing
capacity
factor
as
specified
in
Table 10.6.3.1.2a-1 (dim)
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Nq
=
surcharge (embedment) term (drained or
undrained loading) bearing capacity factor
as specified in Table 10.6.3.1.2a-1 (dim)
Nγ
=
unit weight (footing width) term (drained
loading) bearing capacity factor as
specified in Table 10.6.3.1.2a-1 (dim)
γ
=
total (moist) unit weight of soil above or
below the bearing depth of the footing
(kcf)
Df
=
footing embedment depth (ft)
B
=
footing width (ft)
Cwq,Cwγ =
correction factors to account for the
location of the groundwater table as
specified in Table 10.6.3.1.2a-2 (dim)
sc, sγ,sq =
footing shape correction factors
specified in Table 10.6.3.1.2a-3 (dim)
as
=
correction factor to account for the
shearing resistance along the failure
surface passing through cohesionless
material above the bearing elevation as
specified in Table 10.6.3.1.2a-4 (dim)
ic, iγ, iq =
load inclination factors determined from
Eqs. 10.6.3.1.2a-5 or 10.6.3.1.2a-6, and
10.6.3.1.2a-7 and 10.6.3.1.2a-8 (dim)
dq
For φf
ic
=
0:
(10.6.3.1.2a-5)
= 1 − (nH/cBLN c )
For φf
>
0:
ic = iq − [(1 − iq ) /( N q − 1)]
(10.6.3.1.2a-6)
in which:
H
iq = 1 −
(V + cBL cot φ f )
n
H
iγ = 1 −
V + cBL cot φ f )
(10.6.3.1.2a-7)
( n +1)
(10.6.3.1.2a-8)
2
n = [(2 + L / B ) /(1 + L / B )] cos θ
+ [(2 + B / L ) /(1 + B / L )]sin θ
2
(10.6.3.1.2a-9)
Most geotechnical engineers nationwide have not
used the load inclination factors. This is due, in part, to
the lack of knowledge of the vertical and horizontal
loads at the time of geotechnical explorations and
preparation of bearing resistance recommendations.
Furthermore, the basis of the load inclination
factors computed by Eqs. 10.6.3.1.2a-5 to 10.6.3.1.2a-8
is a combination of bearing resistance theory and small
scale load tests on 1 in. wide plates on London Clay and
Ham River Sand (Meyerhof, 1953). Therefore, the
factors do not take into consideration the effects of
depth of embedment. Meyerhof further showed that for
footings with a depth of embedment ratio of Df /B = 1,
the effects of load inclination on bearing resistance are
relatively small. The theoretical formulation of load
inclination factors were further examined by BrinchHansen (1970), with additional modification by Vesic
(1973) into the form provided in Eqs. 10.6.3.1.2a-5 to
10.6.3.1.2a-8.
It should further be noted that the resistance factors
provided in Article 10.5.5.2.2 were derived for vertical
loads. The applicability of these resistance factors to
design of footings resisting inclined load combinations
is not currently known. The combination of the
resistance factors and the load inclination factors may be
overly conservative for footings with an embedment of
approximately Df /B = 1 or deeper because the load
inclination factors were derived for footings without
embedment.
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2012
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SECTION 10: FOUNDATIONS
10-69
where:
In practice, therefore, for footings with modest
embedment, consideration may be given to omission of
the load inclination factors.
Figure C10.6.3.1.2a-1 shows the convention for
determining the θ angle in Eq. 10.6.3.1.2a-9.
B
=
footing width (ft)
L
=
footing length (ft)
H
=
unfactored horizontal load (kips)
V
=
unfactored vertical load (kips)
θ
=
projected direction of load in the plane of the
footing, measured from the side of length L
(degrees)
Figure C10.6.3.1.2a-1—Inclined Loading Conventions
Table 10.6.3.1.2a-1—Bearing Capacity Factors Nc (Prandtl, 1921), Nq (Reissner, 1924), and Nγ (Vesic, 1975)
φf
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Nc
Nq
5.14
5.4
5.6
5.9
6.2
6.5
6.8
7.2
7.5
7.9
8.4
8.8
9.3
9.8
10.4
11.0
11.6
12.3
13.1
13.9
14.8
15.8
16.9
1.0
1.1
1.2
1.3
1.4
1.6
1.7
1.9
2.1
2.3
2.5
2.7
3.0
3.3
3.6
3.9
4.3
4.8
5.3
5.8
6.4
7.1
7.8
Nγ
0.0
0.1
0.2
0.2
0.3
0.5
0.6
0.7
0.9
1.0
1.2
1.4
1.7
2.0
2.3
2.7
3.1
3.5
4.1
4.7
5.4
6.2
7.1
φf
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
Nc
Nq
18.1
19.3
20.7
22.3
23.9
25.8
27.9
30.1
32.7
35.5
38.6
42.2
46.1
50.6
55.6
61.4
67.9
75.3
83.9
93.7
105.1
118.4
133.9
8.7
9.6
10.7
11.9
13.2
14.7
16.4
18.4
20.6
23.2
26.1
29.4
33.3
37.8
42.9
48.9
56.0
64.2
73.9
85.4
99.0
115.3
134.9
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Nγ
8.2
9.4
10.9
12.5
14.5
16.7
19.3
22.4
26.0
30.2
35.2
41.1
48.0
56.3
66.2
78.0
92.3
109.4
130.2
155.6
186.5
224.6
271.8
2012
Edition
10-70
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 10.6.3.1.2a-2—Coefficients Cwq and Cwγ for Various
Groundwater Depths
Dw
0.0
Df
>1.5B + Df
Cwq
0.5
1.0
1.0
Cwγ
0.5
0.5
1.0
Where the position of groundwater is at a depth less
than 1.5 times the footing width below the footing base,
the bearing resistance is affected. The highest anticipated
groundwater level should be used in design.
Table 10.6.3.1.2a-3—Shape Correction Factors sc, sγ, sq
Factor
Shape Factors
sc, sγ, sq
Friction Angle
φf = 0
φf > 0
Cohesion Term (sc)
B
5L
B Nq
1+
L Nc
32
37
42
Df /B
1
2
4
8
1
2
4
8
1
2
4
8
Surcharge Term (sq)
1.0
1.0
1+
Table 10.6.3.1.2a-4—Depth Correction Factor dq
Friction Angle, φf
(degrees)
Unit Weight Term (sγ)
dq
1.20
1.30
1.35
1.40
1.20
1.25
1.30
1.35
1.15
1.20
1.25
1.30
B
L
1 − 0.4
B
tan φ f
L
1+
The
parent
information
from
which
Table 10.6.3.1.2a-4 was developed covered the indicated
range of friction angle, φf. Information beyond the range
indicated is not available at this time.
The depth correction factor should be used only when
the soils above the footing bearing elevation are as
competent as the soils beneath the footing level;
otherwise, the depth correction factor should be taken as
1.0.
Linear interpolations may be made for friction angles
in between those values shown in Table 10.6.3.1.2a-4.
10.6.3.1.2b—Considerations for Punching
Shear
If local or punching shear failure is possible, the
nominal bearing resistance shall be estimated using
reduced shear strength parameters c* and φ* in
Eqs. 10.6.3.1.2b-1 and 10.6.3.1.2b-2. The reduced shear
parameters may be taken as:
c* = 0.67c
(10.6.3.1.2b-1)
C10.6.3.1.2b
Local shear failure is characterized by a failure
surface that is similar to that of a general shear failure
but that does not extend to the ground surface, ending
somewhere in the soil below the footing. Local shear
failure is accompanied by vertical compression of soil
below the footing and visible bulging of soil adjacent to
the footing but not by sudden rotation or tilting of the
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2012
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SECTION 10: FOUNDATIONS
φ* = tan −1 (0.67 tan φ f )
10-71
(10.6.3.1.2b-2)
where:
c* =
reduced effective stress soil cohesion for
punching shear (ksf)
φ* =
reduced effective stress soil friction angle for
punching shear (degrees)
footing. Local shear failure is a transitional condition
between general and punching shear failure. Punching
shear failure is characterized by vertical shear around the
perimeter of the footing and is accompanied by a vertical
movement of the footing and compression of the soil
immediately below the footing but does not affect the
soil outside the loaded area. Punching shear failure
occurs in loose or compressible soils, in weak soils
under slow (drained) loading, and in dense sands for
deep footings subjected to high loads.
Figure C10.6.3.1.2b-1—Modes of Bearing Capacity Failure
for Footings in Sand
10.6.3.1.2c—Considerations for Footings on
Slopes
C10.6.3.1.2c
For footings bearing on or near slopes:
N q = 0.0
(10.6.3.1.2c-1)
In Eq. 10.6.3.1.2a-1, Nc and Nγ shall be replaced with
Ncq and Nγq, respectively, from Figures 10.6.3.1.2c-1 and
10.6.3.1.2c-2 for footings bearing on or near slopes. In
Figure 10.6.3.1.2c-1, the slope stability factor, Ns, shall be
taken as:
•
For B < Hs:
Ns = 0
•
A rational numerical approach for determining a
modified bearing capacity factor, Ncq, for footings on or
near a slope is given in Bowles (1988).
(10.6.3.1.2c-2)
For B ≥ Hs:
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2012
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10-72
Ns =
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
γH s
(10.6.3.1.2c-3)
c
where:
B
=
Hs =
footing width (ft)
height of sloping ground mass (ft)
Figure 10.6.3.1.2c-1—Modified Bearing Capacity Factors
for Footing in Cohesive Soils and on or adjacent to Sloping
Ground after Meyerhof (1957)
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2012
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SECTION 10: FOUNDATIONS
10-73
Figure 10.6.3.1.2c-2—Modified Bearing Capacity Factors
for Footing in Cohesionless Soils and on or adjacent to
Sloping Ground after Meyerhof (1957)
10.6.3.1.2d—Considerations for Two-Layer
Soil Systems—Critical Depth
Where the soil profile contains a second layer of
soil with different properties affecting shear strength
within a distance below the footing less than Hcrit, the
bearing resistance of the layered soil profile shall be
determined using the provisions for two-layered soil
systems herein. The distance Hcrit, in feet, may be taken
as:
q1
q2
B
2 1 +
L
(3 B )
H crit =
ln
(10.6.3.1.2d-1)
where:
q1 =
nominal bearing resistance of footing supported
in the upper layer of a two-layer system,
assuming the upper layer is infinitely thick (ksf)
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
q2 =
B
nominal bearing resistance of a fictitious
footing of the same size and shape as the actual
footing but supported on surface of the second
(lower) layer of a two-layer system (ksf)
=
footing width (ft)
= footing length (ft)
L
10.6.3.1.2e—Two-Layered Soil System in
Undrained Loading
Where a footing is supported on a two-layered soil
system subjected to undrained loading, the nominal
bearing resistance may be determined using
Eq. 10.6.3.1.2a-1 with the following modifications:
C10.6.3.1.2e
Vesic' (1970) developed a rigorous solution for the
modified bearing capacity factor, Nm, for the weak
undrained layer over strong undrained layer situation.
This solution is given by the following equation:
=
undrained shear strength of the top layer of soil
as depicted in Figure 10.6.3.1.2e-1 (ksf)
Nm =
Ncm =
Nm, a bearing capacity factor as specified below
(dim)
in which:
Nqm =
1.0 (dim)
c1
A = ( κ + 1) N c*2 + (1 + κβm ) N c* + βm − 1
Where the bearing stratum overlies a stiffer
cohesive soil, Nm, may be taken as specified in
Figure 10.6.3.1.2e-2.
Where the bearing stratum overlies a softer cohesive
soil, Nm may be taken as:
1
N m = + κsc N c ≤ sc N c
βm
(C10.6.3.1.2e-2)
B = κ(κ + 1) Nc* + κ + βm − 1
(C10.6.3.1.2e-3)
C = ( N c* + βm ) N c* + βm − 1
(C10.6.3.1.2e-4)
(10.6.3.1.2e-1)
•
in which:
βm =
For circular or square footings:
βm =
BL
(10.6.3.1.2e-2)
2( B + L ) H s 2
c2
c1
(10.6.3.1.2e-3)
B
4H
*
N c = 6.17
•
κ=
κNc* ( N c* + βm − 1) A
(C10.6.3.1.2e-1)
B C − ( κNc* + βm − 1))( Nc* + 1)
(C10.6.3.1.2e-5)
For strip footings:
βm =
B
2H
(C10.6.3.1.2e-6)
N c* = 5.14
where:
βm =
the punching index (dim)
c1
=
undrained shear strength of upper soil layer
(ksf)
c2
=
undrained shear strength of lower soil layer
(ksf)
Hs2 =
distance from bottom of footing to top of the
second soil layer (ft)
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SECTION 10: FOUNDATIONS
sc
=
10-75
shape correction factor
Table 10.6.3.1.2a-3
determined
from
Nc =
bearing capacity factor determined herein (dim)
Nqm =
bearing capacity factor determined herein (dim)
Figure 10.6.3.1.2e-1—Two-Layer Soil Profiles
Figure 10.6.3.1.2e-2—Modified Bearing Factor for TwoLayer Cohesive Soil with Weaker Soil Overlying Stronger
Soil (EPRI, 1983)
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10-76
AASHTO LRFD BRIDGEDESIGNSPECIFICATIONS
I0.6.3.1.2f-Two-Layered
Drained Loading
Soil System in
Where a footing supported on a two-layered soil
system is subjected to a drained loading, the nominal
bearing resistance, in ksf, may be taken as:
CI 0.6.3.I .2j
If the upper layer is a cohesionless soil and 4’ equals
25-50 degrees, Eq. 10.6.3.1.2f-1 reduces to:
(C 10.6.3.1.2f-1)
(10.6.3.1.2f-1)
in which:
(10.6.3.1.2f-2)
where:
q2
=
drained shear strength of the top layer of soil as
depicted in Figure 10.6.3.1.2e-1 (ksf)
=
nominal bearing resistance of a fictitious
footing of the same size and shape as the actual
footing but supported on surface of the second
(lower) layer of a two-layer system (ksf)
=
effective stress angle of internal friction of the
top layer of soil (degrees)
10.6.3.I . 3-Semiempirical Procedures
CI 0.6.3.I . 3
The nominal bearing resistance of foundation soils
may be estimated from the results of in-situ tests or by
observed resistance of similar soils. The use of a
particular in-situ test and the interpretation of test results
should take local experience into consideration. The
following in-situ tests may be used:
0
Standard Penetration Test
0
Cone Penetration Test
The nominal bearing resistance in sand, in ksf,
based on SPT results may be taken as:
(10.6.3.1.3-1)
where:
-
Nl,,
=
In application of these empirical methods, the use of
average SPT blow counts and CPT tip resistances is
specified. The resistance factors recommended for
bearing resistance included in Table 10.5.5.2.2-1 assume
the use of average values for these parameters. The use
of lower bound values may result in an overly
conservative design. However, depending on the
availability of soil property data and the variability of
the geologic strata under consideration, it may not be
possible to reliably estimate the average value of the
properties needed for design. In such cases, the Engineer
may have no choice but to use a more conservative
selection of design input parameters to mitigate the
additional risks created by potential variability or the
paucity of relevant data.
The original derivation of Eqs. 10.6.3.1.3-1 and
10.6.3.1.3-2 did not include inclination factors
(Meyerhof, 1956).
average SPT blow count corrected for both
overburden and hammer efficiency effects
(blows/ft) as specified in Article 10.4.6.2.4.
Average the blow count over a depth range
from the bottom of the footing to 1.5B
below the bottom of the footing.
B
=
footing width (ft)
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SECTION
10: FOUNDATIONS
correction factors to account for the
location of the groundwater table as
specified in Table 10.6.3.1.2a-2 (dim)
Cwq,C,=
Df
10-77
=
footing embedment depth taken to the
bottom of the footing (ft)
The nominal bearing resistance, in ksf, for footings
on cohesionless soils based on CPT results may be taken
as:
(10.6.3.1.3-2)
average cone tip resistance within a depth
range B below the bottom of the footing
(ksf)
footing width (ft)
correction factors to account for the
location of the groundwater table as
specified in Table 10.6.3.1.2a-2 (dim)
footing embedment depth taken to the
bottom of the footing (ft)
10.6.3.1.4-Plate Load Tests
The nominal bearing resistance may be determined
by plate load tests, provided that adequate subsurface
explorations have been made to determine the soil
profile below the foundation. Where plate load tests are
conducted, they should be conducted in accordance with
AASHTO T 235 and ASTM D1194.
The nominal bearing resistance determined from a
plate load test may be extrapolated to adjacent footings
where the subsurface profile is confirmed by subsurface
exploration to be similar.
CI 0.6.3.I .4
Plate load tests have a limited depth of influence
and furthermore may not disclose the potential for longterm consolidation of foundation soils.
Scale effects should be addressed when
extrapolating the results to performance of full scale
footings. Extrapolation of the plate load test data to a full
scale footing should be based on the design procedures
provided herein for settlement (service limit state) and
bearing resistance (strength and extreme event limit
state), with consideration to the effect of the
stratification, i.e., layer thicknesses, depths, and
properties. Plate load test results should be applied only
within a sub-area of the project site for which the
subsurface conditions, i.e., stratification, geologic
history, and properties, are relatively uniform.
10.6.3.2-Bearing Resistance of Rock
10.6.3.2.1-General
The methods used for design of footings on rock
shall consider the presence, orientation, and condition of
discontinuities, weathering profiles, and other similar
profiles as they apply at a particular site.
For footings on competent rock, reliance on simple
and direct analyses based on uniaxial compressive rock
strengths and RQD may be applicable. For footings on
less competent rock, more detailed investigations and
CI 0.6.3.2.1
The design of spread footings bearing on rock is
frequently controlled by either overall stability, i.e., the
orientation and conditions of discontinuities, or load
eccentricity considerations. The designer should verify
adequate overall stability at the service limit state and
size the footing based on eccentricity requirements at the
strength limit state before checking nominal bearing
resistance at both the service and strength limit states.
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AASHTO LRFD BRIDGEDESIGNSPECIFICATIONS
10-78
analyses shall be performed to account for the effects of
weathering and the presence and condition of
discontinuities.
The designer shall judge the competency of a rock
mass by taking into consideration both the nature of the
intact rock and the orientation and condition of
discontinuities of the overall rock mass. Where engineering
judgment does not verify the presence of competent rock,
the competency of the rock mass should be verified using
the procedures for RMR rating in Article 10.4.6.4.
10.6.3.2.2-Semiempirical
Procedures
The nominal bearing resistance of rock should be
determined using empirical correlation with the
Geomechanics Rock Mass Rating system. Local
experience shall be considered in the use of these semiempirical procedures.
The factored bearing stress of the foundation shall
not be taken to be greater than the factored compressive
resistance of the footing concrete.
10.6.3.2.3-Analytic
Method
The nominal bearing resistance of foundations on
rock shall be determined using established rock
mechanics principles based on the rock mass strength
parameters. The influence of discontinuities on the
failure mode shall also be considered.
10.6.3.2.4-Load
CI 0.6.3.2.2
The bearing resistance of jointed or broken rock
may be estimated using the semi-empirical procedure
developed by Carter and Kulhawy (1988). This
procedure is based on the unconfined compressive
strength of the intact rock core sample. Depending on
rock mass quality measured in terms of RMR system, the
nominal bearing resistance of a rock mass varies from a
small fraction to six times the unconfined compressive
strength of intact rock core samples.
CI 0.6.3.2.3
Depending upon the relative spacing of joints and
rock layering, bearing capacity failures for foundations
on rock may take several forms. Except for the case of a
rock mass with closed joints, the failure modes are
different from those in soil. Procedures for estimating
bearing resistance for each of the failure modes can be
found in Kulhawy and Goodman (1987), Goodman
(1989), and Sowers (1979).
Test
Where appropriate, load tests may be performed to
determine the nominal bearing resistance of foundations
on rock.
10.6.3.3-Eccentric Load Limitations
The eccentricity of loading at the strength limit
state, evaluated based on factored loads shall not exceed:
0
One-third of the corresponding footing dimension,
B or L, for footings on soils, or 0.45 of the
corresponding footing dimensions B or L, for
footings on rock.
C10.6.3.3
A comprehensive parametric study was conducted
for cantilevered retaining walls of various heights and
soil conditions. The base widths obtained using the
LRFD load factors and eccentricity of B/3 were
comparable to those of ASD with an eccentricity of B/6.
For foundations on rock, to obtain equivalence with
ASD specifications, a maximum eccentricity of B/2
would be needed for LRFD. However, a slightly smaller
maximum eccentricity has been specified to account for
the potential unknown future loading that could push the
resultant outside the footing dimensions.
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SECTION 10: FOUNDATIONS
10-79
10.6.3.4—Failure by Sliding
C10.6.3.4
Failure by sliding shall be investigated for footings
that support horizontal or inclined load and/or are
founded on slopes.
For foundations on clay soils, the possible presence
of a shrinkage gap between the soil and the foundation
shall be considered. If passive resistance is included as
part of the shear resistance required for resisting sliding,
consideration shall also be given to possible future
removal of the soil in front of the foundation.
The factored resistance against failure by sliding, in
kips, shall be taken as:
RR = ϕRn = ϕ τ Rτ + ϕ ep Rep
(10.6.3.4-1)
where:
Rn =
nominal sliding resistance against failure by
sliding (kips)
ϕτ =
resistance factor for shear resistance between soil
and foundation specified in Table 10.5.5.2.2-1
Rτ =
nominal sliding resistance between soil and
foundation (kips)
ϕep =
resistance factor for passive resistance specified
in Table 10.5.5.2.2-1
Rep =
nominal passive resistance of soil available
throughout the design life of the structure
(kips)
If the soil beneath the footing is cohesionless, the
nominal sliding resistance between soil and foundation
shall be taken as:
Sliding failure occurs if the force effects due to the
horizontal component of loads exceed the more critical
of either the factored shear resistance of the soils or the
factored shear resistance at the interface between the soil
and the foundation.
For footings on cohesionless soils, sliding resistance
depends on the roughness of the interface between the
foundation and the soil.
The magnitudes of active earth load and passive
resistance depend on the type of backfill material, the
wall movement, and the compactive effort. Their
magnitude can be estimated using procedures described
in Sections 3 and 11.
In most cases, the movement of the structure and its
foundation will be small. Consequently, if passive
resistance is included in the resistance, its magnitude is
commonly taken as 50 percent of the maximum passive
resistance. This is the basis for the resistance factor, ϕep,
in Table 10.5.5.2.2-1.
The units for RR, Rn, and Rep are shown in kips. For
elements designed on a unit length basis, these quantities
will have the units of kips per unit length.
Rough footing bases usually occur where footings
are cast in-situ. Precast concrete footings may have
smooth bases.
(10.6.3.4-2)
Rτ = V tan δ
for which:
tan δ
=
tan φf for concrete cast against soil
=
0.8 tan φf for precast concrete footing
φf
=
internal friction angle of drained soil
(degrees)
V
=
total vertical force (kips)
where:
For footings that rest on clay, the sliding resistance
may be taken as the lesser of:
•
The cohesion of the clay, or
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2012
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10-80
•
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Where footings are supported on at least 6.0 in. of
compacted granular material, one-half the normal
stress on the interface between the footing and soil,
as shown in Figure 10.6.3.4-1 for retaining walls.
The following notation shall be taken to apply to
Figure 10.6.3.4-1:
=
unit shear resistance, equal to Su or 0.5 σ′v,
whichever is less
Rτ =
nominal sliding resistance between soil and
foundation (kips) expressed as the shaded area
under the qs diagram
Su =
undrained shear strength (ksf)
σ′v =
vertical effective stress (ksf)
qs
Figure 10.6.3.4-1—Procedure for Estimating Nominal
Sliding Resistance for Walls on Clay
10.6.4—Extreme Event Limit State Design
10.6.4.1—General
Extreme limit state design checks for spread
footings shall include, but not necessarily be limited to:
•
Bearing resistance,
•
Eccentric load limitations (overturning),
•
Sliding, and
•
Overall stability.
Resistance factors shall be as specified in
Article 10.5.5.3.
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SECTION 10: FOUNDATIONS
10-81
10.6.4.2—Eccentric Load Limitations
For footings, whether on soil or on rock, the
eccentricity of loading for extreme limit states shall not
exceed the limits provided in Article 11.6.5.
If live loads act to reduce the eccentricity for the
Extreme I limit state, γEQ shall be taken as 0.0.
10.6.5—Structural Design
The structural design of footings shall comply with
the requirements given in Section 5.
For structural design of an eccentrically loaded
foundation, a triangular or trapezoidal contact stress
distribution based on factored loads shall be used for
footings bearing on all soil and rock conditions.
For purposes of structural design, it is usually
assumed that the bearing stress varies linearly across the
bottom of the footing. This assumption results in the
slightly conservative triangular or trapezoidal contact
stress distribution.
10.7—DRIVEN PILES
10.7.1—General
10.7.1.1—Application
Driven piling should be considered in the following
situations:
•
When spread footings cannot be founded on rock, or
on competent soils at a reasonable cost,
•
At locations where soil conditions would normally
permit the use of spread footings but the potential
exists for scour, liquefaction or lateral spreading, in
which case driven piles bearing on suitable
materials below susceptible soils should be
considered for use as a protection against these
problems,
•
Where right-of-way or other space limitations
would not allow the use spread footings,
•
Where existing soil, contaminated by hazardous
materials, must be removed for the construction of
spread footings, or
•
Where an unacceptable amount of settlement of spread
footings may occur.
10.7.1.2—Minimum Pile Spacing, Clearance, and
Embedment into Cap
Center-to-center pile spacing should not be less than
30.0 in. or 2.5 pile diameters. The distance from the side
of any pile to the nearest edge of the pile cap shall not be
less than 9.0 in.
The tops of piles shall project at least 12.0 in. into
the pile cap after all damaged material has been
removed. If the pile is attached to the cap by embedded
bars or strands, the pile shall extend no less than 6.0 in.
into the cap.
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10-82
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Where a reinforced concrete beam is cast-in-place
and used as a bent cap supported by piles, the concrete
cover on the sides of the piles shall not be less than
6.0 in., plus an allowance for permissible pile
misalignment. Where pile reinforcement is anchored in
the cap satisfying the requirements of Article 5.13.4.1,
the projection may be less than 6.0 in.
10.7.1.3—Piles through Embankment Fill
Piles to be driven through embankments should
penetrate a minimum of 10 ft through original ground
unless refusal on bedrock or competent bearing strata
occurs at a lesser penetration.
Fill used for embankment construction should be a
select material, which does not obstruct pile penetration
to the required depth.
10.7.1.4—Batter Piles
When the lateral resistance of the soil surrounding the
piles is inadequate to counteract the horizontal forces
transmitted to the foundation, or when increased rigidity
of the entire structure is required, batter piles should be
considered for use. Where negative side resistance
(downdrag) loads are expected, batter piles should be
avoided. If batter piles are used in areas of significant
seismic loading, the design of the pile foundation shall
recognize the increased foundation stiffness that results.
10.7.1.5—Pile Design Requirements
Pile design shall address the following issues as
appropriate:
•
Nominal bearing resistance to be specified in the
contract, type of pile, and size of pile group required
to provide adequate support, with consideration of
how nominal bearing pile resistance will be
determined in the field.
•
Group interaction.
•
Pile quantity estimation and estimated pile
penetration required to meet nominal axial
resistance and other design requirements.
•
Minimum pile penetration necessary to satisfy the
requirements caused by uplift, scour, downdrag,
settlement, liquefaction, lateral loads, and seismic
conditions.
C10.7.1.3
If refusal occurs at a depth of less than 10 ft, other
foundation types, e.g., footings or shafts, may be more
effective.
To minimize the potential for obstruction of the piles,
the maximum size of any rock particles in the fill should
not exceed 6.0 in. Pre-drilling or spudding pile locations
should be considered in situations where obstructions in
the embankment fill cannot be avoided, particularly for
displacement piles. Note that predrilling or spudding may
reduce the pile side resistance and lateral resistance,
depending on how the predrilling or spudding is
conducted. The diameter of the predrilled or spudded
hole, and the potential for caving of the hole before the pile
is installed will need to be considered to assess the effect
this will have on side and lateral resistance.
If compressible soils are located beneath the
embankment, piles should be driven after embankment
settlement is complete, if possible, to minimize or
eliminate downdrag forces.
C10.7.1.4
In some cases, it may be desirable to use batter
piles. From a general viewpoint, batter piles provide a
much stiffer resistance to lateral loads than would be
possible with vertical piles. They can be very effective
in resisting static lateral loads.
Due to increased foundation stiffness, batter piles
may not be desirable in resisting lateral dynamic loads if
the structure is located in an area where seismic loads
are potentially high.
C10.7.1.5
The driven pile design process is discussed in detail
in Hannigan et al. (2006).
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SECTION 10: FOUNDATIONS
10-83
•
Foundation deflection to meet the established
movement and associated structure performance
criteria.
•
Pile foundation nominal structural resistance.
•
Pile drivability to confirm that acceptable driving
stresses and blow counts can be achieved at the
nominal bearing resistance, and at the estimated
resistance to reach the minimum tip elevation, if a
minimum tip elevation is required, with an available
driving system.
•
Long-term durability of the pile in service, i.e.
corrosion and deterioration.
10.7.1.6—Determination of Pile Loads
C10.7.1.6.1
10.7.1.6.1—General
The loads and load factors to be
foundation design shall be as specified
Computational assumptions that shall
determining individual pile loads are
Section 4.
used in pile
in Section 3.
be used in
described in
10.7.1.6.2—Downdrag
The provisions of Article 3.11.8 shall apply for
determination of load due to negative side resistance.
Where piles are driven to end bearing on a dense
stratum or rock and the design of the pile is structurally
controlled, downdrag shall be considered at the strength
and extreme limit states.
For friction piles that can experience settlement at
the pile tip, downdrag shall be considered at the service,
strength and extreme limit states. Estimate pile and pile
group settlement according to Article 10.7.2.
The nominal pile resistance available to support
structure loads plus downdrag shall be estimated by
considering only the positive side and tip resistance
below the lowest layer contributing to downdrag
computed as specified in Article 3.11.8.
10.7.1.6.3—Uplift Due to Expansive Soils
Piles penetrating expansive soil shall extend to a
depth into moisture-stable soils sufficient to provide
adequate anchorage to resist uplift. Sufficient clearance
should be provided between the ground surface and
underside of caps or beams connecting piles to preclude
the application of uplift loads at the pile/cap connection
due to swelling ground conditions.
The specification and determination of top of cap
loads is discussed in Section 3. The Engineer should
select different levels of analysis, detail and accuracy as
appropriate for the structure under consideration. Details
are discussed in Section 4.
C10.7.1.6.2
Downdrag occurs when settlement of soils along the
side of the piles results in downward movement of the
soil relative to the pile. See commentary to
Article C3.11.8.
In the case of friction piles with limited tip
resistance, the downdrag load can exceed the
geotechnical resistance of the pile, causing the pile to
move downward enough to allow service limit state
criteria for the structure to be exceeded. Where pile
settlement is not limited by nominal bearing resistance
below the downdrag zone, service limit state tolerances
will govern the geotechnical design.
This design situation is not desirable and the
preferred practice is to mitigate the downdrag induced
foundation settlement through a properly designed
surcharge and/or preloading program, or by extending
the piles deeper for higher resistance.
Instrumented static load tests, dynamic tests with
signal matching, or static analysis procedures in
Article 10.7.3.8.6 may be used to estimate the available
nominal resistance to withstand the downdrag plus
structure loads.
C10.7.1.6.3
Evaluation of potential uplift loads on piles
extending through expansive soils requires evaluation of
the swell potential of the soil and the extent of the soil
strata that may affect the pile. One reasonably reliable
method for identifying swell potential is presented in
Table 10.4.6.3-1. Alternatively, ASTM D4829 may be
used to evaluate swell potential. The thickness of the
potentially expansive stratum must be identified by:
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10-84
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
10.7.1.6.4—Nearby Structures
Where pile foundations are placed adjacent to
existing structures, the influence of the existing structure
on the behavior of the foundation, and the effect of the
new foundation on the existing structures, including
vibration effects due to pile installation, shall be
investigated.
•
Examination of soil samples from borings for the
presence of jointing, slickensiding, or a blocky
structure and for changes in color, and
•
Laboratory testing for determination of soil
moisture content profiles.
C10.7.1.6.4
Vibration due to pile driving can cause settlement of
existing foundations as well as structural damage to the
adjacent facility, especially in loose cohesionless soils.
The combination of taking measures to mitigate the
vibration levels through use of nondisplacement piles,
predrilling, proper hammer choice, etc., and a good
vibration monitoring program should be considered.
10.7.2—Service Limit State Design
10.7.2.1—General
C10.7.2.1
Service limit state design of driven pile foundations
includes the evaluation of settlement due to static loads,
and downdrag loads if present, overall stability, lateral
squeeze, and lateral deformation. Overall stability of a
pile supported foundation shall be evaluated where:
•
The foundation is placed through an embankment,
•
The pile foundation is located on, near or within a
slope,
•
The possibility of loss of foundation support
through erosion or scour exists, or
•
Bearing strata are significantly inclined.
Lateral analysis of pile foundations is conducted to
establish the load distribution between the superstructure
and foundations for all limit states, and to estimate the
deformation in the foundation that will occur due to
those loads. This Article only addresses the evaluation of
the lateral deformation of the foundation resulting from
the distributed loads.
In general, it is not desirable to subject the pile
foundation to unbalanced lateral loading caused by lack
of overall stability or caused by lateral squeeze.
Unbalanced lateral forces caused by lack of overall
stability or lateral squeeze should be mitigated through
stabilization measures, if possible.
10.7.2.2—Tolerable Movements
C10.7.2.2
The provisions of Article 10.5.2.1 shall apply.
See Article C10.5.2.1.
10.7.2.3—Settlement
10.7.2.3.1—Equivalent Footing Analogy
For purposes of calculating the settlements of pile
groups, loads should be assumed to act on an equivalent
footing based on the depth of embedment of the piles
into the layer that provides support as shown in
Figures 10.7.2.3.1-1 and 10.7.2.3.1-2.
Pile group settlement shall be evaluated for pile
foundations in cohesive soils, soils that include cohesive
layers, and piles in loose granular soils. The load used in
calculating settlement shall be the permanently applied
load on the foundation.
In applying the equivalent footing analogy for pile
foundation, the reduction to equivalent dimensions B′
and L′ as used for spread footing design does not apply.
C10.7.2.3.1
Pile design should ensure that strength limit state
considerations are satisfied before checking service limit
state considerations.
For piles embedded adequately into dense granular
soils such that the equivalent footing is located on or
within the dense granular soil, and furthermore are not
subjected to downdrag loads, a detailed assessment of
the pile group settlement may be waived.
Methods for calculating settlement are discussed in
Hannigan et al., (2006).
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SECTION 10: FOUNDATIONS
10-85
Figure 10.7.2.3.1-1—Stress Distribution below Equivalent Footing for Pile Group after Hannigan et al. (2006)
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure 10.7.2.3.1-2—Location of Equivalent Footing
(after Duncan and Buchignani, 1976)
10.7.2.3.2—Pile Groups in Cohesive Soil
Shallow
foundation
settlement
estimation
procedures shall be used to estimate the settlement of a
pile group, using the equivalent footing location
specified in Figure 10.7.2.3-1.1 or Figure 10.7.2.3.1-2.
The settlement of pile groups in cohesionless soils
may be taken as:
Using SPT: ρ =
qI B
N160
(10.7.2.3.2-1)
Using CPT: ρ =
qBI
2qc
(10.7.2.3.2-2)
≥ 0.5
(10.7.2.3.2-3)
C10.7.2.3.2
The provisions are based upon the use of empirical
correlations proposed by Meyerhof (1976). These are
empirical correlations and the units of measure must
match those specified for correct computations. This
method may tend to over-predict settlements.
in which:
I = 1 − 0.125
D′
B
where:
ρ
=
settlement of pile group (in.)
q
=
net foundation pressure applied at 2Db/3,
as shown in Figure 10.7.2.3.1-1; this
pressure is equal to the applied load at the
top of the group divided by the area of the
equivalent footing and does not include the
weight of the piles or the soil between the
piles (ksf)
B
=
width or smallest dimension of pile group
(ft)
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2012
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SECTION 10: FOUNDATIONS
10-87
I
=
influence factor of the effective group
embedment (dim)
D′
=
effective depth taken as 2Db/3 (ft)
Db
=
depth of embedment of piles in layer that
provides support, as specified in
Figure 10.7.2.3.1-1 (ft)
N160
=
SPT blow count corrected for both
overburden and hammer efficiency
effects (blows/ft) as specified in
Article 10.4.6.2.4.
qc
=
static cone tip resistance (ksf)
Alternatively, other methods for computing
settlement in cohesionless soil, such as the Hough
method as specified in Article 10.6.2.4.2 may also be
used in connection with the equivalent footing approach.
The corrected SPT blow count or the static cone tip
resistance should be averaged over a depth equal to the
pile group width B below the equivalent footing. The
SPT and CPT methods (Eqs. 10.7.2.3.2-1 and
10.7.2.3.2-2) shall only be considered applicable to the
distributions shown in Figure 10.7.2.3.1-1b and
Figure 10.7.2.3.1-2.
10.7.2.4—Horizontal Pile Foundation Movement
Horizontal movement induced by lateral loads shall
be evaluated. The provisions of Article 10.5.2.1 shall
apply regarding horizontal movement criteria.
The horizontal movement of pile foundations shall
be estimated using procedures that consider soilstructure interaction. Tolerable horizontal movements of
piles shall be established on the basis of confirming
compatible movements of structural components, e.g.,
pile to column connections, for the loading condition
under consideration.
The effects of the lateral resistance provided by an
embedded cap may be considered in the evaluation of
horizontal movement.
The orientation of nonsymmetrical pile crosssections shall be considered when computing the pile
lateral stiffness.
Lateral resistance of single piles may be determined
by static load test. If a static lateral load test is to be
performed, it shall follow the procedures specified in
ASTM D3966.
The effects of group interaction shall be taken into
account when evaluating pile group horizontal
movement. When the P-y method of analysis is used, the
values of P shall be multiplied by P-multiplier values,
Pm, to account for group effects. The values of Pm
provided in Table 10.7.2.4-1 should be used.
C10.7.2.4
Pile foundations are subjected to lateral loads due to
wind, traffic loads, bridge curvature, vessel or traffic
impact and earthquake. Batter piles are sometimes used
but they are somewhat more expensive than vertical
piles, and vertical piles are more effective against
dynamic loads.
Methods of analysis that use manual computation
were developed by Broms (1964a and 1964b). They are
discussed in detail by Hannigan et al. (2006). Reese
developed analysis methods that model the horizontal
soil resistance using P-y curves. This analysis has been
well developed and software is available for analyzing
single piles and pile groups (Reese, 1986; Williams et
al., 2003; and Hannigan et al., 2006).
Deep foundation horizontal movement at the
foundation design stage may be analyzed using
computer applications that consider soil-structure
interaction. Application formulations are available that
consider the total structure including pile cap, pier and
superstructure (Williams et al., 2003).
If a lateral static load test is used to assess the site
specific lateral resistance of a pile, information on the
methods of analysis and interpretation of lateral load tests
presented in the Handbook on Design of Piles and Drilled
Shafts Under Lateral Load, Reese (1984) and Static
Testing of Deep Foundations, Kyfor et al. (1992) should be
used.
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Table 10.7.2.4-1—Pile P-Multipliers, Pm, for Multiple Row Shading (averaged from Hannigan et al., 2006)
Pile CTC spacing (in the direction of
loading)
3B
5B
Row 1
0.8
1.0
Loading direction and spacing shall be taken as
defined in Figure 10.7.2.4-1. If the loading direction for
a single row of piles is perpendicular to the row (bottom
detail in the Figure), a group reduction factor of less
than 1.0 should only be used if the pile spacing is 5B or
less, i.e., a Pm of 0.8 for a spacing of 3B, as shown in
Figure 10.7.2.4-1.
P-Multipliers, Pm
Row 2
0.4
0.85
Row 3 and higher
0.3
0.7
Since many piles are installed in groups, the
horizontal resistance of the group has been studied and it
has been found that multiple rows of piles will have less
resistance than the sum of the single pile resistance. The
front piles “shade” rows that are further back.
The P-multipliers, Pm, in Table 10.7.2.4-1 are a
function of the center-to-center (CTC) spacing of piles
in the group in the direction of loading expressed in
multiples of the pile diameter, B. The values of Pm in
Table 10.7.2.4-1 were developed for vertical piles only.
Lateral load tests have been performed on pile
groups, and multipliers have been determined that can
be used in the analysis for the various rows. Those
multipliers have been found to depend on the pile
spacing and the row number in the direction of
loading. To establish values of Pm for other pile
spacing values, interpolation between values should
be conducted.
The multipliers are a topic of current research
and may change in the future. Values from recent
research have been tabulated by Hannigan et al.
(2006).
Note that these P-y methods generally apply to
foundation elements that have some ability to bend and
deflect. For large diameter, relatively short foundation
elements, e.g., drilled shafts or relatively short stiff
piles, the foundation element rotates rather than bends,
in which case strain wedge theory (Norris, 1986;
Ashour et al., 1998) may be more applicable. When
strain wedge theory is used to assess the lateral load
response of groups of short, large diameter piles or
shaft groups, group effects should be addressed
through evaluation of the overlap between shear zones
formed due to the passive wedge that develops in front
of each shaft in the group as lateral deflection
increases. Note that Pm in Table 10.7.2.4-1 is not
applicable if strain wedge theory is used.
Batter piles provide a much stiffer lateral response
than vertical piles when loaded in the direction of the
batter.
Figure 10.7.2.4-1—Definition of Loading Direction and
Spacing for Group Effects
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SECTION 10: FOUNDATIONS
10-89
10.7.2.5—Settlement Due to Downdrag
The nominal pile resistance available to support
structure loads plus downdrag shall be estimated by
considering only the positive side and tip resistance
below the lowest layer contributing to the downdrag. In
general, the available factored geotechnical resistance
should be greater than the factored loads applied to the
pile, including the downdrag, at the service limit state.
In the case where it is not possible to obtain adequate
geotechnical resistance below the lowest layer
contributing to downdrag, e.g., piles supported by side
resistance, to fully resist the downdrag, the structure
should be designed to tolerate the full amount of
settlement resulting from the downdrag and the other
applied loads.
If adequate geotechnical resistance is available to
resist the downdrag plus structure loads in the service
limit state, the amount of deformation needed to fully
mobilize the geotechnical resistance should be
estimated, and the structure designed to tolerate the
anticipated movement.
10.7.2.6—Lateral Squeeze
Bridge abutments supported on pile foundations
driven through soft soils that are subject to unbalanced
embankment fill loading shall be evaluated for lateral
squeeze.
C10.7.2.5
The static analysis procedures in Article 10.7.3.8.6
may be used to estimate the available pile nominal
resistance to withstand the downdrag plus structure loads.
Nominal resistance may also be estimated using a
dynamic method, e.g., dynamic measurements with signal
matching analysis, wave equation, pile driving formula,
etc., per Article 10.7.3.8, provided the side resistance
within the zone contributing to downdrag is subtracted
from the nominal bearing resistance determined from the
dynamic method during pile installation. The side
resistance within the zone contributing to downdrag may
be estimated using the static analysis methods specified in
Article 10.7.3.8.6, from signal matching analysis, or from
instrumented pile load test results. Note that the static
analysis methods may have bias that, on average, over or
under predicts the side resistance. The bias of the method
selected to estimate the side resistance within the
downdrag zone should be taken into account as described
in Article 10.7.3.3.
For the establishment of settlement tolerance limits,
see Article 10.5.2.1.
C10.7.2.6
Guidance on evaluating the potential for lateral
squeeze and potential mitigation methods are included
in Hannigan et al., (2006).
10.7.3—Strength Limit State Design
10.7.3.1—General
C10.7.3.1
For strength limit state design, the following shall
be determined:
•
Loads and performance requirements;
•
Pile type, dimensions, and nominal bearing
resistance;
•
Size and configuration of the pile group to provide
adequate foundation support;
•
Estimated pile length to be used in the construction
contract documents to provide a basis for bidding;
•
A minimum pile penetration, if required, for the
particular site conditions and loading, determined
based on the maximum (deepest) depth needed to
meet all of the applicable requirements identified in
Article 10.7.6;
A minimum pile penetration should only be specified
if needed to ensure that uplift, lateral stability, depth
to resist downdrag, depth to satisfy scour concerns, and
depth for structural lateral resistance are met for the
strength limit state, in addition to similar requirements
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
•
The maximum driving resistance expected in order
to reach the minimum pile penetration required, if
applicable, including any soil/pile side resistance
that will not contribute to the long-term nominal
bearing resistance of the pile, e.g., soil contributing
to downdrag, or soil that will be removed by scour;
•
The drivability of the selected pile to achieve the
required nominal axial resistance or minimum
penetration with acceptable driving stresses at a
satisfactory blow count per unit length of
penetration; and
•
The nominal structural resistance of the pile and/or
pile group.
for the service and extreme event limit states. See Article
10.7.6 for additional details. Assuming static load tests,
dynamic methods, e.g., dynamic test with signal matching,
wave equation, pile formulae, etc., are used during pile
installation to establish when the nominal bearing
resistance has been met, a minimum pile penetration
should not be used to ensure that the required nominal pile
bearing, i.e., compression, resistance is obtained.
A nominal resistance measured during driving
exceeding the compressive nominal resistance required
by the contract may be needed in order to reach a
minimum pile penetration specified in the contract.
The drivability analysis is performed to establish
whether a hammer and driving system will likely install
the pile in a satisfactory manner.
10.7.3.2—Point Bearing Piles on Rock
C10.7.3.2.1
10.7.3.2.1—General
As applied to pile compressive resistance, this
Article shall be considered applicable to soft rock, hard
rock, and very strong soils such as very dense glacial
tills that will provide high nominal bearing resistance in
compression with little penetration.
10.7.3.2.2—Piles Driven to Soft Rock
Soft rock that can be penetrated by pile driving shall
be treated in the same manner as soil for the purpose of
design for bearing resistance, in accordance with
Article 10.7.3.8.
10.7.3.2.3—Piles Driven to Hard Rock
The nominal resistance of piles driven to point
bearing on hard rock where pile penetration into the
rock formation is minimal is controlled by the structural
limit state. The nominal bearing resistance shall not
exceed the values obtained from Article 6.9.4.1 with the
resistance factors specified in Article 6.5.4.2 and
Article 6.15 for severe driving conditions. A pile-driving
acceptance criteria shall be developed that will prevent
pile damage. Dynamic pile measurements should be
used to monitor for pile damage.
If pile penetration into rock is expected to be
minimal, the prediction of the required pile length will
usually be based on the depth to rock.
A definition of hard rock that relates to measurable
rock characteristics has not been widely accepted. Local
or regional experience with driving piles to rock
provides the most reliable definition.
In general, it is not practical to drive piles into rock to
obtain significant uplift or lateral resistance. The ability to
obtain sufficient uplift resistance will depend on the
softness of the rock formation. Local experience should
also be considered. If significant lateral or uplift
foundation resistance is required, drilled shaft foundations
should be considered. If it is still desired to use piles, a
pile drivability study should be performed to verify the
feasibility of obtaining the desired penetration into rock.
C10.7.3.2.2
Steel piles driven into soft rock may not require tip
protection.
C10.7.3.2.3
Care should be exercised in driving piles to hard
rock to avoid tip damage. The tips of steel piles driven
to hard rock should be protected by high strength, cast
steel tip protection.
If the rock surface is reasonably flat, installation
with pile tip protection should be considered. In the case
of sloping rock, or when battered piles are driven to
rock, greater difficulty can arise and the use of tip
protection with teeth should be considered. The designer
should perform a wave equation analysis to check
anticipated stresses, and also consider the following to
minimize the risk of pile damage during installation:
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SECTION 10: FOUNDATIONS
10-91
•
Use a relatively small hammer. If a hammer with
adjustable stroke or energy setting is used, it should
be operated with a small stroke to seat the pile. The
nominal axial resistance can then be proven with a
few larger hammer blows.
•
A large hammer should not be used if it cannot be
adjusted to a low stroke. It may be impossible to
detect possible toe damage if a large hammer with
large stroke is used.
•
For any hammer size, specify a limited number of
hammer blows after the pile tip reaches the rock,
and stop immediately. An example of a limiting
criteria is five blows per one half inch.
•
Extensive dynamic testing can be used to verify
bearing resistance on a large percentage of the piles.
This approach could be used to justify larger design
nominal resistances.
If such measures are taken, and successful local
experience is available, it may be acceptable to not
conduct the dynamic pile measurements.
10.7.3.3—Pile Length Estimates for Contract
Documents
Subsurface geotechnical information combined
with static analysis methods (Article 10.7.3.8.6),
preconstruction probe pile programs (Article 10.7.9),
and/or pile load tests (Article 10.7.3.8.2) shall be used to
estimate the depth of penetration required to achieve the
desired nominal bearing resistance to establish contract
pile quantities. If static analysis methods are used,
potential bias in the method selected should be
considered when estimating the penetration depth
required to achieve the desired nominal bearing
resistance. Local pile driving experience shall also be
considered when making pile quantity estimates. If the
depth of penetration required to obtain the desired
nominal bearing, i.e., compressive, resistance is less
than the depth required to meet the provisions of
Article 10.7.6, the minimum penetration required per
Article 10.7.6 should be used as the basis for estimating
contract pile quantities.
C10.7.3.3
The estimated pile length necessary to provide the
required nominal resistance is determined using a static
analysis, local pile driving experience, knowledge of the
site subsurface conditions, and/or results from a static
pile load test program. The required pile length is often
defined by the presence of an obvious bearing layer.
Local pile driving experience with such a bearing layer
should be strongly considered when developing pile
quantity estimates.
In variable soils, a program of probe piles across the
site is often used to determine variable pile order lengths.
Probe piles are particularly useful when driving concrete
piles. The pile penetration depth (i.e., length) used to
estimate quantities for the contract should also consider
requirements to satisfy other design considerations,
including service and extreme event limit states, as well as
minimum pile penetration requirements for lateral stability,
uplift, downdrag, scour, group settlement, etc.
One solution to the problem of predicting pile length
is the use of a preliminary test program at the site. Such a
program can range from a very simple operation of
driving a few piles to evaluate drivability, to an extensive
program where different pile types are driven and static
load and dynamic testing is performed. For large projects,
such test programs may be very cost effective.
In lieu of local pile driving experience, if a static
analysis method is used to estimate the pile length
required to achieve the desired nominal resistance for
establishment of contract pile quantities, to theoretically
account for method bias, the factored resistance used to
determine the number of piles required in the pile group
may be conservativley equated to the factored resistance
estimated using the static analysis method as follows:
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ϕdyn x Rn = ϕstat x Rnstat
(C10.7.3.3-1)
where:
ϕdyn
=
the resistance factor for the dynamic
method used to verify pile bearing
resistance during driving specified in
Table 10.5.5.2.3-1
Rn
=
the nominal pile bearing resistance (kips)
ϕstat
=
the resistance factor for the static analysis
method used to estimate the pile penetration
depth required to achieve the desired bearing
resistance specified in Table 10.5.5.2.3-1
Rnstat
=
the predicted nominal resistance from the
static analysis method used to estimate the
penetration depth required (kips)
Using Eq. C10.7.3.3-1 and solving for Rnstat, use the
static analysis method to determine the penetration
depth required to obtain Rnstat.
The resistance factor for the static analysis method
inherently accounts for the bias and uncertainty in the
static analysis method. However, local experience may
dictate that the penetration depth estimated using this
approach be adjusted to reflect that experience. Where
piles are driven to a well defined firm bearing stratum,
the location of the top of bearing stratum will dictate the
pile length needed, and Eq. C10.7.3.3-1 is likely not
applicable.
Note that Rn is considered to be nominal bearing
resistance of the pile needed to resist the applied loads,
and is used as the basis for determining the resistance to
be achieved during pile driving, Rndr (see Articles 10.7.6
and 10.7.7). Rnstat is only used in the static analysis
method to estimate the pile penetration depth required.
Note that while there is a theoretical basis to this
suggested approach, it can produce apparently erroneous
results if attempting to use extremes in static analysis
and dynamic methods, e.g., using static load test results
and then using the Engineering News formula to control
pile driving, or using a very inaccurate static analysis
method in combination with dynamic testing and signal
matching. Part of the problem is that the available
resistance factors have been established in consideration
of the risk and consequences of pile foundation failure
rather than the risk and consequences of underrunning or
overrunning pile quantities. Therefore, the approach
provided in Eq. C10.7.3.3-1 should be used cautiously,
especially when the difference between the resistance
factors for method used to estimate pile penetration
depth versus the one used for obtaining the required
nominal axial resistance is large.
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SECTION 10: FOUNDATIONS
10-93
10.7.3.4—Nominal Axial Resistance Change
after Pile Driving
10.7.3.4.1—General
C10.7.3.4.1
Consideration should be given to the potential for
change in the nominal axial pile resistance after the end
of pile driving. The effect of soil relaxation or setup
should be considered in the determination of nominal
axial pile resistance for soils that are likely to be subject
to these phenomena.
10.7.3.4.2—Relaxation
If relaxation is possible in the soils at the site the
pile shall be tested in re-strike after a sufficient time has
elapsed for relaxation to develop.
Soil relaxation is not a common phenomenon but
more serious than setup since it represents a reduction in
the reliability of the foundation.
Soil setup is a common phenomenon that can
provide the opportunity for using larger nominal
resistances at no increase in cost. However, it is
necessary that the resistance gain be adequately proven.
This is usually accomplished by restrike testing with
dynamic measurements (Komurka, et. al, 2003).
C10.7.3.4.2
Relaxation is a reduction in axial pile resistance.
While relaxation typically occurs at the pile tip, it can
also occur along the sides of the pile (Morgano and
White, 2004). It can occur in dense sands or sandy silts
and in some shales. Relaxation in the sands and silts will
usually develop fairly quickly after the end of driving
(perhaps in only a few minutes or hours) as a result of
the return of the reduced pore pressure induced by
dilation of the dense sands during driving. In some
shales, relaxation occurs during the driving of adjacent
piles and that will be immediate. There are other shales
where the pile penetrates the shale and relaxation
requires perhaps as much as two weeks to develop. In
some cases, the amount of relaxation can be large.
C10.7.3.4.3
10.7.3.4.3—Setup
Setup in the nominal axial resistance may be used to
support the applied load. Where increase in resistance
due to setup is utilized, the existence of setup shall be
verified after a specified length of time by re-striking the
pile.
Setup is an increase in the nominal axial resistance that
develops over time predominantly along the pile shaft. Pore
pressures increase during pile driving due to a reduction of
the soil volume, reducing the effective stress and the shear
strength. Setup may occur rapidly in cohesionless soils and
more slowly in finer grained soils as excess pore water
pressures dissipate. In some clays, setup may continue to
develop over a period of weeks and even months, and in
large pile groups it can develop even more slowly.
Setup, sometimes called “pile freeze,” can be used to
carry applied load, providing the opportunity for using
larger pile nominal axial resistances, if it can be proven.
Signal matching analysis of dynamic pile measurements
made at the end of driving and later in re-strike can be an
effective tool in evaluating and quantifying setup.
(Komurka et al., 2003; Bogard and Matlock, 1990).
If a wave equation or dynamic formula is used to
determine the nominal pile bearing resistance on re-strike,
care should be used as these approaches require accurate
blow count measurement which is inherently difficult at
the beginning of redrive (BOR). Furthermore, the
resistance factors provided in Table 10.5.5.2.3-1 for
driving formulas were developed for end of driving
conditions and empirically have been developed based
on the assumption that soil setup will occur. See
Article C10.5.5.2.3 for additional discussion on this issue.
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Higher degrees of confidence for the assessment of
setup effects are provided by dynamic measurements of
pile driving with signal matching analyses or static load
tests after a sufficient wait time following pile installation.
The restrike time and frequency should be based on
the time dependent strength change characteristics of the
soil. The following restrike durations are recommended:
Soil Type
Clean Sands
Silty Sands
Sandy Silts
Silts and Clays
Shales
Time Delay until Restrike
1 day
2 days
3-5 days
7-14 days*
7 days
* Longer times are sometimes required.
Specifying a restrike time for friction piles in fine
grained soils which is too short may result in pile length
overruns.
10.7.3.5—Groundwater Effects and Buoyancy
Nominal axial resistance shall be determined using
the groundwater level consistent with that used to
calculate the effective stress along the pile sides and tip.
The effect of hydrostatic pressure shall be considered in
the design.
10.7.3.6—Scour
C10.7.3.5
Unless the pile is bearing on rock, the bearing
resistance is primarily dependent on the effective
surcharge that is directly influenced by the groundwater
level. For drained loading conditions, the vertical
effective stress is related to the groundwater level and
thus it affects pile axial resistance. Lateral resistance
may also be affected.
Buoyant forces may also act on a hollow pile or
unfilled casing if it is sealed so that water does not enter
the pile. During pile installation, this may affect the
driving resistance (blow count) observed, especially in
very soft soils.
For design purposes, anticipated changes in the
groundwater level during construction and over the life
of the structure should be considered with regard to its
effect on pile resistance and constructability.
C10.7.3.6
The effect of scour shall be considered in
determining the minimum pile embedment and the
required nominal driving resistance, Rndr. The pile
foundation shall be designed so that the pile penetration
after the design scour event satisfies the required
nominal axial and lateral resistance.
The resistance factors shall be those used in the
design without scour. The side resistance of the material
lost due to scour should be determined using a static
analysis and it should not be factored, but consideration
should be given to the bias of the static analysis method
used to predict resistance. Method bias is discussed in
Article 10.7.3.3.
The pile foundation shall be designed to resist
debris loads occurring during the flood event in addition
to the loads applied from the structure.
The piles will need to be driven to the required
nominal bearing resistance plus the side resistance that
will be lost due to scour. The nominal resistance of the
remaining soil is determined through field verification.
The pile is driven to the required nominal bearing
resistance plus the magnitude of the side resistance lost as
a result of scour, considering the prediction method bias.
Another approach that may be used takes advantage
of dynamic measurements. In this case, the static analysis
method is used to determine an estimated length. During
the driving of test piles, the side resistance component of
the bearing resistance of pile in the scourable material
may be determined by a signal matching analysis of the
restrike dynamic measurements obtained when the pile tip
is below the scour elevation. The material below the scour
elevation must provide the required nominal resistance
after scour occurs.
In some cases, the flooding stream will carry debris
that will induce horizontal loads on the piles.
Additional information regarding pile design for
scour is provided in Hannigan et al. (2006).
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SECTION 10: FOUNDATIONS
10-95
10.7.3.7—Downdrag
The foundation should be designed so that the
available factored geotechnical resistance is greater than
the factored loads applied to the pile, including the
downdrag, at the strength limit state. The nominal pile
resistance available to support structure loads plus
downdrag shall be estimated by considering only the
positive side and tip resistance below the lowest layer
contributing to the downdrag. The pile foundation shall
be designed to structurally resist the downdrag plus
structure loads.
In the instance where it is not possible to obtain
adequate geotechnical resistance below the lowest layer
contributing to downdrag, e.g., piles supported by side
resistance, to fully resist the downdrag, or if it is
anticipated that significant deformation will be required
to mobilize the geotechnical resistance needed to resist
the factored loads including the downdrag load, the
structure should be designed to tolerate the settlement
resulting from the downdrag and the other applied loads
as specified in Article 10.7.2.5.
C10.7.3.7
The static analysis procedures in Article 10.7.3.8.6
may be used to estimate the available pile nominal
resistance to withstand the downdrag plus structure loads.
Nominal resistance may also be estimated using an
instrumented static load test or dynamic testing during
restrike with signal matching, provided the side
resistance within the zone contributing to downdrag is
subtracted from the resistance determined from the static
load or dynamic test. The side resistance within the zone
contributing to downdrag may be estimated using the
static analysis methods specified in Article 10.7.3.8.6,
from restrike signal matching analysis, or from
instrumented static pile load test results. Note that the
static analysis method may have a bias, on average over
or under predicting the side resistance. The bias of the
method selected to estimate the skin friction should be
taken into account as described in Article C10.7.3.3.
Pile design for downdrag is illustrated in
Figure C10.7.3.7-1.
where:
RSdd
=
side resistance which must be overcome
during driving through downdrag zone (kips)
Qp = ΣγiQi = factored load per pile, excluding downdrag
load (kips)
DD
=
downdrag load per pile (kips)
Dest.
=
estimated pile length needed to obtain
desired nominal resistance per pile (ft)
ϕdyn
=
resistance factor, assuming that a dynamic
method is used to estimate nominal pile
resistance during installation of the pile (if
a static analysis method is used instead,
use ϕstat)
γp
=
load factor for downdrag
The summation of the factored loads (ΣγiQi) should
be less than or equal to the factored resistance (ϕdynRn).
Therefore, the nominal resistance Rn should be greater
than or equal to the sum of the factored loads divided by
the resistance factor ϕdyn. The nominal bearing resistance
(kips) of the pile needed to resist the factored loads,
including downdrag, is therefore taken as:
Rn =
( Σγi Qi )
ϕdyn
+
γ p DD
ϕdyn
(C10.7.3.7-1)
The total nominal driving resistance, Rndr (kips), needed
to obtain Rn, accounting for the side resistance that must be
overcome during pile driving that does not contribute to the
nominal resistance of the pile, is taken as:
Rndr = RSdd + Rn
(C10.7.3.7-2)
where:
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Rndr =
nominal pile driving resistance required (kips)
Note that RSdd remains unfactored in this analysis to
determine Rndr.
(Σγi Qi)/ϕ dyn + γp DD/ϕdyn
Nominal Pile Driving Resistance Required, Rndr
Depth
RSdd
( ΣγiQi)/ ϕdyn + γpDD/ϕdyn
Rndr
Static side resistance
component of
driving resistance
DD
Downdrag
Zone
Total pile
resistance during
driving
Bearing
Zone
Dest.
Figure C10.7.3.7-1—Design of Pile Foundations for Downdrag
10.7.3.8—Determination of Nominal Bearing
Resistance for Piles
10.7.3.8.1—General
C10.7.3.8.1
Nominal pile bearing resistance should be field
verified during pile installation using static load tests,
dynamic tests, wave equation analysis, or dynamic
formula. The resistance factor selected for design
shall be based on the method used to verify pile
bearing resistance as specified in Article 10.5.5.2.3.
The production piles shall be driven to the minimum
blow count determined from the static load test,
dynamic test, wave equation, or dynamic formula
and, if required, to a minimum penetration needed for
uplift, scour, lateral resistance, or other requirements
as specified in Article 10.7.6. If it is determined that
static load testing is not feasible and dynamic methods
are unsuitable for field verification of nominal
bearing resistance, the piles shall be driven to the tip
elevation determined from the static analysis, and to
meet other limit states as required in Article 10.7.6.
This Article addresses the determination of the
nominal bearing (compression) resistance needed to
meet strength limit state requirements, using factored
loads and factored resistance values. From this design
step, the number of piles and pile nominal resistance
needed to resist the factored loads applied to the
foundation are determined. Both the loads and resistance
values are factored as specified in Articles 3.4.1 and
10.5.5.2.3, respectively, for this determination.
In most cases, the nominal resistance of production
piles should be controlled by driving to a required blow
count. In a few cases, usually piles driven into cohesive
soils with little or no toe resistance and very long wait times
to achieve the full pile resistance increase due to soil setup,
piles may be driven to depth. However, even in those cases,
a pile may be selected for testing after a sufficient waiting
period, using either a static load test or a dynamic test.
In cases where the project is small and the time to
achieve soil setup is large compared with the production
time to install all of the piles, no field testing for the
verification of nominal resistance may be acceptable.
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SECTION 10: FOUNDATIONS
10-97
10.7.3.8.2—Static Load Test
C10.7.3.8.2
If a static pile load test is used to determine the pile
nominal axial resistance, the test shall not be performed
less than 5 days after the test pile was driven unless
approved by the Engineer. The load test shall follow the
procedures specified in ASTM D1143, and the loading
procedure should follow the Quick Load Test Procedure.
Unless specified otherwise by the Engineer, the
nominal bearing resistance shall be determined from the
test data as follows:
•
For piles 24 in. or less in diameter (length of side
for square piles), the Davisson Method;
•
For piles larger than 36 in. in diameter (length of
side for square piles), at a pile top movement, sf
(in.), as determined from Eq. 10.7.3.8.2-1; and
•
For piles greater than 24 in. but less than 36 in. in
diameter, criteria to determine the nominal bearing
resistance that is linearly interpolated between the
criteria determined at diameters of 24 and 36 in.
sf =
QL
12 AE
+
B
(10.7.3.8.2-1)
2.5
The Quick Load Test Procedure is preferred because
it avoids problems that frequently arise when performing
a static load test that cannot be completed within an eighthour period. Tests that extend over a longer period are
difficult to perform due to the limited number of
experienced personnel that are usually available. The
Quick Load Test has proven to be easily performed in the
field and the results usually are satisfactory. Static load
tests should be conducted to failure whenever possible
and practical to extract the maximum information,
particularly when correlating with dynamic tests or static
analysis methods. However, if the formation in which the
pile is installed may be subject to significant creep
settlement, alternative procedures provided in ASTM
D1143 should be considered.
The Davisson Method to determine nominal
bearing resistance evaluation is performed by
constructing a line on the static load test curve that is
parallel to the elastic compression line of the pile. The
elastic compression line is calculated by assuming equal
compressive forces are applied to the pile ends. The
elastic compression line is offset by a specified amount
of displacement. The Davisson Method is illustrated in
Figure C10.7.3.8.2-1 and described in more detail in
Hannigan et al. (2006).
where:
Q
=
test load (kips)
L
=
pile length (ft)
A
=
pile cross-sectional area (ft2)
E
=
pile modulus (ksi)
B
=
pile diameter (length of side for square piles)
(ft)
Driving criteria should be established
consideration of the static load test results.
in
Figure C10.7.3.8.2-1—Alternate Method Load Test
Interpretation (Cheney and Chassie, 2000, modified after
Davisson, 1972)
For piles with large cross-sections, i.e., diameters
greater than 24 in., the Davisson Method will under
predict the nominal pile bearing resistance.
Development of driving criteria in consideration of
static load test results is described in Hannigan, et al. (2006).
10.7.3.8.3—Dynamic Testing
Dynamic testing shall be performed according to
the procedures given in ASTM D4945. If possible, the
dynamic test should be performed as a restrike test if the
Engineer anticipates significant time dependent strength
C10.7.3.8.3
The dynamic test may be used to establish the
driving criteria at the beginning of production
driving. A signal matching analysis (Rausche et al.,
1972) of the dynamic test data should always be used
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
change. The nominal pile bearing resistance shall be
determined by a signal matching analysis of the dynamic
pile test data if the dynamic test is used to establish the
driving criteria.
10.7.3.8.4—Wave Equation Analysis
If a wave equation analysis is to be used to establish
the driving criteria, it shall be performed based on the
hammer and pile driving system to be used for pile
installation.
If a wave equation analysis is used for the
determination of the nominal bearing resistance, then the
driving criterion (blow count) may be the value taken
either at the end of driving (EOD) or at the beginning of
redrive (BOR). The latter should be used where the soils
exhibit significant strength changes (setup or relaxation)
with time. When restrike (i.e., BOR) blow counts are
taken, the hammer shall be warmed up prior to restrike
testing and the blow count shall be taken as accurately
as possible for the first inch of restrike.
If the wave equation is used to assess the potential
for pile damage, driving stresses shall not exceed the
values obtained in Article 10.7.8, using the resistance
factors specified or referred to in Table 10.5.5.2.3-1.
Furthermore, the blow count needed to obtain the
maximum driving resistance anticipated shall be less
than the maximum value established based on the
provisions in Article 10.7.8.
to determine bearing resistance if a static load test is
not performed. See Hannigan et al. (2006) for a
description of and procedures to conduct a signal
matching analysis. Re-strike testing should be
performed if setup or relaxation is anticipated.
For example, note that it may not be possible to
adjust the dynamic measurements with signal matching
analysis to match the static load test results if the driving
resistance at the time the dynamic measurement is taken
is too large, i.e., the pile set per hammer blow is too
small. In this case, adequate hammer energy is not
reaching the pile tip to assess end bearing and produce an
accurate match, though in such cases, the prediction will
usually be very conservative. In general, a tip movement
(pile set) of 0.10 to 0.15 in. is needed to provide an
accurate signal matching analysis. See Hannigan, et al.
(2006) for additional guidance on this issue.
In cases where a significant amount of soil setup
occurs and the set at the beginning of redrive (BOR) is
less than 0.10 inch per blow, a more accurate nominal
resistance may be obtained by combining the end
bearing determined using the signal matching analysis
obtained for the end of driving (EOD) with the signal
matching analysis for the shaft resistance at the
beginning of redrive.
Dynamic testing and interpretation of the test data
should only be performed by certified, experienced testers.
C10.7.3.8.4
Note that without dynamic test results with signal
matching analysis and/or pile load test data (see
Articles 10.7.3.8.2 and 10.7.3.8.3), some judgment is
required to use the wave equation to predict the pile
bearing resistance. Unless experience in similar soils
exists, the recommendations of the software provider
should be used for dynamic resistance input. Key soil
input values that affect the predicted nominal resistance
include the soil damping and quake values, the skin
friction distribution, e.g., such as could be obtained from
a static pile bearing analysis, and the anticipated amount
of soil setup or relaxation. The actual hammer
performance is a variable that can only be accurately
assessed through dynamic measurements, though field
observations such as hammer stroke or measured ram
velocity can and should be used to improve the accuracy
of the wave equation prediction.
In general, improved prediction accuracy of nominal
bearing resistance is obtained when targeting the driving
criteria at BOR conditions, if soil setup or relaxation is
anticipated. Using the wave equation to predict nominal
bearing resistance from EOD blow counts requires that an
accurate estimate of the time-dependent changes in
bearing resistance due to soil setup or relaxation be made.
This is generally difficult to do unless site-specific,
longer-term measurements of bearing resistance from
static load tests or dynamic measurements with signal
matching are available. Hence, driving criteria based on
BOR measurements are recommended when using the
wave equation for driving criteria development.
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SECTION 10: FOUNDATIONS
10-99
A wave equation analysis should also be used to
evaluate pile drivability during design.
10.7.3.8.5—Dynamic Formula
C10.7.3.8.5
If a dynamic formula is used to establish the driving
criterion, the FHWA Gates Formula (Eq. 10.7.3.8.5-1)
should be used. The nominal pile resistance as measured
during driving using this method shall be taken as:
Rndr
1.75 Ed log10 (10 Nb ) 100
(10.7.3.8.5-1)
where:
Rndr =
nominal pile driving resistance measured
during pile driving (kips)
Ed =
developed hammer energy. This is the kinetic
energy in the ram at impact for a given blow. If
ram velocity is not measured, it may be
assumed equal to the potential energy of the
ram at the height of the stroke, taken as the ram
weight times the actual stroke (ft-lb)
Nb =
Number of hammer blows for 1.0 in. of pile
permanent set (blows/in.)
The Engineering News formula, modified to
predict a nominal bearing resistance, may be used. The
nominal pile resistance using this method shall be
taken as:
Rndr
12 Ed
(10.7.3.8.5-2)
( s 0.1)
where:
Rndr
=
nominal pile resistance measured during
driving (kips)
Ed
=
developed hammer energy. This is the
kinetic energy in the ram at impact for a
given blow. If ram velocity is not
measured, it may be assumed equal to the
potential energy of the ram at the height of
the stroke, taken as the ram weight times
the stroke (ft-kips)
s
=
pile permanent set, (in.)
It is preferred to use more accurate methods such as
wave equation or dynamic testing with signal matching
to establish driving criteria (i.e., blow count). However,
driving formulas have been in use for many years.
Therefore, driving formulas are provided as an option
for the development of driving criteria.
Two dynamic formulas are provided here for the
Engineer. If a dynamic formula is used for either
determination of the nominal resistance or the driving
criterion, the FHWA Modified Gates formula is preferred
over the Engineering News formula. It is discussed
further in the Design and Construction of Driven Pile
Foundations (Hannigan et al., 2006). Note that the units in
the FHWA Gates formula are not consistent. The
specified units in Eq. 10.7.3.8.5-1 must be used.
The Engineering News formula in its traditional
form contains a factor of safety of 6.0. For LRFD
applications, to produce a nominal resistance, the factor
of safety has been removed. As is true of the FHWA
Gates formula, the units specified in Eq. 10.7.3.8.5-2
must be used for the Engineering News formula. See
Allen (2005, 2007) for additional discussion on the
development of the Engineering News formula and its
modification to produce a nominal resistance.
Driving formula should only be used to determine
end of driving blow count criteria. These driving
formula are empirically based on pile load test results,
and therefore inherently include some degree of soil
setup or relaxation (see Allen, 2007).
If a dynamic formula other than those provided
herein is used, it shall be calibrated based on measured
load test results to obtain an appropriate resistance
factor, consistent with Article C10.5.5.2.
If a drivability analysis is not conducted, for steel
piles, design stresses shall be limited as specified in
Article 6.15.2.
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Dynamic formulas should not be used when the
required nominal resistance exceeds 600 kips.
As the required nominal bearing resistance increases,
the reliability of dynamic formulas tends to decrease. The
FHWA Gates formula tends to underpredict pile nominal
resistance at higher resistances. The Engineering News
formula tends to become unconservative as the nominal
pile resistance increases. If other driving formulas are
used, the limitation on the maximum driving resistance to
be used should be based upon the limits for which the
data is considered reliable, and any tendency of the
formula to over or under predict pile nominal resistance.
10.7.3.8.6—Static Analysis
10.7.3.8.6a—General
C10.7.3.8.6a
Where a static analysis prediction method is used
to determine pile installation criteria, i.e., for bearing
resistance, the nominal pile resistance shall be factored
at the strength limit state using the resistance factors in
Table 10.5.5.2.3-1 associated with the method used to
compute the nominal bearing resistance of the pile.
The factored nominal bearing resistance of piles, RR,
may be taken as:
(10.7.3.8.6a-1)
RR = ϕRn
or:
RR = ϕRn = ϕstat R p + ϕstat Rs
(10.7.3.8.6a-2)
While the most common use of static analysis
methods is solely for estimating pile quantities, a static
analysis may be used to establish pile installation criteria
if dynamic methods are determined to be unsuitable for
field verification of nominal bearing resistance. This is
applicable on projects where pile quantities are
relatively small, pile loads are relatively low, and/or
where the setup time is long so that re-strike testing
would require an impractical wait-period by the
Contractor on the site, e.g., soft silts or clays where a
large amount of setup is anticipated.
For use of static analysis methods for contract pile
quantity estimation, see Article 10.7.3.3.
in which:
R p = q p Ap
(10.7.3.8.6a-3)
Rs = q s As
(10.7.3.8.6a-4)
where:
ϕstat =
resistance factor for the bearing resistance of a
single pile specified in Article 10.5.5.2.3
Rp =
pile tip resistance (kips)
Rs =
pile side resistance (kips)
qp =
unit tip resistance of pile (ksf)
qs =
unit side resistance of pile (ksf)
As =
surface area of pile side (ft2)
Ap =
area of pile tip (ft2)
Both total stress and effective stress methods may
be used, provided the appropriate soil strength
parameters are available. The resistance factors for the
side resistance and tip resistance, estimated using these
methods, shall be as specified in Table 10.5.5.2.3-1. The
limitations of each method as described in
Article C10.5.5.2.3 should be applied in the use of these
static analysis methods.
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SECTION 10: FOUNDATIONS
10-101
10.7.3.8.6b—α-Method
C10.7.3.8.6b
The α-method, based on total stress, may be used to
relate the adhesion between the pile and clay to the
undrained strength of the clay. For this method, the
nominal unit side resistance, in ksf, shall be taken as:
qs = αS u
(10.7.3.8.6b-1)
where:
Su =
α
=
undrained shear strength (ksf)
adhesion factor applied to Su (dim)
The α-method has been used for many years and
gives reasonable results for both displacement and
nondisplacement piles in clay.
In general, this method assumes that a mean value
of Su will be used. It may not always be possible to
establish a mean value, as in many cases, data are too
limited to reliably establish the mean value. The
Engineer should apply engineering judgment and local
experience as needed to establish an appropriate value
for design (see Article C10.4.6).
For H-piles, the perimeter or “box” area should
generally be used to compute the surface area of the pile
side.
The adhesion factor for this method, α, shall be assumed
to vary with the value of the undrained strength, Su, as
shown in Figure 10.7.3.8.6b-1.
Figure 10.7.3.8.6b-1—Design Curves for Adhesion Factors for Piles Driven into Clay Soils after Tomlinson (1980)
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
10.7.3.8.6c—β-Method
C10.7.3.8.6c
The β-method, based on effective stress, may be
used for predicting side resistance of prismatic piles.
The nominal unit skin friction for this method, in ksf,
shall be related to the effective stresses in the ground
as:
(10.7.3.8.6c-1)
qs = βσ′v
The β-method has been found to work best for piles
in normally consolidated and lightly overconsolidated
clays. The method tends to overestimate side resistance of
piles in heavily overconsolidated soils. Esrig and Kirby
(1979) suggested that for heavily overconsolidated clays,
the value of β should not exceed two.
where:
σ′v =
β
vertical effective stress (ksf)
= a factor taken from Figure 10.7.3.8.6c-1
Figure 10.7.3.8.6c-1—β Versus OCR for Displacement
Piles after Esrig and Kirby (1979)
10.7.3.8.6d—λ-Method
C10.7.3.8.6d
The λ-method, based on effective stress (though it
does contain a total stress parameter), may be used to
relate the unit side resistance, in ksf, to passive earth
pressure. For this method, the unit skin friction shall be
taken as:
The value of λ decreases with pile length and was
found empirically by examining the results of load tests
on steel pipe piles.
(10.7.3.8.6d-1)
qs = λ(σ′v + 2 Su )
where:
σ′v + 2Su =
passive lateral earth pressure (ksf)
σ′v
=
the effective vertical stress at midpoint of
soil layer under consideration (ksf)
λ
=
an empirical coefficient
Figure 10.7.3.8.6d-1 (dim)
taken
from
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SECTION 10: FOUNDATIONS
10-103
Figure 10.7.3.8.6d-1—λ Coefficient for Driven Pipe Piles
after Vijayvergiya and Focht (1972)
10.7.3.8.6e—Tip Resistance in Cohesive Soils
The nominal unit tip resistance of piles in saturated
clay, in ksf, shall be taken as:
q p = 9 Su
(10.7.3.8.6e-1)
where:
Su =
undrained shear strength of the clay near the
pile tip (ksf)
10.7.3.8.6f—Nordlund/Thurman Method in
Cohesionless Soils
This effective stress method should be applied only
to sands and nonplastic silts. The nominal unit side
resistance, qs, for this method, in ksf, shall be taken as:
qs = K δCF σ′v
sin(δ + ω)
cos ω
(10.7.3.8.6f-1)
where:
Kδ =
coefficient of lateral earth pressure at mid-point
of soil layer under consideration from
Figures 10.7.3.8.6f-1 through 10.7.3.8.6f-4
(dim)
C10.7.3.8.6f
Detailed
design
procedures
for
the
Nordlund/Thurman method are provided in Hannigan et
al., (2006). This method was derived based on load test
data for piles in sand. In practice, it has been used for
gravelly soils as well.
The effective overburden stress is not limited in
Eq. 10.7.3.8.6f-1.
For H-piles, the perimeter or “box” area should
generally be used to compute the surface area of the pile
side.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
CF =
correction factor for Kδ when δ ≠ φf, from
Figure 10.7.3.8.6f-5
σ′v =
effective overburden stress at midpoint of soil
layer under consideration (ksf)
δ
=
friction angle between pile and soil obtained
from Figure 10.7.3.8.6f-6 (degrees)
ω
=
angle of pile taper from vertical (degrees)
Figure 10.7.3.8.6f-1—Design Curve for Evaluating Kδ for
Piles where φf = 25 degrees (Hannigan et al., 2006 after
Nordlund, 1979)
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SECTION 10: FOUNDATIONS
10-105
Figure 10.7.3.8.6f-2—Design Curve for Evaluating Kδ for
Piles where φf = 30 degrees (Hannigan et al., 2006 after
Nordlund, 1979)
Figure 10.7.3.8.6f-3—Design Curve for Evaluating Kδ for
Piles where φf = 35 degrees (Hannigan et al., 2006 after
Nordlund, 1979)
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Figure 10.7.3.8.6f-4—Design Curve for Evaluating Kδ for
Piles where φf = 40 degrees (Hannigan et al., 2006 after
Nordlund, 1979)
Figure 10.7.3.8.6f-5—Correction Factor for Kδ where
δ ≠ φf (Hannigan et al., 2006 after Nordlund, 1979)
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SECTION 10: FOUNDATIONS
10-107
Figure 10.7.3.8.6f-6—Relation of δ/φf and Pile
Displacement, V, for Various Types of Piles (Hannigan et
al., 2006 after Nordlund, 1979)
The nominal unit tip resistance, qp, in ksf by the
Nordlund/Thurman method shall be taken as:
q p = αt N q′ σ′v ≤ qL
(10.7.3.8.6f-2)
If the friction angle, φf, is estimated from average,
corrected SPT blow counts, N160, the N160 values should
be averaged over the zone from the pile tip to
two diameters below the pile tip.
where:
αt =
coefficient from Figure 10.7.3.8.6f-7 (dim)
N′q =
bearing capacity factor from Figure 10.7.3.8.6f-8
σ′v =
effective overburden stress at pile tip (ksf)
≤3.2 ksf
qL =
limiting
unit
tip
Figure 10.7.3.8.6f-9
resistance
from
Figure 10.7.3.8.6f-7—αt Coefficient (Hannigan et al., 2006
modified after Bowles, 1977)
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10-108
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure 10.7.3.8.6f-8—Bearing Capacity Factor, N′q
(Hannigan et al., 2006 modified after Bowles, 1977)
Figure 10.7.3.8.6f-9—Limiting Unit Pile Tip Resistance
(Hannigan et al., 2006 after Meyerhof, 1976)
10.7.3.8.6g—Using SPT or CPT in
Cohesionless Soils
These methods shall be applied only to sands and
nonplastic silts.
The nominal unit tip resistance for the Meyerhof
method, in ksf, for piles driven to a depth Db into a
cohesionless soil stratum shall be taken as:
qp =
0.8( N 160 ) Db
D
≤ q
(10.7.3.8.6g-1)
C10.7.3.8.6g
In-situ tests are widely used in cohesionless soils
because obtaining good quality samples of cohesionless
soils is very difficult. In-situ test parameters may be used
to estimate the tip resistance and side resistance of piles.
Two frequently used in-situ test methods for
predicting pile axial resistance are the standard
penetration test (SPT) method (Meyerhof, 1976) and the
cone penetration test (CPT) method (Nottingham and
Schmertmann, 1975).
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SECTION 10: FOUNDATIONS
10-109
where:
N160
=
representative SPT blow count near the
pile tip corrected for overburden pressure
as specified in Article 10.4.6.2.4 (blows/ft)
D
=
pile width or diameter (ft)
Db
=
depth of penetration in bearing strata (ft)
qℓ
=
limiting tip resistance taken as eight times
the value of N160 for sands and six times
the value of N160 for nonplastic silt (ksf)
The nominal side resistance of piles in cohesionless
soils for the Meyerhof method, in ksf, shall be taken as:
•
For driven displacement piles:
qs =
N160
25
•
For nondisplacement piles, e.g., steel H-piles:
qs =
(10.7.3.8.6g-2)
N160
(10.7.3.8.6g-3)
50
where:
qs
=
N 160
=
Displacement piles, which have solid sections or
hollow sections with a closed end, displace a relatively
large
volume
of
soil
during
penetration.
Nondisplacement piles usually have relatively small
cross-sectional areas, e.g., steel H-piles and open-ended
pipe piles that have not yet plugged. Plugging occurs
when the soil between the flanges in a steel H-pile or the
soil in the cylinder of an open-ended steel pipe pile
adheres fully to the pile and moves down with the pile
as it is driven.
unit side resistance for driven piles (ksf)
average corrected SPT-blow count along
the pile side (blows/ft)
Tip resistance, qp, for the Nottingham and
Schmertmann method, in ksf, shall be determined as
shown in Figure 10.7.3.8.6g-1.
In which:
qp =
qc1 + qc 2
2
CPT may be used to determine:
•
The cone penetration resistance, qc, which may be
used to determine the tip resistance of piles, and
•
Sleeve friction, fs, which may be used to determine
the side resistance.
(10.7.3.8.6g-4)
where:
q c1 =
average qc over a distance of yD below the pile
tip (path a-b-c); sum qc values in both the
downward (path a-b) and upward (path b-c)
directions; use actual qc values along path a-b
and the minimum path rule along path b-c;
compute qc1 for y-values from 0.7 to 4.0 and
use the minimum qc1 value obtained (ksf)
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2012
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10-110
q c2 =
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
average qc over a distance of 8D above the pile
tip (path c-e); use the minimum path rule as for
path b-c in the qc1, computations; ignore any
minor “x” peak depressions if in sand but
include in minimum path if in clay (ksf)
The minimum average cone resistance between 0.7 and
four pile diameters below the elevation of the pile tip
shall be obtained by a trial and error process, with the
use of the minimum-path rule. The minimum-path rule
shall also be used to find the value of cone resistance for
the soil for a distance of eight pile diameters above the
tip. The two results shall be averaged to determine the
pile tip resistance.
The nominal side resistance of piles for this method,
in kips, shall be taken as:
N1 Li
R s = K s ,c
i =1 8 Di
N2
f si a si hi + f si a si hi
i =1
Li
=
correction factors: Kc for clays and Ks for sands
from Figure 10.7.3.8.6g-2 (dim)
depth to middle of length interval at the point
considered (ft)
Di =
pile width or diameter at the point considered
(ft)
=
unit local sleeve friction resistance from CPT at
the point considered (ksf)
fsi
asi =
pile perimeter at the point considered (ft)
=
length interval at the point considered (ft)
hi
For a pile of constant cross-section (nontapered),
Eq. 10.7.3.8.6g-5 can be written as:
N2
a N1
R s = K s ,c s Li f si hi + a s f si hi
i =1
8 D i =1
(C10.7.3.8.6g-1)
(10.7.3.8.6g-5)
where:
Ks,c =
This process is described in Nottingham and
Schmertmann (1975).
N1 =
number of intervals between the ground surface
and a point 8D below the ground surface
N2 =
number of intervals between 8D below the
ground surface and the tip of the pile
If, in addition to the pile being prismatic, fs is
approximately constant at depths below 8D,
Eq. C10.7.3.8.6g-1 can be simplified to:
R s = K s ,c [a s f s ( Z − 4 D )]
(C10.7.3.8.6g-2)
where:
Z
=
total embedded pile length (ft)
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2012
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SECTION 10: FOUNDATIONS
10-111
Figure 10.7.3.8.6g-1—Pile End-Bearing Computation
Procedure after Nottingham and Schmertmann (1975)
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure 10.7.3.8.6g-2 —Side Resistance Correction Factors
Ks and Kc after Nottingham and Schmertmann (1975)
10.7.3.9—Resistance of Pile Groups in
Compression
For pile groups in clay, the nominal bearing
resistance of the pile group shall be taken as the lesser of:
•
The sum of the individual nominal resistances of
each pile in the group, or
•
The nominal resistance of an equivalent pier
consisting of the piles and the block of soil within
the area bounded by the piles.
If the cap is not in firm contact with the ground and
if the soil at the surface is soft, the individual nominal
resistance of each pile shall be multiplied by an
efficiency factor η, taken as:
•
η = 0.65 for a center-to-center spacing of
2.5 diameters,
•
η = 1.0 for a center-to-center spacing of
6.0 diameters.
For intermediate spacings, the value of η should be
determined by linear interpolation.
C10.7.3.9
The equivalent pier approach checks for block
failure and is generally only applicable for pile groups
within cohesive soils. For pile groups in cohesionless
soils, the sum of the nominal resistances of the
individual piles always controls the group resistance.
When analyzing the equivalent pier, the full shear
strength of the soil should be used to determine the
friction resistance. The total base area of the equivalent
pier should be used to determine the end bearing
resistance.
In cohesive soils, the nominal resistance of a pile
group depends on whether the cap is in firm contact with
the ground beneath. If the cap is in firm contact, the soil
between the pile and the pile group behave as a unit.
At small pile spacings, a block type failure
mechanism may prevail, whereas individual pile failure
may occur at larger pile spacings. It is necessary to
check for both failure mechanisms and design for the
case that yields the minimum capacity.
For a pile group of width X, length Y, and depth Z,
as shown in Figure C10.7.3.9-1, the bearing capacity for
block failure, in kips, is given by:
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2012
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SECTION 10: FOUNDATIONS
10-113
If the cap is in firm contact with the ground, no
reduction in efficiency shall be required. If the cap is not
in firm contact with the ground and if the soil is stiff, no
reduction in efficiency shall be required.
The nominal bearing resistance of pile groups in
cohesionless soil shall be the sum of the resistance of all
the piles in the group. The efficiency factor, η, shall be
1.0 where the pile cap is or is not in contact with the
ground for a center-to-center pile spacing of 2.5
diameters or greater. The resistance factor is the same as
that for single piles, as specified in Table 10.5.5.2.3-1.
For pile groups in clay or sand, if a pile group is
tipped in a strong soil deposit overlying a weak deposit,
the block bearing resistance shall be evaluated with
consideration to pile group punching as a group into the
underlying
weaker
layer.
The
methods
in
Article 10.6.3.1.2a of determining bearing resistance of
a spread footing in a strong layer overlying a weaker
layer shall apply, with the notional footing located as
shown in Article 10.7.2.3.
Q g = (2 X + 2Y ) Z Su + XYN c Su
(C10.7.3.9-1)
in which:
for
Z
≤ 2.5:
X
0.2 X 0.2 Z
N c = 5 1 +
1+
Y
X
for
(C10.7.3.9-2)
Z
> 2.5:
X
0.2 X
N c = 7.5 1 +
Y
(C10.7.3.9-3)
where:
Su =
average undrained shear strength along the
depth of penetration of the piles (ksf)
Su =
undrained shear strength at the base of the
group (ksf)
Figure C10.7.3.9-1—Pile Group Acting as a Block
Foundation
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
10.7.3.10—Uplift Resistance of Single Piles
Uplift on single piles shall be evaluated when
tensile forces are present. The factored nominal tensile
resistance of the pile due to soil failure shall be greater
than the factored pile loads.
The nominal uplift resistance of a single pile should
be estimated in a manner similar to that for estimating
the side resistance of piles in compression specified in
Article 10.7.3.8.6.
Factored uplift resistance in kips shall be taken as:
RR = ϕRn = ϕup Rs
(10.7.3.10-1)
C10.7.3.10
The factored load effect acting on any pile in a
group may be estimated using the traditional elastic
strength of materials procedure for a cross-section under
thrust and moment. The cross-sectional properties
should be based on the pile as a unit area.
Note that the resistance factor for uplift already is
reduced to 80 percent of the resistance factor for static
side resistance. Therefore, the side resistance estimated
based on Article 10.7.3.8.6 does not need to be reduced
to account for uplift effects on side resistance.
where:
Rs =
nominal uplift resistance due to side resistance
(kips)
ϕup =
resistance factor for uplift resistance specified
in Table 10.5.5.2.3-1
Nominal uplift resistance of single piles may be
determined by static load test or by dynamic test with
signal matching. If a static uplift test is to be performed,
it shall follow the procedures specified in ASTM D
3689. Dynamic tests with signal matching, if conducted,
shall be performed as specified in Article 10.7.3.8.3. If
dynamic tests with signal matching are used to
determine uplift, a maximum of 80 percent of the uplift
determined from the dynamic test should be used.
The static pile uplift load test(s) should be used to
calibrate the static analysis method, i.e., back calculate
soil properties, to adjust the calculated uplift resistance
for variations in the stratigraphy. The minimum
penetration criterion to obtain the desired uplift
resistance should be based on the calculated uplift
resistance using the static pile uplift load test results.
10.7.3.11—Uplift Resistance of Pile Groups
The nominal uplift resistance of pile groups shall be
evaluated when the foundation is subjected to uplift
loads.
Pile group factored uplift resistance, in kips, shall
be taken as:
RR = ϕRn = ϕug Rug
Static uplift tests should be evaluated using a
modified Davisson Method as described in Hannigan et
al. (2006).
If using dynamic tests with signal matching to
determine uplift resistance, it may be difficult to
separate the measured end bearing resistance from the
side resistance acting on the bottom section of the pile,
especially if the soil stiffness at the pile tip is not
significantly different from the soil stiffness acting on
the sides of the pile near the pile tip. If it is not clear
what is end bearing and what is side friction near the
pile tip, the side resistance acting on the bottom pile
element should be ignored when estimating uplift
resistance using this method. If the pile length is shorter
than 30 ft. in length, caution should be exercised when
using dynamic tests with signal matching to estimate
uplift.
C10.7.3.11
A net uplift force can act on the foundation. An
example of such a load is the construction load induced
during the erection of concrete segmental girder bridges.
(10.7.3.11-1)
where:
ϕug =
resistance factor specified in Table 10.5.5.2.3-1
Rug =
nominal uplift resistance of the pile group
(kips)
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2012
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SECTION 10: FOUNDATIONS
10-115
The nominal uplift resistance, Rug, of a pile group
shall be taken as the lesser of:
•
The sum of the individual pile uplift resistance, or
•
The uplift resistance of the pile group considered as
a block.
For pile groups in cohesionless soil, the weight of
the block that will be uplifted shall be determined
using a spread of load of 1H in 4V from the base of
the pile group taken from Figure 10.7.3.11-1. Buoyant
unit weights shall be used for soil below the
groundwater level.
In cohesive soils, the block used to resist uplift in
undrained shear shall be taken from Figure 10.7.3.11-2.
The nominal group uplift resistance may be taken as:
(10.7.3.11-2)
Rn = Rug = (2 XZ + 2YZ ) Su + Wg
where:
X
=
width of the group,
Figure 10.7.3.11-2 (ft)
as
shown
in
Y
=
length of the group,
Figure 10.7.3.11-2 (ft)
as
shown
in
Z
=
depth of the block of soil below pile cap taken
from Figure 10.7.3.11-2 (ft)
Su =
average undrained shear strength along the
sides of the pile group (ksf)
Wg =
weight of the block of soil, piles, and pile cap
(kips)
The resistance factor for the nominal group uplift
resistance, Rug, determined as the sum of the individual
pile resistances, shall be taken as the same as that for the
uplift resistance of single piles as specified in
Table 10.5.5.2.3-1.
The resistance factor for the uplift resistance of the
pile group considered as a block shall be taken as
specified in Table 10.5.5.2.3-1 for pile groups in all
soils.
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure 10.7.3.11-1—Uplift of Group of Closely Spaced
Piles in Cohesionless Soils after Tomlinson (1987)
Figure 10.7.3.11-2—Uplift of Group of Piles in Cohesive
Soils after Tomlinson (1987)
10.7.3.12—Nominal Lateral Resistance of Pile
Foundations
The nominal resistance of pile foundations to lateral
loads shall be evaluated based on both geomaterial and
structural properties. The lateral soil resistance along the
piles should be modeled using P-y curves developed for
the soils at the site.
The applied loads shall be factored loads and they
must include both lateral and axial loads. The analysis
may be performed on a representative single pile with
the appropriate pile top boundary condition or on the
entire pile group. The P-y curves shall be modified for
group effects. The P-multipliers in Table 10.7.2.4-1
should be used to modify the curves. If the pile cap will
always be embedded, the P-y lateral resistance of the
soil on the cap face may be included in the nominal
lateral resistance.
C10.7.3.12
Pile foundations are subjected to lateral loads due to
wind, traffic loads, bridge curvature, stream flow, vessel
or traffic impact and earthquake. Batter piles are
sometimes used but they are somewhat more expensive
than vertical piles and vertical piles are more effective
against dynamic loads.
Additional details regarding methods of analysis
using P-y curves, both for single piles and pile groups,
are provided in Article 10.7.2.4. As an alternative to P-y
analysis, strain wedge theory may be used (see
Article 10.7.2.4).
When this analysis is performed, the loads are
factored since the strength limit state is under
consideration, but the resistances as represented by the
P-y curves are not factored since they already represent
the ultimate condition.
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2012
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SECTION 10: FOUNDATIONS
10-117
The minimum penetration of the piles below ground
(see Article 10.7.6) required in the contract should be
established such that fixity is obtained. For this
determination, the loads applied to the pile are factored
as specified in Section 3, and a soil resistance factor of
1.0 shall be used as specified in Table 10.5.5.2.3-1.
If fixity cannot be obtained, additional piles should
be added, larger diameter piles used if feasible to drive
them to the required depth, or a wider spacing of piles in
the group should be considered to provide the necessary
lateral resistance. Batter piles may be added to provide
the lateral resistance needed, unless downdrag is
anticipated. If downdrag is anticipated, batter piles
should not be used. The design procedure, if fixity
cannot be obtained, should take into consideration the
lack of fixity of the pile.
Lateral resistance of single piles may be determined
by static load test. If a static lateral load test is to be
performed, it shall follow the procedures specified in
ASTM D3966.
The strength limit state for lateral resistance is only
structural (see Sections 5 and 6 for structural limit state
design requirements), though the determination of pile
fixity is the result of soil-structure interaction. A failure
of the soil does not occur; the soil will continue to
displace at constant or slightly increasing resistance.
Failure occurs when the pile reaches the structural limit
state, and this limit state is reached, in the general case,
when the nominal combined bending and axial
resistance is reached.
If the lateral resistance of the soil in front of the pile
cap is included in the lateral resistance of the
foundation, the effect of soil disturbance resulting from
construction of the pile cap should be considered. In
such cases, the passive resistance may need to be
reduced to account for the effects of disturbance.
For information on analysis and interpretation of
load tests, see Article 10.7.2.4.
10.7.3.13—Pile Structural Resistance
10.7.3.13.1—Steel Piles
The nominal axial compression resistance in the
structural limit state for piles loaded in compression
shall be as specified in Article 6.9.4.1 for noncomposite
piles and Article 6.9.5.1 for composite piles. If the pile
is fully embedded, λ in Eq. 6.9.5.11 shall be taken as 0.
The nominal axial resistance of horizontally
unsupported noncomposite piles that extend above the
ground surface in air or water shall be determined from
Eqs. 6.9.4.1.1-1 or 6.9.4.1.1-2. The nominal axial
resistance of horizontally unsupported composite piles
that extend above the ground surface in air or water shall
be determined from Eqs. 6.9.5.1-1 or 6.9.5.1-2.
The effective length of laterally unsupported piles
should be determined based on the provisions in
Article 10.7.3.13.4.
The resistance factors for the compression limit
state are specified in Article 6.5.4.2.
10.7.3.13.2—Concrete Piles
The nominal axial compression resistance for
concrete piles and prestressed concrete piles shall be as
specified in Article 5.7.4.4.
The nominal axial compression resistance for
concrete piles that are laterally unsupported in air or
water shall be determined using the procedures given in
Articles 5.7.4.3 and 4.5.3.2. The effective length of
laterally unsupported piles should be determined based
on the provisions in Article 10.7.3.13.4.
The resistance factor for the compression limit state
for concrete piles shall be that given in Article 5.5.4.2.1
for concrete loaded in axial compression.
C10.7.3.13.1
Composite members refer to steel pipe piles that are
filled with concrete.
The effective length given in Article C10.7.3.13.4 is
an empirical approach to determining effective length.
Computer methods are now available that can determine
the axial resistance of a laterally unsupported
compression member using a P-Δ analysis that includes
a numerical representation of the lateral soil resistance
(Williams et al., 2003). These methods are preferred
over the empirical approach in Article C10.7.3.13.4.
C10.7.3.13.2
Article 5.7.4 includes specified limits on
longitudinal reinforcement, spirals and ties. Methods are
given for determining nominal axial compression
resistance but they do not include the nominal axial
compression resistance of prestressed members.
Article C5.7.4.1 notes that compression members are
usually prestressed only where they are subjected to
high levels of flexure. Therefore, a method of
determining nominal axial compression resistance is not
given.
Article 5.7.4.5 specifically permits an analysis
based on equilibrium and strain compatibility. Methods
are also available for performing a stability analysis
(Williams et al., 2003).
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
C10.7.3.13.3
10.7.3.13.3—Timber Piles
The nominal axial compression resistance for
timber piles shall be as specified in Article 8.8.2. The
methods presented there include both laterally supported
and laterally unsupported members.
The effective length of laterally unsupported piles
should be determined based on the provisions in
Article 10.7.3.13.4.
Article 8.5.2.3 requires that a reduction factor for
long term loads of 0.75 be multiplied times the
resistance factor for Strength Load Combination IV.
C10.7.3.13.4
10.7.3.13.4—Buckling and Lateral Stability
In evaluating stability, the effective length of the
pile shall be equal to the laterally unsupported length,
plus an embedded depth to fixity.
The potential for buckling of unsupported pile
lengths and the determination of stability under lateral
loading should be evaluated by methods that consider
soil-structure interaction as specified in Article 10.7.3.12.
For preliminary design, the depth to fixity below the
ground, in ft, may be taken as:
•
For clays:
1.4 [Ep lw / Es ]0.25
•
(C10.7.3.13.4-1)
For sands:
1.8 [Ep lw / nh ]0.2
(C10.7.3.13.4-2)
where:
Ep =
lw
=
modulus of elasticity of pile (ksi)
weak axis moment of inertia for pile (ft4 )
Es =
soil modulus for clays = 0.465 Su (ksi)
Su =
undrained shear strength of clays (ksf)
nh =
rate of increase of soil modulus with depth for
sands as specified in Table C10.4.6.3-2 (ksi/ft)
This procedure is taken from Davisson and
Robinson (1965).
In Eqs. C10.7.3.13.4-1 and C10.7.3.13.4-2, the
loading condition has been assumed to be axial load
only, and the piles are assumed to be fixed at their ends.
Because the equations give depth to fixity from the
ground line, the Engineer must determine the boundary
conditions at the top of the pile to determine the total
unbraced length of the pile. If other loading or pile tip
conditions exist, see Davisson and Robinson (1965).
The effect of pile spacing on the soil modulus has
been studied by Prakash and Sharma (1990), who found
that, at pile spacings greater than 8 times the pile width,
neighboring piles have no effect on the soil modulus or
buckling resistance. However, at a pile spacing of
three times the pile width, the effective soil modulus is
reduced to 25 percent of the value applicable to a single
pile. For intermediate spacings, modulus values may be
estimated by interpolation.
10.7.4—Extreme Event Limit State
The provisions of Article 10.5.5.3 shall apply.
For the applicable factored loads, including those
specified in Article 10.7.1.6, for each extreme event limit
state, the pile foundations shall be designed to have
adequate factored axial and lateral resistance. For seismic
design, all soil within and above the liquefiable zone, if the
soil is liquefiable, shall not be considered to contribute
bearing resistance. Downdrag resulting from liquefaction
C10.7.4
See Article C10.5.5.3.3.
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SECTION 10: FOUNDATIONS
10-119
induced settlement shall be determined as specified in
Article 3.11.8 and included in the loads applied to the
foundation. Static downdrag loads should not be combined
with seismic downdrag loads due to liquefaction.
The pile foundation shall also be designed to resist
the horizontal force resulting from lateral spreading, if
applicable, or the liquefiable soil shall be improved to
prevent liquefaction and lateral spreading. For lateral
soil resistance of the pile foundation, the P-y curve soil
parameters should be reduced to account for
liquefaction. To determine the amount of reduction, the
duration of strong shaking and the ability of the soil to
fully develop a liquefied condition during the period of
strong shaking should be considered.
When designing for scour, the pile foundation design
shall be conducted as described in Article 10.7.3.6, except
that the check flood and resistance factors consistent with
Article 10.5.5.3.2 shall be used.
10.7.5—Corrosion and Deterioration
C10.7.5
The effects of corrosion and deterioration from
environmental conditions shall be considered in the
selection of the pile type and in the determination of the
required pile cross-section.
As a minimum, the following types of deterioration
shall be considered:
Resistivity, pH, chloride content, and sulfate
concentration values have been adapted from those in
Fang (1991) and Tomlinson (1987).
Some states use a coal tar epoxy paint system as a
protective coating with good results.
The criterion for determining the potential for
deterioration varies widely. An alternative set of
recommendations is given by Elias (1990).
A field electrical resistivity survey or resistivity
testing and pH testing of soil and groundwater samples
may be used to evaluate the corrosion potential.
The deterioration potential of steel piles may be
reduced by several methods, including protective
coatings, concrete encasement, cathodic protection, use of
special steel alloys, or increased steel area. Protective
coatings should be resistant to abrasion and have a proven
service record in the corrosive environment identified.
Protective coatings should extend into noncorrosive soils
a few feet because the lower portion of the coating is
more susceptible to abrasion loss during installation.
Concrete encasement through the corrosive zone
may also be used. The concrete mix should be of low
permeability and placed properly. Steel piles protected
by concrete encasement should be coated with a
dielectric coating near the base of the concrete jacket.
The use of special steel alloys of nickel, copper, and
potassium may also be used for increased corrosion
resistance in the atmosphere or splash zone of marine
piling.
Sacrificial steel area may also be used for corrosion
resistance. This technique over sizes the steel section so
that the available section after corrosion meets structural
requirements.
•
Corrosion of steel pile foundations, particularly in
fill soils, low pH soils, and marine environments;
•
Sulfate, chloride, and acid attack of concrete pile
foundations; and
•
Decay of timber piles from wetting and drying
cycles or from insects or marine borers.
The following soil or site conditions should be
considered as indicative of a potential pile deterioration
or corrosion situation:
•
Resistivity less than 2,000 ohm-cm,
•
pH less than 5.5,
•
pH between 5.5 and 8.5 in soils with high organic
content,
•
Sulfate concentrations greater than 1,000 ppm,
•
Landfills and cinder fills,
•
Soils subject to mine or industrial drainage,
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
•
Areas with a mixture of high resistivity soils and
low resistivity high alkaline soils, and
•
Insects (wood piles).
The following water conditions should be
considered as indicative of a potential pile deterioration
or corrosion situation:
•
Chloride content greater than 500 ppm,
•
Sulfate concentration greater than 500 ppm,
•
Mine or industrial runoff,
•
High organic content,
•
pH less than 5.5,
•
Marine borers, and
•
Piles exposed to wet/dry cycles.
When chemical wastes are suspected, a full chemical
analysis of soil and groundwater samples shall be
considered.
Deterioration of concrete piles can be reduced by
design procedures. These include use of a dense
impermeable concrete, sulfate resisting Portland cement,
increased steel cover, air-entrainment, reduced chloride
content in the concrete mix, cathodic protection, and
epoxy-coated reinforcement. Piles that are continuously
submerged are less subject to deterioration. ACI 318,
Section 4.5.2, provides maximum water-cement ratio
requirements for special exposure conditions. ACI 318,
Section 4.5.3, lists the appropriate types of cement for
various types of sulfate exposure.
For prestressed concrete, ACI 318 recommends a
maximum water-soluble chloride ion of 0.06 percent by
weight of cement.
Cathodic protection of reinforcing and prestressing
steel may be used to protect concrete from corrosion
effects. This process induces electric flow from the
anode to the cathode of the pile and reduces corrosion.
An external DC power source may be required to drive
the current. However, cathodic protection requires
electrical continuity between all steel and that
necessitates bonding the steel for electric connection.
This bonding is expensive and usually precludes the use
of cathodic protection of concrete piles.
Epoxy coating of pile reinforcement has been found
in some cases to be useful in resisting corrosion. It is
important to ensure that the coating is continuous and
free of holidays.
More detail on design for corrosion or other forms
of deterioration is contained in Hannigan et al. (2006).
10.7.6—Determination of Minimum Pile Penetration
C10.7.6
The minimum pile penetration, if required for the
particular site conditions and loading, shall be based on
the maximum depth (i.e., tip elevation) needed to meet
the following requirements as applicable:
A minimum pile penetration should only be
specified if necessary to ensure that all of the applicable
limit states are met. A minimum pile penetration should
not be specified solely to meet axial compression
resistance, i.e., bearing, unless field verification of the
pile nominal bearing resistance is not performed as
described in Article 10.7.3.8.
•
Single and pile group settlement (service limit state)
•
Lateral deflection (service limit state)
•
Uplift (strength limit state)
•
Penetration into bearing soils needed to get below
soil causing downdrag loads on the pile foundation
resulting from static consolidation stresses on soft
soil or downdrag loads due to liquefaction (strength
and extreme event limit state, respectively)
•
Penetration into bearing soils needed to get below
soil subject to scour
•
Penetration into bearing soils necessary to obtain
fixity for resisting the applied lateral loads to the
foundation (strength limit state)
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2012
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SECTION 10: FOUNDATIONS
10-121
Axial uplift, and nominal lateral resistance to resist
extreme event limit state loads
•
The contract documents should indicate the
minimum pile penetration, if applicable, as determined
above only if one or more of the requirements listed
above are applicable to the pile foundation. The contract
documents should also include the required nominal axial
compressive resistance, Rndr as specified in Article 10.7.7
and the method by which this resistance will be verified,
if applicable, such that the resistance factor(s) used for
design are consistent with the construction field
verification methods of nominal axial compressive pile
resistance.
10.7.7—Determination of Rndr Used to Establish
Contract Driving Criteria for Nominal Bearing
Resistance
The value of Rndr used for the construction of the
pile foundation to establish the driving criteria to obtain
the nominal bearing resistance shall be the value that
meets or exceeds the following limit states, as
applicable:
•
Strength limit state nominal bearing resistance
specified in Article 10.7.3.8
•
Strength limit state nominal bearing resistance,
including downdrag specified in Article 10.7.3.7
•
Strength limit state nominal bearing resistance,
accounting for scour specified in Article 10.7.3.6
•
Extreme event limit state nominal bearing resistance
for seismic specified in Article 10.7.4
•
Extreme event limit state nominal bearing resistance
for scour specified in Article 10.7.4
10.7.8—Drivability Analysis
C10.7.8
The establishment of the installation criteria for
driven piles should include a drivability analysis. Except
as specified herein, the drivability analysis shall be
performed by the Engineer using a wave equation
analysis, and the driving stresses (σdr) anywhere in the
pile determined from the analysis shall be less than the
following limits:
Wave equation analyses should be conducted
during design using a range of likely hammer/pile
combinations, considering the soil and installation
conditions
at
the
foundation
site.
See
Article 10.7.3.8.4 for additional considerations for
conducting wave equation analyses. These analyses
should be used to assess feasibility of the proposed
foundation system and to establish installation criteria
with regard to driving stresses to limit driving
stresses to acceptable levels. For routine pile
installation applications, e.g., smaller diameter, low
nominal resistance piles, the development of
installation criteria with regard to the limitation of
driving stresses, e.g., minimum or maximum ram
weight, hammer size, maximum acceptable driving
resistance, etc., may be based on local experience,
Steel Piles, compression and tension:
σ dr = 0.9ϕda f y
(10.7.8-1)
where:
fy
=
yield strength of the steel (ksi)
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ϕda =
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
resistance factor as specified in Table 10.5.5.2.3-1
Concrete piles:
•
In compression:
σ dr = ϕda 0.85 f c′
•
(10.7.8-2)
In tension, considering only the steel reinforcement:
σ dr = 0.7 ϕda f y
(10.7.8-3)
where:
f ′c =
fy
=
compressive strength of the concrete (ksi)
yield strength of the steel reinforcement (ksi)
Prestressed concrete piles, normal environments:
•
In compression:
(
σ dr = ϕda 0.85 f c′ − f pe
•
)
(10.7.8-4)
In tension:
(
σ dr = ϕ da 0.095
f c′ + f pe
)
(10.7.8-5)
where:
fpe = effective prestressing stress in concrete (ksi)
Prestressed
concrete
environments:
•
piles,
severe
corrosive
In tension:
σ dr = ϕda f pe
(10.7.8-6)
Timber piles, in compression and tension:
σ dr = ϕda ( Fco )
(10.7.8-7)
where:
Fco =
rather than conducting a detailed wave equation
analysis that is project specific. Local experience
could include previous drivability analysis results and
actual pile driving experience that are applicable to
the project specific situation at hand. Otherwise, a
project specific drivability study should be conducted.
Drivability analyses may also be conducted as
part of the project construction phase. When
conducted during the construction phase, the
drivability analysis shall be conducted using the
contractor’s proposed driving system. This
information should be supplied by the contractor.
This drivability analysis should be used to determine
if the contractor’s proposed driving system is capable
of driving the pile to the maximum resistance
anticipated without exceeding the factored structural
resistance available, i.e., σdr.
base resistance of wood in compression parallel
to the grain as specified in Article 8.4.1.3 (ksi)
In addition to this drivability analysis, the best
approach to controlling driving stresses during pile
installation is to conduct dynamic testing with signal
matching to verify the accuracy of the wave equation
analysis results. Note that if a drivability analysis is
conducted using the wave equation for acceptance of the
contractor’s proposed driving system, but a different
method is used to develop driving resistance, i.e., blow
count, criterion to obtain the specified nominal pile
resistance, e.g., a driving formula, the difference in the
methods regarding the predicted driving resistance should
be taken into account when evaluating the contractor’s
driving system. For example, the wave equation analysis
could indicate that the contractor’s hammer can achieve
the desired bearing resistance, but the driving formula
could indicate the driving resistance at the required
nominal bearing is too high. Such differences should be
considered when setting up the driving system acceptance
requirements in the contract documents, though it
is preferable to be consistent in the method used for
acceptance of the contractor’s driving system and the one
used for developing driving criteria.
The selection of a blow count limit as a definition
of refusal is difficult because it can depend on the site
soil profile, the pile type, hammer performance, and
possibly hammer manufacturer limitations to prevent
hammer damage. In general, blow counts greater than
10–15 blows per inch should be used with care,
particularly with concrete or timber piles. In cases where
the driving is easy until near the end of driving, a higher
blow count may sometimes be satisfactory, but if a high
blow count is required over a large percentage of the
depth, even ten blows per inch may be too large.
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2012
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SECTION 10: FOUNDATIONS
10-123
This drivability analysis shall be based on the
maximum driving resistance needed:
•
To obtain minimum penetration requirements
specified in Article 10.7.6,
•
To overcome resistance of soil that cannot be
counted upon to provide axial or lateral resistance
throughout the design life of the structure, e.g.,
material subject to scour, or material subject to
downdrag, and
•
To obtain the required nominal bearing resistance.
10.7.9—Probe Piles
C10.7.9
Probe piles should be driven at several locations on
the site to establish order length. If dynamic
measurements are not taken, these probe piles should be
driven after the driving criteria have been established.
If dynamic measurements during driving are taken,
both order lengths and driving criteria should be
established after the probe pile(s) are driven.
Probe piles are sometimes known as test piles or
indicator piles. It is common practice to drive probe
piles at the beginning of the project (particularly with
concrete piles) to establish pile order lengths and/or to
evaluate site variability whether or not dynamic
measurements are taken.
10.8—DRILLED SHAFTS
10.8.1—General
10.8.1.1—Scope
C10.8.1.1
The provisions of this Section shall apply to the
design of drilled shafts. Throughout these provisions,
the use of the term “drilled shaft” shall be interpreted to
mean a shaft constructed using either drilling (open hole
or with drilling slurry) or casing plus excavation
equipment and technology.
These provisions shall also apply to shafts that are
constructed using casing advancers that twist or rotate
casings into the ground concurrent with excavation
rather than drilling.
The provisions of this Section shall not be taken as
applicable to drilled piles, e.g., augercast piles, installed
with continuous flight augers that are concreted as the
auger is being extracted.
Drilled shafts may be an economical alternative to
spread footing or pile foundations, particularly when
spread footings cannot be founded on suitable soil or
rock strata within a reasonable depth or when driven
piles are not viable. Drilled shafts may be an economical
alternative to spread footings where scour depth is large.
Drilled shafts may also be considered to resist high
lateral or axial loads, or when deformation tolerances
are small. For example, a movable bridge is a bridge
where it is desirable to keep deformations small.
Drilled shafts are classified according to their
primary mechanism for deriving load resistance either as
floating (friction) shafts, i.e., shafts transferring load
primarily by side resistance, or end-bearing shafts, i.e.,
shafts transferring load primarily by tip resistance.
It is recommended that the shaft design be reviewed
for constructability prior to advertising the project for
bids.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
10.8.1.2—Shaft Spacing, Clearance, and
Embedment into Cap
If the center-to-center spacing of drilled shafts is
less than 4.0 diameters, the interaction effects between
adjacent shafts shall be evaluated. If the center-to-center
spacing of drilled shafts is less than 6.0 diameters, the
sequence of construction should be specified in the
contract documents.
Shafts used in groups should be located such that
the distance from the side of any shaft to the nearest
edge of the cap is not less than 12.0 in. Shafts shall be
embedded sufficiently into the cap to develop the
required structural resistance.
10.8.1.3—Shaft Diameter and Enlarged Bases
If the shaft is to be manually inspected, the shaft
diameter should not be less than 30.0 in. The diameter of
columns supported by shafts should be smaller than or
equal to the diameter of the drilled shaft.
In stiff cohesive soils, an enlarged base (bell, or
underream) may be used at the shaft tip to increase the
tip bearing area to reduce the unit end bearing pressure
or to provide additional resistance to uplift loads.
Where the bottom of the drilled hole is dry, cleaned
and inspected prior to concrete placement, the entire
base area may be taken as effective in transferring load.
10.8.1.4—Battered Shafts
Battered shafts should be avoided. Where increased
lateral resistance is needed, consideration should be
given to increasing the shaft diameter or increasing the
number of shafts.
C10.8.1.2
Larger spacing may be required to preserve shaft
excavation stability or to prevent communication
between shafts during excavation and concrete
placement.
Shaft spacing may be decreased if casing
construction methods are required to maintain
excavation stability and to prevent interaction between
adjacent shafts.
C10.8.1.3
Nominal shaft diameters used for both geotechnical
and structural design of shafts should be selected based
on available diameter sizes.
If the shaft and the column are the same
diameter, it should be recognized that the placement
tolerance of drilled shafts is such that it will likely
affect the column location. The shaft and column
diameter should be determined based on the shaft
placement tolerance, column and shaft reinforcing
clearances, and the constructability of placing the
column reinforcing in the shaft. A horizontal
construction joint in the shaft at the bottom of the
column reinforcing will facilitate constructability.
Making allowance for the tolerance where the column
connects with the superstructure, which could affect
column alignment, can also accommodate this shaft
construction tolerance.
In drilling rock sockets, it is common to use casing
through the soil zone to temporarily support the soil to
prevent cave-in, allow inspection and to produce a seal
along the soil-rock contact to minimize infiltration of
groundwater into the socket. Depending on the method
of excavation, the diameter of the rock socket may need
to be sized at least 6 in. smaller than the nominal casing
size to permit seating of casing and insertion of rock
drilling equipment.
Where practical, consideration should be given to
extension of the shaft to a greater depth to avoid the
difficulty and expense of excavation for enlarged bases.
C10.8.1.4
Due to problems associated with hole stability
during excavation, installation, and with removal of
casing during installation of the rebar cage and concrete
placement, construction of battered shafts is very
difficult.
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SECTION 10: FOUNDATIONS
10-125
10.8.1.5—Drilled Shaft Resistance
Drilled shafts shall be designed to have adequate
axial and structural resistances, tolerable settlements,
and tolerable lateral displacements.
The axial resistance of drilled shafts shall be
determined through a suitable combination of subsurface
investigations, laboratory and/or in-situ tests, analytical
methods, and load tests, with reference to the history of
past performance. Consideration shall also be given to:
•
The difference between the resistance of a single
shaft and that of a group of shafts;
•
The resistance of the underlying strata to support
the load of the shaft group;
•
The effects of constructing the shaft(s) on adjacent
structures;
•
The possibility of scour and its effect;
•
The transmission of forces, such as downdrag
forces, from consolidating soil;
•
Minimum shaft penetration necessary to satisfy the
requirements caused by uplift, scour, downdrag,
settlement, liquefaction, lateral loads and seismic
conditions;
•
Satisfactory behavior under service loads;
•
Drilled shaft nominal structural resistance; and
•
Long-term durability of the shaft in service, i.e.,
corrosion and deterioration.
Resistance factors for shaft axial resistance for the
strength limit state shall be as specified in
Table 10.5.5.2.4-1.
The method of construction may affect the shaft
axial and lateral resistance. The shaft design parameters
shall take into account the likely construction
methodologies used to install the shaft.
C10.8.1.5
The drilled shaft design process is discussed in
detail in Drilled Shafts: Construction Procedures and
Design Methods (O’Neill and Reese, 1999).
The performance of drilled shaft foundations can be
greatly affected by the method of construction,
particularly side resistance. The designer should
consider the effects of ground and groundwater
conditions on shaft construction operations and
delineate, where necessary, the general method of
construction to be followed to ensure the expected
performance. Because shafts derive their resistance from
side and tip resistance, which is a function of the
condition of the materials in direct contact with the
shaft, it is important that the construction procedures be
consistent with the material conditions assumed in the
design. Softening, loosening, or other changes in soil
and rock conditions caused by the construction method
could result in a reduction in shaft resistance and an
increase in shaft displacement. Therefore, evaluation of
the effects of the shaft construction procedure on
resistance should be considered an inherent aspect of the
design. Use of slurries, varying shaft diameters, and post
grouting can also affect shaft resistance.
Soil parameters should be varied systematically to
model the range of anticipated conditions. Both vertical
and lateral resistance should be evaluated in this
manner.
Procedures that may affect axial or lateral shaft
resistance include, but are not limited to, the following:
•
Artificial socket roughening, if included in the
design nominal axial resistance assumptions.
•
Removal of temporary casing where the design is
dependent on concrete-to-soil adhesion.
•
The use of permanent casing.
•
Use of tooling that produces a uniform cross-section
where the design of the shaft to resist lateral loads
cannot tolerate the change in stiffness if telescoped
casing is used.
It should be recognized that the design procedures
provided in these Specifications assume compliance to
construction specifications that will produce a high
quality shaft. Performance criteria should be included in
the construction specifications that require:
•
Shaft bottom cleanout criteria,
•
Appropriate means to prevent side wall movement
or failure (caving) such as temporary casing, slurry,
or a combination of the two,
•
Slurry maintenance requirements including
minimum slurry head requirements, slurry testing
requirements, and maximum time the shaft may be
left open before concrete placement.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
If for some reason one or more of these
performance criteria are not met, the design should be
reevaluated and the shaft repaired or replaced as
necessary.
10.8.1.6—Determination of Shaft Loads
10.8.1.6.1—General
C10.8.1.6.1
The factored loads to be used in shaft foundation
design shall be as specified in Section 3. Computational
assumptions that shall be used in determining individual
shaft loads are also specified in Section 3.
10.8.1.6.2—Downdrag
The provisions of Articles 10.7.1.6.2 and 3.11.8
shall apply.
The specification and determination of top of cap
loads is discussed extensively in Section 3. It should be
noted that Article 3.6.2.1 states that dynamic load
allowance need not be applied to foundation elements
that are below the ground surface. Therefore, if shafts
extend above the ground surface to act as columns the
dynamic load allowance should be included in
evaluating the structural resistance of that part of the
shaft above the ground surface. The dynamic load
allowance may be ignored in evaluating the geotechnical
resistance.
C10.8.1.6.2
See commentary to Articles 10.7.1.6.2 and 3.11.8.
Downdrag loads may be estimated using the αmethod, as specified in Article 10.8.3.5.1b, for
calculating negative shaft resistance. As with positive
shaft resistance, the top 5.0 ft and a bottom length taken
as one shaft diameter should be assumed to not
contribute to downdrag loads.
When using the α-method, an allowance should be
made for a possible increase in the undrained shear
strength as consolidation occurs. Downdrag loads may
also come from cohesionless soils above settling
cohesive soils, requiring granular soil friction methods
be used in such zones to estimate downdrag loads.
10.8.1.6.3—Uplift
C10.8.1.6.3
The provisions in Article 10.7.1.6.3 shall apply.
See commentary to Article C10.7.1.6.3.
10.8.2—Service Limit State Design
10.8.2.1—Tolerable Movements
C10.8.2.1
The requirements of Article 10.5.2.1 shall apply.
See commentary to Article 10.5.2.1.
10.8.2.2—Settlement
10.8.2.2.1—General
The settlement of a drilled shaft foundation
involving either single-drilled shafts or groups of drilled
shafts shall not exceed the movement criteria selected in
accordance with Article 10.5.2.1.
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SECTION 10: FOUNDATIONS
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10.8.2.2.2—Settlement of Single-Drilled Shaft
The settlement of single-drilled shafts shall be
estimated in consideration of:
•
Short-term settlement,
•
Consolidation settlement if constructed in cohesive
soils, and
•
Axial compression of the shaft.
The normalized load-settlement curves shown in
Figures 10.8.2.2.2-1 through 10.8.2.2.2-4 should be used
to limit the nominal shaft axial resistance computed as
specified for the strength limit state in Article 10.8.3 for
service limit state tolerable movements. Consistent values
of normalized settlement shall be used for limiting the
base and side resistance when using these Figures. Longterm settlement should be computed according to
Article 10.7.2 using the equivalent footing method and
added to the short-term settlements estimated using
Figures 10.8.2.2.2-1 through 10.8.2.2.2-4.
Other methods for evaluating shaft settlements that
may be used are found in O’Neill and Reese (1999).
C10.8.2.2.2
O'Neill and Reese (1999) have summarized loadsettlement data for drilled shafts in dimensionless form,
as shown in Figures 10.8.2.2.2-1 through 10.8.2.2.2-4.
These curves do not include consideration of long-term
consolidation settlement for shafts in cohesive soils.
Figures 10.8.2.2.2-1 and 10.8.2.2.2-2 show the loadsettlement curves in side resistance and in end bearing
for shafts in cohesive soils. Figures 10.8.2.2.2-3 and
10.8.2.2.2-4 are similar curves for shafts in cohesionless
soils. These curves should be used for estimating shortterm settlements of drilled shafts.
The designer should exercise judgment relative to
whether the trend line, one of the limits, or some relation
in between should be used from Figures 10.8.2.2.2-1
through 10.8.2.2.2-4.
The values of the load-settlement curves in side
resistance were obtained at different depths, taking into
account elastic shortening of the shaft. Although elastic
shortening may be small in relatively short shafts, it may
be substantial in longer shafts. The amount of elastic
shortening in drilled shafts varies with depth. O’Neill
and Reese (1999) have described an approximate
procedure for estimating the elastic shortening of longdrilled shafts.
Settlements induced by loads in end bearing are
different for shafts in cohesionless soils and in
cohesive soils. Although drilled shafts in cohesive
soils typically have a well-defined break in a loaddisplacement curve, shafts in cohesionless soils often
have no well-defined failure at any displacement. The
resistance of drilled shafts in cohesionless soils
continues to increase as the settlement increases
beyond five percent of the base diameter. The shaft
end bearing Rp is typically fully mobilized at
displacements of two to five percent of the base
diameter for shafts in cohesive soils. The unit end
bearing resistance for the strength limit state (see
Article 10.8.3.3) is defined as the bearing pressure
required to cause vertical deformation equal to
five percent of the shaft diameter, even though this
does not correspond to complete failure of the soil
beneath the base of the shaft.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The curves in Figures 10.8.2.2.2-1 and 10.8.2.2.2-3
also show the settlements at which the side resistance is
mobilized. The shaft skin friction Rs is typically fully
mobilized at displacements of 0.2 percent to 0.8 percent
of the shaft diameter for shafts in cohesive soils. For
shafts in cohesionless soils, this value is 0.1 percent to
1.0 percent.
Figure 10.8.2.2.2-1 Normalized Load Transfer in Side
Resistance versus Settlement in Cohesive Soils (from
O’Neill and Reese, 1999)
Figure 10.8.2.2.2-2—Normalized Load Transfer in End
Bearing versus Settlement in Cohesive Soils (from O’Neill
and Reese, 1999)
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SECTION 10: FOUNDATIONS
10-129
The deflection-softening response typically applies
to cemented or partially cemented soils, or other soils
that exhibit brittle behavior, having low residual shear
strengths at larger deformations. Note that the trend line
for sands is a reasonable approximation for either the
deflection-softening or deflection-hardening response.
Figure 10.8.2.2.2-3—Normalized Load Transfer in Side
Resistance versus Settlement in Cohesionless Soils (from
O’Neill and Reese, 1999)
Figure 10.8.2.2.2-4—Normalized Load Transfer in End
Bearing versus Settlement in Cohesionless Soils (from
O’Neill and Reese, 1999)
10.8.2.2.3—Intermediate Geo Materials (IGMs)
For detailed settlement estimation of shafts in
IGMs, the procedures provided by O’Neill and Reese
(1999) should be used.
C10.8.2.2.3
IGMs are defined by O’Neill and Reese (1999) as
follows:
•
Cohesive IGM—clay shales or mudstones with an
Su of 5 to 50 ksf, and
•
Cohesionless—granular tills or granular residual
soils with N160 greater than 50 blows/ft.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
10.8.2.2.4—Group Settlement
The provisions of Article 10.7.2.3 shall apply. Shaft
group effect shall be considered for groups of 2 shafts or
more.
10.8.2.3—Horizontal Movement of Shafts and
Shaft Groups
The provisions of Articles 10.5.2.1 and 10.7.2.4
shall apply.
C10.8.2.2.4
See commentary to Article 10.7.2.3.
O’Neill and Reese (1999) summarize various
studies on the effects of shaft group behavior. These
studies were for groups that consisted of 1 × 2 to 3 × 3
shafts. These studies suggest that group effects are
relatively unimportant for shaft center-to-center spacing
of 5D or greater.
C10.8.2.3
See commentary to Articles 10.5.2.1 and 10.7.2.4.
10.8.2.4—Settlement Due to Downdrag
C10.8.2.4
The provisions of Article 10.7.2.5 shall apply.
See commentary to Article 10.7.2.5.
10.8.2.5—Lateral Squeeze
C10.8.2.5
The provisions of Article 10.7.2.6 shall apply.
See commentary to Article 10.7.2.6.
10.8.3—Strength Limit State Design
10.8.3.1—General
The nominal shaft resistances that shall be
considered at the strength limit state include:
•
Axial compression resistance,
•
Axial uplift resistance,
•
Punching of shafts through strong soil into a weaker
layer,
•
Lateral geotechnical resistance of soil and rock
stratum,
•
Resistance when scour occurs,
•
Axial resistance when downdrag occurs, and
•
Structural resistance of shafts.
10.8.3.2—Groundwater Table and Buoyancy
C10.8.3.2
The provisions of Article 10.7.3.5 shall apply.
See commentary to Article 10.7.3.5.
10.8.3.3—Scour
C10.8.3.3
The provisions of Article 10.7.3.6 shall apply.
See commentary to Article 10.7.3.6.
10.8.3.4—Downdrag
C10.8.3.4
The provisions of Article 10.7.3.7 shall apply.
See commentary to Article 10.7.3.7.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
SECTION 10: FOUNDATIONS
10-131
10.8.3.5—Nominal Axial Compression
Resistance of Single Drilled Shafts
The factored resistance of drilled shafts, RR, shall be
taken as:
RR = ϕRn = ϕqp R p + ϕqs Rs
(10.8.3.5-1)
in which:
R p = q p Ap
(10.8.3.5-2)
Rs = qs As
(10.8.3.5-3)
where:
Rp =
nominal shaft tip resistance (kips)
Rs =
nominal shaft side resistance (kips)
ϕqp =
resistance factor for tip resistance specified in
Table 10.5.5.2.4-1
ϕqs =
resistance factor for shaft side resistance
specified in Table 10.5.5.2.4-1
qp =
unit tip resistance (ksf)
qs
=
unit side resistance (ksf)
Ap =
area of shaft tip (ft2)
As =
area of shaft side surface (ft2)
The methods for estimating drilled shaft resistance
provided in this Article should be used. Shaft strength
limit state resistance methods not specifically addressed
in this Article for which adequate successful regional or
national experience is available may be used, provided
adequate information and experience is also available to
develop appropriate resistance factors.
C10.8.3.5
The nominal axial compression resistance of a shaft
is derived from the tip resistance and/or shaft side
resistance, i.e., skin friction. Both the tip and shaft
resistances develop in response to foundation
displacement. The maximum values of each are unlikely
to occur at the same displacement, as described in
Article 10.8.2.2.2.
For consistency in the interpretation of both static
load tests (Article 10.8.3.5.6) and the normalized curves
of Article 10.8.2.2.2, it is customary to establish the
failure criterion at the strength limit state at a gross
deflection equal to five percent of the base diameter for
drilled shafts.
O’Neill and Reese (1999) identify several methods
for estimating the resistance of drilled shafts in cohesive
and granular soils, intermediate geomaterials, and rock.
The most commonly used methods are provided in this
Article. Methods other than the ones provided in detail
in this Article may be used provided that adequate local
or national experience with the specific method is
available to have confidence that the method can be
used successfully and that appropriate resistance factors
can be determined. At present, it must be recognized
that these resistance factors have been developed using a
combination of calibration by fitting to previous
allowable stress design (ASD) practice and reliability
theory (see Allen, 2005, for additional details on the
development of resistance factors for drilled shafts).
Such methods may be used as an alternative to the
specific methodology provided in this Article, provided
that:
•
The method selected consistently has been used
with success on a regional or national basis.
•
Significant experience is available to demonstrate
that success.
•
As a minimum, calibration by fitting to allowable
stress design is conducted to determine the
appropriate resistance factor, if inadequate
measured data are available to assess the alternative
method using reliability theory. A similar approach
as described by Allen (2005) should be used to
select the resistance factor for the alternative
method.
10.8.3.5.1—Estimation of Drilled Shaft Resistance
in Cohesive Soils
10.8.3.5.1a—General
Drilled shafts in cohesive soils should be designed
by total and effective stress methods for undrained and
drained loading conditions, respectively.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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10-132
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
10.8.3.5.1b—Side Resistance
C10.8.3.5.1b
The nominal unit side resistance, qs, in ksf, for
shafts in cohesive soil loaded under undrained loading
conditions by the α-Method shall be taken as:
(10.8.3.5.1b-1)
qs = αS u
in which:
α = 0.55 for
Su
pa
(10.8.3.5.1b-2)
≤ 1.5
α = 0.55 − 0.1 ( Su pa − 1.5 )
(10.8.3.5.1b-3)
for 1.5 ≤ Su pa ≤ 2.5
where:
Su =
α
=
pa =
undrained shear strength (ksf)
adhesion factor (dim)
atmospheric pressure (= 2.12 ksf)
The following portions of a drilled shaft, illustrated
in Figure 10.8.3.5.1b-1, should not be taken to
contribute to the development of resistance through skin
friction:
•
At least the top 5.0 ft of any shaft;
•
For straight shafts, a bottom length of the shaft
taken as the shaft diameter;
•
Periphery of belled ends, if used; and
•
Distance above a belled end taken as equal to the
shaft diameter.
When permanent casing is used, the side resistance
shall be adjusted with consideration to the type and
length of casing to be used, and how it is installed.
Values of α for contributing portions of shafts
excavated dry in open or cased holes should be as
specified in Eqs. 10.8.3.5.1b-2 and 10.8.3.5.1b-3.
The α-method is based on total stress. For effective
stress methods for shafts in clay, see O’Neill and Reese
(1999).
The adhesion factor is an empirical factor used to
correlate the results of full-scale load tests with the
material property or characteristic of the cohesive soil.
The adhesion factor is usually related to Su and is
derived from the results of full-scale pile and drilled
shaft load tests. Use of this approach presumes that the
measured value of Su is correct and that all shaft
behavior resulting from construction and loading can be
lumped into a single parameter. Neither presumption is
strictly correct, but the approach is used due to its
simplicity.
Steel casing will generally reduce the side
resistance of a shaft. No specific data is available
regarding the reduction in skin friction resulting from
the use of permanent casing relative to concrete
placed directly against the soil. Side resistance
reduction factors for driven steel piles relative to
concrete piles can vary from 50 to 75 percent,
depending on whether the steel is clean or rusty,
respectively (Potyondy, 1961). Greater reduction in
the side resistance may be needed if oversized cutting
shoes or splicing rings are used.
If open-ended pipe piles are driven full depth with
an impact hammer before soil inside the pile is removed,
and left as a permanent casing, driven pile static analysis
methods may be used to estimate the side resistance as
described in Article 10.7.3.8.6.
The upper 5.0 ft of the shaft is ignored in estimating
Rn, to account for the effects of seasonal moisture
changes, disturbance during construction, cyclic lateral
loading, and low lateral stresses from freshly placed
concrete. The lower 1.0-diameter length above the shaft
tip or top of enlarged base is ignored due to the
development of tensile cracks in the soil near these
regions of the shaft and a corresponding reduction in
lateral stress and side resistance.
Bells or underreams constructed in stiff fissured
clay often settle sufficiently to result in the formation of
a gap above the bell that will eventually be filled by
slumping soil. Slumping will tend to loosen the soil
immediately above the bell and decrease the side
resistance along the lower portion of the shaft.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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SECTION 10: FOUNDATIONS
10-133
Figure 10.8.3.5.1b-1—Explanation of Portions of Drilled
Shafts Not Considered in Computing Side Resistance
(O’Neill and Reese, 1999)
10.8.3.5.1c—Tip Resistance
C10.8.3.5.1c
For axially loaded shafts in cohesive soil, the
nominal unit tip resistance, qp, by the total stress method
as provided in O’Neill and Reese (1999) shall be taken
as:
(10.8.3.5.1c-1)
q p = N c Su ≤ 80.0
in which:
Z
N c = 6 1 + 0.2 ≤ 9
D
The value of α is often considered to vary as a
function of Su. Values of α for drilled shafts are
recommended as shown in Eqs. 10.8.3.5.1b-2 and
10.8.3.5.1b-3, based on the results of back-analyzed,
full-scale load tests. This recommendation is based on
eliminating the upper 5.0 ft and lower 1.0 diameter of
the shaft length during back-analysis of load test results.
The load tests were conducted in insensitive cohesive
soils. Therefore, if shafts are constructed in sensitive
clays, values of α may be different than those obtained
from Eqs. 10.8.3.5.1b-2 and 10.8.3.5.1b-3. Other values
of α may be used if based on the results of load tests.
The depth of 5.0 ft at the top of the shaft may need
to be increased if the drilled shaft is installed in
expansive clay, if scour deeper than 5.0 ft is
anticipated, if there is substantial groundline deflection
from lateral loading, or if there are other long-term
loads or construction factors that could affect shaft
resistance.
A reduction in the effective length of the shaft
contributing to side resistance has been attributed to
horizontal stress relief in the region of the shaft tip,
arising from development of outward radial stresses at
the toe during mobilization of tip resistance. The
influence of this effect may extend for a distance of 1B
above the tip (O’Neill and Reese, 1999). The
effectiveness of enlarged bases is limited when L/D is
greater than 25.0 due to the lack of load transfer to the
tip of the shaft.
The values of α obtained from Eqs. 10.8.3.5.1b-2
and 10.8.3.5.1b-3 are considered applicable for both
compression and uplift loading.
These equations are for total stress analysis. For
effective stress methods for shafts in clay, see O’Neill
and Reese (1999).
The limiting value of 80.0 ksf for qp is not a
theoretical limit but a limit based on the largest
measured values. A higher limiting value may be used if
based on the results of a load test, or previous successful
experience in similar soils.
(10.8.3.5.1c-2)
where:
D
=
diameter of drilled shaft (ft)
Z
=
penetration of shaft (ft)
Su =
undrained shear strength (ksf)
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2012
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10-134
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The value of Su should be determined from the
results of in-situ and/or laboratory testing of undisturbed
samples obtained within a depth of 2.0 diameters below
the tip of the shaft. If the soil within 2.0 diameters of the
tip has Su <0.50 ksf, the value of Nc should be multiplied
by 0.67.
10.8.3.5.2—Estimation of Drilled Shaft Resistance
in Cohesionless Soils
C10.8.3.5.2a
10.8.3.5.2a—General
Shafts in cohesionless soils should be designed by
effective stress methods for drained loading conditions
or by empirical methods based on in-situ test results.
10.8.3.5.2b—Side Resistance
C10.8.3.5.2b
The nominal axial resistance of drilled shafts in
cohesionless soils by the β-method shall be taken as:
qs = βσ′ ≤ 4.0 for 0.25 ≤ β ≤ 1.2
v
(10.8.3.5.2b-1)
in which, for sandy soils:
•
for N60 ≥ 15:
(10.8.3.5.2b-2)
β = 1.5 − 0.135 z
•
for N60 < 15:
β=
N 60
15
The factored resistance should be determined in
consideration of available experience with similar
conditions.
Although many field load tests have been
performed on drilled shafts in clays, very few have
been performed on drilled shafts in sands. The shear
strength of cohesionless soils can be characterized by
an angle of internal friction, φf, or empirically related
to its SPT blow count, N. Methods of estimating shaft
resistance and end bearing are presented below.
Judgment and experience should always be
considered.
O’Neill and Reese (1999) provide additional
discussion of computation of shaft side resistance and
recommend allowing β to increase to 1.8 in gravels and
gravelly sands, however, they recommend limiting the
unit side resistance to 4.0 ksf in all soils.
O’Neill and Reese (1999) proposed a method for
uncemented soils that uses a different approach in that
the shaft resistance is independent of the soil friction
angle or the SPT blow count. According to their
findings, the friction angle approaches a common value
due to high shearing strains in the sand caused by stress
relief during drilling.
(10.8.3.5.2b-3)
(1.5 − 0.135 z )
where:
σ′v =
vertical effective stress at soil layer mid-depth
(ksf)
β
=
load transfer coefficient (dim)
z
=
depth below ground, at soil layer mid-depth (ft)
N60 =
average SPT blow count (corrected only for
hammer efficiency) in the design zone under
consideration (blows/ft)
Higher values may be used if verified by load tests.
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2012
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SECTION 10: FOUNDATIONS
10-135
For gravelly sands and gravels, Eq. 10.8.3.5.2b-4
should be used for computing β where N60 ≥ 15. If
N60 < 15, Eq. 10.8.3.5.2b-3 should be used.
β = 2.0 − 0.06 ( z )
0.75
The detailed development of Eq. 10.8.3.5.2b-4 is
provided in O’Neill and Reese (1999).
(10.8.3.5.2b-4)
When permanent casing is used, the side resistance
shall be adjusted with consideration to the type and
length of casing to be used, and how it is installed.
10.8.3.5.2c—Tip Resistance
C10.8.3.5.2c
The nominal tip resistance, qp, in ksf, for drilled
shafts in cohesionless soils by the O’Neill and Reese
(1999) method shall be taken as:
for N 60 ≤ 50, q p = 1.2 N 60
Steel casing will generally reduce the side
resistance of a shaft. No specific data is available
regarding the reduction in skin friction resulting from
the use of permanent casing relative concrete placed
directly against the soil. Side resistance reduction factors
for driven steel piles relative to concrete piles can vary
from 50 to 75 percent, depending on whether the steel is
clean or rusty, respectively (Potyondy, 1961). Casing
reduction factors of 0.6 to 0.75 are commonly used.
Greater reduction in the side resistance may be needed if
oversized cutting shoes or splicing rings are used.
If open-ended pipe piles are driven full depth with
an impact hammer before soil inside the pile is removed,
and left as a permanent casing, driven pile static analysis
methods may be used to estimate the side resistance as
described in Article 10.7.3.8.6.
(10.8.3.5.2c-1)
O’Neill and Reese (1999) provide additional
discussion regarding the computation of nominal tip
resistance.
See O’Neill and Reese (1999) for background on
IGMs.
where:
N60 =
average SPT blow count (corrected only for
hammer efficiency) in the design zone under
consideration (blows/ft)
The value of qp in Eq. 10.8.3.5.2c-1 should be
limited to 60 ksf, unless greater values can be justified
though load test data.
Cohesionless soils with SPT-N60 blow counts
greater than 50 shall be treated as intermediate
geomaterial (IGM) and the tip resistance, in ksf, taken
as:
p
q p = 0.59 N 60 a
σ 'v
0.8
σ ′v
(10.8.3.5.2c-2)
where:
pa =
atmospheric pressure (= 2.12 ksf)
σ′v =
vertical effective stress at the tip elevation of
the shaft (ksf)
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2012
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10-136
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
N60 should be limited to 100 in Eq. 10.8.3.5.2c-2 if
higher values are measured.
10.8.3.5.3—Shafts in Strong Soil Overlying Weaker
Compressible Soil
Where a shaft is tipped in a strong soil layer
overlying a weaker layer, the base resistance shall be
reduced if the shaft base is within a distance of 1.5B
of the top of the weaker layer. A weighted average
should be used that varies linearly from the full base
resistance in the overlying strong layer at a distance
of 1.5B above the top of the weaker layer to the base
resistance of the weaker layer at the top of the weaker
layer.
C10.8.3.5.3
The distance of 1.5B represents the zone of
influence for general bearing capacity failure based on
bearing capacity theory for deep foundations.
10.8.3.5.4—Estimation of Drilled Shaft Resistance
in Rock
10.8.3.5.4a—General
Drilled shafts in rock subject to compressive
loading shall be designed to support factored loads in:
•
Side-wall shear comprising skin friction on the wall
of the rock socket; or
•
End bearing on the material below the tip of the
drilled shaft; or
•
A combination of both.
The difference in the deformation required to
mobilize skin friction in soil and rock versus what is
required to mobilize end bearing shall be considered
when estimating axial compressive resistance of shafts
embedded in rock. Where end bearing in rock is used as
part of the axial compressive resistance in the design,
the contribution of skin friction in the rock shall be
reduced to account for the loss of skin friction that
occurs once the shear deformation along the shaft sides
is greater than the peak rock shear deformation, i.e.,
once the rock shear strength begins to drop to a residual
value.
C10.8.3.5.4a
Methods presented in this Article to calculate
drilled shaft axial resistance require an estimate of the
uniaxial compressive strength of rock core. Unless the
rock is massive, the strength of the rock mass is most
frequently controlled by the discontinuities, including
orientation, length, and roughness, and the behavior of
the material that may be present within the
discontinuity, e.g., gouge or infilling. The methods
presented are semi-empirical and are based on load test
data and site-specific correlations between measured
resistance and rock core strength.
Design based on side-wall shear alone should be
considered for cases in which the base of the drilled hole
cannot be cleaned and inspected or where it is
determined that large movements of the shaft would be
required to mobilize resistance in end bearing.
Design based on end-bearing alone should be
considered where sound bedrock underlies low strength
overburden materials, including highly weathered rock.
In these cases, however, it may still be necessary to
socket the shaft into rock to provide lateral stability.
Where the shaft is drilled some depth into sound
rock, a combination of sidewall shear and end bearing
can be assumed (Kulhawy and Goodman, 1980).
If the rock is degradable, use of special construction
procedures, larger socket dimensions, or reduced socket
resistance should be considered.
For drilled shafts installed in karstic formations,
exploratory borings should be advanced at each drilled
shaft location to identify potential cavities. Layers of
compressible weak rock along the length of a rock
socket and within approximately three socket diameters
or more below the base of a drilled shaft may reduce the
resistance of the shaft.
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2012
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SECTION 10: FOUNDATIONS
10-137
For rock that is stronger than concrete, the concrete
shear strength will control the available side friction,
and the strong rock will have a higher stiffness, allowing
significant end bearing to be mobilized before the side
wall shear strength reaches its peak value. Note that
concrete typically reaches its peak shear strength at
about 250 to 400 microstrain (for a 10-ft long rock
socket, this is approximately 0.5 in. of deformation at
the top of the rock socket). If strains or deformations
greater than the value at the peak shear stress are
anticipated to mobilize the desired end bearing in the
rock, a residual value for the skin friction can still be
used. Article 10.8.3.5.4d provides procedures for
computing a residual value of the skin friction based on
the properties of the rock and shaft.
10.8.3.5.4b—Side Resistance
C10.8.3.5.4b
For drilled shafts socketed into rock, shaft
resistance, in ksf, may be taken as (Horvath and Kenney,
1979):
qs = 0.65α E pa ( qu pa )
0.5
0.5
< 7.8 pa ( f c′ pa )
(10.8.3.5.4b-1)
where:
qu =
uniaxial compressive strength of rock (ksf)
pa =
atmospheric pressure (= 2.12 ksf)
αE =
reduction factor to account for jointing in rock
as provided in Table 10.8.3.5.4b-1
f′c
=
concrete compressive strength (ksi)
Table 10.8.3.5.4b-1—Estimation of αE (O’Neill and Reese,
1999)
Em/Ei
1.0
0.5
0.3
0.1
0.05
Eq. 10.8.3.5.4b-1 applies to the case where the side
of the rock socket is considered to be smooth or where
the rock is drilled using a drilling slurry. Significant
additional shaft resistance may be achieved if the
borehole is specified to be artificially roughened by
grooving. Methods to account for increased shaft
resistance due to borehole roughness are provided in
Section 11 of O’Neill and Reese (1999).
Eq. 10.8.3.5.4b-1 should only be used for intact
rock. When the rock is highly jointed, the calculated qs
should be reduced to arrive at a final value for design.
The procedure is as follows:
Step 1. Evaluate the ratio of rock mass modulus to
intact rock modulus, i.e., Em/Ei, using
Table C10.4.6.5-1.
Step 2. Evaluate the reduction factor, αE, using
Table 10.8.3.5.4b-1.
Step 3. Calculate qs according to Eq. 10.8.3.5.4b-1.
αE
1.0
0.8
0.7
0.55
0.45
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2012
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10-138
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
C10.8.3.5.4c
10.8.3.5.4c—Tip Resistance
End-bearing for drilled shafts in rock may be taken
as follows:
•
If the rock below the base of the drilled shaft to a
depth of 2.0B is either intact or tightly jointed, i.e.,
no compressible material or gouge-filled seams, and
the depth of the socket is greater than 1.5B (O’Neill
and Reese, 1999):
(10.8.3.5.4c-1)
q p = 2.5qu
•
If the rock below the base of the shaft to a depth of
2.0B is jointed, the joints have random orientation,
and the condition of the joints can be evaluated as:
q p = s
+ (m
s + s ) qu
(10.8.3.5.4c-2)
where:
s, m =
fractured rock mass parameters and are
specified in Table 10.4.6.4-4
qu =
unconfined compressive strength of rock (ksf)
10.8.3.5.4d—Combined Side and Tip
Resistance
Design methods that consider the difference in shaft
movement required to mobilize skin friction in rock
versus what is required to mobilize end bearing, such as
the methodology provided by O’Neill and Reese (1999),
shall be used to estimate axial compressive resistance of
shafts embedded in rock.
If end bearing in the rock is to be relied upon,
and wet construction methods are used, bottom cleanout procedures such as airlifts should be specified to
ensure removal of loose material before concrete
placement.
The use of Eq. 10.8.3.5.4c-1 also requires that there
are no solution cavities or voids below the base of the
drilled shaft.
For further information see O’Neill and Reese
(1999).
Eq. 10.8.3.5.4c-2 is a lower bound solution for
bearing resistance for a drilled shaft bearing on or
socketed in a fractured rock mass. This method is
appropriate for rock with joints that are not necessarily
oriented preferentially and the joints may be open,
closed, or filled with weathered material. Load testing
will likely indicate higher tip resistance than that
calculated using Eq. 10.8.3.5.4c-2. Resistance factors for
this method have not been developed and must therefore
be estimated by the designer.
C10.8.3.5.4d
Typically, the axial compression load on a shaft
socketed into rock is carried solely in shaft side
resistance until a total shaft movement on the order of
0.4 in. occurs.
Designs which consider combined effects of side
friction and end-bearing of a drilled shaft in rock
require that side friction resistance and end bearing
resistance be evaluated at a common value of axial
displacement, since maximum values of side friction
and end-bearing are not generally mobilized at the
same displacement.
Where combined side friction and end-bearing in
rock is considered, the designer needs to evaluate
whether a significant reduction in side resistance will
occur after the peak side resistance is mobilized. As
indicated in Figure C10.8.3.5.4d-1, when the rock is
brittle in shear, much shaft resistance will be lost as
vertical movement increases to the value required to
develop the full value of qp. If the rock is ductile in
shear, i.e., deflection softening does not occur, then
the side resistance and end-bearing resistance can be
added together directly. If the rock is brittle, however,
adding them directly may be unconservative. Load
testing or laboratory shear strength testing, e.g., direct
shear testing, may be used to evaluate whether the
rock is brittle or ductile in shear.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
SECTION 10: FOUNDATIONS
10-139
Developed Resistance
A
Shaft resistance
B
Base resistance
C
Shaft Movement
Figure C10.8.3.5.4d-1—Deflection Softening Behavior of
Drilled Shafts under Compression Loading (after O’Neill
and Reese, 1999).
The method used to evaluate combined side
friction and end-bearing at the strength limit state
requires the construction of a load-vertical
deformation curve. To accomplish this, calculate the
total load acting at the head of the drilled shaft, QT1,
and vertical movement, wT1, when the nominal shaft
side resistance (Point A on Figure C10.8.3.5.4d-1) is
mobilized. At this point, some end bearing is also
mobilized. For detailed computational procedures for
estimating shaft resistance in rock, considering the
combination of side and tip resistance, see O’Neill
and Reese (1999).
10.8.3.5.5—Estimation of Drilled Shaft Resistance
in Intermediate Geo Materials (IGMs)
For detailed base and side resistance estimation
procedures for shafts in IGMs, the procedures provided
by O’Neill and Reese (1999) should be used.
10.8.3.5.6—Shaft Load Test
When used, load tests shall be conducted in
representative soil conditions using shafts constructed in
a manner and of dimensions and materials similar to
those planned for the production shafts. The load test
shall follow the procedures specified in ASTM D1143.
The loading procedure should follow the Quick Load
Test Method, unless detailed longer-term loadsettlement data is needed, in which case the standard
loading procedure should be used.
The nominal resistance shall be determined
according to the failure definition of either:
•
“Plunging” of the drilled shaft, or
•
A gross settlement or uplift of five percent of the
diameter of the shaft if plunging does not occur.
C10.8.3.5.5
See Article 10.8.2.2.3 for a definition of an IGM.
For convenience, since a common situation is to tip
the shaft in a cohesionless IGM, the equation for tip
resistance in a cohesionless IGM is provided in
Article C10.8.3.5.2c.
C10.8.3.5.6
For a larger project where many shafts are to be
used, it may be cost-effective to perform a full-scale
load test on a drilled shaft during the design phase of
a project to confirm response to load.
Load tests should be conducted following
prescribed written procedures that have been
developed from accepted standards and modified, as
appropriate, for the conditions at the site. The Quick
Test Procedure is desirable because it avoids
problems that frequently arise when performing a
static test that cannot be started and completed within
an eight-hour period. Tests that extend over a longer
period are difficult to perform due to the limited
number of experienced personnel that are usually
available. The Quick Test has proven to be easily
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2012
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10-140
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The resistance factors for axial compressive
resistance or axial uplift resistance shall be taken as
specified in Table 10.5.5.2.4-1.
Regarding the use of shaft load test data to
determine shaft resistance, the load test results should be
applied to production shafts that are not load tested by
matching the static resistance prediction to the load test
results. The calibrated static analysis method should
then be applied to adjacent locations within the site to
determine the shaft tip elevation required, in
consideration of variations in the geologic stratigraphy
and design properties at each production shaft location.
The definition of a site and number of load tests required
to account for site variability shall be as specified in
Article 10.5.5.2.3.
performed in the field, and the results usually are
satisfactory. However, if the formation in which the
shaft is installed may be subject to significant creep
settlement, alternative procedures provided in ASTM
D1143 should be considered.
Load tests are conducted on full-scale drilled
shaft foundations to provide data regarding nominal
axial resistance, load-displacement response, and
shaft performance under the design loads, and to
permit assessment of the validity of the design
assumptions for the soil conditions at the test shaft(s).
Tests can be conducted for compression, uplift,
lateral loading, or for combinations of loading. Fullscale load tests in the field provide data that include the
effects of soil, rock, and groundwater conditions at the
site; the dimensions of the shaft; and the procedures
used to construct the shaft.
The results of full-scale load tests can differ even
for apparently similar ground conditions. Therefore, care
should be exercised in generalizing and extrapolating
the test results to other locations.
For large diameter shafts, where conventional
reaction frames become unmanageably large, load testing
using Osterberg load cells may be considered. Additional
discussion regarding load tests is provided in O’Neill and
Reese (1999). Alternatively, smaller diameter shafts may
be load tested to represent the larger diameter shafts (but
no less than one-half the full scale production shaft
diameter), provided that appropriate measures are taken to
account for potential scale effects when extrapolating the
results to the full scale production shafts.
Plunging occurs when a steady increase in
movement results from incrementally small increases in
load, e.g., 2.0 kips.
10.8.3.6—Shaft Group Resistance
C10.8.3.6.1
10.8.3.6.1—General
Reduction in resistance from group effects shall be
evaluated.
10.8.3.6.2—Cohesive Soil
The provisions of Article 10.7.3.9 shall apply.
The resistance factor for the group resistance of an
equivalent pier or block failure provided in
Table 10.5.5.2.4-1 shall apply where the cap is, or is not,
in contact with the ground.
The resistance factors for the group resistance
calculated using the sum of the individual drilled shaft
resistances are the same as those for the single-drilled
shaft resistances.
In addition to the overlap effects discussed below,
drilling of a hole for a shaft less than three shaft
diameters from an existing shaft reduces the effective
stresses against both the side and base of the existing
shaft. As a result, the capacities of individual drilled
shafts within a group tend to be less than the
corresponding capacities of isolated shafts.
If casing is advanced in front of the excavation
heading, this reduction need not be made.
C10.8.3.6.2
The efficiency of groups of drilled shafts in
cohesive soil may be less than that of the individual
shaft due to the overlapping zones of shear deformation
in the soil surrounding the shafts.
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2012
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SECTION 10: FOUNDATIONS
10-141
10.8.3.6.3—Cohesionless Soil
C10.8.3.6.3
The individual nominal resistance of each shaft in a
group should be reduced by applying an adjustment
factor η taken as shown in Table 10.8.3.6.3-1.
For intermediate spacings, the value of η may be
determined by linear interpolation.
The bearing resistance of drilled shaft groups in
sand is less than the sum of the individual shafts due to
overlap of shear zones in the soil between adjacent
shafts and loosening of the soil during construction. The
recommended reduction factors are based in part on
theoretical considerations and on limited load test
results. See O’Neill and Reese (1999) for additional
details and a summary of group load test results. It
should be noted that most of the available group load
test results were obtained for sands above the water
table and for relatively small groups, e.g., groups of 3–9
shafts. For larger shaft groups or for shaft groups of any
size below the water table, more conservative values of
η should be considered.
These reduction factors presume that good shaft
installation practices are used to minimize or eliminate
the relaxation of the soil between shafts and caving. If
this cannot be adequately controlled due to difficult soil
conditions or for other reasons, lower group reduction
factors should be considered, or steps should be taken
during and after shaft construction to restore the soil to
its original condition.
Table 10.8.3.6.3-1—Group Reduction Factors for Bearing Resistance of Shafts in Sand
Shaft Group
Configuration
Shaft Center-toCenter Spacing
Single Row
2D
3D or more
2.5D
3D
4D or more
2D or more
Multiple Row
Single and
Multiple Rows
Single and
Multiple Rows
2D or more
Special Conditions
Shaft group cap in intimate contact with ground
consisting of medium dense or denser soil, and no
scour below the shaft cap is anticipated
Pressure grouting is used along the shaft sides to
restore lateral stress losses caused by shaft
installation, and the shaft tip is pressure grouted
Reduction
Factor for
Group
Effects, η
0.90
1.0
0.67
0.80
1.0
1.0
1.0
10.8.3.6.4—Shaft Groups in Strong Soil Overlying
Weak Soil
For shaft groups that are collectively tipped within a
strong soil layer overlying a soft, cohesive layer, block
bearing resistance shall be evaluated in accordance with
Article 10.7.3.9.
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2012
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10-142
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
10.8.3.7—Uplift Resistance
10.8.3.7.1—General
Uplift resistance shall be evaluated when upward
loads act on the drilled shafts. Drilled shafts subjected to
uplift forces shall be investigated for resistance to
pullout, for their structural strength, and for the strength
of their connection to supported components.
10.8.3.7.2—Uplift Resistance of Single Drilled Shaft
The uplift resistance of a single straight-sided
drilled shaft should be estimated in a manner similar to
that for determining side resistance for drilled shafts in
compression, as specified in Article 10.8.3.3.
In determining the uplift resistance of a belled
shaft, the side resistance above the bell should
conservatively be neglected if the resistance of the bell
is considered, and it can be assumed that the bell
behaves as an anchor.
The factored nominal uplift resistance of a belled
drilled shaft in a cohesive soil, RR, in kips, should be
determined as:
RR = ϕRn = ϕup Rsbell
C10.8.3.7.2
The resistance factors for uplift are lower than those
for axial compression. One reason for this is that drilled
shafts in tension unload the soil, thus reducing the
overburden effective stress and hence the uplift side
resistance of the drilled shaft. Empirical justification for
uplift
resistance
factors
is
provided
in
Article C10.5.5.2.3, and in Allen (2005).
(10.8.3.7.2-1)
in which:
Rs bell = qs bell Au
(10.8.3.7.2-2)
where:
qsbell
=
NuSu (ksf)
Au
=
π(Dp2 – D2)/4 (ft2)
Nu
=
uplift adhesion factor (dim)
Dp
=
diameter of the bell (ft)
Db
=
depth of embedment in the founding layer
(ft)
D
=
shaft diameter (ft)
Su
=
undrained shear strength averaged over a
distance of 2.0 bell diameters (2Dp) above
the base (ksf)
ϕup
=
resistance
factor
Table 10.5.5.2.4-1
specified
Figure C10.8.3.7.2-1—Uplift of a Belled Drilled Shaft
in
If the soil above the founding stratum is expansive,
Su should be averaged over the lesser of either 2.0Dp
above the bottom of the base or over the depth of
penetration of the drilled shaft in the founding stratum.
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2012
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SECTION 10: FOUNDATIONS
10-143
The value of Nu may be assumed to vary linearly
from 0.0 at Db/Dp = 0.75 to a value of 8.0 at Db/Dp = 2.5,
where Db is the depth below the founding stratum. The
top of the founding stratum should be taken at the base
of zone of seasonal moisture change.
The assumed variation of Nu is based on Yazdanbod
et al. (1987).
This method does not include the uplift resistance
contribution due to soil suction and the weight of the
shaft.
10.8.3.7.3—Group Uplift Resistance
The provisions of Article 10.7.3.11 shall apply.
10.8.3.7.4—Uplift Load Test
C10.8.3.7.4
The provisions of Article 10.7.3.10 shall apply.
See commentary to Article 10.7.3.10.
10.8.3.8—Nominal Horizontal Resistance of
Shaft and Shaft Groups
C10.8.3.8
See commentary to Article 10.7.3.12.
The provisions of Article 10.7.3.12 apply.
The design of horizontally loaded drilled shafts
shall account for the effects of interaction between the
shaft and ground, including the number of shafts in the
group.
For shafts used in groups, the drilled shaft head
shall be fixed into the cap.
10.8.3.9—Shaft Structural Resistance
10.8.3.9.1—General
The structural design of drilled shafts shall be in
accordance with the provisions of Section 5 for the
design of reinforced concrete.
10.8.3.9.2—Buckling and Lateral Stability
C10.8.3.9.2
The provisions of Article 10.7.3.13.4 shall apply.
See commentary to Article 10.7.3.13.4.
10.8.3.9.3—Reinforcement
C10.8.3.9.3
Where the potential for lateral loading is
insignificant, drilled shafts may be reinforced for axial
loads only. Those portions of drilled shafts that are not
supported laterally shall be designed as reinforced
concrete columns in accordance with Article 5.7.4.
Reinforcing steel shall extend a minimum of 10.0 ft
below the plane where the soil provides fixity.
Where the potential for lateral loading is significant,
the unsupported portion of the shaft shall be designed in
accordance with Articles 5.10.11 and 5.13.4.6.
The minimum spacing between longitudinal bars, as
well as between transverse bars or spirals, shall be
sufficient to allow free passage of the concrete through
the cage and into the annulus between the cage and the
borehole wall.
Shafts constructed using generally accepted
procedures are not normally stressed to levels such that
the allowable concrete stress is exceeded. Exceptions
include:
•
Shafts with sockets in hard rock,
•
Shafts subjected to lateral loads,
•
Shafts subjected to uplift loads from expansive soils
or direct application of uplift loads, and
•
Shafts with unreinforced bells.
Maintenance of the spacing of reinforcement and
the maximum aggregate size requirements are important
to ensure that the high-slump concrete mixes normally
used for drilled shafts can flow readily between the steel
bars during concrete placement. See Article 5.13.4.5.2
for specifications regarding the minimum clear spacing
required between reinforcing cage bars.
A shaft can be considered laterally supported:
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The minimum requirements to consider the steel
shell to be load carrying shall be as specified in
Article 5.13.4.5.2.
•
Below the zone of liquefaction or seismic loads,
•
In rock, or
•
5.0 ft below the ground surface or the lowest
anticipated scour elevation.
Laterally supported does not mean fixed. Fixity
would occur somewhat below this location and depends
on the stiffness of the supporting soil.
The out-to-out dimension of the assembled
reinforcing cage should be sufficiently smaller than the
diameter of the drilled hole to ensure free flow of
concrete around the reinforcing as the concrete is
placed. See Article 5.13.4.
See commentary to Article 10.7.5 regarding
assessment of corrosivity. In addition, consideration
should be given to the ability of the concrete and steel
shell to bond together.
10.8.3.9.4—Transverse Reinforcement
Transverse reinforcement may be constructed as
hoops of spiral steel.
Seismic provisions shall be in accordance with
Article 5.13.4.6.
10.8.3.9.5—Concrete
The maximum aggregate size, slump, wet or dry
placement, and necessary design strength should be
considered when specifying shaft concrete. The concrete
selected should be capable of being placed and
adequately consolidated for the anticipated construction
condition, and shaft details should be specified. The
maximum size aggregate shall meet the requirements of
Article 10.8.3.9.3.
C10.8.3.9.5
When concrete is placed in shafts, vibration is often
not possible except for the uppermost cross-section.
Vibration should not be used for high slump concrete.
10.8.3.9.6—Reinforcement into Superstructure
Sufficient reinforcement shall be provided at the
junction of the shaft with the shaft cap or column to
make a suitable connection. The embedment of the
reinforcement into the cap shall comply with the
provision for cast-in-place piles in Section 5.
10.8.3.9.7—Enlarged Bases
Enlarged bases shall be designed to ensure that the
plain concrete is not overstressed. The enlarged base
shall slope at a side angle not greater than 30 degrees
from the vertical and have a bottom diameter not greater
than three times the diameter of the shaft. The thickness
of the bottom edge of the enlarged base shall not be less
than 6.0 in.
10.8.4—Extreme Event Limit State
The provisions of Article 10.5.5.3 and 10.7.4 shall
apply.
C10.8.4
See commentary to Articles 10.5.5.3 and 10.7.4.
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SECTION 10: FOUNDATIONS
10-145
10.9—MICROPILES
10.9.1—General
C10.9.1
The provisions of Article 10.7.1 shall apply, except
as noted herein.
Micropiles shall be classified by type based on their
method of installation as follows:
•
Type A micropiles are constructed by placing a
sand-cement mortar or neat cement grout in the pile
under a gravity head only;
•
Type B micropiles are constructed by injecting a
neat cement grout under pressure (typically
6–21 ksf) into the drilled hole while the temporary
drill casing or auger is withdrawn;
•
•
•
Type C micropiles are grouted as for Type A,
followed 15–25 min after primary grouting by
injection of additional grout under pressure
(typically greater than 21 ksf) via a preplaced
sleeved grout pipe.
Type D micropiles are grouted similar to Type C,
but the primary grout is allowed to harden before
injecting the secondary grout under pressure
(typically 42–170 ksf) with a packer to achieve
treatment of specific pile intervals or material
horizons; or
Type E micropiles are constructed by drilling with
grout injection through a continuous-thread,
hollow-core steel bar. The grout injection serves to
flush cuttings, achieve grout penetration into the
ground and stabilize the drill hole. Often the initial
grout has a high water to cement ratio and is then
replaced with a thicker structural grout near the
completion of drilling.
Micropiles should be considered:
•
Where footings cannot be founded on rock, stiff
cohesive, or granular foundation material at a
reasonable expense;
•
At locations where soil conditions would normally
permit the use of spread footings, but the potential
for erosion exists;
•
At locations where pile foundations must penetrate
rock;
•
At locations where difficult subsurface conditions
(e.g., cobbles, boulders, debris fill, running sands)
would hinder installation of driven piles or drilled
shafts;
•
At locations where difficult access or limited
headroom preclude use of other deep foundation
systems;
•
At locations where foundations must bridge over or
penetrate subsurface voids;
•
Where vibration limits preclude conventional pile
driving operations or access by drilled shaft rigs; or
•
When underpinning
foundations.
or
retrofitting
existing
A typical detail for a composite reinforced
micropile is illustrated in Figure C10.9.1-1.
Primary grout, where it provides direct load transfer
along the micropile to the surrounding ground, shall be
Portland cement-based grout injected into the micropile
hole before or after reinforcement installation.
Post grouting, also known as regrouting or
secondary grouting, shall be taken as the injection of
additional Portland cement grout into the bond length of
the micropile after set up of primary grout to enhance
the grout–ground bond.
Figure C10.9.1-1—Typical Detail of Composite Reinforced
Micropile (after Sabatini, et al., 2005)
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
10.9.1.1—Scope
The provisions of this Article shall apply to the
design of micropiles.
The provisions of this section shall not be taken as
applicable to drilled piles, e.g., augercast piles, installed
with continuous flight augers that are concreted as the
auger is being extracted.
10.9.1.2—Minimum Micropile Spacing,
Clearance, and Embedment into Cap
Center-to-center pile spacing should not be less than
30.0 in. or 3.0 pile diameters, whichever is greater.
Otherwise, the provisions of Article 10.7.1.2 shall apply.
10.9.1.3—Micropiles through Embankment Fill
Micropiles extending through embankments shall
penetrate a minimum of 10.0 ft into original ground,
unless the required nominal axial and lateral resistance
occurs at a lesser penetration below the embankment
within bedrock or other suitable support materials.
C10.9.1.3
If compressible soils are located beneath the
embankment, micropiles should be installed after
embankment settlement is complete, if possible, to
minimize or eliminate downdrag forces.
10.9.1.4—Battered Micropiles
C10.9.1.4
The provisions of Article 10.7.1.4 shall apply.
See Article C10.7.1.4.
10.9.1.5—Micropile Design Requirements
C10.9.1.5
Micropile design shall address the following issues
as appropriate:
•
Nominal axial resistance to be specified in the
contract and size of micropile group required to
provide adequate support, with consideration of
how nominal axial micropile resistance will be
determined in the field;
•
Group interaction;
•
Pile quantity estimation from estimated pile
penetration required to meet nominal axial
resistance and other design requirements;
•
Minimum pile penetration necessary to satisfy the
requirements caused by uplift, scour, downdrag,
settlement, liquefaction, lateral loads, and seismic
conditions;
•
Foundation deflection to meet the established
movement and associated structure performance
criteria;
•
Pile foundation nominal structural resistance; and
•
Long-term durability of the micropile in service, i.e.
corrosion and deterioration.
The micropile design process is discussed in detail
in Micropile Design and Construction (Sabatini, et al.,
2005).
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SECTION 10: FOUNDATIONS
10-147
10.9.1.6—Determination of Micropile Loads
C10.9.1.6
The provisions of Article 10.7.1.6 shall apply.
See Article C10.7.1.6.
10.9.1.6.1—Downdrag
C10.9.1.6.1
The provisions of Articles 10.7.1.6.2 and 3.11.8
shall apply.
See Articles C10.7.1.6.2 and C3.11.8.
10.9.1.6.2—Uplift Due to Expansive Soils
C10.9.1.6.2
The provisions in Article 10.7.1.6.3 shall apply.
See Article C10.7.1.6.3.
10.9.1.6.3—Nearby Structures
The provisions of Article 10.7.1.6.4 shall apply.
10.9.2—Service Limit State Design
10.9.2.1—General
C10.9.2.1
The provisions of Article 10.7.2.1 shall apply.
See Article C10.7.2.1.
10.9.2.2—Tolerable Movements
C10.9.2.2
The provisions of Articles 10.5.2.1 and 10.5.2.2
shall apply.
10.9.2.3—Settlement
The provisions of Article 10.7.2.3 shall apply.
See Articles C10.5.2.1 and C10.5.2.2.
C10.9.2.3
See Article C10.7.2.3.
Methods for calculating the settlement of micropiles
are discussed in Sabatini, et al. (2005).
10.9.2.3.1—Micropile Groups in Cohesive Soil
C10.9.2.3.1
The provisions of Article 10.7.2.3.1 shall apply.
See Article 10.7.2.3.1.
10.9.2.3.2—Micropile Groups in Cohesionless Soil
C10.9.2.3.2
The provisions of Article 10.7.2.3.2 shall apply.
See Article C10.7.2.3.2.
10.9.2.4—Horizontal Micropile Foundation
Movement
C10.9.2.4
The provisions of Articles 10.5.2.1 and 10.7.2.4
shall apply.
See Articles C10.5.2.1 and C10.7.2.4.
10.9.2.5—Settlement Due to Downdrag
C10.9.2.5
The provisions of Article 10.7.2.5 shall apply.
See Article C10.7.2.5.
10.9.2.6—Lateral Squeeze
C10.9.2.6
The provisions of Article 10.7.2.6 shall apply.
See Article C10.7.2.6.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
10.9.3—Strength Limit State Design
10.9.3.1—General
C10.9.3.1
For strength limit state design, the following shall
be determined:
•
Loads and performance requirements;
•
Micropile dimensions and nominal axial micropile
resistance;
•
Size and configuration of the micropile group to
provide adequate foundation support;
•
Estimated micropile length to be used in the
construction contract documents to provide a basis
for bidding;
•
A minimum micropile penetration, if required, for
the particular site conditions and loading,
determined based on the maximum (deepest)
penetration needed to meet all of the applicable
requirements identified in Article 10.7.6; and
•
The nominal structural resistance of the micropile
and/or micropile group.
A minimum micropile penetration should only be
specified if needed to insure that uplift, lateral stability,
depth to resist downdrag, depth to resist scour, and
depth for structural lateral resistance are met for the
strength limit state, in addition to similar requirements
for the service and extreme event limit states. See
Article C10.7.6 for additional details.
Punching of micropiles through strong soil into a
weaker layer is not likely for micropiles designed for a
resistance by bond transfer only.
10.9.3.2—Ground Water Table and Bouyancy
C10.9.3.2
The provisions of Article 10.7.3.4 shall apply.
See Article C10.7.3.4.
10.9.3.3—Scour
C10.9.3.3
The provisions of Article 10.7.3.5 shall apply.
See Article C10.7.3.5.
10.9.3.4—Downdrag
C10.9.3.4
The provisions of Article 10.7.3.6 shall apply.
See Article C10.7.3.6.
10.9.3.5—Nominal Axial Compression
Resistance of a Single Micropile
C10.9.3.5.1
10.9.3.5.1—General
Micropiles shall be designed to resist failure of the
bonded length in soil and rock, or for micropiles bearing
on rock, failure of the rock at the micropile tip.
The factored resistance of a micropile, RR, shall be
taken as:
RR = ϕRn = ϕqp R p + ϕqs Rs
(10.9.3.5.1-1)
Micropiles are typically designed based on bond
into soil and rock neglecting tip resistance due to
their relatively small diameter and high grout-toground bond resistance. Tip resistance may be
considered for micropiles bearing on hard rock
although the axial capacity for this case is often
controlled by the structural resistance of the
micropile.
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SECTION 10: FOUNDATIONS
10-149
in which:
R p = q p Ap
(10.9.3.5.1-2)
Rs = qs As
(10.9.3.5.1-3)
where:
Rp =
nominal tip resistance (kips)
Rs =
nominal grout-to-ground bond resistance (kips)
ϕqp =
resistance factor for tip resistance specified in
Table 10.5.5.2.5-1
ϕqs =
resistance factor for grout-to-ground bond
resistance specified in Table 10.5.5.2.5-1
qp =
unit tip resistance (ksf)
qs
=
Both the tip and bond resistances develop in
response to foundation displacement. The maximum
values of each are unlikely to occur at the same
displacement. The bond resistance is typically fully
mobilized at displacements of about 0.1 to 0.4 in. The
tip capacity, however, is mobilized after the micropile
settles about six percent of its diameter (Jeon and
Kulhawy, 2001), and is generally neglected in the design
of micropiles in soil.
The methods for estimating micropile axial
resistance provided in this article should be used.
Micropile strength limit state resistance methods not
specifically addressed in this Article for which adequate
successful regional or national experience is available
may be used, provided adequate information and
experience is also available to develop appropriate
resistance factors.
unit grout-to-ground bond resistance (ksf)
Ap =
area of micropile tip (ft2)
As =
area of grout-to-ground bond surface (ft2)
For final design, micropile resistance shall be
verified through the performance of micropile load tests
as described in Article 10.9.3.5.4. The resistance factors
for micropiles shall be taken as specified in
Table 10.5.5.2.5-1.
10.9.3.5.2—Estimation of Grout-to-Ground Bond
Resistance
The nominal grout-to-ground bond resistance over
the bonded length of a micropile, Rs , in kips shall be
taken as:
Rs = πd b α b Lb
(10.9.3.5.2-1)
where:
db =
diameter of micropile drill hole through bonded
length (ft)
αb =
nominal micropile
strength (ksf)
Lb =
micropile bonded length (ft)
grout-to-ground
bond
For final design, micropile capacity shall be verified
through the performance of micropile load tests as
described in Article 10.9.3.5.4.
C10.9.3.5.2
The value of nominal unit grout-to-ground bond
strength, either estimated empirically or determined
through load testing, is typically taken as the average
value over the entire bond length.
Micropile grout-to-ground bond strength is
influenced by soil and rock conditions, method of
micropile drilling and installation, and grouting
pressure. The final micropile geotechnical design should
be performed by a specialty contractor qualified to
perform micropile design and construction. As a guide,
Table C10.9.3.5.2-1 may be used to estimate the
nominal (ultimate) unit grout-to-ground bond strength
for Types A, B, C, D, and E micropiles bonded into soil
and/or rock for preliminary design.
For preliminary design, the grout-to-ground bond
resistance of micropiles may be based on the results of
micropile load tests; estimated based on a review of
geologic and boring data, soil and rock samples,
laboratory testing, and pervious experience; or estimated
using published soil/rock-grout bond guidelines.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table C10.9.3.5.2-1—Summary of Typical αb Values (Grout-to-Ground Bond) for Preliminary Micropile Design (modified
after Sabatini, et al., 2005)
Typical Range of Grout-to-Ground Bond Nominal Resistance for Micropile Types(1) (ksf)
Soil/Rock Description
Type A
Type B
Type C
Type D
Silt & Clay (some sand)
(soft medium plastic)
0.7–1.4
0.7–2.0
0.7–2.5
0.7–3.0
0.7–2.0
Silt & Clay (some sand)
(stiff, dense to very dense)
0.7–2.5
1.4–4.0
2.0–4.0
2.0–4.0
1.4–4.0
Sand (some silt)
(fine, loose-medium dense)
1.4–3.0
1.4–4.0
2.0–4.0
2.0–5.0
1.4–5.0
Sand (some silt, gravel)
(fine-coarse, medium-very dense)
2.0–4.5
2.5–7.5
3.0–7.5
3.0–8.0
2.5–7.5
Gravel (some sand)
(medium-very dense)
2.0–5.5
2.5–7.5
3.0–7.5
3.0–8.0
2.5–7.5
Glacial Till (silt, sand, gravel)
(medium-very dense, cemented)
2.0–4.0
2.0–6.5
2.5–6.5
2.5–7.0
2.0–6.5
Soft Shales (fresh-moderate
fracturing, little to no weathering)
4.3–11.5
N/A
N/A
N/A
N/A
Slates and Hard Shales (freshmoderate fracturing, little to no
weathering)
10.8–28.8
N/A
N/A
N/A
N/A
Limestone (fresh-moderate
fracturing, little to no weathering)
21.6–43.2
N/A
N/A
N/A
N/A
Sandstone (fresh-moderate
fracturing, little to no weathering)
10.8–36.0
N/A
N/A
N/A
N/A
Granite and Basalt (fresh-moderate
fracturing, little to no weathering)
28.8–87.7
N/A
N/A
N/A
N/A
(1)
Type E
Refer to Article 10.9.1 for description of micropile types.
10.9.3.5.3—Estimation of Micropile Tip Resistance
in Rock
The methods used for design of micropiles bearing
on rock shall consider the presence, orientation, and
condition of discontinuities, weathering profiles, and
other similar profiles as they apply at a particular site.
The designer shall judge the competency of a rock mass
in accordance with the provisions of Article 10.4.6.4.
For micropiles founded on competent rock, tip
resistance may be estimated in accordance with the
provisions of Article 10.8.3.5.4c.
C10.9.3.5.3
Micropiles are generally designed based on bond
into rock rather than tip resistance. Tip resistance is
generally considered only for micropiles bearing on
competent rock.
For micropiles founded on competent rock, the rock
is usually so sound that the structural capacity will
govern the design.
Weak rock includes some shales and mudstones or
poor-quality weathered rocks. The term “weak” has no
generally accepted, quantitative definition; therefore,
judgment and experience are required to make this
determination.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
SECTION 10: FOUNDATIONS
10-151
10.9.3.5.4—Micropile Load Test
The load test shall follow the procedures specified
in ASTM D1143 for compression and ASTM D3689 for
tension. The loading procedure should follow the Quick
Load Test Method, unless detailed longer-term loadsettlement data is needed, in which case the standard
loading procedure should be used. Unless specified
otherwise by the Engineer, the pile axial resistance shall
be determined from the test data using the Davisson
Method as presented in Article 10.7.3.8.2.
The number of load tests required to account for site
variability shall be as specified in Article 10.5.5.2.2. The
number of test micropiles required should be increased
in nonuniform subsurface conditions.
In addition, proof tests loaded to the required
factored load shall be performed on one pile per
substructure unit or five percent of the piles, whichever
is greater, unless specified otherwise by the Engineer.
The resistance factors for axial compressive
resistance or axial uplift resistance shall be taken as
specified in Table 10.5.5.2.5-1.
10.9.3.6—Resistance of Micropile Groups in
Compression
Reduction in resistance from group effects shall be
evaluated in accordance with the provisions of
Article 10.7.3.9.
10.9.3.7—Nominal Uplift Resistance of a Single
Micropile
Uplift resistance shall be evaluated when upward
loads act on the micropiles. Micropiles subjected to
uplift forces shall be investigated for resistance to
pullout, for their structural strength, and for the strength
of their connection to supported components.
10.9.3.8—Nominal Uplift Resistance of Micropile
Groups
The provisions of Article 10.7.3.11 shall apply.
C10.9.3.5.4
See Article C10.8.3.5.6.
Load Tests on micropiles are performed to
determine micropile installation characteristics, evaluate
micropile capacity with depth, and establish micropile
bond lengths.
During the performance of ASTM tests, the
Contractor may perform several load cycles on the test
micropile for diagnostic purposes.
Test micropiles may not be required where previous
experience exists with the same micropile type and
ultimate micropile capacity in similar subsurface
conditions. However, load tests can differ even for
apparently similar ground conditions. Therefore, care
should be exercised in generalizing and extrapolating
the test results to other locations.
Test micropiles are frequently planned for each
substructure.
With approval of the Engineer, the number of load
tests and proof tests can be reduced based on:
•
Previous micropile load tests in similar ground
using similar methods, or
•
Site-specific tests showing much higher than
required factored resistance or consistent proof test.
C10.9.3.6
See Article C10.7.3.9.
C10.9.3.7
Resistance factors in Article 10.5.5.2.5 assume a
tension load test is performed. In the event that tension
load tests are not performed, the resistance factor for
presumptive values may be used or the tension
resistance estimated as 50 percent of the compression
resistance.
C10.9.3.8
Group uplift resistance in rock should consider the
depth of soil overburden, rock discontinuity spacing and
condition, and rock mass shear strength, as well as bond
between micropiles and rock.
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
10.9.3.9—Nominal Horizontal Resistance of
Micropiles and Micropile Groups
The provisions of Article 10.7.3.12 apply.
The design of horizontally loaded micropiles shall
account for the effects of interaction between the
micropiles and ground, including the number and
spacing of micropiles in the group.
For micropiles used in groups, the micropile head
shall be embedded into the cap and the degree of fixity
shall be considered in the design.
C10.9.3.9
See Article C10.7.3.12.
10.9.3.10—Structural Resistance
C10.9.3.10.1
10.9.3.10.1—General
The structural design of micropiles shall be in
accordance with the provisions of Section 5 for the
design of reinforced concrete and Section 6 for the
design of steel.
The cased and uncased length of each micropile
shall be designed to resist the forces distributed to the
micropile based on the micropile inclination and
spacing.
The resistance factors for structural design shall be
as specified in Table 10.5.5.2.5-2.
Articles 5.6.3.4, 5.7.4, 5.7.6, 5.13.4, and 6.15
provide specific provisions applicable to design of
concrete and steel micropiles.
The design of micropiles supporting axial
compression load only requires an allowance for
unintended eccentricity. This has been accounted for by
use of the equations in Article 5.7.4.4 for reinforced
concrete columns that already contain an eccentricity
allowance.
10.9.3.10.2—Axial Compressive Resistance
The upper cased section of a micropile subjected to
compression loading shall be designed structurally to
support the full factored load on the micropile. The
lower uncased section of a micropile subjected to
compression loading shall be designed structurally to
support the maximum full factored load on the micropile
less the load transferred to the surrounding ground from
the cased portion of the pile in the plunge length (if
used), as described in Article 10.9.3.10.4.
For micropiles extending through a weak upper soil
layer, extending above ground, subject to scour,
extending through mines/caves, or extending through
soil that may liquefy, the effect of any laterally
unsupported length shall be considered in the
determination of axial compression resistance.
The factored structural resistance of a micropile to
axial compression loading, RC , in kips may be taken as:
RC = ϕC Rn
(10.9.3.10.2-1)
where:
φC =
resistance factor specified in Table 10.5.5.2.5-2
for structural resistance of micropiles in axial
compression
Rn =
nominal axial compression resistance of
micropile specified in Articles 10.9.3.10.2a and
10.9.3.10.2b (kips)
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2012
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SECTION 10: FOUNDATIONS
10-153
10.9.3.10.2a—Cased Length
C10.9.3.10.2a
The factored structural resistance of the upper cased
length of a micropile having no unsupported length and
loaded in compression, RCC , in kips may be taken as:
The design compressive stress in the steel is limited
to the stress at which the strain equals 0.003 to maintain
compatibility with the strain in the grout.
(10.9.3.10.2a-1)
RCC = ϕCC Rn
for which:
[
Rn = 0.85 0.85 f c′Ag + f y ( Ab + Ac )
]
(10.9.3.10.2a-2)
where:
φCC =
resistance factor specified in Table 10.5.5.2.5-2
for structural resistance of the cased section of
a micropile subjected to compression loading
f ′c =
specified compressive strength of micropile grout
at 28 days unless another age is specified (ksi)
Ag =
cross-sectional area of grout within micropile
(in.2)
=
specified minimum yield strength of
reinforcement bar or steel casing, or stress in
steel reinforcement bar or casing at a strain of
0.003, whichever is less (ksi)
Ab =
cross-sectional area of steel reinforcing bar (in.2)
Ac =
cross-sectional area of steel casing (in.2)
fy
10.9.3.10.2b—Uncased Length
The factored structural resistance of the lower,
uncased length of a micropile having no unsupported
length and loaded in compression, RCU , in kips may be
taken as:
(10.9.3.10.2b-1)
RCU = ϕCU Rn
for which:
[
Rn = 0.85 0.85 f c′Ag + f y Ab
]
(10.9.3.10.2b-2)
where:
φCU =
resistance factor specified in Table 10.5.5.2.5-2
for structural resistance of the uncased section
of a micropile subjected to compression
loading
f ′c =
specified compressive strength of micropile grout
at 28 days unless another age is specified (ksi)
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Ag =
cross-sectional area of grout within micropile
(in.2)
=
specified minimum yield strength of
reinforcement bar or stress in steel reinforcement
bar at a strain of 0.003, whichever is less (ksi)
Ab =
cross-sectional area of steel reinforcing bar (in.2)
fy
10.9.3.10.3—Axial Tension Resistance
The upper cased section of a micropile subjected to
tension loading shall be designed structurally to support
the full factored load on the micropile. The lower
uncased section of a micropile subjected to tension
loading shall be designed structurally to support the
maximum full factored load on the micropile less the
load transferred to the surrounding ground from the
cased portion of the micropile in the plunge length, as
described in Article 10.9.3.10.4.
The factored structural resistance of a micropile
subjected to tension, RT , may be taken as:
(10.9.3.10.3-1)
RT = ϕT Rn
where:
φT =
resistance factor specified in Table 10.5.5.2.5-2
for structural resistance of a micropile
subjected to tension loading (dim)
Rn =
nominal axial tension resistance of micropile
specified in Articles 10.9.3.10.3a and
10.9.3.10.3b
C10.9.3.10.3a
10.9.3.10.3a—Cased Length
The factored structural resistance of the upper cased
length of a micropile subjected to tension loading, RTC ,
in kips may be taken as:
RTC = ϕTC Rn
The design compressive stress in the steel is limited
to the stress at which the strain equals 0.003 to maintain
compatibility with the strain in the grout.
(10.9.3.10.3a-1)
for which:
Rn = f y ( Ab + Act )
(10.9.3.10.3a-2)
where:
φTC =
resistance factor specified in Table 10.5.5.2.5-2
for structural resistance of the cased section of
a micropile subjected to tension loading (dim)
=
specified minimum yield strength of
reinforcement bar or steel casing, whichever is
less (ksi)
Ab =
cross-sectional area of steel reinforcing bar (in.2)
Act =
cross-sectional area of steel casing considering
reduction for threads (in.2)
fy
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
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SECTION 10: FOUNDATIONS
10-155
10.9.3.10.3b—Uncased Length
The factored structural resistance of the lower
uncased length of a micropile subjected to tension
loading, RTU , in kips may be taken as:
(10.9.3.10.3b-1)
RTU = ϕTU Rn
for which:
(10.9.3.10.3b-2)
Rn = f y Ab
where:
φTU =
fy
resistance factor specified in Table 10.5.5.2.5-2
for structural resistance of the uncased section of
a micropile subjected to tension loading (dim)
=
specified minimum yield
reinforcement bar (kip)
strength
of
cross-sectional area of steel reinforcing bar (in.2)
Ab =
10.9.3.10.4—Plunge Length Transfer Load
C10.9.3.10.4
The factored axial load transferred to the ground
through the plunge length of the cased portion of a
micropile, Pt , in kips, may be taken as:
[
]
Pt = ϕ π d b α b L p
(10.9.3.10.4-1)
where:
=
resistance factor specified in Table 10.5.5.2.5-1
for geotechnical bearing or uplift resistance, as
appropriate, of a single micropile
db =
diameter of micropile drill hole through bonded
length (ft)
αb =
nominal micropile
strength (ksf)
Lp =
micropile casing plunge length (ft)
φ
grout-to-ground
An optional procedure for construction of a
composite reinforced micropile includes insertion of the
pile casing into the top of the grouted bond zone to effect
a transition between the upper cased portion to the lower
uncased portion of a micropile. The length of casing
inserted into the bond zone by the plunge length is shown
in Figure C10.9.1-1. As a result, a portion of the factored
axial load on a micropile is transferred to the surrounding
ground by the cased portion of the pile, reducing the load
that must be supported by the weaker uncased portion of
the pile. The reduction in load applied to the uncased
length is termed the transfer load Pt.
bond
If load transfer through the plunge length of the
cased portion of a micropile is considered to reduce the
load on the lower uncased portion of the micropile, the
factored axial load on the uncased portion of the
micropile in compression or tension, PU ,in kips, may be
taken as:
(10.9.3.10.4-2)
Pu = Q − Pt
where:
Q
=
η γ Q
=
total factored axial load on micropile (kips)
i i
i
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2012
Edition
10-156
Pt
=
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
plunge
length
transfer
Eq. 10.9.3.10.4-1 (kips)
load
from
10.9.3.10.5—Grout-to-Steel Bond
Casing-to-grout bond shall be checked and
reinforcement bar development length shall be checked
in accordance with the provisions of Section 5.
C10.9.3.10.5
Grout-to-steel bond does not typically govern
micropile design, except for overlap of reinforcing bars
into upper casing.
The bond between the cement grout and the
reinforcing steel is the mechanism for transfer of the pile
load from the reinforcing steel to the ground. Typical
ultimate bond values range from 0.15 to 0.25 ksi for
smooth bars and pipe, and 0.30 to 0.50 ksi for deformed
bars (Armour, et al., 2000). Refer to Section 5 for bar
development requirements.
As is the case with any reinforcement, the surface
condition will affect the attainable bond. A film of rust
may be beneficial, but the presence of loose debris or
lubricant or paint is not desirable. Normal methods for
the handling and storage of reinforcing bars apply to
micropile construction. For the permanent casing that is
also used to drill the hole, cleaning of the casing surface
can occur during drilling, particularly in granular soils.
10.9.3.10.6—Buckling and Lateral Stability
The provisions of Article 10.7.3.13.4 shall apply.
10.9.3.10.7—Reinforcement into Superstructure
C10.9.3.10.7
Sufficient reinforcement shall be provided at the
junction of the micropile with the micropile footing or
column to make a suitable connection. The embedment
of the reinforcement into the cap shall comply with the
provision for cast-in-place piles in Section 5.
Refer to Sabatini, et al. (2005) for typical micropile
to footing connection details.
10.9.4—Extreme Event Limit State
C10.9.4
The provisions of Articles 10.5.5.3 and 10.7.4 shall
apply.
10.9.5—Corrosion and Deterioration
The provisions of Article 10.7.5 shall apply.
See Articles C10.5.5.3 and C10.7.4.
C10.9.5
Corrosion protection methods and design presented
in Article C10.7.5 apply to micropiles as well. In
addition, other micropile specific design options
including plastic encapsulation of central reinforcing
bars is provided in Sabatini (2005).
10.10—REFERENCES
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and Transportation Officials, Washington, DC.
AASHTO. 2002. Standard Specifications for Highway Bridges, 17th Edition, HB-17. American Association of State
Highway and Transportation Officials, Washington, DC.
AASHTO. 2011. AASHTO Guide Specifications for LRFD Seismic Design, Second Edition, LRFDSEIS-2. American
Association of State Highway and Transportation Officials, Washington, DC.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 10: FOUNDATIONS
10-157
Allen, T. M. 2005. Development of Geotechnical Resistance Factors and Downdrag Load Factors for LRFD
Foundation Strength Limit State Design, FHWA-NHI-05-052, Federal Highway Administration, U.S. Department of
Transportation, Washington, DC.
Allen, T. M., 2007, “Development of New Pile-Driving Formula and Its Calibration for Load and Resistance Factor
Design,” Transportation Research Record: Journal of the Transportation Research Board, No. 2004, Transportation
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Arman, A., N. Samtani, R. Castelli, and G. Munfakh. 1997. Subsurface Investigations: Training Course in
Geotechnical and Foundation Engineering, FHWA-HI-97-021. Federal Highway Administration, U.S. Department of
Transportation, Washington, DC.
Ashour, M., G. M. Norris, and P. Pilling. 1998, “Lateral Loading of a Pile in Layered Soil Using the Strain Wedge
Model,” ASCE Journal of Geotechnical and Geoenvironmental Engineering. American Society of Civil Engineers,
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ASTM D6429, Standard Guide for Selecting Surface Geophysical Methods
Baguelin, F., J. F. Jezequel, and D. H. Shields. 1987. The Pressuremeter and Foundation Engineering. Trans Tech
Publications, Clausthal-Zellerfeld, Germany, p. 617.
Barkdale, R. D., and R. C. Bachus. 1983. Design and Construction of Stone Columns—Vol. 1, FHWA/RD-83/02C.
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Barker, R. M., J. M. Duncan, K. B. Rojiani, P. S. K. Ooi, C. K. Tan, and S. G. Kim. 1991. Manuals for the Design of
Bridge Foundations. NCHRP Report 343. Transportation Research Board, National Research Council, Washington,
DC.
Barton, N. R. 1976. “The Shear Strength of Rock and Rock Joints,” Engineering Geology. Elsevier Science
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Bieniawski, Z. T. 1984. Rock Mechanics Design in Mining and Tunneling. A. A. Balkema, Rotterdam/Boston, p. 272.
Bogard, J. D., and H. Matlock. 1990. “Application of Model Pile Tests to Axial Pile Design.” In Proc., 22nd Annual
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Boulanger, R. W., and I. M. Idriss. 2006. “Liquefaction Susceptibility Criteria for Silts and Clays,” Journal of
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No. 11, pp. 1413–1426.
Bowles, J. E. 1977. Foundation Analysis and Design, Second Edition. McGraw–Hill Book Company, New York, NY.
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p. 1004.
Bray, J. D., and R. B. Sancio. 2006. “Assessment of the Liquefaction Susceptibility of Fine-Grained Soils,” Journal of
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Broms, B. B. 1964a. “Lateral Resistance of Piles in Cohesive Soil,” ASCE Journal for Soil Mechanics and
Foundation Engineering. American Society of Civil Engineers, Reston, VA, Vol. 90, SM2, pp. 27–63.
Broms, B.B. 1964b. “Lateral Resistance of Piles in Cohesionless Soil,” ASCE Journal for Soil Mechanics and
Foundation Engineering. American Society of Civil Engineers, Reston, VA, Vol. 90, SM3, pp. 123–156.
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Campanella, R. G. 1994. “Field Methods for Dynamic Geotechnical Testing: An Overview of Capabilities and
Needs.” In Dynamic Geotechnical Testing II, Special Technical Publication No. 1213, American Society for Testing
and Materials, Philadelphia, PA, pp. 3–23.
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Ltd., Vancouver, British Columbia, Canada, p. 460.
Carter, J. P., and F. H. Kulhawy. 1988. Analysis and Design of Foundations Socketed into Rock, Report No. EL-5918.
Empire State Electric Engineering Research Corporation and Electric Power Research Institute, New York, NY,
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Journal of Geotechnical and Geoenvironmental Engineering. American Society of Civil Engineers, Reston, VA, Vol.
130, No. 12, pp. 1314–1340.
Cheney, R. and R. Chassie. 2000. Soils and Foundations Workshop Reference Manual, NHI-00-045. National
Highway Institute, Federal Highway Administration, U.S. Department of Transportation, Washington, DC.
Davisson, M. T. 1972. “High Capacity Piles.” Proceedings Lecture Series, Innovations in Foundation Construction,
Illinois Section, American Society of Civil Engineers, Reston, VA.
Davisson, M. T., and K. E. Robinson. 1965. “Bending and Buckling of Partially Embedded Piles.” In Proc., Sixth
International Conference S. M. and F. E. University of Toronto Press, Montreal, Canada, pp. 243–246.
DiMillio, A. F. 1982. Performance of Highway Bridge Abutments Supported by Spread Footings on Compacted Fill,
FHWA/RD-81/184 (NTIS PB83-201822). FHWA Staff Study.
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APPENDIX A10—SEISMIC ANALYSIS AND DESIGN OF FOUNDATIONS
A10.1—INVESTIGATION
Slope instability, liquefaction, fill settlement, and increases in lateral earth pressure have often been major factors
contributing to bridge damage in earthquakes. These earthquake hazards may be significant design factors for peak
earthquake accelerations in excess of 0.1 g and should form part of a site-specific investigation if the site conditions
and the associated acceleration levels and design concepts suggest that such hazards may be of importance.
A10.2—FOUNDATION DESIGN
The commonly accepted practice for the seismic design of foundations is to utlize a pseudo-static approach,
where earthquake-induced foundation loads are determined from the reaction forces and moments necessary for
structural equilibrium. Although traditional bearing capacity design approaches are also applied, with appropriate
capacity reduction factors if a margin of safety against “failure” is desired, a number of factors associated with the
dynamic nature of earthquake loading should always be borne in mind.
Under cyclic loading at earthquake frequencies, the strength capable of being mobilized by many soils is greater
than the static strength. For unsaturated cohesionless soils, the increase may be about ten percent, whereas for
cohesive soils, a 50 percent increase could occur. However, for softer saturated clays and saturated sands, the potential
for strength and stiffness degradation under repeated cycles of loading must also be recognized. For bridges classified
as Zone 2, the use of static soil strengths for evaluating ultimate foundation capacity provides a small implicit measure
of safety and, in most cases, strength and stiffness degradation under repeated loading will not be a problem because
of the smaller magnitudes of seismic events. However, for bridges classified as Zones 3 and 4, some attention should
be given to the potential for stiffness and strength degradation of site soils when evaluating ultimate foundation
capacity for seismic design.
As earthquake loading is transient in nature, “failure” of soil for a short time during a cycle of loading may not be
significant. Of perhaps greater concern is the magnitude of the cyclic foundation displacement or rotation associated
with soil yield, as this could have a significant influence on structural displacements or bending moments and shear
distributions in columns and other members.
As foundation compliance influences the distribution of forces or moments in a structure and affects computation
of the natural period, equivalent stiffness factors for foundation systems are often required, In many cases, use is made
of various analytical solutions that are available for footings or piles where it is assumed that soil behaves in an elastic
medium. In using these formulae, it should be recognized that equivalent elastic moduli for soils are a function of
strain amplitude, and for seismic loads modulus values could be significantly less than those appropriate for low levels
of seismic loading. Variation of shear modulus with shearing strain amplitude in the case of sands is shown in
Figure A10.2-1. Additional discussion of this topic can be found in the AASHTO Guide Specifications for LRFD
Seismic Design.
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Figure A10.2-1—Variation of Shear Modulus with Shearing Strain for Sands
On the basis of field and experimental observations, it is becoming more widely recognized that transient
foundation uplift or rocking during earthquake loading, resulting in separation of the foundation from the subsoil, is
acceptable provided that appropriate design precautions are taken (Taylor and Williams, 1979). Experimental studies
suggest that rotational yielding beneath rocking foundation can provide a useful form of energy dissipation. However,
care must be taken to avoid significant induced vertical deformations accompanying possible soil yield during
earthquake rocking as well as excessive pier movement. These could lead to design difficulties with relative
displacements.
Lateral Loading of Piles—Most of the well-known solutions for computing the lateral stiffness of vertical piles
are based on the assumption of elastic behavior and utilize equivalent cantilever beam concepts (Davisson and Gill,
1960), the beam on an elastic Inkler foundation method (Matlock and Reese, 1960), or elastic continuum solutions
(Poulos, 1971). However, the use of methods incorporating nonlinear subgrade reaction behavior that allows for soil
failure may be important for high lateral loading of piles in soft clay and sand. Such a procedure is encompassed in the
American Petroleum Institute (API) recommendations for offshore platform design. The method utilizes nonlinear
subgrade reaction or P-y curves for sands and clays that have been developed experimentally from field loading tests.
The general features of the API analysis in the case of sands are illustrated in Figure A10.2-2. Under large loads,
a passive failure zone develops near the pile head. Test data indicate that the ultimate resistance, pu, for lateral loading
is reached for pile deflections, yu, of about 3d/80, where d is the pile diameter. Note that most of the lateral resistance
is mobilized over a depth of about 5d. The API method also recognizes degradation in lateral resistance with cylic
loading, although in the case of saturated sands, the degradation postulated does not reflect pore water pressure
increases. The degradation in lateral resistance due to earthquake-induced, free-field pore water pressure increases in
saturated sands has been described by Finn and Martin (1979). A numerical method that allows the use of API P-y
curves to compute pile stiffness characteristics forms the basis of the computer program BMCOL 76 described by
Bogard and Matlock (1977).
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Figure A10.2-2—Lateral Loading of Piles in Sand Using API Criteria
The influence of group action on pile stiffness is a somewhat controversial subject. Solutions based on elastic
theory can be misleading where yield near the pile head occurs. Experimental evidence tends to suggest that group
action is not significant for pile spacings greater than 4d to 6d.
For batter pile systems, the computation of lateral pile stiffness is complicated by the stiffness of the piles in axial
compression and tension. It is also important to recognize that bending deformations in batter pile groups may
generate high reaction forces on the pile cap.
It should be noted that although battered piles are economically attractive for resisting horizontal loads, such piles
are very rigid in the lateral direction if arranged so that only axial loads are induced. Hence, large relative lateral
displacements of the more flexible surrounding soil may occur during the free-field earthquake response of the site
(particularly if large changes in soil stiffness occur over the pile length), and these relative displacements may in turn
induce high pile bending moments. For this reason, more flexible vertical pipe systems where lateral load is resisted
by bending near the pile heads are recommended. However, such pile systems must be designed to be ductile because
large lateral displacements may be necessary to resist the lateral load. A compromise design using battered piles
spaced some distance apart may provide a system that has the benefits of limited flexibility and the economy of axial
load resistance to lateral load.
Soil-Pile Interaction—The use of pile stiffness characteristics to determine earthquake-induced pile bending
moments based on a pseudo-static approach assumes that moments are induced only by lateral loads arising from
inertial effects on the bridge structure. However, it must be remembered that the inertial loads are generated by
interaction of the free-field earthquake ground motion with the piles and that the free-field displacements themselves
can influence bending moments. This is illustrated in an idealized manner in Figure A10.2-3. The free-field
earthquake displacement time histories provide input into the lateral resistance interface elements, which in turn
transfer motion to the pile. Near the pile heads, bending moments will be dominated by the lateral interaction loads
generated by inertial effects on the bridge structure. At greater depth (e.g., greater than 10d), where soil stiffness
progressively increases with respect to pile stiffness, the pile will be constrained to deform in a manner similar to that
of the free field, and pile bending moments become a function of the curvatures induced by free-field displacements.
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Figure A10.2-3—Mechanism of Soil-Pile Interaction during Seismic Loading
To illustrate the nature of free-field displacements, reference is made to Figure A10.2-4, which represents a 200-ft
deep cohesionless soil profile subjected to the El Centro earthquake. The free-field response was determined using a
nonlinear, one-dimensional response analysis. From the displacement profiles shown at specific times, curvatures can
be computed and pile bending moments calculated if it is assumed that the pile is constrained to displace in phase with
the free-field response.
Figure A10.2-4—Typical Earthquake Displacement Profiles
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SECTION 10: FOUNDATIONS
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Large curvatures could develop at interfaces between soft and rigid soils and, clearly, in such cases emphasis
should be placed on using flexible ductile piles. Margason (1979) suggests that curvatures of up to 6 × 10 –4 in. –1 could
be induced by strong earthquakes, but these should pose no problem to well-designed steel or prestressed concrete
piles.
Studies incorporating the complete soil-pile structure interaction system, as presented in Figure A10.2-3, have
been described by Penzien (1970) for a bridge piling system in a deep soft clay. A similar but somewhat simpler soilpile structure interaction system (SPASM) to that used by Penzien has been described by Matlock et al. (1978). The
model used is, in effect, a dynamic version of the previously mentioned BMCOL program.
A10.3—SPECIAL PILE REQUIREMENTS
The uncertainties of ground and bridge response characteristics lead to the desirability of providing tolerant pile
and foundation systems. Toughness under induced curvature and shears is required, and hence piles such as steel Hsections and concrete filled steel-cased piles are favored for highly seismic areas. Unreinforced concrete piles are
brittle in nature, so nominal longitudinal reinforcing is specified to reduce this hazard. The reinforcing steel should be
extended into the footing to tie elements together and to assist in load transfer from the pile to the pile cap.
Experience has shown that reinforced concrete piles tend to hinge or shatter immediately below the pile cap.
Hence, tie spacing is reduced in this area so that the concrete is better confined. Driven precast piles should be
constructed with considerable spiral confining steel to ensure good shear strength and tolerance of yield curvatures
should these be imparted by the soil or structural response. Clearly, it is desirable to ensure that piles do not fail below
ground level and that flexural yielding in the columns is forced to occur above ground level. The additional pile
design requirements imposed on piles for bridges classified as Zones 3 and 4, for which earthquake loading is more
severe, reflect a design philosophy aimed at minimizing below-ground damage that is not easily inspected following a
major earthquake.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
TABLE OF CONTENTS
11
11.1—SCOPE ............................................................................................................................................................. 11-1
11.2—DEFINITIONS................................................................................................................................................. 11-1
11.3—NOTATION ..................................................................................................................................................... 11-2
11.3.1—General ................................................................................................................................................... 11-2
11.4—SOIL PROPERTIES AND MATERIALS ....................................................................................................... 11-5
11.4.1—General ................................................................................................................................................... 11-5
11.4.2—Determination of Soil Properties............................................................................................................ 11-5
11.5—LIMIT STATES AND RESISTANCE FACTORS ......................................................................................... 11-6
11.5.1—General ................................................................................................................................................... 11-6
11.5.2—Service Limit States ............................................................................................................................... 11-6
11.5.3—Strength Limit State ............................................................................................................................... 11-7
11.5.4—Extreme Event Limit State ..................................................................................................................... 11-7
11.5.4.1—General Requirements ................................................................................................................. 11-7
11.5.4.2—Extreme Event I, No Analysis ..................................................................................................... 11-8
11.5.5—Resistance Requirement ....................................................................................................................... 11-10
11.5.6—Load Combinations and Load Factors ................................................................................................. 11-10
11.5.7—Resistance Factors—Service and Strength........................................................................................... 11-13
11.5.8—Resistance Factors—Extreme Event Limit State ................................................................................. 11-16
11.6—ABUTMENTS AND CONVENTIONAL RETAINING WALLS ................................................................ 11-16
11.6.1—General Considerations ........................................................................................................................ 11-16
11.6.1.1—General....................................................................................................................................... 11-16
11.6.1.2—Loading ...................................................................................................................................... 11-17
11.6.1.3—Integral Abutments .................................................................................................................... 11-18
11.6.1.4 —Wingwalls ................................................................................................................................. 11-18
11.6.1.5—Reinforcement ........................................................................................................................... 11-18
11.6.1.5.1—Conventional Walls and Abutments ................................................................................ 11-18
11.6.1.5.2—Wingwalls ........................................................................................................................ 11-18
11.6.1.6 —Expansion and Contraction Joints............................................................................................. 11-18
11.6.2—Movement and Stability at the Service Limit State.............................................................................. 11-19
11.6.2.1—Abutments .................................................................................................................................. 11-19
11.6.2.2—Conventional Retaining Walls ................................................................................................... 11-19
11.6.2.3—Overall Stability ......................................................................................................................... 11-19
11.6.3—Bearing Resistance and Stability at the Strength Limit State ............................................................... 11-20
11.6.3.1—General....................................................................................................................................... 11-20
11.6.3.2—Bearing Resistance..................................................................................................................... 11-20
11.6.3.3—Eccentricity Limits..................................................................................................................... 11-22
11.6.3.4—Subsurface Erosion .................................................................................................................... 11-22
11.6.3.5—Passive Resistance ..................................................................................................................... 11-23
11.6.3.6—Sliding........................................................................................................................................ 11-23
11.6.4—Safety against Structural Failure .......................................................................................................... 11-23
11.6.5—Seismic Design for Abutments and Conventional Retaining Walls..................................................... 11-23
11.6.5.1—General....................................................................................................................................... 11-23
11.6.5.2—Calculation of Seismic Acceleration Coefficients for Wall Design ........................................... 11-26
11.6.5.2.1—Characterization of Acceleration at Wall Base ................................................................ 11-26
11.6.5.2.2—Estimation of Acceleration Acting on Wall Mass ........................................................... 11-26
11-i
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
11-ii
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.6.5.3—Calculation of Seismic Active Earth Pressures .......................................................................... 11-27
11.6.5.4—Calculation of Seismic Earth Pressure for Nonyielding Abutments and Walls ......................... 11-30
11.6.5.5—Calculation of Seismic Passive Earth Pressure .......................................................................... 11-31
11.6.5.6—Wall Details for Improved Seismic Performance.......................................................................11-32
11.6.6—Drainage ............................................................................................................................................... 11-33
11.7—PIERS ............................................................................................................................................................. 11-33
11.7.1—Load Effects in Piers ............................................................................................................................ 11-33
11.7.2—Pier Protection ...................................................................................................................................... 11-34
11.7.2.1—Collision ..................................................................................................................................... 11-34
11.7.2.2—Collision Walls........................................................................................................................... 11-34
11.7.2.3—Scour .......................................................................................................................................... 11-34
11.7.2.4—Facing......................................................................................................................................... 11-34
11.8—NONGRAVITY CANTILEVERED WALLS ............................................................................................... 11-34
11.8.1—General ................................................................................................................................................. 11-34
11.8.2—Loading ................................................................................................................................................ 11-34
11.8.3—Movement and Stability at the Service Limit State .............................................................................. 11-34
11.8.3.1—Movement .................................................................................................................................. 11-34
11.8.3.2—Overall Stability ......................................................................................................................... 11-35
11.8.4—Safety against Soil Failure at the Strength Limit State ......................................................................... 11-35
11.8.4.1—Overall Stability ......................................................................................................................... 11-35
11.8.5—Safety against Structural Failure .......................................................................................................... 11-36
11.8.5.1—Vertical Wall Elements .............................................................................................................. 11-36
11.8.5.2—Facing......................................................................................................................................... 11-36
11.8.6—Seismic Design of Nongravity Cantilever Walls.................................................................................. 11-38
11.8.6.1—General ....................................................................................................................................... 11-38
11.8.6.2—Seismic Active Lateral Earth Pressure ....................................................................................... 11-38
11.8.6.3—Seismic Passive Lateral Earth Pressure...................................................................................... 11-40
11.8.6.4—Wall Displacement Analyses to Determine Earth Pressures ...................................................... 11-41
11.8.7—Corrosion Protection ............................................................................................................................ 11-42
11.8.8—Drainage ............................................................................................................................................... 11-43
11.9—ANCHORED WALLS ................................................................................................................................... 11-43
11.9.1—General ................................................................................................................................................. 11-43
11.9.2—Loading ................................................................................................................................................ 11-44
11.9.3—Movement and Stability at the Service Limit State .............................................................................. 11-44
11.9.3.1—Movement .................................................................................................................................. 11-44
11.9.3.2—Overall Stability ......................................................................................................................... 11-45
11.9.4—Safety against Soil Failure.................................................................................................................... 11-45
11.9.4.1—Bearing Resistance ..................................................................................................................... 11-45
11.9.4.2—Anchor Pullout Capacity ............................................................................................................ 11-46
11.9.4.3—Passive Resistance ..................................................................................................................... 11-49
11.9.5—Safety against Structural Failure .......................................................................................................... 11-49
11.9.5.1—Anchors ...................................................................................................................................... 11-49
11.9.5.2—Vertical Wall Elements .............................................................................................................. 11-51
11.9.5.3—Facing......................................................................................................................................... 11-51
11.9.6—Seismic Design ..................................................................................................................................... 11-51
11.9.7—Corrosion Protection ............................................................................................................................ 11-52
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
TABLE OF CONTENTS
11-iii
11.9.8—Construction and Installation ............................................................................................................... 11-53
11.9.8.1—Anchor Stressing and Testing .................................................................................................... 11-53
11.9.9—Drainage............................................................................................................................................... 11-54
11.10—MECHANICALLY STABILIZED EARTH WALLS ................................................................................. 11-54
11.10.1—General ............................................................................................................................................... 11-54
11.10.2—Structure Dimensions ......................................................................................................................... 11-56
11.10.2.1—Minimum Length of Soil Reinforcement ................................................................................. 11-57
11.10.2.2—Minimum Front Face Embedment ........................................................................................... 11-58
11.10.2.3—Facing ...................................................................................................................................... 11-58
11.10.2.3.1—Stiff or Rigid Concrete, Steel, and Timber Facings ....................................................... 11-59
11.10.2.3.2—Flexible Wall Facings .................................................................................................... 11-59
11.10.2.3.3—Corrosion Issues for MSE Facing .................................................................................. 11-60
11.10.3—Loading .............................................................................................................................................. 11-60
11.10.4—Movement and Stability at the Service Limit State............................................................................ 11-60
11.10.4.1—Settlement ................................................................................................................................ 11-60
11.10.4.2—Lateral Displacement ............................................................................................................... 11-61
11.10.4.3—Overall Stability ....................................................................................................................... 11-61
11.10.5—Safety against Soil Failure (External Stability) .................................................................................. 11-62
11.10.5.1—General..................................................................................................................................... 11-62
11.10.5.2—Loading .................................................................................................................................... 11-63
11.10.5.3—Sliding ...................................................................................................................................... 11-64
11.10.5.4—Bearing Resistance................................................................................................................... 11-64
11.10.5.5—Overturning .............................................................................................................................. 11-64
11.10.6—Safety against Structural Failure (Internal Stability).......................................................................... 11-65
11.10.6.1—General..................................................................................................................................... 11-65
11.10.6.2—Loading .................................................................................................................................... 11-65
11.10.6.2.1—Maximum Reinforcement Loads ................................................................................... 11-66
11.10.6.2.2—Reinforcement Loads at Connection to Wall Face ........................................................ 11-70
11.10.6.3—Reinforcement Pullout ............................................................................................................. 11-70
11.10.6.3.1—Boundary between Active and Resistant Zones............................................................. 11-70
11.10.6.3.2—Reinforcement Pullout Design ....................................................................................... 11-72
11.10.6.4—Reinforcement Strength ........................................................................................................... 11-74
11.10.6.4.1—General .......................................................................................................................... 11-74
11.10.6.4.2—Design Life Considerations ........................................................................................... 11-76
11.10.6.4.2a—Steel Reinforcements ............................................................................................ 11-76
11.10.6.4.2b—Geosynthetic Reinforcements ............................................................................... 11-78
11.10.6.4.3—Design Tensile Resistance ............................................................................................. 11-80
11.10.6.4.3a—Steel Reinforcements ............................................................................................ 11-80
11.10.6.4.3b—Geosynthetic Reinforcements ............................................................................... 11-80
11.10.6.4.4—Reinforcement/Facing Connection Design Strength...................................................... 11-82
11.10.6.4.4a—Steel Reinforcements ............................................................................................ 11-82
11.10.6.4.4b—Geosynthetic Reinforcements ............................................................................... 11-82
11.10.7—Seismic Design of MSE Walls ........................................................................................................... 11-86
11.10.7.1—External Stability ..................................................................................................................... 11-86
11.10.7.2—Internal Stability ...................................................................................................................... 11-87
11.10.7.3—Facing Reinforcement Connections ......................................................................................... 11-91
11.10.7.4—Wall Details for Improved Seismic Performance .................................................................... 11-93
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
11-iv
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.10.8—Drainage ............................................................................................................................................. 11-94
11.10.9—Subsurface Erosion............................................................................................................................. 11-94
11.10.10—Special Loading Conditions ............................................................................................................. 11-95
11.10.10.1—Concentrated Dead Loads ...................................................................................................... 11-95
11.10.10.2—Traffic Loads and Barriers ..................................................................................................... 11-96
11.10.10.3—Hydrostatic Pressures ............................................................................................................. 11-98
11.10.10.4—Obstructions in the Reinforced Soil Zone .............................................................................. 11-98
11.10.11—MSE Abutments ............................................................................................................................... 11-99
11.11—PREFABRICATED MODULAR WALLS ................................................................................................ 11-101
11.11.1—General ............................................................................................................................................. 11-101
11.11.2—Loading ............................................................................................................................................ 11-102
11.11.3—Movement at the Service Limit State ............................................................................................... 11-102
11.11.4—Safety against Soil Failure................................................................................................................ 11-102
11.11.4.1—General ................................................................................................................................... 11-102
11.11.4.2—Sliding .................................................................................................................................... 11-102
11.11.4.3—Bearing Resistance ................................................................................................................. 11-102
11.11.4.4—Overturning ............................................................................................................................ 11-103
11.11.4.5 —Subsurface Erosion ............................................................................................................... 11-103
11.11.4.6—Overall Stability ..................................................................................................................... 11-103
11.11.4.7—Passive Resistance and Sliding .............................................................................................. 11-103
11.11.5—Safety against Structural Failure ...................................................................................................... 11-103
11.11.5.1—Module Members ................................................................................................................... 11-103
11.11.6—Seismic Design for Prefabricated Modular Walls ............................................................................ 11-104
11.11.7—Abutments ........................................................................................................................................ 11-105
11.11.8—Drainage ........................................................................................................................................... 11-105
11.12—REFERENCES ........................................................................................................................................... 11-105
APPENDIX A11—SEISMIC DESIGN OF RETAINING STRUCTURES ........................................................... 11-109
A11.1—GENERAL ................................................................................................................................................ 11-109
A11.2—PERFORMANCE OF WALLS IN PAST EARTHQUAKES................................................................... 11-109
A11.3—CALCULATION OF SEISMIC ACTIVE PRESSURE ............................................................................ 11-110
A11.3.1—Mononobe-Okabe Method .............................................................................................................. 11-110
A11.3.2—Modification of Mononabe-Okabe Method to Consider Cohesion ................................................. 11-112
A11.3.3—Generalized Limit Equilibrium (GLE) Method ............................................................................... 11-115
A11.4—SEISMIC PASSIVE PRESSURE ............................................................................................................. 11-115
A11.5—ESTIMATING WALL SEISMIC ACCELERATION CONSIDERING WAVE SCATTERING AND WALL
DISPLACEMENT .................................................................................................................................................. 11-120
A11.5.1—Kavazanjian et al., (1997) ................................................................................................................ 11-121
A11.5.2—NCHRP Report 611—Anderson et al. (2008) ................................................................................. 11-121
A11.5.3—Bray et al. (2010), and Bray and Travasarou (2009) ....................................................................... 11-124
A11.6—APPENDIX REFERENCES ..................................................................................................................... 11-124
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 11
WALLS, ABUTMENTS, AND PIERS
11.1—SCOPE
This Section provides requirements for design of
abutments and walls. Conventional retaining walls,
nongravity cantilevered walls, anchored walls,
mechanically stabilized earth (MSE) walls, and
prefabricated modular walls are considered.
11
11.2—DEFINITIONS
Abutment—A structure that supports the end of a bridge span, and provides lateral support for fill material on which
the roadway rests immediately adjacent to the bridge. In practice, different types of abutments may be used. These
include:
•
Stub Abutment—Stub abutments are located at or near the top of approach fills, with a backwall depth sufficient
to accommodate the structure depth and bearings which sit on the bearing seat.
•
Partial-Depth Abutment—Partial-depth abutments are located approximately at middepth of the front slope of the
approach embankment. The higher backwall and wingwalls may retain fill material, or the embankment slope
may continue behind the backwall. In the latter case, a structural approach slab or end span design must bridge
the space over the fill slope, and curtain walls are provided to close off the open area. Inspection access should be
provided for this situation.
•
Full-Depth Abutment—Full-depth abutments are located at the approximate front toe of the approach
embankment, restricting the opening under the structure.
•
Integral Abutment—Integral abutments are rigidly attached to the superstructure and are supported on a spread or
deep foundations capable of permitting necessary horizontal movements.
Anchored Wall—An earth retaining system typically composed of the same elements as nongravity cantilevered walls,
and that derive additional lateral resistance from one or more tiers of anchors.
Mechanically Stabilized Earth Wall—A soil-retaining system, employing either strip or grid-type, metallic, or
polymeric tensile reinforcements in the soil mass, and a facing element that is either vertical or nearly vertical.
Nongravity Cantilever Wall—A soil-retaining system that derives lateral resistance through embedment of vertical
wall elements and supports retained soil with facing elements. Vertical wall elements may consist of discrete
elements, e.g., piles, drilled shafts or auger-cast piles spanned by a structural facing, e.g., lagging, panels or shotcrete.
Alternatively, the vertical wall elements and facing may be continuous, e.g., sheet piles, diaphragm wall panels,
tangent-piles, or tangent drilled shafts.
Pier—That part of a bridge structure that provides intermediate support to the superstructure. Different types of piers
may be used. These include:
•
Solid Wall Piers—Solid wall piers are designed as columns for forces and moments acting about the weak axis
and as piers for those acting about the strong axis. They may be pinned, fixed or free at the top, and are
conventionally fixed at the base. Short, stubby types are often pinned at the base to eliminate the high moments
which would develop due to fixity. Earlier, more massive designs were considered gravity types.
•
Double Wall Piers—Double wall piers consist of two separate walls, spaced in the direction of traffic, to provide
support at the continuous soffit of concrete box superstructure sections. These walls are integral with the
superstructure and must also be designed for the superstructure moments which develop from live loads and
erection conditions.
11-1
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
11-2
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
•
Bent Piers—Bent-type piers consist of two or more transversely spaced columns of various solid cross-sections,
and these types are designed for frame action relative to forces acting about the strong axis of the pier. They are
usually fixed at the base of the pier and are either integral with the superstructure or with a pier cap at the top. The
columns may be supported on a spread- or pile-supported footing, or a solid wall shaft, or they may be extensions
of the piles or shaft above the ground line.
•
Single-Column Piers—Single-column piers, often referred to as “T” or “Hammerhead” piers, are usually
supported at the base by a spread-, drilled shaft- or pile-supported footing, and may be either integral with, or
provide independent support for, the superstructure. Their cross-section can be of various shapes and the column
can be prismatic or flared to form the pier cap or to blend with the sectional configuration of the superstructure
cross-section. This type of pier can avoid the complexities of skewed supports if integrally framed into the
superstructure and their appearance reduces the massiveness often associated with superstructures.
•
Tubular Piers—A hollow core section which may be of steel, reinforced concrete or prestressed concrete, of such
cross-section to support the forces and moments acting on the elements. Because of their vulnerability to lateral
loadings, tubular piers shall be of sufficient wall thickness to sustain the forces and moments for all loading
situations as are appropriate. Prismatic configurations may be sectionally precast or prestressed as erected.
Prefabricated Modular Wall—A soil-retaining system employing interlocking soil-filled timber, reinforced concrete,
or steel modules or bins to resist earth pressures by acting as gravity retaining walls.
Rigid Gravity and Semi-Gravity (Conventional) Retaining Wall—A structure that provides lateral support for a mass
of soil and that owes its stability primarily to its own weight and to the weight of any soil located directly above its
base.
In practice, different types of rigid gravity and semi-gravity retaining walls may be used. These include:
•
A gravity wall depends entirely on the weight of the stone or concrete masonry and of any soil resting on the
masonry for its stability. Only a nominal amount of steel is placed near the exposed faces to prevent surface
cracking due to temperature changes.
•
A semi-gravity wall is somewhat more slender than a gravity wall and requires reinforcement consisting of
vertical bars along the inner face and dowels continuing into the footing. It is provided with temperature steel
near the exposed face.
•
A cantilever wall consists of a concrete stem and a concrete base slab, both of which are relatively thin and fully
reinforced to resist the moments and shears to which they are subjected.
•
A counterfort wall consists of a thin concrete face slab, usually vertical, supported at intervals on the inner side
by vertical slabs or counterforts that meet the face slab at right angles. Both the face slab and the counterforts are
connected to a base slab, and the space above the base slab and between the counterforts is backfilled with soil.
All the slabs are fully reinforced.
11.3—NOTATION
11.3.1—General
Ac
AS
=
=
B
b
bf
C
CRcr
=
=
=
=
=
cross-sectional area of reinforcement unit (in.2) (11.10.6.4.1)
peak seismic ground acceleration coefficient modified by short-period site factor (11.6.5) (C11.8.6)
(11.10.7.1)
wall base width (ft) (11.10.2)
unit width of reinforcement; width of bin module (ft) (11.10.6.4.1) (11.11.5.1)
width of applied footing load (ft) (11.10.10.2)
overall reinforcement surface area geometry factor (dim.) (11.10.6.3.2)
long-term connection strength reduction factor to account for reduced ultimate strength resulting from
connection (dim.) (11.10.6.4.4b)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 11: WALLS, ABUTMENTS, AND PIERS
CRu
=
Cu
=
D
D*
Do
d
=
=
=
=
Ec
En
Es
=
=
=
e
Fp
FT
Fv
Fy
F*
Gu
=
=
=
=
=
=
=
H
Hh
Hu
H1
h
ha
=
=
=
=
=
hi
hp
i
ib
K
KAE
ka
kaf
kh
kh0
kv
kr
ky
L
=
=
=
=
=
=
=
=
=
=
=
=
=
=
La
Lb
Le
Lei
M
MARV
Mmax
N
=
=
=
=
=
=
=
=
n
PAE
Pa
Pb
PGA
PH
=
=
=
=
=
=
11-3
short-term connection strength reduction factor to account for reduced ultimate strength resulting from
the connection (dim.) (11.10.6.4.4b)
coefficient of uniformity defined as ratio of the particle size of soil that is 60 percent finer in size (D60) to
the particle size of soil that is ten percent finer in size (D10) (dim.) (11.10.6.3.2)
design embedment depth of vertical element (ft); diameter of bar or wire (in.) (11.10.6.3.2) (C11.8.4.1)
diameter of bar or wire corrected for corrosion loss (ft) (11.10.6.4.1)
embedment for which net passive pressure is sufficient to provide moment equilibrium (ft) (C11.8.4.1)
diameter of anchor drill hole (ft); the lateral wall displacement (in.); fill above wall (ft) (C11.6.5)
(11.9.4.2) (11.10.8)
thickness of metal reinforcement at end of service life (mil.) (11.10.6.4.1)
nominal thickness of steel reinforcement at construction (mil.) (11.10.6.4.2a)
sacrificial thickness of metal expected to be lost by uniform corrosion during service life (mil.)
(11.10.6.4.2a)
eccentricity of load from centerline of foundation (ft) (11.10.8)
static lateral force due to a concentrated surcharge load (kips/ft) (11.6.5.1)
resultant force of active lateral earth pressure (kips/ft) (11.6.3.2)
site class adjustment factor for the 1-sec. spectral acceleration (dim.) (A11.5)
minimum yield strength of steel (ksi) (11.10.6.4.3a)
reinforcement pullout friction factor (dim.) (11.10.6.3.2)
distance from center of gravity of a horizontal segmental facing block unit, including aggregate fill,
measured from the front of the unit (ft) (11.10.6.4.4b)
height of wall (ft) (11.6.5.1)
hinge height for segmental facing (ft) (11.10.6.4.4b)
segmental facing block unit height (ft) (11.10.6.4.4b)
equivalent wall height (ft) (11.10.6.3.1)
vertical distance between ground surface and wall base at the back of wall heel (ft) (11.6.3.2) (11.10.7.1)
distance between the base of the wall, or the mudline in front of the wall, and the resultant active seismic
earth pressure force (ft) (A11.3.1)
height of reinforced soil zone contributing horizontal load to reinforcement at level i (ft) (11.10.6.2.1)
vertical distance between the wall base and the static surcharge lateral force Fp (ft) (11.6.5.1)
backfill slope angle (degrees) (A11.3.1)
slope of facing base downward into backfill (degrees) (11.10.6.4.4b)
seismic passive pressure coefficient (dim.) (A11.3.1)
seismic active pressure coefficient (dim.) (A11.3.1)
active earth pressure coefficient (dim.) (11.8.4.1)
active earth pressure coefficient of backfill (dim.) (11.10.5.2)
horizontal seismic acceleration coefficient (dim.) (11.8.6)
horizontal seismic acceleration coefficient at zero displacement (dim.) (11.6.5.2)
vertical seismic acceleration coefficient (dim.) (11.6.5.3)
horizontal earth pressure coefficient of reinforced fill (dim.) (11.10.5.2)
yield acceleration in sliding block analysis that results in sliding of the wall (dim) (A11.5)
spacing between vertical elements or facing supports (ft); length of reinforcing elements in an MSE wall
and correspondingly its foundation (ft) (11.8.5.2) (11.10.2)
length of reinforcement in active zone (ft) (11.10.2)
anchor bond length (ft) (11.9.4.2)
length of reinforcement in resistance zone (ft) (11.10.2)
effective reinforcement length for layer i (ft) (11.10.7.2)
moment magnitude of design earthquake (dim.) (A11.5)
minimum average roll value (11.10.6.4.3b)
maximum bending moment in vertical wall element or facing (kip-ft or kip-ft/ft) (11.8.5.2)
normal component of resultant on base of foundation or standard penetration resistance from SPT
(kips/ft or blows/ft, respectively) (11.6.3.2) (A11.5)
total number of reinforcement layers in the wall (dim) (11.10.7.2)
dynamic active horizontal thrust, including static earth pressure (kips/ft) (11.10.7.1)
resultant active earth pressure force per unit width of wall (kips/ft) (11.8.6.2)
pressure inside bin module (ksf) (11.10.5.1)
peak ground acceleration (dim.) (11.6.5.1)
lateral force due to superstructure or other concentrated loads (kips/ft) (11.10.10.1)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
11-4
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Pi
=
PIR
Pir
Pis
PPE
Pr
Pseis
Pv
P′v
PVG
p
=
=
=
=
=
=
=
=
=
=
Qn
QR
qs
qmax
R
RBH
Rc
Rn
RR
RF
=
=
=
=
=
=
=
=
=
=
RFc
=
RFCR
RFD
=
=
RFID
Sh
St
Su
Sv
Srs
Srt
S1
Tac
Taℓ
Tcrc
=
=
=
=
=
=
=
=
=
=
=
Tlot
=
Tmd
Tultconn
Tult
Tmax
To
t
Ts
Ttotal
Vs
V1
V2
Ws
Wu
Ww
W1
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
factored horizontal force per mm of wall transferred to soil reinforcement at level i; internal inertial
force, due to the weight of the backfill within the active zone (kips/ft) (11.10.6.2.1) (11.10.7.2)
horizontal inertial force (kips/ft) (11.10.7.1)
horizontal inertial force caused by acceleration of reinforced backfill (kips/ft) (11.10.7.1)
internal inertial force caused by acceleration of sloping surcharge (kips/ft) (11.10.7.1)
dynamic passive horizontal thrust, including static earth pressure (kips/ft) (11.8.6.2)
ultimate soil reinforcement pullout resistance per unit of reinforcement width (kips/ft) (11.10.6.3.2)
total lateral force applied to a wall during seismic loading (kips/ft) (11.6.5.1)
load on strip footing (kips/ft) (11.10.10.1)
load on isolated rectangular footing or point load (kips) (11.10.10.1)
peak ground velocity (in./sec.) (A11.5)
average lateral pressure, including earth, surcharge and water pressure, acting on the section of wall
element being considered (ksf) (11.9.5.2)
nominal (ultimate) anchor resistance (kips) (11.9.4.2)
factored anchor resistance (kips) (11.9.4.2)
surcharge pressure (ksf) (11.10.5.2)
maximum unit soil pressure on base of foundation (ksf) (11.6.3.2)
resultant force at base of wall (kips/ft) (11.6.3.2)
basal heave ratio (C11.9.3.1)
reinforcement coverage ratio (dim.) (11.10.6.3.2)
nominal resistance (kips or kips/ft) (11.5.4)
factored resistance (kips or kips/ft) (11.5.4)
combined strength reduction factor to account for potential long-term degradation due to installation
damage, creep and chemical/biological aging of geosynthetic reinforcements (dim.) (11.10.6.4.2b)
combined strength reduction factor for long-term degradation of geosynthetic reinforcement facing
connection (dim.) (11.10.6.4.4b)
strength reduction factor to prevent long-term creep rupture of reinforcement (dim.) (11.10.6.4.3b)
strength reduction factor to prevent rupture of reinforcement due to chemical and biological degradation
(dim.) (11.10.6.4.3b)
strength reduction factor to account for installation damage to reinforcement (dim.) (11.10.6.4.3b)
horizontal reinforcement spacing (ft) (11.10.6.4.1)
spacing between transverse grid elements (in.) (11.10.6.3.2)
undrained shear strength (ksf) (11.9.5.2)
vertical spacing of reinforcements (ft) (11.10.6.2.1)
ultimate reinforcement tensile resistance required to resist static load component (kips/ft) (11.10.7.2)
ultimate reinforcement tensile resistance required to resist transient load component (kips/ft) (11.10.7.2)
1-sec. spectral acceleration coefficient (dim.) (A11.5)
nominal long-term reinforcement/facing connection design strength (kips/ft) (11.10.6.4.1)
nominal long-term reinforcement design strength (kips/ft) (11.10.6.4.1)
creep reduced connection strength per unit of reinforcement width determined from the stress rupture
envelope at the specified design life as produced from a series of long-term connection creep tests
(kips/ft) (11.10.6.4.4b)
ultimate wide width tensile strength per unit of reinforcement width (ASTM D4595 or D6637) for the
reinforcement material lot used for the connection strength testing (kips/ft) (11.10.6.4.4b)
factored incremental dynamic inertia force (kips/ft) (11.10.7.2)
ultimate connection strength per unit of reinforcement width (kips/ft) (11.10.6.4.4b)
ultimate tensile strength of reinforcement (kips/ft) (11.10.6.4.3b)
applied load to reinforcement (kips/ft) (11.10.6.2.1)
factored tensile load at reinforcement/facing connection (kips/ft) (11.10.6.2.2)
thickness of transverse elements (in.) (11.10.6.3.2)
fundamental period of wall (sec.) (A11.5)
total load on reinforcement layer (static & dynamic) per unit width of wall (kips/ft) (11.10.7.2)
shear wave velocity of soil behind wall (ft/sec.) (A11.5)
weight of soil carried by wall heel, not including weight of soil surcharge (kips/ft) (11.6.3.2)
weight of soil surcharge directly above wall heel (kips/ft) (11.6.3.2)
weight of the soil that is immediately above the wall, including the wall heel (kips/ft) (11.6.5.1)
unit width of segmental facing (ft) (11.10.2.3.2)
weight of the wall (kips/ft) (11.6.5.1)
weight of wall stem (kips/ft) (11.6.3.2)
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
W2
x
Z
Zp
=
=
=
=
α
=
β
γEQ
γP
γs
γ′s
γr
γf
ΔσH
=
=
=
=
=
=
=
=
Δσv
δ
δmax
δR
θ
θMO
ρ
φ
φf
φr
φ′f
σH
σHmax
σv
σV1
τn
ω
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
11-5
weight of wall footing or base (kips/ft) (11.6.3.2)
spacing between vertical element supports (ft) (11.9.5.2)
depth below effective top of wall or to reinforcement (ft) (11.10.6.2.1)
depth of soil at reinforcement layer at beginning of resistance zone for pullout calculation (ft)
(11.10.6.2.1)
scale effect correction factor, or wall height acceleration reduction factor for wave scattering (dim.)
(11.10.6.3.2) (A11.5)
inclination of ground slope behind face of wall (degrees) (11.5.5)
load factor for live load applied simultaneously with seismic loads in Article 3.4.1 (dim.) (11.6.5)
load factor for vertical earth pressure in Article 3.4.1 (dim.) (11.10.6.2.1)
soil unit weight (kcf)
effective soil unit weight (kcf) (C11.8.4.1)
unit weight of reinforced fill (kcf) (11.10.5.2)
unit weight of backfill (kcf) (11.10.5.2)
horizontal stress on reinforcement from concentrated horizontal surcharge (ksf); traffic barrier impact
stress applied over reinforcement tributary area (ksf) (11.10.6.2.1) (11.10.10.2)
vertical stress due to footing load (ksf) (11.10.8)
wall-backfill interface friction angle (degrees) (11.5.5)
maximum displacement (ft) (11.10.4.2)
relative displacement coefficient (11.10.4.2)
wall batter from horizontal (degrees) (11.10.6.2.1)
arc tan [kh/(1-kv)] for M-O analysis (degrees) (11.6.5.3)
soil-reinforcement angle of friction (degrees) (11.10.5.3)
resistance factor (11.5.4)
internal friction angle of foundation or backfill soil (degrees) (11.10.2)
internal friction angle of reinforced fill (degrees) (11.10.5.2)
effective internal friction angle of soil (degrees) (11.8.4.1)
factored horizontal stress at reinforcement level (ksf) (11.10.6.2.1)
maximum stress in soil reinforcement in abutment zones (11.10.8)
vertical stress in soil (ksf) (11.10.6.2.1)
vertical soil stress over effective base width (ksf) (11.10.8)
nominal anchor bond stress (ksf) (11.9.4.2)
wall batter due to setback of segmental facing units (degrees) (11.10.6.4.4b)
11.4—SOIL PROPERTIES AND MATERIALS
11.4.1—General
C11.4.1
Backfill materials should be granular, free-draining
materials. Where walls retain in-situ cohesive soils,
drainage shall be provided to reduce hydrostatic water
pressure behind the wall.
Much of the knowledge and experience with MSE
structures has been with select, cohesionless backfill as
specified in Section 7 of AASHTO LRFD Bridge
Construction Specifications. Hence, knowledge about
internal stress distribution, pullout resistance and failure
surface shape is constrained and influenced by the
unique engineering properties of granular soils. While
cohesive soils have been successfully used, problems
including excessive deformation and complete collapse
have also occurred. Most of these problems have been
attributed to poor drainage. Drainage requirements for
walls constructed with poor draining soils are provided
in Berg et al. (2009).
11.4.2—Determination of Soil Properties
The provisions of Articles 2.4 and 10.4 shall apply.
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11-6
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.5—LIMIT STATES AND RESISTANCE
FACTORS
11.5.1—General
C11.5.1
Design of abutments, piers and walls shall satisfy
the criteria for the service limit state specified in
Article 11.5.2, and for the strength limit state specified
in Article 11.5.3.
Abutments, piers and retaining walls shall be
designed to withstand lateral earth and water pressures,
including any live and dead load surcharge, the self
weight of the wall, temperature and shrinkage effects,
and earthquake loads in accordance with the general
principles specified in this Section.
Earth retaining structures shall be designed for a
service life based on consideration of the potential
long-term effects of material deterioration, seepage,
stray currents and other potentially deleterious
environmental factors on each of the material
components comprising the structure. For most
applications, permanent retaining walls should be
designed for a minimum service life of 75 years.
Retaining wall applications defined as temporary shall
be considered to have a service life of 36 months or less.
A greater level of safety and/or longer service life,
i.e., 100 years, may be appropriate for walls which
support bridge abutments, buildings, critical utilities, or
other facilities for which the consequences of poor
performance or failure would be severe.
Permanent structures shall be designed to retain an
aesthetically pleasing appearance, and be essentially
maintenance free throughout their design service life.
Design of walls to be essentially maintenance free
does not preclude the need for periodic inspection of the
wall to assess its condition throughout its design life.
11.5.2—Service Limit States
C11.5.2
Abutments, piers, and walls shall be investigated for
excessive vertical and lateral displacement, and overall
stability, at the service limit state. Tolerable vertical and
lateral deformation criteria for retaining walls shall be
developed based on the function and type of wall,
anticipated service life, and consequences of
unacceptable movements to the wall and any potentially
affected nearby structures, i.e., both structural and
aesthetic. Overall stability shall be evaluated using limit
equilibrium methods of analysis.
The provisions of Articles 10.6.2.2, 10.7.2.2, and
10.8.2.1 shall apply to the investigation of vertical wall
movements. For anchored walls, deflections shall be
estimated in accordance with the provisions of
Article 11.9.3.1. For MSE walls, deflections shall be
estimated in accordance with the provisions of
Article 11.10.4.
Vertical wall movements are primarily the result of
soil settlement beneath the wall. For gravity and
semigravity walls, lateral movement results from a
combination of differential vertical settlement between
the heel and the toe of the wall and the rotation
necessary to develop active earth pressure conditions
(see Article C3.11.1).
Tolerable
total
and
differential
vertical
deformations for a particular retaining wall are
dependent on the ability of the wall to deflect without
causing damage to the wall elements or adjacent
structures, or without exhibiting unsightly deformations.
Surveys of the performance of bridges indicate that
horizontal abutment movements less than 1.5 in. can
usually be tolerated by bridge superstructures without
significant damage, as reported in Bozozuk (1978);
Walkinshaw (1978); Moulton et al. (1985); and Wahls
(1990). Earth pressures used in design of abutments
should be selected consistent with the requirement that
the abutment should not move more than 1.5 in.
laterally.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-7
Regarding impact to the wall itself, differential
settlement along the length of the wall and to some
extent from front to back of wall is the best indicator of
the potential for retaining wall structural damage or
overstress. Wall facing stiffness and ability to adjust
incrementally to movement affect the ability of a given
wall system to tolerate differential movements. The total
and differential vertical deformation of a retaining wall
should be small for rigid gravity and semigravity
retaining walls, and for soldier pile walls with a cast-inplace facing. For walls with anchors, any downward
movement can cause significant stress relaxation of the
anchors.
MSE walls can tolerate larger total and differential
vertical deflections than rigid walls. The amount of total
and differential vertical deflection that can be tolerated
depends on the wall facing material, configuration and
timing of facing construction. A cast-in-place facing has
the same vertical deformation limitations as the more
rigid retaining wall systems. However, an MSE wall
with a cast-in-place facing can be specified with a
waiting period before the cast-in-place facing is
constructed so that vertical (as well as horizontal)
deformations have time to occur. An MSE wall with
welded wire or geosynthetic facing can tolerate the most
deformation. An MSE wall with multiple precast
concrete panels cannot tolerate as much vertical
deformation as flexible welded wire or geosynthetic
facings because of potential damage to the precast
panels and unsightly panel separation.
11.5.3—Strength Limit State
Abutments, walls, and piers shall be investigated at
the strength limit states using Eq. 1.3.2.1-1 for:
•
Bearing resistance failure,
•
Lateral sliding,
•
Loss of base contact due to eccentric loading,
•
Pullout failure of anchors or soil reinforcements,
and
•
Structural failure.
11.5.4—Extreme Event Limit State
11.5.4.1—General Requirements
Abutments, walls, and piers shall be investigated at
the extreme event limit state for:
•
Overall stability failure,
•
Bearing resistance failure,
•
Lateral sliding,
•
Loss of base contact due to eccentric loading,
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2012
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11-8
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
•
Pullout failure of anchors or soil reinforcements,
and
•
Structural failure.
The site-adjusted peak ground acceleration, As (i.e.,
Fpga × PGA, as specified in Article 3.10.3.2), used for
seismic design of retaining walls shall be determined in
accordance with Article 3.10.
11.5.4.2—Extreme Event I, No Analysis
A seismic design shall not be considered mandatory
for walls located in Seismic Zones 1 through 3, or for
walls at sites where the site adjusted peak ground
acceleration, As, is less than or equal to 0.4g, unless one
or more of the following is true:
•
Liquefaction induced lateral spreading or slope
failure, or seismically induced slope failure, due to
the presence of sensitive clays that lose strength
during the seismic shaking, may impact the stability
of the wall for the design earthquake.
•
The wall supports another structure that is required,
based on the applicable design code or specification
for the supported structure, to be designed for
seismic loading and poor seismic performance of
the wall could impact the seismic performance of
that structure.
The no-seismic-analysis option should be limited to
internal and external seismic stability design of the wall.
If the wall is part of a bigger slope, overall seismic
stability of the wall and slope combination should still
be evaluated.
These no-seismic-analysis provisions shall not be
considered applicable to walls functioning as support
piers for bridges.
The levels of peak ground acceleration at the
ground surface in some areas will be low enough that a
check on seismic loading is not required as other limit
states will control the design.
C11.5.4.2
Article 11.5.4.2, related to specific seismic zones,
may also be considered applicable to the corresponding
Seismic design categories (SDC) A, B, and C, if using
AASHTO’s Guide Specifications for LRFD Seismic
Bridge Design.
A summary of previous performance of walls in
earthquakes, as well as key research findings that provide
support to the provisions in Article 11.5.4.2, are provided
in Appendix A11. In general, wall performance in past
earthquakes has been very good, even in the largest, most
damaging earthquakes, and cases where either wall
collapse or severe wall displacements have occurred are
rare. For those cases where collapse or severe
displacement of walls did occur, those cases were mostly
limited to situations where significant liquefaction
occurred, where soil conditions behind or below the wall
were very poor (e.g., soft silts and clays, marginally stable
soils, water build up behind the wall) and ground
accelerations were high, or where the wall was subjected
to direct shear displacement of the fault. Furthermore,
most of those failures were limited to walls that were very
old. These wall failure situations are all well outside the
limits specified in Article 11.5.4.2 where these
specifications allow the designer to not conduct a detailed
wall seismic design. However, walls meeting the
requirements in Article 11.5.4.2 that allow a seismic
analysis to not be conducted have demonstrated
consistently good performance in past earthquakes.
Based on previous experience, walls that form
tunnel portals have tended to exhibit more damage due
to earthquakes than free standing walls. It is likely that
the presence of the tunnel restricts the ability of the
portal wall to move, increasing the seismic forces to
which the wall is subjected. Therefore, a more detailed
seismic analysis of tunnel portal walls should be
considered even if the walls meet all the other no
seismic analysis conditions specified in Article 11.5.4.2.
For walls that cross an active fault which could
result in significant differential movement within the
wall, a detailed seismic analysis should be considered
even if the wall is located in Seismic Zones 1, 2, or 3.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-9
Examples of other structures include bridges (e.g.,
the abutment foundation), buildings, pipelines or major
utilities, pipe arches, or dams. If the wall supports
another wall, a seismic design is not required for the
lower wall, provided that the upper and lower wall can
be designed as a single tiered structure and the
limitations on the tiered structure for these provisions in
Article 11.5.4.2, if in Seismic Zone 3 or lower, are met.
If the wall has abrupt changes in its alignment
geometry (e.g., corners and short radius turns at an
enclosed angle of 120 degrees or less), a seismic
analysis of the wall should be considered for Seismic
Zone 2 or higher. Based on past experience in
earthquakes, wall corners tend to attract greater loads
than free standing walls with generally straight
alignments and have therefore suffered greater damage.
The seismic details discussed in Articles 11.6.5.6 and
11.10.7.4 and their commentary will help to reduce the
potential problems at corners that have occurred in past
earthquakes. Note that the corner or abrupt alignment
change enclosed angle as defined in Article 11.5.4.2 can
either be internal or external to the wall.
A seismic analysis should be considered for Seismic
Zone 2 or higher if either of the following is greater than
30 ft:
•
The exposed wall height plus the average depth
over the width of the wall of any soil surcharge
present, or
•
For tiered walls the sum of the exposed height of all
the tiers plus the average soil surcharge depth, is
greater than 30 ft.
A seismic analysis should be considered if in
Seismic Zone 2 or higher, and if, for gravity and
semigravity walls, the wall backfill does not meet the
requirements of Article 7.3.6.3 of the AASHTO LRFD
Bridge Construction Specifications, due to the
possibility that the backfill will not be adequately
drained to prevent water build-up in the backfill.
For Seismic Zone 2 or higher, if a seismic design is not
conducted, it is still important to use good seismic details as
specified in Articles 11.6.5.6 and Article 11.10.7.4.
If the wall is part of a bigger slope that potentially
could fail during seismic loading, the overall seismic
stability of the wall and slope as defined in Article
11.6.2.3 should be evaluated, as specified in Articles
11.5.4.1 and 11.5.8. If the wall is determined to have
only a minor destabilizing effect on the overall stability
of the slope during seismic loading, for example, a wall
placed within a large slope or existing landslide that is
marginally stable during static loading, it may not be
practical to design the wall to be stable for overall
stability for the Extreme Event I limit state. Addressing
the landslide overall stability during seismic loading
should be considered a separate effort not specifically
addressed by these Specifications.
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11-10
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.5.5—Resistance Requirement
C11.5.5
Abutments, piers and retaining structures and their
foundations and other supporting elements shall be
proportioned by the appropriate methods specified in
Articles 11.6, 11.7, 11.8, 11.9, 11.10, or 11.11 so that
their resistance satisfies Article 11.5.6.
The factored resistance, RR, calculated for each
applicable limit state shall be the nominal resistance, Rn,
multiplied by an appropriate resistance factor, φ,
specified in Table 11.5.7-1.
Procedures for calculating nominal resistance are
provided in Articles 11.6, 11.7, 11.8, 11.9, 11.10, and
11.11 for abutments and retaining walls, piers,
nongravity cantilevered walls, anchored walls,
mechanically stabilized earth walls, and prefabricated
modular walls, respectively.
11.5.6—Load Combinations and Load Factors
C11.5.6
Abutments, piers and retaining structures and their
foundations and other supporting elements shall be
proportioned for all applicable load combinations
specified in Article 3.4.1.
Figures C11.5.6-1 and C11.5.6-2 show the typical
application of load factors to produce the total extreme
factored force effect for external stability of retaining walls
for the strength limit state. Where live load surcharge is
applicable, the factored surcharge force is generally
included over the backfill immediately above the wall only
for evaluation of foundation bearing resistance and
structure design, as shown in Figure C11.5.6-3. The live
load surcharge is not included over the backfill for
evaluation of eccentricity, sliding or other failure
mechanisms for which such surcharge would represent
added resistance to failure. Likewise, the live load on a
bridge abutment is included only for evaluation of
foundation bearing resistance and structure design. The
load factor for live load surcharge is the same for both
vertical and horizontal load effects. Figure C11.5.6-3 is
also applicable to seismic loading (i.e., Extreme Event I),
except that the load factor for live load surcharge is γEQ
instead of LL.
Figure C11.5.6-4 shows the typical application of
load factors to produce the total extreme factored force
effect for external stability of retaining walls for the
Extreme Event I limit state.
The permanent and transient loads and forces
shown in the figures include, but are not limited to:
•
Permanent Loads
= dead load of structural components
and nonstructural attachments
DW = dead load of wearing surfaces and
utilities
EH = horizontal earth pressure load
ES = earth surcharge load
EV = vertical pressure from dead load of
earth fill
DC
•
Transient Loads
LS = live load surcharge
WA = water load and stream pressure
The subscripts V and H in Figure C11.5.6-4 denote
vertical and horizontal components, respectively, of
each force.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-11
For the Extreme Event I limit state, the peak seismic
lateral pressures acting on the wall should not be based
on the maximum ground water elevation due to the low
probability that the design peak seismic acceleration
would be combined with the maximum ground water
level. Instead, it is more appropriate to use the timeaveraged mean groundwater elevation or a reasonable
engineering estimate of this elevation.
Figure C11.5.6-1—Typical Application of Load Factors for
Bearing Resistance
Figure C11.5.6-2—Typical Application of Load Factors for
Sliding and Eccentricity
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11-12
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure C11.5.6-3—Typical Application of Live Load Surcharge
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-13
Figure C11.5.6-4—Typical Application of Load Factors for Bearing and
Sliding Resistance and for Eccentricity in the Extreme Event I Limit State
For seismic loading effects on lateral earth pressure,
the seismic load factor shall be applied to the entire
lateral earth pressure load created by the earth mass
retained by the wall or abutment. For any surcharge
loads acting on the wall (e.g., ES) in combination with
seismic load, EQ, the load factor for seismic loads, shall
be applied.
Seismic loading of an earth mass retained by a wall
is calculated using an extension of Coulomb theory or
by limit equilibrium slope stability methods. The
seismic loading causes the active soil wedge to increase,
resulting in increased total load. The static loading
cannot be separated from the seismic loading in this
analysis, other than by artificial means through
subtracting the static earth pressure from the total earth
pressure calculated for seismic loading. Past allowable
stress design practice has been to apply a single reduced
safety factor to the entire lateral earth load combination.
Therefore, one seismic load factor (typically a load
factor of 1.0) is applied to the total earth pressure that
occurs during seismic loading.
Regarding other loads acting in combination with
the seismic loading and earth pressure, the load
combination philosophy described for earth pressure
also applies to be consistent with past allowable stress
design practice for a no collapse design objective.
11.5.7—Resistance Factors—Service and Strength
C11.5.7
Resistance factors for the service limit states shall
be taken as 1.0, except as provided for overall stability
in Article 11.6.2.3.
For the strength limit state, the resistance factors
provided in Table 11.5.7-1 shall be used for wall design,
unless region specific values or substantial successful
experience is available to justify higher values.
The resistance factors given in Table 11.5.7-1, other
than those referenced back to Section 10, were
calculated by direct correlation to allowable stress
design rather than reliability theory.
Since the resistance factors in Table 11.5.7-1 were
based on direct correlation to allowable stress design,
the differences between the resistance factors for tensile
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2012
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11-14
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Resistance factors for geotechnical design of
foundations that may be needed for wall support, unless
specifically identified in Table 11.5.7-1, are as specified
in Tables 10.5.5.2.2-1, 10.5.5.2.3-1, and 10.5.5.2.4-1.
If methods other than those prescribed in these
Specifications are used to estimate resistance, the
resistance factors chosen shall provide the same
reliability as those given in Tables 10.5.5.2.2-1,
10.5.5.2.3-1, 10.5.5.2.4-1, and Table 11.5.7-1.
Vertical elements, such as soldier piles, tangentpiles and slurry trench concrete walls shall be treated as
either shallow or deep foundations, as appropriate, for
purposes of estimating bearing resistance, using
procedures described in Articles 10.6, 10.7, and 10.8.
Some increase in the prescribed resistance factors
may be appropriate for design of temporary walls
consistent with increased allowable stresses for
temporary structures in allowable stress design.
resistance of metallic versus geosynthetic reinforcement
are based on historical differences in the level of safety
applied to reinforcement designs for these two types of
reinforcements. See Article C11.10.6.2.1 for additional
comments regarding the differences between the
resistance factors for metallic versus geosynthetic
reinforcement.
Region-specific resistance factor values should be
determined based on substantial statistical data
combined with calibration or substantial successful
experience to justify higher values. Smaller resistance
factors should be used if site or material variability is
anticipated to be unusually high or if design assumptions
are required that increase design uncertainty that has not
been mitigated through conservative selection of design
parameters. See Allen et al. (2005) for additional
guidance on calibration of resistance factors.
The evaluation of overall stability of walls or earth
slopes with or without a foundation unit should be
investigated at the service limit state based on the
Service I Load Combination and an appropriate
resistance factor.
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2012
Edition
SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-15
Table 11.5.7-1—Resistance Factors for Permanent Retaining Walls
Wall-Type and Condition
Nongravity Cantilevered and Anchored Walls
Axial compressive resistance of vertical elements
Passive resistance of vertical elements
Pullout resistance of anchors (1)
• Cohesionless (granular) soils
• Cohesive soils
• Rock
(2)
Pullout resistance of anchors
• Where proof tests are conducted
Tensile resistance of anchor
• Mild steel (e.g., ASTM A615 bars)
tendon
• High strength steel (e.g., ASTM A722
bars)
Flexural capacity of vertical elements
Mechanically Stabilized Earth Walls, Gravity Walls, and Semigravity Walls
Bearing resistance
• Gravity and semigravity walls
• MSE walls
Sliding
Tensile resistance of metallic
Strip reinforcements (4)
reinforcement and connectors
• Static loading
Grid reinforcements (4) (5)
• Static loading
Tensile resistance of geosynthetic • Static loading
reinforcement and connectors
Pullout resistance of tensile
• Static loading
reinforcement
Resistance Factor
Article 10.5 applies
0.75
0.65 (1)
0.70 (1)
0.50 (1)
1.0 (2)
0.90 (3)
0.80 (3)
0.90
0.55
0.65
1.0
0.75
0.65
0.90
0.90
Prefabricated Modular Walls
Bearing
Sliding
Passive resistance
Article 10.5 applies
Article 10.5 applies
Article 10.5 applies
(1)
Apply to presumptive ultimate unit bond stresses for preliminary design only in Article C11.9.4.2.
(2)
Apply where proof test(s) are conducted on every production anchor to a load of 1.0 or greater times the factored load on the
anchor.
(3)
Apply to maximum proof test load for the anchor. For mild steel apply resistance factor to Fy. For high-strength steel apply the
resistance factor to guaranteed ultimate tensile strength.
(4)
Apply to gross cross-section less sacrificial area. For sections with holes, reduce gross area in accordance with Article 6.8.3
and apply to net section less sacrificial area.
(5)
Applies to grid reinforcements connected to a rigid facing element, e.g., a concrete panel or block. For grid reinforcements
connected to a flexible facing mat or which are continuous with the facing mat, use the resistance factor for strip
reinforcements.
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2012
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11-16
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.5.8—Resistance Factors—Extreme Event Limit
State
C11.5.8
Unless otherwise specified, all resistance factors
shall be taken as 1.0 when investigating the extreme
event limit state.
For overall stability of the retaining wall when
earthquake loading is included, a resistance factor, φ, of
0.9 shall be used. For bearing resistance, a resistance
factor of 0.8 shall be used for gravity and semigravity
walls and 0.9 for MSE walls.
For tensile resistance of metallic reinforcement and
connectors, when earthquake loading is included, the
following resistance factors shall be used:
A resistance factor of 1.0 is recommended for the
extreme event limit state in view of the unlikely
occurrence of the loading associated with the design
earthquake. The choice of 1.0 is influenced by the
following factors:
•
Strip reinforcements, φ = 1.0
•
Grid reinforcement, φ = 0.85
Table 11.5.7-1 Notes 4 and 5 also apply to these
resistance factors for metallic reinforcements.
For tensile resistance of geosynthetic reinforcement
and connectors, a resistance factor, φ, of 1.20 shall be
used.
For pullout resistance of metallic and geosynthetic
reinforcement, a resistance factor, φ, of 1.20 shall be
used.
•
For competent soils that are not expected to lose
strength during seismic loading (e.g., due to
liquefaction of saturated cohesionless soils or
strength reduction of sensitive clays), the use of
static strengths for seismic loading is usually
conservative, as rate-of-loading effects tend to
increase soil strength for transient loading.
•
Earthquake loads are transient in nature and hence,
if soil yield occurs, the net effect is an accumulated
small deformation as opposed to foundation failure.
This assumes that global stability is adequate.
Using a resistance factor of 1.0 for soil assumes
ductile behavior. While this is a correct assumption for
many soils, it is inappropriate for brittle soils where
there is a significant post-peak strength loss (e.g., stiff
over-consolidated clays, sensitive soils). For such
conditions, special studies will be required to determine
the appropriate combination of resistance factor and soil
strength.
For bearing resistance, a slightly lower resistance
factor of 0.8 is recommended for gravity and
semigravity walls and 0.9 for MSE walls to reduce the
possibility that a bearing resistance failure could occur
before the wall moves laterally in sliding, reducing the
likelihood of excessive wall tilting or collapse,
consistent with the design objective of no collapse.
11.6—ABUTMENTS AND CONVENTIONAL
RETAINING WALLS
11.6.1—General Considerations
C11.6.1.1
11.6.1.1—General
Rigid gravity and semigravity retaining walls may
be used for bridge substructures or grade separation and
are generally for permanent applications.
Rigid gravity and semigravity walls shall not be
used without deep foundation support where the bearing
soil/rock is prone to excessive total or differential
settlement.
Conventional retaining walls are generally
classified as rigid gravity or semigravity walls, examples
of which are shown in Figure C11.6.1.1-1. These types
of walls can be effective for both cut and fill wall
applications.
Excessive differential settlement, as defined in
Article C11.6.2.2 can cause cracking, excessive bending
or shear stresses in the wall, or rotation of the wall
structure.
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2012
Edition
SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-17
Figure C11.6.1.1-1—Typical Rigid Gravity and Semigravity
Walls
11.6.1.2—Loading
for:
C11.6.1.2
Abutments and retaining walls shall be investigated
•
Lateral earth and water pressures, including any live
and dead load surcharge;
•
The self weight of the abutment/wall;
•
Loads applied from the bridge superstructure;
•
Temperature and shrinkage deformation effects; and
•
Earthquake loads, as specified herein, in Section 3
and elsewhere in these Specifications.
The provisions of Articles 3.11.5 and 11.5.5 shall
apply. For stability computations, the earth loads shall
be multiplied by the maximum and/or minimum load
factors given in Table 3.4.1-2, as appropriate.
The design shall be investigated for any
combination of forces which may produce the most
severe condition of loading. The design of abutments on
mechanically stabilized earth and prefabricated modular
walls shall be in accordance with Articles 11.10.11 and
11.11.6.
For computing load effects in abutments, the weight
of filling material directly over an inclined or stepped
rear face, or over the base of a reinforced concrete
spread footing may be considered as part of the effective
weight of the abutment.
Where spread footings are used, the rear projection
shall be designed as a cantilever supported at the
abutment stem and loaded with the full weight of the
superimposed material, unless a more exact method
is used.
Cohesive backfills are difficult to compact. Because
of the creep of cohesive soils, walls with cohesive
backfills designed for active earth pressures will
continue to move gradually throughout their lives,
especially when the backfill is soaked by rain or rising
groundwater levels. Therefore, even if wall movements
are tolerable, walls backfilled with cohesive soils should
be designed with extreme caution for pressures between
the active and at-rest cases assuming the most
unfavorable conditions. Consideration must be given for
the development of pore water pressure within the soil
mass in accordance with Article 3.11.3. Appropriate
drainage provisions should be provided to prevent
hydrostatic and seepage forces from developing behind
the wall. In no case shall highly plastic clay be used
for backfill.
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2012
Edition
11-18
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.6.1.3—Integral Abutments
2013 Revision
Integral abutments shall be designed to resist and/or
absorb creep, shrinkage and thermal deformations of the
superstructure.
Movement calculations shall consider temperature,
creep, and long-term prestress shortening in determining
potential movements of abutments.
Maximum span lengths, design considerations,
details should comply with recommendations outlined in
FHWA Technical Advisory T 5140.13 (1980), except
where substantial local experience indicates otherwise.
To avoid water intrusion behind the abutment, the
approach slab should be connected directly to the
abutment (not to wingwalls), and appropriate provisions
should be made to provide for drainage of any entrapped
water.
C11.6.1.3
Deformations are discussed in Article 3.12.
Integral abutments should not be constructed on
spread footings founded or keyed into rock unless one
end of the span is free to displace longitudinally.
11.6.1.4 —Wingwalls
Wingwalls may either be designed as monolithic
with the abutments, or be separated from the abutment
wall with an expansion joint and designed to be free
standing.
The wingwall lengths shall be computed using the
required roadway slopes. Wingwalls shall be of
sufficient length to retain the roadway embankment and
to furnish protection against erosion.
11.6.1.5—Reinforcement
11.6.1.5.1—Conventional Walls and Abutments
Reinforcement to resist the formation of
temperature and shrinkage cracks shall be designed as
specified in Article 5.10.8.
11.6.1.5.2—Wingwalls
Reinforcing bars or suitable rolled sections shall be
spaced across the junction between wingwalls and
abutments to tie them together. Such bars shall extend
into the masonry on each side of the joint far enough to
develop the strength of the bar as specified for bar
reinforcement, and shall vary in length so as to avoid
planes of weakness in the concrete at their ends. If bars
are not used, an expansion joint shall be provided and
the wingwall shall be keyed into the body of the
abutment.
11.6.1.6 —Expansion and Contraction Joints
Contraction joints shall be provided at intervals not
exceeding 30.0 ft and expansion joints at intervals not
exceeding 90.0 ft for conventional retaining walls and
abutments. All joints shall be filled with approved filling
material to ensure the function of the joint. Joints in
abutments shall be located approximately midway between
the longitudinal members bearing on the abutments.
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2012
Edition
SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-19
11.6.2—Movement and Stability at the Service Limit
State
11.6.2.1—Abutments
The provisions of Articles 10.6.2.4, 10.6.2.5,
10.7.2.3 through 10.7.2.5, 10.8.2.2 through 10.8.2.4, and
11.5.2 shall apply as applicable.
11.6.2.2—Conventional Retaining Walls
The provisions of Articles 10.6.2.4, 10.6.2.5,
10.7.2.3 through 10.7.2.5, 10.8.2.2 through 10.8.2.4, and
11.5.2 apply as applicable.
11.6.2.3—Overall Stability
The overall stability of the retaining wall, retained
slope and foundation soil or rock shall be evaluated for
all walls using limiting equilibrium methods of analysis.
The overall stability of temporary cut slopes to facilitate
construction shall also be evaluated. Special exploration,
testing and analyses may be required for bridge
abutments or retaining walls constructed over soft
deposits.
The evaluation of overall stability of earth slopes
with or without a foundation unit should be investigated
at the Service I Load Combination and an appropriate
resistance factor. In lieu of better information, the
resistance factor, φ, may be taken as:
•
Where the geotechnical parameters are well
defined, and the slope does not support or contain a
structural element............................................... 0.75
•
Where the geotechnical parameters are based on
limited information, or the slope contains or
supports a structural element ............................. 0.65
C11.6.2.2
For a conventional reinforced concrete retaining
wall, experience suggests that differential wall
settlements on the order of 1 in 500 to 1 in 1,000 may
overstress the wall.
C11.6.2.3
Figure C11.6.2.3-1—Retaining Wall Overall Stability
Failure
Figure C11.6.2.3-1 shows a retaining wall overall
stability failure. Overall stability is a slope stability
issue, and, therefore, is considered a service limit state
check.
The Modified Bishop, simplified Janbu or Spencer
methods of analysis may be used.
Soft soil deposits may be subject to consolidation
and/or lateral flow which could result in unacceptable
long-term settlements or horizontal movements.
With regard to selection of a resistance factor for
evaluation of overall stability of walls, examples of
structural elements supported by a wall that may justify
the use of the 0.65 resistance factor include a bridge or
pipe arch foundation, a building foundation, a pipeline, a
critical utility, or another retaining wall. If the structural
element is located beyond the failure surface for external
stability behind the wall illustrated conceptually in
Figure 11.10.2-1, a resistance factor of 0.75 may be used.
Available slope stability programs produce a single
factor of safety, FS. The specified resistance factors are
essentially the inverse of the FS that should be targeted
in the slope stability program.
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2012
Edition
11-20
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.6.3—Bearing Resistance and Stability at the
Strength Limit State
11.6.3.1—General
Abutments and retaining walls shall be proportioned
to ensure stability against bearing capacity failure,
overturning, and sliding. Safety against deep-seated
foundation failure shall also be investigated, in
accordance with the provisions of Article 10.6.2.5.
11.6.3.2—Bearing Resistance
C11.6.3.2
Bearing resistance shall be investigated at the
strength limit state using factored loads and resistances,
assuming the following soil pressure distributions:
•
Where the wall is supported by a soil foundation:
the vertical stress shall be calculated assuming a
uniformly distributed pressure over an effective
base area as shown in Figure 11.6.3.2-1.
See Figure 11.10.10.1-1 for an example of how to
calculate the vertical bearing stress where the loading is
more complex. Though this figure shows the application
of superposition principles to mechanically stabilized
earth walls, these principles can also be directly applied
to conventional walls.
See Article C11.5.5 for application of load factors
for bearing resistance and eccentricity.
The vertical stress shall be calculated as follows:
σv =
V
B − 2e
(11.6.3.2-1)
where:
ΣV =
•
the summation of vertical forces, and
the other variables are as defined in
Figure 11.6.3.2-1
Where the wall is supported by a rock foundation:
the vertical stress shall be calculated assuming a
linearly distributed pressure over an effective base
area as shown in Figure 11.6.3.2-2. If the resultant
is within the middle one-third of the base:
σvmax =
V
B
e
1 + 6 B
(11.6.3.2-2)
σvmin =
V
B
e
1 − 6 B
(11.6.3.2-3)
where the variables are as defined in
Figure 11.6.3.2-2. If the resultant is outside the
middle one-third of the base:
σvmax =
2 V
3[( B / 2) − e)]
(11.6.3.2-4)
(11.6.3.2-5)
σvmin = 0
where the variables
Figure 11.6.3.2-2.
are
as
defined
in
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2012
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-21
Figure 11.6.3.2-1—Bearing Stress Criteria for Conventional Wall Foundations on Soil
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11-22
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure 11.6.3.2-2—Bearing Stress Criteria for Conventional Wall Foundations on Rock
11.6.3.3—Eccentricity Limits
C11.6.3.3
For foundations on soil, the location of the resultant
of the reaction forces shall be within the middle twothirds of the base width.
For foundations on rock, the location of the
resultant of the reaction forces shall be within the middle
nine-tenths of the base width.
The specified criteria for the location of the
resultant, coupled with investigation of the bearing
pressure, replace the investigation of the ratio of
stabilizing moment to overturning moment. Location of
the resultant within the middle two-thirds of the base
width for foundations on soil is based on the use of
plastic bearing pressure distribution for the limit state.
11.6.3.4—Subsurface Erosion
C11.6.3.4
For walls constructed along rivers and streams,
scour of foundation materials shall be evaluated during
design, as specified in Article 2.6.4.4.2. Where potential
problem conditions are anticipated, adequate protective
measures shall be incorporated in the design.
The provisions of Article 10.6.1.2 shall apply.
The hydraulic gradient shall not exceed:
•
For silts and cohesive soils:
0.20
•
For other cohesionless soils:
0.30
Where water seeps beneath a wall, the effects of
uplift and seepage forces shall be considered.
The measures most commonly used to ensure that
piping does not occur are:
•
Seepage control,
•
Reduction of hydraulic gradient, and
•
Protective filters.
Seepage effects may be investigated by constructing
a flow net, or in certain circumstances, by using
generally accepted simplified methods.
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2012
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11.6.3.5—Passive Resistance
Passive resistance shall be neglected in stability
computations, unless the base of the wall extends below
the depth of maximum scour, freeze-thaw or other
disturbances. In the latter case, only the embedment
below the greater of these depths shall be considered
effective.
Where passive resistance is utilized to ensure
adequate wall stability, the calculated passive resistance
of soil in front of abutments and conventional walls
shall be sufficient to prevent unacceptable forward
movement of the wall.
The passive resistance shall be neglected if the soil
providing passive resistance is, or is likely to become
soft, loose, or disturbed, or if the contact between the
soil and wall is not tight.
11-23
C11.6.3.5
Unacceptable deformations may occur before
passive resistance is mobilized. Approximate
deformations required to mobilize passive resistance are
discussed in Article C3.11.1, where H in
Table C3.11.1-1 is the effective depth of passive
restraint.
11.6.3.6—Sliding
The provisions of Article 10.6.3.4 shall apply.
11.6.4—Safety against Structural Failure
The structural design of individual wall elements
and wall foundations shall comply with the provisions of
Sections 5, 6, 7, and 8.
The provisions of Article 10.6.1.3 shall be used to
determine the distribution of contact pressure for
structural design of footings.
11.6.5—Seismic Design for Abutments and
Conventional Retaining Walls
11.6.5.1—General
C11.6.5.1
Rigid gravity and semigravity retaining walls and
abutments shall be designed to meet overall stability,
external stability, and internal stability requirements
during seismic loading. The procedures specified in
Article 11.6.2.3 for overall stability, Article 11.6.3 for
bearing stability, and Article 10.6.3.4 for sliding
stability shall be used but including seismically induced
earth pressure and inertial forces and using Extreme
Event I limit state load and resistance factors as
specified in Article 11.5.8.
For seismic eccentricity evaluation of walls with
foundations on soil and rock, the location of the
resultant of the reaction forces shall be within the middle
two-thirds of the base for γEQ = 0.0 and within the
middle eight-tenths of the base for γEQ = 1.0. For values
of γEQ between 0.0 and 1.0, the resultant location
restriction shall be obtained by linear interpolation of the
values given in this Article.
The estimation of seismic design forces should
account for wall inertia forces in addition to the
equivalent static-forces. For semigravity walls in which
the footing protrudes behind the back of the wall face
(i.e., the heel), the weight of the soil located directly
above the heel of the footing should be included in the
calculated wall inertial force.
Where a wall supports a bridge structure, the
seismic design forces should also include seismic forces
transferred from the bridge through bearing supports
which do not freely slide, e.g., elastomeric bearings in
accordance with Article 14.6.3.
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2012
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11-24
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
For bridge abutments, the abutment seismic design
should be conducted in accordance with Articles 5.2 and
6.7 of AASHTO’s Guide Specifications for LRFD
Seismic Bridge Design but with the following
exceptions:
•
kh should be determined
Article 11.6.5.2 and
as
specified
in
•
Lateral earth pressures should be estimated in
accordance with Article 11.6.5.3.
To evaluate safety against structural failure (i.e.,
internal stability) for seismic design, the structural
design of the wall elements shall comply with the
provisions of Sections 5, 6, 7, and 8.
The total lateral force to be applied to the wall due
to seismic and earth pressure loading, Pseis, should be
determined considering the combined effect of PAE and
PIR, in which:
PIR = kh(Ww + Ws)
(11.6.5.1-1)
and where:
PAE =
PIR =
kh =
Ww =
Ws =
dynamic lateral earth pressure force
horizontal inertial force due to seismic loading
of the wall mass
seismic horizontal acceleration coefficient
the weight of the wall
the weight of soil that is immediately above the
wall, including the wall heel
To investigate the wall stability considering the
combined effect of PAE and PIR and considering them not
to be concurrent, the following two cases should be
investigated:
•
Combine 100 percent of the seismic earth pressure
PAE with 50 percent of the wall inertial force PIR and
•
Combine 50 percent of PAE but no less than the
static active earth pressure force (i.e., F1 in
Figure 11.10.5.2-1), with 100 percent of the wall
inertial force PIR.
The most conservative result from these two
analyses should be used for design of the wall.
Alternatively, if approved by the Owner, more
sophisticated numerical methods may be used to
investigate nonconcurrence. For competent soils that do
not lose strength under seismic loading, static strength
parameters should be used for seismic design.
•
For cohesive soils, total stress strength parameters
based on undrained tests should be used during the
seismic analysis.
•
For clean cohesionless soils, the effective stress
friction angle should be used.
The static lateral earth pressure force acting behind
the wall is already included in PAE (i.e., PAE is the
combination of the static and seismic lateral earth
pressure). See Articles 3.11.6.3 and 11.10.10.1 for
definition of terms in Figure 11.6.5.1-1 not specifically
defined in this Article.
Since PAE is the combined lateral earth pressure force
resulting from static earth pressure plus dynamic effects,
the static earth pressure as calculated based on the lateral
earth pressure coefficient Ka should not be added to the
seismic earth pressure calculated in Article 11.6.5.3. The
static lateral earth pressure coefficient, Ka, is, in effect,
increased during seismic loading to KAE (see
Article 11.6.5.3) due to seismically induced inertial forces
on the active wedge, and the potential increase in the
volume of the active wedge itself due to flattening of the
active failure surface. PAE does not include any additional
lateral forces caused by permanent surcharge loads located
above the wall (e.g., the static force Fp, and the dynamic
force khWsurcharge in Figure 11.6.5.1-1, in which Wsurcharge is
the weight of the surcharge). If the generalized limit
equilibrium method (GLE) is used to calculate seismic
lateral earth pressure on the wall, the effect of the surcharge
on the total lateral force acting on the wall during seismic
loading may, however, be taken directly into account when
determining PAE. Note that the inertial force due to the
weight of the concentrated surcharge load, khWsurcharge, and
the static force Fp are separate and both act during seismic
loading. They must therefore both be included in the
seismic wall stability analysis. Fp is calculated as specified
in Article 3.11.6.
For evaluating external stability of the wall and for
evaluating safety against structural failure of the wall
(internal stability), the simplest design approach that
will ensure a safe result is to combine the total seismic
earth pressure force with the inertial response of the wall
section, assuming both are in phase. This approach is
conservative in that the peak inertial response of the wall
mass is not likely to occur at the same time as the peak
seismic active pressure. Previous design practice, at least
for MSE walls, has been to combine the full wall inertial
force with only 50 percent of the dynamic increment of
the total earth pressure (i.e., PAE – PA) to account for this
lack of concurrence in the design forces.
Research using centrifuge testing of reduced scale
walls by Al Atik and Sitar (2010) indicated that these two
seismic forces are out of phase, in that when dynamic
earth pressure was at its maximum, the wall inertial force
was at its minimum and was very close to zero. When the
wall inertial force was at its maximum, the total seismic
earth pressure (i.e., PAE) was close to its static value. They
also indicated, however, that more coincidence between
these two forces may still be possible for some wall
configurations and ground motions. Nakamura (2006)
made similar observations regarding lack of concurrence
of these forces based on dynamic centrifuge testing he
conducted. This research indicates that treating the two
forces as nonconcurrent is justified in most cases.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
SECTION 11: WALLS, ABUTMENTS, AND PIERS
•
11-25
For sensitive cohesive soils or saturated
cohesionless soils, the potential for earthquakeinduced strength loss shall be addressed in the
analysis.
See Al Atik and Sitar (2010) and Nakamura (2006)
for examples of the application of numerical methods to
investigate this issue of nonconcurrent forces.
The inertial force associated with the soil mass on
the wall heel behind the retaining wall is not added to
the active seismic earth pressure when structurally
designing the retaining wall. The basis for excluding this
inertial force is that movement of this soil mass is
assumed to be in phase with the structural wall system
with the inertial load transferred through the heel of the
wall. Based on typical wave lengths associated with
seismic loading, this is considered a reasonable
assumption. However, the inertial force for the soil mass
over the wall heel is included when determining the
external stability of the wall.
Additional discussion and guidance on the selection
of soil parameters for seismic design of walls and the
potential consideration of soil cohesion are provided by
Anderson et al. (2008).
Figure 11.6.5.1-1—Seismic Force Diagram for Gravity Wall External Stability Evaluation
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2012
Edition
11-26
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.6.5.2—Calculation of Seismic Acceleration
Coefficients for Wall Design
11.6.5.2.1—Characterization of Acceleration at
Wall Base
The seismic horizontal acceleration coefficient (kh)
for computation of seismic lateral earth pressures and
loads shall be determined on the basis of the PGA at the
ground surface (i.e., kh0 = Fpga PGA = As, where kh0 is the
seismic horizontal acceleration coefficient assuming
zero wall displacement occurs). The acceleration
coefficient determined at the original ground surface
should be considered to be the acceleration coefficient
acting at the wall base. For walls founded on Site Class
A or B soil (hard or soft rock), kh0 shall be based on 1.2
times the site-adjusted peak ground acceleration
coefficient (i.e., kh0 = 1.2FpgaPGA).
The seismic vertical acceleration coefficient, kv,
should be assumed to be zero for the purpose of
calculating lateral earth pressures, unless the wall is
significantly affected by near fault effects (see
Article 3.10), or if relatively high vertical accelerations
are likely to be acting concurrently with the horizontal
acceleration.
11.6.5.2.2—Estimation of Acceleration Acting on
Wall Mass
The seismic lateral wall acceleration coefficient, kh,
shall be determined considering the effects of wave
scattering or ground motion amplification within the
wall and the ability of the wall to displace laterally. For
wall heights less than 60.0 ft, simplified pseudostatic
analyses may be considered acceptable for use in
determining the design wall mass acceleration. For wall
heights greater than 60.0 ft, special dynamic soil
structure interaction design analyses should be
performed to assess the effect of spatially varying
ground motions within and behind the wall and lateral
deformations on the wall mass acceleration.
The height of wall, h, shall be taken as the distance
from the bottom of the heel of the retaining structure to
the ground surface directly above the heel.
If the wall is free to move laterally under the
influence of seismic loading and if lateral wall
movement during the design seismic event is acceptable
to the Owner, kh0 should be reduced to account for the
allowed lateral wall deformation. The selection of a
maximum acceptable lateral deformation should take
into consideration the effect that deformation will have
on the stability of the wall under consideration, the
desired seismic performance level, and the effect that
deformation could have on any facilities or structures
supported by the wall. Where the wall is capable of
displacements of 1.0 to 2.0 in. or more during the design
seismic event, kh may be reduced to 0.5kh0 without
conducting a deformation analysis using the Newmark
C11.6.5.2.1
As is determined as specified in Article 3.10.
In most situations, vertical and horizontal
acceleration are at least partially out of phase. Therefore,
kv is usually rather small when kh is near its maximum
value. The typical assumption is to assume that kv is zero
for wall design.
C11.6.5.2.2
The designer may use kh for wall design without
accounting for wave scattering and lateral deformation
effects; however, various studies have shown that the
ground motions in the mass of soil behind the wall will
often be lower than kh0 at the ground surface,
particularly for taller walls. However, in some cases, it
is possible to have amplification of the ground motion in
the wall relative to the wall base ground motion.
The desired performance of walls during a design
seismic event can range from allowing limited damage
to the wall or displacement of the wall to requiring
damage-free, post-earthquake conditions. In many cases,
a well-designed gravity or semigravity wall could slide
several inches and perhaps even a foot or more, as well
as tilt several degrees, without affecting the function of
the wall or causing collapse, based on past performance
of walls in earthquakes. However, the effect of such
deformation on the facilities or structures located above,
behind, or in front of the wall must also be considered
when establishing an allowable displacement.
Recent work completed as part of NCHRP
Report 611 (Anderson et al., 2008) concluded that, when
using the Newmark method, the amount of permanent
ground displacement associated with kh = 0.5kh0 will in
most cases be less than 1.0 to 2.0 in. (i.e., use of
kh = 0.5kh0 provides conservative results).
Details of specific simplified procedures that may
be used to estimate wave scattering effects and lateral
wall deformations to determine kh are provided in
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
method (Newmark, 1965) or a simplified version of it.
This reduction in kh shall also be considered applicable
to the investigation of overall stability of the wall and
slope.
A Newmark sliding block analysis or a simplified
form of that type of analysis should be used to estimate
lateral deformation effects, unless the Owner approves
the use of more sophisticated numerical analysis
methods to establish the relationship between kh and the
wall displacement. Simplified Newmark analyses should
only be used if the assumptions used to develop them
are valid for the wall under consideration.
11.6.5.3—Calculation of Seismic Active Earth
Pressures
Seismic active and passive earth pressures for
gravity and semigravity retaining walls shall be
determined following the methods described in this
Article. Site conditions, soil and retaining wall
geometry, and the earthquake ground motion determined
for the site shall be considered when selecting the most
appropriate method to use.
The seismic coefficient (kh) used to calculate seismic
earth pressures shall be the site-adjusted peak ground
surface acceleration identified in Article 11.6.5.2.1 (i.e.,
As) after adjustments for 1) spectral or wave scattering
effects and 2) limited amounts of permanent deformation
as determined appropriate for the wall and anything the
wall movement could affect (Article 11.6.5.2.2). The
vertical acceleration coefficient (kv) should be assumed to
be zero for design as specified in Article 11.6.5.2.1.
For seismic active earth pressures, either the
Mononobe-Okabe (M-O) Method or the Generalized
Limit Equilibrium (GLE) Method should be used. For
wall geometry or site conditions for which the M-O
Method is not suitable, the GLE Method should be used.
The M-O Method shall be considered acceptable for
determination of seismic active earth pressures only where:
•
The material behind the wall can be reasonably
approximated as a uniform, cohesionless soil within
a zone defined by a 3H:1V wedge from the heel of
the wall,
•
The backfill is not saturated and in a loose enough
condition such that it can liquefy during shaking,
and
11-27
Appendix A11. Those simplified procedures include
Kavazanjian et al. (2003), Anderson et al. (2008), and
Bray et al. (2009, 2010). Additional background needed
to conduct a full Newmark sliding block analysis is also
provided in Appendix A11.
Alternate Methods of Estimating Permanent
Displacement
The simplified, Newmark Method-based equations
given above present a relatively quick method
of estimating the yield acceleration for a given
maximum acceptable displacement or, alternatively, the
displacements that will occur if the capacity to demand
(C/D) ratio for a limiting equilibrium stability analysis is
less than 1.0. Alternatively, two-dimensional numerical
methods that allow seismic time history analyses may be
used to estimate permanent displacements. Such models
require considerable expertise in the set-up and
interpretation of model results, particularly relative to the
selection of strength parameters consistent with seismic
loading. For this reason, use of this alternate approach
should be adopted only with the Owner’s concurrence.
C11.6.5.3
The suitability of the method used to determine
active and passive earth seismic pressures should be
determined after a review of features making up the
static design, such as backfill soils and slope above the
retaining wall. These conditions, along with the ground
motion for a site, will affect the method selection.
The complete M-O equation is provided in
Appendix A11. The M-O equation for seismic active
earth pressure is based on the Coulomb earth pressure
theory and is therefore limited to design of walls that
have homogeneous, dry cohesionless backfill. The M-O
equation has been shown to be most applicable when the
backfill is homogenous and can be characterized as
cohesionless.
Another important limitation of the M-O equation is
that there are combinations of acceleration and slope
angle in which real solutions to the equation are no
longer possible or that result in values that rapidly
approach infinity. The contents of the radical in this
equation must be positive for a real solution to be
possible. In past practice, when the combination of
acceleration and slope angle results in a negative
number within the radical in the equation, rather than
allowing that quantity to become negative, it was
artificially set at zero. While this practice made it
possible to get a value of KAE, it also tended to produce
excessively conservative results. Therefore, in such
cases it is better to use an alternative method.
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2012
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11-28
•
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The combination of peak ground acceleration and
backslope angle do not exceed the friction angle of
the soil behind the wall, as specified in Eq. 11.6.5.3-1.
k
φ ≥ i + θMO = i + arctan h
1 − kv
(11.6.5.3-1)
where:
φ
i
kh
kv
=
=
=
=
the wall backfill friction angle
backfill slope angle (degrees)
the horizontal acceleration coefficient
the vertical acceleration coefficient
Once KAE is determined, the seismic active force,
PAE, shall be determined as:
PAE = 0.5 γ h2 KAE
(11.6.5.3-2)
where:
KAE =
γ =
h =
seismic active earth pressure coefficient (dim)
the soil unit weight behind the wall (kips/ft3)
the total wall height, including any soil
surcharge present, at the back of the wall
The external active force computed from the
generalized limit equilibrium method, distributed over
the wall height h, shall be used as the seismic earth
pressure.
The equivalent pressure representing the total static
and seismic active force (PAE) as calculated by either
method should be distributed using the same distribution
as the static earth pressure used to design the wall when
used for external stability evaluations, as illustrated in
Figure 11.6.5.1-1, but no less than H/3. For the case
when a sloping soil surcharge is present behind the wall
face (h in Figure 11.6.5.1-1), this force shall be
distributed over the total height, h.
For complex wall systems or complex site
conditions, with the owner’s approval, dynamic
numerical soil structure interaction (SSI) methods
should also be considered.
For many situations, gravity and semigravity walls
are constructed by cutting into an existing slope where
the soil properties differ from the backfill that is used
behind the retaining wall. In situations where soil
conditions are not homogeneous and the failure surface
is flatter than the native slope, seismic active earth
pressures computed for the M-O equation using the
backfill properties may no longer be valid, particularly if
there is a significant difference in properties between the
native and backfill soils.
However, the M-O Method has been used in past
design practice for estimating seismic earth pressures for
many of these situations due to lack of an available
alternative. Various approaches to force the method to
be usable for such situations have been used, such as
estimating some type of average soil property for
layered soil conditions or limiting the acceleration to
prevent the radical in the equation from being negative,
among others. With the exception of seismic passive
pressure estimation, this practice has typically resulted
in excessively conservative designs and it is not
recommended to continue this practice.
The GLE Method consists of conducting a seismic
slope stability analysis in which kh is used as the
acceleration coefficient, typically using a computer
program in which the applied force necessary to
maintain equilibrium (i.e., a capacity/demand ratio of
1.0) under seismic loading is determined. This force is
PAE. Specific procedures used to conduct this method are
provided in Appendix A11. The GLE Method should be
used when the M-O Method is not suitable due to the
wall geometry, seismic acceleration level, or site
conditions.
The Coulomb Wedge Equilibrium Method, also
referred to as the trial wedge method, as described in
Peck et al. (1974) and Caltrans (2010), may also be used
for situations when the M-O method is not suitable but a
hand calculation method is desired, provided that the
soil conditions are not too complex (e.g., layered soil
conditions behind the wall). Other than the potential
ability to use the trial wedge method as a hand
calculation method, it has no real advantages over the
GLE method.
Recent studies have indicated that classic limit
equilibrium based methods such as the M-O, GLE, and
the Coulomb Wedge Equilibrium methods may be
overly conservative even if the limitations listed above
are considered. See Bray et al. (2010) and Lew et al.
(2010a, 2010b) with regard to the generation of seismic
earth pressures behind walls and the applicability of the
Mononobe-Okabe or similar method.
For cases in which the wall seismic design result
appears to be excessively conservative relative to past
experience in earthquakes, other than taking advantage
of the no seismic analysis provisions in Article 11.5.4.2,
there are no simple solutions; numerical dynamic soil
structure interaction (SSI) modeling may need to be
considered. See Bray et al. (2010) for an example.
Dynamic numerical SSI solutions may also be needed
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2012
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-29
for more complex wall systems and for walls in which
the seismic loading is severe. Due to the complexities of
such analyses, an independent peer review of the
analysis and results is recommended.
Past practice for locating the resultant of the static
and seismic earth pressure for external wall stability has
been to either assume a uniform distribution of lateral
earth pressure for the combined static plus seismic stress
or, if the static and seismic components of earth pressure
are treated separately, using an inverted trapezoid for the
seismic component, with the seismic force located at
0.6h above the wall base, and combining that force with
the normal static earth pressure distribution (Seed and
Whitman, 1970). More recent research indicates the
location of the resultant of the total earth pressure (static
plus seismic) should be located at h/3 above the wall
base (Clough and Fragaszy, 1977; Al Atik and Sitar,
2010; Bray et al., 2010; and Lew et al., 2010a and b).
See Appendix A11 for additional discussion on this
issue. As a minimum, the combined resultant of the
active and seismic earth pressure (i.e., PAE) should be
located no lower, relative to the wall base, than the static
earth pressure resultant. However, a slightly higher
combined static/seismic resultant location (e.g., 0.4h to
0.5h) may be considered, since there is limited evidence
the resultant could be higher, especially for walls in
which the impact of failure is relatively high.
Most natural cohesionless soils have some fines
content that contributes cohesion, particularly for shortterm loading conditions. Similarly, cohesionless
backfills are rarely fully saturated and partial saturation
provides for some apparent cohesion, even for most
clean sands. The effects of cohesion, whether actual or
apparent, are an important issue to be considered in
practical design problems.
The M-O equation has been extended to c-φ soils by
Prakash and Saran (1966), where solutions were
obtained for cases including the effect of tension cracks
and wall adhesion. Similar solutions have also been
discussed by Richards and Shi (1994) and Chen and Liu
(1990).
Results of analyses by Anderson et al. (2008) show
a significant reduction in the seismic active pressure for
small values of cohesion. From a design perspective,
this means that even a small amount of cohesion in the
soil could reduce the demand required for retaining wall
design.
From a design perspective, the uncertainties in the
amount of cohesion or apparent cohesion make it
difficult to explicitly incorporate the contributions of
cohesion in many situations, particularly in cases where
clean backfill materials are being used, regardless of the
potential benefits of apparent cohesion that could occur
if the soil is partially saturated. Realizing these
uncertainties, the following guidelines are suggested.
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
•
Where cohesive soils are being used for backfill or
where native soils have a clear cohesive strength
component, the designer should give consideration
to incorporating some effects of cohesion in the
determination of the seismic coefficient.
•
If the cohesion in the soil behind the wall results
primarily from capillarity stresses, especially in
relatively low fines content soils, it is recommended
that cohesion be neglected when estimating seismic
earth pressure.
The groundwater within the active wedge or
submerged conditions (e.g., as in the case of a retaining
structure in a harbor or next to a lake or river) can
influence the magnitude of the seismic active earth
pressure. The time-averaged mean groundwater
elevation should be used when assessing groundwater
effects.
If the soil within the wedge is fully saturated, then
the total unit weight (γt) should be used to estimate the
earth pressure when using the M-O Method, under the
assumption that the soil and water move as a unit during
seismic loading. This situation will apply for soils that
are not free draining.
If the backfill material is a very open granular
material, such as quarry spalls, it is possible that the
water will not move with the soil during seismic
loading. In this case, the effective unit weight should be
used in the pressure determination and an additional
force component due to hydrodynamic effects should be
added to the wall pressure. Various methods are
available to estimate the hydrodynamic pressure (see
Kramer, 1996). Generally, these methods involve a form
of the Westergaard solution.
11.6.5.4—Calculation of Seismic Earth Pressure
for Nonyielding Abutments and Walls
For abutment walls and other walls that are
considered nonyielding, the value of kh used to calculate
seismic earth pressure shall be increased to 1.0kh0,
unless the Owner approves the use of more sophisticated
numerical analysis techniques to determine the
seismically induced earth pressure acting on the wall,
considering the ability of the wall to yield in response to
lateral loading. In this case, kh should not be corrected
for wall displacement, since displacement is assumed to
be zero. However, kh should be corrected for wave
scattering effects as specified in Article 11.6.5.2.2.
C11.6.5.4
The lateral earth pressure calculation methodologies
provided in Article 11.6.5.3 assume that the abutment or
wall is free to laterally yield a sufficient amount to
mobilize peak soil strengths in the backfill. Examples of
walls that may be nonyielding are integral abutments,
abutment walls with structural wing walls, tunnel portal
walls, and tied back cylinder pile walls. For granular
soils, peak soil strengths can be assumed to be mobilized
if deflections at the wall top are about 0.5 percent of the
abutment or wall height. For walls restrained from
movement by structures, batter piles, or anchors, lateral
forces induced by backfill inertial forces could be
greater than those calculated by M-O or GLE methods
of analysis. Simplified elastic solutions presented by
Wood (1973) for rigid nonyielding walls also indicate
that pressures are greater than those given by M-O and
GLE analysis. These solutions also indicate that a higher
resultant location for the combined effect of static and
seismic earth pressure of h/2 may be warranted for
nonyielding abutments and walls and should be
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-31
considered for design. The use of a factor of 1.0 applied
to kh0 is recommended for design where doubt exists that
an abutment or wall can yield sufficiently to mobilize
backfill soil strengths. In general, if the lack of ability of
the wall to yield requires that the wall be designed for K0
conditions for the strength limit state, then a kh of 1.0kh0
should be used for seismic design.
Alternatively, numerical methods may be used to
better quantify the yielding or nonyielding nature of the
wall and its effect on the seismic earth pressures that
develop, if approved by the Owner.
11.6.5.5—Calculation of Seismic Passive Earth
Pressure
For estimating seismic passive earth pressures, wall
friction and the deformation required to mobilize the
passive resistance shall be considered and a log spiral
design methodology shall be used. The M-O Method
shall not be used for estimating passive seismic earth
pressure.
Seismic passive earth pressures shall be estimated
using procedures that account for the friction between
the retaining wall and the soil, the nonlinear failure
surface that develops in the soil during passive pressure
loading, and for wall embedment greater than or equal to
5.0 ft, the inertial forces in the passive pressure zone in
front of the wall from the earthquake. For wall
embedment depths less than 5.0 ft, passive pressure
should be calculated using the static methods provided
in Section 3.
In the absence of any specific guidance or research
results for seismic loading, a wall interface friction equal
to two-thirds of the soil friction angle should be used
when calculating seismic passive pressures.
C11.6.5.5
The seismic passive earth pressure becomes
important for walls that develop resistance to sliding
from the embedded portion of the wall. For these
designs, it is important to estimate passive pressures that
are not overly conservative or unconservative for the
seismic loading condition. This is particularly the case if
displacement-based design methods are used but it can
also affect the efficiency of designs based on limitequilibrium methods.
If the depth of embedment of the retaining wall is
less than 5.0 ft, the passive pressure can be estimated
using static methods given in Section 3 of these
Specifications. For this depth of embedment, the inertial
effects from earthquake loading on the development of
passive pressures will be small.
For greater depths of embedment, the inertial effects
of ground shaking on the development of passive
pressures should be considered. This passive zone
typically extends three to five times the embedment
depth beyond the face of the embedded wall.
Shamsabadi et al. (2007) have developed a
methodology for estimating the seismic passive
pressures while accounting for wall friction and the
nonlinear failure surface within the soil. Appendix A11
of this Section provides charts based on this
development for a wall friction of two-thirds of the soil
friction angle (φ) and a range of seismic coefficients, φ
values, and soil cohesion (c).
The seismic coefficient used in the passive seismic
earth pressure calculation is the same value as used for
the seismic active earth pressure calculation. Wave
scattering reductions are also appropriate to account for
incoherency of ground motions in the soil if the depth of
the passive zone exceeds 20.0 ft. For most wall designs
the difference between the seismic coefficient behind the
wall relative to seismic coefficient of the soil in front of
the wall is too small to warrant use of different values.
The M-O equation for seismic passive earth
pressure is not recommended for use in determining the
seismic passive pressure, despite its apparent simplicity.
For passive earth pressure determination, the M-O
equation is based on the Coulomb method of
determining passive earth pressure; this method can
overestimate the earth pressure in some cases.
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
A key consideration during the determination of
static and seismic passive pressures is the wall friction.
Common practice is to assume that some wall friction
will occur for static loading. The amount of interface
friction for static loading is often assumed to range from
50 percent to 80 percent of the soil friction angle.
Similar guidance is not available for seismic loading.
Another important consideration when using the
seismic passive earth pressure is the amount of
deformation required to mobilize this force. The
deformation to mobilize the passive earth pressure
during static loading is usually assumed to be large—
typically 2 percent to 6 percent of the embedded wall
height. Similar guidance is not available for seismic
loading and therefore the normal approach during design
for seismic passive earth pressures is to assume that the
displacement to mobilize the seismic passive earth
pressure is the same as for static loading.
11.6.5.6—Wall Details for Improved Seismic
Performance
Details that should be addressed for gravity and
semigravity walls in seismically active areas, defined as
Seismic Zone 2 or higher, or a peak ground acceleration
As greater than 0.15g, include the following:
•
Vertical Slip Joints, Expansion Joints, and Vertical
Joints between an Abutment Curtain Wall and the
Free-Standing Wall: Design to prevent joint from
opening up and allowing wall backfill to flow
through the open joint without sacrificing the joint’s
ability to slip to allow differential vertical
movement. This also applies to joints at wall
corners. Compressible joint fillers, bearing pads,
and sealants should be used to minimize damage to
facing units due to shaking. The joint should also be
designed in a way that allows a minimum amount of
relative movement between the adjacent facing
units to prevent stress build-up between facing units
during shaking (Extreme Event I), as well as due to
differential deformation between adjacent wall
sections at the joint for the service and strength
limit states.
•
Coping at Wall Top: Should be used to prevent
toppling of top facing units and excessive
differential lateral movement of the facing.
•
Wall Corners and Abrupt Facing Alignment
Changes: Should be designed for the potential for
higher loads to develop during shaking than would
be determined using two-dimensional analysis. Wall
corners and short radius turns are defined as having
an enclosed angle of 120 degrees or less.
•
Wall Backfill Stability: Backfill should be well
graded and angular enough to interlock/bind
together well to minimize risk of fill spilling
C11.6.5.6
These recommended details are based on previous
experiences with walls in earthquakes (e.g., Yen et al.,
2011). Walls that did not utilize these details tended to
have a higher frequency of problems than walls that did
utilize these details.
With regard to preventing joints from opening up
during shaking, this can be addressed through use of a
backup panel placed behind the joint, a slip joint cover
placed in front of the joint, or the placement of the
geotextile strip behind the facing panels to bridge across
the joint. The special units should allow differential
vertical movement between facing units to occur while
maintaining the functionality of the joint. The amount of
overlap between these joint elements and the adjacent
facing units is determined based on the amount of
relative movement between facing units that is
anticipated in much the same way that the bridge seat
width is determined for bridges.
Little guidance on the amount of overlap between
the backing panel and the facing panels is available for
walls but past practice has been to provide a minimum
overlap of 2.0 to 4.0 in. A geotextile strip may also be
placed between the backfill soil and the joint or joint and
backing panel combination. Typical practice has been to
use a minimum overlap of the geotextile beyond the
edges of the joint of 6.0 to 9.0 in. and the geotextile is
usually attached to the back of the panel using adhesive.
Typically, a Class 1 or Class 2 high elongation
(>50 percent strain at peak strength) drainage geotextile
in accordance with AASHTO M 288 is used. Similarly,
this technique may be applied to the joint between the
facing units and protrusions through the wall facing.
For wall corners, not cast monolithically, a special
facing unit formed to go across the corner, providing
overlap with adjacent panels, should be used. Regarding
the design of wall corners and abrupt changes in the
facing alignment, both static and seismic earth pressure
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2012
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
through open wall joints.
•
Wall Backfill Silt and Clay Content: Wall backfills
classified as a silt or clay should in general not be
used in seismically active areas.
•
Structures and Foundations within the Wall Active
Zone: The effect of these structures and foundations
on the wall seismic loading shall be evaluated and
the wall designed to take the additional load.
•
Protrusions through the Wall Face: The additional
seismic force transmitted to the wall, especially the
facing, through the protruding structure (e.g., a
culvert or drainage pipe) shall be evaluated. The
effect of differential deformation between the
protrusion and the wall face shall also be
considered. Forces transmitted to the wall face by
the protruding structure should be reduced through
the use of compressible joint filler or bearing pads
and sealant.
11-33
loading may be greater than what would be determined
from two-dimensional analysis. Historically, corners and
abrupt alignment changes in walls have had a higher
incidence of performance problems during earthquakes
than relatively straight sections of the wall alignment, as
the corners tend to attract dynamic load and increased
earth pressures. This should be considered when
designing a wall corner for seismic loading.
Note that the corner or abrupt alignment change
enclosed angle as defined in the previous paragraph can
either be internal or external to the wall.
With regard to wall backfill materials, walls that
have used compacted backfills with high silt or clay
content have historically exhibited more performance
problems during earthquakes than those that have
utilized compacted granular backfills. This has
especially been an issue if the wall backfill does not
have adequate drainage features to keep water out of the
backfill and the backfill fully drained. Also, very
uniform clean sand backfill, especially if it lacks
angularity, has also been problematic with regard to wall
seismic performance. The issue is how well it can be
compacted and remain in a compacted state. A backfill
soil coefficient of uniformity of greater than 4 is
recommended and, in general, the backfill particles
should be classified as subangular or angular rather than
rounded or subrounded. The less angular the backfill
particles, the more well graded the backfill material
needs to be.
For additional information on good wall details, see
Berg et al. (2009). While this reference is focused on
MSE wall details, similar details could be adapted for
gravity and semigravity walls.
11.6.6—Drainage
C11.6.6
Backfills behind abutments and retaining walls shall
be drained or, if drainage cannot be provided, the
abutment or wall shall be designed for loads due to earth
pressure, plus full hydrostatic pressure due to water in
the backfill.
Weep holes or geocomposite panel drains at the
wall face do not assure fully drained conditions.
Drainage systems should be designed to completely
drain the entire retained soil volume behind the retaining
wall face.
11.7—PIERS
11.7.1—Load Effects in Piers
Piers shall be designed to transmit the loads on the
superstructure, and the loads acting on the pier itself,
onto the foundation. The loads and load combinations
shall be as specified in Section 3.
The structural design of piers shall be in accordance
with the provisions of Sections 5, 6, 7, and 8, as
appropriate.
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2012
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11-34
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.7.2—Pier Protection
11.7.2.1—Collision
Where the possibility of collision exists from
highway or river traffic, an appropriate risk analysis
should be made to determine the degree of impact
resistance to be provided and/or the appropriate
protection system. Collision loads shall be determined as
specified in Articles 3.6.5 and 3.14.
11.7.2.2—Collision Walls
Collision walls may be required by railroad owners
if the pier is in close proximity to the railroad.
C11.7.2.2
Collision walls are usually required by the railroad
owner if the column is within 25.0 ft of the rail. Some
railroad owners require a collision wall 6.5 ft above the
top of the rail between columns for railroad overpasses.
11.7.2.3—Scour
The scour potential shall be determined and the
design shall be developed to minimize failure from this
condition as specified in Article 2.6.4.4.2.
11.7.2.4—Facing
C11.7.2.4
Where appropriate, the pier nose should be designed
to effectively break up or deflect floating ice or drift.
In these situations, pier life can be extended by
facing the nosing with steel plates or angles, and by
facing the pier with granite.
11.8—NONGRAVITY CANTILEVERED WALLS
11.8.1—General
C11.8.1
Nongravity cantilevered walls may be considered
for temporary and permanent support of stable and
unstable soil and rock masses. The feasibility of using a
nongravity cantilevered wall at a particular location shall
be based on the suitability of soil and rock conditions
within the depth of vertical element embedment to
support the wall.
Depending on soil conditions, nongravity
cantilevered walls less than about 15 ft in height are
usually feasible, with the exception of cylinder or
tangent pile walls, where greater heights can be used.
11.8.2—Loading
C11.8.2
The provisions of Article 11.6.1.2 shall apply. The
load factor for lateral earth pressure (EH) shall be
applied to the lateral earth pressures for the design of
nongravity cantilevered walls.
Lateral earth pressure distributions for design of
nongravity cantilevered walls are provided in
Article 3.11.5.6.
11.8.3—Movement and Stability at the Service Limit
State
11.8.3.1—Movement
The provisions of Articles 10.7.2.2 and 10.8.2.1
shall apply. The effects of wall movements on adjacent
facilities shall be considered in the selection of the
design earth pressures in accordance with the provisions
of Article 3.11.1.
C11.8.3.1
Table C3.11.1-1 provides approximate magnitudes
of relative movements required to achieve active earth
pressure conditions in the retained soil and passive earth
pressure conditions in the resisting soil.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-35
11.8.3.2—Overall Stability
The provisions of Article 11.6.2.3 shall apply.
C11.8.3.2
Use of vertical wall elements to provide resistance
against overall stability failure is described in
Article C11.9.3.2. Discrete vertical elements penetrating
across deep failure planes can provide resistance against
overall stability failure. The magnitude of resistance will
depend on the size, type, and spacing of the vertical
elements.
11.8.4—Safety against Soil Failure at the Strength
Limit State
11.8.4.1—Overall Stability
The provisions of Article 11.6.2.3 shall apply.
The provisions of Article 11.6.3.5 shall apply.
Vertical elements shall be designed to support the full
design earth, surcharge and water pressures between the
elements. In determining the embedment depth to
mobilize passive resistance, consideration shall be given
to planes of weakness, e.g., slickensides, bedding planes,
and joint sets that could reduce the strength of the soil or
rock determined by field or laboratory tests. Embedment
in intact rock, including massive to appreciably jointed
rock which should not fail through a joint surface, shall be
based on the shear strength of the rock mass.
C11.8.4.1
Discrete vertical elements penetrating across deep
failure planes can provide resistance against failure. The
magnitude of resistance will depend on the size, type,
and spacing of vertical elements.
The maximum spacing between vertical supporting
elements depends on the relative stiffness of the vertical
elements. Spans of 6.0 to 10.0 ft are typical, depending
on the type and size of facing.
In determining the embedment depth of vertical wall
elements, consideration should be given to the presence of
planes of weakness in the soil or rock that could result in
a reduction of passive resistance. For laminated, jointed,
or fractured soils and rocks, the residual strength along
planes of weakness should be considered in the design
and, where the planes are oriented at other than an angle
of (45 degrees − φ′f /2) from the horizontal in soil or
45 degrees from the horizontal in rock toward the
excavation, the orientation of the planes should also be
considered. Where the wall is located on a bench above a
deeper excavation, consideration should be given to the
potential for bearing failure of a supporting wedge of soil
or rock through intact materials along planes of weakness.
In designing permanent nongravity cantilevered
walls with continuous vertical elements, the simplified
earth pressure distributions in Figure 3.11.5.6-3 may be
used with the following procedure (Teng, 1962):
•
Determine the magnitude of lateral pressure on the
wall due to earth pressure, surcharge loads and
differential water pressure over the design height of
the wall using ka1.
•
Determine the magnitude of lateral pressure on the
wall due to earth pressure, surcharge loads and
differential water pressure over the design height of
the wall using ka2.
•
Determine in the following equation the value x as
defined in Figure 3.11.5.6-3 to determine the
distribution of net passive pressure in front of the
wall below the design height:
(
)
x = [ γka 2 γ ′s1 H ] / φk p 2 − γka 2 γ ′s 2
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All rights reserved. Duplication is a violation of applicable law.
(C11.8.4.1-1)
2012
Edition
11-36
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
where:
γ
=
ka2 =
γ′s1 =
H
φ
=
=
kp2 =
γ′s2 =
load factor for horizontal earth
pressure, EH (dim.)
the active earth pressure coefficient for
soil 2 (dim.)
the effective soil unit weight for soil 1
(kcf)
the design height of the wall (ft)
the resistance factor for passive
resistance in front of the wall (dim.)
the passive earth pressure coefficient
for soil 2 (dim.)
the effective soil unit weight for soil 2
(kcf)
•
Sum moments about the point of action of F (the
base of the wall) to determine the embedment (Do)
for which the net passive pressure is sufficient to
provide moment equilibrium.
•
Determine the depth at which the shear in the wall
is zero, i.e., the point at which the areas of the
driving and resisting pressure diagrams are
equivalent.
•
Calculate the maximum bending moment at the
point of zero shear.
•
Calculate the design depth, D =1.2Do, to account for
errors inherent in the simplified passive pressure
distribution.
11.8.5—Safety against Structural Failure
11.8.5.1—Vertical Wall Elements
Vertical wall elements shall be designed to resist all
horizontal earth pressure, surcharge, water pressure, and
earthquake loadings.
C11.8.5.1
Discrete vertical wall elements include driven piles,
drilled shafts, and auger-cast piles, i.e., piles and builtup sections installed in preaugered holes.
Continuous vertical wall elements are continuous
throughout both their length and width, although vertical
joints may prevent shear and/or moment transfer
between adjacent sections. Continuous vertical wall
elements include sheet piles, precast or cast-in-place
concrete diaphragm wall panels, tangent-piles, and
tangent drilled shafts.
The maximum bending moments and shears in
vertical wall elements may be determined using the
loading diagrams in Article 3.11.5.6, and appropriate
load and resistance factors.
11.8.5.2—Facing
C11.8.5.2
The maximum spacing between discrete vertical
wall elements shall be determined based on the relative
stiffness of the vertical elements and facing, the type and
condition of soil to be supported, and the type and
condition of the soil in which the vertical wall elements
are embedded. Facing may be designed assuming simple
support between elements, with or without soil arching,
or assuming continuous support over several elements.
In lieu of other suitable methods, for preliminary
design the maximum bending moments in facing may be
determined as follows:
•
For simple spans without soil arching:
M max = 0.125 pL2
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(C11.8.5.2-1)
2012
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
If timber facing is used, it shall be stress-grade
pressure-treated lumber in conformance with Section 8.
If timber is used where conditions are favorable for the
growth of decay-producing organisms, wood should be
pressure-treated with a wood preservative unless the
heartwood of a naturally decay-resistant species is
available and is considered adequate with respect to the
decay hazard and expected service life of the structure.
11-37
•
For simple spans with soil arching:
M max = 0.083 pL2
•
For continuous spans without soil arching:
M max = 0.1 pL2
•
(C11.8.5.2-2)
(C11.8.5.2-3)
For continuous spans with soil arching:
M max = 0.083 pL2
(C11.8.5.2-4)
where:
Mmax
=
p
=
L
=
factored flexural moment on a unit width
or height of facing (kip-ft/ft)
average factored lateral pressure, including
earth, surcharge and water pressure acting
on the section of facing being considered
(ksf/ft)
spacing between vertical elements or other
facing supports (ft)
If the variations in lateral pressure with depth are
large, moment diagrams should be constructed to
provide more accuracy. The facing design may be varied
with depth.
Eq. C11.8.5.2-1 is applicable for simply supported
facing behind which the soil will not arch between
vertical supports, e.g., in soft cohesive soils or for rigid
concrete facing placed tightly against the in-place soil.
Eq. C11.8.5.2-2 is applicable for simply supported facing
behind which the soil will arch between vertical supports,
e.g., in granular or stiff cohesive soils with flexible facing
or rigid facing behind which there is sufficient space to
permit the in-place soil to arch. Eqs. C11.8.5.2-3 and
C11.8.5.2-4 are applicable for facing which is continuous
over several vertical supports, e.g., reinforced shotcrete or
concrete.
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2012
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11-38
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.8.6—Seismic Design of Nongravity Cantilever
Walls
11.8.6.1—General
C11.8.6.1
The effect of earthquake loading shall be
investigated using the Extreme Event I limit state of
Table 3.4.1-1 with resistance factor φ=1.0 and load
factor γp =1.0 and an accepted methodology, with the
exception of overall stability of the wall, in which case a
resistance factor of 0.9 should be used as specified in
Article 11.5.8.
The seismic analysis of the nongravity cantilever
retaining wall shall demonstrate that the cantilever wall
will maintain overall stability and withstand the seismic
earth pressures induced by the design earthquake
without excessive structural moments and shear on the
cantilever wall section. Limit equilibrium methods or
numerical displacement analyses shall be used to
confirm acceptable wall performance.
Design checks should also be performed for failures
below the excavation level but through the structure.
These analyses should include the contributions of the
structural section to slope stability. If the structural
contribution to resistance is being accounted for in the
stability assessment, the moments and shears developed
by the structural section should be checked to confirm
that specified structural limits are not exceeded.
11.8.6.2—Seismic Active Lateral Earth Pressure
Lateral earth pressures and inertial forces for
seismic design of nongravity cantilever walls shall be
determined as specified in Article 11.6.5. The resulting
active seismic earth pressure shall be distributed as
specified in Article 11.6.5.3, above the excavation level
as shown in Figure 11.8.6.2-1.
To reduce the lateral seismic acceleration
coefficient kh0 for the effects of horizontal wall
displacement in accordance with Article 11.6.5.2.2,
analyses shall demonstrate that the displacements
associated with the yield acceleration do not result in
any of the following:
During seismic loading, the nongravity cantilever
wall develops resistance to load through the passive
resistance of the soil below the excavation depth. The
stiffness of the structural wall section above the
excavation depth must be sufficient to transfer seismic
forces from the soil behind the wall, through the
structural section, to the soil below. The seismic
evaluation of the nongravity cantilever wall requires,
therefore, determination of the demand on the wall from
the seismic active earth pressure and the capacity of the
soil from the seismic passive soil resistance.
For flexible cantilevered walls, forces resulting
from wall inertia effects may be ignored in estimating
the seismic design forces. However, for very massive
nongravity cantilever wall systems, such as tangent or
secant pile walls, wall mass inertia effects should be
included in the seismic analysis of the wall.
Two types of stability checks are conducted for the
nongravity cantilever wall: global stability and internal
stability. In contrast to gravity and semigravity walls,
sliding, overturning, and bearing stability are not design
considerations for this wall type. By sizing the wall to
meet earth pressures, the equilibrium requirements for
external stability are also satisfied.
The global stability check for seismic loading
involves a general slope failure analysis that extends
below the base of the wall. Typically, the embedment
depth of the wall is 1.5 to 2 times the wall height above
the excavation level. For these depths, global stability is
not normally a concern, except where soft layers are
present below the toe of the wall.
The global stability analysis is performed with a
slope stability program. The failure surfaces used in the
analysis should normally extend below the depth of the
structure member.
Internal stability for a nongravity cantilever wall
refers to the moments and shear forces developed in the
wall from the seismic loads.
C11.8.6.2
In most situations, the nongravity cantilever wall
moves enough during seismic loading to develop
seismic active earth pressures; however, the amount of
movement may not be the 1.0 to 2.0 in. necessary to
allow reduction in the seismic coefficient by 50 percent,
unless analyses demonstrate that permanent wall
movements will occur without damaging the wall
components. Beam-column analyses involving p-y
modeling of the vertical wall elements will usually be
required to make this assessment.
If the effect of cohesion in reducing the seismic
active earth pressure acting on the wall is considered,
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2012
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-39
•
Yield of structural members making up the wall,
such as with a pile-supported wall,
•
Loads applied to the lateral support systems (e.g.,
ground anchors in anchored wall systems; see
Article 11.9.6) that exceed the available factored
resistance, and
•
Unacceptable deformation or damage to any
facilities located in the vicinity of the wall.
the reduction in earth pressure due to cohesion should
not be combined with a reduction in earth pressure due
to horizontal wall displacement.
As described in Article 11.6.5.3, an alternate
approach for determining the seismic active earth
pressure involves use of the generalized limit
equilibrium method. If used for the design of a
nongravity cantilever wall, the geometry of the slope
stability model should extend from the ground surface to
the bottom or toe of the sheet pile or other nongravity
cantilever walls in which the wall is continuous both
above and below the excavation line in front of the wall.
For soldier pile walls, the analysis extends to the
excavation level. The seismic active pressure is
determined as described in Appendix A11.
The static lateral earth pressure force acting behind
the wall is already included in PAE (i.e., PAE is the
combination of the static and seismic lateral earth
pressure). See Articles 3.11.6.3 and 11.10.10.1 for
definition of terms in Figure 11.8.6.2-1 not specifically
defined in this Article.
Concentrated Dead
Load Surcharge, ∆σv
KhWsurcharge
FP = Kaf ∆σv
h
PAE
Design
Grade
PPE
KhWw
hp
h/3
Pa
Figure 11.8.6.2-1—Seismic Force Diagram for Nongravity Cantilever Wall External Stability Evaluation
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2012
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11-40
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.8.6.3—Seismic Passive Lateral Earth
Pressure
The method used to compute the seismic passive
pressure shall consider wall interface friction, the
nonlinear failure surface that develops during passive
pressure loading, and the inertial response of the soil
within the passive pressure wedge for depths greater
than 5.0 ft. Cohesion and frictional properties of the
soil shall be included in the determination. Passive
pressure under seismic loading shall be determined as
specified in Article 11.6.5.5.
In the absence of any specific guidance or
research results for seismic loading, a wall interface
friction equal to two-thirds of the soil friction angle
should be used when calculating seismic passive
pressures.
The seismic passive pressure shall be applied as a
triangular pressure distribution similar to that for
static loading. The amount of displacement to
mobilize the passive pressure shall also be considered
in the analyses.
The peak seismic passive pressure should be
based on:
•
The time-averaged mean groundwater elevation,
•
The full depth of the below-ground structural
element, not neglecting the upper 2.0 ft of soil as
typically done for static analyses,
•
The strength of the soil for undrained loading,
and
•
The wall friction in the passive pressure estimate
taken as two-thirds times the soil strength
parameters from a total stress analysis.
In the absence of specific guidance for seismic
loading, a reduction factor of 0.67 should be applied
to the seismic passive pressure during the seismic
check to limit displacement required to mobilize the
passive earth pressure.
C11.8.6.3
The effects of live loads are usually neglected in
the computation of seismic passive pressure.
Reductions in the seismic passive earth pressure
may be warranted to limit the amount of deformation
required to mobilize the seismic passive earth pressure,
if a limit equilibrium method of analysis is used, to
make sure that the wall movement does not result in
the collapse of the wall or of structures directly
supported by the wall. However, a passive resistance
reduction factor near 1.0 may be considered if, in the
judgment of the engineer, such deformations to
mobilize the passive resistance would not result in wall
or supported structure collapse.
If the nongravity cantilever wall uses soldier piles
to develop reaction to active pressures, adjustments
must be made in the passive earth pressure
determination to account for the three-dimensional
effects below the excavation level as soil reactions are
developed. In the absence of specific seismic studies
dealing with this issue, it is suggested that methods
used for static loading be adopted. One such method,
documented in the California Department of
Transportation (Caltrans) Shoring Manual (2010),
suggests that soldier piles located closer than three pile
diameters be treated as a continuous wall. For soldier
piles spaced at greater distances, the approach in the
Shoring Manual depends on the type of soil:
•
For cohesive soils, the effective pile width that
accounts for arching ranges from one pile diameter
for very soft soil to two diameters for stiff soils.
•
For cohesionless soils, the effective width is
defined as 0.08φB up to three pile diameters. In
this relationship, φ is the soil friction angle and B
is the soldier pile width.
During seismic loading, the inertial response of the
soil within the passive pressure failure wedge will
decrease the soil resistance during a portion of each
loading cycle. Figures provided in Appendix A11 can
be used to estimate the passive soil resistance for
different friction values and normalized values of
cohesion. A preferred methodology for computing
seismic earth pressures with consideration of wall
friction, nonlinear soil failure surface, and inertial
effects involves use of the procedures documented by
Shamsabadi et al. (2007).
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2012
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11.8.6.4—Wall Displacement Analyses to
Determine Earth Pressures
Numerical displacement analyses, if used, shall
show that moments, shear forces, and structural
displacements resulting from the peak ground surface
accelerations are within acceptable levels. These
analyses shall be conducted using a model of the wall
system that includes the structural stiffness of the wall
section, as well as the load displacement response of
the soil above and below the excavation level.
11-41
C11.8.6.4
Numerical displacement methods offer a more
accurate and preferred method of determining the
response of nongravity cantilever walls during seismic
loading. Either of two numerical approaches can be
used. One involves a simple beam-column approach;
the second involves the use of a two-dimensional
computer model. Both approaches need to
appropriately represent the load displacement behavior
of the soil and the structural members during loading.
For soils, this includes nonlinear stress-strain effects;
for structural members, consideration must be given to
ductility of the structure, including the use of cracked
versus uncracked section properties if concrete
structures are being used.
Beam-Column Approach
The pseudostatic seismic response of a nongravity
cantilever wall can be determined by representing the
wall in a beam-column model with the soil
characterized by p-y springs. This approach is available
within commercially available computer software. The
total seismic active pressure above the excavation level
is used for wall loading. Procedures given in
Article 11.8.6.2 should be used to make this estimate.
For this approach, the p-y curves below the
excavation level need to be specified. For discrete
structural elements (e.g.., soldier piles), conventional
p-y curves for piles may be used. For continuous walls
or walls with pile elements at closer than 3 diameter
spacing, p- and y-modifiers have been developed by
Anderson et al. (2008) to represent a continuous (sheet
pile or secant pile) retaining wall. The procedure
involves:
•
Developing conventional isolated pile p-y curves
using a 4.0-ft diameter pile following API (1993)
procedures for sands or clays.
•
Normalizing the isolated p-y curves by dividing
the p values by 4.0 ft.
•
Applying the following p- and y-multipliers,
depending on the type of soil, in a conventional
beam-column analysis.
Soil Type
Sand
Clay
p-multiplier
0.5
1.0
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y-multiplier
4.0
4.0
2012
Edition
11-42
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
It should be noted that the starting point of using a
4.0 ft diameter pile has nothing to do with the actual
diameter of the vertical elements in the wall. It is simply
a starting point in the procedure to obtain p-y curves that
are applicable to a wall. The p-y curves obtained in the
final step of this process are intended to be applicable to
a continuous wall.
Supporting information for the development and use
of the p-y approach identified above is presented in
Volume 1 of NCHRP 611 Report (Anderson et al.,
2008). The earth pressure used as the load in the beam
column analysis is determined from one of the limit
equilibrium methods, including M-O with or without
cohesion or the generalized limit equilibrium procedure,
as discussed in Article 11.6.5. The benefit of the p-y
approach is that it enforces compatibility of deflections,
earth pressure, and flexibility of the wall system. The
method is in contrast to the limit equilibrium method in
which the effects of the wall flexibilities are ignored.
This is very important for the seismic design and
performance of the wall during seismic event. The
deformation and rotation of the wall can easily be
captured using the p-y approach.
Finite Difference or Finite Element Modeling
Pseudostatic or dynamic finite element or finite
difference procedures in computer programs can also be
used to evaluate the seismic response of nongravity
cantilever walls during seismic loading. For twodimensional models, it may be necessary to “smear” the
stiffness of the structural section below the excavation
level to adjust the model to an equivalent twodimensional representation if the below-grade portion of
the wall is formed from discrete piles (e.g., soldier
piles).
The finite difference or finite element approach to
evaluating wall response will involve a number of
important assumptions; therefore, this approach should
be discussed with and agreed to by the Owner before
being adopted. As part of the discussions, the possible
limitations and the assumptions being made for the
model should be reviewed.
11.8.7—Corrosion Protection
C11.8.7
The level and extent of corrosion protection shall be
a function of the ground environment and the potential
consequences of a wall failure.
Corrosion protection for piles and miscellaneous
hardware and material should be consistent with the
design life of the structure.
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2012
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-43
11.8.8—Drainage
C11.8.8
The provisions of Article 3.11.3 shall apply.
Seepage shall be controlled by installation of a
drainage medium behind the facing with outlets at or
near the base of the wall. Drainage panels shall maintain
their drainage characteristics under the design earth
pressures and surcharge loadings, and shall extend from
the base of the wall to a level 1.0 ft below the top of the
wall.
Where thin drainage panels are used behind walls,
and saturated or moist soil behind the panels may be
subjected to freezing and expansion, either insulation
shall be provided on the walls to prevent freezing of the
soil, or the wall shall be designed for the pressures
exerted on the wall by frozen soil.
In general, the potential for development of
hydrostatic pressures behind walls with discrete vertical
elements and lagging is limited due to the presence of
openings in the lagging, and the disturbance of soil
behind lagging as the wall is constructed. However, the
potential for leakage through the wall should not be
counted upon where the ground water level exceeds onethird the height of the wall because of the potential for
plugging and clogging of openings in the wall with time
by migration of soil fines. It is probable that, under such
conditions, a wall with continuous vertical elements, i.e.,
a cutoff wall constructed with a drainage system
designed to handle anticipated flows will be required.
Water pressures may be considered reduced in
design only if positive drainage, e.g., drainage blanket,
geocomposite drainage panels, gravel drains with outlet
pipes is provided to prevent buildup of hydrostatic
pressure behind the wall. Thin drains at the back of the
wall face may not completely relieve hydrostatic
pressure and may increase seepage forces on the back of
the wall face due to rainwater infiltration, Terzaghi and
Peck (1967), and Cedergren (1989). The effectiveness of
drainage control measures should be evaluated by
seepage analyses.
11.9—ANCHORED WALLS
11.9.1—General
C11.9.1
Anchored walls, whose elements may be
proprietary, employ grouted in anchor elements, vertical
wall elements and facing.
Anchored walls, illustrated in Figure 11.9.1-1, may
be considered for both temporary and permanent support
of stable and unstable soil and rock masses.
The feasibility of using an anchored wall at a
particular location should be based on the suitability of
subsurface soil and rock conditions within the bonded
anchor stressing zone.
Where fill is placed behind a wall, either around or
above the unbonded length, special designs and
construction specifications shall be provided to prevent
anchor damage.
Depending on soil conditions, anchors are usually
required for support of both temporary and permanent
nongravity cantilevered walls higher than about 10.0 to
15.0 ft.
The availability or ability to obtain underground
easements and proximity of buried facilities to anchor
locations should also be considered in assessing
feasibility.
Anchored walls in cuts are typically constructed
from the top of the wall down to the base of the wall.
Anchored walls in fill must include provisions to protect
against anchor damage resulting from backfill and
subsoil settlement or backfill and compaction activities
above the anchors.
The minimum distance between the front of the
bond zone and the active zone behind the wall of 5.0 ft
or H/5 is needed to insure that no load from the bonded
zone is transferred into the no load zone due to load
transfer through the grout column in the no load zone.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure 11.9.1-1—Anchored Wall Nomenclature and
Anchor Embedment Guidelines
11.9.2—Loading
C11.9.2
The provisions of Article 11.6.1.2 shall apply,
except that shrinkage and temperature effects need not
be considered.
Lateral earth pressures on anchored walls are a
function of the rigidity of the wall-anchor system, soil
conditions, method and sequence of construction, and
level of prestress imposed by the anchors. Apparent
earth pressure diagrams that are commonly used can be
found in Article 3.11.5.7 and Sabatini et al. (1999).
11.9.3—Movement and Stability at the Service Limit
State
11.9.3.1—Movement
The provisions of Articles 10.6.2.2, 10.7.2.2, and
10.8.2.1 shall apply.
The effects of wall movements on adjacent facilities
shall be considered in the development of the wall
design.
C11.9.3.1
Settlement of vertical wall elements can cause
reduction of anchor loads, and should be considered in
design.
The settlement profiles in Figure C11.9.3.1-1 were
recommended by Clough and O′Rourke (1990) to
estimate ground surface settlements adjacent to braced
or anchored excavations caused during the excavation
and bracing stages of construction. Significant
settlements may also be caused by other construction
activities, e.g., dewatering or deep foundation
construction within the excavation, or by poor
construction techniques, e.g., soldier pile, lagging, or
anchor installation. The field measurements used to
develop Figure C11.9.3.1-1 were screened by the
authors to not include movements caused by other
construction activities or poor construction techniques.
Therefore, such movements should be estimated
separately.
Where noted in the definition of the various curves
in Figure C11.9.3.1-1, the basal heave ratio, RBH, shall
be taken as:
RBH =
5.1Su
γ s H + qs
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(C11.9.3.1-1)
2012
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-45
where:
Su
γs
H
qs
=
=
=
=
undrained shear strength of cohesive soil (ksf)
unit weight of soil (kcf)
height of wall (ft)
surcharge pressure (ksf)
See Sabatini et al. (1999) for additional information
on the effect of anchored wall construction and design
on wall movement.
Curve I
Curve II
Curve III
Curve IV
=
=
=
=
Sand
Stiff to very hard clay
Soft to medium clay, RBH = 2.0
Soft to medium clay, RBH = 1.2
Figure C11.9.3.1-1—Settlement Profiles behind Braced or
Anchored Walls (adapted from Clough and O'Rourke,
1990)
11.9.3.2—Overall Stability
The provisions of Article 11.6.2.3 shall apply.
C11.9.3.2
Detailed guidance for evaluating the overall
stability of anchored wall systems, including how to
incorporate anchor forces in limit equilibrium slope
stability analyses, is provided by Sabatini et al. (1999).
The effect of discrete vertical elements penetrating
deep failure planes and acting as in-situ soil improvement
may be negligible if the percentage of reinforcement
provided by the vertical elements along the failure surface
is small. However, it is possible to consider the effect of
the discrete vertical elements by modeling the elements as
a cohesion along the failure surface, or by evaluating the
passive capacity of the elements.
11.9.4—Safety against Soil Failure
11.9.4.1—Bearing Resistance
The provisions of Articles 10.6.3, 10.7.3, and 10.8.3
shall apply.
Bearing resistance shall be determined assuming
that all vertical components of loads are transferred to
the embedded section of the vertical wall elements.
C11.9.4.1
For drilled in place vertical wall elements, e.g.,
drilled-in soldier piles, in sands, if the β-method is used
to calculate the skin friction capacity, the depth z should
be referenced to the top of the wall. The vertical
overburden stress, σv′, however, should be calculated
with reference to the elevation of the midheight of the
exposed wall, with β and σv′ evaluated at the midpoint of
each soil layer.
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2012
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11-46
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.9.4.2—Anchor Pullout Capacity
C11.9.4.2
Prestressed anchors shall be designed to resist
pullout of the bonded length in soil or rock. The factored
pullout resistance of a straight shaft anchor in soil or
rock, QR, is determined as:
nominal anchor pullout resistance (kips)
Anchor pullout capacity is influenced by soil and
rock conditions, method of anchor hole advancement,
hole diameter, bonded length, grout type and grouting
pressure. Information on anchor pullout capacity may be
found in Sabatini et al. (1999), PTI (1996), Cheney
(1984) and Weatherby (1982). As a guide, the
presumptive values provided in Tables C11.9.4.2-1,
C11.9.4.2-2, and C11.9.4.2-3 may be used to estimate
the nominal (ultimate) bond for small diameter anchors
installed in cohesive soils, cohesionless soils and rock,
respectively. It should be recognized that the values
provided in the tables may be conservative.
Table C11.9.4.2-1—Presumptive Ultimate Unit Bond Stress
for Anchors in Cohesive Soils
(11.9.4.2-1)
QR = φQn = φπd τa Lb
where:
φ
=
Qn =
resistance factor for anchor pullout (dim.)
d
=
diameter of anchor drill hole (ft)
τn
=
nominal anchor bond stress (ksf)
Lb =
anchor bond length (ft)
For preliminary design, the resistance of anchors may
either be based on the results of anchor pullout load
tests; estimated based on a review of geologic and
boring data, soil and rock samples, laboratory testing
and previous experience; or estimated using published
soil/rock-grout bond guidelines. For final design, the
contract documents may require preproduction tests
such as pullout tests or extended creep tests on
sacrificial anchors be conducted to establish anchor
lengths and capacities that are consistent with the
contractor′s chosen method of anchor installation. Either
performance or proof tests shall be conducted on every
production anchor to 1.0 or greater times the factored
load to verify capacity.
Anchor/Soil Type
(Grout Pressure)
Gravity Grouted
Anchors (<50 psi)
Soil Stiffness or
Unconfined
Compressive
Strength (tsf)
Presumptive
Ultimate Unit
Bond Stress,
τn (ksf)
Silt-Clay
Mixtures
Pressure Grouted
Anchors (50 psi–
400 psi)
Stiff to Very Stiff
1.0–4.0
0.6 to 1.5
High Plasticity
Clay
Stiff 1.0–2.5
V. Stiff 2.5–4.0
0.6 to 2
1.5 to 3.6
Medium Plasticity
Clay
Stiff 1.0–2.5
V. Stiff 2.5–4.0
2.0 to 5.2
2.9 to 7.3
Medium Plasticity
Sandy Silt
V. Stiff 2.5–4.0
5.8 to 7.9
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2012
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-47
Table C11.9.4.2-2—Presumptive Ultimate Unit Bond Stress
for Anchors in Cohesionless Soils
Anchor/Soil Type
(Grout Pressure)
Gravity Grouted
Anchors (<50 psi)
Soil Compactness
or SPT Resistancea
Sand or SandGravel Mixtures
Pressure Grouted
Anchors (50 psi–
400 psi)
Medium Dense to
Dense 11–50
1.5 to 2.9
Fine to Medium
Sand
Medium Dense to
Dense 11–50
1.7 to 7.9
Medium to Coarse
Sand w/ Gravel
Medium Dense
11–30
2.3 to 14
Dense to Very
Dense 30–50
5.2 to 20
Sandy Gravel
Glacial Till
3.5 to 8.5
—
Silty Sands
a
Presumptive
Ultimate Unit
Bond Stress,
τn (ksf)
Medium Dense to
Dense 11–40
4.4 to 29
Dense to Very
Dense 40–50+
5.8 to 29
Dense 31–50
6.3 to 11
Corrected for overburden pressure.
Table C11.9.4.2-3—Presumptive Ultimate Unit Bond Stress
for Anchors in Rock
Rock Type
Granite or Basalt
Dolomitic Limestone
Soft Limestone
Slates & Hard Shales
Sandstones
Weathered Sandstones
Soft Shales
Presumptive Ultimate
Unit Bond Stress, τn
(ksf)
36 to 65
29 to 44
21 to 29
17 to 29
17 to 36
15 to 17
4.2 to 17
The presumptive ultimate anchor bond stress values
presented in Tables C11.9.4.2-1 through C11.9.4.2-3 are
intended for preliminary design or evaluation of the
feasibility of straight shaft anchors installed in small
diameter holes. Pressure-grouted anchors may achieve
much higher capacities. The total capacity of a pressuregrouted anchor may exceed 500 kips in soil or 2000 to
3000 kips in rock, although such high capacity anchors
are seldom used for highway applications. Post-grouting
can also increase the load carrying capacity of straight
shaft anchors by 20–50 percent or more per phase of
post-grouting.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The anchor load shall be developed by suitable
embedment outside of the critical failure surface in the
retained soil mass.
Determination of the unbonded anchor length,
inclination, and overburden cover shall consider:
•
The location of the critical failure surface furthest
from the wall,
The resistance factors in Table 11.5.7-1, in
combination with the load factor for horizontal active
earth pressure (Table 3.4.1-2), are consistent with what
would be required based on allowable stress design, for
preliminary design of anchors for pullout (Sabatini et al.,
1999). These resistance factors are also consistent with
the results of statistical calibration of full scale anchor
pullout tests relative to the minimum values of
presumptive ultimate unit bond stresses shown in
Tables C11.9.4.2-1 through C11.9.4.2-3. Use of the
resistance factors in Table 11.5.7-1 and the load factor
for apparent earth pressure for anchor walls in
Table 3.4.1-2, with values of presumptive ultimate unit
bond stresses other than the minimum values in
Tables C11.9.4.2-1 through C11.9.4.2-3 could result in
unconservative designs unless the Engineer has previous
experience with the particular soil or rock unit in which
the bond zone will be established.
Presumptive bond stresses greater than the
minimum values shown in Tables C11.9.4.2-1 through
C11.9.4.2-3 should be used with caution, and be based
on past successful local experience, such as a high
percentage of passing proof tests in the specified or
similar soil or rock unit at the design bond stress chosen,
or anchor pullout test results in the specified or similar
soil or rock unit. Furthermore, in some cases the
specified range of presumptive bond stresses is
representative of a range of soil conditions. Soil
conditions at the upper end of the specified range,
especially if coupled with previous experience with the
particular soil unit, may be considered in the selection of
anchor bond stresses above the minimum values shown.
Selection of a presumptive bond stress for preliminary
anchor sizing should consider the risk of failing proof
tests if the selected bond stress was to be used for final
design. The goal of preliminary anchor design is to
reduce the risk of having a significant number of
production anchors fail proof or performance tests as
well as the risk of having to redesign the anchored wall
to accommodate more anchors due to an inadequate
easement behind the wall, should the anchor capacities
predicted during preliminary design not be achievable.
See Article 11.9.8.1 for guidance on anchor testing.
Significant increases in anchor capacity for anchor
bond lengths greater than approximately 40.0 ft cannot
be achieved unless specialized methods are used to
transfer load from the top of the anchor bond zone
towards the end of the anchor. This is especially critical
for strain sensitive soils, in which residual soil strength
is significantly lower than the peak soil strength.
Anchor inclination and spacing will be controlled
by soil and rock conditions, the presence of geometric
constraints and the required anchor capacity. For tremiegrouted anchors, a minimum angle of inclination of
about 10 degrees and a minimum overburden cover of
about 15.0 ft are typically required to assure grouting of
the entire bonded length and to provide sufficient
ground cover above the anchorage zone. For pressuregrouted anchors, the angle of inclination is generally not
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
•
The minimum length required to ensure minimal
loss of anchor prestress due to long-term ground
movements,
•
The depth to adequate anchoring strata, as indicated
in Figure 11.9.1-1, and
•
The method of anchor installation and grouting.
The minimum horizontal spacing of anchors should
be the larger of three times the diameter of the bonded
zone, or 5.0 ft. If smaller spacings are required to
develop the required load, consideration may be given to
differing anchor inclinations between alternating
anchors.
11.9.4.3—Passive Resistance
The provisions of Articles 11.6.3.5, 11.6.3.6, and
11.8.4.1 shall apply.
11-49
critical and is governed primarily by geometric
constraints, and the minimum overburden cover is
typically 6.0–15.0 ft. Steep inclinations may be required
to avoid anchorage in unsuitable soil or rock. Special
situations may require horizontal or near horizontal
anchors, in which case proof of sufficient overburden
and full grouting should be required.
The minimum horizontal spacing specified for
anchors is intended to reduce stress overlap between
adjacent anchors.
Anchors used for walls constructed in fill situations,
i.e., bottom-up construction, should be enclosed in
protective casing to prevent damage during backfill
placement, compaction and settlement.
Selection of anchor type depends on anticipated
service life, soil and rock conditions, ground water level,
subsurface environmental conditions, and method of
construction.
C11.9.4.3
It is recommended in Sabatini et al. (1999) that
methods such as the Broms Method or the Wang and
Reese method be used to evaluate passive resistance and
the wall vertical element embedment depth needed.
However, these methods have not been calibrated for
this application for LRFD as yet.
11.9.5—Safety against Structural Failure
11.9.5.1—Anchors
C11.9.5.1
The horizontal component of anchor design force
shall be computed using the provisions of Article 11.9.2
and any other horizontal pressure components acting on
the wall in Article 3.11. The total anchor design force
shall be determined based on the anchor inclination. The
horizontal anchor spacing and anchor capacity shall be
selected to provide the required total anchor design
force.
Anchor tendons typically consist of steel bars, wires
or strands. The selection of anchor type is generally the
responsibility of the contractor.
A number of suitable methods for the determination
of anchor loads are in common use. Sabatini et al.
(1999) provides two methods which can be used: the
Tributary Area Method, and the Hinge Method. These
methods are illustrated in Figures C11.5.9.1-1 and
C11.5.9.1-2. These figures assume that the soil below
the base of the excavation has sufficient strength to
resist the reaction force R. If the soil providing passive
resistance below the base of the excavation is weak and
is inadequate to carry the reaction force R, the lowest
anchor should be designed to carry both the anchor load
as shown in the figures as well as the reaction force. See
Article 11.8.4.1 for evaluation of passive resistance.
Alternatively, soil-structure interaction analyses, e.g.,
beam on elastic foundation, can be used to design
continuous beams with small toe reactions, as it may be
overly conservative to assume that all of the load is
carried by the lowest anchor.
In no case should the maximum test load be less
than the factored load for the anchor.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Tributary area method
Hinge method
T1 = Load over length H1 + H2/2
R = Load over length H2/2
T1 Calculated from ΣMC = 0
R = Total earth pressure – T1
Figure C11.9.5.1-1—Calculation of Anchor Loads for OneLevel Wall after Sabatini et al. (1999)
Tributary Area Method
Hinge Method
T1 = Load over length H1 + H2/2
T2 = Load over length H2/2 + Hn/2
Tn = Load over length Hn/2 + Hn+1/2
R = Load over length Hn+1/2
T1 Calculated from ΣMC = 0
T2u = Total earth pressure (ABCGF) – T1
T2L = Calculated from ΣMD = 0
Tnu = Total earth pressure (CDIH) – T2L
TnL = Calculated from ΣME = 0
R = Total earth pressure – T1 – T2 – Tn
T2 = T2u = T2L
Tn = Tnu + TnL
Figure C11.9.5.1-2—Calculation of Anchor Loads for Multilevel Wall
after Sabatini et al. (1999)
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2012
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11.9.5.2—Vertical Wall Elements
Vertical wall elements shall be designed to resist all
horizontal earth pressure, surcharge, water pressure,
anchor, and seismic loadings, as well as the vertical
component of the anchor loads and any other vertical
loads. Horizontal supports may be assumed at each
anchor location and at the bottom of the excavation if
the vertical element is sufficiently embedded below the
bottom of the excavation.
11-51
C11.9.5.2
Discrete vertical wall elements are continuous
throughout their length and include driven piles,
caissons, drilled shafts, and auger-cast piles, i.e., piles
and built-up sections installed in preaugured holes and
backfilled with structural concrete in the passive zone
and lean concrete in the exposed section of the wall.
Continuous vertical wall elements are continuous
throughout both their length and width, although vertical
joints may prevent shear and/or moment transfer
between adjacent sections. Continuous vertical wall
elements include sheet piles, precast or cast-in-place
concrete diaphragm wall panels, tangent-piles, and
tangent caissons.
For structural analysis methods, see Section 4.
For walls supported in or through soft clays with
Su < 0.15γs′H, continuous vertical elements extending
well below the exposed base of the wall may be required
to prevent heave in front of the wall. Otherwise, the
vertical elements are embedded approximately 3.0 ft or
as required for stability or end bearing.
11.9.5.3—Facing
The provisions of Article 11.8.5.2 shall apply.
11.9.6—Seismic Design
C11.9.6
The provisions of Article 11.8.6 shall apply except
as modified in this Article.
The seismic analysis of the anchored retaining wall
shall demonstrate that the anchored wall can maintain
overall stability and withstand the seismic earth
pressures induced by the design earthquake without
exceeding the capacity of the anchors or the structural
wall section supporting the soil. Limit equilibrium
methods or numerical displacement analyses shall be
used to confirm acceptable wall performance.
Anchors shall be located behind the limit
equilibrium failure surface for seismic loading. The
location of the failure surface for seismic loading shall
be established using methods that account for the
seismic coefficient and the soil properties (i.e., c and φ)
within the anchored zone.
See Article C11.8.6.
The seismic design of an anchored wall involves
many of the same considerations as the nongravity
cantilever wall. However, the addition of one or more
anchors to the wall introduces some important
differences in the seismic design check as identified in
this Article.
The earth pressures above the excavation level
result from the inertial response of the soil mass behind
the wall. In contrast to a nongravity cantilever wall, the
soil mass includes anchors that have been tensioned to
minimize wall deflections under static earth pressures.
During seismic loading, the bars or strands making up
the unbonded length of the anchor are able to stretch
under the imposed incremental seismic loads. In most
cases, the amount of elastic elongation in the strand or
bar under the incremental seismic load is sufficient to
develop seismic active earth pressures but may not be
sufficient to allow the horizontal seismic acceleration
coefficient, kh0, and associated earth pressure to be
reduced to account for permanent horizontal wall
displacement. The ability of the wall to deform laterally
should be specifically investigated before reducing kh0 to
account for horizontal wall displacement.
The passive pressure for the embedded portion of
the soldier pile or sheet pile wall also plays a part in the
stability assessment, as it helps provide stability for the
portion of the wall below the lowest anchor. This
passive pressure is subject to seismically induced inertial
forces that will reduce the passive resistance relative to
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2012
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11-52
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
the static capacity of the pile or wall section. Most often,
the embedded portion of the pile involves discrete
structural members spaced at 8.0 to 10.0 ft; however, the
embedded portion could also involve a continuous wall
in the case of a sheet pile or secant pile wall.
Anchors should be located behind the failure
surface associated with the calculation of PAE. The
location of this failure surface can be determined using
either the wedge equilibrium or the generalized limit
equilibrium (slope stability) method. Note that this
failure surface will likely be flatter than the
requirements for anchor location under static loading.
When using the wedge equilibrium or the generalized
limit equilibrium method, PAE and its associated critical
surface should be determined without the anchor forces.
Once the location of the anchor bond zone is
defined, an external stability check should be conducted
with the anchor forces included, using the anchor test
load to define ultimate anchor capacities. This check is
performed to confirm that the C/D ratio is greater than
1.0. Under this loading condition, the critical surface
will flatten and could pass through or behind some
anchors. However, as long as the C/D ratio is greater
than 1.0, the design is satisfactory.
If the C/D ratio is less than 1.0, either the unbonded
length of the anchor must be increased or the length of
the grouted zone must be lengthened. The design check
would then be repeated.
The global stability check is performed to confirm
that a slope stability failure does not occur below the
anchored wall; external stability is checked to confirm
the anchors will have sufficient reserve capacity to meet
seismic load demands; and internal stability is checked
to confirm that moments and shear forces within the
structural members, including the anchor strand or bar
tensile loads and the head connection, are within
acceptable levels for the seismic load.
11.9.7—Corrosion Protection
C11.9.7
Prestressed anchors and anchor heads shall be
protected against corrosion consistent with the ground
and groundwater conditions at the site. The level and
extent of corrosion protection shall be a function of the
ground environment and the potential consequences of
an anchor failure. Corrosion protection shall be applied
in accordance with the provisions of AASHTO LRFD
Bridge Construction Specifications, Section 6, “Ground
Anchors.”
Corrosion protection for piles, wales, and
miscellaneous hardware and material should be
consistent with the level of protection for the anchors
and the design life of the structure.
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2012
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-53
11.9.8—Construction and Installation
11.9.8.1—Anchor Stressing and Testing
All production anchors shall be subjected to load
testing and stressing in accordance with the provisions of
AASHTO LRFD Bridge Construction Specifications,
Article 6.5.5, “Testing and Stressing.” Preproduction load
tests may be specified when unusual conditions are
encountered to verify the safety with respect to the design
load to establish the ultimate anchor load (pullout test), or
to identify the load at which excessive creep occurs.
At the end of the testing of each production anchor,
the anchor should be locked off to take up slack in the
anchored wall system to reduce post-construction wall
deformation. The lock-off load should be determined
and applied as described in AASHTO LRFD Bridge
Construction Specifications, Article 6.5.5.6.
C11.9.8.1
Common anchor load tests include pullout tests
performed on sacrificial preproduction anchors, and
creep, performance, and proof tests performed the
production anchors. None of the production anchor tests
determine the actual ultimate anchor load capacity. The
production anchor test results only provide an indication
of serviceability under a specified load. Performance
tests consist of incremental loading and unloading of
anchors to verify sufficient capacity to resist the test
load, verify the free length and evaluate the permanent
set of the anchor. Proof tests, usually performed on each
production anchor, consist of a single loading and
unloading cycle to verify sufficient capacity to resist the
test load and to prestress the anchor. Creep tests,
recommended for cohesive soils with a plasticity index
greater than 20 percent or a liquid limit greater than
50 percent, and highly weathered, soft rocks, consist of
incremental, maintained loading of anchors to assess the
potential for loss of anchor bond capacity due to ground
creep.
Pullout tests should be considered in the following
circumstances:
•
If the preliminary anchor design using unit bond
stresses provided in the tables above indicate that
anchored walls are marginally infeasible, requiring
that a more accurate estimate of anchor capacity be
obtained during wall design. This may occur due to
lack of adequate room laterally to accommodate the
estimated anchor length within the available rightof-way or easement;
•
If the anticipated anchor installation method or
soil/rock conditions are significantly different than
those assumed to develop the presumptive values in
Tables C11.9.4.2-1 through C11.4.9.2-3 and
inadequate site specific experience is available to
make a reasonably accurate estimate of the
soil/rock-grout anchor bond stresses.
The FHWA recommends load testing anchors to
125 percent to 150 percent of the unfactored design
load, Cheney (1984). Maximum load levels between
125 percent and 200 percent have been used to evaluate
the potential for tendon overstress in service, to
accommodate unusual or variable ground conditions or
to assess the effect of ground creep on anchor capacity.
Test load levels greater than 150 percent of the
unfactored design load are normally applied only to
anchors in soft cohesive soil or unstable soil masses
where loss of anchor prestress due to creep warrants
evaluation. The area of prestressing steel in the test
anchor tendon may require being increased to perform
these tests.
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Note that the test details provided in the AASHTO
LRFD Bridge Construction Specifications, Article 6.5.5,
at least with regard to the magnitude of the incremental
test loads, were developed for allowable stress design.
These incremental test loads should be divided by the
load factor for apparent earth pressure for anchored
walls provided in Table 3.4.1-2 when testing to factored
anchor loads.
Typically, the anchor lock-off load is equal to 80 to
100 percent of the nominal (unfactored) anchor load to
ensure that the slack in the anchored wall system is
adequately taken up so that post-construction wall
deformation is minimized. However, a minimum lockoff load of 50 percent is necessary to properly engage
strand anchor head wedges.
11.9.9—Drainage
C11.9.9
The provisions of Article 11.8.8 shall apply.
Thin drains at the back of the wall face may not
completely relieve hydrostatic pressure and may
increase seepage forces on the back of the wall face due
to rainwater infiltration, Terzaghi and Peck (1967), and
Cedergren (1989). The effectiveness of drainage control
measures should be evaluated by seepage analyses.
11.10—MECHANICALLY STABILIZED EARTH
WALLS
11.10.1—General
C11.10.1
MSE walls may be considered where conventional
gravity, cantilever, or counterforted concrete retaining
walls and prefabricated modular retaining walls are
considered, and particularly where substantial total and
differential settlements are anticipated.
When two intersecting walls form an enclosed angle
of 70 degrees or less, the affected portion of the wall
shall be designed as an internally tied bin structure with
at-rest earth pressure coefficients.
MSE walls shall not be used under the following
conditions:
Mechanically stabilized earth (MSE) systems,
whose elements may be proprietary, employ either
metallic (strip or grid type) or geosynthetic (geotextile,
strip, or geogrid) tensile reinforcements in the soil mass,
and a facing element which is vertical or near vertical.
MSE walls behave as a gravity wall, deriving their
lateral resistance through the dead weight of the
reinforced soil mass behind the facing. For relatively
thick facings, the dead weight of the facing may also
provide a significant contribution to the capacity of the
wall system. Typical MSE walls are shown in
Figure C11.10.1-1.
All available data indicates that corrosion in MSE
walls is not accelerated by stray currents from electric
rail lines due to the discontinuity of the earth
reinforcements in a direction parallel to the source of the
stray current. Where metallic reinforcements are used in
areas of anticipated stray currents within 200 ft of the
structure, and the metallic reinforcements are
continuously connected in a direction parallel to the
source of stray currents, a corrosion expert should
evaluate the potential need for corrosion control
requirements. More detailed information on stray current
corrosion issues is provided by Sankey and Anderson
(1999).
Where future access to utilities may be gained
without disrupting reinforcements and where leakage
from utilities would not create detrimental hydraulic
•
Where utilities other than highway drainage are to
be constructed within the reinforced zone unless
access is provided to utilities without disrupting
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-55
reinforcements and breakage or rupture of utility
lines will not have a detrimental effect on the
stability of the structure.
conditions or degrade reinforcements, utilities in the
reinforced zone may be acceptable.
•
Where floodplain erosion or scour may undermine
the reinforced fill zone or facing, or any supporting
footing.
•
With reinforcements exposed to surface or ground
water contaminated by acid mine drainage, other
industrial pollutants, or other environmental
conditions defined as aggressive in Article 7.3.6.3
of the AASHTO LRFD Bridge Construction
Specifications, unless environmental-specific, longterm corrosion, or degradation studies are
conducted.
The potential for catastrophic failure due to scour is
high for MSE walls if the reinforced fill is lost during a
scour occurrence. Consideration may be given to
lowering the base of the wall or to alternative methods
of scour protection, such as sheetpile walls and/or riprap
of sufficient size, placed to a sufficient depth to preclude
scour.
Figure C11.10.1-1—Typical Mechanically Stabilized Earth Walls
MSE walls shall be designed for external stability of
the wall system as well as internal stability of the
reinforced soil mass behind the facing. Overall and
compound stability failure shall be considered. Structural
design of the wall facing shall also be considered.
The specifications provided herein for MSE walls
do not apply to geometrically complex MSE wall
systems such as tiered walls (walls stacked on top of one
another), back-to-back walls, or walls which have
trapezoidal sections. Design guidelines for these cases
are provided in FHWA-NHI-10-024 (Berg et al., 2009).
For simple structures with rectangular geometry,
relatively uniform reinforcement spacing, and a near
vertical face, compound failures passing both through
the unreinforced and reinforced zones will not generally
be critical. However, if complex conditions exist such as
changes in reinforced soil types or reinforcement
lengths, high surcharge loads, sloping faced structures, a
slope at the toe of the wall, or stacked structures,
compound failures must be considered.
Internal design of MSE wall systems requires
knowledge of short- and long-term properties of the
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Compound stability should also be evaluated for these
complex MSE wall systems (see Article 11.10.4.3).
materials used as soil reinforcements as well as the soil
mechanics which govern MSE wall behavior.
11.10.2—Structure Dimensions
An illustration of the MSE wall element dimensions
required for design is provided in Figure 11.10.2-1.
The size and embedment depth of the reinforced
soil mass shall be determined based on:
•
Requirements for stability and geotechnical
strength, as specified in Article 11.10.5 consistent
with requirements for gravity walls,
•
Requirements for structural resistance within the
reinforced soil mass itself, as specified in Article
11.10.6, for the panel units, and for the development
of reinforcement beyond assumed failure zones, and
•
Traditional requirements for reinforcement length
not less than 70 percent of the wall height, except as
noted in Article 11.10.2.1.
Figure 11.10.2-1—MSE Wall Element Dimensions Needed for Design
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-57
11.10.2.1—Minimum Length of Soil
Reinforcement
For sheet-, strip-, and grid-type reinforcement, the
minimum soil reinforcement length shall be 70 percent
of the wall height as measured from the leveling pad.
Reinforcement length shall be increased as required for
surcharges and other external loads, or for soft
foundation soils.
The reinforcement length shall be uniform
throughout the entire height of the wall, unless
substantiating evidence is presented to indicate that
variation in length is satisfactory.
C11.10.2.1
In general, a minimum reinforcement length of
8.0 ft, regardless of wall height, has been recommended
based on historical practice, primarily due to size
limitations of conventional spreading and compaction
equipment. Shorter minimum reinforcement lengths, on
the order of 6.0 ft, but no less than 70 percent of the wall
height, can be considered if smaller compaction
equipment is used, facing panel alignment can be
maintained, and minimum requirements for wall
external stability are met.
The requirement for uniform reinforcement length
equal to 70 percent of the structure height has no
theoretical justification, but has been the basis of many
successful designs to-date. Parametric studies
considering minimum acceptable soil strengths have
shown that structure dimensions satisfying all of the
requirements of Article 11.10.5 require length to height
ratios varying from 0.8H for low structures, i.e., 10.0 ft,
to 0.63H for high structures, i.e., 40.0 ft.
Significant shortening of the reinforcement
elements below the minimum recommended ratio of
0.7H may only be considered when accurate, site
specific determinations of the strength of the
unreinforced fill and the foundation soil have been
made. Christopher et al. (1990) presents results which
strongly suggest that shorter reinforcing length to height
ratios, i.e., 0.5H to 0.6H, substantially increase
horizontal deformations.
A nonuniform reinforcement length may be
considered under the following circumstances:
•
Lengthening of the uppermost reinforcement layers
to beyond 0.7H to meet pullout requirements, or to
address seismic or impact loads.
•
Lengthening of the lowermost reinforcement layers
beyond 0.7H to meet overall (global) stability
requirements based on the results of a detailed
global stability analysis.
•
Shortening of the bottom reinforcement layers to
less than 0.7H to minimize excavation
requirements, provided the wall is bearing on rock
or very competent foundation soil (see below).
For walls on rock or very competent foundation
soil, e.g., SPT > 50, the bottom reinforcements may be
shortened to a minimum of 0.4H with the upper
reinforcements lengthened to compensate for external
stability issues in lieu of removing rock or competent
soil for construction. Design guidelines for this case are
provided in FHWA-NHI-10-024 (Berg et al., 2009).
For conditions of marginal stability, consideration
must be given to ground improvement techniques to
improve foundation stability, or to lengthening of
reinforcement.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.10.2.2—Minimum Front Face Embedment
The minimum embedment depth of the bottom of
the reinforced soil mass (top of the leveling pad) shall
be based on bearing resistance, settlement, and
stability requirements determined in accordance with
Section 10.
Unless constructed on rock foundations, the
embedment at the front face of the wall in ft shall not be
less than:
•
a depth based on the prevailing depth of frost
penetration, if the soil below the wall is frost
susceptible, and the external stability requirement,
and
•
2.0 ft on sloping ground (4.0H:1V or steeper) or
where there is potential for removal of the soil in
front of the wall toe due to erosion or future
excavation, or 1.0 ft on level ground where there is
no potential for erosion or future excavation of the
soil in front of the wall toe.
For walls constructed along rivers and streams,
embedment depths shall be established at a minimum of
2.0 ft below potential scour depth as determined in
accordance with Article 11.6.3.5.
As an alternative to locating the wall base below
the depth of frost penetration where frost susceptible
soils are present, the soil within the depth and lateral
extent of frost penetration below the wall can be
removed and replaced with nonfrost susceptible clean
granular soil.
A minimum horizontal bench width of 4.0 ft shall
be provided in front of walls founded on slopes. The
bench may be formed or the slope continued above that
level as shown in Figure 11.10.2-1.
The lowest backfill reinforcement layer shall not be
located above the long-term ground surface in front of
the wall.
11.10.2.3—Facing
C11.10.2.2
The minimum embedment guidelines provided in
Table C11.10.2.2-1 may be used to preclude local bearing
resistance failure under the leveling pad or footing due to
higher vertical stresses transmitted by the facing.
Table C11.10.2.2-1—Guide for Minimum Front Face
Embedment Depth
Slope in Front of Structures
for walls
Horizontal
for abutments
3.0H:1.0V
walls
2.0H:1.0V
walls
1.5H:1.0V
walls
Minimum
Embedment
Depth
H/20.0
H/10.0
H/10.0
H/7.0
H/5.0
For structures constructed on slopes, minimum
horizontal benches are intended to provide resistance to
local bearing resistance failure consistent with resistance
to general bearing resistance failure and to provide
access for maintenance inspections.
C11.10.2.3
Facing elements shall be designed to resist the
horizontal force in the soil reinforcements at the
reinforcement to facing connection, as specified in
Articles 11.10.6.2.2 and 11.10.7.3.
In addition to these horizontal forces, the facing
elements shall also be designed to resist potential
compaction stresses occurring near the wall face during
erection of the wall.
The tension in the reinforcement may be assumed to
be resisted by a uniformly distributed earth pressure on
the back of the facing.
The facing shall be stabilized such that it does not
deflect laterally or bulge beyond the established tolerances.
See Article C3.11.2 for guidance. Additional
information on compaction stresses can be found in
Duncan and Seed (1986) and Duncan et al. (1991).
Alternatively, compaction stresses can be addressed
through the use of facing systems which have a proven
history of being able to resist the compaction activities
anticipated behind the wall and which have performed
well in the long-term.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11.10.2.3.1—Stiff or Rigid Concrete, Steel, and
Timber Facings
Facing elements shall be structurally designed in
accordance with Sections 5, 6, and 8 for concrete, steel,
and timber facings, respectively.
The minimum thickness for concrete panels at, and
in the zone of stress influence of, embedded connections
shall be 5.5 in. and 3.5 in. elsewhere. The minimum
concrete cover shall be 1.5 in. Reinforcement shall be
provided to resist the average loading conditions for
each panel. Temperature and shrinkage steel shall be
provided as specified in Article 5.10.8.
The structural integrity of concrete face panels shall
be evaluated with respect to the shear and bending
moment between reinforcements attached to the facing
panel in accordance with Section 5.
For segmental concrete facing blocks, facing
stability calculations shall include an evaluation of the
maximum vertical spacing between reinforcement
layers, the maximum allowable facing height above the
uppermost reinforcement layer, inter-unit shear capacity,
and resistance of the facing to bulging. The maximum
spacing between reinforcement layers shall be limited to
twice the width, Wu illustrated in Figure 11.10.6.4.4b-1,
of the segmental concrete facing block unit or 2.7 ft,
whichever is less. The maximum facing height up to the
wall surface grade above the uppermost reinforcement
layer shall be limited to 1.5Wu illustrated in
Figure 11.10.6.4.4b-1 or 24.0 in., whichever is less,
provided that the facing above the uppermost
reinforcement layer is demonstrated to be stable against
a toppling failure through detailed calculations. The
maximum depth of facing below the lowest
reinforcement layer shall be limited to the width, Wu, of
the proposed segmental concrete facing block unit.
11.10.2.3.2—Flexible Wall Facings
If welded wire, expanded metal, or similar facing is
used, they shall be designed in a manner which prevents
the occurrence of excessive bulging as backfill behind
the facing compresses due to compaction stresses or self
weight of the backfill. This may be accomplished by
limiting the size of individual facing elements vertically
and the vertical and horizontal spacing of the soil
reinforcement layers, and by requiring the facing to have
an adequate amount of vertical slip and overlap between
adjacent elements.
The top of the flexible facing at the top of the wall
shall be attached to a soil reinforcement layer to provide
stability to the top facing.
11-59
C11.10.2.3.1
The specified minimum panel thicknesses and
concrete cover recognize that MSE walls are often
employed where panels may be exposed to salt spray
and/or other corrosive environments. The minimum
thicknesses also reflect the tolerances on panel
thickness, and placement of reinforcement and
connectors that can reasonably be conformed to in
precast construction.
Based on research by Allen and Bathurst (2001),
facings consisting of segmental concrete facing blocks
behave as a very stiff facing, due to the ability of the
facing blocks to transmit moment in a vertical direction
throughout the facing column, and appear to have even
greater stiffness than incremental precast concrete
panels.
Experience has shown that for walls with segmental
concrete block facings, the gap between soil
reinforcement sections or strips at a horizontal level
should be limited to a maximum of one block width to
limit bulging of the facing between reinforcement levels
or build up of unacceptable stresses that could result in
performance problems. The ability of the facing to carry
moment horizontally to bridge across the gaps in the
reinforcement horizontally should be evaluated if
horizontally discontinuous reinforcement is used, i.e., a
reinforcement coverage ratio Rc < 1.
C11.10.2.3.2
Experience has shown that for welded wire,
expanded metal, or similar facings, vertical
reinforcement spacing should be limited to a maximum
of 2.0 ft and the gap between soil reinforcement at a
horizontal level limited to a maximum of 3.0 ft to limit
bulging of the panels between reinforcement levels. The
section modulus of the facing material should be
evaluated and calculations provided to support
reinforcement spacings, which will meet the bulging
requirements stated in Article C11.10.4.2.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Geosynthetic facing elements shall not, in general,
be left exposed to sunlight (specifically ultraviolet
radiation) for permanent walls. If geosynthetic facing
elements must be left exposed permanently to sunlight,
the geosynthetic shall be stabilized to be resistant to
ultraviolet radiation. Product specific test data shall be
provided which can be extrapolated to the intended
design life and which proves that the product will be
capable of performing as intended in an exposed
environment.
11.10.2.3.3—Corrosion Issues for MSE Facing
Steel-to-steel
contact
between
the
soil
reinforcement connections and the concrete facing steel
reinforcement shall be prevented so that contact between
dissimilar metals, e.g., bare facing reinforcement steel
and galvanized soil reinforcement steel, does not occur.
A corrosion protection system shall be provided
where salt spray is anticipated.
C11.10.2.3.3
Steel-to-steel contact in this case can be prevented
through the placement of a nonconductive material
between the soil reinforcement face connection and the
facing concrete reinforcing steel. Examples of measures
which can be used to mitigate corrosion include, but are
not limited to, coatings, sealants, or increased panel
thickness.
11.10.3—Loading
The provisions of Article 11.6.1.2 shall apply,
except that shrinkage and temperature effects need not
be considered to come in contact with steel wall
elements.
11.10.4—Movement and Stability at the Service
Limit State
11.10.4.1—Settlement
The provisions of Article 11.6.2 shall apply as
applicable.
The allowable settlement of MSE walls shall be
established based on the longitudinal deformability of
the facing and the ultimate purpose of the structure.
Where foundation conditions indicate large
differential settlements over short horizontal distances,
vertical full-height slip joints shall be provided.
Differential settlement from the front to the back of
the wall shall also be evaluated, especially regarding the
effect on facing deformation, alignment, and connection
stresses.
C11.10.4.1
For systems with rigid concrete facing panels and
with a maximum joint width of 0.75 in., the maximum
tolerable slope resulting from calculated differential
settlement may be taken as given in Table C11.10.4.1-1.
Table C11.10.4.1-1—Guide for Limiting Distortion for
Precast Concrete Facings of MSE Walls
Joint Width
(in.)
0.75
0.50
0.25
Limiting Differential Settlement
30 ft2 ≤ Area ≤
2
75 ft2
Area ≤ 30 ft
1/100
1/200
1/200
1/300
1/300
1/600
For MSE walls with full height precast concrete
facing panels, total settlement should be limited to
2.0 in., and the limiting differential settlement should be
1/500. For walls with segmental concrete block facings,
the limiting differential settlement should be 1/200. For
walls with welded wire facings or walls in which castin-place concrete or shotcrete facing is placed after wall
settlement is essentially complete, the limiting
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-61
differential settlement should be 1/50. These limiting
differential settlement criteria consider only structural
needs of the facing. More stringent differential
settlement criteria may be needed to meet aesthetic
requirements.
11.10.4.2—Lateral Displacement
Lateral wall displacements shall be estimated as a
function of overall structure stiffness, compaction
intensity, soil type, reinforcement length, slack in
reinforcement-to-facing connections, and deformability
of the facing system or based on monitored wall
performance.
C11.10.4.2
A first order estimate of lateral wall displacements
occurring during wall construction for simple MSE walls on
firm foundations can be obtained from Figure C11.10.4.2-1.
If significant vertical settlement is anticipated or heavy
surcharges are present, lateral displacements could be
considerably greater. Figure C11.10.4.2-1 is appropriate as a
guide to establish an appropriate wall face batter to obtain a
near vertical wall or to determine minimum clearances
between the wall face and adjacent objects or structures.
Figure C11.10.4.2-1—Empirical Curve for Estimating
Anticipated Lateral Displacement during Construction for
MSE Walls
For additional explanation on how to use this figure,
see Berg et al. (2009).
For welded wire or similarly faced walls such as
gabion faced walls, the maximum tolerable facing bulge
between connections, both horizontally and vertically,
with soil reinforcement is approximately 2.0 in. For
geosynthetic facings, the maximum facing bulge
between reinforcement layers should be approximately
2.75 in. for 1.0 ft vertical reinforcement spacing to
5.0 in. for 2.0 ft vertical reinforcement spacing.
11.10.4.3—Overall Stability
The provisions of Article 11.6.2.3 shall apply.
Additionally for MSE walls with complex geometrics,
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
compound failure surfaces which pass through a portion
of the reinforced soil mass as illustrated in
Figure 11.10.4.3-1 shall be investigated, especially where
the wall is located on sloping or soft ground where overall
stability may be inadequate. The long-term strength of
each backfill reinforcement layer intersected by the
failure surface should be considered as restoring forces in
the limit equilibrium slope stability analysis.
Figure 11.10.4.3-1—Overall and Compound Stability of
Complex MSE Wall Systems
11.10.5—Safety against Soil Failure (External
Stability)
11.10.5.1—General
C11.10.5.1
MSE structures shall be proportioned to satisfy
eccentricity and sliding criteria normally associated with
gravity structures.
Safety against soil failure shall be evaluated by
assuming the reinforced soil mass to be a rigid body.
The coefficient of active earth pressure, ka, used to
compute the earth pressure of the retained soil behind
the reinforced soil mass shall be determined using the
friction angle of the retained soil. In the absence of
specific data, a maximum friction angle of 30 degrees
may be used for granular soils. Tests should be
performed to determine the friction angle of cohesive
soils considering both drained and undrained conditions.
Eccentricity requirements seldom govern design.
Sliding and overall stability usually govern design of
structures greater than 30.0 ft in height, structures
constructed on weak foundation soils, or structures
loaded with sloping surcharges.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11.10.5.2—Loading
11-63
C11.10.5.2
Lateral earth pressure distributions for design of
MSE walls shall be taken as specified in
Article 3.11.5.8. Application of loads for external and
internal stability shall be taken as specified in
Articles 11.10.5 and 11.10.6, respectively. Application
of surcharge loads shall be taken as specified in
Article 11.10.11. Application of load factors for these
loads shall be taken as specified in Article 11.5.5.
For external stability calculations only, the active
earth pressure coefficients for retained backfill, i.e., fill
behind the reinforced soil mass, shall be taken as
specified in Article 3.11.5.3 with δ = β.
Dead load surcharges, if present, shall be taken into
account in accordance with Article 11.10.10.
For investigation of sliding stability and
eccentricity, the continuous traffic surcharge loads shall
be considered to act beyond the end of the reinforced
zone as shown in Figure 11.10.5.2-1. Application of
load factors for these loads shall be taken as specified in
Article 11.5.5.
Figures 3.11.5.8.1-1, 3.11.5.8.1-2, and 3.11.5.8.1-3
illustrate lateral earth pressure distributions for external
stability of MSE walls with horizontal backslope,
inclined backslope, and broken backslope, respectively.
Figure 11.10.5.2-1—External Stability for Wall with Horizontal Backslope and Traffic Surcharge
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.10.5.3—Sliding
C11.10.5.3
The provisions of Article 10.6.3.4 shall apply.
The coefficient of sliding friction at the base of the
reinforced soil mass shall be determined using the
friction angle of the foundation soil. For discontinuous
reinforcements, e.g., strips, the angle of sliding friction
shall be taken as the lesser of φr of the reinforced fill and
φf of the foundation soil. For continuous reinforcements,
e.g., grids and sheets, the angle of sliding friction shall
be taken as the lesser of φr, φf and ρ, where ρ is the soilreinforcement interface friction angle. In the absence of
specific data, a maximum friction angle, φf, of
30 degrees and a maximum soil-reinforcement interface
angle, ρ, of 2/3 φf may be used.
11.10.5.4—Bearing Resistance
For the purpose of computing bearing resistance, an
equivalent footing shall be assumed whose length is the
length of the wall, and whose width is the length of the
reinforcement strip at the foundation level. Bearing
pressures shall be computed using a uniform base
pressure distribution over an effective width of footing
determined in accordance with the provisions of
Articles 10.6.3.1 and 10.6.3.2.
Where soft soils or sloping ground in front of the
wall are present, the difference in bearing stress
calculated for the wall reinforced soil zone relative to
the local bearing stress beneath the facing elements shall
be considered when evaluating bearing capacity. In both
cases, the leveling pad shall be embedded adequately to
meet bearing capacity requirements.
11.10.5.5—Overturning
For relatively thick facing elements, it may be
desirable to include the facing dimensions and weight in
sliding and overturning calculations, i.e., use B in lieu of
L as shown in Figure 11.10.5.2-1.
C11.10.5.4
The effect of eccentricity and load inclination is
accommodated by the introduction of an effective width,
B′ = L−2e, instead of the actual width.
For relatively thick facing elements, it may be
reasonable to include the facing dimensions and weight
in bearing calculations, i.e., use B in lieu of L as shown
in Figure 11.10.2-1.
Note, when the value of eccentricity e is negative:
B′ = L.
Due to the flexibility of MSE walls, a triangular
pressure distribution at the wall base cannot develop,
even if the wall base is founded on rock, as the
reinforced soil mass has limited ability to transmit
moment. Therefore, an equivalent uniform base pressure
distribution is appropriate for MSE walls founded on
either soil or rock.
Concentrated bearing stresses from the facing
weight on soft soil could create concentrated stresses at
the connection between the facing elements and the wall
backfill reinforcement.
2013 Revision
The provisions of Article 11.6.3.3 shall apply.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-65
11.10.6—Safety against Structural Failure (Internal
Stability)
11.10.6.1—General
C11.10.6.1
Safety against structural failure shall be evaluated
with respect to pullout and rupture of reinforcement.
A preliminary estimate of the structural size of the
stabilized soil mass may be determined on the basis of
reinforcement pullout beyond the failure zone, for which
resistance is specified in Article 11.10.6.3.
11.10.6.2—Loading
The resistance factors, specified in Article 11.5.6,
are consistent with the use of select backfill in the
reinforced zone, homogeneously placed and carefully
controlled in the field for conformance with Section 7 of
AASHTO LRFD Bridge Construction Specifications.
The basis for the factors is the successful construction of
thousands of structures in accordance with these criteria,
and the use of conservative pullout resistance factors
representing high confidence limits.
C11.10.6.2
The load in the reinforcement shall be determined at
two critical locations: the zone of maximum stress and
the connection with the wall face. Potential for
reinforcement rupture and pullout are evaluated at the
zone of maximum stress, which is assumed to be located
at the boundary between the active zone and the resistant
zone in Figure 11.10.2-1. Potential for reinforcement
rupture and pullout are also evaluated at the connection
of the reinforcement to the wall facing.
The maximum friction angle used for the
computation of horizontal force within the reinforced
soil mass shall be assumed to be 34 degrees, unless the
specific project select backfill is tested for frictional
strength by triaxial or direct shear testing methods,
AASHTO T 296 and T 297 or T 236, respectively. A
design friction angle of greater than 40 degrees shall not
be used with the Simplified Method even if the
measured friction angle is greater than 40 degrees.
Loads carried by the soil reinforcement in
mechanically stabilized earth walls are the result of
vertical and lateral earth pressures, which exist within
the reinforced soil mass, reinforcement extensibility,
facing stiffness, wall toe restraint, and the stiffness and
strength of the soil backfill within the reinforced soil
mass. The soil reinforcement extensibility and material
type are major factors in determining reinforcement
load. In general, inextensible reinforcements consist of
metallic strips, bar mats, or welded wire mats, whereas
extensible reinforcements consist of geotextiles or
geogrids. Inextensible reinforcements reach their peak
strength at strains lower than the strain required for the
soil to reach its peak strength. Extensible reinforcements
reach their peak strength at strains greater than the strain
required for soil to reach its peak strength. Internal
stability failure modes include soil reinforcement
rupture (strength limit state), and excessive
reinforcement elongation under the design load (service
limit state). The service limit state is not evaluated in
current practice for internal stability design. Internal
stability is determined by equating the factored tensile
load applied to the reinforcement to the factored tensile
resistance of the reinforcement, the tensile resistance
being governed by reinforcement rupture and pullout.
Analysis of full scale wall data in comparison to the
Simplified Method or other widely accepted design
methods (see Article 11.10.6.2.1) indicates that these
methods will significantly underestimate reinforcement
loads if design soil friction angles greater than
40 degrees are used. This recommendation applies to
soil friction angles as determined using triaxial or direct
shear tests, as the Simplified Method was calibrated
using triaxial or direct shear soil strengths (see Allen et
al., 2001).
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.10.6.2.1—Maximum Reinforcement Loads
Maximum reinforcement loads shall be calculated
using the Simplified Method or the Coherent Gravity
Method. The Simplified Method shall be considered to
apply to both steel and geosynthetic reinforced wall
systems. The Coherent Gravity Method shall be applied
primarily to steel soil reinforcement systems. For the
Simplified Method, the load in the reinforcements shall be
obtained by multiplying the vertical earth pressure at the
reinforcement by a lateral earth pressure coefficient, and
applying the resulting lateral pressure to the tributary area
for the reinforcement. For the Coherent Gravity Method,
the load in the reinforcements shall be obtained in the same
way as the Simplified Method, except as follows:
•
The vertical earth pressure at each reinforcement
level shall be computed using an equivalent uniform
base pressure distribution over an effective width of
reinforced wall mass determined in accordance with
the provisions of Articles 11.6.3.1 and 11.6.3.2, and
•
For steel reinforced wall systems, the lateral earth
pressure coefficient used shall be equal to k0 at the
point of intersection of the theoretical failure
surface with the ground surface at or above the wall
top, transitioning to ka at a depth of 20.0 ft below
that intersection point, and constant at ka at depths
greater than 20.0 ft. If used for geosynthetic
reinforced systems, ka shall be used throughout the
wall height.
All other provisions in this article are applicable to both
methods.
Other widely accepted and published design
methods for calculation of reinforcement loads may be
used at the discretion of the wall owner or approving
agency, provided the designer develops method-specific
resistance factors for the method employed.
For the Simplified Method, factored horizontal
stress, σH, at each reinforcement level shall be
determined as:
σ H = γ P ( σv kr + Δσ H )
(11.10.6.2.1-1)
where:
γP =
kr =
σv =
the load factor for vertical earth pressure EV
from Table 3.4.1-2
horizontal pressure coefficient (dim.)
pressure due to resultant of gravity forces from
soil self weight within and immediately above
the reinforced wall backfill, and any surcharge
loads present (ksf)
C11.10.6.2.1
The development of the Simplified Method for
estimating reinforcement loads is provided in Allen,
et al. (2001). The Coherent Gravity Method has been
used in MSE wall design practice for many years for
steel reinforced wall systems. Detailed procedures for
the Coherent Gravity Method are provided in Allen,
et al. (2001) and in Mitchell and Villet (1987). Its
application to geosynthetic soil reinforcement systems
results in conservative designs.
The design specifications provided herein assume
that the wall facing combined with the reinforced
backfill acts as a coherent unit to form a gravity
retaining structure. Research by Allen and Bathurst
(2003) and Allen et al. (2003) indicates that
reinforcement load is linear with reinforcement spacing
to a reinforcement vertical spacing of 2.7 ft or more,
though a vertical spacing of this magnitude should not
be attempted unless the facing is considered to be
adequately stiff to prevent excessive bulging between
layers (see Article C11.10.2.3.2).
These MSE wall specifications also assume that
inextensible reinforcements are not mixed with
extensible reinforcements within the same wall. MSE
walls which contain a mixture of inextensible and
extensible reinforcements are not recommended.
The calculation method for Tmax is empirically
derived, based on reinforcement strain measurements,
converted to load based on the reinforcement modulus,
from full scale walls at working stress conditions. The
load factor EV, on the other hand, was determined in
consideration of vertical earth pressure exerted by a soil
mass without inclusions, and was calibrated to address
uncertainties implied by allowable stress design for
external stability for walls. EV is not directly applicable
to internal reinforcement loads in MSE walls, since the
calibration of EV was not performed with internal
stability of a reinforced system in mind.
The use of EV for the load factor in this case for
both methods (i.e., the Simplified and Coherent Gravity
Methods) should be considered an interim measure until
research is completed to quantify load prediction bias
and uncertainty.
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2012
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-67
ΔσH = horizontal stress at reinforcement level
resulting from any applicable concentrated
horizontal surcharge load as specified in
Article 11.10.10.1 (ksf)
For the Simplified Method, vertical stress for
maximum reinforcement load calculations shall be
determined as shown in Figures 11.10.6.2.1-1 and
11.10.6.2.1-2. For the Coherent Gravity Method, vertical
stress shall be calculated at each reinforcement level
using an equivalent uniform base pressure that accounts
for load eccentricity caused by the lateral earth pressure
acting at the back of the reinforced soil mass above the
reinforcement level being considered. This base pressure
shall be applied over an effective width of reinforced
wall mass determined in accordance with the provisions
of Articles 11.6.3.1 and 11.6.3.2. As is true for the
Simplified Method, live load is not included in the
vertical stress calculation to determine Tmax for assessing
pullout loads when using the Coherent Gravity Method.
Sloping soil surcharges are taken into account
through an equivalent uniform surcharge and assuming a
level backslope condition. For these calculations, the
depth Z is referenced from the top of the wall at the wall
face, excluding any copings and appurtenances.
Note that Tmax, the factored tensile load in the soil
reinforcement, must be calculated twice for internal
stability design as follows: (1) for checking
reinforcement and connection rupture, determine Tmax
with live load surcharge included in the calculation of
σv; (2) for checking pullout, determine Tmax with live
load surcharge excluded from the calculation of σv.
Max Stress: σv = γ r Z + q + Δσv
Pullout: σv = γ r Z + Δσv
Note: Δσv is determined from Figure 11.10.10.1-1.
H is the total wall height at the face.
Figure 11.10.6.2.1-1—Calculation of Vertical Stress for Horizontal Backslope Condition,
Including Live Load and Dead Load Surcharges for Internal Stability Analysis
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Max Stress: S = (1/ 2 ) L tanβ
σv = γ r Z + (1/ 2 ) L ( tanβ ) γ f
Determine kaf using a slope angle of β
Determine kr from Figure 11.10.6.2.1-3
Pullout: σv = γ r Z p and Z p ≥ Z + S
Note: H is the total height of the wall at the face.
Figure 11.10.6.2.1-2—Calculation of Vertical Stress for Sloping Backslope Condition for Internal
Stability Analysis
For the Simplified Method, the lateral earth pressure
coefficient kr is determined by applying a multiplier to
the active earth pressure coefficient, ka. The ka multiplier
for the Simplified Method shall be determined as shown
in Figure 11.10.6.2.1-3. For assessment of reinforcement
pullout, the Simplified Method multiplier for steel strip
walls shall be used for all steel reinforced walls. For
reinforcement rupture, the multiplier applicable to the
specific type of steel reinforcement shall be used. For
the Coherent Gravity Method, the lateral earth pressure
coefficient used for internal stability design of steel
reinforced MSE wall systems shall be determined as
shown in Figure 11.10.6.2.1-4. For geosynthetic
reinforced wall systems, ka is used throughout the wall
height. For both methods, ka shall be determined using
Eq. 3.11.5.3-1, assuming no wall friction, i.e., δ = β. For
the Coherent Gravity Method, k0 shall be determined
using Eq. 3.11.5.2-1.
Since it is assumed that δ = β, and β is assumed to
always be zero for internal stability, for a vertical wall,
the Coulomb equation simplifies mathematically to the
simplest form of the Rankine equation.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-69
The applied factored load to the reinforcements,
Tmax, shall be determined using a load per unit of wall
width basis as follows:
Tmax = σ H Sv
(11.10.6.2.1-2)
φ′f
ka = tan 2 45 −
2
If the wall face is battered, the following simplified
form of the Coulomb equation can be used:
where:
σH =
Sv
=
factored horizontal soil stress at
reinforcement (ksf)
vertical spacing of the reinforcement (ft)
the
A vertical spacing, Sv, greater than 2.7 ft should not
be used without full scale wall data (e.g., reinforcement
loads and strains, and overall deflections) that support
the acceptability of larger vertical spacing.
Live loads shall be positioned for extreme force
effect. The provisions of Article 3.11.6 shall apply.
(C11.10.6.2.1-1)
ka =
sin 2 ( θ + φ′f
)
sin φ′f
sin 3 θ 1 +
sin θ
2
(C11.10.6.2.1-2)
with variables as defined in Figure 3.11.5.3-1.
Based on Figure 11.10.6.2.1-3, the ka multiplier is a
function of the reinforcement type and the depth of the
reinforcement below the wall top. Multipliers for other
reinforcement types can be developed as needed through
analysis of measurements of reinforcement load and
strain in full scale structures.
Figure 11.10.6.2.1-3—Variation of the Coefficient of
Lateral Stress Ratio kr/ka with Depth in a Mechanically
Stabilized Earth Wall
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
0.3H1
Ka
Ko
β
H1/2
H
Active Zone
H1
20 ft
H1/2
L
Figure 11.10.6.2.1-4—Determination of Lateral Earth
Pressure Coefficients for Internal Stability Design of Steel
Reinforced MSE Walls Using the Coherent Gravity
Method
11.10.6.2.2—Reinforcement Loads at Connection to
Wall Face
The factored tensile load applied to the soil
reinforcement connection at the wall face, To, shall be
equal to the maximum factored reinforcement tension,
Tmax, for all wall systems regardless of facing and
reinforcement type.
11.10.6.3—Reinforcement Pullout
11.10.6.3.1—Boundary between Active and
Resistant Zones
The location of the zone of maximum stress for
inextensible and extensible wall systems, i.e., the
boundary between the active and resistant zones, is
determined as shown in Figure 11.10.6.3.1-1. For all
wall systems, the zone of maximum stress shall be
assumed to begin at the back of the facing elements at
the toe of the wall.
For extensible wall systems with a face batter of
less than ten degrees from the vertical, the zone of
maximum stress should be determined using the
Rankine method. Since the Rankine method cannot
account for wall face batter or the effect of concentrated
surcharge loads above the reinforced backfill zone, the
Coulomb method shall be used for walls with extensible
reinforcement in cases of significant batter, defined as
ten degrees from vertical or more, and concentrated
surcharge loads to determine the location of the zone of
maximum stress.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-71
(a) Inextensible Reinforcements
For walls with a face batter 10 degrees or more from the vertical,
tan ( Ψ − φr ) =
− tan ( φ r − β ) + tan ( φr − β ) [ tan ( φ r − β ) + cot ( φr + θ − 90 )] [1 + tan ( δ + 90 − θ ) cot ( φr + θ − 90 )]
1 + tan ( δ + 90 − θ ) [ tan ( φr − β ) + cot ( φr + θ − 90 )]
with δ = β and all other variables defined in Figure 3.11.5.3-1.
(b) Extensible Reinforcements
Figure 11.10.6.3.1-1—Location of Potential Failure Surface for Internal Stability Design of MSE Walls
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11-72
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.10.6.3.2—Reinforcement Pullout Design
C11.10.6.3.2
The reinforcement pullout resistance shall be
checked at each level against pullout failure. Only the
effective pullout length which extends beyond the
theoretical failure surfaces in Figure 11.10.6.3.1-1 shall
be used in this calculation. A minimum length, Le, in the
resistant zone of 3.0 ft shall be used. The total length of
reinforcement required for pullout is equal to La + Le as
shown in Figure 11.10.6.3.1-1.
Note that traffic loads are neglected in pullout
calculations (see Figure 11.10.6.2.1-1).
The effective pullout length shall be determined
using the following equation:
Le ≥
Tmax
φF *ασv CRc
(11.10.6.3.2-1)
F*ασvCLe is the ultimate pullout resistance Pr per
unit of reinforcement width.
where:
Le =
Tmax =
=
φ
F* =
α =
σv =
C
=
Rc =
length of reinforcement in resisting zone (ft)
applied factored load in the reinforcement
from Eq. 11.10.6.2.1-2 (kips/ft)
resistance factor for reinforcement pullout from
Table 11.5.7-1 (dim.)
pullout friction factor (dim.)
scale effect correction factor (dim.)
unfactored vertical stress at the reinforcement
level in the resistant zone (ksf)
overall reinforcement surface area geometry
factor based on the gross perimeter of the
reinforcement and is equal to 2 for strip, grid and
sheet-type reinforcements, i.e., two sides (dim.)
reinforcement
coverage
ratio
from
Article 11.10.6.4.1 (dim.)
F* and α shall be determined from product-specific
pullout tests in the project backfill material or equivalent
soil, or they can be estimated empirically/theoretically.
For standard backfill materials (see AASHTO LRFD
Bridge Construction Specifications, Article 7.3.6.3), with
the exception of uniform sands, i.e., coefficient of
uniformity Cu=D60/D10 < 4, in the absence of test data it is
acceptable to use conservative default values for F* and α
as shown in Figure 11.10.6.3.2-1 and Table 11.10.6.3.2-1.
For ribbed steel strips, if the specific Cu for the wall
backfill is unknown at the time of design, a Cu of 4.0
should be assumed for design to determine F*.
Table 11.10.6.3.2-1—Default Values for the Scale Effect
Correction Factor, α
Reinforcement Type
All Steel Reinforcements
Geogrids
Geotextiles
Default Value for α
1.0
0.8
0.6
Pullout testing and interpretation procedures (and
direct shear testing for some parameters), as well as typical
empirical data, are provided in Appendix A of FHWANHI-10-025 (Berg et al., 2009).
Recent experience with pullout test results on new
geogrids coming into the market has indicated that some
materials have pullout values that are lower than the
previous F* default value of 0.8 tan φ. Data obtained by
D’Appolonia (1999) also indicates that 0.8 tan φ is
closer to a mean value rather than a default lower bound
value for geogrids. The default values for other
reinforcement types shown in Figure 11.10.6.3.2-1 are
more representative of lower bound values. The F*
default value has thus been lowered to a more
conservative value of 0.67 tan φ in consideration of
these results.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-73
For grids, the spacing between transverse grid
elements, St, shall be uniform throughout the length of
the reinforcement rather than having transverse grid
members concentrated only in the resistant zone.
Figure 11.10.6.3.2-1—Default Values for the Pullout Friction Factor, F*
These pullout calculations assume that the factored
long-term strength of the reinforcement (see
Article 11.10.6.4.1) in the resistant zone is greater than
Tmax.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.10.6.4—Reinforcement Strength
C11.10.6.4.1
11.10.6.4.1—General
The reinforcement strength shall be checked at
every level within the wall, both at the boundary
between the active and resistant zones (i.e., zone of
maximum stress), and at the connection of the
reinforcement to the wall face, for applicable strength
limit states as follows:
At the zone of maximum stress:
Tmax ≤ φTal Rc
The serviceability limit state is not specifically
evaluated in current practice to design backfill
reinforcement for internal stability. A first order
estimate of lateral deformation of the entire wall
structure, however, can be obtained as shown in
Article 11.10.4.2.
(11.10.6.4.1-1)
where:
Tmax =
φ
=
Taℓ =
Rc =
applied factored load to the reinforcement
determined from Eq. 11.10.6.2.1-2 (kips/ft)
resistance factor for reinforcement tension,
specified in Table 11.5.7-1 (dim.)
nominal long-term reinforcement design
strength (kips/ft)
reinforcement coverage ratio specified in
Article 11.10.6.4.1 (dim.)
Taℓ shall be determined as specified in
Article 11.10.6.4.3a for steel reinforcement and
Article 11.10.6.4.3b for geosynthetic reinforcement.
At the connection with the wall face:
To ≤ φTac Rc
(11.10.6.4.1-2)
where:
To =
φ
=
Tac =
Rc =
applied factored load at reinforcement/facing
connection specified in Article 11.10.6.2.2
(kips/ft)
resistance factor for reinforcement tension in
connectors specified in Table 11.5.7-1 (dim.)
nominal
long-term
reinforcement/facing
connection design strength (kips/ft)
reinforcement coverage ratio specified in
Article 11.10.6.4.1 (dim.)
Tac shall be determined at the wall face connection
as specified in Article 11.10.6.4.4a for steel
reinforcement and Article 11.10.6.4.4b for geosynthetic
reinforcement. The difference in the environment
occurring immediately behind the wall face relative to
the environment within the reinforcement backfill zone
and its effect on the long-term durability of the
reinforcement/connection shall be considered when
determining Tac.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-75
Taℓ shall be determined on a long-term strength per
unit of reinforcement width basis and multiplied by the
reinforcement coverage ratio Rc so that it can be directly
compared to Tmax which is determined on a load per unit
of wall width basis (this also applies to Tac and To). For
discrete, i.e., not continuous, reinforcements, such as
steel strips or bar mats, the strength of the reinforcement
is converted to a strength per unit of wall width basis as
shown in Figures 11.10.6.4.1-1 and 11.10.6.4.1-2. For
continuous reinforcement layers, b = 1 and Rc = 1.
Figure 11.10.6.4.1-1—Reinforcement Coverage Ratio for Metal Reinforcement
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure 11.10.6.4.1-2—Reinforcement Coverage Ratio for Geosynthetic Reinforcement
11.10.6.4.2—Design Life Considerations
The provisions of Article 11.5.1 shall apply.
11.10.6.4.2a—Steel Reinforcements
Steel soil reinforcements shall comply with the
provisions of AASHTO LRFD Bridge Construction
Specifications, Article 7.6.4.2, “Steel Reinforcements.”
The structural design of steel soil reinforcements
and connections shall be made on the basis of a
thickness, Ec, as follows:
Ec = En − Es
(11.10.6.4.2a-1)
where:
Ec =
En =
thickness of metal reinforcement at end of
service life as shown in Figure 11.10.6.4.1-1
(mil.)
nominal thickness of steel reinforcement at
construction (mil.)
C11.10.6.4.2a
Corrosion loss rates summarized in Yannas (1985)
and supplemented by field data developed under other
FHWA research studies have been used to establish the
sacrificial thicknesses herein.
The backfill specifications contained in AASHTO
LRFD Bridge Construction Specifications, Section 7, for
MSE structures using steel reinforcements present
minimum electrochemical requirements, which will
generally ensure a mild to moderate potential for
corrosion. Where deicing salts are used, adequate
drainage provisions for salt laden runoff is required. In
some cases, an impervious membrane may be required
between the pavement structure and the select backfill.
Criteria for evaluating potential corrosion losses are
given in Elias et. al (2009).
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
Es =
sacrificial thickness of metal expected to be lost
by uniform corrosion during service life of
structure (mil.)
For structural design, sacrificial thicknesses shall be
computed for each exposed surface as follows, assuming
that the soil backfill used is nonaggressive:
•
•
11-77
Loss of galvanizing
Loss of carbon steel
=
0.58 mil./yr. for
first 2 years
=
0.16 mil./yr. for
subsequent years
=
0.47 mil./yr. after
zinc depletion
Soils shall typically be considered nonaggressive if they
meet the following criteria:
•
pH = 5 to 10
•
Resistivity ≥3000 ohm-cm
•
Chlorides ≤100 ppm
•
Sulfates ≤200 ppm
•
Organic Content ≤1 percent
If the resistivity is greater than or equal to
5000 ohm-cm, the chlorides and sulfates requirements
may be waived. For bar mat or grid-type reinforcements,
the sacrificial thickness listed above shall be applied to
the radius of the wire or bar when computing the
cross-sectional area of the steel remaining after
corrosion losses.
Transverse and longitudinal grid members shall be
sized in accordance with ASTM A185. The transverse
wire diameter shall be less than or equal to the
longitudinal wire diameter.
Galvanized coatings shall be a minimum of 2 oz./ft2
or 3.4 mils. in thickness, applied in conformance to
AASHTO M 111M/M 111 (ASTM A123/A 123M) for
strip-type reinforcements or ASTM A641 for bar mat or
grid-type steel reinforcement.
These sacrificial thicknesses account for potential
pitting mechanisms and much of the uncertainty due to
data scatter, and are considered to be maximum
anticipated losses for soils which are defined as
nonaggressive.
Recommended test methods for soil chemical
property determination include AASHTO T 289 I for
pH, AASHTO T 288 I for resistivity, AASHTO T 291 I
for chlorides and AASHTO T 290 I for sulfates.
These sacrificial thickness requirements are not
applicable for soils which do not meet one or more of
the nonaggressive soil criteria. Additionally, these
sacrificial thickness requirements are not applicable in
applications where:
•
The MSE wall will be exposed to a marine or other
chloride rich environment,
•
The MSE wall will be exposed to stray currents
such as from nearby underground power lines or
adjacent electric railways,
•
The backfill material is aggressive, or
•
The galvanizing thickness is less than specified in
these guidelines.
Each of these situations creates a special set of
conditions which should be specifically analyzed by a
corrosion specialist. Alternatively, noncorrosive
reinforcing elements can be considered. Furthermore,
these corrosion rates do not apply to other metals. The
use of alloys such as aluminum and stainless steel is not
recommended.
Requiring the transverse wire diameter to be less
than or equal to the longitudinal wire diameter will
preclude local overstressing of the longitudinal wires.
Corrosion-resistant coatings should generally be
limited to galvanization.
There is insufficient evidence at this time regarding
the long-term performance of epoxy coatings for these
coatings to be considered equivalent to galvanizing. If
epoxy-type coatings are used, they should meet the
requirements of ASTM A884 for bar mat and grid
reinforcements, or AASHTO M 284M/M 284 for strip
reinforcements, and have a minimum thickness of
16 mils.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.10.6.4.2b—Geosynthetic Reinforcements
Within specific limits of wall application, soil
conditions, and polymer type, strength degradation due
to environmental factors can be anticipated to be
minimal and relatively consistent from product-toproduct, and the impact of any degradation which does
occur will be minimal. This allows application of a
single default reduction factor, RF, to the ultimate
tensile strength to account for long-term strength losses,
as described in Article 11.10.6.4.3b.
Where wall application limits, soil aggressiveness
and polymer requirements are consistent with the
conditions below, a single default reduction factor
specified herein may be used:
•
Poor performance of failure will not have severe
consequences
•
The soil is considered nonaggressive
•
The polymer material meets the requirements
provided in Table 11.10.6.4.2b-1
C11.10.6.4.2b
The durability of geosynthetic reinforcement is
influenced by environmental factors such as time,
temperature, mechanical damage, stress levels and
chemical exposure, e.g., oxygen, water, and pH, which
are the most common chemical factors. Microbiological
attack may also affect certain polymers, although not
most polymers used for carrying load in soil
reinforcement applications. The effects of these factors
on product durability are dependent on the polymer type
used, i.e., resin type, grade, additives, and
manufacturing process, and the macrostructure of the
reinforcement. Not all of these factors will have a
significant effect on all geosynthetic products.
Therefore, the response of geosynthetic reinforcements
to these long-term environmental factors is product
specific.
1) Structure Application Issues: Identification of
applications for which the consequences of poor
performance or failure are severe shall be as
described in Article 11.5.1. In such applications, a
single default reduction factor shall not be used for
final design.
2)
Determination of Soil Aggressiveness: Soil
aggressiveness for geosynthetics shall be assessed
based on the soil pH, gradation, plasticity, organic
content, and in-ground temperature. Soil shall be
defined as nonaggressive if the following criteria
are met:
•
pH, as determined by AASHTO T 289, I = 4.5 to 9
for permanent applications and 3 to 10 for
temporary applications,
•
Maximum soil particle size is less than 0.75 in.,
unless full scale installation damage tests are
conducted in accordance with ASTM D5818,
•
Soil organic content, as determined by AASHTO
T 267 for material finer than the 0.0787 in. (No. 10)
sieve ≤1 percent, and
•
Design temperature at wall site:
≤ 86°F for permanent applications
≤ 95°F for temporary applications
Soil backfill not meeting these requirements as
provided herein shall be considered to be aggressive.
The environment at the face, in addition to that within
the wall backfill, shall be evaluated, especially if the
stability of the facing is dependent on the strength of the
geosynthetic at the face, i.e., the geosynthetic
The effective design temperature is defined as the
temperature which is halfway between the average
yearly air temperature and the normal daily air
temperature for the warmest month at the wall site. Note
that for walls which face the sun, it is possible that the
temperature immediately behind the facing could be
higher than the air temperature. This condition should be
considered when assessing the design temperature,
especially for wall sites located in warm, sunny
climates.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-79
reinforcement forms the primary connection between the
body of the wall and the facing.
The chemical properties of the native soil
surrounding the mechanically stabilized soil backfill
shall also be considered if there is potential for seepage
of groundwater from the native surrounding soils to the
mechanically stabilized backfill. If this is the case, the
surrounding soils shall also meet the chemical criteria
required for the backfill material if the environment is to
be considered nonaggressive, or adequate long-term
drainage around the geosynthetic reinforced mass shall
be provided to ensure that chemically aggressive liquid
does not enter into the reinforced backfill.
3) Polymer Requirements: Polymers which are likely
to have good resistance to long-term chemical
degradation shall be used if a single default
reduction factor is to be used, to minimize the risk
of the occurrence of significant long-term
degradation. The polymer material requirements
provided in Table 11.10.6.4.2b-1 shall, therefore, be
met if detailed product specific data as described in
AASHTO PP 66 and Elias, et al. (2009) is not
obtained. Polymer materials not meeting the
requirements in Table 11.10.6.4.2b-1 may be used if
this detailed product specific data extrapolated to
the design life intended for the structure are
obtained.
Guidelines for product-specific studies to determine
RF are provided in Elias et al. (2001) and Elias (2000).
For applications involving:
Guidelines for product-specific studies to determine
RF are provided in Elias et al. (2009) and AASHTO
PP 66, a provisional standard that is based on WSDOT
Standard Practice T925 (WSDOT, 2009). Independent
product-specific data from which RF may be determined
can be obtained from the AASHTO National
Transportation Product Evaluation Program (NTPEP)
website at http://www.ntpep.org.
•
Severe consequences of poor performance or
failure,
•
Aggressive soil conditions,
•
Polymers not meeting the specific requirements set
in Table 11.10.6.4.2b-1, or
•
A desire to use an overall reduction factor less than
the default reduction factor recommended herein,
then product-specific durability studies shall be carried
out prior to product use to determine the productspecific long-term strength reduction factor, RF. These
product-specific studies shall be used to estimate the
short-term and long-term effects of these environmental
factors on the strength and deformational characteristics
of the geosynthetic reinforcement throughout the
reinforcement design life.
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2012
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11-80
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 11.10.6.4.2b-1—Minimum Requirements for Geosynthetic Products to Allow Use of Default Reduction Factor for
Long-Term Degradation
Polymer Type
Polypropylene
Property
UV Oxidation Resistance
Test Method
ASTM D4355
Polyethylene
UV Oxidation Resistance
ASTM D4355
Polypropylene
Polyester
Thermo-Oxidation
Resistance
Thermo-Oxidation
Resistance
Hydrolysis Resistance
Polyester
Hydrolysis Resistance
ENV ISO 13438:1999,
Method A
ENV ISO 13438:1999,
Method B
Intrinsic Viscosity Method
(ASTM D4603) and GRI
Test Method GG8, or
Determine Directly Using
Gel Permeation
Chromatography
ASTM D7409
All Polymers
Survivability
All Polymers
% Post-Consumer
Recycled Material by
Weight
Polyethylene
Weight per Unit Area
(ASTM D5261)
Certification of Materials
Used
Criteria to Allow Use of
Default RF
Minimum 70% strength
retained after 500 hrs. in
weatherometer
Minimum 70% strength
retained after 500 hrs. in
weatherometer
Minimum 50% strength
retained after 28 days
Minimum 50% strength
retained after 56 days
Minimum Number
Average Molecular
Weight of 25000
Maximum of Carboxyl
End Group Content of 30
Minimum 270 g/m2
Maximum of 0%
11.10.6.4.3—Design Tensile Resistance
11.10.6.4.3a—Steel Reinforcements
The nominal reinforcement tensile resistance is
determined by multiplying the yield stress by the
cross-sectional area of the steel reinforcement after
corrosion losses (see Figure 11.10.6.4.1-1). The loss in
steel cross-sectional area due to corrosion shall be
determined in accordance with Article 11.10.6.4.2a. The
reinforcement tensile resistance shall be determined as:
Tal =
Ac Fy
b
(11.10.6.4.3a-1)
where:
Taℓ =
Fy =
Ac =
b
=
nominal long-term reinforcement design
strength (kips/ft)
minimum yield strength of steel (ksi)
area of reinforcement corrected for corrosion
loss (Figure 11.10.6.4.1-1) (in.2)
unit width of reinforcement (Figure 11.10.6.4.1-1)
(ft)
11.10.6.4.3b—Geosynthetic Reinforcements
The nominal long-term reinforcement tensile
strength shall be determined as:
C11.10.6.4.3b
Taℓ is the long-term tensile strength required to
prevent rupture calculated on a load per unit of
reinforcement width basis. Tult is the ultimate tensile
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2012
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
Tal =
Tult
RF
(11.10.6.4.3b-1)
where:
RF = RFID × RFCR × RFD
(11.10.6.4.3b-2)
11-81
strength of the reinforcement determined from wide
width tensile tests specified in ASTM D4595 for
geotextiles and ASTM D6637 for geogrids. The value
selected for Tult is the minimum average roll value
(MARV) for the product to account for statistical
variance in the material strength.
and:
Taℓ
=
Tult
=
RF
=
RFID
=
RFCR
=
RFD
=
nominal long-term reinforcement design
strength (kips/ft)
minimum average roll value (MARV)
ultimate tensile strength (kips/ft)
combined strength reduction factor to
account
for
potential
long-term
degradation due to installation damage,
creep and chemical aging (dim.)
strength reduction factor to account for
installation damage to reinforcement
(dim.)
strength reduction factor to prevent longterm creep rupture of reinforcement (dim.)
strength reduction factor to prevent rupture
of reinforcement due to chemical and
biological degradation (dim.)
Values for RFID, RFCR, and RFD shall be determined
from product specific test results as specified in
Article 11.10.6.4.2b. Even with product specific test
results, neither RFID nor RFD shall be less than 1.1.
For wall applications which are defined as not
having severe consequences should poor performance or
failure occur, having nonaggressive soil conditions, and
if the geosynthetic product meets the minimum
requirements listed in Table 11.10.6.4.3b-1, the longterm tensile strength of the reinforcement may be
determined using a default reduction factor for RF as
provided in Table 11.10.6.4.3b-1 in lieu of productspecific test results.
Guidelines for determination of RFID, RFCR, and
RFD from product-specific data are provided in
AASHTO PP 66 and Elias et al. (2009). PP 66 is based
on WSDOT Standard Practice T925 (WSDOT, 2009).
Independent product-specific data from which RFID,
RFCR, and RFD may be determined can be obtained from
the AASHTO National Transportation Product
Evaluation
Program
(NTPEP)
website
at
http://www.ntpep.org.
Note that RFD is generally not based on long-term
performance testing unless the soil is considered to be
chemically aggressive. Instead, for typical soil defined
as chemically nonaggressive, the index tests and criteria
identified in Table 11.10.6.4.2b-1 are used to establish a
default value for RFD that can be used in combination
with the product specific values of RFID and RFCR to
determine a product specific value of RF to use for
design. For products meeting the requirements in Table
11.10.6.4.2b-1 used in chemically nonaggressive soil, a
default value of RFD of 1.3 may be used (AASHTO,
2010; WSDOT, 2009; Berg, et al., 2009). Additional
guidance on the selection of RFD is provided in Berg, et
al. (2009).
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2012
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11-82
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 11.10.6.4.3b-1—Default and Minimum Values for the Total Geosynthetic Ultimate Limit State Strength Reduction
Factor, RF
Application
All applications, but with product-specific data obtained and
analyzed in accordance with AASHTO PP 66
Permanent applications not having severe consequences should poor
performance or failure occur, nonaggressive soils, and polymers
meeting the requirements listed in Table 11.10.6.4.2b-1
Temporary applications not having severe consequences should poor
performance or failure occur, nonaggressive soils, and polymers
meeting the requirements listed in Table 11.10.6.4.2b-1 provided
product-specific data are not available
Total Reduction Factor, RF
All reduction factors shall be based on
product specific data. Neither RFID nor RFD
shall be less than 1.1.
7.0
3.5
11.10.6.4.4—Reinforcement/Facing Connection
Design Strength
11.10.6.4.4a—Steel Reinforcements
Connections shall be designed to resist
stresses resulting from active forces, To, in
Article 11.10.6.2.2, as well as from differential
movements between the reinforced backfill and the wall
facing elements.
Elements of the connection which are embedded in
the facing element shall be designed with adequate bond
length and bearing area in the concrete to resist the
connection forces. The capacity of the embedded
connector shall be checked by tests as required in
Article 5.11.3. Connections between steel reinforcement
and the wall facing units, e.g., welds, bolts, pins, etc.,
shall be designed in accordance with Article 6.13.3.
Connection materials shall be designed to
accommodate losses due to corrosion in accordance with
Article 11.10.6.4.2a. Potential differences between the
environment at the face relative to the environment
within the reinforced soil mass shall be considered when
assessing potential corrosion losses.
11.10.6.4.4b—Geosynthetic Reinforcements
The portion of the connection embedded in the
concrete facing shall be designed in accordance with
Article 5.11.3.
The nominal long-term geosynthetic connection
strength Tac on a load per unit reinforcement width basis
shall be determined as follows:
Tac =
Tult × CRcr
RFD
(11.10.6.4.4b-1)
where:
Tac
=
nominal long-term reinforcement/facing
connection design strength per unit of
reinforcement width at a specified
confining pressure (kips/ft)
C11.10.6.4.4b
The long-term creep reduced geosynthetic strength at
the connection with the wall facing is obtained by
reducing Tult by CRcr using the connection/seam strength
determined in accordance with long-term connection
strength test protocol as described in Appendix A of Elias
et al. (2001). The connection test is similar in nature to a
wide width tensile test (ASTM D4595 or ASTM D6637),
except that one end of the reinforcement material is
sandwiched between two courses of concrete blocks to
form one of the grips. This protocol consists of a series of
connection creep tests carried out over an extended period
of time to evaluate the potential for creep rupture at the
connection. CRcr is taken as the creep reduced connection
strength, Tcrc, extrapolated to the specified design life,
divided by the ultimate wide width tensile strength
(ASTM D4595 or D6637) for the reinforcement material
lot used for the connection strength testing, Tlot.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
Tult
=
CRcr
=
RFD
=
minimum average roll value (MARV)
ultimate tensile strength of soil
reinforcement (kips/ft)
long-term connection strength reduction
factor to account for reduced ultimate
strength resulting from connection (dim.)
reduction factor to prevent rupture of
reinforcement due to chemical and biological
degradation (Article 11.10.6.4.3b) (dim.)
11-83
CRcr may also be obtained from short-term connection
test (ASTM D4884 for seam connections, or NCMA Test
Method SRWU-1 in Simac et al. (1993) for segmental
concrete block connections) results, which are to obtain a
short-term ultimate connection strength reduction factor
CRu. Cru is taken as the ultimate connection strength Tultconn
from SRWU-1 or ASTM D4884, divided by Tlot as
described above. In this case, CRu must be further reduced
by the creep reduction factor RFCR (Article 11.10.6.4.3b) in
order to account for the potential of creep rupture as
follows:
CRcr =
CRu
RFCR
(C11.10.6.4.4b-1)
For reinforcements connected to the facing through
embedment between facing elements, e.g., segmental
concrete block faced walls, the capacity of the
connection is conceptually governed by one of two
failure modes: rupture, or pullout of the reinforcement.
This is consistent with the evaluation of internal wall
stability in the reinforced backfill zone, where both the
rupture and pullout mode of failure must be considered.
The objective of the connection design is to assess
the long-term capacity of the connection. If rupture is
the mode of failure, the long-term effects of creep and
durability on the geosynthetic reinforcement at the
connection, as well as on the connector materials, must
be taken into account, as the capacity of the connection
is controlled by the reinforcement or connector longterm strength. If pullout is the mode of failure, the
capacity of the connection is controlled by the frictional
interface between the facing blocks and the geosynthetic
reinforcement. It is assumed for design that this interface
is not significantly affected by time dependent
mechanisms such as creep or chemical degradation. This
again is consistent with the design of the soil
reinforcement within the wall backfill. The load bearing
fibers or ribs of the geosynthetic do not necessarily have
to experience rupture in the connection test for the mode
of failure to be rupture. If the connector is a material that
is susceptible to creep, failure of the connectors between
blocks due to creep rupture of the connector could result
in long-term connection strength losses. In these cases,
the value of CRcr and RFD to be used in
Eq. C11.10.6.4.4b-1 should be based on the durability of
the connector, not the geosynthetic.
Regardless of the failure mode, the long-term
connection test referenced in Elias et al. (2001)
addresses the long-term capacity of the connection.
Eq. C11.10.6.4.4b-1 above should also be considered to
conservatively apply to both failure modes, if the longterm connection test is not performed.
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2012
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11-84
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Values for RFCR and RFD shall be determined from
product-specific test results, except as otherwise
specified herein. The environment at the wall face
connection may be different than the environment away
from the wall face in the wall backfill. This shall be
considered when determining RFCR and RFD.
CRcr shall be determined at the anticipated vertical
confining pressure at the wall face between the facing
blocks. The vertical confining pressure shall be
calculated using the Hinge Height Method as shown in
Figure 11.10.6.4.4b-1 for a face batter, ω, of greater than
8 degrees. Tac should not be greater than Taℓ.
Geosynthetic walls may be designed using a
flexible reinforcement sheet as the facing using only an
overlap with the main soil reinforcement. The overlaps
shall be designed using a pullout methodology. By
replacing Tmax with To, Eq. 11.10.6.3.2-1 may be used to
determine the minimum overlap length required, but in
no case shall the overlap length be less than 3.0 ft. If tan
ρ is determined experimentally based on soil to
reinforcement contact, tan ρ shall be reduced by
30 percent where reinforcement to reinforcement contact
is anticipated.
If the connectors between blocks are intended to be
used for maintaining block alignment during wall
construction and are not intended for long-term
connection shear capacity, the alignment connectors
should be removed before assessing the connection
capacity
for
the
selected
block-geosynthetic
combination. If the pins or other connection devices are
to be relied upon for long-term capacity, the durability
of the connector material must be established.
Requirements for determining RFCR and RFD from
product-specific data are provided in Article 11.10.6.4.3b
and its commentary. The use of default reduction factors
may be acceptable where the reinforcement load is
maximum, i.e., in the middle of the wall backfill, and still
not be acceptable at the facing connection if the facing
environment is defined as aggressive.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-85
Figure 11.10.6.4.4b-1—Determination of Hinge Height for Segmental Concrete Block Faced MSE Walls
The hinge height, Hh, shown in Figure 11.10.6.4.4b-1,
shall be determined as:
H h = 2 [(Wu − Gu − 0.5 H u tan ib ) cos ib ] tan ( ω + ib )
(11.10.6.4.4b-2)
where:
Hu =
Wu =
Gu =
ω =
H =
Hh =
segmental facing block unit height (ft)
segmental facing block unit width, front to
back (ft)
distance to the center of gravity of a horizontal
segmental facing block unit, including
aggregate fill, measured from the front of the
unit (ft)
wall batter due to setback per course (degrees)
total height of wall (ft)
hinge height (ft)
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.10.7—Seismic Design of MSE Walls
11.10.7.1—External Stability
C11.10.7.1
External stability evaluation of MSE walls for
seismic loading conditions shall be conducted as
specified in Article 11.6.5, except as modified in this
Article for MSE wall design.
Wall mass inertial forces (PIR) shall be calculated
based on an effective mass having a minimum width
equal to the structural facing width (Wu) plus a portion
of the reinforced backfill equal to 50 percent of the
effective height of the wall. For walls in which the wall
backfill surface is horizontal, the effective height shall
be taken equal to H in Figure 11.10.7.1-1. For walls with
sloping backfills, the inertial force, PIR, shall be based
on an effective mass having a height H2 and a base
width equal to a minimum of 0.5 H2, in which H2 is
determined as follows:
H2 = H +
0.5 H tan ( β )
1 − 0.5 tan ( β )
Since the reinforced soil mass is not really a rigid
block, the inertial forces generated by seismic shaking
are unlikely to peak at the same time in different
portions of the reinforced mass when reinforcing strips
or layers start becoming very long, as in the case of
MSE walls with steep backslopes in moderately- tohighly seismic areas. This introduces excessive
conservatism if the full length of the reinforcing strips is
used in the inertia determination. Past design practice, as
represented in previous editions of these Specifications,
recommended that wall mass inertial force be limited to
a soil volume equal to 50 percent of the effective height
of the wall.
(11.10.7.1-1)
where:
β
=
slope of backfill (degrees)
PIR for sloping backfills shall be determined as:
PIR = Pir + Pis
(11.10.7.1-2)
where:
Pir =
Pis =
the inertial force caused by acceleration of the
reinforced backfill (kips/ft)
the inertial force caused by acceleration of the
sloping soil surcharge above the reinforced
backfill (kips/ft)
PIR shall act at the combined centroid of reinforced
wall mass inertial force, Pir, and the inertial force
resulting from the mass of the soil surcharge above the
reinforced wall volume, Pis. Pir shall include the inertial
force from the wall facing. The determination of
the MSE wall inertial forces shall be as illustrated in
Figure 11.10.7.1-1.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-87
Reinforcement Layer
Mass for Inertial Force
Reinforced
Soil Mass
Retained
Backfill
Φr γr K r
Φ f Yf k af
Center of
Dynamic Mass
PIR
H
PAE
W
H
3
0.5H
B
Mass for Resisting Forces
(a) Level Backfill Condition
β
Mass for Inertial Force
Retained
Backfill
Φf
Retained
Backfill
Φ f γf k af
γf k af
Pis
Reinforced
Soil Mass
h
Φr γr k r
PIR
H2
H
γr
Center of
Dynamic Mass
PAE
β
Pir
W
h
3
0.5H2
Mass for Resisting Forces
(b) Sloping Backfill Condition
Figure 11.10.7.1-1—Seismic External Stability of an MSE Wall
11.10.7.2—Internal Stability
Reinforcements shall be designed to withstand
horizontal forces generated by the internal inertia force,
Pi, and the static forces. The total inertia force, Pi, per
unit length of structure shall be considered equal to the
mass of the active zone times the wall acceleration
coefficient, kh, reduced for lateral displacement of the
wall during shaking. The reduced acceleration
coefficient, kh, should be consistent with the value of kh
used for external stability.
C11.10.7.2
In past design practice, as presented in previous
editions of these Specifications, the design method for
seismic internal stability assumes that the internal
inertial forces generating additional tensile loads in the
reinforcement act on an active pressure zone that is
assumed to be the same as that for the static loading
case. A bilinear zone is defined for inextensible
reinforcements such as metallic strips and a linear zone
for extensible strips.
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
For walls with inextensible (e.g., steel)
reinforcement, this inertial force shall be distributed to
the reinforcements proportionally to their resistant areas
on a load per unit width of wall basis as follows:
Tmd = γPi
Lei
(11.10.7.2-1)
m
( Lei )
i =1
For walls with extensible reinforcement, this
inertial force shall be distributed uniformly to the
reinforcements on a load per unit width of wall basis as
follows:
P
Tmd = γ i
n
(11.10.7.2-2)
where:
Tmd
=
γ
=
Pi
=
KhWa
=
n
=
Lei
=
factored incremental dynamic inertia force
at Layer i (kips/ft)
load factor for EQ loads from Table
3.4.1-1 (dim.)
internal inertia force due to the weight of
backfill within the active zone, i.e., the
shaded area on Figure 11.10.7.2-1 (kips/ft)
where Wa is the weight of the active zone
and Kh is calculated as specified in
Article 11.6.5.1.
total number of reinforcement layers in the
wall (dim)
effective reinforcement length for layer i
(ft)
This pressure distribution should be determined
from the total inertial force using kh (after reduction for
wave scattering and lateral displacement).
The total factored load applied to the reinforcement
on a load per unit of wall width basis as shown in
Figure 11.10.7.2-1 is determined as follows:
(11.10.7.2-3)
Ttotal = Tmax + Tmd
where:
Tmax = the factored static
the
reinforcements
Eq. 11.10.6.2.1-2.
Whereas it could reasonably be anticipated that
these active zones would extend outwards for seismic
cases, as for M-O analyses, results from numerical and
centrifuge models indicate that the reinforcement
restricts such outward movements and only relatively
small changes in location are seen.
In past design practice, as presented in previous
editions of these Specifications, the total inertial force is
distributed to the reinforcements in proportion to the
effective resistant lengths, Lei. This approach follows the
finite element modeling conducted by Segrestin and
Bastick (1988) and leads to higher tensile forces in
lower reinforcement layers.
In the case of internal stability evaluation, Vrymoed
(1989) used a tributary area approach that assumes that
the inertial load carried by each reinforcement layer
increases linearly with height above the toe of the wall
for equally spaced reinforcement layers. A similar
approach was used by Ling et al. (1997) in limit
equilibrium analyses as applied to extensible
geosynthetic reinforced walls. This concept would
suggest that longer reinforcement lengths could be
needed at the top of walls with increasing acceleration
levels, and the AASHTO approach could be
unconservative, at least for geosynthetic reinforced
walls. Numerical modeling of both steel and
geosynthetic reinforced walls by Bathurst and Hatami
(1999) shows that the distribution of the reinforcement
load increase caused by seismic loading tends to become
more uniform with depth as the reinforcement stiffness
decreases, resulting in a uniform distribution for
geosynthetic reinforced wall systems and a triangular
distribution for typical steel reinforced wall systems.
Hence, the Segrestin and Bastick (1988) method has
been preserved for steel reinforced wall systems and, for
geosynthetic reinforced wall systems, a uniform load
distribution approach is specified.
With regard to the horizontal acceleration
coefficient, kh, past editions of these Specifications have
not allowed kh to be reduced to account for lateral
deformation. Based on the excellent performance of
MSE walls in earthquakes to date, it appears that this is
likely a conservative assumption and it is therefore
reasonable to allow reduction of kh for internal stability
design corresponding to the lateral displacement
permitted in the design of the wall for external stability.
load applied to
determined
using
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
ψ
11-89
= angle of active zone boundary as determined from Figure 11.10.6.3.1-1.
Figure 11.10.7.2-1—Seismic Internal Stability of an MSE Wall
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2012
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11-90
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
For geosynthetic reinforcement rupture, the
reinforcement shall be designed to resist the static and
dynamic components of the load determined as:
For the static component:
S rs ≥
Tmax RF
φRc
(11.10.7.2-4)
For the dynamic component:
S rt ≥
Tmd RFID RFD
φRc
(11.10.7.2-5)
where:
φ
=
Srs
=
Srt
=
Rc
=
RF
=
RFID
=
RFD
=
The reinforcement must be designed to resist the
dynamic component of the load at any time during its
design life. Design for static loads requires the strength
of the reinforcement at the end of the design life to be
reduced to account for creep and other degradation
mechanisms. Strength loss in polymeric materials due to
creep requires long term, sustained loading. The
dynamic component of load for seismic design is a
transient load and does not cause strength loss due to
creep. The resistance of the reinforcement to the static
component of load, Tmax, must, therefore, be handled
separately from the dynamic component of load, Tmd.
The strength required to resist Tmax must include the
effects of creep, but the strength required to resist Tmd
should not include the effects of creep.
resistance
factor
for
combined
static/earthquake
loading
from
Table 11.5.7-1 (dim.)
ultimate reinforcement tensile resistance
required to resist static load component
(kips/ft)
ultimate reinforcement tensile resistance
required to resist dynamic load component
(kips/ft)
reinforcement coverage ratio specified in
Article 11.10.6.4.1 (dim.)
combined strength reduction factor to
account
for
potential
long-term
degradation due to installation damage,
creep, and chemical aging specified in
Article 11.10.6.4.3b (dim.)
strength reduction factor to account for
installation damage to reinforcement
specified in Article 11.10.6.4.3b (dim.)
strength reduction factor to prevent rupture
of reinforcement due to chemical and
biological degradation specified in
Article 11.10.6.4.3b (dim.)
The required ultimate tensile resistance of the
geosynthetic reinforcement shall be determined as:
Tult = S rs + S rt
(11.10.7.2-6)
For pullout of steel or geosynthetic reinforcement:
Le ≥
Ttotal
φ (0.8F ∗ α σv C Rc )
(11.10.7.2-7)
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-91
where:
Le
=
Ttotal
=
φ
=
F*
α
σv
=
=
=
C
=
Rc
=
length of reinforcement in resisting zone
(ft)
maximum factored reinforcement tension
from Eq. 11.10.7.2-2 (kips/ft)
resistance factor for reinforcement pullout
from Table 11.5.7-1 (dim.)
pullout friction factor (dim.)
scale effect correction factor (dim.)
unfactored vertical stress at the
reinforcement level in the resistant zone
(ksf)
overall reinforcement surface area
geometry factor (dim.)
reinforcement coverage ratio specified in
Article 11.10.6.4.1 (dim.)
For seismic loading conditions, the value of F*, the
pullout resistance factor, shall be reduced to 80 percent
of the value used for static design, unless dynamic
pullout tests are performed to directly determine the F*
value.
11.10.7.3—Facing Reinforcement Connections
C11.10.7.3
Facing elements shall be designed to resist the
seismic
loads
determined
as
specified
in
Article 11.10.7.2, i.e., Ttotal. Facing elements shall be
designed in accordance with applicable provisions of
Sections 5, 6, and 8 for reinforced concrete, steel, and
timber, respectively, except that for the Extreme Event I
limit state, all resistance factors should be 1.0, unless
otherwise specified for this limit state.
For segmental concrete block faced walls, the
blocks located above the uppermost backfill
reinforcement layer shall be designed to resist toppling
failure during seismic loading.
For geosynthetic connections subjected to seismic
loading, the factored long-term connection strength,
φTac, must be greater than Tmax + Tmd. If the connection
strength is partially or fully dependent on friction
between the facing blocks and the reinforcement, the
connection strength to resist seismic loads shall be
reduced to 80 percent of its static value as follows:
For the static component of the load:
S rs ≥
Tmax RFD
0.8φCRcr Rc
(11.10.7.3-1)
For the dynamic component of the load:
S rt ≥
Tmd RFD
0.8φCRu Rc
(11.10.7.3-2)
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
where:
Srs
=
Tmax
RFD
=
=
φ
CRcr
=
=
Rc
=
Srt
=
Tmd
=
CRu
=
ultimate reinforcement tensile resistance
required to resist static load component
(kip/ft)
applied load to reinforcement (kip/ft)
reduction factor to prevent rupture of
reinforcement due to chemical and
biological degradation specified in
Article 11.10.6.4.4b (dim.)
resistance factor from Table 11.5.7-1 (dim.)
long-term connection strength reduction
factor to account for reduced ultimate
strength resulting from connection (dim.)
reinforcement coverage ratio from
Article 11.10.6.4.1 (dim.)
ultimate reinforcement tensile resistance
required to resist dynamic load component
(kip/ft)
factored incremental dynamic inertia force
(kip/ft)
short-term reduction factor to account
for reduced ultimate strength resulting
from connection as specified in
Article C11.10.6.4.4b (dim.)
For mechanical connections that do not rely on a
frictional component, the 0.8 multiplier may be removed
from Eqs. 11.10.7.3-1 and 11.10.7.3-2.
The required ultimate tensile resistance of the
geosynthetic reinforcement at the connection is:
Tult = S rs + S rt
(11.10.7.3-3)
For structures in seismic performance Zones 3 or 4,
facing connections in segmental block faced walls shall
use shear resisting devices between the facing blocks
and soil reinforcement such as shear keys, pins, etc., and
shall not be fully dependent on frictional resistance
between the soil reinforcement and facing blocks.
The connection capacity of a facing/reinforcement
connection system that is fully dependent on the shear
resisting devices for the connection capacity will not be
significantly influenced by the normal stress between
facing blocks. The percentage of connection load carried
by the shear resisting devices relative to the frictional
resistance to meet the specification requirements should
be determined based on past successful performance of
the connection system.
Some judgment may be required to determine
whether or not a specific shear resisting device or
combination of devices is sufficient to meet this
requirement in Seismic Performance Zones 3 and 4. The
ability of the shear resisting device or devices to keep
the soil reinforcement connected to the facing, should
vertical acceleration significantly reduce the normal
force between the reinforcement and the facing blocks,
should be evaluated. Note that in some cases, coarse
angular gravel placed within the hollow core of the
facing blocks, provided that the gravel can remain
interlocked during shaking, can function as a shear
restraining device to meet the requirements of this
Article.
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2012
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11.10.7.4—Wall Details for Improved Seismic
Performance
The details specified in Article 11.6.5.6 for gravity
walls should also be addressed for MSE walls in
seismically active areas, defined as Seismic Zone 2 or
higher. The following additional requirements should
also be addressed for MSE walls:
•
Second Stage Fascia Panels: The connections used
to connect the fascia panels to the main gravity wall
structure should be designed to minimize movement
between panels during shaking.
•
Soil Reinforcement Length: A minimum soil
reinforcement length of 0.7H should be used. A
greater soil reinforcement length in the upper 2 to
4.0 ft of wall height (a minimum of two
reinforcement layers) should also be considered to
improve the seismic performance of the wall. If the
wall is placed immediately in front of a very steep
slope, existing shoring, or permanent wall, the
reinforcement within the upper 2.0 to 4.0 ft of wall
height (a minimum of two reinforcement layers,
applicable to wall heights of 10.0 ft or more) should
be extended to at least 5.0 ft behind the steep slope
or existing wall.
•
Wall Corners and Abrupt Facing Alignment
Changes: Should be designed using specially
formed facing units to bridge across the corner and
overlap with the adjacent wall facing units to
prevent the corner from opening up during shaking.
Wall corners should also be designed for the
potential for higher loads to develop than would be
determined using two-dimensional analysis. Wall
corners and short radius turns are defined as having
an enclosed angle of 120 degrees or less.
11-93
C11.10.7.4
These recommended details are based on previous
experiences with walls in earthquakes (e.g., see Yen et
al., 2011). Walls that did not address these details tended
to have a higher frequency of problems than walls that
did consider these details.
With regard to preventing joints from opening
up during shaking, corners details, and details
for addressing protrusions through the wall face,
Article C11.6.5.6 applies. For panel-faced MSE walls
placed against a cast-in-place (CIP) concrete curtain
wall or similar structure, a 4.0-in. lip on the CIP
structure to cover the joint with the MSE wall facing has
been used successfully.
Regarding the design of wall corners and abrupt
changes in the facing alignment (e.g., corners and short
radius turns at an enclosed angle of 120 degrees or less),
both static and seismic earth pressure loading may be
greater than what would be determined from twodimensional analysis. Historically, corners and abrupt
alignment changes in walls have had a higher incidence
of performance problems during earthquakes than
relatively straight sections of the wall alignment, as the
corners tend to attract dynamic load and increased earth
pressures. This should be considered when designing a
wall corner for seismic loading. For that portion of the
corner or abrupt wall facing alignment change where the
soil reinforcement cannot achieve its full length required
to meet internal stability requirements, the end of the
reinforcement layer should be structurally tied to the
back of the adjacent panel. Reinforcement layers should
be placed in both directions. In addition, the special
corner facing element should also have reinforcement
layers attached to it to provide stability for the corner
panel. The reinforcement layers that are tied to both
sides of the corner should be designed for the higher
earth pressures considering the corner as a bin structure.
Note that the corner or abrupt alignment change
enclosed angle as defined in the previous paragraph can
either be internal or external to the wall.
With regard to wall backfill materials, the
provisions of Article 11.6.5.6 shall apply.
When structures and foundations within the active
zone of the reinforced wall backfill are present
significant wall movements and damage have occurred
during earthquakes due to inadequate reinforcement
length behind the facing due to the presence of a
foundation, drainage structure, or other similar structure.
The details provided in Article 11.10.10.4 are especially
important to implement for walls subjected to seismic
loading.
Past experience with second stage precast
incremental facing panels indicates that performance
problems can occur if the connections between the
panels and the first stage wall can rotate or otherwise
have some looseness, especially if wall settlement is not
complete. Therefore, incremental second stage facia
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
panels should be avoided for walls located in seismically
active areas. Full height second stage precast or cast-inplace concrete panels have performed more consistently,
provided the panels are installed after wall settlement is
essentially complete.
A minimum soil reinforcement length of 0.7H has
been shown to consistently provide good performance of
MSE walls in earthquakes. Extending the upper two
layers of soil reinforcement a few feet behind the 0.7H
reinforcement length has in general resulted in modest
improvement in the wall deformation in response to
seismic loading, especially if higher silt content backfill
must be used. If MSE walls are placed in front of
structures or hard soil or rock steep slopes that could
have different deformation characteristics than the MSE
wall reinforced backfill, there is a tendency for a crack
to develop at the vertical or near-vertical boundary of
the two materials. Soil reinforcements that extend an
adequate distance behind the boundary have been shown
to prevent such a crack from developing. It is especially
important to extend the length of the upper
reinforcement layers if there is inadequate room to have
a reinforcement length of 0.7H in the bottom portion of
the wall, provided the requirements of Article 11.10.2.1
and commentary are met.
For additional information on good wall details for
MSE walls, see Berg et al. (2009).
11.10.8—Drainage
Internal drainage measures shall be considered for
all structures to prevent saturation of the reinforced
backfill and to intercept any surface flows containing
aggressive elements.
MSE walls in cut areas and side-hill fills with
established groundwater levels shall be constructed with
drainage blankets in back of, and beneath, the reinforced
zone.
For MSE walls supporting roadways which are
chemically deiced in the winter, an impervious
membrane may be required below the pavement and just
above the first layer of soil reinforcement to intercept
any flows containing deicing chemicals. The membrane
shall be sloped to drain away from the facing to an
intercepting longitudinal drain outletted beyond the
reinforced zone. Typically, a roughened surface PVC,
HDPE or LLDPE geomembrane with a minimum
thickness of 30 mils. should be used. All seams in the
membrane shall be welded to prevent leakage.
11.10.9—Subsurface Erosion
The provisions of Article 11.6.3.5 shall apply.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-95
11.10.10—Special Loading Conditions
11.10.10.1—Concentrated Dead Loads
The distribution of stresses within and behind the
wall resulting from concentrated loads applied to the
wall top or behind the wall shall be determined in
accordance with Article 3.11.6.3.
Figure 11.10.10.1-1 illustrates the combination of
loads using superposition principles to evaluate external
and internal wall stability. Depending on the size and
location of the concentrated dead load, the location of
the boundary between the active and resistant zones may
have to be adjusted as shown in Figure 11.10.10.1-2.
Notes:
These equations assume that concentrated dead load #2 is located within the active zone behind the reinforced soil mass.
For relatively thick facing elements, (e.g., segmental concrete facing blocks), it is acceptable to include the facing dimensions and
weight in sliding, overturning, and bearing capacity calculations (i.e., use B in lieu of L).
PV1, PH1, Δσv1, Δσv2, ΔσH2, and I2 are as determined from Figures 3.11.6.3-1 and 3.11.6.3-2, and Fp results from PV2 (i.e., KΔσv2
from Figure 3.11.6.3-1. H is the total wall height at the face. hp is the distance between the centroid of the trapezoidal distribution
shown and the bottom of that distribution.
Figure 11.10.10.1-1—Superposition of Concentrated Dead Loads for External and Internal Stability Evaluation
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure 11.10.10.1-2—Location of Maximum Tensile Force Line in Case of Large Surcharge Slabs
(Inextensible Reinforcements)
11.10.10.2—Traffic Loads and Barriers
Traffic loads shall be treated as uniform surcharge
loads in accordance with the criteria outlined in
Article 3.11.6.2. The live load surcharge pressure shall
not be less than 2.0 ft of earth. Parapets and traffic
barriers, constructed over or in line with the front face of
the wall, shall be designed to resist overturning moments
by their own mass. Base slabs shall not have any
transverse joints, except construction joints, and adjacent
slabs shall be joined by shear dowels. The upper layer(s)
of soil reinforcements shall have sufficient tensile
capacity to resist a concentrated horizontal load of γPH
where PH = 10 kips distributed over a barrier length of 5.0
ft. This force distribution accounts for the local peak force
in the soil reinforcements in the vicinity of the
concentrated load. This distributed force would be equal
to γPH1 where PH1 = 2.0 kips/ft and is applied as shown in
Figure 3.11.6.3-2a. γPH1 would be distributed to the
reinforcements assuming bf equal to the width of the base
slab. Adequate space shall be provided laterally between
the back of the facing panels and the traffic barrier/slab to
allow the traffic barrier and slab to resist the impact load
in sliding and overturning without directly transmitting
load to the top facing units.
For checking pullout safety of the reinforcements, the
lateral traffic impact load shall be distributed to the upper
C11.10.10.2
The force distribution for pullout calculations is
different than that used for tensile calculations because
the entire base slab must move laterally to initiate a
pullout failure due to the relatively large deformation
required.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-97
soil reinforcement using Figure 3.11.6.3-2a, assuming bf
equal to the width of the base slab. The full-length of
reinforcements shall be considered effective in resisting
pullout due to the impact load. The upper layer(s) of soil
reinforcement shall have sufficient pullout capacity to
resist a horizontal load of γPH1 where PH1 = 10.0 kips
distributed over a 20.0 ft base slab length.
Due to the transient nature of traffic barrier impact
loads, when designing for reinforcement rupture, the
geosynthetic reinforcement must be designed to resist
the static and transient (impact) components of the load
as follows:
Refer to C11.10.7.2 which applies to transient
loads, such as impact loads on traffic barriers, as well as
earthquake loads.
For the static component, see Eq. 11.10.7.2-3.
For the transient components:
Δσ H Sv ≤
φS rt Rc
RFID RFD
(11.10.10.2-1)
where:
ΔσH
=
Sv
Srt
=
=
Rc
=
RFID =
RFD
=
traffic barrier impact stress applied over
reinforcement
tributary
area
per
Article 11.10.10.1 (ksf)
vertical spacing of reinforcement (ft)
ultimate reinforcement tensile resistance
required to resist dynamic load component
(kips/ft)
reinforcement coverage ratio from
Article 11.10.6.4.1 (dim.)
strength reduction factor to account for
installation damage to reinforcement from
Article 11.10.6.4.3b (dim.)
strength reduction factor to prevent rupture
of reinforcement due to chemical
and
biological
degradation
from
Article 11.10.6.4.3b (dim.)
The reinforcement strength required for the static
load component must be added to the reinforcement
strength required for the transient load component to
determine the required total ultimate strength using
Eq. 11.10.7.3-3.
Parapets and traffic barriers shall satisfy crash
testing requirements as specified in Section 13. The
anchoring slab shall be strong enough to resist the
ultimate strength of the standard parapet.
Flexible post and beam barriers, when used, shall be
placed at a minimum distance of 3.0 ft from the wall
face, driven 5.0 ft below grade, and spaced to miss the
reinforcements where possible. If the reinforcements
cannot be missed, the wall shall be designed accounting
for the presence of an obstruction as described in
Article 11.10.10.4. The upper two rows of reinforcement
shall be designed for an additional horizontal load γPH1,
where PH1 = 300 lbs. per linear ft of wall, 50 percent of
which is distributed to each layer of reinforcement.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.10.10.3—Hydrostatic Pressures
For structures along rivers and streams, a minimum
differential hydrostatic pressure equal to 3.0 ft of water
shall be considered for design. This load shall be applied
at the high-water level. Effective unit weights shall be
used in the calculations for internal and external stability
beginning at levels just below the application of the
differential hydrostatic pressure.
11.10.10.4—Obstructions in the Reinforced Soil
Zone
C11.10.10.3
Situations where the wall is influenced by tide or
river fluctuations may require that the wall be designed
for rapid drawdown conditions, which could result in
differential hydrostatic pressure considerably greater
than 3.0 ft, or alternatively rapidly draining backfill
material such as shot rock or open graded coarse gravel
can be used as backfill. Backfill material meeting the
gradation requirements in the AASHTO LRFD Bridge
Construction Specifications for MSE structure backfill is
not considered to be rapid draining.
C11.10.10.4
If the placement of an obstruction in the wall soil
reinforcement zone such as a catch basin, grate inlet,
signal or sign foundation, guardrail post, or culvert
cannot be avoided, the design of the wall near the
obstruction shall be modified using one of the following
alternatives:
1) Assuming reinforcement layers must be partially or
fully severed in the location of the obstruction,
design the surrounding reinforcement layers to carry
the additional load which would have been carried
by the severed reinforcements.
Field cutting of longitudinal or transverse wires of
metal grids, e.g., bar mats, should not be allowed unless
one of the alternatives in Article 11.10.10.4 is followed
and compensating adjustment is made in the wall
design.
2) Place a structural frame around the obstruction
capable of carrying the load from the reinforcements
in front of the obstruction to reinforcements
connected to the structural frame behind the
obstruction as illustrated in Figure 11.10.10.4-1.
3) If the soil reinforcements consist of discrete strips
and depending on the size and location of the
obstruction, it may be possible to splay the
reinforcements around the obstruction.
For Alternative 1, the portion of the wall facing in
front of the obstruction shall be made stable against a
toppling (overturning) or sliding failure. If this cannot
be accomplished, the soil reinforcements between the
obstruction and the wall face can be structurally
connected to the obstruction such that the wall face does
not topple, or the facing elements can be structurally
connected to adjacent facing elements to prevent this
type of failure.
For the second alternative, the frame and
connections shall be designed in accordance with
Section 6 for steel frames.
For the third alternative, the splay angle, measured
from a line perpendicular to the wall face, shall be
small enough that the splaying does not generate
moment in the reinforcement or the connection of the
reinforcement to the wall face. The tensile resistance of
the splayed reinforcement shall be reduced by the
cosine of the splay angle.
Typically, the splay of reinforcements is limited to a
maximum of 15 degrees.
Note that it may be feasible to connect the soil
reinforcement directly to the obstruction depending on
the reinforcement type and the nature of the
obstruction.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-99
If the obstruction must penetrate through the face of
the wall, the wall facing elements shall be designed to fit
around the obstruction such that the facing elements are
stable, i.e., point loads should be avoided, and such that
wall backfill soil cannot spill through the wall face
where it joins the obstruction. To this end, a collar next
to the wall face around the obstruction may be needed.
If driven piles or drilled shafts must be placed
through the reinforced zone, the recommendations
provided in Article 11.10.11 shall be followed.
Figure 11.10.10.4-1—Structural Connection of Soil Reinforcement around Backfill Obstructions
11.10.11—MSE Abutments
C11.10.11
Abutments on MSE walls shall be proportioned to
meet the criteria specified in Article 11.6.2 through
11.6.6.
The MSE wall below the abutment footing shall be
designed for the additional loads imposed by the footing
pressure and supplemental earth pressures resulting from
horizontal loads applied at the bridge seat and from the
backwall. The footing load may be distributed as
described in Article 11.10.10.1.
The factored horizontal force acting on the
reinforcement at any reinforcement level, Tmax, shall be
taken as:
Tmax = σ Hmax Sv
(11.10.11-1)
where:
σHmax
=
factored horizontal stress at layer i, as
defined by Eq.11.10.11-2 (ksf)
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Sv
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
=
vertical spacing of reinforcement (ft)
Horizontal stresses in abutment reinforced zones
shall be determined by superposition as follows, and as
specified in Article 11.10.10.1:
σ Hmax = γ p (σv k r + Δσv kr + Δσ H )
(11.10.11-2)
where:
γp
=
ΔσH
=
σv
=
Δσv
kr
=
=
ka
=
load factor for vertical earth pressure in
Table 3.4.1-2
magnitude of lateral pressure due to
surcharge (ksf)
vertical soil stress over effective base
width (B – 2e) (ksf)
vertical soil stress due to footing load (ksf)
earth pressure coefficient varying as a
function of ka as specified in
Article 11.10.6.2.1
active earth pressure coefficient specified
in Article 3.11.5.8
The effective length used for calculations of internal
stability under the abutment footing shall be as
described in Article 11.10.10.1 and Figure 11.10.10.1-2.
The minimum distance from the centerline of the
bearing on the abutment to the outer edge of the facing
shall be 3.5 ft. The minimum distance between the back
face of the panel and the footing shall be 6.0 in.
Where significant frost penetration is anticipated,
the abutment footing shall be placed on a bed of
compacted coarse aggregate 3.0 ft thick as described in
Article 11.10.2.2.
The density, length, and cross-section of the soil
reinforcements designed for support of the abutment
shall be carried on the wingwalls for a minimum
horizontal distance equal to 50 percent of the height of
the abutment.
In pile or drilled shaft supported abutments, the
horizontal forces transmitted to the deep foundation
elements shall be resisted by the lateral capacity of the
deep foundation elements by provision of additional
reinforcements to tie the drilled shaft or pile cap into the
soil mass, or by batter piles. Lateral loads transmitted
from the deep foundation elements to the reinforced
backfill may be determined using a P-Y lateral load
analysis technique. The facing shall be isolated from
horizontal loads associated with lateral pile or drilled
shaft deflections. A minimum clear distance of 1.5 ft
shall be provided between the facing and deep
foundation elements. Piles or drilled shafts shall be
specified to be placed prior to wall construction and
cased through the fill if necessary.
The minimum length of reinforcement, based on
experience, has been the greater of 22.0 ft or
0.6 (H + d) + 6.5 ft. The length of reinforcement should
be constant throughout the height to limit differential
settlements across the reinforced zone. Differential
settlements could overstress the reinforcements.
The permissible level of differential settlement at
abutment structures should preclude damage to
superstructure units. This subject is discussed in
Article 10.6.2.2. In general, abutments should not be
constructed on mechanically stabilized embankments if
anticipated differential settlements between abutments
or between piers and abutments are greater than one-half
the limiting differential settlements described in
Article C10.5.2.2.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-101
The equilibrium of the system should be checked at
each level of reinforcement below the bridge seat.
Due to the relatively high bearing pressures near the
panel connections, the adequacy and ultimate capacity
of panel connections should be determined by
conducting pullout and flexural tests on full-sized
panels.
Moments should be taken at each level under
consideration about the centerline of the reinforced mass
to determine the eccentricity of load at each level. A
uniform vertical stress is then calculated using a
fictitious width taken as (B − 2e), and the corresponding
horizontal stress should be computed by multiplying by
the appropriate coefficient of lateral earth pressure.
11.11—PREFABRICATED MODULAR WALLS
11.11.1—General
C11.11.1
Prefabricated modular systems may be considered
where conventional gravity, cantilever or counterfort
concrete retaining walls are considered.
Prefabricated modular wall systems, whose
elements may be proprietary, generally employ
interlocking soil-filled reinforced concrete or steel
modules or bins, rock filled gabion baskets, precast
concrete units, or dry cast segmental masonry concrete
units (without soil reinforcement) which resist earth
pressures by acting as gravity retaining walls.
Prefabricated modular walls may also use their structural
elements to mobilize the dead weight of a portion of the
wall backfill through soil arching to provide resistance
to lateral loads. Typical prefabricated modular walls are
shown in Figure C11.11.1-1.
Figure C11.11.1-1—Typical Prefabricated Modular Gravity Walls
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11-102
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Prefabricated modular wall systems shall not be
used under the following conditions:
•
On curves with a radius of less than 800 ft, unless
the curve can be substituted by a series of chords.
•
Steel modular systems shall not be used where the
groundwater or surface runoff is acid contaminated
or where deicing spray is anticipated.
11.11.2—Loading
The provisions of Articles 11.6.1.2 and 3.11.5.9
shall apply, except that shrinkage and temperature
effects need not be considered.
11.11.3—Movement at the Service Limit State
C11.11.3
The provisions of Article 11.6.2 shall apply as
applicable.
Calculated longitudinal differential settlements
along the face of the wall should result in a slope less
than 1/200.
11.11.4—Safety against Soil Failure
11.11.4.1—General
For sliding and overturning stability, the system
shall be assumed to act as a rigid body. Determination of
stability shall be made at every module level.
Passive pressures shall be neglected in stability
computations, unless the base of the wall extends below
the depth of maximum scour, freeze-thaw, or other
disturbance. For these cases only, the embedment below
the greater of these depths may be considered effective
in providing passive resistance.
11.11.4.2—Sliding
The provisions of Article 10.6.3.4 shall apply.
Computations for sliding stability may consider that
the friction between the soil-fill and the foundation soil,
and the friction between the bottom modules or footing
and the foundation soil are effective in resisting sliding.
The coefficient of sliding friction between the soil-fill
and foundation soil at the wall base shall be the lesser of
φf of the soil fill and φf of the foundation soil. The
coefficient of sliding friction between the bottom
modules or footing and the foundation soil at the wall
base shall be reduced, as necessary, to account for any
smooth contact areas.
In the absence of specific data, a maximum friction
angle of 30 degrees shall be used for φf for granular
soils. Tests should be performed to determine the
friction angle of cohesive soils considering both drained
and undrained conditions.
11.11.4.3—Bearing Resistance
The provisions of Article 10.6.3 shall apply.
Bearing resistance shall be computed by assuming
C11.11.4.3
Concrete modular systems are relatively rigid and
are subject to structural damage due to differential
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-103
that dead loads and earth pressure loads are resisted by
point supports per unit length at the rear and front of the
modules or at the location of the bottom legs. A
minimum of 80 percent of the soil weight inside the
modules shall be considered to be transferred to the front
and rear support points. If foundation conditions require
a footing under the total area of the module, all of the
soil weight inside the modules shall be considered.
11.11.4.4—Overturning
settlements, especially in the longitudinal direction.
Therefore, bearing resistance for footing design should
be determined as specified in Article 10.6.
C11.11.4.4
The provisions of Article 11.6.3.3 shall apply.
A maximum of 80 percent of the soil-fill inside the
modules is effective in resisting overturning moments.
The entire volume of soil within the module cannot
be counted on to resist overturning, as some soil will not
arch within the module. If a structural bottom is
provided to retain the soil within the module, no
reduction of the soil weight to compute overturning
resistance is warranted.
11.11.4.5 —Subsurface Erosion
Bin walls may be used in scour-sensitive areas only
where their suitability has been established. The
provisions of Article 11.6.3.5 shall apply.
11.11.4.6—Overall Stability
The provisions of Article 11.6.2.3 shall apply.
11.11.4.7—Passive Resistance and Sliding
The provisions of Articles 10.6.3.4 and 11.6.3.6
shall apply, as applicable.
11.11.5—Safety against Structural Failure
11.11.5.1—Module Members
C11.11.5.1
Prefabricated modular units shall be designed for
the factored earth pressures behind the wall and for
factored pressures developed inside the modules. Rear
face surfaces shall be designed for both the factored
earth pressures developed inside the modules during
construction and the difference between the factored
earth pressures behind and inside the modules after
construction. Strength and reinforcement requirements
for concrete modules shall be in accordance with
Section 5.
Strength requirements for steel modules shall be in
accordance with Section 6. The net section used for
design shall be reduced in accordance with
Article 11.10.6.4.2a.
Factored bin pressures shall be the same for each
module and shall not be less than:
Pb = γ γ s b
Structural design of module members is based on
the difference between pressures developed inside the
modules (bin pressures) and those resulting from the
thrust of the backfill. The recommended bin pressure
relationships are based on relationships obtained for
long trench geometry, and are generally conservative.
(11.11.5.1-1)
where:
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Pb =
γs =
γ =
b
=
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
factored pressure inside bin module (ksf)
soil unit weight (kcf)
load factor for vertical earth pressure specified
in Table 3.4.1-2
width of bin module (ft)
Steel reinforcing shall be symmetrical on both faces
unless positive identification of each face can be ensured
to preclude reversal of units. Corners shall be adequately
reinforced.
11.11.6—Seismic Design for Prefabricated Modular
Walls
The provisions of Article 11.6.5 shall apply.
C11.11.6
The prefabricated modular wall develops resistance
to seismic loads from both the geometry and the weight
of the wall section. The primary design issues for
seismic loading are global stability, external stability
(i.e., sliding, overturning, and bearing), and internal
stability. External stability includes the ability of each
lift within the wall to also meet external stability
requirements. Interlocking between individual structural
sections and the soil fill within the wall needs to be
considered in this evaluation.
The primary difference for this wall type relative to
a gravity or semigravity wall is that sliding and
overturning can occur at various heights between the
base and top of the wall, as this class of walls typically
uses gravity to join sections of the wall together.
The interior of the prefabricated wall elements is
normally filled with soil; this provides both additional
weight and shear between structural elements. The
contributions of the earth, as well as the batter on the
wall, need to be considered in the analysis.
Similar to the other external stability checks, the
overall (global) stability check needs to consider failure
surfaces that pass through the wall section, as well as
below the base of the wall. The check on stability at
midlevel must consider the contributions of both the soil
within the wall and any structural interlocking that
occurs for the particular modular wall type.
When checking stability at the mid level of a wall,
the additional shear resistance from interlocking of
individual wall components will depend on the specific
wall type. Usually, interlocking resistance between wall
components is provided by the wall supplier.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-105
11.11.7—Abutments
Abutment seats constructed on modular units shall
be designed by considering earth pressures and
supplemental horizontal pressures from the abutment
seat beam and earth pressures on the backwall. The top
module shall be proportioned to be stable under the
combined actions of normal and supplementary earth
pressures. The minimum width of the top module shall
be 6.0 ft. The centerline of bearing shall be located a
minimum of 2.0 ft from the outside face of the top
precast module. The abutment beam seat shall be
supported by, and cast integrally with, the top module.
The front face thickness of the top module shall be
designed for bending forces developed by supplemental
earth pressures. Abutment beam-seat loadings shall be
carried to foundation level and shall be considered in the
design of footings.
Differential settlement provisions, specified in
Article 11.10.4, shall apply.
11.11.8—Drainage
In cut and side-hill fill areas, prefabricated modular
units shall be designed with a continuous subsurface
drain placed at, or near, the footing grade and outletted
as required. In cut and side-hill fill areas with
established or potential groundwater levels above the
footing grade, a continuous drainage blanket shall be
provided and connected to the longitudinal drain system.
For systems with open front faces, a surface
drainage system shall be provided above the top of the
wall.
11.12—REFERENCES
2013 Revision
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ASCE Earth Retention Conference 3, Bellevue, WA. American Society of Civil Engineers, Reston, VA, pp. 638–655.
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p. 465.
Chen, W. F. and X.L. Liu. 1990. Limit Analysis in Soil Mechanics. Elsevier, Maryland Heights, MO.
Cheney, R. S. 1984. Permanent Ground Anchors. FHWA-DP-68-1R Demonstration Project. Federal Highway
Administration, U.S. Department of Transportation, Washington, DC, p. 132.
Clough, G. W., and T. D. O′Rouke. 1990. “Construction Induced Movement of In-Situ Walls.” Proceedings ASCE
Specialty Conference Design and Performance of Earth Retaining Structures, Cornell University, Ithaca, NY, 1990.
D’Appolonia. 1999. “Developing New AASHTO LRFD Specifications for Retaining Walls.” Final Report for
NCHRP Project 20-7, Task 88. Transportation Research Board, National Research Council, Washington, DC.
Duncan, J. M., and R. B. Seed. 1986. “Compaction Induced Earth Pressures under Ko-Conditions,” ASCE Journal of
Geotechnical Engineering. American Society of Civil Engineers, New York, NY, Vol. 112, No. 1, pp. 1–22.
Duncan, J. M., G. W. Williams, A. L. Sehn, and R. B. Seed. 1991. “Estimation of Earth Pressures Due to
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Elias, V., Fishman, K. L., Christopher, B. R., and Berg, R. R. 2009. Corrosion/Degradation of Soil Reinforcements for
Mechanically Stabilized Earth Walls and Reinforced Soil Slopes, FHWA-NHI-09-087, Federal Highway
Administration.
FHWA. 1980. Technical Advisory T5140.13. Federal Highways Administration, U.S. Department of Transportation,
Washington, DC.
GRI. 1998. “Carboxyl End Group Content of Polyethylene Terephthalate. PET Yarns.” Geosynthetic Research
Institute Test Method GG7.
GRI. 1998. Determination of the Number Average Molecular Weight of Polyethylene Terephthalate. PET Yarns based
on a Relative Viscosity Value, Test Method GG8. Geosynthetic Research Institute, Philadelphia, PA.
International Standards Organization (ISO). 1999. Geotextiles and Geotextile-Related Products - Screening Test
Method for Determining the Resistance to Oxidation, ENV ISO 13438:1999. International Standards
Organization, Geneva, Switzerland.
Kavazanjian, E., N. Matasovic, T. Hadj-Hamou, and P. J. Sabatini. 1997. “Design Guidance: Geotechnical Earthquake
Engineering for Highways,” Geotechnical Engineering Circular No. 3, Vol. 1—Design Principles,
FHWA-SA-97-076. Federal Highway Administration, U.S. Department of Transportation, Washington, DC.
Kramer, S. L. 1996. Geotechnical Earthquake Engineering. Prentice Hall, Upper Saddle River, NJ.
Lew, M., N. Sitar, and L. Al Atik. 2010a. Seismic Earth Pressures: Fact or Fiction. In Proc., ASCE Earth Retention
Conference
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Lew, M., N. Sitar, L. Al Atik, M. Pouranjani, and M. B. Hudson. 2010b. Seismic Earth Pressures on Deep Building
Basements. In Proc., SEAOC 2010 Convention., September 22–25, 2010, Indian Wells, CA. Structural Engineers
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Ling, H. I., D. Leschinsky, and E. B. Perry. 1997. “Seismic Design and Performance of Geosynthetic-Reinforced Soil
Structures,” Geotechnique. Thomas Tellford, London, UK, Vol. 47, No. 5, pp. 933–952.
Mitchell, J. K. and W. C. B. Villet. 1987. Reinforcement of Earth Slopes and Embankments, NCHRP Report 290.
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Bridges, FHWA RD-85-107. Federal Highway Administration, U.S. Department of Transportation, Washington, DC,
p. 118.
Nakamura, S. 2006. “Reexamination of Mononobe-Okabe Theory of Gravity Retaining Walls Using Centrifuge
Model Tests,” Soils and Foundations. Japanese Geotechnical Society, Tokyo, Japan, Vol. 46, No. 2,
pp. 135–146.
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Hoboken, NJ.
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Symposium on Earthquake Engineering, Roorkee, India, November 1966. Vol. 1, pp. 273–288.
PTI. 1996. Recommendations for Prestressed Rock and Soil Anchors, Third Edition. Post-Tensioning Institute,
Phoenix, AZ.
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Richards R. and X. Shi. 1994. “Seismic Lateral Pressures in Soils with Cohesion,” Journal of Geotechnical
Engineering. American Society of Civil Engineers, Reston, VA, Vol. 120, No. 7, pp. 1230–1251.
Sabatini, P. J., D. G. Pass, and R. C. Bachus. 1999. “Ground Anchors and Anchored Systems.” Geotechnical
Engineering Circular No. 4, FHWA-SA-99-015. Federal Highway Administration, U.S. Department of
Transportation, Washington, DC, p. 281.
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Reinforced Earth Structures,” Transportation Research Record 1675. Transportation Research Board, National
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Seed, H. B. and R. V. Whitman. 1970. “Design of Earth Retaining Structures for Dynamic Loads.” In Proc., ASCE
Specialty Conference on Lateral Stresses in the Ground and Design of Earth Retaining Structures. American Society
of Civil Engineers, NY, pp. 103–147.
Segrestin, P. and M. L. Bastick. 1988. Seismic Design of Reinforced Earth Retaining Walls—The Contribution of
Finite Element Analysis. International Geotechnical Symposium on Theory and Practice of Earth Reinforcement,
Fukuoka, Japan, October 1988.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-109
APPENDIX A11—SEISMIC DESIGN OF RETAINING STRUCTURES
A11.1—GENERAL
This Appendix provides information that supplements the provisions contained in Section 11 regarding the design
walls and free standing abutments for seismic loads. Detailed design methodology is provided for the calculation of
seismic earth pressures, both active and passive. Design methodology is also provided for the estimation of
deformation effects on the seismic acceleration a wall will experience.
A11.2—PERFORMANCE OF WALLS IN PAST EARTHQUAKES
Even as early as 1970, Seed and Whitman (1970) concluded that “many walls adequately designed for static earth
pressures will automatically have the capacity to withstand earthquake ground motions of substantial magnitudes and,
in many cases, special seismic provisions may not be needed.” Seed and Whitman further indicated that this
statement applies to gravity and semigravity walls with peak ground accelerations up to 0.25g. More recently, Bray et
al. (2010) and Lew et al. (2010a, 2010b) indicate that lateral earth pressure increases due to seismic ground motion are
likely insignificant for peak ground accelerations of 0.3g to 0.4g or less, indicating that walls designed to resist static
loads (i.e., the strength and service limit states) will likely have adequate stability for the seismic loading case,
especially considering that load and resistance factors used for Extreme Event I limit state design are at or near 1.0.
Following the 1971 San Fernando earthquake, Clough and Fragaszy (1977) assessed damage to floodway
structures, consisting of reinforced concrete cantilever (vertical) walls structurally tied to a floor slab forming a
continuous U-shaped structure. They found that no damage was observed where peak ground accelerations along the
structures were less than 0.5g. However, damage and wall collapse was observed where accelerations were higher
than 0.5g or localized damage where the structures crossed the earthquake fault and the damage was quite localized.
They noted that while higher strength steel rebar was used in the actual structure than required by the static design, the
structure was not explicitly designed to resist seismic loads. Gazetas et al. (2004) observed that cantilever semigravity
walls with little or no soil surcharge exposed to shaking in the 1999 Athens earthquake performed well for peak
ground accelerations up to just under 0.5g even though the walls were not specifically designed to handle seismic
loads. Lew et al. (1995) made similar observations with regard to tied back shoring walls in the 1994 Northridge
Earthquake and Tatsuoka (1996) similarly observed good wall performance for MSE type gravity walls in the 1995
Kobe earthquake. See Bray et al. (2010), Lew et al. (2010a, 2010b), and Al Atik and Sitar (2010) for additional
background on observed wall performance and the generation of seismic earth pressures.
Walls meeting the requirements in Article 11.5.4.2 that allow a seismic analysis to not be conducted have
demonstrated consistently good performance in past earthquakes. For wall performance in specific earthquakes, see
the following:
•
Gravity and semigravity cantilever walls in the 1971 San Fernando Earthquake (Clough and Fragaszy, 1977).
•
Gravity and semigravity cantilever walls in the 1999 Athens Earthquake (Gazetas et al., 2004).
•
Soil nail walls and MSE walls in the 1989 Loma Prieta, California earthquake (Vucetic et al., 1998 and and Collin
et al.,1992, respectively).
•
MSE walls in the 1994 Northridge, California earthquake (Bathurst and Cai, 1995).
•
MSE walls and reinforced concrete gravity walls in the 1995 Kobe, Japan earthquake (Tatsuoka et al., 1996).
•
MSE walls and concrete gravity and semigravity walls in the 2010 Maule, Chile earthquake (Yen et al., 2011).
•
Summary of the performance of various types of walls (Koseki et al., 2006).
•
Reinforced earth walls withstand Northridge Earthquake (Frankenberger et al., 1996).
•
The Performance of Reinforced Earth Structures in the Vicinity of Kobe during the Great Hanshin Earthquake
(Kobayashi et al, 1996).
•
Evaluation of Seismic Performance in Mechanically Stabilized Earth Structures (Sankey et al., 2001).
However, there have been some notable wall failures in past earthquakes. For example, Seed and Whitman (1970)
indicated that some concrete gravity walls and quay walls (both gravity structures and anchored sheet pile nongravity
cantilever walls), in the great Chilean Earthquake of 1960 and in the Niigata, Japan Earthquake of 1964, suffered
severe displacements or even complete collapse. In most of those cases, significant liquefaction behind or beneath the
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wall was the likely cause of the failure. Hence, Article 11.5.4.2 specifies that a seismic analysis should be performed
if liquefaction or severe strength loss in sensitive clays can cause instability of the wall. Seed and Whitman (1970)
indicate, however, that collapse of walls located above the water table has been an infrequent occurrence.
Tatsuoka et al. (1996) indicated that several of the very old (1920s to 1960s) unreinforced masonry gravity walls
and concrete gravity structures exposed to strong shaking in the 1995 Kobe Japan earthquake did collapse. In those
cases, collapse was likely due to the presence of weak foundation soils that had inadequate bearing and sliding
resistance and, in a few cases, due to the presence of a very steep sloping surcharge (e.g., 1.5H:1V) combined with
poor soil conditions. Soil liquefaction may have been a contributing factor in some of those cases. These wall
collapses were mostly located in the most severely shaken areas (e.g., as high as 0.6g to 0.8g). As noted previously,
Clough and Fragaszy (1977) observed concrete cantilever walls supporting open channel floodways that had collapsed
where peak ground accelerations were 0.5g or more in the 1971 San Fernando earthquake. However, in that case, soil
conditions were good. All of these wall cases where collapse or severe damage/deformations occurred are well outside
of the conditions and situations where Article 11.5.4.2 allows the seismic design of walls to be waived.
Setting the limit at 0.4g for the Article 11.5.4.2 no seismic analysis provision represents a reasonable compromise
between observations from laboratory modeling and full-scale wall situations (i.e., lab modeling indicates that seismic
earth pressures are very low, below 0.4g, and walls in actual earthquakes start to have serious problems, including
collapses even in relatively good soils, when the acceleration is greater than 0.5g and the wall has not been designed
for the full seismic loading). However, if soil strength loss and flow due liquefaction or strength loss in sensitive silts
and clays occurs, wall collapse can occur at lower acceleration values. Note that for the lab model studies, the 0.4g
limit represents the limit at which significant seismic earth pressure does not appear to develop. However, for walls
with a significant structural mass, the inertial force on the wall mass itself can still occur at accelerations less than
0.4g. At 0.4g, the combination of seismic earth pressure and wall inertial force is likely small enough still to not
control the forces in the wall and its stability, provided the wall mass is not large. For typical gravity walls, the wall
mass would not be large enough to offset the lack of seismically increased earth pressure below 0.4g. A possible
exception regarding wall mass inertial forces is reinforced soil walls, though that inertial mass consists of soil within
the reinforced soil zone. However, due to their flexibility, reinforced soil walls perform better than reinforced concrete
walls, so the inertial mass issue may not be as important for that type of wall. Note that experience with walls in actual
earthquakes in which the walls have not been designed for seismic loads is limited. So while all indications are that
major wall problems do not happen until the acceleration is greater than As of 0.5g, the majority of those walls where
such observations could be made have been strengthened to resist some degree of seismic loading. If walls are not
designed for seismic loads, it is reasonable to back off a bit from the observed 0.5g threshold. Hence, 0.4g represents a
reasonable buffer relative to potential severe wall damage or collapse as observed for walls in earthquakes at 0.5g or
more.
Based on previous experience, walls that form tunnel portals have tended to exhibit more damage due to
earthquakes than free-standing walls. It is likely that the presence of the tunnel restricts the ability of the portal wall to
move, increasing the seismic forces to which the wall is subjected. Hence, a seismic design is recommended in such
cases.
A11.3—CALCULATION OF SEISMIC ACTIVE PRESSURE
Seismic active earth pressures have historically been estimated using the Mononabe-Okabe Method. However,
this method is not applicable in some situations. More recently, Anderson et al. (2008) have suggested a generalized
limit equilibrium method (GLE) that is more broadly applicable. Both methods are provided herein. Specifications
which should be used to select which method to use are provided in Article 11.6.5.3.
A11.3.1—Mononobe-Okabe Method
2013 Revision
The method most frequently used for the calculation of the seismic soil forces acting on a bridge abutment or
free-standing wall is a pseudostatic approach developed in the 1920s by Mononobe (1929) and Okabe (1926). The
Mononobe-Okabe analysis is an extension of the Coulomb sliding-wedge theory, taking into account horizontal and
vertical inertia forces acting on the soil. The analysis is described in detail by Seed and Whitman (1970) and Richards
and Elms (1979). The following assumptions are made:
1.
The abutment is free to yield sufficiently to enable full soil strength or active pressure conditions to be mobilized.
If the abutment is rigidly fixed and unable to move, the soil forces will be much higher than those predicted by
the Mononobe-Okabe analysis.
2.
The backfill is cohesionless, with a friction angle of φ.
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SECTION 11: WALLS, ABUTMENTS, AND PIERS
3.
11-111
The backfill is unsaturated, so that liquefaction problems will not arise.
The M-O Method is illustrated in Figure A11.3.1-1 and the equation used to calculate KAE follows the figure.
Figure A11.3.1-1—Mononobe-Okabe Method Force Diagrams
K AE
sin ( φ + δ ) sin ( φ − θMO − i )
=
× 1 −
2
cos ( δ + β + θMO ) cos ( i − β )
cos θMO cos β cos ( δ + β + θMO )
cos 2 ( φ − θMO − B )
−2
(A11.3.1-1)
where:
KAE
γ
H
h
φf
θMO
δ
kh
kv
i
β
=
=
=
=
=
=
=
=
=
=
=
seismic active earth pressure coefficient (dim)
unit weight of soil (kcf)
height of wall (ft)
height of wall at back of wall heel considering height of sloping surcharge, if present (ft)
friction angle of soil (degrees)
arc tan [kh/(1 – kv)] (degrees)
wall backfill interface friction angle (degrees)
horizontal seismic acceleration coefficient (dim.)
vertical seismic acceleration coefficient (dim.)
backfill slope angle (degrees)
slope of wall to the vertical, negative as shown (degrees)
In discussion of the M-O method to follow, H and h should be considered interchangeable, depending on the type
of wall under consideration (see Figure A11.3.1-1).
Mononobe and Matsuo (1932) originally suggested that the resultant of the active earth pressure during seismic
loading remain the same as for when only static forces are present (i.e., H/3 or h/3). However, theoretical
considerations by Wood (1973), who found that the resultant of the dynamic pressure acted approximately at
midheight and empirical considerations from model studies summarized by Seed and Whitman (1970) who suggested
that ha could be obtained by assuming that the static component of the soil force acts at H/3 from the bottom of the
wall and the additional dynamic effect acts at a height of 0.6H, resulted in increasing the height of the resultant
location above the wall base. Therefore, in past practice, designers have typically assumed that ha = H/2 with a
uniformly distributed pressure. Note that if the wall has a protruding heel or if the wall is an MSE wall then replace H
with h in the preceding discussion.
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Back analysis of full-scale walls in earthquakes, however, indicates earth pressure resultants located higher than
h/3 will overestimate the force, resulting in a prediction of wall failure when in reality the wall performed well
(Clough and Fragaszy, 1977). Recent research indicates the location of the resultant of the total earth pressure (static
plus seismic) should be located one-third up from the wall based on centrifuge model tests on gravity walls (Al Atik
and Sitar, 2010; Bray et al., 2010; and Lew et al., 2010). However, recent work by others (Nakamura, 2006) also
indicates that the resultant location could be slightly higher, depending on the specifics of the ground motion and the
wall details.
A reasonable approach is to assume that for routine walls, the combined static/seismic resultant should be located
at the same location as static earth pressure resultant but no less than h/3. Because there is limited evidence that in
some cases the combined static/seismic resultant location could be slightly higher than the static earth pressure
resultant, a slightly higher resultant location (e.g., 0.4h to 0.5h) for seismic design of walls for which the impact of
wall failure is relatively high should be considered. However, for routine wall designs, a combined static/seismic
resultant location equal to that used for static design (e.g., h/3) is sufficient.
The effects of abutment inertia are not taken into account in the Mononobe-Okabe analysis. Many current
procedures assume that the inertia forces due to the mass of the abutment itself may be neglected in considering
seismic behavior and seismic design. This is not a conservative assumption, and for those abutments relying on their
mass for stability, it is also an unreasonable assumption in that to neglect the mass is to neglect a major aspect of their
behavior. The effects of wall inertia are discussed further by Richards and Elms (1979), who show that wall inertia
forces should not be neglected in the design of gravity-retaining walls.
A11.3.2—Modification of Mononabe-Okabe Method to Consider Cohesion
The M-O equation for seismic active earth pressure determination has many limitations, as discussed in Anderson
et al. (2008). These limitations include the inability to account for cohesion that occurs in the soil. This limitation has
been addressed by rederiving the seismic active earth pressure using a Coulomb-type wedge analysis. Generally, soils
with more than 15 percent fines content can be assumed to be undrained during seismic loading. For this loading
condition, total stress soil parameters, γ and c, should be used.
Eq. A11.3.2-1 that is provided by Anderson et al. (2008), and Figure A11.3.2-1 shows the terms in the equation.
This equation is very simple and practical for the design of the retaining walls and the equation has been calibrated
with slope stability computer programs.
W [ (1− kv )tan(α− φ) + kh ] − C L [sin α tan(α− φ) + cos α] − CA H [ tan(α− φ)cos ω+ sin ω ]
PAE =
[1 + tan(δ+ω)tan(α−φ)] *cos(δ+ω)
A11.3.2-1
The only variables in Eq. A11.3.2-1 are the failure plane angle α and the trial wedge surface length L. Values of
friction angle (φ), seismic horizontal coefficient (kh), seismic vertical coefficient (kv), soil cohesion (C), soil wall
adhesion (Ca), soil wall friction (δ), and soil wall angle (ω) are defined by the designer on the basis of the site
conditions and the U.S. Geological Survey seismic hazard maps shown in Section 3.
The recommended approach in this Section is to assume that kv = 0, and kh = the PGA adjusted for site effects
(i.e., As, kh0, or kh, or some combination thereof, if the wall is greater than 20.0 ft in height and horizontal wall
displacement can occur and is acceptable). A 50 percent reduction in the resulting seismic coefficient is used when
defining kh if 1.0 to 2.0 in. of permanent ground deformation is permitted during the design seismic event. Otherwise,
the peak ground acceleration coefficient should be used. Eq. A11.3.2-1 can be easily calculated in a spreadsheet.
Using a simple spreadsheet, the user can search for the angle α and calculate maximum value of PAE.
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Figure A11.3.2-1—Active Seismic Wedge
The following charts were developed using Eq. A11.3.2-1. These charts are based on level ground behind the wall
and a wall friction (δ) of 0.67φ. Generally, for active pressure determination, the wall interface friction has a minor
effect on the seismic pressure coefficient. However, Eq. A11.3.2-1, the generalized limit equilibrium method, or the
charts can be rederived for the specific interface wall friction if this effect is of concern or interest.
1.0
0.8
C/Ɣ.H=0.00
0.6
Kae
C/Ɣ.H=0.05
C/Ɣ.H=0.10
0.4
C/Ɣ.H=0.15
C/Ɣ.H=0.20
0.2
C/Ɣ.H=0.25
C/Ɣ.H=0.30
0.0
0
0.1
0.2
0.3
0.4
0.5
kh (g)
0.6
0.7
0.8
0.9
1
Figure A11.3.2-2—Seismic Active Earth Pressure Coefficient for φ = 30 degrees (c = soil cohesion, γ = soil unit weight, and
H = retaining wall height)
Note: kh = As = kh0 for wall heights greater than 20 ft. This could be H or h as defined in Figure A11.3.1-1.
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1.0
0.8
C/Ɣ.H=0.00
0.6
Kae
C/Ɣ.H=0.05
C/Ɣ.H=0.10
0.4
C/Ɣ.H=0.15
C/Ɣ.H=0.20
C/Ɣ.H=0.25
0.2
C/Ɣ.H=0.30
0.0
0
0.1
0.2
0.3
0.4
0.5
kh (g)
0.6
0.7
0.8
0.9
1
Figure A11.3.2-3—Seismic Active Earth Pressure Coefficient for φ = 35 degrees (c = soil cohesion, γ = soil unit weight, and
H = retaining wall height)
1.0
0.8
C/Ɣ.H=0.00
0.6
C/Ɣ.H=0.05
Kae
C/Ɣ.H=0.10
C/Ɣ.H=0.15
C/Ɣ.H=0.20
0.4
C/Ɣ.H=0.25
C/Ɣ.H=0.30
0.2
0.0
0
0.1
0.2
0.3
0.4
0.5
kh (g)
0.6
0.7
0.8
0.9
1
Figure A11.3.2-4—Seismic Active Earth Pressure Coefficient for φ = 40 degrees (c = soil cohesion, γ = soil unit weight, and
H = retaining wall height)
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A11.3.3—Generalized Limit Equilibrium (GLE) Method
In some situations, the M-O equation is not suitable due to the geometry of the backfill, the angle of the failure
surface relative to the cut slope behind the wall, the magnitude of ground shaking, or some combination of these
factors (see Article C11.6.5.3). In such situations, a generalized limit equilibrium method involving the use of a
computer program for slope stability is likely to be more suitable for determining the earth pressures required for
retaining wall design.
Steps in the generalized limit equilibrium (GLE) analysis are as follows:
•
Set up the model geometry, groundwater profile, and design soil properties. The internal vertical face at the wall
heel or the plane where the earth pressure needs to be calculated should be modeled as a free boundary.
•
Choose an appropriate slope stability analysis method. Spencer’s method generally yields good results because it
satisfies the equilibrium of forces and moments.
•
Choose an appropriate sliding surface search scheme. Circular, linear, multi-linear, or random surfaces can be
examined in many commercial slope stability analysis programs.
•
Apply the earth pressure as a boundary force on the face of the retained soil. For seismic cases, the location of the
force may be initially assumed at 1/3H) of the retained soil. However, different application points between 1/3H
and 0.6H from the base may be examined to determine the maximum seismic earth pressure force. The angle of
applied force depends on assumed friction angle between the wall and the fill soil (typically 2/3φf for rigid gravity
walls) or the fill friction angle (semigravity walls). If static (i.e., nonseismic) forces are also needed, the location
of the static force is assumed at one-third from base (1/3H, where H is retained soil height).
•
Search for the load location and failure surface giving the maximum load for limiting equilibrium (capacity-todemand ratio of 1.0, i.e., FS = 1.0).
•
Verify design assumptions and material properties by examining the loads on individual slices in the output as
needed.
Additional discussion and guidance regarding this approach is provided in NCHRP Report 611 (Anderson et al.,
2008).
A11.4—SEISMIC PASSIVE PRESSURE
This Section provides charts for determination of seismic passive earth pressures coefficients for a soil with both
cohesion and friction based on the log spiral method. These charts were developed using a pseudostatic equilibrium
method reported in Anderson et al. (2008). The method includes inertial forces within the soil mass, as well as
variable soil surface geometries and loads.
Equations used in this approach are given below. Figure A11.4-1 defines the terms used in the equation.
d Ei =
W i (1 − K v ) [ tan ( α i + φ ) − K h ] + C L i [sin α i tan ( α i + φ ) + co s α i ]
[1 − tan δ i tan ( α i
− φ ) ] * co s δ i
(A11.4-1)
i
PP n =
KPn =
dE
1
1 − tan δ w tan ( α w − φ ) * co s δ w
2 PP
(A11.4-2)
(A11.4-3)
γ h2
where φ is the soil friction angle, c is the cohesion, and δ is wall interface friction.
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Figure A11.4-1—Limits and Shape Seismic Interslice Force Function (reported in Anderson et al., 2008)
As shown, the method of analysis divides the sliding mass of the backfill into many slices. It is assumed that the
shear forces dissipate from a maximum at the wall face (AB) to the induced seismic shear forces at the face (CD) of
the first slice as seen in Figure A11.4-1.
The methodology described above was used to develop a series of charts (Figures A11.4-2 through A11.4-4) for a
level backfill condition. These charts can be used to estimate the seismic passive pressure coefficient. The interface
friction for these charts is 0.67φ. These procedures and charts can be used to estimate the seismic passive coefficient
for other interface conditions and soil geometries.
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Figure A11.4-2—Seismic Passive Earth Pressure Coefficient Based on Log Spiral Procedure for c/γH = 0 and 0.05 (c = soil
cohesion, γ = soil unit weight, and H = height or depth of wall over which the passive resistance acts)
Note: kh = As = kho for wall heights greater than 20 ft.
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Figure A11.4-3—Seismic Passive Earth Pressure Coefficient Based on Log Spiral Procedure for c/γH = 0.1 and 0.15 (c = soil
cohesion, γ = soil unit weight, and H = retaining wall height or depth of wall over which the passive resistance acts)
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Figure A11.4-4—Seismic Passive Earth Pressure Coefficient Based on Log Spiral Procedure for c/γH = 0.2 and 0.25 (c = soil
cohesion, γ = soil unit weight, and H = retaining wall height or depth of wall over which the passive resistance acts)
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A11.5—ESTIMATING WALL SEISMIC ACCELERATION CONSIDERING WAVE SCATTERING AND
WALL DISPLACEMENT
The seismic acceleration acting on a wall during an earthquake is affected by both wave scattering and wall
displacement (see Article 11.6.5.2 and commentary).
With regard to the effects of wall deformation during shaking, the Newmark sliding block concept (Newmark,
1965) was originally developed to evaluate seismic slope stability in terms of earthquake-induced slope displacement
as opposed to a factor of safety against yield under peak slope accelerations. The concept is illustrated in Figure
A11.5-1, where a double integration procedure on accelerations exceeding the yield acceleration of the slope leads to
an accumulated downslope displacement.
The concept of allowing gravity walls to slide during earthquake loading and displacement-based design (i.e.,
using a Newmark sliding block analysis to compute displacements when accelerations exceed the horizontal limiting
equilibrium, yield acceleration for the wall-backfill system) was introduced by Richards and Elms (1979). Based on
this concept, Elms and Martin (1979) suggested that a design acceleration coefficient of 0.5would be adequate for
limit equilibrium pseudostatic design, provided allowance be made for a horizontal wall displacement of 10 PGA in
inches. The PGA term in Elms and Martin is equivalent to the FPGA PGA or kh0 in these Specifications.
For many situations, Newmark analysis or simplifications of it (e.g., displacement design charts or equations
based on the Newmark analysis method for certain typical cases, or the use of kh = 0.5kh0) are sufficiently accurate.
However, as the complexity of the site or the wall-soil system increases, more rigorous numerical modeling methods
may become necessary.
Figure A11.5-1—Newmark Sliding Block Concept
To assess the effects of wave scattering and lateral deformation on the design acceleration coefficient, kh, three
simplified design procedures to estimate the acceleration coefficient are provided in detail in the sub-sections that
follow. The first method (Kavazanjian et al., 1997) does not directly address wave scattering and, since wave
scattering tends to reduce the acceleration, the first method is likely conservative. The second and third methods
account for both wave scattering and wall deformation but are considerably more complex than the first method. With
regard to estimation of wave scattering effects, the second method (Anderson et al. 2008) uses a simplified model that
considers the effect of the soil mass, but not specifically the effect of the wall as a structure, whereas the third method
(Bray et al., 2010) provides a simplified response spectra for the wall, considering the wall to be a structure with a
fundamental period. With regard to the effect of lateral wall deformation on the wall acceleration, both methods are
based on many Newmark analyses, using those analyses to develop empirical relationships between the yield
acceleration for the wall and the soil it retains and the amount of deformation that occurs. The Anderson et al. (2008)
method estimates the wall deformation for input yield acceleration, peak ground acceleration, and peak ground
velocity, whereas the third method (Bray et al. 2010) estimates the reduced acceleration, kh, for a specified
deformation and spectral acceleration at a specified period. The three alternative design procedures should not be
mixed together in any way.
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A11.5.1—Kavazanjian et al., (1997)
Kavazanjian et al. (1997) provided the following simplified relationship based on Newmark sliding analysis,
assuming that the velocity, in the absence of information on the time history of the ground motion, is equal to 30A:
A
kh = 0.74 AS S 0.25
d
(A11.5.1-1)
where:
AS =
kh =
d =
earthquake ground acceleration coefficient as specified in Eq. 3.10.4.2-2 (dim.)
horizontal seismic acceleration coefficient (dim.)
lateral wall displacement (in.)
This equation was included in past editions of these Specifications. This equation should not be used for
displacements of less than 1.0 in. or greater than approximately 8 in., as this equation is an approximation of a more
rigorous Newmark analysis. However, the amount of deformation which is tolerable will depend on the nature of the
wall and what it supports, as well as what is in front of the wall. This method may be more conservative than the more
complex methods that follow. Note that this method does not address wave scattering within the wall, which in most
cases will be conservative.
A11.5.2—NCHRP Report 611—Anderson et al. (2008)
For values of h (as defined in Article 11.6.5.2.2) greater than 20.0 ft but less than 60.0 ft, the seismic coefficient
used to compute lateral loads acting on a freestanding retaining wall may be modified to account for the effects of
spatially varying ground motions behind the wall, using the following equation:
kh = αkh0
(A11.5.2-1)
where:
Kh0 =
α =
αkh0
wall height acceleration reduction factor to account for wave scattering
For Site Class C, D, and E:
α = 1 + 0.01h ( 0.5β − 1)
(A11.5.2-2)
where:
h
β
S1
Fv
=
=
=
=
wall height (ft)
FvS1/ kh0
spectral acceleration coefficient at 1 sec
site class adjustment factor
For Site Classes A and B (hard and soft rock foundation soils), note that kh0 is increased by a factor of 1.2 as specified
in Article 11.6.5.2.1. Eq. A11.5.2-1 provides the value of kh if only wave scattering is considered and not lateral wall
displacement.
For wall heights greater than 60.0 ft, special seismic design studies involving the use of dynamic numerical
models should be conducted. These special studies are required in view of the potential consequences of failure of
these very tall walls, as well as limitations in the simplified wave scattering methodology.
The basis for the height-dependent reduction factor described above is related to the response of the soil mass
behind the retaining wall. Common practice in selecting the seismic coefficient for retaining wall design has been to
assume rigid body soil response in the backfill behind a retaining wall. In this approach the horizontal seismic
coefficient (kh0) is assumed equal to the FPGAPGA when evaluating lateral forces acting on an active pressure failure
zone. Whereas this assumption may be reasonable for wall heights less than about 20.0 ft, for higher walls, the
magnitude of accelerations in soils behind the wall will vary spatially as shown schematically in Figure A11.5.2-1.
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The nature and variation of the ground motions within a wall is complex and could be influenced by the dynamic
response of the wall-soil system to the input earthquake ground motions. In addition to wall height, the acceleration
distribution will depend on factors such as the frequency characteristics of the input ground motions, the stiffness
contrast between backfill and foundation soils, the overall stiffness and damping characteristics of the wall, and wall
slope. From a design standpoint, the net effect of the spatially varying ground motions can be represented by an
averaging process over a potential active pressure zone, leading to a time history of average acceleration and hence a
maximum average acceleration or seismic coefficient as shown in Figure A11.5.2-1.
To evaluate this averaging process, the results of a series of analytical studies are documented in NCHRP Report
611 (Anderson et al., 2008). An evaluation of these results forms the basis for the simplified Eqs. A11.5.2-1 and
A11.5.2-2. The analytical studies included wave scattering analyses assuming elastic soil media using different slope
heights, with slopes ranging from near vertical for short walls to significantly battered for tall walls, as well as slopes
more typical of embankments (3H:1V) and with a range of earthquake time histories. The properties of the continuum
used for these analyses were uniform throughout and therefore did not consider the potential effect of impedance
contrasts between different materials (i.e., the properties of the wall vs. that of the surrounding soil). The acceleration
time histories simulated spectral shapes representative of Western United States (WUS) and Central and Eastern
United States (CEUS) sites and reflected different earthquake magnitudes and site conditions.
Additional height-dependent, one-dimensional SHAKE (Schnaebel et al., 1972) analyses were also conducted to
evaluate the influence of nonlinear soil behavior and stiffness contrasts between backfill and foundation soils. These
studies were also calibrated against finite element studies for MSE walls documented by Segrestin and Bastick (1988),
which form the basis for the average maximum acceleration equation (a function of As) given in previous editions of
these Specifications. The results of these studies demonstrate that the ratio of the maximum average seismic
coefficient (kh) to As (the α factor) is primarily dependent on the wall or slope height and the shape of the acceleration
spectra (the β factor). The acceleration level has a lesser effect.
Figure A11.5.2-1—Average Seismic Coefficient Concept
Sliding block displacement analyses were conducted as part of NCHRP Report 611 (Anderson et al., 2008) using
an extensive database of earthquake records. The objective of these analyses was to establish updated relationships
between wall displacement (d) and the following three terms: the ratio ky/kh0, kh0 as determined in Article 11.6.5.2.1,
and PGV. Two broad groups of ground motions were used to develop these equations, CEUS and WUS, as shown in
Figure A11.5.2-2 (Anderson et al., 2008). Regressions of those analyses result in the following equations that can be
used to estimate the relationship between wall displacement and acceleration.
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Figure A11.5.2-2—Boundary between WUS and CEUS Ground Motions
For all sites except CEUS rock sites (Categories A and B), the mean displacement (in.) for a given yield acceleration
may be estimated as:
1− ky
k
log d = −1.51 − 0.74 log v + 3.27 log
− 0.80 log kh 0 + 1.59 log ( PGV )
kh 0
kh 0
(A11.5.2-3)
where:
ky
=
yield acceleration
For CEUS rock sites (Categories A and B), this mean displacement (in.) may be estimated as:
k
log d = −1.31 − 0.93log v
kh 0
kv
+ 4.52 log 1 −
− 0.46 log ( kh 0 ) + 1.12 log ( PGV )
kh 0
(A11.5.2-4)
Note that the above displacement equations represent mean values.
In Eqs. A11.5.2-3 and A11.5.2-4 it is necessary to estimate the peak ground velocity (PGV) and the yield
acceleration (ky). Values of PGV may be determined using the following correlation between PGV and spectral
ordinates at 1 sec (S1).
(A11.5.2-5)
PGV (in./sec) =38FvS1
where S1 is the spectral acceleration coefficient at 1 sec and Fv is the site class adjustment factor.
The development of the PGV-S1 correlation is based on a simplification of regression analyses conducted on an
extensive earthquake database established from recorded and synthetic accelerograms representative of both rock and
soil conditions for WUS and CEUS. The study is described in NCHRP Report 611 (Anderson et al., 2008). It was
found that earthquake magnitude need not be explicitly included in the correlation, as its influence on PGV is captured
by its influence on the value of S1. The equation is based on the mean from the simplification of the regression
analysis.
Values of the yield acceleration (ky) can be established by computing the seismic coefficient for global stability
that results in a capacity to demand (C/D) ratio of 1.0 (i.e., for overall stability of the wall/slope, the FS = 1.0). A
conventional slope stability program is normally used to determine the yield acceleration. For these analyses, the total
stress (undrained) strength parameters of the soil should usually be used in the stability analysis. See guidance on the
use of soil cohesion for seismic analyses discussed in Article 11.6.5.3 and its commentary.
Once ky is determined, the combined effect of wave scattering and lateral wall displacement d on kh is determined
as follows:
kh = αky
(A11.5.2-6)
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A11.5.3—Bray et al. (2010), and Bray and Travasarou (2009)
The Bray et al. (2010) method (see also Bray and Travasarou, 2009) for estimating the value of kh applied to the
wall mass considers both the wave scattering and lateral deformation of the wall. The method was developed using
688 ground motion records. The method characterizes the ground motion using a spectral acceleration at five percent
damping, the moment magnitude, M, as a proxy for duration of shaking, the fundamental period of the wall, Ts, and
the lateral wall deformation allowed during shaking. In this method, kh is determined as follows:
−a + b
kh = exp
0.66
(A11.5.3-1)
where:
a
b
Sa
d
M
Ts
ε
=
=
=
=
=
=
=
2.83 – 0.566ln(Sa)
a2 – 1.33[ln(d) + 1.10 – 3.04ln(Sa) + 0.244(ln(Sa))2 – 1.5Ts – 0.278(M – 7) – ε]
the five percent damped spectral acceleration coefficient from the site response spectra
the maximum wall displacement allowed, in centimeters
the moment magnitude of the design earthquake
the fundamental period of the wall
a normally distributed random variable with zero mean and a standard deviation of 0.66.
ε should be set equal to zero to estimate kh considering Da to be a mean displacement. To calculate the fundamental
period of the wall, Ts, use the following equation:
Ts = 4H′/Vs
(A11.5.3-2)
where:
H′ =
Vs =
80 percent of the height of the wall, as measured from the bottom of the heel of the wall to the ground surface
directly above the wall heel (or the total wall height at the back of the reinforced soil zone for MSE walls)
the shear wave velocity of the soil behind the wall
Note that Vs and H′ must have consistent units. Shear wave velocities may be obtained from in-situ measurements or
through the use of correlations to the Standard Penetration Resistance (SPT) or cone resistance (qc). An example of
this type of correlation for granular wall backfill materials is shown in Eq. A11.5.3-3 (Imai and Tonouchi, 1982).
Vs = 107N-0.314
(A11.5.3-3)
where:
N = the Standard Penetration Resistance (SPT) of the fill material, uncorrected for overburden pressure but corrected
for hammer efficiency.
The spectral acceleration, Sa, is determined at a degraded period of 1.5Ts from the five percent damped response
spectra for the site (i.e., either the response spectra determined using the general procedure or using a site-specific
response spectra).
To estimate lateral wall displacement for a given acceleration value, see Bray et al. (2010) and Bray and
Travasarou (2009) for details.
A11.6—APPENDIX REFERENCES
Anderson, D. G., G. R. Martin, I. P. Lam, and J. N. Wang. 2008. Seismic Analysis and Design of Retaining Walls,
Slopes and Embankments, and Buried Structures, NCHRP Report 611 National Cooperative Highway Research
Program, Transportation Research Board, National Research Council, Washington, DC.
Bathurst, R. J. and Z. Cai, Z. 1995. “Psuedo-Static Seismic Analysis of Geosynthetic-Reinforced Segmental Retaining
Walls,” Geosynthetics International. International Geosynthetic Society, Jupiter, FL, Vol. 2, No. 5, pp. 787–-830.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 11: WALLS, ABUTMENTS, AND PIERS
11-125
Bray, J. D. and T. Travasarou. 2009. “Pseudostatic Coefficient for Use in Simplified Seismic Slope Stability
Evaluation,” J. of Geotechnical & Geoenvironmental Engineering.American Society of Civil Enginers, Reston, VA,
Vol. 135, No. 9, pp. 1336–1340.
Bray, J. D., T. Travasarou, Tand J. Zupan. 2010. Seismic Displacement Design of Earth Retaining Structures. In
Proc., ASCE Earth Retention Conference 3, Bellevue, WA. American Society of Civil Enginers, Reston, VA,
pp. 638–655.
Clough, G. W. and R. F. Fragaszy. 1977. A Study of Earth Loadings on Floodway Retaining Structures in the 1971
San Fernando Valley Earthquake. In Proc., Sixth World Conference on Earthquake Engineering, New Delhi, India,
January 10–14, 1977, pp. 7-37–7-42. Available in: BSSA. 1978. Bulletin of the Seismological Society of America.
Seismological Society of America, El Cerrito, CA, Vol. 68, No. 2.
Collin, J. G., V. E. Chouery-Curtis, and R. R. Berg, R. R. 1992. “Field Observation of Reinforced Soil Structures
under Seismic Loading,” Earth Reinforcement Practice, S. Havashi, H. Ochiai, and J. Otani,, eds. Taylor & Francis,
Inc., Florence, KY, Vol. 1, pp. 223–228.
Elms, D. A. and G. R. Martin. 1979. Factors Involved in the Seismic Design of Bridge Abutments.” In Proc.,
Workshop on Seismic Problems Related to Bridges. Applied Technology Council, Berkeley, CA.
Frankenberger. P. C., R. A. Bloomfield, and P. L. Anderson. 1996. Reinforced Earth Walls Withstand Northridge
Earthquake. In Proc., International Symposium on Earth Reinforcement, Fukuoka, Kyushu, Japan, November 12–14,
1996. Taylor & Francis, Inc., Florence, KY, pp 345–350.
Gazetas, G., P. N. Psarropoulos, I. Anastasopoulos, and N. Gerolymos. 2004. “Seismic Behavior of Flexible Retaining
Systems Subjected to Short-Duration Moderately Strong Excitation,” Soil Dynamics and Earthquake Engineering.
Elsevier, Maryland Heights, MO, Vol. 24, No. 7, pp. 537–550.
Imai, T. and K. Tonouchi. 1982. Correlations of N value with S-wave velocity and shear modulus. In Proc., Second
European Symposium on Penetration Testing, Amsterdam, The Netherlands, May 24–27, 1982. A. A. Balkema
Publishers, London, UK, pp. 24–27.
International Standards Organization (ISO), 1999. Geotextiles and Geotextile-Related Products—Screening Test
Method for Determining the Resistance to Oxidation, ENV ISO 13438:1999. International Standards Organization,
Geneva, Switzerland.
Kobayashi, K. et al. 1996 The Performance of Reinforced Earth Structures in the Vicinity of Kobe during the Great
Hanshin Earthquake, In Proc., International Symposium on Earth Reinforcement, Fukuoka, Kyushu, Japan, November
12–14, 1996. Taylor & Francis, Inc., Florence, KY, pp. 395–400.
Koseki, J., R. J. Bathurst, E. Guler, J. Kuwano, amd M. Maugeri, M. 2006. Seismic Stability of Reinforced Soil Walls.
Invited Keynote Paper, Eighth International Conference on Geosynthetics, Yokohama, Japan, September 18–22,
2006. IOS Press, Amsterdam, The Netherlands, pp. 1–28.
Lew, M., E. Simantob, and M. E. Hudson. 1995. Performance of shored earth retaining systems during the January 17,
1994, Northridge Earthquake. In Proc., Third International Conference on Recent Advances in Geotechnical
Earthquake Engineering and Soil Dynamics, St. Louis, MO, April 2–7. Vol. 3.
Lew, M., N. Sitar, and L. Al Atik. 2010a. Seismic Earth Pressures: Fact or Fiction. In Proc., ASCE Earth Retention
Conference 3, Bellevue, WA. American Society of Civil Engineers, Reston, VA, pp. 656–673.
Lew, M., N. Sitar, L. Al Atik, M. Pouranjani, and M. B. Hudson. 2010b. Seismic Earth Pressures on Deep Building
Basements. In Proc., SEAOC 2010 Convention, September 22–25, 2010, Indian Wells, CA. Structural Engineers
Association of California, Sacramento, CA, pp. 1–12.
Mononobe, N. 1929. Earthquake-Proof Construction of Masonry Dams. In Proc., World Engineering Congress,
Tokyo, Japan, October–November 1929. Vol. 9, p. 275.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
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Nakamura, S. 2006. “Reexamination of Mononobe-Okabe Theory of Gravity Retaining Walls Using Centrifuge
Model Tests,” Soils and Foundations. Japanese Geotechnical Society, Tokyo, Japan, Vol. 46, No. 2, pp. 135–146.
Newmark, N. M. 1965. “Effects of Earthquakes on Dams and Embankments,” Geotechnique. Thomas Telford Ltd.,
London, UK, Vol. 14, No. 2, pp. 139–160.
Okabe, S. 1926. “General Theory of Earth Pressure.” Journal of the Japanese Society of Civil Engineers, Vol. 12,
No. 1.
Richards, R. and D. G. Elms. 1979. “Seismic Behavior of Gravity Retaining Walls.” Journal of the Geotechnical
Engineering Division, American Society of Civil Engineers, New York, NY, Vol. 105, No. GT4, pp. 449–464.
Sankey, J. E. and P. Segrestin. 2001. “Evaluation of Seismic Performance in Mechanically Stabilized Earth
Structures.” Landmarks in Earth Reinforcement: Proceedings of the International Symposium on Earth Reinforcement
Practice, Fukuoka, Kyushu, Japan, Vol. 1, pp. 449–452.
Seed, H. B. and R. V. Whitman. 1970. Design of Earth Retaining Structures for Dynamic Loads.” In Proc., ASCE
Specialty Conference on Lateral Stresses in the Ground and Design of Earth Retaining Structures. American Society
of Civil Engineers, Reston, VA, pp. 103–147.
Schnabel, P. B., J. Lysmer, and H. B. Seed. 1972. SHAKE: A Computer Program for Earthquake Response Analysis
of Horizontally Layered Sites, Report No. EERC 72-12. Earthquake Engineering Research Center, University of
California, Berkeley, CA.
Segrestin, P. and M. L. Bastick 1988. Seismic Design of Reinforced Earth Retaining Walls—The Contribution of
Finite Element Analysis. In Proc., International Geotechnical Symposium on Theory and Practice of Earth
Reinforcement, Fukuoka, Japan, October 1988. Thomas Telford Ltd., London, UK.
Tatsuoka, F., J. Koseki, and M. Tateyama. 1996. Performance of Reinforced Soil Structures during the 1995 Hyogoken Nanbu Earthquake, IS Kyushu ’96 Special Report. In Proc., International Symposium on Earth Reinforcement,
Fukuoka, Kyushu, Japan, November 12–14, 1996, Ochiai et al., eds. Taylor and Francis, Inc., Florence, KY, pp. 1–36.
Vucetic, M., M. R. Tufenkjian, G. Y. Felio, P. Barar, and K. R. Chapman. 1998. Analysis of Soil-Nailed Excavations
Stability during the 1989 Loma Prieta Earthquake, Professional Paper 1552-D, T. L. Holzer, ed. U.S. Geological
Survey, Washington, DC, pp. 27–46.
Yen, W. P., G. Chen, I. G. Buckle, T. M. Allen, D. Alzamora, J. Ger, and J. G. Arias. 2011. Postearthquake
Reconnaissance Report on Transportation Infrastructure Impact of the February 27, 2010 Offshore Maule
Earthquake in Chile, FHWA Report No. FHWA-HRT-11-030. Federal Highways Administration, U.S. Department of
Transportation, Washington, DC.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12
TABLE OF CONTENTS
12.1—SCOPE ............................................................................................................................................................. 12-1
12.2—DEFINITIONS................................................................................................................................................. 12-1
12.3—NOTATION ..................................................................................................................................................... 12-1
12.4—SOIL AND MATERIAL PROPERTIES ......................................................................................................... 12-6
12.4.1—Determination of Soil Properties............................................................................................................ 12-6
12.4.1.1—General......................................................................................................................................... 12-6
12.4.1.2—Foundation Soils .......................................................................................................................... 12-6
12.4.1.3—Envelope Backfill Soils ............................................................................................................... 12-6
12.4.2—Materials ................................................................................................................................................ 12-7
12.4.2.1—Aluminum Pipe and Structural Plate Structures .......................................................................... 12-7
12.4.2.2—Concrete ....................................................................................................................................... 12-7
12.4.2.3—Precast Concrete Pipe .................................................................................................................. 12-7
12.4.2.4—Precast Concrete Structures ......................................................................................................... 12-7
12.4.2.5—Steel Pipe and Structural Plate Structures ....................................................................................... 12-7
12.4.2.6—Deep Corrugated Structures ......................................................................................................... 12-8
12.4.2.7—Steel Reinforcement..................................................................................................................... 12-8
12.4.2.8—Thermoplastic Pipe ...................................................................................................................... 12-8
12.5—LIMIT STATES AND RESISTANCE FACTORS ......................................................................................... 12-8
12.5.1—General ................................................................................................................................................... 12-8
12.5.2—Service Limit State ................................................................................................................................. 12-9
12.5.3—Strength Limit State ............................................................................................................................... 12-9
12.5.4—Load Modifiers and Load Factors .......................................................................................................... 12-9
12.5.5—Resistance Factors................................................................................................................................ 12-10
12.5.6—Flexibility Limits and Construction Stiffness ...................................................................................... 12-12
12.5.6.1—Corrugated Metal Pipe and Structural Plate Structures.............................................................. 12-12
12.5.6.2—Spiral Rib Metal Pipe and Pipe Arches ...................................................................................... 12-12
12.5.6.3—Flexibility Limits and Construction Stiffness—Thermoplastic Pipe ......................................... 12-13
12.5.6.4—Steel Tunnel Liner Plate ............................................................................................................ 12-13
12.6—GENERAL DESIGN FEATURES ................................................................................................................ 12-13
12.6.1—Loading ................................................................................................................................................ 12-13
12.6.2—Service Limit State ............................................................................................................................... 12-14
12.6.2.1—Tolerable Movement .................................................................................................................. 12-14
12.6.2.2—Settlement .................................................................................................................................. 12-14
12.6.2.2.1—General ............................................................................................................................ 12-14
12.6.2.2.2—Longitudinal Differential Settlement ............................................................................... 12-14
12.6.2.2.3—Differential Settlement between Structure and Backfill .................................................. 12-14
12.6.2.2.4—Footing Settlement ........................................................................................................... 12-14
12.6.2.2.5—Unbalanced Loading ........................................................................................................ 12-15
12.6.2.3—Uplift.......................................................................................................................................... 12-18
12.6.3—Safety against Soil Failure ................................................................................................................... 12-18
12.6.3.1—Bearing Resistance and Stability ............................................................................................... 12-18
12-i
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
12.6.3.2—Corner Backfill for Metal Pipe Arches ...................................................................................... 12-19
12.6.4—Hydraulic Design ................................................................................................................................. 12-19
12.6.5—Scour .................................................................................................................................................... 12-19
12.6.6—Soil Envelope ....................................................................................................................................... 12-19
12.6.6.1—Trench Installations .................................................................................................................... 12-19
12.6.6.2—Embankment Installations .......................................................................................................... 12-19
12.6.6.3—Minimum Cover ......................................................................................................................... 12-20
12.6.7—Minimum Spacing between Multiple Lines of Pipe ............................................................................. 12-21
12.6.8—End Treatment ...................................................................................................................................... 12-22
12.6.8.1—General ....................................................................................................................................... 12-22
12.6.8.2—Flexible Culverts Constructed on Skew ..................................................................................... 12-22
12.6.9—Corrosive and Abrasive Conditions ..................................................................................................... 12-23
12.7—METAL PIPE, PIPE ARCH, AND ARCH STRUCTURES .......................................................................... 12-24
12.7.1—General ................................................................................................................................................. 12-24
12.7.2—Safety against Structural Failure .......................................................................................................... 12-24
12.7.2.1—Section Properties ...................................................................................................................... 12-24
12.7.2.2—Thrust ......................................................................................................................................... 12-24
12.7.2.3—Wall Resistance .......................................................................................................................... 12-25
12.7.2.4—Resistance to Buckling ............................................................................................................... 12-25
12.7.2.5—Seam Resistance ......................................................................................................................... 12-25
12.7.2.6—Handling and Installation Requirements .................................................................................... 12-25
12.7.3—Smooth Lined Pipe ............................................................................................................................... 12-26
12.7.4—Stiffening Elements for Structural Plate Structures .............................................................................. 12-26
12.7.5—Construction and Installation ............................................................................................................... 12-26
12.8—LONG-SPAN STRUCTURAL PLATE STRUCTURES .............................................................................. 12-26
12.8.1—General ................................................................................................................................................. 12-26
12.8.2—Service Limit State ............................................................................................................................... 12-27
12.8.3—Safety against Structural Failure .......................................................................................................... 12-27
12.8.3.1—Section Properties ...................................................................................................................... 12-27
12.8.3.1.1—Cross-Section ................................................................................................................... 12-27
12.8.3.1.2—Shape Control .................................................................................................................. 12-28
12.8.3.1.3—Mechanical and Chemical Requirements ......................................................................... 12-28
12.8.3.2—Thrust ......................................................................................................................................... 12-29
12.8.3.3—Wall Area ................................................................................................................................... 12-29
12.8.3.4—Seam Strength ............................................................................................................................ 12-29
12.8.3.5—Acceptable Special Features ...................................................................................................... 12-29
12.8.3.5.1—Continuous Longitudinal Stiffeners ................................................................................. 12-29
12.8.3.5.2—Reinforcing Ribs .............................................................................................................. 12-29
12.8.4—Safety against Structural Failure—Foundation Design ........................................................................ 12-29
12.8.4.1—Settlement Limits ....................................................................................................................... 12-29
12.8.4.2—Footing Reactions in Arch Structures ........................................................................................ 12-30
12.8.4.3—Footing Design ........................................................................................................................... 12-31
12.8.5—Safety against Structural Failure—Soil Envelope Design .................................................................... 12-31
12.8.5.1—General ....................................................................................................................................... 12-31
12.8.5.2—Construction Requirements ........................................................................................................ 12-31
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12-iii
12.8.5.3—Service Requirements ................................................................................................................ 12-32
12.8.6—Safety against Structural Failure—End Treatment Design .................................................................. 12-33
12.8.6.1—General....................................................................................................................................... 12-33
12.8.6.2—Standard Shell End Types .......................................................................................................... 12-33
12.8.6.3—Balanced Support ....................................................................................................................... 12-35
12.8.6.4—Hydraulic Protection .................................................................................................................. 12-35
12.8.6.4.1—General ............................................................................................................................ 12-35
12.8.6.4.2—Backfill Protection ........................................................................................................... 12-36
12.8.6.4.3—Cut-Off (Toe) Walls ........................................................................................................ 12-36
12.8.6.4.4—Hydraulic Uplift ............................................................................................................... 12-36
12.8.6.4.5—Scour ................................................................................................................................ 12-36
12.8.7—Concrete Relieving Slabs ..................................................................................................................... 12-36
12.8.8—Construction and Installation ............................................................................................................... 12-37
12.8.9—Deep Corrugated Structural Plate Structures ....................................................................................... 12-37
12.8.9.1—General....................................................................................................................................... 12-37
12.8.9.2—Width of Structural Backfill ...................................................................................................... 12-37
12.8.9.2.1—Deep Corrugated Structures with Ratio of Crown Radius to Haunch Radius ≤5 ............ 12-37
12.8.9.2.2—Deep Corrugated Structures with Ratio of Crown Radius to Haunch Radius >5 ............ 12-37
12.8.9.3—Safety against Structural Failure ................................................................................................ 12-38
12.8.9.3.1—Structural Plate Requirements ......................................................................................... 12-38
12.8.9.3.2—Structural Analysis .......................................................................................................... 12-38
12.8.9.4—Minimum Depth of Fill .............................................................................................................. 12-38
12.8.9.5—Combined Thrust and Moment .................................................................................................. 12-39
12.8.9.6—Global Buckling ......................................................................................................................... 12-40
12.8.9.7—Connections ............................................................................................................................... 12-40
12.9—STRUCTURAL PLATE BOX STRUCTURES ............................................................................................ 12-40
12.9.1—General ................................................................................................................................................. 12-40
12.9.2—Loading ................................................................................................................................................ 12-41
12.9.3—Service Limit State ............................................................................................................................... 12-41
12.9.4—Safety against Structural Failure .......................................................................................................... 12-41
12.9.4.1—General....................................................................................................................................... 12-41
12.9.4.2—Moments Due to Factored Loads ............................................................................................... 12-42
12.9.4.3—Plastic Moment Resistance ........................................................................................................ 12-44
12.9.4.4—Crown Soil Cover Factor, CH..................................................................................................... 12-45
12.9.4.5—Footing Reactions ...................................................................................................................... 12-45
12.9.4.6—Concrete Relieving Slabs ........................................................................................................... 12-46
12.9.5—Construction and Installation ............................................................................................................... 12-47
12.10—REINFORCED CONCRETE PIPE ............................................................................................................. 12-47
12.10.1—General ............................................................................................................................................... 12-47
12.10.2 Loading ................................................................................................................................................ 12-48
12.10.2.1 Standard Installations ................................................................................................................. 12-48
12.10.2.2 Pipe Fluid Weight ...................................................................................................................... 12-52
12.10.2.3—Live Loads ............................................................................................................................... 12-52
12.10.3—Service Limit State ............................................................................................................................. 12-52
12.10.4—Safety against Structural Failure ........................................................................................................ 12-52
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2012
Edition
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
12.10.4.1—General ..................................................................................................................................... 12-52
12.10.4.2—Direct Design Method .............................................................................................................. 12-53
12.10.4.2.1—Loads and Pressure Distribution .................................................................................... 12-53
12.10.4.2.2—Analysis for Force Effects with the Pipe Ring ............................................................... 12-54
12.10.4.2.3—Process and Material Factors ......................................................................................... 12-55
12.10.4.2.4—Flexural Resistance at the Strength Limit State ............................................................. 12-55
12.10.4.2.4a—Circumferential Reinforcement ............................................................................. 12-55
12.10.4.2.4b—Minimum Reinforcement ...................................................................................... 12-55
12.10.4.2.4c—Maximum Flexural Reinforcement without Stirrups ............................................ 12-56
12.10.4.2.4d—Reinforcement for Crack Width Control .............................................................. 12-57
12.10.4.2.4e—Minimum Concrete Cover .................................................................................... 12-58
12.10.4.2.5 —Shear Resistance without Stirrups................................................................................. 12-58
12.10.4.2.6—Shear Resistance with Radial Stirrups ........................................................................... 12-60
12.10.4.2.7—Stirrup Reinforcement Anchorage ................................................................................. 12-61
12.10.4.2.7a—Radial Tension Stirrup Anchorage ........................................................................ 12-61
12.10.4.2.7b—Shear Stirrup Anchorage ....................................................................................... 12-61
12.10.4.2.7c—Stirrup Embedment ............................................................................................... 12-61
12.10.4.3—Indirect Design Method ........................................................................................................... 12-61
12.10.4.3.1—Bearing Resistance ......................................................................................................... 12-61
12.10.4.3.2—Bedding Factor ............................................................................................................... 12-62
12.10.4.3.2a—Earth Load Bedding Factor for Circular Pipe ....................................................... 12-62
12.10.4.3.2b—Earth Load Bedding Factor for Arch and Elliptical Pipe ...................................... 12-63
12.10.4.3.2c—Live Load Bedding Factors ................................................................................... 12-64
12.10.4.4—Development of Quadrant Mat Reinforcement ........................................................................ 12-64
12.10.4.4.1—Minimum Cage Reinforcement ...................................................................................... 12-64
12.10.4.4.2—Development Length of Welded Wire Fabric ................................................................ 12-64
12.10.4.4.3—Development of Quadrant Mat Reinforcement Consisting of Welded
Plain Wire Fabric ................................................................................................................................. 12-64
12.10.4.4.4—Development of Quadrant Mat Reinforcement Consisting of Deformed
Bars, Deformed Wire, or Deformed Wire Fabric ................................................................................ 12-65
12.10.5—Construction and Installation ............................................................................................................. 12-65
12.11—REINFORCED CONCRETE CAST-IN-PLACE AND PRECAST BOX CULVERTS AND
REINFORCED CAST-IN-PLACE ARCHES .......................................................................................................... 12-65
12.11.1—General ............................................................................................................................................... 12-65
12.11.2—Loads and Live Load Distribution ..................................................................................................... 12-66
12.11.2.1—General ..................................................................................................................................... 12-66
12.11.2.2—Modification of Earth Loads for Soil-Structure Interaction ..................................................... 12-66
12.11.2.2.1—Embankment and Trench Conditions ............................................................................. 12-66
12.11.2.2.2—Other Installations .......................................................................................................... 12-69
12.11.2.3—Distribution of Concentrated Loads to Bottom Slab of Box Culvert ....................................... 12-69
12.11.2.4—Distribution of Concentrated Loads in Skewed Box Culverts ................................................. 12-69
12.11.3—Service Limit State ............................................................................................................................. 12-69
12.11.4—Safety against Structural Failure ........................................................................................................ 12-70
12.11.4.1—General ..................................................................................................................................... 12-70
12.11.4.2—Design Moment for Box Culverts ............................................................................................ 12-70
12.11.4.3—Minimum Reinforcement ......................................................................................................... 12-70
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TABLE OF CONTENTS
12-v
12.11.4.3.1—Cast-in-Place Structures................................................................................................. 12-70
12.11.4.3.2—Precast Box Structures ................................................................................................... 12-70
12.11.4.4—Minimum Cover for Precast Box Structures ............................................................................ 12-71
12.11.5—Construction and Installation ............................................................................................................. 12-71
12.12—THERMOPLASTIC PIPES ......................................................................................................................... 12-71
12.12.1—General ............................................................................................................................................... 12-71
12.12.2—Service Limit States ........................................................................................................................... 12-71
12.12.2.1—General..................................................................................................................................... 12-71
12.12.2.2—Deflection Requirement ........................................................................................................... 12-71
12.12.3—Safety against Structural Failure ........................................................................................................ 12-73
12.12.3.1—General..................................................................................................................................... 12-73
12.12.3.2—Section Properties .................................................................................................................... 12-73
12.12.3.3—Chemical and Mechanical Requirements ................................................................................. 12-73
12.12.3.4—Thrust ....................................................................................................................................... 12-74
12.12.3.5—Factored and Service Loads ..................................................................................................... 12-74
12.12.3.6—Handling and Installation Requirements .................................................................................. 12-78
12.12.3.7—Soil Prism ................................................................................................................................ 12-79
12.12.3.8—Hydrostatic Pressure ................................................................................................................ 12-80
12.12.3.9—Live Load ................................................................................................................................. 12-80
12.12.3.10—Wall Resistance ..................................................................................................................... 12-81
12.12.3.10.1—Resistance to Axial Thrust ........................................................................................... 12-81
12.12.3.10.1a—General................................................................................................................ 12-81
12.12.3.10.1b—Local Buckling Effective Area ........................................................................... 12-81
12.12.3.10.1c—Compression Strain ............................................................................................. 12-82
12.12.3.10.1d—Thrust Strain Limits ............................................................................................ 12-83
12.12.3.10.1e—General Buckling Strain Limits .......................................................................... 12-83
12.12.3.10.2—Bending and Thrust Strain Limits ................................................................................ 12-84
12.12.3.10.2a—General................................................................................................................ 12-84
12.12.3.10.2b—Combined Strain ................................................................................................. 12-84
12.12.4—Construction and Installation ............................................................................................................. 12-86
12.13—STEEL TUNNEL LINER PLATE............................................................................................................... 12-87
12.13.1—General ............................................................................................................................................... 12-87
12.13.2—Loading .............................................................................................................................................. 12-87
12.13.2.1—Earth Loads .............................................................................................................................. 12-87
12.13.2.2—Live Loads ............................................................................................................................... 12-88
12.13.2.3—Grouting Pressure .................................................................................................................... 12-88
12.13.3—Safety against Structural Failure ........................................................................................................ 12-88
12.13.3.1—Section Properties .................................................................................................................... 12-88
12.13.3.2—Wall Area ................................................................................................................................. 12-88
12.13.3.3—Buckling................................................................................................................................... 12-89
12.13.3.4—Seam Strength .......................................................................................................................... 12-89
12.13.3.5—Construction Stiffness .............................................................................................................. 12-89
12.14—PRECAST REINFORCED CONCRETE THREE-SIDED STRUCTURES ............................................... 12-91
12.14.1—General ............................................................................................................................................... 12-91
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12.14.2—Materials............................................................................................................................................. 12-91
12.14.2.1—Concrete ................................................................................................................................... 12-91
12.14.2.2—Reinforcement .......................................................................................................................... 12-91
12.14.3—Concrete Cover for Reinforcement .................................................................................................... 12-91
12.14.4—Geometric Properties .......................................................................................................................... 12-91
12.14.5—Design ................................................................................................................................................ 12-91
12.14.5.1—General ..................................................................................................................................... 12-91
12.14.5.2—Distribution of Concentrated Load Effects in Top Slab and Sides........................................... 12-92
12.14.5.3—Distribution of Concentrated Loads in Skewed Culverts ......................................................... 12-92
12.14.5.4—Shear Transfer in Transverse Joints between Culvert Sections ................................................ 12-92
12.14.5.5—Span Length ............................................................................................................................. 12-92
12.14.5.6—Resistance Factors .................................................................................................................... 12-93
12.14.5.7—Crack Control ........................................................................................................................... 12-93
12.14.5.8—Minimum Reinforcement ......................................................................................................... 12-93
12.14.5.9—Deflection Control at the Service Limit State .......................................................................... 12-93
12.14.5.10—Footing Design ....................................................................................................................... 12-93
12.14.5.11—Structural Backfill .................................................................................................................. 12-93
12.14.5.12—Scour Protection and Waterway Considerations .................................................................... 12-93
12.15—REFERENCES ............................................................................................................................................. 12-94
APPENDIX A12—PLATE, PIPE, AND PIPE ARCH PROPERTIES..................................................................... 12-97
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 12
BURIED STRUCTURES AND TUNNEL LINERS
12.1—SCOPE
C12.1
2013 Revision
This Section provides requirements for the selection
of structural properties and dimensions of buried
structures, e.g., culverts, and steel plate used to support
tunnel excavations in soil.
Buried structure systems considered herein are
metal pipe, structural plate pipe, long-span structural
plate, deep corrugated plate, structural plate box,
reinforced concrete pipe, reinforced concrete
cast-in-place and precast arch, box and elliptical
structures, and thermoplastic pipe.
The type of liner plate considered is cold-formed
steel panels.
2013 Revision
For buried structures, refer to Article 2.6.6 for
hydraulic design considerations and FHWA (1985) for
design methods related to location, length, and waterway
openings.
12.2—DEFINITIONS
Abrasion—Loss of section or coating of a culvert by the mechanical action of water conveying suspended bed load of
sand, gravel, and cobble-size particles at high velocities with appreciable turbulence.
Buried Structure—A generic term for a structure built by embankment or trench methods.
Corrosion—Loss of section or coating of a buried structure by chemical and/or electrochemical processes.
Culvert—A curved or rectangular buried conduit for conveyance of water, vehicles, utilities, or pedestrians.
Deep Corrugated Plate—Structural Plate in AASHTO M 167 with a corrugation depth greater than 5 in.
FEM—Finite Element Method
Narrow Trench Width—The outside span of rigid pipe, plus 1.0 ft.
Projection Ratio—Ratio of the vertical distance between the outside top of the pipe and the ground or bedding surface
to the outside vertical height of the pipe, applicable to reinforced concrete pipe only.
Side Radius—For deep corrugated plate structures, the side radius is the radius of the plate in the section adjacent to
crown (top) section of the structure. In box shaped structures, this is often called the haunch radius.
Soil Envelope—Zone of controlled soil backfill around culvert structure required to ensure anticipated performance
based on soil-structure interaction considerations.
Soil-Structure Interaction System—A buried structure whose structural behavior is influenced by interaction with the
soil envelope.
Tunnel—A horizontal or near horizontal opening in soil excavated to a predesigned geometry by tunneling methods
exclusive of cut-and-cover methods.
12.3—NOTATION
A
Aeff
Ag
AL
=
=
=
=
As
Asmax
AT
=
=
=
2013 Revision
wall area (in.2/ft) (12.7.2.3)
effective wall area (in.2/in.) (12.12.2.2)
gross wall area within a length of one period (in.2/in.) (12.12.3.5)
axle load, taken as 50 percent of all axle loads that can be placed on the structure at one time (kip); sum
of all axle loads in an axle group (kip); total axle load on single axle or tandem axles (kip) (12.8.4.2)
(12.9.4.2) (12.9.4.3)
tension reinforcement area on cross-section width, b (in.2/ft) (C12.10.4.2.4a) (C12.11.3) (C12.11.4)
minimum flexural reinforcement area without stirrups (in.2/ft) (12.10.4.2.4c)
area of the top portion of the structure above the springline (ft2) (12.8.4.2)
12-1
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
12-2
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Avr
=
Avs
B
Bc
Bc
Bd
BFE
BFLL
B1
b
be
CA
Cc
Cd
Cdt
CH
CL
Cn
Cℓℓ
CN
Cs
C1
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
C2
=
D
=
D-load
Df
Di
DL
Do
d
=
=
=
=
=
=
d
d1
E
Em
Ep
E(x)
=
=
=
=
=
=
E50
E75
F
Fc
Fcr
=
=
=
=
=
Fd
=
Fe
FF
Fn
Frp
Frt
Ft
=
=
=
=
=
=
stirrup reinforcement area to resist radial tension forces on cross-section width, b in each line of stirrups
at circumferential spacing, sv (in.2/ft) (12.10.4.2.6)
required area of stirrups for shear reinforcement (in.2/ft) (12.10.4.2.6)
width of culvert (ft) (C12.6.2.2.5)
outside diameter or width of the structure (ft) (12.6.6.3)
out-to-out vertical rise of pipe (ft) (12.6.6.3)
horizontal width of trench at top of pipe (ft) (12.11.2.2)
earth load bedding factor (12.10.4.3.1)
live load bedding factor (12.10.4.3.1)
crack control coefficient for effect of cover and spacing of reinforcement (C12.10.4.2.4d)
width of section (12.10.4.2.4c)
element effective width (in.) (12.12.3.10.1b)
constant corresponding to the shape of the pipe (12.10.4.3.2a)
load coefficient for positive pipe projection (12.10.4.3.2a)
load coefficient for trench installation (12.11.2.2)
load coefficient for tunnel installation (12.13.2.1)
adjustment factor for shallow cover heights over metal box culverts (12.9.4.4)
live load distribution coefficient (12.12.2.2)
calibration factor to account for nonlinear effects (12.12.3.10.1e)
live load adjusted for axle loads, tandem axles, and axles with other than four wheels; C1 C2 AL (kip) (12.9.4.2)
parameter that is a function of the vertical load and vertical reaction (12.10.4.3.2a)
construction stiffness for tunnel liner plate (kip/in.) (12.5.6.4)
1.0 for single axles and 0.5 + S/50 ≤ 1.0 for tandem axles; adjustment coefficient for number of axles;
crack control coefficient for various types of reinforcement (12.9.4.2) (12.9.4.3) (C12.10.4.2.4d)
adjustment factor for number of wheels on a design axle as specified in Table 12.9.4.2-1; adjustment
coefficient for number of wheels per axle (12.9.4.2) (12.9.4.3)
straight leg length of haunch (in.); pipe diameter (in.); required D-load capacity of reinforced concrete
pipe (klf); diameter to centroid of pipe wall (in.) (12.9.4.1) (12.6.6.2) (12.10.4.3.1) (12.12.2.2)
resistance of pipe from three-edge bearing test load to produce a 0.01-in. crack (klf) (12.10.4.3)
shape factor (12.12.3.10.2b)
inside diameter of pipe (in.) (12.10.4.3.1)
deflection lag factor (12.12.2.2)
outside diameter of pipe (in.) (12.12.2.2)
required envelope width adjacent to the structure (ft); distance from compression face to centroid of
tension reinforcement (in.) (12.8.5.3) (12.10.4.2.4a) (C12.11.3)
width of warped embankment fill to provide adequate support for skewed installation (ft) (C12.6.8.2)
distance from the structure (ft) (12.8.5.3)
modulus of elasticity of the plastic (ksi); initial modulus of elasticity (ksi) (12.12.3.3) (12.12.3.6)
modulus of elasticity of metal (ksi) (12.7.2.4)
short- or long-term modulus of pipe material as specified in Table 12.12.3.3-1 (ksi) (12.12.2.2)
lateral unbalanced distributed load on culvert below sloping ground and skewed at end wall (lbs.)
(C12.6.2.2.5)
50-yr modulus of elasticity (ksi) (12.12.3.3)
75-year modulus of elasticity (ksi) (12.12.3.3)
concentrated load acting at the crown of a culvert (kip) (C12.6.2.2.5)
curvature correction factor (12.10.4.2.5)
factor for adjusting crack control relative to average maximum crack width of 0.01 in. corresponding to
Fcr = 1.0 (12.10.4.2.4d)
factor for crack depth effect resulting in increase in diagonal tension, shear, and strength with decreasing
d (12.10.4.2.5)
soil-structure interaction factor for embankment installations (12.10.2.1)
flexibility factor (in./kip) (12.5.6.3) (12.7.2.6)
coefficient for effect of thrust on shear strength (12.10.4.2.5)
factor for process and local materials affecting radial tension strength of pipe (12.10.4.2.3)
factor for pipe size effect on radial tension strength (12.10.4.2.4c)
soil-structure interaction factor for trench installations (12.10.2.1)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
Fu
=
Fvp
Fy
f′c
fcr
fs
fy
H
=
=
=
=
=
=
=
HAF
HD
Hdesign
HL
Hs
Hw
H1
=
=
=
=
=
=
=
H2
=
h
=
I
ID
IM
Ip
i
j
K
=
=
=
=
=
=
=
KB
Kh
Kh1
Kh2
Kt
Kwa
K1
K2
KγE
k
=
=
=
=
=
=
=
=
=
=
L
=
LLDF
L0
=
=
Lw
=
Mdℓ
=
Mdℓu
Mℓℓ
Mℓℓu
Mnu
=
=
=
=
MP
Mpc
=
=
12-3
specified minimum tensile strength (ksi); material yield strength for design load duration (ksi) (12.7.2.4)
(12.12.3.10.1b)
factor for process and local materials that affect the shear strength of the pipe (12.10.4.2.3)
yield strength of metal (ksi) (12.7.2.3)
compressive strength of concrete (ksi) (12.4.2.2)
critical buckling stress (ksi) (12.7.2.4)
maximum stress in reinforcing steel at service limit state (ksi) (C12.11.3)
specified minimum yield point for reinforcing steel (ksi) (12.10.4.2.4a)
rise of culvert (ft); height of cover from the box culvert rise to top of pavement (ft); height of cover over
crown (ft); height of fill above top of pipe (ft) (C12.6.2.2.5) (12.9.4.2) (12.9.4.4) (12.10.2.1)
horizontal arching factor (12.10.2.1)
vertical distance from mid-depth of corrugation to top grade (12.8.9.4)
design height of cover above top of culvert or above crown of arches or pipes (ft) (C12.6.2.2.5)
headwall strip reaction (kip) (C12.6.2.2.5)
depth of water table above springline of pipe (ft) (12.12.3.4)
depth of water table above springline of pipe (ft) (12.12.3.7)
depth of crown of culvert below ground surfaces (ft); height of cover above the footing to traffic surface
(ft) (C12.6.2.2.5) (12.8.4.2)
actual height of cover above top of culvert or above crown of arches or pipes (ft); height of cover from
the structure springline to traffic surface (ft) (C12.6.2.2.5) (12.8.4.2)
vertical distance from the top of cover for design height to point of horizontal load application (ft); wall
thickness of pipe or box culvert (in.); height of ground surface above top of pipe (ft) (C12.6.2.2.5)
(12.10.4.2.4a) (C12.11.3)
moment of inertia (in.4/in.) (12.7.2.6)
inside diameter (in.) (12.6.6.3)
dynamic load allowance as specified in Table 3.6.1.1.2-1 (percent) (12.12.3.9)
moment of inertia of pipe profile per unit length of pipe (in.4/in.) (12.12.2.2)
coefficient for effect of axial force at service limit state, fs (12.10.4.2.4d) (C12.11.3)
coefficient for moment arm at service limit state, fs (12.10.4.2.4d) (C12.11.3)
ratio of the unit lateral effective soil pressure to unit vertical effective soil pressure, i.e., Rankine
coefficient of active earth pressure (12.10.4.2)
bedding coefficient (12.12.2.2)
lateral earth pressure for culvert under sloping ground (psf/lf) (C12.6.2.2.5)
lateral earth pressure distribution acting on upslope surface of culvert (psf/lf) (C12.6.2.2.5)
lateral earth pressure distribution acting on downslope surface of culvert (psf/lf) (C12.6.2.2.5)
time factor as specified in Table 12.12.3.10.1b-1 (12.12.3.10.1b)
factor for uncertainty in level of ground water table (12.12.3.8)
coefficient to consider design location (in.) (12.12.3.9)
coefficient to account for thrust variation around circumference (12.12.3.5)
installation factor (12.12.3.5)
soil stiffness factor; edge support coefficient; plate buckling coefficient (12.7.2.4) (12.13.3.3)
(12.12.3.10.1b)
distance along length of culvert from expansion joint to the centerline of the headwall (ft); length of
stiffening rib on leg (in.) (C12.6.2.2.5) (12.9.4.1)
factor for distribution of live load through earth fills as specified in Article 3.6.1.2.6 (12.12.3.5)
length of live load surface contact area parallel to pipe diameter as specified in Article 3.6.1.2.5 (in.)
(12.12.3.9)
lane width (ft); horizontal live load distribution width in the circumferential direction, at the elevation of
the crown (in.) (12.8.4.2) (12.12.3.5)
dead load moment (kip-ft/ft); sum of the nominal crown and haunch dead load moments (kip-ft/ft)
(12.9.4.2)
factored dead load moment as specified in Article 12.9.4.2 (kip-ft) (12.9.4.3)
live load moment (kip-ft/ft); sum of the nominal crown and haunch live load moments (kip-ft/ft) (12.9.4.2)
factored live load moment as specified in Article 12.9.4.2 (kip-ft) (12.9.4.3)
factored moment acting on cross-section width, b, as modified for effects of compressive or tensile thrust
(kip-in./ft) (12.10.4.2.6)
plastic moment capacity of deep corrugated structure (k-ft/ft) (12.8.9.4)
crown plastic moment capacity (kip-ft/ft) (12.9.4.3)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
12-4
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Mph
Ms
=
=
Mu
m
Ns
=
=
=
Nu
n
P
PBrg
Pc
PF
PL
=
=
=
=
=
=
=
Ps
Psp
Pst
Pu
Pw
P1
p
p
q
R
=
=
=
=
=
=
=
=
=
=
RAL
Rc
Rd
Rf
=
=
=
=
RH
Rh
Rn
Rr
RT
RV
r
rc
rh
rs
rsd
S
=
=
=
=
=
=
=
=
=
=
=
=
SH
Si
Sℓ
S1, S2
sv
T
TL
Ts
Tu
t
tb
=
=
=
=
=
=
=
=
=
=
=
V
=
haunch plastic moment capacity (kip-ft/ft) (12.9.4.3)
bending moment at service limit state (kip-in./ft); moment acting on a cross-section of width, b, at service
limit state taken as an absolute value in design equations (kip-in./ft); constrained soil modulus specified in
Table 12.12.3.5-1 (ksi); soil modulus (ksi) (12.10.4.2.4d) (C12.11.3) (12.12.2.2) (12.12.3.5)
ultimate moment acting on cross-section width, b (kip-in./ft) (12.10.4.2.4a)
multiple presence factor as specified in Table 3.6.1.1.2-1 (12.12.3.9)
axial thrust acting on a cross-section width, b, at service limit state taken as positive when compressive
and negative when tensile (kip/ft) (12.10.4.2.4d) (C12.11.3)
axial thrust acting on cross-section width, b, at strength limit state (kip/ft) (12.10.4.2.4a)
number of adjoining traffic lanes (12.8.4.2)
design wheel load as specified in Article 3.6.2.2 (lb) (12.12.3.9)
allowable bearing pressure to limit compressive strain in the trench wall or embankment (ksf) (12.8.5.3)
proportion of total moment carried by crown of metal box culvert (12.9.4.3)
factored vertical crown pressure due to earth and live loads (ksf) (12.7.2.2)
pressure due to live load (LL) and dynamic load allowance (IM) (psi); service load on culvert (12.12.2.2)
(12.12.3.9)
design service load (psi) (12.12.2.2)
soil prism pressure (psi) (12.12.2.2)
stub compression capacity from T 341 (lb/in.) (12.12.3.10.1b)
design factored load (psi) (12.12.3.5)
hydrostatic water pressure (psi) (12.12.3.5)
horizontal pressure from the structure at a distance, d1 (ksf) (12.8.5.3)
positive projection ratio (12.10.4.3.2a)
negative projection ratio (12.10.4.3.2a)
ratio of the total lateral pressure to the total vertical pressure (12.10.4.3.2a)
rise of structure (ft); rise of box culvert or long-span structural plate structures (ft); radius to centroid of
pipe wall profile (in.) (12.8.4.1) (12.9.4.1) (12.12.2.2)
axle load correction factor (12.9.4.6)
corner radius of the structure (ft); concrete strength correction factor (12.8.5.3) (12.9.4.6)
ratio of resistance factors specified in Article 5.5.4.2 for shear and moment (12.10.4.2.4c)
factor related to required relieving slab thickness, applicable for box structures where the span is less
than 26.0 ft (12.9.4.6)
horizontal footing reaction component (kip/ft) (12.8.4.2)
haunch moment reduction factor; correction factor for backfill soil geometry (12.9.4.3) (12.12.3.10.1e)
nominal resistance (klf) (12.5.1)
factored resistance (klf); factored resistance to thrust (kip/ft) (12.5.1) (12.12.3.5)
top arc radius of long-span structural plate structures (ft) (12.8.3.2)
vertical footing reaction component (kip/ft) (12.8.4.2)
radius of gyration (in.); radius to centerline of concrete pipe wall (in.) (12.7.2.4) (12.10.4.2.5)
radius of crown (ft) (12.9.4.1)
radius of haunch (ft) (12.9.4.1)
radius of the inside reinforcement (in.) (12.10.4.2.4c)
settlement ratio parameter (12.10.4.3.2a)
pipe, tunnel, or box diameter or span (in.) or (ft) as indicated; span of structure between springlines of
long-span structural plate structures (ft); box culvert span (ft) (12.6.6.3) (12.8.4.1) (12.9.4.2) (12.12.3.6)
hoop stiffness factor (12.12.3.5)
internal diameter or horizontal span of the pipe (in.) (12.10.4.2.4b)
spacing of circumferential reinforcement (in.) (12.10.4.2.4d)
shear forces acting along culvert bearing lines (lbs.) (C12.6.2.2.5)
spacing of stirrups (in.) (12.10.4.2.6)
total dead load and live load thrust in the structure (kip/ft) (12.8.5.3)
factored thrust (kip/ft) (12.7.2.2)
service thrust per unit length (lb/in.) (12.12.2.2)
factored thrust per unit length (lb/in.) (12.12.3.10.1c)
required thickness of cement concrete relieving slab (in.); thickness of element (in.) (12.9.4.6) (12.12.3.10.1b)
basic thickness of cement concrete relieving slab (in.); clear cover over reinforcement (in.) (12.9.4.6)
(12.10.4.2.4d)
unfactored footing reaction (kip/ft) (12.9.4.5)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
VAF
Vc
=
=
VDL
VL
VLL
Vn
Vr
Vu
WE
WF
WL
W0
WT
w
=
=
=
=
=
=
=
=
=
=
=
=
x
=
α
=
β
γb
γEV
γLL
γs
=
=
=
=
=
γw
γWA
ΔA
Δf
Δt
εbck
εf
εsc
εuc
εyc
εyt
ηEV
ηLL
λ
μ
ν
ρ
φ
φbck
φf
φfs
φr
φs
φT
Ψ
ω
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
12-5
vertical arching factor (12.10.2.1)
factored shear force acting on cross-section width, b, which produces diagonal tension failure without
stirrup reinforcement (kip/ft) (12.10.4.2.6)
[H2(S) – AT] γs/2 (kip/ft) (12.8.4.2)
headwall strip reaction (kip) (C12.6.2.2.5)
n(AL)/(8 + 2 H1) (kip/ft) (12.8.4.2)
nominal shear resistance of pipe section without radial stirrups per unit length of pipe (kip/ft) (12.10.4.2.5)
factored shear resistance per unit length (kip/ft) (12.10.4.2.5)
ultimate shear force acting on cross-section width, b (kip/ft) (12.10.4.2.5)
total earth load on pipe or liner (kip/ft) (12.10.2.1)
fluid load in the pipe (kip/ft) (12.10.4.3.1)
total live load on pipe or liner (kip/ft) (12.10.4.3.1)
width of live load ground-surface contact area parallel to flow in pipe (in.) (12.12.3.5)
total dead and live load on pipe or liner (kip/ft) (12.10.4.3.1)
unit weight of soil (pcf); total clear width of element between supporting elements (in.) (12.10.2.1)
(12.12.3.10.1b)
parameter which is a function of the area of the vertical projection of the pipe over which active lateral
pressure is effective (12.10.4.3.2a)
skew angle between the highway centerline or tangent thereto and the culvert headwall (degrees)
(C12.6.2.2.5)
angle of fill slope measured from horizontal (degrees) (C12.6.2.2.5)
unit weight of buoyant soil (lb/ft3) (12.12.3.7)
load factor for vertical pressure from dead load of earth fill (12.12.3.5)
load factor for live load (12.12.3.5)
unit weight of backfill (kcf) ; soil unit weight (kcf); wet unit weight of soil (lb/ft3) (C12.9.2) (12.9.4.2)
(12.12.3.7)
unit weight of water (lb/ft3) (12.12.3.8)
load factor for hydrostatic pressure (12.12.3.5)
total allowable deflection of pipe (in.) (12.12.2.2)
deflection of pipe due to flexure (in.) (12.12.3.10.2b)
total deflection of pipe (in.) (12.12.2.2)
nominal strain capacity for general buckling (12.12.3.10.1e)
factored strain due to flexure (12.12.3.10.2b)
service compressive strain (in./in.) (12.12.2.2)
factored compressive strain due to thrust (12.12.3.10.1c)
factored compressive strain limit as specified in Table 12.12.3.3-1 (12.12.3.10.1b)
service long-term strain limit as specified in Table 12.12.3.3-1 (12.12.3.10.2b)
load modifier, specified in Article 1.3.2, as they apply to vertical earth loads on culverts (12.12.3.5)
load modifier as they apply to live loads on culverts (12.12.3.5)
slenderness factor (12.12.3.10.1b)
coefficient of friction between the pipe and soil (12.10.2.1)
Poisson’s ratio of soil (12.12.3.10.1e)
effective width factor (12.12.310.1b)
resistance factor (12.5.1)
resistance factor for buckling (12.12.3.10.1e)
resistance factor for flexure (12.10.4.2.4c)
coefficient of friction between the fill material and the sides of the trench (12.10.4.3.2a)
resistance factor for radial tension (12.10.4.2.4c)
resistance factor for soil stiffness, φs = 0.9; resistance factor for soil pressure (12.12.3.5) (12.12.3.10.1e)
resistance factor for thrust effects (12.12.3.10.1d)
central angle of pipe subtended by assumed distribution of external reactive force (degrees) (12.10.4.2.1)
spacing of corrugation (in.) (12.12.3.10.1b)
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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12-6
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
12.4—SOIL AND MATERIAL PROPERTIES
12.4.1—Determination of Soil Properties
12.4.1.1—General
C12.4.1.1
Subsurface exploration shall be carried out to
determine the presence and influence of geologic and
environmental conditions that may affect the
performance of buried structures. For buried structures
supported on footings and for pipe arches and large
diameter pipes, a foundation investigation should be
conducted to evaluate the capacity of foundation
materials to resist the applied loads and to satisfy the
movement requirements of the structure.
The following information may be useful for design:
Strength and
materials;
compressibility
of
foundation
Chemical characteristics of soil and surface waters,
e.g., pH, resistivity, and chloride content of soil and
pH, resistivity, and sulfate content of surface water;
Stream hydrology, e.g., flow rate and velocity,
maximum width, allowable headwater depth, and
scour potential; and
Performance and condition survey of culverts in the
vicinity.
12.4.1.2—Foundation Soils
The type and anticipated behavior of the foundation
soil shall be considered for stability of bedding and
settlement under load.
12.4.1.3—Envelope Backfill Soils 2013 Revision
The type, compacted density and strength properties
of the soil envelope adjacent to the buried structure shall
be established. The backfill soils comprising the soil
envelope shall conform to the requirements of AASHTO
M 145 as follows:
For standard flexible pipes and concrete structures:
A-1, A-2, or A-3 (GW, GP, SW, SP, GM, SM, SC,
GC),
For metal box culverts and long-span structures
with cover less than 12.0 ft: A-1, A-2-4, A-2-5, or
A-3 (GW, GP, SW, SP, GM, SM, SC, GC),
For long-span metal structures with cover not less
than 12.0 ft: A-1 or A-3 (GW, GP, SW, SP, GM,
SM), and
For structural plate culverts with deep corrugations:
A-1, A-2-4, A-2-5, or A-3 (ASTM D2487) (GW,
GP, SW, SP, GM, SM, SC, GC) and the culvert
manufacturer’s requirements.
For thermoplastic culverts, bedding, and backfill
materials: A-1, A-2-4, A-2-5, or A-3 soils. A
maximum of 50 percent of the particle sizes may
pass the No. 100 sieve and a maximum of 20
percent may pass the No. 200 sieve.
C12.4.1.2
Refer to Article 10.4 for general guidance regarding
foundation soil properties. The performance of rigid
pipes is dependent on foundation and bedding stability.
C12.4.1.3
2013 Revision
Refer to Sections 26, 27, and 30 of the AASHTO
LRFD Bridge Construction Specifications, for
compaction criteria of soil backfill for flexible and rigid
culverts.
Wall stresses in buried structure are sensitive to the
relative stiffness of the soil and pipe. Buckling stability
of flexible culverts is dependent on soil stiffness.
In the selection of a type of backfill for the
envelope, the quality of the material and its suitability
for achieving the requirements of the design should be
considered. The order of preference for selecting
envelope backfill based on quality may be taken as
follows:
Angular, well-graded sand and gravel;
Nonangular, well-graded sand and gravel;
Flowable materials, e.g., cement-soil-fly ash
mixtures, which result in low density/low strength
backfill, for trench applications only;
Uniform sand or gravel, provided that placement is
confirmed to be dense and stable, but which may
require a soil or geofabric filter to prevent the
migration of fines;
Clayey sand or gravel of low plasticity; and
Stabilized soil, which should be used only under the
supervision of an Engineer familiar with the
behavior of the material.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-7
The restriction on materials passing the No. 100
sieve and No. 200 sieve for thermoplastic culverts are
intended to eliminate uniform fine sands for use as pipe
embedment. Such materials are difficult to work with,
are sensitive to moisture content, and do not provide
support comparable to coarser or more broadly graded
materials at the same percentage of maximum density.
The Engineer may permit exceptions to these restrictions
in special cases. If so, a suitable plan should be
submitted for control of moisture content and
compaction procedures. These silty and clayey materials
should never be used in a wet site. Increased inspection
levels should be considered if such a plan is approved.
12.4.2—Materials
12.4.2.1—Aluminum Pipe and Structural Plate
Structures
Aluminum for corrugated metal pipe and
pipe-arches shall comply with the requirements of
AASHTO M 196 (ASTM B745). Aluminum for
structural plate pipe, pipe-arch, arch, and box structures
shall meet the requirements of AASHTO M 219 (ASTM
B746).
12.4.2.2—Concrete
Concrete shall conform to Article 5.4, except that
f c may be based on cores.
12.4.2.3—Precast Concrete Pipe
Precast concrete pipe shall comply with the
requirements of AASHTO M 170 (ASTM C76) and
M 242M/M 242 (ASTM C655M and C655). Design
wall thickness, other than the standard wall dimensions,
may be used, provided that the design complies with all
applicable requirements of this Section.
12.4.2.4—Precast Concrete Structures
Precast concrete arch, elliptical, and box structures
shall comply with the requirements of AASHTO
M 206M/M 206 (ASTM C506M and C506),
M 207M/M 207 (ASTM C507M and C507), M 259
(ASTM C789), and M 273 (ASTM C850).
12.4.2.5—Steel Pipe and Structural Plate
Structures
Steel for corrugated metal pipe and pipe-arches
shall comply with the requirements of AASHTO M 36
(ASTM A760). Steel for structural plate pipe, pipe-arch,
arch, and box structures shall meet the requirements of
AASHTO M 167M/M 167 (ASTM A761/A761M).
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2012
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12-8
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
12.4.2.6—Deep Corrugated Structures
C12.4.2.6
Steel for deep corrugated structural plate shall
comply with the requirements of AASHTO M 167.
Deep corrugated structural plate may be reinforced.
Reinforcement for deep corrugated structures may
consist of structural shapes, or deep corrugated
structural plate meeting the requirements of AASHTO
M 167, with or without nonshrink grout, complete with
shear studs.
12.4.2.7—Steel Reinforcement
Reinforcement shall comply with the requirements of
Article 5.4.3, and shall conform to one of the following:
AASHTO M 31M/M 31 (ASTM A615/A615M),
M 32M/M 32 (ASTM A82/A82M), M 55M/M 55
(ASTM A185/A185M), M 221M/M 221 (ASTM A497),
or M 225M/M 225 (ASTM A496/A496M).
For smooth wire and smooth welded wire fabric, the
yield strength may be taken as 65.0 ksi. For deformed
welded wire fabric, the yield strength may be taken as
70.0 ksi.
12.4.2.8—Thermoplastic Pipe
C12.4.2.8
2013 Revision
Plastic pipe may be solid wall, corrugated, or profile
wall and may be manufactured of polyethylene (PE) or
polyvinyl chloride (PVC).
PE pipe shall comply with the requirements of
ASTM F714 for solid wall pipe, AASHTO M 294 for
corrugated pipe, and ASTM F894 for profile wall pipe.
PVC pipe shall comply with the requirements of
AASHTO M 278 for solid wall pipe, ASTM F679 for
solid wall pipe, and AASHTO M 304 for profile wall
pipe.
2013 Revision
The AASHTO materials specifications also include
a provisional specification, MP 20, for steel-reinforced
polyethylene pipe (PE) ribbed pipe, 12.0 to 36.0 in.
diameter. The steel ribs are the main load carrying
members for the pipe and the thermoplastic material
braces the steel ribs from distortion or buckling. The
thermoplastic also distributes the load between the ribs.
It is necessary to evaluate the composite system of
thermoplastic liner and steel rib for adequacy. It is
important to ensure that the tensile strains within the
thermoplastic do not exceed the long-term strain
capacity for the thermoplastic material used in the
construction of the pipe. Three-dimensional finite
element analysis of the profile which has been calibrated
against
results
for
full
scale
tests
is
recommended. Design specifications for this product
will be considered for inclusion in these Specifications
when a satisfactory number of instrumented installations
are documented to validate performance.
12.5—LIMIT STATES AND RESISTANCE
FACTORS
12.5.1—General
C12.5.1
2013 Revision
2013 Revision
Buried structures and their foundations shall be
designed by the appropriate methods specified in
Articles 12.7 through 12.12 so that they resist the
factored loads given by the load combinations specified
in Articles 12.5.2 and 12.5.3.
The factored resistance, Rr, shall be calculated for
each applicable limit state as:
•
Metal pipe, pipe arches, and arch structures;
•
Long-span structural plate;
•
Structural plate box structures;
(12.5.1-1)
•
Reinforced precast concrete pipe;
Rr = φRn
Procedures for determining nominal resistance are
provided in Articles 12.7 through 12.12 for:
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2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
where:
Rn =
=
the nominal resistance
the resistance factor specified in Table 12.5.5-1
12-9
Reinforced concrete cast-in-place and precast box
structures
Thermoplastic pipe; and
Deep corrugated structural plate structures.
12.5.2—Service Limit State
2013 Revision
Buried structures shall be investigated at Service
Load Combination I, as specified in Table 3.4.1-1.
Deflection of metal structures, tunnel liner plate,
and thermoplastic pipe, and
Crack width in reinforced concrete structures.
C12.5.2
Deflection of a tunnel liner depends significantly on
the amount of overexcavation of the bore and is affected
by delay in backpacking or inadequate backpacking. The
magnitude of deflection is not primarily a function of
soil modulus or the liner plate properties, so it cannot be
computed with usual deflection formulae.
Where the tunnel clearances are important, the
designer should oversize the structure to allow for
deflection.
12.5.3—Strength Limit State 2013 Revision
C12.5.3
Buried structures and tunnel liners shall be investigated
for construction loads and at Strength Load Combinations I
and II, as specified in Table 3.4.1-1, as follows:
Strength Load Combinations III and IV and the
extreme event limit state do not control due to the
relative magnitude of loads applicable to buried
structures as indicated in Article 12.6.1. Buried
structures have been shown not to be controlled by
fatigue.
Flexibility limit requirement is waived for some
metal structures. See design provisions in Article 12.8.
For metal structures:
o
Wall area
o
Buckling
o
Seam failure
o
Flexibility limit for construction
o
Flexure of box and deep corrugated structures
only
2013 Revision
For concrete structures:
o
Flexure
o
Shear
o
Thrust
o
Radial tension
For thermoplastic pipe:
o
Wall area
o
Buckling
o
Flexibility limit
Thermoplastic pipe have many profile wall
geometries and some of these are made up of thin
sections that may be limited based on local buckling.
The strength limit state for wall area includes evaluating
the section capacity for local buckling.
For tunnel liner plate:
o
Wall area
o
Buckling
o
Seam strength
o
Construction stiffness
12.5.4—Load Modifiers and Load Factors
Load modifiers shall be applied to buried structures
and tunnel liners as specified in Article 1.3, except that
the load modifiers for construction loads should be taken
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2012
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12-10
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
as 1.0. For strength limit states, buried structures shall
be considered nonredundant under earth fill and
redundant under live load and dynamic load allowance
loads. Operational classification shall be determined on
the basis of continued function and/or safety of the
roadway.
12.5.5—Resistance Factors
2013 Revision
Resistance factors for buried structures shall be
taken as specified in Table 12.5.5-1. Values of resistance
factors for the geotechnical design of foundations for
buried structures shall be taken as specified in
Section 10.
C12.5.5
The standard installations for direct design of
concrete pipe were developed based on extensive
parameter studies using the soil structure interaction
program, SPIDA. Although past research validates that
SPIDA soil structure models correlate well with field
measurements, variability in culvert installation methods
and materials suggests that the design for Type I
installations be modified. This revision reduces soil
structure interaction for Type I installations by
ten percent until additional performance documentation
on installation in the field is obtained.
The new thermoplastic design method evaluates
more load conditions than prior specifications. Separate
resistance factors are provided for each mode of
behavior. The resistance factor for buckling is set at 0.7
and preserves the same level of safety as prior editions
of these Specifications with the inclusion of the
installation factor of Article 12.12.3.5. Buckling is an
undesirable failure mode for culverts. Buckling can
result in near total collapse of the culvert and blockage
of the waterway.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-11
Table 12.5.5-1—Resistance Factors for Buried Structures
Structure Type
Metal Pipe, Arch, and Pipe Arch Structures
Helical pipe with lock seam or fully welded seam:
Minimum wall area and buckling
Annular pipe with spot-welded, riveted, or bolted seam:
Minimum wall area and buckling
Minimum longitudinal seam strength
Bearing resistance to pipe arch foundations
Structural plate pipe:
Minimum wall area and buckling
Minimum longitudinal seam strength
Bearing resistance to pipe arch foundations
Resistance Factor
1.00
1.00
0.67
Refer to Section 10
1.00
0.67
Refer to Section 10
Long-Span Structural Plate and Tunnel Liner Plate Structures
Minimum wall area
Minimum seam strength
Bearing resistance of pipe arch foundations
0.67
0.67
Refer to Section 10
Structural Plate Box Structures
Plastic moment strength
Bearing resistance of pipe arch foundations
1.00
Refer to Section 10
Direct design method:
Type 1 installation:
Flexure
Shear
Radial tension
Other type installations:
Flexure
Shear
Radial tension
Flexure
Shear
0.90
0.82
0.82
1.00
0.90
0.90
Reinforced Concrete Cast-in-Place Box Structures
Reinforced Concrete Precast Box Structures
Flexure
Shear
Flexure
Shear
Reinforced Concrete Pipe
Reinforced Concrete Precast Three-Sided Structures
PE and PVC pipe:
Thrust, T
Soil stiffness, s
Global buckling,
Flexure, f
0.90
0.85
1.00
0.90
0.95
0.90
Thermoplastic Pipe
1.00
0.90
0.70
1.00
bck
Deep Corrugated Structural Plate Structures
Minimum wall area and general buckling, b
Plastic hinge, φh
Soil, s
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0.70
0.90
0.90
2012
Edition
12-12
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
12.5.6—Flexibility Limits and Construction Stiffness
12.5.6.1—Corrugated Metal Pipe and Structural
Plate Structures
2013 Revision
Flexibility factors for corrugated metal pipe and
structural plate structures shall not exceed the values
specified in Table 12.5.6.1-1.
C12.5.6.1
Limits on construction stiffness and plate flexibility
are construction requirements that do not represent any
limit state in service.
Table 12.5.6.1-1—Flexibility Factor Limit
Type of Construction Material
Steel Pipe
Aluminum Pipe
Steel Plate
Aluminum Plate
Corrugation Size (in.)
0.25
0.5
1.0
0.25 and 0.50
0.060 Material Thk.
0.075 Material Thk.
All Others
1.0
6.0 2.0
Pipe
Pipe-Arch
Arch
9.0 2.5
Pipe
Pipe-Arch
Arch
Flexibility Factor
(in./kip)
43
43
33
31
61
92
60
20
30
30
25
36
36
12.5.6.2—Spiral Rib Metal Pipe and Pipe Arches
Flexibility factors for spiral rib metal pipe and pipe
arches shall not exceed the values, specified in
Table 12.5.6.2-1,
for
embankment
installations
conforming to the provisions of Articles 12.6.6.2 and
12.6.6.3 and for trench installations conforming to the
provisions of Articles 12.6.6.1 and 12.6.6.3.
Table 12.5.6.2-1—Flexibility Factor Limits
Material
Steel
Condition
Embankment
Trench
Aluminum
Embankment
Trench
Corrugation Size
(in.)
0.75 0.75 7.5
0.75 1.0 11.5
0.75 0.75 7.5
0.75 1.0 11.5
0.75 0.75 7.5
0.75 1.0 11.5
0.75 0.75 7.5
0.75 1.0 11.5
Flexibility Factor
(in./kip)
217I1/3
140I1/3
263I1/3
163I1/3
340I1/3
175I1/3
420I1/3
215I1/3
Values of inertia, I, for steel and aluminum pipes
and pipe arches shall be taken as tabulated in
Tables A12-2 and A12-5.
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12.5.6.3—Flexibility Limits and Construction
Stiffness—Thermoplastic Pipe
2013 Revision
Flexibility factor, FF, of thermoplastic pipe shall
not exceed 95.0 in./kip.
12.5.6.4—Steel Tunnel Liner Plate
Construction stiffness, Cs, in kip/in., shall not be
less than the following:
Two-flange liner plate
12-13
C12.5.6.3
PE and PVC are thermoplastic materials that exhibit
higher flexibility factors at high temperatures and lower
flexibility factors at low temperatures. The specified
flexibility factor limits are defined in relation to pipe
stiffness values in accordance with ASTM D2412 at
73.4°F.
C12.5.6.4
Assembled liner using two- and four-flange liner
plates does not provide the same construction stiffness
as a full steel ring with equal stiffness.
Cs ≥ 0.050 (kip/in.)
Four-flange liner plate
Cs ≥ 0.111 (kip/in.)
12.6—GENERAL DESIGN FEATURES
12.6.1—Loading
C12.6.1
Buried structures shall be designed for force effects
resulting from horizontal and vertical earth pressure,
pavement load, live load, and vehicular dynamic load
allowance. Earth surcharge, live load surcharge,
downdrag loads, and external hydrostatic pressure shall
be evaluated where construction or site conditions
warrant. Water buoyancy loads shall be evaluated for
buried structures with inverts below the water table to
control flotation, as indicated in Article 3.7.2.
Earthquake loads should be considered only where
buried structures cross active faults.
For vertical earth pressure, the maximum load
factor from Table 3.4.1-2 shall apply.
Wheel loads shall be distributed through earth fills
according to the provisions of Article 3.6.1.2.6.
Buried structures benefit from both earth shelter and
support that reduce or eliminate from concern many of
the loads and load combinations of Article 3.4. Wind,
temperature, vehicle braking, and centrifugal forces
typically have little effect due to earth protection.
Structure dead load, pedestrian live load, and ice loads
are insignificant in comparison with force effects due to
earth fill loading. External hydrostatic pressure, if
present, can add significantly to the total thrust in a
buried pipe.
Vehicular collision forces are applicable to
appurtenances such as headwalls and railings only.
Water, other than buoyancy and vessel collision loads,
can act only in the noncritical longitudinal direction of
the culvert.
Due to the absence or low magnitude of these
loadings, Service Load Combination I, Strength Load
Combinations I and II, or construction loads control the
design.
The finite element analyses used in the preparation
of these metal box structure provisions are based on
conservative soil properties of low plasticity clay (CL)
compacted to 90 percent density as specified in
AASHTO T 99. Although low plasticity clay is not
considered an acceptable backfill material, as indicated
in Article 12.4.1.3, the FEM results have been shown to
yield conservative, upperbound moments.
The loading conditions that cause the maximum
flexural moment and thrust are not necessarily the same,
nor are they necessarily the conditions that will exist at
the final configuration.
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2012
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12-14
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
12.6.2—Service Limit State
12.6.2.1—Tolerable Movement
Tolerable movement criteria for buried structures
shall be developed based on the function and type of
structure, anticipated service life, and consequences of
unacceptable movements.
12.6.2.2—Settlement
12.6.2.2.1—General
Settlement shall be determined as specified in
Article 10.6.2. Consideration shall be given to potential
movements resulting from:
Longitudinal differential settlement along the length
of the pipe,
Differential settlement between the pipe and
backfill, and
Settlement of footings and unbalanced loading of
skewed structures extending through embankment
slopes.
12.6.2.2.2—Longitudinal Differential Settlement
Differential settlement along the length of buried
structures shall be determined in accordance with
Article 10.6.2.4. Pipes and culverts subjected to
longitudinal differential settlements shall be fitted with
positive joints to resist disjointing forces meeting the
requirements of Sections 26 and 27, AASHTO LRFD
Bridge Construction Specifications.
Camber may be specified for an installation to
ensure hydraulic flow during the service life of the
structure.
12.6.2.2.3—Differential Settlement between
Structure and Backfill
Where differential settlement of arch structures is
expected between the structure and the side fill, the
foundation should be designed to settle with respect to
the backfill.
Pipes with inverts shall not be placed on
foundations that will settle much less than the adjacent
side fill, and a uniform bedding of loosely compacted
granular material should be provided.
12.6.2.2.4—Footing Settlement
Footings shall be designed to provide uniform
longitudinal and transverse settlement. The settlement of
footings shall be large enough to provide protection
against possible downdrag forces caused by settlement
of adjacent fill. If poor foundation materials are
encountered, consideration shall be given to excavation
C12.6.2.2.3
The purpose of this provision is to minimize
downdrag loads.
C12.6.2.2.4
Metal pipe arch structures, long-span arch
structures, and box culvert structures should not be
supported on foundation materials that are relatively
unyielding compared with the adjacent sidefill. The use
of massive footings or piles to prevent settlement of
such structures is not recommended.
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2012
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
of all or some of the unacceptable material and its
replacement with compacted acceptable material.
Footing design shall comply with the provisions of
Article 10.6.
Footing reactions for metal box culvert structures
shall be determined as specified in Article 12.9.4.5.
The effects of footing depth shall be considered in
the design of arch footings. Footing reactions shall be
taken as acting tangential to the arch at the point of
connection to the footing and to be equal to the thrust in
the arch at the footing.
12.6.2.2.5—Unbalanced Loading
Buried structures skewed to the roadway alignment
and extending through an embankment fill shall be
designed in consideration of the influence of
unsymmetrical loading on the structure section.
12-15
In general, provisions to accommodate uniform
settlement between the footings are desirable, provided
that the resulting total settlement is not detrimental to
the function of the structure.
C12.6.2.2.5
Disregard of the effect of lateral unbalanced forces
in the headwall design can result in failure of the
headwall and adjacent culvert sections.
Due to the complexity of determining the actual
load distribution on a structure subjected to unbalanced
loading, the problem can be modeled using numerical
methods or the following approximate method. The
approximate method consists of analyzing 1.0-ft wide
culvert strips for the unbalanced soil pressures wherein
the strips are limited by planes perpendicular to the
culvert centerline. Refer to Figure C12.6.2.2.5-1 for this
method of analysis for derivation of force F. For
semicomplete culvert strips, the strips may be assumed
to be supported as shown in the lower part of the plan.
The headwall shall be designed as a frame carrying the
strip reactions, VL and HLcosα, in addition to the
concentrated force, F, assumed to be acting on the
crown. Force F is determined using the equations given
herein.
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2012
Edition
12-16
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure C12.6.2.2.5-1—Forces on Culvert—Approximate
Analysis
The unbalanced distributed load may be estimated
by the following relationships:
E ( x)
( P11
P21 )
2
( P12
3
P22 )
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All rights reserved. Duplication is a violation of applicable law.
1
( P13
3
P23 )
(C12.6.2.2.5-1)
2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-17
in which:
B
tan
2
2
P11
1
K h1 H 1 x
2
B
tan
2
2
P21
1
K h2 H 1 x
2
P12
1
K h1 H H 1 x
2
B
tan
2
P22
1
K h2 H H 1 x
2
B
tan
2
P13
1
K h1 H H
2
H1 x
B
tan
2
P23
1
K h2 H H
2
H1 x
B
tan
2
(C12.6.2.2.5-2)
When the pressures are substituted
Eq. C12.6.2.2.5-1, the following results:
E ( x)
A2 x 2 A1 x A0
into
(C12.6.2.2.5-3)
in which:
A2
1
2
H1 L
A1
1
2
H1 L
A0
L
L
2
( K h1 K h 2 )
[ B( K h1 K h 2 ) tan
H ( K h1 K h 2 )]
1
[(3B 2 tan 2
4 H 2 )( K h1 K h 2 )
24
6 HB( K h1 K h 2 ) tan ]
(C12.6.2.2.5-4)
The support forces for the unbalanced distribution
load, E(x), are:
F
S1
S2
1
L sec (2 A2 L2 3 A1 L 6 A0 )
6
1 L
[ A2 L 2(3L 2 B tan ) A1 L(4 L
12 B
3B tan ) 6 A0 ( L B tan )]
1 L
[ A2 L 2(3L 2 B tan ) A1 L(4 L
12 B
3B tan ) 6 A0 ( L B tan )]
(C12.6.2.2.5-5)
For values of Kh, see Figure C12.6.2.2.5-2.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
12-18
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure C12.6.2.2.5-2—Lateral Earth Pressure as a Function of Ground Slope
12.6.2.3—Uplift
C12.6.2.3
Uplift shall be considered where structures are
installed below the highest anticipated groundwater
level.
To satisfy this provision, the dead load on the crown
of the structure should exceed the buoyancy of the
culvert, using load factors as appropriate.
12.6.3—Safety against Soil Failure
12.6.3.1—Bearing Resistance and Stability
Pipe structures and footings for buried structures
shall be investigated for bearing capacity failure and
erosion of soil backfill by hydraulic gradients.
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2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-19
12.6.3.2—Corner Backfill for Metal Pipe Arches
The corner backfill for metal pipe arches shall be
designed to account for corner pressure taken as the arch
thrust divided by the radius of the pipe-arch corner. The
soil envelope around the corners of pipe arches shall
resist this pressure. Placement of select structural
backfill compacted to unit weights higher than normal
may be specified.
12.6.4—Hydraulic Design
Design criteria, as specified in Article 2.6 and
―
Hydraulic Design of Highway Culverts,‖ FHWA
(1985), for hydraulic design considerations shall apply.
12.6.5—Scour
Buried structures shall be designed so that no
movement of any part of the structure will occur as a
result of scour.
In areas where scour is a concern, the wingwalls
shall be extended far enough from the structure to
protect the structural portion of the soil envelope
surrounding the structure. For structures placed over
erodible deposits, a cut-off wall or scour curtain,
extending below the maximum anticipated depth of
scour or a paved invert, shall be used. The footings of
structures shall be placed not less than 2.0 ft below the
maximum anticipated depth of scour.
12.6.6—Soil Envelope
12.6.6.1—Trench Installations
The minimum trench width shall provide sufficient
space between the pipe and the trench wall to ensure
sufficient working room to properly and safely place and
compact backfill material.
The contract documents shall require that stability
of the trench be ensured by either sloping the trench
walls or providing support of steeper trench walls in
conformance with OSHA or other regulatory
requirements.
12.6.6.2—Embankment Installations
The minimum width of the soil envelope shall be
sufficient to ensure lateral restraint for the buried
structure. The combined width of the soil envelope and
embankment beyond shall be adequate to support all the
loads on the culvert and to comply with the movement
requirements specified in Article 12.6.2.
C12.6.6.1
As a guide, the minimum trench width should not
be less than the greater of the pipe diameter plus 16.0 in.
or the pipe diameter times 1.5 plus 12.0 in. The use of
specially designed equipment may enable satisfactory
installation and embedment even in narrower trenches.
If the use of such equipment provides an installation
meeting the requirements of this Article, narrower
trench widths may be used as approved by the Engineer.
For trenches excavated in rock or high-bearing
soils, decreased trench widths may be used up to the
limits required for compaction. For these conditions, the
use of a flowable backfill material, as specified in
Article 12.4.1.3, allows the envelope to be decreased to
within 6.0 in. along each side of the pipe.
C12.6.6.2
As a guide, the minimum width of the soil envelope
on each side of the buried structure should not be less
than the widths specified in Table C12.6.6.2-1:
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2012
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12-20
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table C12.6.6.2-1—Minimum Width of Soil Envelope
Diameter, S (in.)
Minimum Envelope Width (ft)
<24
24–144
>144
12.6.6.3—Minimum Cover
2013 Revision
The minimum cover, including a well-compacted
granular subbase and base course, shall not be less than
that specified in Table 12.6.6.3-1, where:
S
Bc
Bc
ID
=
=
=
=
diameter of pipe (in.)
outside diameter or width of the structure (ft)
out-to-out vertical rise of pipe (ft)
inside diameter (in.)
S/12
2.0
5.0
C12.6.6.3
McGrath et al. (2005) has shown that the significant
thermal expansion in thermoplastic pipe can affect
pavement performance under shallow fills. Depending
on the pipe material and the pavement type above it, the
minimum cover may include the pavement thickness and
base course, along with the sub-base.
If the minimum cover provided in Table 12.6.6.3-1
is not sufficient to avoid placement of the pipe within
the pavement layer, then the minimum cover should be
increased to a minimum of the pavement thickness,
unless an analysis is performed to determine the effect
on both the pipe and the pavement.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-21
Table 12.6.6.3-1—Minimum Cover
Type
Corrugated Metal Pipe
Spiral Rib Metal Pipe
Condition
Structural Plate Pipe
Structures
Long-Span Structural Plate
Pipe Structures
Structural Plate Box
Structures
Deep Corrugated Structural Plate
Structures
Thermoplastic Pipe
Minimum Cover*
S/8 > 12.0 in.
S/4 > 12.0 in.
S/2 > 12.0 in.
Steel Conduit
Aluminum Conduit where S
< 48.0 in.
Aluminum Conduit where S
> 48.0 in.
___
S/2.75 > 24.0 in.
S/8 > 12.0 in.
___
Refer to Table 12.8.3.1.1-1
___
1.4 ft. as specified in
Article 12.9.1
See Article 12.8.9.4
___
Under unpaved areas
Under paved roads
* Minimum cover taken from top of rigid pavement or bottom of flexible pavement
Type
Condition
Reinforced Concrete Pipe
Under unpaved areas or top of flexible
pavement
ID/8 > 12.0 in.
ID/2 > 24.0 in.
Type
Reinforced Concrete Pipe
Minimum Cover
9.0 in.
Condition
Under bottom of rigid pavement
Minimum Cover
Bc/8 or B’c/8, whichever is greater, >
12.0 in.
If soil cover is not provided, the top of precast or
cast-in-place reinforced concrete box structures shall be
designed for direct application of vehicular loads.
Additional cover requirements during construction
shall be taken as specified in Article 30.5.5 of the
AASHTO LRFD Bridge Construction Specifications.
12.6.7—Minimum Spacing between Multiple Lines of
Pipe
C12.6.7
The spacing between multiple lines of pipe shall be
sufficient to permit the proper placement and
compaction of backfill below the haunch and between
the structures.
Contract documents should require that backfilling
be coordinated to minimize unbalanced loading between
multiple, closely spaced structures. Backfill should be
kept level over the series of structures when possible.
The effects of significant roadway grades across a series
of structures shall be investigated for the stability of
flexible structures subjected to unbalanced loading.
As a guide, the minimum spacing between pipes
should not be less than that shown in Table C12.6.7-1.
Table C12.6.7-1—Minimum Pipe Spacing
Type of Structure
Minimum Distance Between
Pipes (ft)
Round Pipes Diameter, D
(ft)
<2.0
2.0–6.0
>6.0
1.0
D/2
3.0
Pipe Arches
Span, S (ft)
<3.0
3.0–9.0
9.0–16.0
1.0
S/3
3.0
Arches
Span, S (ft)
All Spans
2.0
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2012
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12-22
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The minimum spacing can be reduced if a flowable
backfill material, as specified in Article 12.4.1.3, is
placed between the structures.
12.6.8—End Treatment
12.6.8.1—General
C12.6.8.1
Protection of end slopes shall be given special
consideration where backwater conditions occur or
where erosion or uplift could be expected. Traffic safety
treatments, such as a structurally adequate grating that
conforms to the embankment slope, extension of the
culvert length beyond the point of hazard, or provision
of guide rail, should be considered.
12.6.8.2—Flexible Culverts Constructed on Skew
The end treatment of flexible culverts skewed to the
roadway alignment and extending through embankment
fill shall be warped to ensure symmetrical loading along
either side of the pipe or the headwall shall be designed
to support the full thrust force of the cut end.
Culvert ends may represent a major traffic hazard.
When backwater conditions occur, pressure flow at
the outlet end of culverts can result in uplift of pipe
sections having inadequate cover and scour of erosive
soils due to high water flow velocities. Measures to
control these problems include anchoring the pipe end in
a concrete headwall or burying it in riprap having
sufficient mass to resist uplift forces as well as lining
outlet areas with riprap or concrete to prevent scour.
C12.6.8.2
For flexible structures, additional reinforcement of
the end is recommended to secure the metal edges at
inlet and outlet against hydraulic forces. Reinforcement
methods include reinforced concrete or structural steel
collars, tension tiebacks or anchors in soil, partial
headwalls, and cut-off walls below invert elevation.
As a guide in Figure C12.6.8.2-1, limits are
suggested for skews to embankments unless the
embankment is warped. It also shows examples of
warping an embankment cross-section to achieve a
square-ended pipe for single and multiple flexible pipe
installations where the minimum width of the warped
embankment, d , is taken as 1.50 times the sum of the
rise of the culvert and the cover or three times the span
of the culvert, whichever is less.
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2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-23
Figure C12.6.8.2-1—End Treatment of Skewed Flexible
Culvert
12.6.9—Corrosive and Abrasive Conditions
C12.6.9
The degradation of structural resistance due to
corrosion and abrasion shall be considered.
Several long-term tests of the field performance of
buried structures have resulted in development of
empirical guidelines for estimating the effects of
corrosion and abrasion. A representative listing includes
Bellair and Ewing (1984), Koepf and Ryan (1986), Hurd
(1984), Meacham et al. (1982), Potter (1988), NCHRP
Synthesis No. 50 (1978), and Funahashi and Bushman
(1991).
For highly abrasive conditions, a special design may
be required. Protective coatings may be shop- or fieldapplied in accordance with AASHTO M 190, M 224,
M 243, and M 245 (ASTM A762).
If the design of a metal or thermoplastic culvert is
controlled by flexibility factors during installation, the
requirements for corrosion and/or abrasion protection
may be reduced or eliminated, provided that it is
demonstrated that the degraded culvert will provide
adequate resistance to loads throughout the service life
of the structure.
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2012
Edition
12-24
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
12.7—METAL PIPE, PIPE ARCH, AND ARCH
STRUCTURES
2013 Revision
12.7.1—General
C12.7.1
The provisions herein shall apply to the design of
buried corrugated and spiral rib metal pipe and structural
plate pipe structures.
Corrugated metal pipe and pipe-arches may be of
riveted, welded, or lockseam fabrication with annular or
helical corrugations. Structural plate pipe, pipe-arches,
and arches shall be bolted with annular corrugations
only.
The rise-to-span ratio of structural plate arches shall
not be less than 0.3.
The provisions of Article 12.8 shall apply to
structures with a radius exceeding 13.0 ft.
These structures become part of a composite system
comprised of the metal pipe section and the soil
envelope, both of which contribute to the structural
behavior of the system.
For information regarding the manufacture of
structures and structural components referred to herein,
AASHTO M 196 (ASTM B745) for aluminum, M 36
(ASTM A760) for steel corrugated metal pipe and pipearches, and M 167M/M 167 (ASTM A761/A761M) for
steel and M 219 (ASTM B746) for aluminum structural
plate pipe may be consulted.
12.7.2—Safety against Structural Failure
Corrugated and spiral rib metal pipe and pipe arches
and structural plate pipe shall be investigated at the
strength limit state for:
Wall area of pipe,
Buckling strength, and
Seam resistance for structures with longitudinal
seams.
12.7.2.1—Section Properties
2013 Revision
Dimensions and properties of pipe cross-sections;
minimum seam strength; mechanical and chemical
requirements for aluminum corrugated and steel
corrugated pipe and pipe-arch sections; and aluminum
and steel corrugated structural plate pipe, pipe-arch, and
arch sections, may be taken as given in Appendix A12.
12.7.2.2—Thrust
C12.7.2.2
2013 Revision
The factored thrust, TL, per unit length of wall shall
be taken as:
TL
PF
S
24
(12.7.2.2-1)
Factored vertical crown pressure is calculated as the
factored free-field soil pressure at the elevation of the
top of the structure, plus the factored live load pressure
distributed through the soil cover to the top of the
structure.
where:
TL =
S =
PF =
factored thrust per unit length (kip/ft)
pipe span (in.)
factored vertical crown pressure due to earth
and live loads (ksf)
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2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-25
12.7.2.3—Wall Resistance
The factored axial resistance, Rn, per unit length of
wall, without consideration of buckling, shall be taken
as:
Rn
Fy A
(12.7.2.3-1)
where:
A =
Fy =
=
wall area (in.2/ft)
yield strength of metal (ksi)
resistance factor as specified in Article 12.5.5
12.7.2.4—Resistance to Buckling
C12.7.2.4
The wall area, calculated using Eq. 12.7.2.3-1, shall
be investigated for buckling. If fcr < Fy, A shall be
recalculated using fcr in lieu of Fy.
r
k
If S
24 Em
, then f cr
Fu
Fu kS
r
48Em
Fu
2
The use of 0.22 for the soil stiffness is thought to be
conservative for the types of backfill material allowed
for pipe and arch structures. This lower bound on soil
stiffness has a long history of use in previous editions of
the Standard Specifications.
(12.7.2.4-1)
r
k
If S
24 Em
, then f cr
Fu
12 Em
kS
r
(12.7.2.4-2)
2
where:
S
Em
Fu
fcr
r
k
=
=
=
=
=
=
diameter of pipe or span of plate structure (in.)
modulus of elasticity of metal (ksi)
tensile strength of metal (ksi)
critical buckling stress (ksi)
radius of gyration of corrugation (in.)
2013 Revision
soil stiffness factor taken as 0.22
12.7.2.5—Seam Resistance
For pipe fabricated with longitudinal seams, the
factored resistance of the seam shall be sufficient to
develop the factored thrust in the pipe wall, TL.
12.7.2.6—Handling and Installation
Requirements
C12.7.2.6
Handling flexibility shall be indicated by a
flexibility factor determined as:
FF
2
S
Em I
Transverse stiffeners may be used to assist
corrugated structural plate structures to meet flexibility
factor requirements.
(12.7.2.6-1)
2013 Revision
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2012
Edition
12-26
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Values of the flexibility factors for handling and
installation shall not exceed the values for steel and
aluminum pipe and plate pipe structures as specified in
Article 12.5.6.
12.7.3—Smooth Lined Pipe
Corrugated metal pipe composed of a smooth liner
and corrugated shell attached integrally at helical seams,
spaced not more than 30.0 in. apart, may be designed on
the same basis as a standard corrugated metal pipe
having the same corrugations as the shell and a weight
per ft not less than the sum of the weights per ft of liner
and helically corrugated shell.
The pitch of corrugations shall not exceed 3.0 in.,
and the thickness of the shell shall not be less than
60 percent of the total thickness of the equivalent
standard pipe.
12.7.4—Stiffening Elements for Structural Plate
Structures
The stiffness and flexural resistance of structural
plate structures may be increased by adding
circumferential stiffening elements to the crown.
Stiffening elements shall be symmetrical and shall span
from a point below the quarter-point on one side of the
structure, across the crown, and to the corresponding
point on the opposite side of the structure.
C12.7.4
Acceptable stiffening elements are:
Continuous longitudinal structural stiffeners
connected to the corrugated plates at each side of
the top arc: metal or reinforced concrete, either
singly or in combination; and
Reinforcing ribs formed from structural shapes,
curved to conform to the curvature of the plates,
fastened to the structure to ensure integral action
with the corrugated plates, and spaced at such
intervals as necessary.
12.7.5—Construction and Installation
The contract documents shall require that
construction and installation conform to Section 26,
AASHTO LRFD Bridge Construction Specifications.
12.8—LONG-SPAN STRUCTURAL PLATE
STRUCTURES
12.8.1—General
C12.8.1
The provisions herein and in Article 12.7 shall
apply to the structural design of buried long-span
structural plate corrugated metal structures.
The following shapes, illustrated in Figure 12.8.1-1,
shall be considered long-span structural plate structures:
Structural plate pipe and arch shape structures that
require the use of special features specified in
Article 12.8.3.5, and
These structures become part of a composite system
comprised of the metal structure section and the soil
envelope, both of which contribute to the behavior of the
system.
Special shapes of any size having a radius of
curvature greater than 13.0 ft in the crown or side
plates. Metal box culverts are not considered
long-span structures and are covered in
Article 12.9.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-27
Figure 12.8.1-1—Long-Span Shapes
12.8.2—Service Limit State
No service limit state criteria need be required.
C12.8.2
Soil design and placement requirements for longspan structures are intended to limit structure
deflections. The contract documents should require that
construction procedures be monitored to ensure that
severe deformations do not occur during backfill
placement and compaction.
12.8.3—Safety against Structural Failure
C12.8.3
With the exception of the requirements for buckling
and flexibility, the provisions of Article 12.7 shall apply,
except as described herein.
Dimensions and properties of structure crosssections, minimum seam strength, mechanical and
chemical requirements, and bolt properties for long-span
structural plate sections shall be taken as specified in
Appendix A12 or as described herein.
Most long-span culverts are designed for a larger
load factor; however, the limit states of flexure and
buckling are ignored for those structures. Considering
these limit states reduces the uncertainty in the final
design and permits use of a lower load factor. This is the
same approach used for metal box culverts.
12.8.3.1—Section Properties
12.8.3.1.1—Cross-Section
C12.8.3.1.1
The provisions of Article 12.7 shall apply, except as
specified.
Structures not described herein shall be regarded as
special designs.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
12-28
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table A12-3 shall apply. Minimum requirements
for section properties shall be taken as specified in
Table 12.8.3.1.1-1. Covers that are less than that shown
in Table 12.8.3.1-1 and that correspond to the minimum
plate thickness for a given radius may be used if ribs are
used to stiffen the plate. If ribs are used, the plate
thickness may not be reduced below the minimum
shown for that radius, and the moment of inertia of the
rib and plate section shall not be less than that of the
thicker unstiffened plate corresponding to the fill height.
Use of soil cover less than the minimum values shown
for a given radius shall require a special design.
Design not covered in Table 12.8.3.1.1-1 should not
be permitted unless substantiated by documentation
acceptable to the Owner.
Sharp radii generate high soil pressures. Avoid high
ratios when significant heights of fill are involved.
Table 12.8.3.1.1-1—Minimum Requirements for Long-Span Structures with Acceptable Special Features
Top Radius (ft)
6" 2" Corrugated
Steel Plate—Top Arc
Minimum Thickness
(in.)
≤15.0
0.111
Top Arc Minimum Thickness (in.)
15.0–17.0
17.0–20.0
0.140
0.170
The following geometric limits shall apply:
20.0–23.0
0.218
23.0–25.0
0.249
20.0–23.0
23.0–25.0
—
—
—
—
3.0
3.0
3.0
—
—
—
—
—
4.0
4.0
Geometric Limits
Maximum plate radius—25.0 ft
Maximum central angle of top arc—80.0°
Minimum ratio, top arc radius to side arc radius—2
Maximum ratio, top arc radius to side arc radius—5
Top Radius (ft)
Steel thickness
without ribs (in.)
0.111
0.140
0.170
0.188
0.218
0.249
0.280
≤ 15.0
2.5
2.5
2.5
2.5
2.0
2.0
2.0
Minimum Cover (ft)
15.0–17.0
17.0–20.0
—
3.0
3.0
3.0
2.5
2.0
2.0
—
—
3.0
3.0
2.5
2.5
2.5
12.8.3.1.2—Shape Control
The requirements of Articles 12.7.2.4 and 12.7.2.6
shall not apply for the design of long-span structural
plate structures.
12.8.3.1.3—Mechanical and Chemical
Requirements
Tables A12-3, A12-8, and A12-10 shall apply.
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2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-29
12.8.3.2—Thrust
The factored thrust in the wall shall be determined
by Eq. 12.7.2.2-1, except the value of S in the Equation
shall be replaced by twice the value of the top arc radius,
RT.
12.8.3.3—Wall Area
The provisions of Article 12.7.2.3 shall apply.
12.8.3.4—Seam Strength
The provisions of Article 12.7.2.5 shall apply.
12.8.3.5—Acceptable Special Features
12.8.3.5.1—Continuous Longitudinal Stiffeners
Continuous longitudinal stiffeners shall be
connected to the corrugated plates at each side of the top
arc. Stiffeners may be metal or reinforced concrete
either singly or in combination.
12.8.3.5.2—Reinforcing Ribs
Reinforcing ribs formed from structural shapes may
be used to stiffen plate structures. Where used, they
should be:
Curved to conform to the curvature of the plates,
Fastened to the structure as required to ensure
integral action with the corrugated plates, and
Spaced at such intervals as necessary to increase the
moment of inertia of the section to that required for
design.
12.8.4—Safety against Structural Failure—
Foundation Design
12.8.4.1—Settlement Limits
C12.8.4.1
A geotechnical survey of the site shall be made to
determine that site conditions will satisfy the
requirement that both the structure and the critical
backfill zone on each side of the structure be properly
supported. Design shall satisfy the requirements of
Article 12.6.2.2, with the following factors to be
considered when establishing settlement criteria:
Once the structure has been backfilled over the
crown, settlements of the supporting backfill
relative to the structure must be limited to control
dragdown forces. If the sidefill will settle more than
the structure, a detailed analysis may be required.
Settlements along the longitudinal centerline of arch
structures must be limited to maintain slope and
preclude footing cracks in arches.
Once the top arc of the structure has been
backfilled, dragdown forces may occur if the structure
backfill settles into the foundation more than the
structure. This results in the structure carrying more soil
load than the overburden directly above it. If undertaken
prior to erecting the structure, site improvements such as
surcharging, foundation compacting, etc., often
adequately correct these conditions.
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2012
Edition
12-30
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Calculated differential settlements across the
structure taken from springline-to-springline, Δ, shall
satisfy:
0.01S 2
R
(12.8.4.1-1)
Where the structure will settle uniformly with the
adjacent soils, long-spans with full inverts can be built
on a camber to achieve a proper final grade.
For design, differential settlement between the
footings taken across the structure is limited to avoid
excessive eccentricity. The limit on any settlementinduced rotation of the structure maintains the top arc
centerline within one percent of span, as shown in
Figure C12.8.4.1-1.
where:
S
=
R
=
span of structure between springlines of longspan structural plate structures (ft)
rise of structure (ft)
More restrictive settlement limits may be required where
needed to protect pavements or to limit longitudinal
differential deflections.
Figure C12.8.4.1-1—Differential Settlement
The rotation of the structure, θ, may be determined as:
tan
12.8.4.2—Footing Reactions in Arch Structures
Footing reactions may be taken as:
RV
VDL VLL cos
(12.8.4.2-1)
RH
VDL VLL sin
(12.8.4.2-2)
in which:
VDL =
VLL =
n =
[H2(S) – AT] γs/2
n(AL)/(8 + 2 H1)
integer (2H1/Lw + 2) ≤ number of adjoining
traffic lanes
1
S
(C12.8.4.1-1)
C12.8.4.2
Footing reactions are calculated by simple statics to
support the vertical loads. Soil load footing reactions
(VDL) are taken as the weight of the fill and pavement
above the springline of the structure. Where footings
extend out beyond the springline and the foundation has
not previously carried the design overburden, this
additional soil load (Ev) may need to be added to VDL in
an embankment installation.
Live loads that provide relatively limited pressure
zones acting on the crown of the structure may be
distributed to the footings as indicated in
Figure C12.8.4.2-1.
where:
RV
RH
Δ
AL
=
=
=
=
vertical footing reaction component (kip/ft)
horizontal footing reaction component (kip/ft)
return angle of the structure (degrees)
axle load (kip), taken as 50 percent of all axle
loads that can be placed on the structure at one
time, i.e.:
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-31
32.0 kip for the design truck axle
50.0 kip for the design tandem axle pair
160.0 kip for E80 railroad loading
AT =
H1 =
H2 =
Lw =
γs =
S =
area of the top portion of the structure above
the springline (ft2)
height of cover above the footing to traffic
surface (ft)
height of cover from the springline of the
structure to traffic surface (ft)
lane width (ft)
unit weight of soil (kcf)
span (ft)
The distribution of live load through the fill shall be
based on any accepted methods of analysis.
Figure C12.8.4.2-1—Live-Load Footing Reaction Due to
Axles of the Design Truck, per Footing
12.8.4.3—Footing Design
Reinforced concrete footings shall be designed in
accordance with Article 10.6 and shall be proportioned
to satisfy settlement requirements of Article 12.8.4.1.
12.8.5—Safety against Structural Failure—Soil
Envelope Design
12.8.5.1—General
C12.8.5.1
Structural backfill material in the envelope around
the structure shall satisfy the requirements of
Article 12.4.1.3 for long-span structures. The width of
the envelope on each side of the structure shall be
proportioned to limit shape change during construction
activities outside the envelope and to control deflections
at the service limit state.
12.8.5.2—Construction Requirements
The structural backfill envelope shall either extend
to the trench wall and be compacted against it or extend
a distance adequate to protect the shape of the structure
from construction loads. The remaining trench width
may be filled with suitable backfill material compacted
Structure erection, backfill, and construction shall
meet all the requirements of Section 26, AASHTO LRFD
Bridge Construction Specifications. The performance of
the structure depends upon the in-situ embankment or
other fill materials beyond the structural backfill. Design
must consider the performance of all materials within
the zone affected by the structure.
C12.8.5.2
The purpose of this provision is to control shape
change from construction activities outside the envelope
in trench conditions.
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2012
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12-32
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
to satisfy the requirements of Article 12.8.5.3. In
embankment conditions, the minimum structural backfill
width shall be taken as 6.0 ft. Where dissimilar materials
not meeting geotechnical filter criteria are used adjacent
to each other, a suitable geotextile shall be provided to
avoid migration.
12.8.5.3—Service Requirements
C12.8.5.3
The width of the envelope on each side of the
structure shall be adequate to limit horizontal
compression strain to one percent of the structure’s span
on each side of the structure.
Determination of the horizontal compressive strain
shall be based on an evaluation of the width and quality
of the structural backfill material selected as well as the
in-situ embankment or other fill materials within the
zone on each side of the structure taken to extend to a
distance equal to the rise of the structure, plus its cover
height as indicated in Figure 12.8.5.3-1.
Forces acting radially off the small radius corner arc
of the structure at a distance, d1, from the structure may
be taken as:
P1
T
Rc
d1
(12.8.5.3-1)
The purpose of this provision is to limit defections
under service loads. The limit on soil compression limits
the theoretical design increase in span to two percent.
This is a design limit, not a performance limit. Any span
increase that occurs is principally due to the
consolidation of the side support materials as the
structure is loaded during backfilling. These are
construction movements that attenuate when full cover
is reached.
Eqs. 12.8.5.3-1 and 12.8.5.3-2 conservatively
assume that the pressure from the structure acts radially
outward from the corner arc without further dissipation.
Figure C12.8.5.3-1 provides the geometric basis of these
Equations.
where:
P1 =
d1 =
T =
Rc =
horizontal pressure from the structure at a
distance, d1 (ksf)
distance from the structure (ft)
total dead load and live load thrust in the
structure (Article 12.8.3.2) (kip/ft)
corner radius of the structure (ft)
The required envelope width adjacent the pipe, d,
may be taken as:
d
T
PBrg
Rc
Figure C12.8.5.3-1—Radial Pressure Diagram
(12.8.5.3-2)
where:
d
=
PBrg
=
required envelope width adjacent to the
structure (ft)
allowable bearing pressure to limit
compressive strain in the trench wall or
embankment (ksf)
The structural backfill envelope shall be taken to
continue above the crown to the lesser of:
The minimum cover level specified for that
structure,
The bottom of the pavement or granular base course
where a base course is present below the pavement,
or
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-33
The bottom of any relief slab or similar construction
where one is present.
Figure 12.8.5.3-1—Typical Structural Backfill Envelope
and Zone of Structure Influence
12.8.6—Safety against Structural Failure—End
Treatment Design
12.8.6.1—General
C12.8.6.1
End treatment selection and design shall be
considered as an integral part of the structural design.
12.8.6.2—Standard Shell End Types
The standard end types for the corrugated plate shell
shall be taken to be those shown in Figure 12.8.6.2-1.
Proper end treatment design ensures proper support
of the ends of the structure while providing protection
from scour, hydraulic uplift, and loss of backfill due to
erosion forces.
C12.8.6.2
Standard end types refer to the way the structural
plate structure’s ends are cut to match the fill slope,
stream banks, etc. While the type of end selected may
have aesthetic or hydraulic considerations, the structural
design must ensure adequate structural strength and
protection from erosion. Hydraulic considerations may
require wingwalls, etc.
Step bevel, full bevel, and skewed ends all involve
cutting the plates within a ring. Each has its own
structural considerations.
The square end is the simplest arrangement. No
plates are cut and the barrel retains its integrity.
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12-34
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
(A) SQUARE END
(B) STEP BEVEL
(C) SKEW CUT END
(REQUIRES FULL HEADWALL)
Figure 12.8.6.2-1—Standard Structure End Types
The following considerations shall apply to step
bevels:
The rise of the top step shall be equal to or greater
than the rise of the top arc, i.e., plates in the top arc
are left uncut.
Step bevels cut the corner (and side on pear and
high profile arch shapes) plates on a diagonal (bevel) to
match the fill slope.
Step bevels are widely used. The plates in the large
radius top arc are left uncut to support the sides of the
structure near each end.
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
For structures with inverts, the bottom step shall
satisfy the requirements for a top step.
For arches, the bottom step shall be a minimum of
6.0 in. high.
The slope of the cut plates generally should be no
flatter than 3:1.
The upper edge of the cut plates shall be bolted to
and supported by a structural concrete slope collar,
slope pavement, or similar device.
Full bevel ends shall be used in special design only.
Structures with full inverts shall have a bottom step
conforming to the requirements for step bevel ends.
The bevel cut edge of all plates shall be supported
by a suitable, rigid concrete slope collar.
Skew cut ends shall be fully connected to and
supported by a headwall of reinforced concrete or other
rigid construction. The headwall shall extend an
adequate distance above the crown of the structure to be
capable of reacting the ring compression thrust forces
from the cut plates. In addition to normal active earth
and live load pressures, the headwall shall be designed
to react a component of the radial pressure exerted by
the structure as specified in Article 12.8.5.
12.8.6.3—Balanced Support
Designs and details shall provide soil support that is
relatively balanced from side-to-side, perpendicularly
across the structure. In lieu of a special design, slopes
running perpendicularly across the structure shall not
exceed ten percent for cover heights of 10.0 ft or less
and 15 percent for higher covers.
When a structure is skewed to an embankment, the
fill shall be detailed to be warped to maintain balanced
support and to provide an adequate width of backfill and
embankment soil to support the ends.
12-35
Invert plates must be left uncut to avoid leaving the
invert as triangular shaped elements, when viewed in
plan, running upstream and downstream.
Diagonally cut corner and side plates become a
retaining wall, supporting the fill slope beside them.
They must be provided with suitable, rigid support at the
top that acts as a top wale beam and be limited in length.
These plates have limited longitudinal strength and
inadequate bending strength or fixity to act as a
cantilevered retaining wall.
When a full bevel cuts the top plates, additional
support is necessary to backfill the structure. Typically,
the top step is left in place and field cut only after a
suitable rigid concrete slope collar has been poured and
adequately cured.
Ring compressive thrust forces act circumferentially
around the structure following the corrugations. At the
skew cut ends of the plate, these forces act tangentially
to the plate and must be resisted by a headwall.
Additionally, because a skew cut structure is not
perpendicular to the headwall, a portion of the radial
pressure from the structure acts normal to the back of
the headwall.
C12.8.6.3
Flexible structures have relatively low bending
strength. If the earth support is not balanced, the
structure in effect becomes a retaining wall. An
excessive imbalance causes shape distortion and
ultimately failure.
When a structure is skewed to an embankment, two
diagonally opposite areas at the ends of the structure are
not adequately supported. This must be corrected by
extending the embankment an adequate distance out
beside the structure.
In lieu of a special design, details provided in
Article C12.6.8.2 may be considered.
A properly warped embankment is characterized by
equal elevation topographical lines crossing the structure
perpendicularly and extending beyond it a suitable
distance so that the volume of earth included in the warp
provides a gravity retaining wall capable of supporting
the radial pressures from the structure with adequate
safety.
12.8.6.4—Hydraulic Protection
12.8.6.4.1—General
In hydraulic applications, provisions shall be made
to protect the structure, taken to include the shell,
footings, structural backfill envelope, and other fill
materials within the zone influenced by the structure.
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12-36
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
12.8.6.4.2—Backfill Protection
Design or selection of backfill gradation shall
include consideration of loss of backfill integrity due to
piping. If materials prone to piping are used, the
structure and ends of the backfill envelope shall be
adequately sealed to control soil migration and/or
infiltration.
C12.8.6.4.2
Backfill piping and migration is always a major
consideration in selecting its specific gradation. The
ends of the backfill envelope may be sealed using one or
a combination of a compacted clay cap, concrete slope
pavements, grouted riprap, headwalls to the design
storm elevation, and similar details.
12.8.6.4.3—Cut-Off (Toe) Walls
All hydraulic structures with full inverts shall be
designed and detailed with upstream and downstream
cut-off walls. Invert plates shall be bolted to cut-off
walls at a maximum 20.0-in. center-to-center spacing
using 0.75-in. bolts.
The cut-off wall shall extend to an adequate depth
to limit hydraulic percolation to control uplift forces as
specified in Article 12.8.6.4.4 and scour as specified in
Article 12.8.6.4.5.
12.8.6.4.4—Hydraulic Uplift
Hydraulic uplift shall be considered for hydraulic
structures with full inverts where the design flow level
in the pipe can drop quickly. The design shall provide
means to limit the resulting hydraulic gradients, with the
water level higher in the backfill than in the pipe, so that
the invert will not buckle and the structure will not float.
Buckling may be evaluated as specified in
Article 12.7.2.4, with the span of the structure taken as
twice the invert radius.
12.8.6.4.5—Scour
C12.8.6.4.4
Structural plate structures are not watertight and
allow for both infiltration and exfiltration through the
structure’s seams, bolt holes, and other discontinuities.
Where uplift can be a concern, designs typically employ
adequate cut-off walls and other means to seal off water
flow into the structural backfill.
C12.8.6.4.5
Scour design shall satisfy the requirements of
Article 12.6.5. Where erodible soils are encountered,
conventional means of scour protection may be
employed to satisfy these requirements.
Deep foundations such as piles or caissons should
not be used unless a special design is provided to
consider differential settlement and the inability of
intermittent supports to retain the structural backfill if
scour proceeds below the pile cap.
Structures with full inverts eliminate footing scour
considerations when adequate cut-off walls are used. For
arches, reinforced concrete invert pavements, riprap,
grouted riprap, etc., can be employed to provide scour
protection.
12.8.7—Concrete Relieving Slabs
C12.8.7
Concrete relieving slabs may be used to reduce
moments in long-span structures.
The length of the concrete relieving slab shall be at
least 2.0 ft greater than the span of the structure. The
relieving slab shall extend across the width subject to
vehicular loading, and its depth shall be determined as
specified in Article 12.9.4.6.
Application of a typical concrete relieving slab is
shown in Figure 12.9.4.6-1.
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-37
12.8.8—Construction and Installation
The construction documents shall require that
construction and installation conform to Section 26 of
the AASHTO LRFD Bridge Construction Specifications.
12.8.9—Deep Corrugated Structural Plate Structures
12.8.9.1—General
C12.8.9.1
The provisions of this Section shall apply to the
structural design of buried, deep corrugated structural
plate. These structures are designed as long-span
culverts but must also meet provisions for flexure and
general buckling. These structures may be manufactured
in multiple shapes. Flexibility criteria and special
features are not applicable to deep corrugated structures.
The rise to span limit of 0.3 in Article 12.7.1 does not
apply.
The design of long-span metal structures in these
Specifications is currently completed with empirical
procedures that limit the shapes and plate thicknesses for
the structures and require special features. If the
provisions are met, then no design is required for flexure
or buckling. NCHRP Report 473 recommended
updating design provisions for long-span structures and
included provisions to allow structures outside the
current limits for long-span structures but included limit
states for flexure and general buckling. Article 12.8.9
provides a design procedure for such structures. The
provisions of Article 12.8.9 apply to structures
fabricated from deep corrugated plate, defined in Article
12.2 as corrugated plate with a corrugation depth greater
than 5.0 in.
12.8.9.2—Width of Structural Backfill
12.8.9.2.1—Deep Corrugated Structures with Ratio
of Crown Radius to Haunch Radius ≤5
The structural backfill zone around deep corrugated
structures with ratio of crown radius to haunch radius ≤5
shall extend to at least the minimum cover height above
the crown. At the sides of the structure, the minimum
extent of the structural backfill from the outside of the
structure springline shall meet one of the following:
Structure constructed in a trench in which the
natural soil is at least as stiff as the engineered soil:
8.0 ft or
Structure constructed in an embankment or in a
trench in which the natural soil is less stiff than the
engineered soil: one-third of the structure span but
not less than 10.0 ft or more than 17.0 ft.
but not less than required by culvert-soil interaction
analysis.
12.8.9.2.2—Deep Corrugated Structures with Ratio
of Crown Radius to Haunch Radius >5
The structural backfill zone around deep corrugated
structures with ratio of crown radius to haunch radius >5
shall extend to at least the minimum cover height above
the crown. At the sides of the structure, the minimum
extent of structural backfill shall meet one of the
following:
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12-38
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
For structures with spans up to and including 25.0 ft
5.0 in. and less than 5.0 ft of cover: a minimum of
3.5 ft beyond the widest part of the structure or
For structures with spans up to and including 25.0 ft
5.0 in. and greater than 5.0 ft of cover and for
structures with spans greater than 25.0 ft 5.0 in. at
all depths of fill: a minimum of one-fifth of the
structure span beyond the widest part of the
structure but not less than 5.0 ft nor more than
17.0 ft.
but not less than required by culvert-soil interaction
analysis.
12.8.9.3—Safety against Structural Failure
Deep corrugated structures shall be designed in
accordance with the provisions of Articles 12.8.1 to
12.8.8 except for modified or additional provisions as
follow in Article 12.8.9.
12.8.9.3.1—Structural Plate Requirements
Deep corrugated structural plate used to
manufacture structures designed under this section shall
meet the requirements of AASHTO M 167M/M 167.
Sections may be stiffened. If stiffening is provided
by ribs, the ribs shall be bolted to the structural plate
corrugation prior to backfilling using a bolt spacing of
not more than 16 in. The cross-section properties in
Table A12-14 shall apply.
12.8.9.3.2—Structural Analysis
Structures designed under the provisions of this
Article shall be analyzed by accepted finite element
analysis methods that consider both the strength and
stiffness properties of the structural plate and the soil. The
analysis shall produce thrust and moments for use in
design. The analysis must consider all applicable
combinations of construction, earth, live, and other
applicable load conditions. Springline thrust due to earth
load used in wall resistance, buckling, and seam
resistance design shall not be less than 1.3 times the
earth load thrust computed in accordance with
Article 12.7.2.2.
C12.8.9.3.1
It is acceptable to measure bolt spacing either at the
centroid or crest of the structural plate corrugation.
C12.8.9.3.2
The computer program CANDE was developed by
the FHWA specifically for the design of buried culverts
and has the necessary soil and culvert material models to
complete designs.
Because distribution of live loads to all long-span
culverts does not consider arching, application of the 1.3
factor should be limited to just the earth load component
of Article 12.7.2.2.
12.8.9.4—Minimum Depth of Fill
For deep corrugated structural plate structures, the
minimum depth of cover (HD) shall be the smaller of
3.0 ft or the limits for long-span structural plate
structures based on top radius and plate thickness in
Table 12.8.3.1.1-1. For deep corrugated structures with
the ratio of crown radius to haunch radius > 5, minimum
cover shall be 1.5 ft for spans ≤ 25.0 ft 5.0 in. and 2.0 ft
for spans > 25.0 ft 5.0 in. The minimum depth of cover
in all cases shall not be less than that required by
culvert-soil interaction analysis.
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12.8.9.5—Combined Thrust and Moment
C12.8.9.5
The combined effects of moment and thrust at all
stages of construction shall meet the following
requirement:
Tf
2
Rt
Mu
Mn
(12.8.9.5-1)
1.00
where:
Tf
Rt
Mu
Mn
Mp
=
=
=
=
=
factored thrust
factored thrust resistance = hFy A
factored applied moment
factored moment resistance = hMp
plastic moment capacity of section
12-39
The equation for combined moment and thrust is
taken from the provision for buried structures in the
Canadian Highway Bridge Design Code CSA S6 06.
The equation is more liberal than the AASHTO
equations for combined moment and thrust (axial force)
for steel structures in Article 12.8.9.6. However, the
provisions in Article 12.8.9.6 are based on strong axis
bending of wide flange sections. The equation for
combined moment and thrust is taken from the provision
for buried structures in the Canadian Highway Bridge
Design Code CSA S6 06. The equation is more liberal
than the AASHTO equations for combined moment and
thrust (axial force) for steel structures in Article 6.9.2.2.
However, the provisions in Article 6.9.2.2 are based on
strong axis bending of wide flange sections.
Figure C12.8.9.5-1—Strength Curves for Member of Zero Length:
(a) Strong-Axis; (b) Weak-Axis from White and Clark (1997)
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2012
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12-40
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
12.8.9.6—Global Buckling
C12.8.9.6
The factored thrust in the culvert wall under the
final installed condition shall not exceed the nominal
resistance to general buckling capacity of the culvert,
computed as:
Rb = 1.2 φb Cn ( E p I p
1
)3
(φ s M s Kb
2
3
)
Rh
The proposed buckling equations are taken from
the recommendations of NCHRP Report 473,
Recommended Specifications for Large-Span Culverts.
(12.8.9.6-1)
where:
Rb =
φb =
Cn =
Ep =
Ip
=
φs =
Ms =
Kb =
ν =
Rh =
=
S =
H =
nominal axial force in culvert wall to cause
general buckling
resistance factor for general buckling
scalar calibration factor to account for some
nonlinear effects = 0.55
modulus of elasticity of pipe wall material,
(ksi)
moment of inertia of stiffened culvert wall per
unit length, (in.4)
resistance factor for soil
constrained
modulus
of
embedment
(Table 12.12.3.5-1)
(1 − 2ν) / (1 − ν 2 )
Poisson’s ratio of soil
correction factor for backfill geometry
11.4/(11+S/H)
culvert span
depth of fill over top of culvert
C12.8.9.7
12.8.9.7—Connections
The factored moment resistance of longitudinal
connections shall be at least equal to the factored applied
moment but not less than the greater of:
•
75 percent of the factored moment resistance of the
member or
•
The average of the factored applied moment and the
factored moment resistance of the member.
The AASHTO LRFD Bridge Construction
Specifications require longitudinal joints to be staggered
to avoid a continuous line of bolts on a structure.
Moment resistance of connections may be obtained from
qualified tests or published standards.
12.9—STRUCTURAL PLATE BOX STRUCTURES
12.9.1—General
C12.9.1
The design method specified herein shall be limited
to depth of cover from 1.4 to 5.0 ft.
The provisions of this Article shall apply to the
design of structural plate box structures, hereinafter
called “metal box culverts.” The provisions of
Articles 12.7 and 12.8 shall not apply to metal box
culvert designs, except as noted.
If rib stiffeners are used to increase the flexural
resistance and moment capacity of the plate, the
transverse stiffeners shall consist of structural steel or
These Specifications are based on three types of
data:
•
Finite element soil-structure interaction analyses,
•
Field loading tests on instrumented structures, and
•
Extensive field experience.
These Specifications conform to the same standards
as those structures completed since about 1980.
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2012
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-41
Ribs shall be bolted to the plates to develop the plastic
flexural resistance of the composite section. Spacing
between ribs shall not exceed 2.0 ft on the crown and
4.5 ft on the haunch. Rib splices shall develop the plastic
flexural resistance required at the location of the splice.
reinforced rib plate structures of approximately
rectangular shape. They are intended for shallow covers
and low wide waterway openings. The shallow covers
and extreme shapes of box culverts require special
design procedures.
Metal box culverts differ greatly from conventional
metal culvert shapes. Metal box culverts are relatively
flat at the top and require a large flexural capacity due to
extreme geometry and shallow depths of cover of 5.0 ft
or less. Analyses over the range of sizes permitted under
these Specifications indicate that flexural requirements
govern the choice of section in all cases. The effects of
thrust are negligible in comparison with those of flexure.
This difference in behavior requires a different approach
in design.
For information regarding the manufacture of
structures and structural components referred to herein,
see AASHTO M 167M/M 167 (ASTM A761/A761M)
for steel and M 219 (ASTM B746) for aluminum.
12.9.2—Loading
C12.9.2
For live loads, the provisions of Article 3.6.1 shall
apply.
Unit weights for soil backfill, other than 0.12 kcf,
may be considered as specified in Article 12.9.4.2.
The earth loads for the design procedure described
herein are based upon soil backfill having a standard
unit weight, γs, of 0.12 kcf.
12.9.3—Service Limit State
C12.9.3
No service limit state criteria need be applied in the
design of box culvert structures.
Soil design and placement requirements for box
culvert structures can limit structure deflections
satisfactorily. The contract documents should require
that construction procedures be monitored to ensure that
severe deformations do not occur during backfill
placement and compaction, in which case no deflection
limits should be imposed on the completed structure.
12.9.4—Safety against Structural Failure
12.9.4.1—General
C12.9.4.1
The resistance of corrugated box culverts shall be
determined at the strength limit state in accordance with
Articles 12.5.3, 12.5.4, and 12.5.5 and the requirements
specified herein.
Box culvert sections for which these Articles apply are
defined in Figure 12.9.4.1-1 and Table 12.9.4.1-1.
Table A12-10 shall apply.
Finite element analyses covering the range of metal
box culvert shapes described in this Article have shown
that flexural requirements govern the design in all cases.
Effects of thrust are negligible when combined with
flexure.
The structural requirements for metal box culverts
are based on the results of finite element analyses and
field measurements of in-service box culverts.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
12-42
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure 12.9.4.1-1—Geometry of Box Culverts
Table 12.9.4.1-1—Geometric Requirements for Box
Culverts with Spans from 8 ft 9 in. to 25 ft 5 in.
Span, S: 8 ft 9 in. to 25 ft 5 in.
Rise, R: 2 ft 6 in. to 10 ft 6 in.
Radius of crown, rc ≤ 24 ft 9 1/2 in.
Radius of haunch, rh ≥ 2 ft 6 in.
Haunch radius included angle, Δ,: 50° to 70°
Length of leg, D: measured to the bottom of the
plate, may vary from 4 3/4 to 71 in.
Minimum length of rib on leg, L, least of 19.0 in.,
(D − 3.0) in. or to within 3.0 in. of the top of a
concrete footing
Table 12.9.4.1-2—Geometric Requirements for Box
Culverts with Spans from 25 ft 6 in. to 36 ft 0 in.
Span, S: 25 ft 6 in. to 36 ft 0 in.
Rise, R: 5 ft 7 in. to 14 ft 0 in.
Radius of crown, rc 26 ft 4 in.
Radius of haunch, rh 3 ft 8 in.
Haunch radius included angle, : 48 to 68
Length of leg, D: measured to the bottom of the
plate, may vary from 4 3/4 to 71 in.
Minimum length of rib on leg, L, least of 28.0 in.,
(D – 3.0) in., or to within 3.0 in. of the top of a
concrete footing
The flexural resistance of corrugated plate box
structures shall be determined using the specified yield
strength of the corrugated plate.
The flexural resistance of plate box structures with
ribbed sections shall be determined using specified yield
strength values for both rib and corrugated shell.
Computed values may be used for design only after
confirmation by representative flexural testing. Rib
splices shall develop the plastic moment capacity
required at the location of the splice.
12.9.4.2—Moments Due to Factored Loads
Unfactored crown and haunch dead and live load
moments, Mdℓ and Mℓℓ, may be taken as:
For spans 25 ft 5 in.:
C12.9.4.2
The number of “ wheels per notional axle group‖
determines the value of C2 in Table 12.9.4.2-1. The
following guidelines are consistent with the
development of Table 12.9.4.2-1:
© 2012
the American
Association
of Highway
State Highway
and Transportation
Officials.
© 2012
by theby
American
Association
of State
and Transportation
Officials.
All rights
reserved.
Duplication
is a violation
of applicable
All rights
reserved.
Duplication
is a violation
of applicable
law. law.
2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
3
Md
s
S 0.0053 0.00024 S 12
0.053 H 1.4 S
12-43
2
(12.9.4.2-1)
For spans from 25 ft 6 in. through 36 ft 0 in. with a
geometry profile that meets rc = 26 ft, rh = 3 ft 8 7/8 in.
and = 49.16 degrees:
Md
λs
M
S 3 0.00194 0.0002 S 26 H 1.1
H 1.4 0.053S 2
C K1
0.6 S 26
2
(12.9.4.2-2)
S
K2
(12.9.4.2-3)
where:
Mdℓ =
Mℓℓ =
S
γs
H
=
=
=
Cℓℓ =
=
AL =
C1 =
C2 =
sum of the nominal crown and haunch dead
load moments (kip-ft/ft)
sum of the nominal crown and haunch live load
moments (kip-ft/ft)
box culvert span (ft)
soil unit weight (kcf)
height of cover from the box culvert rise to top
of pavement (ft)
adjusted live load
C1 C2 AL (kip)
sum of all axle loads in an axle group (kip)
1.0 for single axles and 0.5 + S/50 ≤ 1.0 for
tandem axles
adjustment factor for number of wheels on a
design axle as specified in Table 12.9.4.2-1
Use “ 2‖ as the number of wheels when the design is
based on an axle with two wheels, e.g., two 16.0-kip
wheels on one 32.0-kip axle.
Use “4‖ as the number of wheels where the design
is based on either an axle with four wheels, e.g., two
8.0-kip wheels on each end of a 32.0-kip axle; or
two axles with two wheels each, e.g., two 12.5-kip
wheels on each of two tandem 25.0-kip axles.
Use “ 8‖ as the number of wheels when the design is
based on two axles, each with a pair of wheels at
each end of each axle.
For spans from 25 ft 6 in. through 36 ft 0 in. with
profiles that do not meet the requirements of
Eq. 12.9.4.2-2, finite element modeling that employs
soil structure interaction may be performed to obtain the
nominal crown and haunch moments.
in which:
K1
K1
K2
0.08
H
S
0.2
, for 8
S
20
0.08 0.002 ( S 20)
H
S
0.2
(12.9.4.2-4)
, for 20
0.54H 2 0.4H 5.05, for 1.4
K2 1.90H 3, for 3.0 H
5.0
S
26 (12.9.4.2-5)
H < 3.0
(12.9.4.2-6)
(12.9.4.2-7)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
12-44
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 12.9.4.2-1—Adjustment Coefficient Values (C2) for
Number of Wheels per Axle
Wheels per
Notional Axle
Group
2
4
8
1.4
1.18
1.00
0.63
Cover Depth (ft)
2.0
3.0
5.0
1.21
1.24
1.02
1.00
1.00
1.00
0.70
0.82
0.93
Unless otherwise specified, the design truck
specified in Article 3.6.1.2.2 should be assumed to have
four wheels on an axle. The design tandem specified in
Article 3.6.1.2.3 should be assumed to be an axle group
consisting of two axles with four wheels on each axle.
The factored moments, Mdℓu and Mℓℓu as referred to
in Article 12.9.4.3, shall be determined as specified in
Table 3.4.1-1, except that the live load factor used to
compute Mℓℓu shall be 2.0. The factored reactions shall
be determined by factoring the reactions specified in
Article 12.9.4.5.
12.9.4.3—Plastic Moment Resistance
C12.9.4.3
The plastic moment resistance of the crown, Mpc,
and the plastic moment resistance of the haunch, Mph,
shall not be less than the proportioned sum of adjusted
dead and live load moments. The values of Mpc and Mph
shall be determined as follows:
M pc
CH Pc M d
M ph
CH 1.0 Pc
u
M
Md
(12.9.4.3-1)
u
u
Rh M
u
(12.9.4.3-2)
where:
CH =
Pc =
RH =
Mdℓu =
Mℓℓu =
crown soil cover factor specified in
Article 12.9.4.4
allowable range of the ratio of total moment
carried by the crown as specified in
Table 12.9.4.3-1
acceptable values of the haunch moment
reduction factor as specified in Table 12.9.4.3-2
factored dead load moment as specified in
Article 12.9.4.2 (kip-ft)
factored live load moment as specified in
Article 12.9.4.2 (kip-ft)
Some discretion is allowed relative to the total
flexural capacity assigned to the crown and haunches of
box culverts.
The distribution of moment between the crown and
haunch, described in Article C12.9.4.2, is accomplished
in the design using the crown moment proportioning
factor, Pc, which represents the proportion of the total
moment that can be carried by the crown of the box
culvert and that varies with the relative flexural
capacities of the crown and haunch components.
The requirements given herein can be used to
investigate products for compliance with these
Specifications. Using the actual crown flexural capacity,
Mpc, provided by the metal box structure under
consideration and the loading requirements of the
application, Eq. 12.9.4.3-1 can be solved for the factor
Pc, which should fall within the allowable range of
Table 12.9.4.3-1. Knowing Pc, Eq. 12.9.4.3-2 can be
solved for Mph, which should not exceed the actual
haunch flexural resistance provided by the structure
section. If Eq. 12.9.4.3-1 indicates a higher value of Pc
than permitted by the allowable ranges in
Table 12.9.4.3-1, the actual crown is over designed,
which is acceptable. However, in this case, only the
maximum value of Pc, allowed by Table 12.9.4.3-1,
should be used to calculate the required Mph from
Eq. 12.9.4.3-2.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-45
Table 12.9.4.3-1—Crown Moment Proportioning Values,
Pc, for Spans ≤25 ft 5 in.
Allowable Range of Pc
0.55–0.70
0.50–0.70
0.45–0.70
0.45–0.60
Span (ft)
<10.0
10.0–15.0
15.0–20.0
20.0–25.4
Table 12.9.4.3-2—Crown Moment Positioning Values, Pc,
for Spans from 25 ft 6 in. to 36 ft 0 in.
Depth of Fill (ft)
1.4–2.5
2.5–4.0
4.0–5.0
Allowable Range of Pc
0.55–0.65
0.45–0.55
0.35–0.55
Table 12.9.4.3-3—Haunch Moment Reduction Values, RH,
for Spans ≤25 ft 5 in.
1.4
0.66
RH
Cover Depth (ft)
2.0
3.0
4.0 to 5.0
0.74
0.87
1.00
For spans from 25 ft 6 in. to 36 ft 0 in., RH = 1.0 for all
cover depths.
12.9.4.4—Crown Soil Cover Factor, CH
For depths of soil cover greater than or equal to 3.5 ft,
the crown soil cover factor, CH, shall be taken as 1.0.
For crown cover depth between 1.4 and 3.5 ft, the
crown soil cover factor shall be taken as:
CH
1.15
H 1.4
14
(12.9.4.4-1)
C12.9.4.4
The results of finite element analyses and field
monitoring studies to evaluate the effects of loadinduced deformations and in-plane deformed geometries
indicate that the design moments should be increased
where the cover is less than 3.5 ft.
Eq. 12.9.4.4-1 is discussed in Boulanger et al.
(1989).
where:
H
=
depth of cover over crown (ft)
12.9.4.5—Footing Reactions
Reactions at the box culvert footing shall be
determined as:
V
s
HS
2.0
S2
40.0
AL
8 2 H
R
(12.9.4.5-1)
where:
V
γs
H
R
=
=
=
=
unfactored footing reaction (kip/ft)
unit weight of backfill (kcf)
depth of cover over crown (ft)
rise of culvert (ft)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
12-46
S =
AL =
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
span (ft)
total axle load (kip)
12.9.4.6—Concrete Relieving Slabs
C12.9.4.6
Relieving slabs may be used to reduce flexural
moments in box culverts. Relieving slabs shall not be in
contact with the crown as shown in Figure 12.9.4.6-1.
The length of the concrete relieving slab shall be at
least 2.0 ft greater than the culvert span and sufficient to
project 1.0 ft beyond the haunch on each side of the
culvert. The relieving slab shall extend across the width
subject to vehicular loading.
The depth of reinforced concrete relieving slabs
shall be determined as:
t
tb RAL Rc R f
(12.9.4.6-1)
where:
t
tb
=
=
RAL =
Rc =
Rf
=
minimum depth of slab (in.)
basic
slab
depth
as
specified
in
Table 12.9.4.6-1 (in.)
axle load correction factor specified in
Table 12.9.4.6-2
concrete strength correction factor specified in
Table 12.9.4.6-3
factor taken as 1.2 for box structures having
spans less than 26.0 ft
The box culvert design procedure described herein
does not directly incorporate consideration of concrete
relieving slabs on the influence of concrete pavement.
Therefore, the procedures described in Duncan et al.
(1985) should be used instead. At this time, the
beneficial effect of a relieving slab can only be
determined by refined soil-structure interaction analyses.
The provisions given herein are applicable only for box
structures having spans under 26.0 ft. The purpose of
avoiding contact between the relieving slab and the
culvert is to avoid concentration of the load applied
through the slab to the crown of the culvert. As little as
1.0- to 3.0-in. clearance is thought to be sufficient to
distribute the load.
Where an Owner requires design for an axle other
than the standard 32.0-kip axle, the factor RAL may be
used to adjust the depth of a concrete relieving slab as
specified in Eq. 12.9.4.6-1.
Figure 12.9.4.6-1—Metal Box Culverts with Concrete
Relieving Slab
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All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-47
Table 12.9.4.6-1—Basic Slab Depth, tb (in.) (Duncan et al.,
1985)
Relative Compaction—
% of Standard
AASHTO Maximum
Dry Unit Weight
100
95
90
Basic Slab Depth (in.)
7.5
8.0
8.5
8.0
8.5
9.0
8.5
9.0
9.5
Unified Classification of
Subgrade Beneath Slab
GW, GP, SW, SP, or SM
SM-SC or SC
ML or CL
Table 12.9.4.6-2—Axle Load Correction Factor, RAL
(Duncan et al., 1985)
Single Axle Load (kip)
10.0
20.0
30.0
32.0
40.0
45.0
50.0
RAL
0.60
0.80
0.97
1.00
1.05
1.10
1.15
Table 12.9.4.6-3—Concrete Strength Correction Factor, Rc
(Duncan et al., 1985)
Concrete Compressive Strength, f c
(ksi)
3.0
3.5
4.0
4.5
5.0
5.5
6.0
Rc
1.19
1.15
1.10
1.05
1.01
0.97
0.94
12.9.5—Construction and Installation
The contract documents shall require that
construction and installation conform to Section 26,
―
Metal Culverts,‖ AASHTO LRFD Bridge Construction
Specifications.
12.10—REINFORCED CONCRETE PIPE
12.10.1—General
C12.10.1
The provisions herein shall apply to the structural
design of buried precast reinforced concrete pipes of
circular, elliptical, and arch shapes.
The structural design of the types of pipes indicated
above may proceed by either of two methods:
These structures become part of a composite system
comprised of the reinforced concrete buried section and
the soil envelope.
Standard dimensions for these units are shown in
AASHTO M 170 (ASTM C76), M 206M/M 206 (ASTM
C506M and C506), M 207M/M 207 (ASTM C507M and
C507), and M 242M/M 242 (ASTM C655M and C655).
The direct design method at the strength limit state
as specified in Article 12.10.4.2, or
The indirect design method at the service limit state
as specified in Article 12.10.4.3.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
12-48
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
12.10.2 Loading
12.10.2.1 Standard Installations
C12.10.2.1
The contract documents shall specify that the
foundation bedding and backfill comply with the
provisions of Article 27.5.2 of the AASHTO LRFD
Construction Specifications.
Minimum compaction requirements and bedding
thickness for standard embankment installations and
standard trench installations shall be as specified in
Tables 12.10.2.1-1 and 12.10.2.1-2, respectively.
The four standard installations replace the historic
bedding classes. A comprehensive soil-structure
interaction analysis and design program (SPIDA) was
developed and used to perform soil-structure interaction
analyses for the various soil and installation parameters
encompassed in the provisions. The SPIDA studies used
to develop the standard installations were conducted for
positive projection embankment conditions to provide
conservative results for other embankment and trench
conditions. These studies also conservatively assume a
hard foundation and bedding existing beneath the invert
of the pipe, plus void and/or poorly compacted material
in the haunch areas, 15 degrees to 40 degrees each side
of the invert, resulting in a load concentration such that
calculated moments, thrusts, and shears are increased.
Table 12.10.2.1-1—Standard Embankment Installation Soils and Minimum Compaction Requirements
Installation Type
Type 1
Type 2—Installations are
available for horizontal
elliptical, vertical elliptical,
and arch pipe
Type 3—Installations are
available for horizontal
elliptical, vertical elliptical,
and arch pipe
Type 4
The
following
Table 12.10.2.1-1:
Bedding Thickness
For soil foundation, use Bc/2.0 ft
minimum, not less than 3.0 in. For
rock foundation, use Bc ft
minimum, not less than 6.0 in.
For soil foundation, use Bc/2.0 ft
minimum, not less than 3.0 in. For
rock foundation, use Bc ft
minimum, not less than 6.0 in.
For soil foundation, use Bc/2.0 ft
minimum, not less than 3.0 in. For
rock foundation, use Bc ft
minimum, not less than 6.0 in.
For soil foundation, no bedding
required. For rock foundation, use
Bc/2.0 ft minimum, not less than
6.0 in.
interpretations
apply
Haunch and
Outer Bedding
95% SW
Lower Side
90% SW, 95% ML, or
100% CL
90% SW or 95% ML
85% SW, 90% ML, or 95%
CL
85% SW, 90% ML, or 95%
CL
85% SW, 90% ML, or 95%
CL
No compaction required,
except if CL, use 85% CL
No compaction required,
except if CL, use 85% CL
to
Compaction and soil symbols, i.e., “ 95 percent
SW,‖ shall be taken to refer to SW soil material
with a minimum standard proctor compaction of 95
percent. Equivalent modified proctor values shall be
as given in Table 27.5.2.2-3 of the AASHTO LRFD
Bridge Construction Specifications.
Soil in the outer bedding, haunch, and lower side
zones, except within Bc/3 from the pipe springline,
shall be compacted to at least the same compaction
as the majority of soil in the overfill zone.
The minimum width of a subtrench shall be 1.33Bc, or
wider if required for adequate space to attain the
specified compaction in the haunch and bedding
zones.
For subtrenches with walls of natural soil, any
portion of the lower side zone in the subtrench wall
A subtrench is defined as a trench in the natural
material under an embankment used to retain
bedding material with its top below finished grade
by more than ten percent of the depth of soil cover
on the top of the culvert or pipe. For roadways, the
top of a subtrench is at an elevation lower than
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-49
shall be at least as firm as an equivalent soil placed
to the compaction requirements specified for the
lower side zone and as firm as the majority of soil
in the overfill zone. Otherwise, it shall be removed
and replaced with soil compacted to the specified
level.
1.0 ft below the bottom of the pavement base
material.
Table 12.10.2.1-2—Standard Trench Installation Soils and Minimum Compaction Requirements
Installation Type
Type 1
Type 2—Installations are
available for horizontal
elliptical, vertical elliptical,
and arch pipe
Type 3—Installations are
available for horizontal
elliptical, vertical elliptical,
and arch pipe
Type 4
The
following
Table 12.10.2.1-2:
Bedding Thickness
For soil foundation, use Bc/2.0 ft
minimum, not less than 3.0 in. For rock
foundation, use Bc ft minimum, not less
than 6.0 in.
For soil foundation, use Bc/2.0 ft
minimum, not less than 3.0 in. For rock
foundation, use Bc ft minimum, not less
than 6.0 in.
For soil foundation, use Bc/4.0 ft
minimum, not less than 3.0 in. For rock
foundation, use Bc ft minimum, not less
than 6.0 in.
For soil foundation, no bedding
required. For rock foundation, use Bc ft
minimum, not less than 6.0 in.
interpretations
apply
Haunch and
Outer Bedding
95% SW
Lower Side
90% SW, 95% ML, or
100% CL, or natural
soils of equal firmness
90% SW or 95% ML
85% SW, 90% ML,
95% CL, or natural
soils of equal firmness
85% SW, 90% ML or
95% CL
85% SW, 90% ML,
95% CL, or natural
soils of equal firmness
No compaction required,
except if CL, use 85%
CL
85% SW, 90% ML,
95% CL, or natural soil
of equal firmness
to
Compaction and soil symbols, i.e., ―
95 percent
SW,‖ shall be taken to refer to SW soil material
with minimum standard proctor compaction of 95
percent. Equivalent modified proctor values shall be
as given in Table 27.5.2.2-3 of the AASHTO LRFD
Bridge Construction Specifications.
The trench top elevation shall be no lower than
0.1H below finish grade; for roadways, its top shall
be no lower than an elevation of 1.0 ft below the
bottom of the pavement base material.
Soil in bedding and haunch zones shall be
compacted to at least the same compaction as
specified for the majority of soil in the backfill
zone.
If required for adequate space to attain the specified
compaction in the haunch and bedding zones the
trench width shall be wider than that shown in
Figures 27.5.2.2-1 and 27.5.2.2-2 of the AASHTO
LRFD Bridge Construction Specifications.
For trench walls that are within 10 degrees of
vertical, the compaction or firmness of the soil in
the trench walls and lower side zone need not be
considered.
For trench walls with greater than 10 degrees slopes
that consist of embankment, the lower side shall be
compacted to at least the same compaction as
specified for the soil in the backfill zone.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
12-50
as:
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The unfactored earth load, WE, shall be determined
WE
Fe wBc H
(12.10.2.1-1)
where:
WE =
Fe =
Bc =
H =
w =
unfactored earth load (kip/ft)
soil-structure interaction factor for the specified
installation as defined herein
out-to-out horizontal dimension of pipe (ft)
height of fill over pipe (ft)
unit weight of soil (pcf)
The unit weight of soil used to calculate earth load
shall be the estimated unit weight for the soils specified
for the pipe soil installation but shall not be taken to be
less than 110 lb./ft3.
Standard installations for both embankments and
trenches shall be designed for positive projection,
embankment loading conditions where Fe shall be taken
as the vertical arching factor, VAF, specified in
Table 12.10.2.1-3 for each type of standard installation.
For standard installations, the earth pressure
distribution shall be the Heger pressure distribution
shown in Figure 12.10.2.1-1 and Table 12.10.2.1-3 for
each type of standard installation.
The product wBcH is sometimes referred to as the
prism load, PL, the weight of the column of earth over
the outside diameter of the pipe.
The earth load for designing pipe using a standard
installation is obtained by multiplying the weight of the
column of earth above the outside diameter of the pipe
by the soil-structure interaction factor, Fe, for the design
installation type. Fe accounts for the transfer of some of
the overburden soil above the regions at the sides of the
pipe because the pipe is more rigid than the soil at the
side of the pipe for pipe in embankment and wide trench
installations. Because of the difficulty of controlling
maximum trench width in the field with the widespread
use of trench boxes or sloped walls for construction
safety, the potential reduction in earth load for pipe in
trenches of moderate to narrow width is not taken into
account in the determination of earth load and earth
pressure distribution on the pipe. Both trench and
embankment installations are to be designed for
embankment (positive projecting) loads and pressure
distribution in direct design or bedding factors in
indirect design.
The earth pressure distribution and lateral earth
force for a unit vertical load is the Heger pressure
distribution and horizontal arching factor, HAF. The
normalized pressure distribution and HAF values were
obtained for each standard installation type from the
results of soil-structure interaction analyses using
SPIDA, together with the minimum soil properties for
the soil types and compaction levels specified for the
installations.
When nonstandard installations are used, the earth
load and pressure distribution should be determined by
an appropriate soil-structure interaction analysis.
Figure 12.10.2.1-1—Heger Pressure Distribution and
Arching Factors
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All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-51
Table 12.10.2.1-3—Coefficients for Use with
Figure 12.10.2.1-1
VAF
HAF
A1
A2
A3
A4
A5
A6
a
b
c
e
f
u
v
1
1.35
0.45
0.62
0.73
1.35
0.19
0.08
0.18
1.40
0.40
0.18
0.08
0.05
0.80
0.80
Installation Type
2
3
1.40
1.40
0.40
0.37
0.85
1.05
0.55
0.35
1.40
1.40
0.15
0.10
0.08
0.10
0.17
0.17
1.45
1.45
0.40
0.36
0.19
0.20
0.10
0.12
0.05
0.05
0.82
0.85
0.70
0.60
4
1.45
0.30
1.45
0.00
1.45
0.00
0.11
0.19
1.45
0.30
0.25
0.00
—
0.90
—
The following shall apply to Table 12.10.2.1-3:
VAF and HAF are vertical and horizontal arching
factors.
These
coefficients
represent
nondimensional total vertical and earth loads on the
pipe, respectively. The actual total vertical and
horizontal loads are (VAF)
(PL) and (HAF)
(PL), respectively, where PL is the prism load.
Coefficients A1 through A6 represent the integration
of nondimensional vertical and horizontal
components of soil pressure under the indicated
portions of the component pressure diagrams, i.e.,
the area under the component pressure diagrams.
The pressures are assumed to vary either parabolically
or linearly, as shown in Figure 12.10.2.1-1, with the
nondimensional magnitudes at governing points
represented by h1, h2, uh1, vh2, a, and b.
Nondimensional horizontal and vertical dimensions
of component pressure regions are defined by c, d,
e, uc, vd, and f coefficients,
where:
d
0.5 c e
(12.10.2.1-2)
h1
1.5 A1 / c 1 u
(12.10.2.1-3)
h2
1.5 A2 /
d 1 v
2e
(12.10.2.1-4)
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2012
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12-52
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
12.10.2.2 Pipe Fluid Weight
The unfactored weight of fluid, WF, in the pipe shall
be considered in design based on a fluid weight of
62.4 lb./ft3, unless otherwise specified. For standard
installations, the fluid weight shall be supported by
vertical earth pressure that is assumed to have the same
distribution over the lower part of the pipe as given in
Figure 12.10.2.1-1 for earth load.
12.10.2.3—Live Loads
Live loads shall be as specified in Article 3.6 and
shall be distributed through the earth cover as specified
in Article 3.6.1.2.6. For standard installations, the live
load on the pipe shall be assumed to have a uniform
vertical distribution across the top of the pipe and the
same distribution across the bottom of the pipe as given
in Figure 12.10.2.1-1.
12.10.3—Service Limit State
The width of cracks in the wall shall be investigated
at the service limit state for moment and thrust.
Generally, the crack width should not exceed 0.01 in.
12.10.4—Safety against Structural Failure
12.10.4.1—General
C12.10.4.1
The resistance of buried reinforced concrete pipe
structures against structural failure shall be determined
at the strength limit state for:
Flexure,
Thrust,
Shear, and
Radial tension.
The dimensions of pipe sections shall be determined
using either the analytically-based direct design method
or the empirically-based indirect design method.
When quadrant mats, stirrups, and/or elliptical
cages are specified in the contract documents, the
orientation of the pipe installation shall be specified,
and the design shall account for the possibility of an
angular misorientation of 10 degrees during the pipe
installation.
The direct design method uses a pressure
distribution on the pipe from applied loads and bedding
reactions based on a soil-structure interaction analysis or
an elastic approximation. The indirect design method
uses empirically-determined bedding factors that relate
the total factored earth load to the concentrated loads
and reactions applied in three-edge bearing tests.
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2012
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-53
12.10.4.2—Direct Design Method
12.10.4.2.1—Loads and Pressure Distribution
The total vertical load acting on the pipe shall be
determined as specified in Article 12.10.2.1.
The pressure distribution on the pipe from applied
loads and bedding reaction shall be determined from
either a soil-structure analysis or from a rational
approximation, either of which shall permit the
development of a pressure diagram, shown
schematically in Figure 12.10.4.2.1-1, and the analysis
of the pipe.
C12.10.4.2.1
The direct design method was accepted in 1993 by
ASCE and is published in ASCE 93-15, Standard
Practice for Direct Design of Buried Precast Concrete
Pipe Using Standard Installations (SIDD). The design
method was developed along with the research
performed on the standard installations. However, the
design equations are applied after the required bending
moments, thrusts, and shear forces at all critical
sections have been determined using any one of the
acceptable pressure distributions. Therefore, the use of
the design equations herein is not limited to the
standard installations or any one assumed pressure
distribution.
Direct design requires:
The determination of earth loads and live load
pressure distributions on the structure for the
bedding and installation conditions selected by the
Engineer;
Analysis to determine thrust, moments, and shears;
and
Design to determine circumferential reinforcement.
The procedures for analysis and design are similar
to those used for other reinforced concrete structures.
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2012
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12-54
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure 12.10.4.2.1-1—Suggested Design Pressure
Distribution around a Buried Concrete Pipe for Analysis
by Direct Design
12.10.4.2.2—Analysis for Force Effects with the
Pipe Ring
Force effects in the pipe shall be determined by an
elastic analysis of the pipe ring under the assumed
pressure distribution or a soil-structure analysis.
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2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-55
12.10.4.2.3—Process and Material Factors
Process and material factors, Frp for radial tension
and Fvp for shear strength, for design of plant-made
reinforced concrete pipe should be taken as 1.0. Higher
values of these factors may be used if substantiated by
sufficient testing in accordance with AASHTO
M 242M/M 242 (ASTM C655M and C655).
12.10.4.2.4—Flexural Resistance at the Strength
Limit State
12.10.4.2.4a—Circumferential Reinforcement
C12.10.4.2.4a
Reinforcement for flexural resistance provided in a
length, b, usually taken as 12.0 in. shall satisfy:
As ≥
2
g φd − N u − g g ( φd ) − N u ( 2φd − h ) − 2 M u
fy
(12.10.4.2.4a-1)
in which:
g = 0.85bf c′
(12.10.4.2.4a-2)
where:
As =
fy
d
=
=
h =
Mu =
Nu =
φ
=
area of reinforcement per length of pipe, b
(in.2/ft)
specified yield strength of reinforcing (ksi)
distance from compression face to centroid of
tension reinforcement (in.)
wall thickness of pipe (in.)
moment due to factored loads (kip-in./ft)
thrust due to factored load, taken to be positive
for compression (kip/ft)
resistance factor for flexure specified in
Article 12.5.5
The required area of steel, As, as determined by
Eq. 12.10.4.2.4a-1, should be distributed over a unit
length of the pipe, b, which is typically taken as 12.0 in.
The factored actions should also be consistent with
the selected unit width.
12.10.4.2.4b—Minimum Reinforcement
The reinforcement, As, per ft of pipe shall not be
less than:
•
For inside face of pipe with two layers of
reinforcement:
As ≥
•
( Si + h ) 2
≥ 0.07
1, 000 f y
(12.10.4.2.4b-1)
For outside face of pipe with two layers of
reinforcement:
As ≥ 0.60
( Si + h ) 2
≥ 0.07
1, 000 f y
(12.10.4.2.4b-2)
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
For elliptical reinforcement in circular pipe and for
33.0-in. diameter and smaller pipe with a single
cage of reinforcement in the middle third of the pipe
wall:
As
2
( Si h ) 2
1, 000 f y
(12.10.4.2.4b-3)
0.07
where:
Si
=
h
fy
=
=
internal diameter or horizontal span of the pipe
(in.)
wall thickness of pipe (in.)
yield strength of reinforcement (ksi)
12.10.4.2.4c—Maximum Flexural
Reinforcement without Stirrups
The flexural reinforcement per ft of pipe without
stirrups shall satisfy:
For inside steel in radial tension:
As max
0.506rs Frp
f c ( R ) Frt
fy
(12.10.4.2.4c-1)
where:
rs
fc
fy
R
=
=
=
=
Frp =
radius of the inside reinforcement (in.)
compressive strength of concrete (ksi)
specified yield strength of reinforcement (ksi)
( r/ f); ratio of resistance factors for radial
tension and moment specified in Article 12.5.5
1.0 unless a higher value substantiated by test
data and approved by the Engineer
in which:
For 12.0 in. ≤ Si ≤ 72.0 in.
Frt = 1 + 0.00833 (72 − Si)
For 72.0 in. < Si ≤ 144.0 in.:
Frt
(144 Si ) 2
26, 000
0.80
For Si > 144.0 in.:
Frt = 0.80
For reinforcing steel in compression:
Asmax
55 g d
87 f y
0.75 N u
fy
(12.10.4.2.4c-2)
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-57
in which:
g
b f c [0.85
0.85 b fc
g
0.05 ( f c
4.0 )]
0.65 b f c
(12.10.4.2.4c-3)
(12.10.4.2.4c-4)
where:
b
=
=
width of section taken as 12.0 in.
resistance factor for flexure as specified in
Article 5.5.4.2
12.10.4.2.4d—Reinforcement for Crack Width
Control
The crack width factor, Fcr, may be determined as:
If Ns is compressive, it is taken as positive and:
B1
30 dAs
Fcr
Ms
Ns d
ij
h
2
0.0316C1bh 2
fc
(12.10.4.2.4d-1)
C12.10.4.2.4d
The crack control coefficients, B1 and C1, are
dependent on the type of reinforcement.
Crack control is assumed to be 1.0 in. from the
closest tension reinforcement, even if the cover over the
reinforcement is greater than or less than 1.0 in. The
crack control factor, Fcr, in Eq. 12.10.4.2.4d-1 indicates
the probability that a crack of a specified maximum
width will occur.
If the ratio of e/d is less than 1.15, crack control will
not govern.
If Ns is tensile, it is taken as negative and:
B1
30dAs
Fcr
1.1M s
(12.10.4.2.4d-2)
in which:
j 0.74
0.1
1
i
Ms
Ns
tb S
2n
B1
h
2
d
1
3
0.9
(12.10.4.2.4d-3)
(12.10.4.2.4d-4)
jd
e
1
e
e
d
0.6 N s d 0.0316C1bh 2 f c
(12.10.4.2.4d-5)
(12.10.4.2.4d-6)
where:
Ms =
Ns =
d =
h
=
flexural moment at service limit state
(kip-in./ft)
axial thrust at service limit state (kip/ft)
distance from compression face to centroid of
tension reinforcement (in.)
wall thickness (in.)
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
fc =
C1 =
As
b
tb
Sℓ
n
n
specified compressive strength of concrete (ksi)
crack control coefficient for various types of
reinforcement as specified in Table 12.10.4.2.4d-1
area of steel (in.2/ft)
width of section taken as 12.0 in.
clear cover over reinforcement (in.)
spacing of circumferential reinforcement (in.)
1.0 when tension reinforcement is a single layer
2.0 when tension reinforcement is made of
multiple layers
resistance factor for flexure as specified in
Article 12.5.5
=
=
=
=
=
=
=
Table 12.10.4.2.4d-1—Crack Control Coefficients
Type
1
2
Reinforcement
Smooth wire or plain bars
Welded smooth wire fabric with
8.0-in. maximum spacing of
longitudinals, welded deformed
wire fabric, or deformed wire
Deformed bars or any
reinforcement with stirrups
anchored thereto
3
C1
1.0
1.5
1.9
For Type 2 reinforcement in Table 12.10.4.2.4d-1
having tb2Si/n > 3.0, the crack width factor, Fcr, shall
also be investigated using coefficients B1 and C1
specified for Type 3 reinforcement, and the larger value
for Fcr shall be used.
Higher values for C1 may be used if substantiated
by test data and approved by the Engineer.
Where Fcr = 1.0, the specified reinforcement is
expected to produce an average maximum crack width
of 0.01 in. For Fcr < 1.0, the probability of a 0.01-in.
crack is reduced, and for Fcr > 1.0, it is increased.
12.10.4.2.4e—Minimum Concrete Cover
The provisions of Article 5.12.3 shall apply to
minimum concrete cover, except as follows:
If the wall thickness is less than 2.5 in., the cover
shall not be less than 0.75 in., and
If the wall thickness is not less than 2.5 in., the
cover shall not be less than 1.0 in.
12.10.4.2.5 —Shear Resistance without Stirrups
C12.10.4.2.5
The section shall be investigated for shear at a
critical section taken where Mnu/(Vud) = 3.0. The
factored shear resistance without radial stirrups, Vr, shall
be taken as:
Vr
Vn
(12.10.4.2.5-1)
in which:
Vn
0.0316bdFvp
f c (1.1 63 )
Fd Fn
Fc
(12.10.4.2.5-2)
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2012
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
As
bd
(12.10.4.2.5-3)
0.02
For pipes with two cages or a single elliptical cage:
Fd
12-59
0.8
1.6
1.3
d
For the purpose of this Article, a cage is considered
to be a layer of reinforcement.
(12.10.4.2.5-4)
For pipes not exceeding 36.0-in. diameter with a
single circular cage:
Fd
0.8
1.6
d
1.4
(12.10.4.2.5-5)
If Nu is compressive, it is taken as positive and:
Fn
1
Nu
24h
(12.10.4.2.5-6)
If Nu is tensile, it is taken as negative and:
Fn
1
Nu
6h
(12.10.4.2.5-7)
Fc
1
d
2r
(12.10.4.2.5-8)
M nu
Mu
Nu
4h d
8
(12.10.4.2.5-9)
The algebraic sign in Eq. 12.10.4.2.5-8 shall be taken
as positive where tension is on the inside of the pipe and
negative where tension is on the outside of the pipe.
where:
f cmax
b
d
=
=
=
h
=
=
r
=
Nu
Vu
Fvp
=
=
=
7.0 ksi
width of design section taken as 12.0 in.
distance from compression face to centroid
of tension reinforcement (in.)
wall thickness (in.)
resistance factor for shear as specified in
Article 5.5.4.2
radius to centerline of concrete pipe wall
(in.)
thrust due to factored loads (kip/ft)
shear due to factored loads (kip/ft)
process and material factor specified in
Article 12.10.4.2.3
If the factored shear resistance, as determined
herein, is not adequate, radial stirrups shall be provided
in accordance with Article 12.10.4.2.6.
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2012
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12-60
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
12.10.4.2.6—Shear Resistance with Radial Stirrups
Radial tension and shear stirrup reinforcement shall
not be less than:
For radial tension:
1.1sv ( M u 0.45 N u rd )
f y rs rd
Avr
sv
0.75 rd
(12.10.4.2.6-1)
(12.10.4.2.6-2)
For shear:
Avs
sv
1.1sv
Vu Fc Vc
f y vd
0.75 vd
Avr
(12.10.4.2.6-3)
(12.10.4.2.6-4)
in which:
4Vr
M nu
1
Vu d
Vc
0.0633 v bd f c
(12.10.4.2.6-5)
where:
Mu =
Mnu =
Nu
Vu
Vc
d
=
=
=
=
fy
=
rs =
sv =
Vr =
Avr =
Avs =
fc =
=
v
flexural moment due to factored loads
(kip-in./ft)
factored moment acting on cross-section width,
b, as modified for effects of compressive or
tensile thrust (kip-in./ft)
thrust due to factored loads (kip/ft)
shear due to factored loads (kip/ft)
shear resistance of concrete section (kip/ft)
distance from compression face to centroid of
tension reinforcement (in.)
specified yield strength for reinforcement; the
value of fy shall be taken as the lesser of the
yield strength of the stirrup or its developed
anchorage capacity (ksi)
radius of inside reinforcement (in.)
spacing of stirrups (in.)
factored shear resistance of pipe section
without radial stirrups per unit length of pipe
(kip/ft)
stirrup reinforcement area to resist radial
tension forces on cross-section width, b, in each
line of stirrups at circumferential spacing, sv
(in.2/ft)
required area of stirrups for shear
reinforcement (in.2/ft)
compressive strength of concrete (ksi)
resistance factor for shear as specified in
Article 12.5.5
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2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
r
=
Fc =
12-61
resistance factor for radial tension as specified
in Article 12.5.5
curvature
factor
as
determined
by
Eq. 12.10.4.2.5-8
12.10.4.2.7—Stirrup Reinforcement Anchorage
12.10.4.2.7a—Radial Tension Stirrup
Anchorage
When stirrups are used to resist radial tension, they
shall be anchored around each circumferential of the
inside cage to develop the resistance of the stirrup, and
they shall also be anchored around the outside cage or
embedded sufficiently in the compression side to
develop the required resistance of the stirrup.
C12.10.4.2.7a
Stirrup reinforcement anchorage development
research by pipe manufacturers has demonstrated that
the free ends of loop-type stirrups need only be anchored
in the compression zone of the concrete cross-section to
develop the full tensile strength of the stirrup wire.
Stirrup loop lengths equivalent to 70 percent of the wall
thickness may be considered to provide adequate
anchorage.
12.10.4.2.7b—Shear Stirrup Anchorage
Except as specified herein, when stirrups are not
required for radial tension but required for shear, their
longitudinal spacing shall be such that they are anchored
around each tension circumferential or every other
tension circumferential. The spacing of such stirrups
shall not exceed 6.0 in.
12.10.4.2.7c—Stirrup Embedment
Stirrups intended to resist forces in the invert and
crown regions shall be anchored sufficiently in the
opposite side of the pipe wall to develop the required
resistance of the stirrup.
12.10.4.3—Indirect Design Method
12.10.4.3.1—Bearing Resistance
C12.10.4.3.1
Earth and live loads on the pipe shall be determined
in accordance with Article 12.10.2 and compared to
three-edge bearing strength D-load for the pipe. The
service limit state shall apply using the criterion of
acceptable crack width specified herein.
The D-load for a particular class and size of pipe
shall be determined in accordance with AASHTO
M 242M/M 242 (ASTM C655M and C655).
The three-edge bearing resistance of the reinforced
concrete pipe, corresponding to an experimentally
observed 0.01-in. width crack, shall not be less than the
design load determined for the pipe as installed, taken
as:
D=
12
Si
WE WF
BFE
WL
BFLL
The indirect design method has been the most
commonly utilized method of design for buried
reinforced concrete pipe. It is based on observed
successful past installations.
The required D-load at which the pipe develops its
ultimate strength in a three-edge bearing test is the
design D-load at a 0.01-in. crack multiplied by a
strength factor specified in AASHTO M 170 or
M 242M/M 242 (ASTM C76 or C655M and C655) for
circular pipe, M 206M/M 206 (ASTM C506M and
C506) for arch pipe, and M 207M/M 207 (ASTM
C507M or C507) for elliptical pipe.
(12.10.4.3.1-1)
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2012
Edition
12-62
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
where:
BFE
=
BFLL
=
Si
WE
=
=
WF
=
WL
=
earth load bedding factor specified in
Article 12.10.4.3.2a or Article 12.10.4.3.2b
live load bedding factor specified in
Article 12.10.4.3.2c
internal diameter of pipe (in.)
total unfactored earth load specified in
Article 12.10.2.1 (kip/ft)
total unfactored fluid load in the pipe as
specified in Article 12.10.2.2 (kip/ft)
total unfactored live load on unit length
pipe specified in Article 12.10.2.3 (kip/ft)
For Type 1 installations, D loads, as calculated
above, shall be modified by multiplying by an
installation factor of 1.10.
12.10.4.3.2—Bedding Factor
C12.10.4.3.2
The
minimum
compaction
specified
in
Tables 12.10.2.1-1 and 12.10.2.1-2 shall be required by
the contract document.
12.10.4.3.2a—Earth Load Bedding Factor for
Circular Pipe
Earth load bedding factors, BFE, for circular pipe are
presented in Table 12.10.4.3.2a-1.
For pipe diameters, other than those listed in
Table 12.10.4.3.2a-1, embankment condition bedding
factors, BFE, may be determined by interpolation.
The bedding factor is the ratio of the moment at
service limit state to the moment applied in the threeedge bearing test. The standard supporting strength of
buried pipe depends on the type of installation. The
bedding factors given herein are based on the minimum
levels of compaction indicated.
C12.10.4.3.2a
The bedding factors for circular pipe were developed
using the bending moments produced by the Heger
pressure distributions from Figure 12.10.2.1-1 for each of
the standard embankment installations. The bedding
factors for the embankment condition are conservative for
each installation. This conservatism is based on assuming
voids and poor compaction in the haunch areas and a hard
bedding beneath the pipe in determining the moments,
thrusts, and shears used to calculate the bedding factors.
The modeling of the soil pressure distribution used to
determine moments, thrusts, and shears is also
conservative by 10–20 percent, compared with the actual
SPIDA analysis.
Table 12.10.4.3.2a-1—Bedding Factors for Circular Pipe
Pipe Diameter, in.
12
24
36
72
144
Type 1
4.4
4.2
4.0
3.8
3.6
Standard Installations
Type 2
Type 3
3.2
2.5
3.0
2.4
2.9
2.3
2.8
2.2
2.8
2.2
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Type 4
1.7
1.7
1.7
1.7
1.7
2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-63
12.10.4.3.2b—Earth Load Bedding Factor for
Arch and Elliptical Pipe
The bedding factor for installation of arch and
elliptical pipe shall be taken as:
CA
C N xq
BFE
(12.10.4.3.2b-1)
where:
CA =
CN =
=
=
constant corresponding to the shape of the pipe,
as specified in Table 12.10.4.3.2b-1
parameter that is a function of the distribution
of the vertical load and vertical reaction, as
specified in Table 12.10.4.3.2b-1
parameter that is a function of the area of the
vertical projection of the pipe over which
lateral pressure is effective, as specified in
Table 12.10.4.3.2b-1
ratio of the total lateral pressure to the total
vertical fill load specified herein
Design values for CA, CN, and x are listed in
Table 12.10.4.3.2b-1.
Table 12.10.4.3.2b-1—Design Values of Parameters in Bedding Factor Equation
CA
Pipe Shape
Horizontal
Elliptical
and
Arch
Installation Type
2
CN
0.630
3
0.763
2
0.516
3
0.615
1.337
Vertical
Elliptical
1.021
Projection Ratio, p
0.9
0.7
0.5
0.3
0.9
0.7
0.5
0.3
x
0.421
0.369
0.268
0.148
0.718
0.639
0.457
0.238
The value of the parameter q is taken as:
For arch and horizontal elliptical pipe:
q
0.23
B
p
1 0.35 p c
Fe
H
(12.10.4.3.2b-2)
For vertical elliptical pipe:
q
where:
p
=
0.48
B
p
1 0.73 p c
Fe
H
(12.10.4.3.2b-3)
projection ratio, ratio of the vertical distance
between the outside top of the pipe, and the
ground of bedding surface to the outside
vertical height of the pipe
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2012
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12-64
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
12.10.4.3.2c—Live Load Bedding Factors
2013 Revision
The bedding factors for live load, WL, for both
circular pipe and arch and for elliptical pipe are given in
Table 12.10.4.3.2c-1. If BFE is less than BFLL, use BFE
instead of BFLL, for the live load bedding factor. For pipe
diameters not listed in Table 12.10.4.3.2c-1, the bedding
factor may be determined by interpolation.
Table 12.10.4.3.2c-1—Bedding Factors, BFLL, for the Design Truck
Fill Height, ft
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
12
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
24
1.7
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
36
1.4
1.7
2.1
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
Pipe Diameter, in.
60
72
84
1.3
1.1
1.1
1.4
1.3
1.3
1.5
1.4
1.4
1.8
1.5
1.5
2.0
1.8
1.7
2.2
2.2
1.8
2.2
2.2
1.9
2.2
2.2
2.1
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
48
1.3
1.5
1.8
2.0
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
96
1.1
1.3
1.3
1.4
1.5
1.7
1.8
1.9
2.0
2.2
2.2
2.2
2.2
108
1.1
1.1
1.3
1.4
1.4
1.5
1.7
1.8
1.9
2.0
2.2
2.2
2.2
120
1.1
1.1
1.3
1.3
1.4
1.5
1.5
1.7
1.8
1.9
2.0
2.1
2.2
144
1.1
1.1
1.1
1.3
1.3
1.4
1.4
1.5
1.7
1.8
1.9
2.0
2.2
12.10.4.4—Development of Quadrant Mat
Reinforcement
12.10.4.4.1—Minimum Cage Reinforcement
In lieu of a detailed analysis, when quadrant mat
reinforcement is used, the area of the main cage shall be
no less than 25 percent of the area required at the point
of maximum moment.
12.10.4.4.2—Development Length of Welded Wire
Fabric
Unless modified herein,
Article 5.11.2.5 shall apply.
the
provisions
of
12.10.4.4.3—Development of Quadrant Mat
Reinforcement Consisting of Welded Plain Wire
Fabric
The embedment of the outermost longitudinals on
each end of the circumferentials shall not be less than:
The greater of 12 circumferential bar diameters or
three-quarters of the wall thickness of the pipe
beyond the point where the quadrant reinforcement
is no longer required by the orientation angle, and
A distance beyond the point of maximum flexural
stress by the orientation angle plus the development
length, ℓd, where ℓd is specified in Article 5.11.2.5.2.
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-65
The mat shall contain no less than two longitudinals
at a distance 1.0 in. greater than that determined by the
orientation angle from either side of the point requiring
the maximum flexural reinforcement.
The point of embedment of the outermost
longitudinals of the mat shall be at least a distance
determined by the orientation angle past the point where
the continuing reinforcement is no less than double the
area required for flexure.
12.10.4.4.4—Development of Quadrant Mat
Reinforcement Consisting of Deformed Bars,
Deformed Wire, or Deformed Wire Fabric
When deformed bars, deformed wire, or deformed
wire fabric is used, the circumferential bars in quadrant
mat reinforcement shall satisfy the following
requirements:
Circumferentials shall extend past the point where
they are no longer required by the orientation angle
plus the greater of 12 wire or bar diameters or threequarters of the wall thickness of the pipe,
Circumferentials shall extend on either side of the
point of maximum flexural stress not less than the
orientation angle plus the development length, ℓhd,
as required by Article 5.11.2.5.1 and modified by
the applicable modification factor or factors, and
Circumferentials shall extend at least a distance
determined by the orientation angle past the point
where the continuing reinforcement is no less than
double the area required for flexure.
12.10.5—Construction and Installation
The contract documents shall require that the
construction and installation conform to Section 27,
―
Concrete Culverts,‖ AASHTO LRFD Bridge
Construction Specifications.
12.11—REINFORCED CONCRETE CAST-INPLACE AND PRECAST BOX CULVERTS AND
REINFORCED CAST-IN-PLACE ARCHES
12.11.1—General
C12.11.1
The provisions herein shall apply to the structural
design of cast-in-place and precast reinforced concrete
box culverts and cast-in-place reinforced concrete arches
with the arch barrel monolithic with each footing.
Designs shall conform to applicable Articles of
these Specifications, except as provided otherwise
herein.
These structures become part of a composite system
comprised of the box or arch culvert structure and the
soil envelope.
Precast reinforced concrete box culverts may be
manufactured using conventional structural concrete and
forms, or they may be machine made with dry concrete
and vibrating form pipe making methods.
Standard dimensions for precast reinforced concrete
box culverts are shown in AASHTO M 259 (ASTM
C789) and M 273 (ASTM C850).
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
12.11.2—Loads and Live Load Distribution
12.11.2.1—General
C12.11.2.1
Loads and load combinations specified in
Table 3.4.1-1 shall apply. Live load shall be considered as
specified in Article 3.6.1.3. Distribution of wheel loads
and concentrated loads for culverts with less than 2.0 ft of
fill shall be taken as specified in Article 4.6.2.10. For
traffic traveling parallel to the span, box culverts shall be
designed for a single loaded lane with the single lane
multiple presence factor applied to the load.
Requirements for bottom distribution reinforcement in top
slabs of such culverts shall be as specified in
Article 9.7.3.2 for mild steel reinforcement and
Article 5.14.4.1 for prestressed reinforcement.
Distribution of wheel loads to culverts with 2.0 ft or
more of cover shall be as specified in Article 3.6.1.2.6.
The dynamic load allowance for buried structures
shall conform to Article 3.6.2.2.
For cast-in-place box culverts, and for precast box
culverts with top slabs having span to thickness ratios
(s/t) >18 or segment lengths <4.0 ft, edge beams shall be
provided as specified in Article 4.6.2.1.4 as follows:
At ends of culvert runs where wheel loads travel
within 24.0 in. from the end of culvert,
At expansion joints of cast-in-place culverts where
wheel loads travel over or adjacent to the expansion
joint.
2013 Revision
Research into live load distribution on box culverts
(McGrath et al., 2004) has shown that design for a single
loaded lane with a multiple presence factor of 1.2 on the
live load and using the live load distribution widths in
Article 4.6.2.10 will provide adequate design loading for
multiple loaded lanes with multiple presence factors of
1.0 or less when the traffic direction is parallel to the
span.
The edge beam provisions are only applicable for
culverts with less than 2.0 ft of fill. Precast box culverts
with span to thickness ratios (s/t) ≤18 have been shown
to have significantly more strength than would be
predicted by Article 5.8.3 (Abolmaali and Garg, 2007).
While the distribution of the load when it is applied to
the edge of these structures would not be as large as
would be predicted by Article 4.6.2.10, the residual
strength in the structure more than compensates for the
liberal load distribution.
12.11.2.2—Modification of Earth Loads for SoilStructure Interaction
12.11.2.2.1—Embankment and Trench Conditions
In lieu of a more refined analysis, the total
unfactored earth load, WE, acting on the culvert may be
taken as:
For embankment installations:
WE
Fe s Bc H
(12.11.2.2.1-1)
in which:
Fe
1 0.20
H
Bc
(12.11.2.2.1-2)
For trench installations:
WE
Ft s Bc H
(12.11.2.2.1-3)
in which:
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
Ft
Cd Bd 2
HBc
Fe
12-67
(12.11.2.2.1-4)
where:
WE =
Bc =
H
=
Fe =
Ft
=
γs =
Bd =
Cd =
total unfactored earth load (kip/ft)
outside width of culvert as specified in
Figures 12.11.2.2.1-1 or 12.11.2.2.1-2, as
appropriate (ft)
depth
of
backfill
as
specified
in
Figures 12.11.2.2.1-1 or 12.11.2.2.1-2 (ft)
soil-structure
interaction
factor
for
embankment installation specified herein
soil-structure interaction factor for trench
installations specified herein
unit weight of backfill (kcf)
horizontal width of trench as specified in
Figure 12.11.2.2.1-2 (ft)
a coefficient specified in Figure 12.11.2.2.1-3
Fe shall not exceed 1.15 for installations with
compacted fill along the sides of the box section, or 1.40
for installations with uncompacted fill along the sides of
the box section.
For wide trench installations where the trench width
exceeds the horizontal dimension of the culvert across
the trench by more than 1.0 ft, Ft shall not exceed the
value specified for an embankment installation.
Figure 12.11.2.2.1-1—Embankment Condition—Precast
Concrete Box Sections
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure 12.11.2.2.1-2—Trench Condition—Precast
Concrete Box Sections
Figure 12.11.2.2.1-3—Coefficient Cd for Trench
Installations
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-69
12.11.2.2.2—Other Installations
Methods of installation other than embankment or
trench may be used to reduce the loads on the culvert,
including partial positive projection, 0.0 projection,
negative projection, induced trench, and jacked
installations. The loads for such installations may be
determined by accepted methods based on tests, soilstructure interaction analyses, or previous experience.
12.11.2.3—Distribution of Concentrated Loads
to Bottom Slab of Box Culvert
The width of the top slab strip used for distribution
of
concentrated
wheel
loads,
specified
in
Article 12.11.2, shall also be used for the determination
of moments, shears, and thrusts in the side walls and the
bottom slab.
C12.11.2.3
Restricting the live load distribution width for the
bottom slab to the same width used for the top slab
provides designs suitable for multiple loaded lanes, even
though analysis is only completed for a single loaded
lane (as discussed in Article C12.11.2.1).
While typical designs assume a uniform pressure
distribution across the bottom slab, a refined analysis
that considers the actual soil stiffness under box sections
will result in pressure distributions that reduce bottom
slab shear and moment forces (McGrath et al., 2004).
Such an analysis requires knowledge of in-situ soil
properties to select the appropriate stiffness for the
supporting soil. A refined analysis taking this into
account may be beneficial when analyzing existing
culverts.
12.11.2.4—Distribution of Concentrated Loads
in Skewed Box Culverts
Wheel distribution specified in Article 12.11.2.3
need not be corrected for skew effects.
12.11.3—Service Limit State
C12.11.3
The provisions of Article 5.7.3.4 shall apply to
crack width control in reinforced concrete cast-in-place
and precast box culverts and reinforced cast-in-place
arches.
Buried box culverts are subject to high compressive
thrust forces compared to most flexural members and
this thrust can result in a substantial reduction in the
stresses at the service limit state that is often ignored in
design. The following Equations, derived from ACI
SP-3 can be used to consider the effect of thrust on
stresses at the service limit state:
fs
Ms
Ns d
h
2
( As jid )
(C12.11.3-1)
in which:
e
M s / Ns
i 1/ 1
j
d h/2
jd / e
0.74 0.1 e / d
0.9
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
where:
Ms
=
Ns
d
=
=
h
As
=
=
fs
=
e/d min =
flexural moment at service limit state
(kip-in./ft)
axial thrust at service limit state (kip/ft)
distance from compression face to centroid
of tension reinforcement (in.)
wall thickness (in.)
area of reinforcement per unit length
(in.2/ft)
reinforcement stress under service load
condition (ksi)
1.15 (dim.)
12.11.4—Safety against Structural Failure
12.11.4.1—General
All sections shall be designed for the applicable
factored loads specified in Table 3.4.1-1 at the strength
limit state, except as modified herein. Shear in culverts
shall be investigated
in conformance with
Article 5.14.5.3.
12.11.4.2—Design Moment for Box Culverts
Where monolithic haunches inclined at 45 degrees
are specified, negative reinforcement in walls and slabs
may be proportioned based on the flexural moment at
the intersection of the haunch and uniform depth
member. Otherwise, the provisions of Section 5 shall
apply.
12.11.4.3—Minimum Reinforcement
12.11.4.3.1—Cast-in-Place Structures
Reinforcement shall not be less than that specified
in Article 5.7.3.3.2 at all cross-sections subject to
flexural tension, including the inside face of walls.
Shrinkage and temperature reinforcement shall be
provided near the inside surfaces of walls and slabs in
accordance with Article 5.10.8.
12.11.4.3.2—Precast Box Structures
2013 Revision
At all cross-sections subjected to flexural tension,
the ratio of primary flexural reinforcement in the
direction of the span to gross concrete area shall be not
less than 0.002. Such minimum reinforcement shall be
provided at the inside faces of walls and in each
direction at the top of slabs of box sections having less
than 2.0 ft of cover.
The provisions of Article 5.10.8 shall not apply to
precast concrete box sections fabricated in lengths not
exceeding 16.0 ft. Where the fabricated length exceeds
16.0 ft, the minimum longitudinal reinforcement for
shrinkage and temperature should be in conformance
with Article 5.10.8.
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2012
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12.11.4.4—Minimum Cover for Precast Box
Structures
12-71
2013 Revision
The provisions of Article 5.12.3 shall apply unless
modified herein for precast box structures.
If the height of the fill is <2.0 ft, the minimum
cover in the top slab shall be 2.0 in. for all types of
reinforcement.
Where welded wire fabric is used, the minimum
cover shall be the greater of three times the diameter of
the wire or 1.0 in.
12.11.5—Construction and Installation
The contract documents shall require that
construction and installation conform to Section 27,
“Concrete Culverts,” AASHTO LRFD Bridge
Construction Specifications.
12.12—THERMOPLASTIC PIPES
12.12.1—General
2013 Revision
C12.12.1
The provisions herein shall apply to the structural
design of buried thermoplastic pipe with solid,
corrugated, or profile wall, manufactured of PE or PVC.
2013 Revision
These structures become part of a composite system
comprised of the plastic pipe and the soil envelope.
The following specifications are applicable:
For PE:
•
Solid Wall—ASTM F714,
•
Corrugated—AASHTO M 294, and
•
Profile—ASTM F894.
For PVC:
•
Solid Wall—AASHTO M 278 and
•
Profile—AASHTO M 304.
12.12.2—Service Limit States
12.12.2.1—General
C12.12.2.1
The allowable maximum localized distortion of
installed plastic pipe shall be limited based on the
service requirements and overall stability of the
installation. The extreme fiber tensile strain shall not
exceed
the
allowable
long-term
strain
in
Table 12.12.3.3-1. The net tension strain shall be the
numerical difference between the bending tensile strain
and ring compression strain.
12.12.2.2—Deflection Requirement
The allowable long-term strains should not be
reached in pipes designed and constructed in accordance
with this Specification. Deflections resulting from
conditions imposed during pipe installation should also
be considered in design.
2013 Revision
Total deflection, Δt, shall be less than the allowable
deflection, ΔA, as follows:
C12.12.2.2
Deflection
is
controlled
through
proper
construction in the field, and construction contracts
should place responsibility for control of deflections on
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12-72
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Δt ≤ Δ A
(12.12.2.2-1)
where:
Δt
=
total deflection of pipe expressed as a reduction
of the vertical diameter taken as positive for
reduction of the vertical diameter and
expansion of horizontal diameter. (in.)
total allowable deflection of pipe, reduction of
vertical diameter (in.)
ΔA =
the contractor. However, feasibility of a specified
installation needs to be checked prior to writing the
project specifications.
The construction specifications set the allowable
deflection, ǻA, for thermoplastic pipe at five percent as
a generally appropriate limit. The Engineer may allow
alternate deflection limits for specific projects if
calculations using the design method in this section
show that the pipe meets all of the strength-limit-state
requirements.
Total deflection, calculated using Spangler’s
expression for predicting flexural deflection in
combination with the expression for circumferential
shortening, shall be determined as:
Δt =
(
)
K B DL Psp + CL PL Do
(
1000 E p I p R 3 + 0.061 M s
)
+ ε sc D
(12.12.2.2-2)
in which:
ε sc =
Ts
(
1000 Aeff E p
§D ·
Ts = Ps ¨ o ¸
© 2 ¹
)
(12.12.2.2-3)
Eq. 12.12.2.2-2 uses the constrained soil modulus,
Ms, as the soil property. Note that the soil prism load is
used as input, rather than the reduced load used to
compute thrust.
This check should be completed to determine that
the expected field deflection based on thrust and flexure
is lower than the maximum allowable deflection for the
project.
(12.12.2.2-4)
where:
εsc =
Ts
DL
KB
Psp
=
=
=
=
CL =
PL =
Do =
Ep =
Ip
=
R
=
service compressive strain due to thrust, as
specified in Article 12.12.3.10.1c and taken as
positive for compression
service thrust per unit length (lb/in.)
deflection lag factor , a value of 1.5 is typical
bedding coefficient , a value of 0.10 is typical
soil prism pressure (EV), evaluated at pipe
springline (psi)
live load distribution coefficient
design live load pressure including vehicle,
dynamic load allowance, and multiple presence
effect (psi)
outside diameter of pipe (in.) as shown in
Figure C12.12.2.2-1
short- or long-term modulus of pipe material as
specified in Table 12.12.3.3-1 (ksi)
moment of inertia of pipe profile per unit
length of pipe (in.4/in.)
radius from center of pipe to centroid of pipe
profile (in.) as shown in Figure C12.12.2.2-1
Thrust and hoop strain in the pipe wall are defined
positive for compression.
There are no standard values for the deflection lag
factor. Values from 1.0 to 6.0 have been recommended.
The highest values are for installations with quality
backfill and low initial deflections and do not generally
control designs. A value of 1.5 provides some allowance
for increase in deflection over time for installations with
initial deflection levels of several percent.
The bedding coefficient, KB varies from 0.083 for
full support to 0.110 for line support at the invert.
Haunching is always specified to provide good support;
however, it is still common to use a value of KB equal to
0.10 to account for inconsistent haunch support.
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2012
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
D
=
Ms =
Ps =
Aeff =
12-73
diameter to centroid of pipe profile (in.) as
shown in Figure C12.12.2.2-1
secant constrained soil modulus, as specified in
Article 12.12.3.5-1 (ksi)
design service load (psi)
effective area of pipe wall per unit length of
pipe as specified in Article 12.12.3.10.1b
(in.2/in.)
Figure C12.12.2.2-1²Schematic for Thermoplastic Pipe
Terms
12.12.3²Safety against Structural Failure
C12.12.3.1
12.12.3.1²General
Buried thermoplastic culverts shall be investigated
at the strength limit states for thrust, general and local
buckling, and combined strain.
Total compressive strain in a thermoplastic pipe can
cause yielding or buckling, and total tensile strain can
cause cracking.
12.12.3.2²Section Properties
C12.12.3.2
Section properties for thermoplastic pipe, including
wall area, moment of inertia, and profile geometry
should be determined from cut sections of pipe or
obtained from the pipe manufacturer.
12.12.3.3²Chemical and Mechanical
Requirements
Historically, AASHTO bridge specifications have
contained minimum values for the moment of inertia and
wall area of thermoplastic pipe; however, these values
have been minimum values and are not meaningful for
design. This is particularly so since provisions to
evaluate local buckling were introduced in 2001. These
provisions require detailed profile geometry that varies
with manufacturer. Thus, there is no way to provide
meaningful generic information on section properties. A
convenient method for determining section properties
for profile wall pipe is to make optical scans of pipe wall
cross-sections and determine the properties with a
computer drafting program.
2013 Revision
Mechanical properties for design shall be as
specified in Table 12.12.3.3-1.
Except for buckling, the choice of either initial or
long-term mechanical property requirements, as
appropriate for a specific application, shall be
determined by the Engineer. Investigation of general
buckling shall be based on the value of modulus of
elasticity that represents the design life of the project.
C12.12.3.3
2013 Revision
Properties in Table 12.12.3.3- LQFOXGH ³LQLWLDO´ DQG
long-term values. No product standard requires
determining the actual long-term properties; thus, there is
some uncertainty in the actual values. However, pipe
designed with the Table 12.12.3.3-1 values for 50-yr
modulus of elasticity have performed well, and the
properties are assumed to be reasonably conservative.
Estimated values for a modulus of elasticity for a 75-yr
design life have been estimated from relaxation tests on
PVC and PE in parallel plate tests. The tests were
conducted for over two years and show that the modulus
of elasticity reduces approximately linearly with the
logarithm of time. Further, with a log-linear extrapolation,
the differences between 50-yr and 75-yr modulus values
are very small. These values should be reasonably
conservative, with the same reliability as the 50-yr values.
Pipe and thermoplastic resin suppliers should be asked to
provide confirmation of long-term modulus values for any
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12-74
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
particular product. Values should meet or exceed those
provided in Table 12.12.3.3-1. Where service life is in
excess of 75 yr, test data may be used for the desired life.
The service long-term tension strain limit and the
factored compression strain limit in Table 12.12.3.3-1
need to be multiplied by the appropriate resistance
factors to obtain the strain limits.
Table 12.12.3.3-1—Mechanical Properties of Thermoplastic Pipe
Type of Pipe
Solid Wall PE
Pipe –
ASTM F714
Corrugated PE
Pipe –
AASHTO
M 294
Profile PE
Pipe –
ASTM F894
Solid Wall
PVC Pipe –
AASHTO
M 278,
ASTM F679
Profile PVC
Pipe –
AASHTO
M 304
Minimum
Cell Class
ASTM
D3350,
335434C
ASTM
D3350,
435400C
ASTM
D3350,
334433C
ASTM
D3350,
335434C
ASTM
D1784,
12454C
ASTM
D1784,
12364C
ASTM
D1784,
12454C
ASTM
D1784,
12364C
Service LongTerm
Tension
Strain Limit,
Initial
Factored Compr.
50-yr
75-yr
5.0
Strain Limit, İyc
(%)
4.1
Fu
min
(ksi)
3.0
E min
(ksi)
110.0
Fu min
(ksi)
1.44
E min
(ksi)
22
Fu min
(ksi)
1.40
E min
(ksi)
21
5.0
4.1
3.0
110.0
0.90
22
0.90
21
5.0
4.1
3.0
80.0
1.12
20
1.10
19
5.0
4.1
3.0
110.0
1.44
22
1.40
21
5.0
2.6
7.0
400.0
3.70
140
3.60
137
3.5
2.6
6.0
440.0
2.60
158
2.50
156
5.0
2.6
7.0
400.0
3.70
140
3.60
137
3.5
2.6
6.0
440.0
2.60
158
2.50
156
İyt (%)
12.12.3.4—Thrust
C12.12.3.4
Loads on buried thermoplastic pipe shall be based
on the soil prism load, modified as necessary to consider
the effects of pipe-soil interaction. Calculations shall
consider the duration of a load when selecting pipe
properties to be used in design. Live loads need not be
considered for the long-term loading condition.
Because of the time-dependent nature of
thermoplastic pipe properties, the load will vary with
time.
Time of loading is an important consideration for
some types of thermoplastic pipe. Live loads and
occasional flood conditions are normally considered
short-term loads. Earth loads or permanent high
groundwater are normally considered long-term loads.
12.12.3.5—Factored and Service Loads 2013 Revision C12.12.3.5
The factored load, Pu, in psi shall be taken as:
(
Pu = ηEV γ EV K γE K 2VAF P sp + γWA P w
+ ηLL γ LL P L C L
)
(12.12.3.5-1)
The service load, Ps, in psi shall be taken as:
For η factors, refer to Article 12.5.4 regarding
assumptions about redundancy for earth loads and live
loads.
The factor K2 is introduced to consider variation in
thrust around the circumference, which is necessary
when combining thrust with moment or thrust due to
earth and live load under shallow fill. K2 is set at 1.0 to
determine thrust at the springline and 0.6 to determine
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
Ps = K 2VAF P sp + P L C L + P w
(12.12.3.5-2)
in which:
S − 1.17
VAF = 0.76 − 0.71 H
S H + 2.92
(12.12.3.5-3)
SH =
φs M s R
E p Ag
(12.12.3.5-4)
CL =
Lw
≤ 1.0
Do
(12.12.3.5-5)
Lw = L0 + 12 ⋅ LLDF ( H )
12-75
thrust at the crown. The term PL is also modified for this
reason in later sections.
Figure C3.11.3-1 shows the effect of groundwater
on the earth pressure. Psp does not include the
hydrostatic pressure. Psp is the pressure due to the
weight of soil above the pipe and should be calculated
based on the wet density for soil above the water table
and based on the buoyant density for soil below the
water table. See Table 3.5.1-1 for common unit weights.
(12.12.3.5-6)
In computing Lw, add axle spacing (and increase
total live load) if depth is sufficient for axle loads to
interact.
The factor KγE is introduced to provide the same
safety level as traditionally used for thermoplastic
culverts. Designers may consider using values of KγE as
low as 1.0 provided that procedures are implemented to
ensure compliance with construction specifications. For
culvert designs completed with an installation factor less
than 1.5, the designer is required to specify additional
minimum performance measures such as testing,
monitoring, construction controls, gradation and backfill
requirements including active monitoring of the backfill
gradation and compaction (see Article 30.7.4 of
AASHTO LRFD Bridge Construction Specifications).
The
construction
controls
include
deflection
measurements and shall require the Contractor to submit
and get approval from the Owner's Engineer for his/her
construction plan to be used to achieve the more
stringent performance measures which allowed for the
use of a smaller installation factor in the design. Backfill
placement and monitoring shall be done at levels along
the side of the culvert and includes measurement of
change in vertical pipe diameter when the backfill
reaches the top of the pipe. As the backfill nears the top
of pipe the vertical pipe diameter should be greater than
the vertical diameter prior to backfilling, but not more
than three percent greater than the vertical diameter prior
to backfilling.
where:
KγE
=
installation factor typically taken as 1.5 to
provide traditional safety. Use of a value
less than 1.5 requires additional monitoring
of the installation during construction and
provisions for such monitoring shall be
provided on the contract documents.
K2
=
VAF
=
=
=
coefficient to account for variation of
thrust around the circumference
1.0 for thrust at the springline
0.6 for thrust at the crown
vertical arching factor
The use of the vertical arching factor is based on the
behavior, demonstrated by Burns and Richard (1964),
that pipe with high hoop-stiffness ratios (SH, ratio of soil
stiffness to pipe hoop stiffness) carry substantially less
load than the weight of the prism of soil directly over the
pipe. This behavior was demonstrated experimentally by
Hashash and Selig (1990) and analytically by Moore
(1995). McGrath (1999) developed the simplified form
of the equation presented in this Section.
The VAF approach is only developed for the
embankment load case. No guidance is currently
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
SH
=
hoop stiffness factor
Pw
=
CL
Lw
=
=
H
EV
=
=
EV
=
Psp
=
WA
=
LL
=
LL
=
PL
=
s
=
hydrostatic water pressure at the springline
of the pipe (psi)
live load distribution coefficient
live load distribution width in the
circumferential direction at the elevation of
the crown (in.)
depth of cover (ft)
load modifier as specified in Article 1.3.2,
as they apply to vertical earth loads on
culverts
load factor for vertical pressure from dead
load of earth fill, as specified in
Article 3.4.1
soil prism pressure (EV), evaluated at pipe
springline (psi)
load factor for hydrostatic pressure, as
specified in Article 3.4.1
load modifier as specified in Article 1.3.2,
as they apply to live loads on culverts
load factor for live load, as specified in
Article 3.4.1
live load pressure (LL) with dynamic load
allowance (psi)
resistance factor for soil stiffness
Ms
=
secant constrained soil modulus
specified in Table 12.12.3.5-1 (ksi)
R
=
Ep
=
Ag
=
radius from center of pipe to centroid of
pipe profile (in.)
short- or long-term modulus of pipe
material as specified in Table 12.12.3.3-1
(ksi)
gross area of pipe wall per unit length of
pipe (in.2/in.)
as
available to predict the reduced loads on pipe in trench
conditions. The only trench load theory proposed for
flexible pipe was that by Spangler, which does not have
good guidance on selection of input parameters. It is
conservative to use the VAF approach as presented for
embankments.
If evaluating the short-term load condition, then use
the initial modulus of elasticity to compute SH. Similarly,
if evaluating the long-term loading condition, then use the
long-term modulus of elasticity to compute SH.
The term s appears in Eq. 12.12.3.5-4 to account
for variability in backfill compaction. A lower level of
compaction increases the applied thrust force on the
pipe.
For selecting values of the constrained soil
modulus, Ms, prior editions of the specifications
contained the commentary ―
Suggested practice is to
design for a standard Proctor backfill density five
percent less than specified by the contract documents.‖
This statement is not considered necessary with the
addition of post-construction inspection guidelines to the
AASHTO LRFD Bridge Construction Specifications,
which should provide reasonable assurance that the
design condition is achieved.
For culverts in trench installations under depths of
fill greater than 10.0 ft, evaluation of the values of Ms for
in-situ soil for a width one diameter either side of the
pipe is not necessary, provided the in-situ soil has
adequate vertical; and lateral stiffness. Stable trench
walls, during the excavation process, are predictive of
adequate vertical and lateral stiffness.
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
Do
W0
=
=
LLDF
=
outside diameter of pipe (in.)
width of live load ground-surface contact
area parallel to flow in pipe as specified in
Article 3.6.1.2.5 (in.)
factor for distribution of live load through
earth fills in Article 3.6.1.2.6
In the absence of site-specific data, the secant
constrained soil modulus, Ms, may be selected from
Table 12.12.3.5-1 based on the backfill type and density
and the geostatic earth pressure, Psp. Linear interpolation
between soil stress levels may be used for the
determination of Ms.
For culverts in embankment or wide trench
installations under depths of fill up to 10.0 ft, the soil
type and density selected from Table 12.12.3.5-1 shall
be representative of the conditions for a width of onehalf diameter each side of the culvert, but never less
than 18.0 in. on each side of the culvert. For culverts
under depths of fill greater than 10.0 ft, the soil type and
density selected shall be representative of the conditions
for a width of one diameter on each side of the culvert.
The constrained modulus may also be determined
experimentally using the stress-strain curve resulting
from a uniaxial strain test on a sample of soil compacted
to the field-specified density. The constrained modulus
is the slope of the secant from the origin of the curve to
a point on the curve corresponding to the soil prism
pressure, Psp, Figure C12.12.3.5-1.
12-77
Installation in narrow trenches reduces the vertical
load, provided vertical stiffness of the soil is adequate
to carry the load that is distributed around the pipe due
to arching, as represented by the vertical arching factor
(VAF) in the design method and adequate space is
preserved at the side of the pipe to place and compact
backfill. The minimum trench widths provided in the
AASHTO LRFD Bridge Construction Specifications are
set to provide adequate space. Narrow trenches yield a
desirable level of conservatism, since the transfer of
the load to in-situ trench wall is not considered in
flexible pipe design.
If the structural backfill material is compacted
crushed stone, then the secant constrained soil modulus,
Ms, values for Sn-100 may be used. If the backfill is
uncompacted (dumped) crushed stone, use the modulus
values for Sn-90. While it is not common practice to
monitor density of crushed stone backfills, experience
has found that a modest compaction effort improves
culvert performance and allows the use of the compacted
values.
The width of structural backfill is an important
consideration when the in situ soil in the trench wall or
the embankment fill at the side of the structural backfill
is soft. Currently, only AWWA Manual M45, The
Fiberglass Pipe Design Manual, addresses this issue.
Figure C12.12.3.5-1—Schematic One-Dimensional
Stress-Strain Curve of Soil Backfill
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 12.12.3.5-1—Ms Based on Soil Type and Compaction Condition
Psp Stress Level
(psi)
1.0
5.0
10.0
20.0
40.0
60.0
Psp Stress Level
(psi)
1.0
5.0
10.0
20.0
40.0
60.0
Psp Stress Level
(psi)
1.0
5.0
10.0
20.0
40.0
60.0
1.
2.
Sn-100
(ksi)
2.350
3.450
4.200
5.500
7.500
9.300
Sn-95
(ksi)
2.000
2.600
3.000
3.450
4.250
5.000
Si-95
(ksi)
1.415
1.670
1.770
1.880
2.090
Sn-90
(ksi)
1.275
1.500
1.625
1.800
2.100
2.500
Si-90
(ksi)
0.670
0.740
0.750
0.790
0.900
Sn-85
(ksi)
0.470
0.520
0.570
0.650
0.825
1.000
Si-85
(ksi)
0.360
0.390
0.400
0.430
0.510
Cl-95
(ksi)
0.530
0.625
0.690
0.740
0.815
0.895
Cl-90
(ksi)
0.255
0.320
0.355
0.395
0.460
0.525
Cl-85
(ksi)
0.130
0.175
0.200
0.230
0.285
0.345
The soil types are defined by a two-letter designation that indicates general soil classification, Sn for sands and gravels, Si for
silts and Cl for clays. Specific soil groups that fall into these categories, based on ASTM D2487 and AASHTO M 145, are
listed in Table 12.12.3.5-2.
The numerical suffix to the soil type indicates the compaction level of the soil as a percentage of maximum dry density
determined in accordance with AASHTO T 99.
Table 12.12.3.5-2—Equivalent ASTM and AASHTO Soil Classifications
Basic Soil Type (1)
ASTM D2487
Sn
(Gravelly sand, SW)
SW, SP (2)
GW, GP
sands and gravels with 12% or less fines
GM, SM, ML
also GC and SC with less than 20% passing a No.
200 sieve
CL, MH, GC, SC
also GC and SC with more than 20% passing a
No. 200 sieve
Si
(Sandy silt, ML)
Cl
(Silty clay, CL)
1.
2.
AASHTO M 145
A1, A3 (2)
A-2-4, A-2-5, A4
A-2-6, A-2-7, A5, A6
The soil classification listed in parentheses is the type that was tested to develop the constrained soil modulus values in
Table 12.12.3.5-1. The correlations to other soil types are approximate.
Uniformly graded materials with an average particle size smaller than a No. 40 sieve shall not be used as backfill for
thermoplastic culverts unless specifically allowed in the contract documents and special precautions are taken to control
moisture content and monitor compaction levels.
12.12.3.6—Handling and Installation
Requirements
The flexibility factor, FF, in./kip shall be taken as:
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-79
2
FF =
S
EI
(12.12.3.6-1)
where:
I
E
S
=
=
=
moment of inertia (in.4/in.)
initial modulus of elasticity (ksi)
diameter of pipe (in.)
The flexibility factor, FF, shall be limited as specified in
Article 12.5.6.3.
12.12.3.7—Soil Prism
C12.12.3.7
The soil-prism load shall be calculated as a pressure
representing the weight of soil above the pipe springline.
The pressure shall be calculated for three conditions:
•
If the water table is above the top of the pipe and at
or above the ground surface:
Do
§
¨ H + 0.11 12
Psp = ©
144
•
(12.12.3.7-1)
If the water table is above the top of the pipe and
below the ground surface:
ª ª§
« «¨ HW
1 « ¬©
Psp =
144 «
«
¬«
•
·
¸ γb
¹
The soil prism load and vertical arching factor,
VAF, serve as a common reference for the load on all
types of pipe.
The soil prism calculation needs to consider the unit
weight of the backfill over the pipe. Use the wet unit
weight above the water table and the buoyant unit
weight below the water table. In cases where the water
table fluctuates, multiple conditions may need to be
evaluated.
Figure C3.11.3-1 shows the effect of groundwater
on the earth pressure. See Table 3.5.1-1 for common unit
weights.
º
Do ·
D º
+ 0.11 o » γ b + »
24 ¸¹
12 ¼
»
ª
Do · º »
§
«H − ¨ Hw −
»γs »
24 ¸¹ ¼ ¼»
©
¬
−
(12.12.3.7-2)
If the water table is below the top of the pipe:
Do
§
¨ H + 0.11 12
Psp = ©
144
·
¸ γs
¹
(12.12.3.7-3)
where:
Psp =
Do
γb
H
Hw
=
=
=
=
γs
=
soil-prism pressure (EV), evaluated at pipe
springline (psi)
outside diameter of pipe (in.)
unit weight of buoyant soil (lb/ft3)
depth of fill over top of pipe (ft)
depth of water table above springline of pipe
(ft)
wet unit weight of soil (lb/ft3)
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12-80
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
12.12.3.8—Hydrostatic Pressure
C12.12.3.8
The pressure due to ground water shall be
calculated as:
γ w K wa H w
144
Pw =
(12.12.3.8-1)
Hydrostatic loading due to external water pressure
should be calculated in all cases where water table may
be above the pipe springline at any time. This load
contributes to hoop thrust but does not affect deflection.
where:
Pw =
γw =
Ka =
hydrostatic water pressure at the springline of
the pipe (psi)
unit weight of water (lb/ft3)
factor for uncertainty in level of groundwater
table
12.12.3.9—Live Load
2013 Revision
The live load shall be determined as a pressure
applied at the pipe crown. The live load magnitude shall
be based on the design vehicular live load in Article
3.6.1.2 and shall include modifiers for multiple
presence/overload, dynamic load allowance, and
distribution through cover soils.
The live load pressure, PL, shall be taken as:
PL =
There is often uncertainty in the level of the
groundwater table and its annual variations. The designer
may use the factor Kwa with values up to 1.3 to account
for this uncertainty or may select conservative values of
Hw with a lower value of Kwa but not less than 1.
C12.12.3.9
Live load calculations are included here to
demonstrate the computation of live load thrust at the
crown and springline. NCHRP Project 15-29 to revise
this is nearing completion. This project is proposing no
changes to the live load distribution.
P (1 + IM /100 ) m
[ L0 + (12 H + K 1) LLDF ][W0 + (12 H + K1 ) LLDF ]
(12.12.3.9-1)
where:
PL
P
=
=
IM
=
m
=
L0
=
H
LLDF
=
=
W0
=
K1
=
=
=
service live load on culvert (psi)
design wheel load as specified in
Article 3.6.1.2 (lbs)
dynamic load allowance as specified in
Article 3.6.2.2 (%)
multiple presence factor as specified in
Table 3.6.1.1.2-1
length of live load surface contact area
parallel to pipe diameter as specified in
Article 3.6.1.2.5 (in.)
depth of fill over top of pipe (ft)
factor for distribution of live load through
earth fills as specified in Article 3.6.1.2.6
width of live load ground surface contact
area parallel to flow in pipe as specified in
Article 3.6.1.2.5 (in.)
coefficient to consider design location (in.)
0 for live load at the crown of the pipe
D0/2 for live load at the springline
Increase as necessary if depth is sufficient for
wheels and/or axles to interact.
Add axle spacing if depth is sufficient for axles to
interact.
Add wheel spacing if depth is sufficient for wheels
to interact.
Setting the term K1 to 0 is the normal assumption in
distributing live loads to the pipe and accounts for the
load attenuating to the top of the pipe; however, the load
continues to spread longitudinally along the pipe as it
attenuates from the crown to the springline. Using the
term K1 = D0/2 provides a means to account for this.
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-81
12.12.3.10—Wall Resistance
12.12.3.10.1—Resistance to Axial Thrust
12.12.3.10.1a—General
Elements of profile wall pipe shall be designed to
resist local buckling. To determine local buckling
resistance, profile-wall pipe geometry shall be idealized
as specified herein and an effective area determined in
accordance with the following provisions.
2013 Revision
12.12.3.10.1b—Local Buckling Effective Area
For the determination of buckling resistance, profile
wall pipe shall be idealized as straight elements. Each
element shall be assigned a width based on the clear
distance between the adjoining elements and a thickness
based on the thickness at the center of the element. The
idealization of a typical corrugated profile should be
based on the approximation in Figure 12.12.3.10.1b-1.
C12.12.3.10.1b
To complete the local buckling calculations, the
profile is idealized into a group of rectangular elements.
To complete the idealization, it should include:
The actual total area.
If the crest element is curved, it should be
idealized at the centroid of the curvature. The
idealized element need not touch the idealized
webs.
See McGrath et al (2009) for guidance on other profile
types.
Figure 12.12.3.10.1b-1—Typical and Idealized CrossSection of Profile Wall Pipe
To evaluate the resistance to axial thrust, the area of
the profile shall be reduced to an effective area, Aeff, for
local buckling effects. The effective area of the profile
shall be determined by subtracting the ineffective area of
each element from the gross section area, as:
Aeff
(w be )t
Ag
(12.12.3.10.1b-1)
The resistance to local buckling is based on the
effective width concept used by the cold formed steel
industry. This theory assumes that even though buckling
is initiated in the center of a plate element, the element
still has substantial post-buckling strength at the edges
where the element is supported. This concept is
demonstrated in Figure C12.12.3.10.1b-1.
in which:
be
w
1
(12.12.3.10.1b-2)
0.22
(12.12.3.10.1b-3)
w
t
yc
k
0.673
(12.12.3.10.1b-4)
Figure C12.12.3.10.1b-1—Effective Width Concept
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The local buckling evaluation reduces the capacity
of pipe wall sections with high ratios of width to
thickness.
The calculations in Eqs. 12.12.3.10.1b-1 to
12.12.3.10.1b-4 must be repeated for each element in the
idealized profile.
where:
Aeff =
be
ω
=
=
=
=
εyc =
Ag =
t
w
=
=
k
=
effective area of pipe wall per unit length of
pipe (in.2/in.)
element effective width (in.)
effective width factor
slenderness factor
spacing of corrugation (in.) as specified in
Figure 12.12.3.10.1b-1
factored compressive strain limit as specified in
Table 12.12.3.3-1
gross area of pipe wall per unit length of pipe
(in.2/in.)
thickness of element (in.)
total clear width of element between supporting
elements (in.)
plate buckling coefficient, k=4 for supported
elements, k = 0.43 for unsupported elements,
such as free standing ribs
As an alternate to determining the effective area by
the calculation procedure presented above, the results of
the stub compression test, AASHTO T 341, may be
used, in which case the effective area Aeff shall satisfy:
Pst K t
Fu
in which:
Aeff
Ag
The plate buckling coefficient is analogous to the
effective length factor, k, in column buckling.
The stub compression test has been incorporated as
a requirement into AASHTO product standards M 294
and M 304. The test data should be readily available
from manufacturers and quality control tests.
(12.12.3.10.1b-5)
Pst = stub compression capacity from T 341 (kip/in.)
Kt = time factor as specified in Table 12.12.3.10.1b-1
Fu = material yield strength for design load duration
(ksi)
Table 12.12.3.10.1b-1—Time Factor
Time Period
Initial
50 yr
75 yr (est.)
PE
0.9
0.3
0.25
PVC
0.95
0.6
0.5
12.12.3.10.1c—Compression Strain
2013 Revision
The factored compressive strain due to factored
thrust, uc, and the service compressive strain due to
service thrust, sc, shall be taken as:
uc
Tu
1000 Aeff E p
(12.12.3.10.1c-1)
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
ε sc =
Ts
(
1000 Aeff E p
12-83
(12.12.3.10.1c-2)
)
in which:
§D ·
Tu = Pu ¨ o ¸
© 2 ¹
(12.12.3.10.1c-3)
where:
εuc
εsc
Tu
Ts
Aeff
=
=
=
=
=
factored compressive strain due to thrust
service compressive strain due to thrust
factored thrust per unit length (lb/in.)
service thrust per unit length (lb/in.)
effective area of pipe wall per unit length of
pipe (in.2/in.)
short-term modulus for short-term loading or
long-term modulus of pipe material for longterm loading as specified in Table 12.12.3.3-1
(ksi)
outside diameter of pipe (in.)
factored load as specified in Eq. 12.12.3.5-1
Ep =
Do =
Pu =
12.12.3.10.1d—Thrust Strain Limits
The factored compression strain due to thrust, εuc,
shall satisfy:
(12.12.3.10.1d-1)
εuc ≤ φT ε yc
where:
εuc =
φT =
εyc =
factored compressive strain due to thrust
resistance factor for thrust effects
factored compression strain limit of the pipe
wall material as specified in Table 12.12.3.3-1
12.12.3.10.1e—General Buckling Strain Limits
The factored compression strain due to thrust,
incorporating local buckling effects, εuc, shall satisfy:
(12.12.3.10.1e-1)
εuc ≤ φbck εbck
C12.12.3.10.1e
The equations for global resistance presented here
are a conservative simplification of the continuum
buckling theory presented by Moore (1990). Detailed
analysis using the full theory may be applied in lieu of
the calculations in this section.
The nominal strain capacity for general buckling of
the pipe shall be determined as:
εbck =
(
1.2Cn E p I p
Aeff E p
2
1
) 3 ª« φs M s (1 − 2ν ) º» 3 R
«¬
(1 − ν )2
»¼
h
(12.12.3.10.1e-2)
in which:
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LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
12-84
Rh =
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
11.4
D
11 +
12 H
(12.12.3.10.1e-3)
where:
εuc =
φbck =
εbck =
factored compressive strain due to thrust
resistance factor for global buckling
nominal strain capacity for general buckling
Rh =
correction factor for backfill soil geometry
The term φs appears in this expression for εbck to
account for backfills compacted to levels below that
specified in the design. Lower levels of compaction
increases the thrust force in the pipe.
For designs meeting all other requirements of these
specifications and the AASHTO LRFD Bridge
Construction Specifications, the correction for backfill
soil geometry, Rh, is equal to value at left.
The complete theory proposed by Moore (1990)
provides variations in Rh that consider nonuniform
backfill support. In the extreme case where the width of
structural backfill at the side of the culvert is 0.1 times
the span and the modulus of the soil outside of the
structural backfill is 0.1 times the modulus of the
backfill, then:
Rh =
Cn = calibration factor to account for nonlinear effects
= 0.55
Ep = short- or long-term modulus of pipe material as
specified in Table 12.12.3.3-1 (ksi)
Ip = moment of inertia of pipe profile per unit length
of pipe (in.4/in.)
Aeff = effective area of pipe profile per unit length of
pipe (in.2/in.)
φs = resistance factor for soil pressure
Ms = secant constrained soil modulus as specified in
Table 12.12.3.5-1 (ksi)
ν = Poisson’s ratio of soil
D
H
=
=
diameter to centroid of pipe profile (in.)
depth of fill over top of pipe (ft)
20
56 +
D
12 H
(C12.12.3.10.1e-1)
Poisson’s ratio is used to convert the constrained
modulus of elasticity to the plane strain modulus. Values
for Poisson’s ratio of soils are provided in many
geotechnical references. One reference is Selig (1990).
12.12.3.10.2—Bending and Thrust Strain Limits
12.12.3.10.2a—General
To ensure adequate flexural capacity the combined
strain at the extreme fibers of the pipe profile must be
evaluated at the allowable deflection limits against the
limiting strain values.
12.12.3.10.2b—Combined Strain
2013 Revision
If summation of axial strain, εuc, and bending strain,
εf, produces tensile strain in the pipe wall, the combined
C12.12.3.10.2b
The criteria for combined compressive strain are
based on limiting local buckling. A higher strain limit is
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
strain at the extreme fiber where flexure causes tension
shall satisfy:
f
uc
f
(12.12.3.10.2b-1)
yt
The combined strain at the extreme fiber where
flexure causes compression shall satisfy:
f
uc
T
1.5
(12.12.3.10.2b-2)
yc
where:
f
uc
yt
f
T
yc
=
=
=
factored strain due to flexure
factored compressive strain due to thrust
service long-term tension strain limit of the
pipe wall material as specified in
Table 12.12.3.3-1
= resistance factor for flexure
= resistance factor for thrust
= factored compression strain limit of the pipe
wall material as specified in Table 12.12.3.3-1
In the absence of a more-detailed analysis, the
flexural strain may be determined based on the empirical
relationship between strain and deflection as:
EV D f
f
c
R
f
D
(12.12.3.10.2b-3)
in which:
f
A
sc D
(12.12.3.10.2b-4)
where:
f
sc
f
EV
Df
c
R
D
A
=
=
=
factored strain due to flexure
service compression strain due to thrust
reduction of vertical diameter due to flexure
(in.)
= load factor for vertical pressure from dead load
of earth fill, as specified in Article 3.4.1
= shape factor as specified in Table 12.12.3.10.2b-1.
The shape factors for corrugated PE pipe can be
reduced by 1.0 from the table values to account
for the effect of the low hoop stiffness ratio.
= the larger of the distance from neutral axis of
profile to the extreme innermost or outermost
fiber (in.)
= radius from center of pipe to centroid of pipe
profile (in.)
= diameter to centroid of pipe profile (in.)
= total allowable deflection of pipe, reduction of
vertical diameter (in.)
12-85
allowed for combined strains because under bending, the
web elements have a low stress near the centroid of the
element and are thus unlikely to buckle. Thus the
unbuckled web elements increase the stability of the
crest and valley elements.
The strain limit for combined compression strain is
50 percent higher than that for hoop compression alone
because the web elements, which experience low strains
due to bending, are not likely to buckle, thus increasing
the stability of elements near the crest and valley. While
this behavior would be more accurately modeled as an
increase in the k factor of Eq. 12.12.3.10.1b-4, the
increase in the limiting strain is considered adequate for
this simplified design method.
For thrust capacity, the section is limited by
consideration of hoop compression capacity alone. The
check of combined compression strain, hoop plus
bending, is used to limit the allowable pipe deflection.
Elements subjected primarily to bending (such as a
web element in Figure 12.12.3.10.1b-1 when the pipe is
deflected) are not highly stressed near the centroid,
where buckling initiates, and theoretical k factors for
plates in bending are greater than 20. To simplify the
analysis for combined bending and thrust, elements,
such as the web whose centroid is within c/3 of the
centroid of the entire profile wall, may be analyzed only
for the effect of hoop compression strains. That is,
increases in strain due to bending may be ignored.
Past practice has used tensile strain limits specified
in Table 12.12.3.3-1, with no guidance on ultimate strain
limits. For purposes of design calculations, assume that
ultimate tensile strain capacity is 50 percent greater than
the service capacities provided in Table 12.12.3.3-1.
A higher strain limit is allowed under combined
bending and compression. This increase is permitted
because the web element under flexure has a low stress
at the center of the element, reducing the likelihood of
buckling, and allowing it to provide more stability to the
crest and valley elements.
Flexural strains are always taken as positive.
Peak flexural stress occurs near the crown for live
load conditions and near the haunch/invert region for
deep burial cases. The factors K1 and K2 should be used
in the thrust computations to determine the thrust strains
used in Eqs. 12.12.3.10.2b-1 and 12.12.3.10.2b-2.
The service compressive strain is used for
determination of the factored strain due to flexure
instead of the factored compressive strain. The use of the
factored compressive strain would result in an
unconservative flexural strain demand.
The empirical shape factor is used in the design of
fiberglass pipe and is presented in AWWA Manual of
Practice M45 Fiberglass Pipe Design (1996). It
demonstrates that bending strains are highest in low
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2012
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12-86
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
stiffness pipe backfilled in soils that require substantial
compactive effort (silts and clays), and is lowest in high
stiffness pipe backfilled in soils that require little
compactive effort (sands and gravels).
Table 12.12.3.10.2b-1 does not cover all possible
backfills and density levels. Designers should interpolate
or extrapolate the Table as necessary for specific
projects.
More detailed analyses must consider the likelihood
of inconsistent soil support to the pipe in the haunch
zone, and of local deformations during placement and
compaction of backfill.
Bending strains typically cannot be accurately
predicted during design due to variations in backfill
materials and compactive effort used during installation.
Installation deflection limits are specified in the
construction specifications to assure that design
parameters are not exceeded.
The deflection design limit is five percent reduction
of the vertical diameter as specified in the construction
specification. The pipe must be designed to permit this
deflection, unless extraordinary measures are specified
in contract documents to minimize compactive effort
and to control deflections.
The AASHTO Bridge Construction Specifications
currently restrict the allowable total vertical deflection to
five percent.
Table 12.12.3.10.2b-1—Shape Factors, Df, based on Pipe Stiffness, Backfill and Compaction Level
Pipe
Stiffness
(F/Δy, ksi)
= EI / 0.149 R3
0.009
1.
2.
3.
4.
Pipe Zone Embedment Material and Compaction Level
Gravel (1)
Sand (2)
Dumped to
Moderate to
Dumped to
Moderate to
Slight (3)
High (4)
Slight (3)
High (4)
5.5
7.0
6.0
8.0
0.018
4.5
5.5
5.0
6.5
0.036
3.8
4.5
4.0
5.5
0.072
3.3
3.8
3.5
4.5
GW, GP, GW-GC, GW-GM, GP-GC and GP-GM per ASTM D2487 (includes crushed rock)
SW, SP, SM, SC, GM and GC or mixtures per ASTM D2487
<85% of maximum dry density per AASHTO T 99, < 40% relative density (ASTM D4253 and D4254)
≥85% of maximum dry density per AASHTO T 99, ≥ 40% relative density (ASTM D4253 and D4254)
12.12.4—Construction and Installation
The contract documents shall require that the
construction and installation conform to Section 30,
―
Thermoplastic Culverts,‖ AASHTO LRFD Bridge
Construction Specifications.
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2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-87
12.13—STEEL TUNNEL LINER PLATE
12.13.1—General
C12.13.1
The provisions of this Article shall apply to the
structural design of steel tunnel liner plates.
Construction shall conform to Section 25, ―
Steel and
Concrete Tunnel Liners,‖ AASHTO LRFD Bridge
Construction Specifications.
The supporting capacity of a nonrigid tunnel lining,
such as a steel liner plate, results from its ability to
deflect under load, so that side restraint developed by the
lateral resistance of the soil constrains further deflection.
Thus, deflection tends to equalize radial pressures and to
load the tunnel liner as a compression ring.
The tunnel liner plate may be two-flange, fully
corrugated with lapped longitudinal seams or fourflange, partially corrugated with flanged longitudinal
seams. Both types shall be bolted together to form
annular rings.
12.13.2—Loading
C12.13.2
The provisions for earth loads
Article 3.11.5 shall not apply to tunnels.
given
in
12.13.2.1—Earth Loads
C12.13.2.1
The provisions of Article 12.4.1 shall apply. When
more refined methods of soil analysis are not employed,
the earth pressure may be taken as:
WE
Cdt sS
The earth load to be carried by the tunnel liner is a
function of the type of soil. In granular soil with little or
no cohesion, the load is a function of the angle of
internal friction of the soil and the diameter of the
tunnel. In cohesive soils such as clays, the load to be
carried by the tunnel liner is dependent on the shearing
strength of the soil above the roof of the tunnel.
(12.13.2.1-1)
Eq. 12.13.2.1-1 is a form of the Marston formula. It
proportions the amount of total overburden pressure
acting on the tunnel based on the internal friction angle
of the soil to be tunneled.
In the absence of adequate borings and soil tests,
use f = 0 when calculating WE.
where:
Cdt =
γs =
WE =
S =
load coefficient for tunnel installation specified
in Figure 12.13.2.1-1
total unit weight of soil (kcf)
earth pressure at the crown (ksf)
tunnel diameter or span (ft)
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure 12.13.2.1-1—Diagram for Coefficient Cdt for Tunnel
in Soil
in which:
H
=
height of soil over top of tunnel (ft)
12.13.2.2—Live Loads
The provisions of Article 12.6.1 shall apply.
12.13.2.3—Grouting Pressure
If the grouting pressure is greater than the computed
design load, the design load, WT, on the tunnel liner shall
be the grouting pressure.
12.13.3—Safety against Structural Failure
12.13.3.1—Section Properties
Steel tunnel liner plate shall meet the minimum
requirements of Table 12.13.3.1-1 for cross-sectional
properties, Table 12.13.3.1-2 for seam strength, and
Table 12.13.3.1-3 for mechanical properties.
12.13.3.2—Wall Area
The requirements of Articles 12.7.2.2 and 12.7.2.3
shall apply using effective area from Table 12.13.3.1-1.
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2012
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12.13.3.3—Buckling
12-89
C12.13.3.3
The requirements of Article 12.7.2.4 shall apply,
except that the soil stiffness factor, k, may vary from
0.22 to 0.44 depending upon the quality and extent of
the backpacking material used.
Wall buckling is a function of the stiffness, k, of the
surrounding soil bearing on the plates. Where portland
cement grouting or quality backpacking (meeting the
requirements of Section 25, ―
Steel and Concrete Tunnel
Liners,‖ AASHTO LRFD Bridge Construction
Specifications) material fill the void outside the plates,
k = 0.22 is applicable. For other soils or in-situ
backpacking material, k = 0.44 is suggested. Where
tunneled soils slough or voids are left in the
backpacking, additional consideration as to the value of
k may be required.
12.13.3.4—Seam Strength
The requirements of Article 12.7.2.5 shall apply.
12.13.3.5—Construction Stiffness
C12.13.3.5
Construction stiffness shall be indicated by a
construction stiffness factor as:
EI
CS
S
(12.13.3.5-1)
2
where:
S
E
I
=
=
=
diameter or span (in.)
modulus of elasticity (ksi)
moment of inertia (in.4/in.)
The value of CS from Eq. 12.13.3.5-1 shall not be
less than the values for steel tunnel liner plate as given
in Article 12.5.6.4.
The liner plate ring should have sufficient rigidity to
resist the unbalanced loads of normal construction from
grouting, local slough-ins, and miscellaneous
concentrated loads.
The minimum construction stiffness required for
these loads, CS, can be expressed for convenience by the
formula below. It must be recognized, however, that the
limiting values given here are only recommended
minimums. Actual job conditions may require greater
effective stiffness. Final determination of this factor
should be based on intimate knowledge of the project
and on practical experience.
The construction stiffness, CS, given by
Eq. 12.13.3.5-1, considers the moment of inertia of an
individual plate.
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2012
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12-90
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 12.13.3.1-1—Cross-Sectional Properties—Steel Tunnel Liner Plate
2-Flange Tunnel Liner Plates
Thickness
(in.)
0.075
0.105
0.135
0.164
0.179
0.209
0.239
Thickness
(in.)
0.1050
0.1196
0.1350
0.1640
0.1790
0.2090
0.2390
0.2500
0.3125
0.3750
Effective Area
Moment of Inertia
(in.2/in.)
(in.4/in.)
0.096
0.034
0.135
0.049
0.174
0.064
0.213
0.079
0.233
0.087
0.272
0.103
0.312
0.118
4-Flange Tunnel Liner Plates
Area
(in.2/in.)
0.133
0.152
0.170
0.209
0.227
0.264
0.300
0.309
0.386
0.460
Effective Area
(in.2/in.)
0.067
0.076
0.085
0.105
0.114
0.132
0.150
0.155
0.193
0.230
Radius of Gyration
(in.)
0.595
0.602
0.606
0.609
0.611
0.615
0.615
Moment of Inertia
(in.4/in.)
0.042
0.049
0.055
0.070
0.075
0.087
0.120
0.101
0.123
0.143
Radius of Gyration
(in.)
0.561
0.567
0.568
0.578
0.555
0.574
0.632
0.571
0.564
0.557
Table 12.13.3.1-2—Minimum Longitudinal Seam Strength with Bolt and Nut Requirements for Steel Tunnel Plate Liner
2-Flange Plate
Longitudinal Seam Bolts
Plate Thickness
(in.)
0.075
0.105
0.135
0.164
0.179
0.209
0.239
0.313
0.375
Diameter
(in.)
0.625
0.625
0.625
0.625
0.625
0.625
0.625
0.625
0.625
Material
ASTM
A307
A307
A307
A307
A307
A449
A449
—
—
Ultimate
Seam
Strength
(kip/ft)
20
30
47
55
62
87
92
—
—
4-Flange Plate
Longitudinal Seam Bolts
Diameter
(in.)
—
0.500
0.500
0.500
0.625
0.625
0.625
0.625
0.625
Material
ASTM
—
A307
A307
A307
A307
A307
A307
A307
A307
Ultimate
Seam
Strength
(kip/ft)
—
26
43
50
54
67
81
115
119
All nuts shall conform to ASTM A307, Grade A or better.
Circumferential seam bolts shall conform to ASTM A307 or better for all plate thicknesses.
Table 12.13.3.1-3—Mechanical Properties—Steel Tunnel
Liner Plate (Plate before Cold Forming)
Minimum Tensile Strength
Minimum Yield Strength
Elongation, 2.0 in.
Modulus of Elasticity
42.0 ksi
28.0 ksi
30%
29,000 ksi
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2012
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-91
12.14—PRECAST REINFORCED CONCRETE
THREE-SIDED STRUCTURES
12.14.1—General
C12.14.1
The provisions herein shall apply to the design of
precast reinforced concrete three-sided structures
supported on a concrete footing foundation.
Units may be manufactured using conventional
structural concrete and forms (formed) or machine made
using dry concrete and vibrating forms.
12.14.2—Materials
12.14.2.1—Concrete
Concrete shall conform to Article 5.4.2, except that
evaluation of f c may also be based on cores.
12.14.2.2—Reinforcement
Reinforcement shall meet the requirements of
Article 5.4.3, except that for welded wire fabric a yield
strength of 65,000 psi may be used. For wire fabric, the
spacing of longitudinal wires shall be a maximum of
8.0 in. Circumferential welded wire fabric spacing shall
not be greater than 4.0 in. or less than 2.0 in.
Prestressing, if used, shall be in accordance with
Article 5.9.
12.14.3—Concrete Cover for Reinforcement
The minimum concrete cover for reinforcement in
precast three-sided structures reinforced with welded
wire fabric shall be taken as three times the wire
diameter, but not less than 1.0 in., except for the
reinforcement in the top of the top slab of structures
covered by less than 2.0 ft of fill, in which case the
minimum cover shall be taken as 2.0 in.
12.14.4—Geometric Properties
Except as noted herein, the shape of the precast
three-sided structures may vary in span, rise, wall
thickness, haunch dimensions, and curvature. Specific
geometric properties shall be specified by the
manufacturer. Wall thicknesses shall be a minimum of
8.0 in. for spans under 24.0 ft and 10.0 in. for 24.0 ft and
larger spans.
12.14.5—Design
12.14.5.1—General
Designs shall conform to applicable sections of
these Specifications, except as provided otherwise
herein. Analysis shall be based on a pinned connection
at the footing and shall take into account anticipated
footing movement.
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
12.14.5.2—Distribution of Concentrated Load
Effects in Top Slab and Sides
Distribution of wheel loads and concentrated loads
for the top slab and sides of three-sided structures shall
be taken as specified in Article 12.11.2.1.
12.14.5.3—Distribution of Concentrated Loads
in Skewed Culverts
Wheel loads on skewed culverts shall be distributed
using the same provisions as given for culverts with
main reinforcement parallel to traffic. For culvert
elements with skews greater than 15 degrees, the effect
of the skew shall be considered in analysis.
12.14.5.4—Shear Transfer in Transverse Joints
between Culvert Sections
The provisions of Article 4.6.2.10.4 shall apply.
In addition, except as provided herein, a means of
shear transfer between adjacent units shall be provided
in the top slab of structures having flat tops under less
than 2.0 ft of fill and subjected to vehicular live loads.
Shear transfer between adjacent units may be considered
adequate where the thickness of the top slab is equal to
or greater than:
For prestressed slabs:
S/28
(12.14.5.4-1)
For non-prestressed slabs:
(S + 10)/30
(12.14.5.4-2)
where:
S = clear span (ft) measured parallel to the joint
with the adjacent section
C12.14.5.4
Flat top structures with less than 2.0 ft of fill and
with top slabs that are thinner than specified in this
Article may experience differential deflection of
adjacent units which can cause pavement cracking if a
means of shear transfer is not utilized.
The specified minimum slab thickness and span to
slab thickness ratios reflect years of experience in the
design and construction of flat top three-sided structures
and are influenced by Table 9.5(a) of ACI 318-08 and
Table 8.9.2 of the AASHTO Standard Specifications for
Highway Bridges, 17th Edition. Past performance of flat
top three-sided structures designed in accordance with
these provisions provides additional support for this
exception.
For skewed sections, design is based on the span
measured parallel to the joint with the adjacent section.
This is a longer span than measured perpendicular to the
end walls. However, designing for a longer span
provides additional reinforcement to address the nonuniform stresses introduced by the skewed geometry
which are not explicitly considered for modest skew
angles.
Arch-top structures, because of their geometry and
interaction with the surrounding soil, do not exhibit
significant differential deflections that could cause
pavement cracking for structures with less than 2.0 ft of
fill. Thus, the requirements of this Article do not apply
to arch-top structures.
The minimum thickness provision of this Section
pertains only to addressing the need for shear transfer
between adjacent three-sided sections. All other
provisions of this Specification must be met.
12.14.5.5—Span Length
When monolithic haunches inclined at 45 degrees
are taken into account, negative reinforcement in walls
and slabs may be proportioned on the basis of bending
moment at the intersection of the haunch and uniform
depth member.
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SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-93
12.14.5.6—Resistance Factors
The provisions of Articles 5.5.4.2 and 1.3.1 shall
apply as appropriate.
12.14.5.7—Crack Control
The provisions of Article 5.7.3.4 for buried
structures shall apply.
12.14.5.8—Minimum Reinforcement
The provisions of Article 5.10.8 shall not be taken
to apply to precast three-sided structures.
The primary flexural reinforcement in the direction
of the span shall provide a ratio of reinforcement area to
gross concrete area at least equal to 0.002. Such
minimum reinforcement shall be provided at all crosssections subject to flexural tension, at the inside face of
walls, and in each direction at the top of slabs of threesided sections with less than 2.0 ft of fill.
12.14.5.9—Deflection Control at the Service
Limit State
The deflection limits for concrete structures
specified in Article 2.5.2.6.2 shall be taken as mandatory
and pedestrian usage as limited to urban areas.
12.14.5.10—Footing Design
Design shall include consideration of differential
horizontal and vertical movements and footing rotations.
Footing design shall conform to the applicable Articles
in Sections 5 and 10.
12.14.5.11—Structural Backfill
Specification of backfill requirements shall be
consistent with the design assumptions used. The
contract documents should require that a minimum
backfill compaction of 90 percent Standard Proctor
Density be achieved to prevent roadway settlement
adjacent to the structure. A higher backfill compaction
density may be required on structures utilizing a soilstructure interaction system.
12.14.5.12—Scour Protection and Waterway
Considerations
The provisions of Article 2.6 shall apply as
appropriate.
2013 Revision
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2012
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12-94
12.15—REFERENCES
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
2013 Revision
AA. 1983. Aluminum Drainage Products Manual, 1st Edition. Aluminum Association, Washington, DC, p. 86.
AASHTO. 2010. AASHTO LRFD Bridge Construction Specifications, Third Edition, LRFDCONS-3. American
Association of State Highway and Transportation Officials, Washington, DC. Pending.
AASHTO. 2011. Standard Specifications for Transportation Materials and Methods of Sampling and Testing,
31st Edition, HM-31, American Association of State Highway and Transportation Officials, Washington, DC.
Includes AASHTO M, R, and T standards, which are also available individually in downloadable form.
Abolmaali, I., I. Garg, et al. 2007. “ Experimental and Finite Element Based Investigations of Shear Behavior in
Reinforced Concrete Box Culverts,‖ Journal Title. Publisher, Locale, Vol. X, No. Y.
AWWA. 1996. “ Fiberglass Pipe Design.‖ AWWA Manual of Water Supply Practice M45. American Water Works
Association, Denver, CO.
Bellair, P. J., and J. P. Ewing. 1984. Metal Loss Rates of Uncoated Steel and Aluminum Culverts in New York,
Research Report 115. Engineering Research and Development Bureau, New York State Department of
Transportation, Albany, NY.
Boulanger, R. W., R. B. Seed, R. D. Baird, and J. C. Schluter. 1989. “ Measurements and Analyses of Deformed
Flexible Box Culverts.‖ Transportation Research Record 1231. Transportation Research Board, National Research
Council, Washington, DC, pp. 25–35.
Burns, J. Q., and R. M. Richard. 1964. “ Attenuation of Stresses for Buried Cylinders.‖ Proceedings of the Conference
on Soil Structure Interaction. University of Arizona, Tucson, AZ, pp. 378–392.
CSA. 2006. Canadian Highway Bridge Design Code, CAN/CSA-S6-06. Canadian Standards Association, Rexdale,
ON, Canada.
Duncan, J. M., R. B. Seed, and R. H. Drawsky. 1985. “ Design of Corrugated Metal Box Culverts.‖ Transportation
Research Record 1008. Transportation Research Board, National Research Council, Washington, DC, pp. 33–41.
Frederick, G. R., C. V. Ardis, K. M. Tarhini, and B. Koo. 1988. “ Investigation of the Structural Adequacy of C 850
Box Culverts.‖ Transportation Research Record 1191. Transportation Research Board, National Research Council,
Washington, DC.
Funahashi, M., and J. B. Bushman. 1991. “Technical Review of 100 mV Polarization Shift Criterion for Reinforcing
Steel in Concrete.‖ Corrosion, Vol. 47, No. 5, May 1991, pp. 376–386.
Hashash, N., and E. T. Selig. 1990. “Analysis of the Performance of a Buried High Density Polyethylene Pipe.‖
Proceedings of the First National Conference on Flexible Pipes. Columbus, OH, October 1990, pp. 95–103.
Hurd, J. O. 1984. “ Field Performance of Concrete Pipe and Corrugated Steel Pipe Culverts and Bituminous Protection
of Corrugated and Steel Pipe Culverts.‖ Transportation Research Record 1001. Transportation Research Board,
National Research Council, Washington, DC, pp. 40–48.
FHWA. 1985. Hydraulic Design of Highway Culverts, FHWA-IP-85-15. Federal Highway Administration, U.S.
Department of Transportation, Washington, DC, Hydraulic Design Series No. 5, p. 272.
James, R. W. 1984. “ Behavior of ASTM C 850 Concrete Box Culverts Without Shear Connectors.‖ Transportation
Research Record 1001. Transportation Research Board, National Research Council, Washington, DC.
Koepf, A. H., and P. H. Ryan. 1986. “ Abrasion Resistance of Aluminum Culvert Based on Long-Term Field
Performance.‖ Transportation Research Record 1087. Transportation Research Board, National Research Council,
Washington, DC, pp. 15–25.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-95
McGrath, T. J. 1996. A Proposed Design Method for Calculating Loads and Hoop Compression Stresses for Buried
Pipe. Draft report submitted to the Polyethylene Pipe Design Task Group of the AASHTO Flexible Culvert Liaison
Committee.
McGrath, T. J. 1999. “ Calculating Loads on Buried Culverts Based on Pipe Hoop Stiffness.‖ Transportation Research
Record 1656. Transportation Research Board, National Research Council, Washington, DC.
McGrath, T. J. 2004. “ Live Load Distribution Widths for Reinforced Concrete Box Culverts,‖ Journal Title.
Publisher, Locale, Vol. X, No. Y.
McGrath, T. J. 2005. Structural Investigation of Metal Box Section with Spans up to 36 ft Prepared for CONTECH
Construction Products, Inc. by Simpson Gumpertz & Heger.Inc Waltham, MA.
McGrath, T. J., A. A. Liepins, J. L. Beaver, and B.P. Strohman. 2004. Live Load Distribution Widths for Reinforced
Concrete Box Culverts. A study for the Pennsylvania Department of Transportation conducted by Simpson Gumpertz
and Heger, Inc., Waltham, MA.
McGrath, T. J., I. D. Moore, E. T. Selig, M. C. Webb, and B. Taleb. 2002. Recommended Specifications for LargeSpan Culverts, NCHRP Report 473. Transportation Research Board, National Research Council, Washington, DC.
McGrath, T. J., I. D. Moore, and G. Y. Hsuan. 2009. Updated Test and Design Methods for Thermoplastic Drainage
Pipe, NCHRP Report 631. National Cooperative Highway Research Program, Transportation Research Board,
National Research Council, Washington, DC.
McGrath, T. J., and J. L. Beaver. 2005. Performance of Thermoplastic Pipe under Highway Vehicle Loading,
Simpson Gumpertz & Heger Inc., Oakdale, MN. Research Report to Minnesota Department of Transportation.
McGrath, T. J., and V. E. Sagan. 1999. LRFD Specifications for Plastic Pipe and Culverts, NCHRP Report 438.
Transportation Research Board, National Research Council, Washington, DC.
Meacham, D. G., J. O. Hurd, and W. W. Shislar. 1982. Culvert Durability Study, Report No. ODOT/LandD/82-1.
Ohio Department of Transportation, Columbus, OH.
Moore, I. D. 1990. “ Three-Dimensional Response of Elastic Tubes,‖ International Journal of Solids and Structures.
Elsevier, Maryland Heights, MO, Vol. 26, No. 4.
Moore, I. D. 1995. “ Three-Dimensional Response of Deeply Buried Profiled Polyethylene Pipe.‖ Transportation
Research Record 1514. Transportation Research Board, National Research Council, Washington, DC, pp. 49–58.
NRC. 1978. “ Durability of Drainage Pipe.‖ NCHRP Synthesis of Highway Practice No. 50. Transportation Research
Board, National Research Council, Washington, DC, p. 37.
Potter, J. C. 1988. Life Cycle Cost for Drainage Structures, Technical Report GL-88-2. Prepared for the Department
of the Army by the Waterways Experiment Station, Vicksburg, MS, p. 72.
Selig, E.T. 1990. “ Soil Properties for Plastic Pipe Installation,‖ Buried Plastic Pipe Technology, ASTM STP 1093,
George S. Buczala and Michael J. Cassady, eds. American Society for Testing and Materials, Philadelphia, PA.
White, D. W., and M. J. Clarke. 1997. “ Design of Beam-Columns in Steel Frames II: Comparison of Standards,‖
Journal of Structural Engineering. American Society of Civil Engineers, Reston, VA, Vol. 123, No. 12.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-97
APPENDIX A12—PLATE, PIPE, AND PIPE ARCH PROPERTIES
Table A12-1—Corrugated Steel Pipe—Cross-Section
Properties
Thickness
(in.)
0.028
0.034
0.040
0.052
0.064
0.079
0.109
0.138
0.168
Thickness
(in.)
0.040
0.052
0.064
0.079
0.109
0.138
0.168
Thickness
(in.)
0.064
0.079
0.109
0.138
0.168
Thickness
(in.)
0.064
0.079
0.109
0.138
0.168
1 1/2
1/4 in. Corrugation
A
r
(in.2/ft)
(in.)
0.304
—
0.380
—
0.456
0.0816
0.608
0.0824
0.761
0.0832
0.950
0.0846
1.331
0.0879
1.712
0.0919
2.098
0.0967
I 10–3
(in.4/in.)
—
—
0.253
0.344
0.439
0.567
0.857
1.205
1.635
2 2/3
1/2 in. Corrugation
A
r
(in.2/ft)
(in.)
0.465
0.1702
0.619
0.1707
0.775
0.1712
0.968
0.1721
1.356
0.1741
1.744
0.1766
2.133
0.1795
I 10–3
(in.4/in.)
1.121
1.500
1.892
2.392
3.425
4.533
5.725
3
5
1 in. Corrugation
A
r
(in.2/ft)
(in.)
0.890
0.3417
1.113
0.3427
1.560
0.3448
2.008
0.3472
2.458
0.3499
1 in. Corrugation
A
r
(in.2/ft)
(in.)
0.794
0.3657
0.992
0.3663
1.390
0.3677
1.788
0.3693
2.186
0.3711
I 10–3
(in.4/in.)
8.659
10.883
15.459
20.183
25.091
I 10–3
(in.4/in.)
8.850
11.092
15.650
20.317
25.092
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
12-98
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table A12-2—Spiral Rib Steel Pipe—Cross-Section
Properties
3/4
Thickness
(in.)
0.064
0.079
0.109
0.138
3/4
7 1/2 in. Corrugation
A
r
I 10–3
2
(in. /ft)
(in.)
(in.4/in.)
0.509
0.258
2.821
0.712
0.250
3.701
1.184
0.237
5.537
1.717
0.228
7.433
3/4
Thickness
(in.)
0.064
0.079
0.109
1
11 1/2 in. Corrugation
A
r
I 10–3
2
(in. /ft)
(in.)
(in.4/in.)
0.374
0.383
4.58
0.524
0.373
6.08
0.883
0.355
9.26
Note: Effective section properties are taken at full yield stress.
Table A12-3—Steel Structural Plate—Cross-Section Properties
Thickness
(in.)
0.110
0.140
0.170
0.188
0.218
0.249
0.280
0.318
0.380
6 2 in. Corrugations
I
A
r
(in.2)
(in.)
(in.4/in. 10–3)
1.556
0.682
60.4
2.003
0.684
78.2
2.449
0.686
96.2
2.739
0.688
108.0
3.199
0.690
126.9
3.650
0.692
146.2
4.119
0.695
165.8
4.671
0.698
190.0
5.613
0.704
232.0
Table A12-4—Corrugated Aluminum Pipe—Cross-Section
Properties
Thickness
(in.)
0.048
0.060
Thickness
(in.)
0.060
0.075
0.105
0.135
0.164
1 1/2
1/4 in. Corrugation
A
r
(in.2/ft)
(in.)
0.608
0.0824
0.761
0.0832
2 2/3
1/2 in. Corrugation
A
r
(in.2/ft)
(in.)
0.775
0.1712
0.968
0.1721
1.356
0.1741
1.745
0.1766
2.130
0.1795
I 10–3
(in.4/in.)
0.344
0.349
I 10–3
(in.4/in.)
1.892
2.392
3.425
4.533
5.725
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-99
Table A12-4—Corrugated Aluminum Pipe—Cross-Section
Properties (continued)
Thickness
(in.)
0.060
0.075
0.105
0.135
0.164
3 × 1 in. Corrugation
r
A
(in.)
(in.2/ft)
0.890
0.3417
1.118
0.3427
1.560
0.3448
2.088
0.3472
2.458
0.3499
Effective
Thickness
(in.)
0.060
0.075
0.105
0.135
0.164
6 × 1 in. Corrugation
Effective
A
Area
(in.2/ft)
(in.2/ft)
0.775
0.387
0.968
0.484
1.356
0.678
1.744
0.872
2.133
1.066
I × 10–3
(in.4/in.)
8.659
10.883
15.459
20.183
25.091
r
(in.)
0.3629
0.3630
0.3636
0.3646
0.3656
Table A12-5—Aluminum Spiral Rib Pipe—Cross-Section
Properties
3/4 × 3/4 × 7 1/2 in. Corrugation
r
Thickness
A
I × 10–3
2
(in.)
(in.)
(in. /ft)
(in.4/in.)
0.060
0.415
0.272
2.558
0.075
0.569
0.267
3.372
0.105
0.914
0.258
5.073
0.135
1.290
0.252
6.826
3/4 × 1 × 11 1/2 in. Corrugation
r
Thickness
A
I × 10–3
2
(in.)
(in.)
(in. /ft)
(in.4/in.)
0.060
0.312
0.396
4.08
0.075
0.427
0.391
5.45
0.105
0.697
0.380
8.39
0.135
1.009
0.369
11.48
Note: Effective section properties are taken at full yield stress.
Table A12-6—Corrugated Aluminum Structural Plate or Pipe Arch—Cross-Section Properties
Thickness
(in.)
0.100
0.125
0.150
0.175
0.200
0.225
0.250
A
(in.2/ft)
1.404
1.750
2.100
2.449
2.799
3.149
3.501
9 × 2 1/2 in. Corrugations
r
(in.)
0.8438
0.8444
0.8449
0.8454
0.8460
0.8468
0.8473
I
(in.4/in. × 10–3)
83.1
104.0
124.9
145.9
167.0
188.2
209.4
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
12-100
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table A12-7—Minimum Longitudinal Seam Strength Corrugated Aluminum and Steel Pipe—Riveted or Spot Welded
Thickness
(in.)
0.060
0.075
0.105
0.135
0.164
2
1/2 and 2 2/3
1/2 in. Corrugated Aluminum Pipe
Rivet Size
Single Rivets
(in.)
(kip/ft)
5/16
9.0
5/16
9.0
3/8
15.6
3/8
16.2
3/8
16.8
Double Rivets
(kip/ft)
14.0
18.0
31.5
33.0
34.0
3
1 in. Corrugated Aluminum Pipe
Rivet
Double
Thickness
Size
Rivets
(in.)
(in.)
(kip/ft)
0.060
3/8
16.5
0.075
3/8
20.5
0.105
1/2
28.0
0.135
1/2
42.0
0.164
1/2
54.5
6
1 in. Corrugated Aluminum Pipe
Rivet
Double
Thickness
Size
Rivets
(in.)
(in.)
(kip/ft)
0.060
1/2
16.0
0.075
1/2
19.9
0.105
1/2
27.9
0.135
1/2
35.9
0.167
1/2
43.5
Thickness
(in.)
0.064
0.079
0.109
0.138
0.168
3
Thickness
(in.)
0.064
0.079
0.109
0.138
0.168
2
1/2 and 2 2/3 1/2 in. Corrugated Steel Pipe
Rivet Size
Single Rivets
(in.)
(kip/ft)
5/16
16.7
5/16
18.2
3/8
23.4
3/8
24.5
3/8
25.6
Double Rivets
(kip/ft)
21.6
29.8
46.8
49.0
51.3
1 in. Corrugated Steel Pipe
Rivet Size
Double Rivets
(in.)
(kip/ft)
3/8
28.7
3/8
35.7
7/16
53.0
7/16
63.7
7/16
70.7
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-101
Table A12-8—Minimum Longitudinal Seam Strengths Steel and Aluminum Structural Plate Pipe—Bolted
Bolt Thickness
(in.)
0.109
0.138
0.168
0.188
0.218
0.249
0.280
0.318
0.380
6
Bolt Diameter
(in.)
3/4
3/4
3/4
3/4
3/4
3/4
3/4
7/8
7/8
2 in. Steel Structural Plate Pipe
4 Bolts/ft
6 Bolts/ft
(kip/ft)
(kip/ft)
43.0
—
62.0
—
81.0
—
93.0
—
112.0
—
132.0
—
144.0
180.0
—
—
—
—
—
—
—
—
194.0
235.0
285.0
—
—
9
Thickness
(in.)
0.100
0.125
0.150
0.175
0.200
0.225
0.250
8 Bolts/ft
(kip/ft)
2 1/2 in. Aluminum Structural Plate Pipe
Steel Bolts
Bolt Diameter
5.5 Bolts per ft
(in.)
(kip/ft)
3/4
28.0
3/4
41.0
3/4
54.1
3/4
63.7
3/4
73.4
3/4
83.2
3/4
93.1
Aluminum Bolts
5.5 Bolts per ft
(kip/ft)
26.4
34.8
44.4
52.8
52.8
52.8
52.8
Table A12-9—Mechanical Properties for Spiral Rib and Corrugated Metal Pipe and Pipe Arch
Minimum Tensile
Strength, Fu
(ksi)
Minimum Yield
Stress, Fy
(ksi)
Modulus of
Elasticity, Em
(ksi)
Aluminum H34(1)&(4)
31.0
24.0
10,000
Aluminum H32(2)&(4)
27.0
20.0
10,000
Steel(3)
45.0
33.0
29,000
Material
1.
2.
3.
4.
Shall meet the requirements of AASHTO M 197 (ASTM B744), for Alclad Alloy 3004-H34
Shall meet the requirements of AASHTO M 197 (ASTM B744), for Alclad Alloy 3004-H32
Shall meet the requirements of AASHTO M 167M/M 167 (ASTM A761/A761M), M 218, and M 246 (ASTM A742)
H34 temper material shall be used with riveted pipe to achieve seam strength. Both H32 and H34 temper material
may be used with helical pipe
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
12-102
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table A12-10—Mechanical Properties—Corrugated Aluminum and Steel Plate
Material
Aluminum Plate Thickness (in.)
0.100–0.175
0.176–0.250
Steel(2) Plate Thickness (in.)
All
Steel Deep Corrugated Plate
(1)
1.
2.
Minimum Tensile
Strength
(ksi)
Minimum Yield
Stress
(ksi)
Modulus of
Elasticity
(ksi)
35.0
34.0
24.0
24.0
10,000
10,000
45.0
55.0
33.0
44.0
29,000
29,000
Shall meet the requirements of AASHTO M 219 (ASTM B746), Alloy 5052
Shall meet the requirements of AASHTO M 167M/M 167 (ASTM A761/A761M)
Table A12-11—PE Corrugated Pipes (AASHTO M 294)
Min. ID
(in.)
11.8
14.8
17.7
23.6
29.5
35.5
41.5
47.5
Nominal Size
(in.)
12
15
18
24
30
36
42*
48*
Max. OD
(in.)
14.7
18.0
21.5
28.7
36.4
42.5
48.0
55.0
Min. A
(in.2/ft)
1.5
1.9
2.3
3.1
3.9
4.5
4.69
5.15
Min. c
(in.)
0.35
0.45
0.50
0.65
0.75
0.90
1.11
1.15
Min. I
(in.4/in.)
0.024
0.053
0.062
0.116
0.163
0.222
0.543
0.543
For the 42.0-in. and 48.0-in. pipe, the wall thickness should be designed using the long-term tensile strength provision, i.e., 900 psi,
until new design criteria are established in the AASHTO bridge and structures specifications.
Table A12-12—PE Ribbed Pipes (ASTM F894)
Nominal Size
(in.)
18
21
24
27
30
33
36
42
48
Min. ID
(in.)
17.8
20.8
23.8
26.75
29.75
32.75
35.75
41.75
47.75
Max. OD
(in.)
21.0
24.2
27.2
30.3
33.5
37.2
40.3
47.1
53.1
Min. A
(in.2/ft)
2.96
4.15
4.66
5.91
5.91
6.99
8.08
7.81
8.82
Min. c
(in.)
0.344
0.409
0.429
0.520
0.520
0.594
0.640
0.714
0.786
Cell Class
334433C
0.052
0.070
0.081
0.125
0.125
0.161
0.202
0.277
0.338
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
Min. I
(in.4/in.)
Cell Class
335434C
0.038
0.051
0.059
0.091
0.091
0.132
0.165
0.227
0.277
2012
Edition
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12-103
Table A12-13—PVC Profile Wall Pipes (AASHTO M 304)
Nominal
Size
(in.)
12
15
18
21
24
30
36
42
48
Min. I.D.
(in.)
11.7
14.3
17.5
20.6
23.4
29.4
35.3
41.3
47.3
Max. O.D.
(in.)
13.6
16.5
20.0
23.0
26.0
32.8
39.5
46.0
52.0
Min. A
(in.2/ft)
1.20
1.30
1.60
1.80
1.95
2.30
2.60
2.90
3.16
Min. c
(in.)
0.15
0.17
0.18
0.21
0.23
0.27
0.31
0.34
0.37
Cell Class
12454C
0.004
0.006
0.009
0.012
0.016
0.024
0.035
0.047
0.061
Min. I
(in.4/in.)
Cell Class
12364C
0.003
0.005
0.008
0.011
0.015
0.020
0.031
0.043
0.056
Table A12-14—Steel Structural Plate with Deep Corrugations—Cross Properties
Coating Thickness
(in.)
15
A
(in.2/ft)
0.140
5 1/2 in. Corrugations
r
(in.)
I
(in.4/in.)
2.26
1.948
0.714
0.170
2.762
1.949
0.875
0.188
3.088
1.950
0.979
0.218
3.604
1.952
1.144
0.249
4.118
1.953
1.308
0.280
4.633
1.954
1.472
Table A12-15—Minimum Longitudinal Seam Strengths, Deep Corrugated Structures—Bolted
Coating Thickness
(in.)
0.140
0.170
0.188
0.218
0.249
0.280
0.249
0.280
15
5 1/2 in. Corrugations
Bolt Diameter
(in.)
3/4
3/4
3/4
3/4
3/4
3/4
7/8
7/8
6 Bolts/Corrugation
(lb/ft of seam)
66 000
87 000
102 000
127 000
144 000
144 000
159 000
177 000
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 13: RAILINGS
TABLE OF CONTENTS
13
13.1—SCOPE ............................................................................................................................................................. 13-1
13.2—DEFINITIONS ................................................................................................................................................. 13-1
13.3—NOTATION ..................................................................................................................................................... 13-2
13.4—GENERAL ....................................................................................................................................................... 13-3
13.5—MATERIALS ................................................................................................................................................... 13-5
13.6—LIMIT STATES AND RESISTANCE FACTORS .......................................................................................... 13-5
13.6.1—Strength Limit State ............................................................................................................................... 13-5
13.6.2—Extreme Event Limit State ..................................................................................................................... 13-5
13.7—TRAFFIC RAILING ........................................................................................................................................ 13-5
13.7.1—Railing System ....................................................................................................................................... 13-5
13.7.1.1—General......................................................................................................................................... 13-5
13.7.1.2—Approach Railings ....................................................................................................................... 13-6
13.7.1.3—End Treatment.............................................................................................................................. 13-6
13.7.2—Test Level Selection Criteria .................................................................................................................. 13-7
13.7.3—Railing Design ....................................................................................................................................... 13-8
13.7.3.1—General......................................................................................................................................... 13-8
13.7.3.1.1—Application of Previously Tested Systems ........................................................................ 13-8
13.7.3.1.2—New Systems ..................................................................................................................... 13-9
13.7.3.2—Height of Traffic Parapet or Railing ............................................................................................ 13-9
13.8—PEDESTRIAN RAILING ................................................................................................................................ 13-9
13.8.1—Geometry ............................................................................................................................................... 13-9
13.8.2—Design Live Loads ............................................................................................................................... 13-10
13.9—BICYCLE RAILINGS ................................................................................................................................... 13-11
13.9.1—General ................................................................................................................................................. 13-11
13.9.2—Geometry ............................................................................................................................................. 13-11
13.9.3—Design Live Loads ............................................................................................................................... 13-11
13.10—COMBINATION RAILINGS ...................................................................................................................... 13-12
13.10.1—General ............................................................................................................................................... 13-12
13.10.2—Geometry ........................................................................................................................................... 13-12
13.10.3—Design Live Loads ............................................................................................................................. 13-12
13.11—CURBS AND SIDEWALKS ....................................................................................................................... 13-12
13.11.1—General ............................................................................................................................................... 13-12
13.11.2—Sidewalks ........................................................................................................................................... 13-13
13.11.3—End Treatment of Separation Railing ................................................................................................. 13-13
13.12—REFERENCES............................................................................................................................................. 13-13
APPENDIX A13—RAILINGS................................................................................................................................. 13-15
13-i
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
13-ii
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
A13.1—GEOMETRY AND ANCHORAGES ......................................................................................................... 13-15
A13.1.1—Separation of Rail Elements ..............................................................................................................13-15
A13.1.2—Anchorages ........................................................................................................................................13-17
A13.2—TRAFFIC RAILING DESIGN FORCES .................................................................................................... 13-17
A13.3—DESIGN PROCEDURE FOR RAILING TEST SPECIMENS ................................................................... 13-19
A13.3.1—Concrete Railings ..............................................................................................................................13-19
A13.3.2—Post-and-Beam Railings ....................................................................................................................13-21
A13.3.3—Concrete Parapet and Metal Rail .......................................................................................................13-22
A13.3.4—Wood Barriers ...................................................................................................................................13-24
A13.4—DECK OVERHANG DESIGN ................................................................................................................... 13-25
A13.4.1—Design Cases .....................................................................................................................................13-25
A13.4.2—Decks Supporting Concrete Parapet Railings ....................................................................................13-25
A13.4.3—Decks Supporting Post-and-Beam Railings .......................................................................................13-26
A13.4.3.1—Overhang Design ..................................................................................................................... 13-26
A13.4.3.2—Resistance to Punching Shear.................................................................................................. 13-27
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
SECTION 13
RAILINGS
13.1—SCOPE
C13.1
This Section applies to railings for new bridges and
for rehabilitated bridges to the extent that railing
replacement is determined to be appropriate.
This Section provides six bridge railing test levels and
their associated crash test requirements. Guidance for
determining the level to meet the warrants for the more
common types of bridge sites and guidance for structural
and geometric design of railings are provided.
A process for the design of crash test specimens to
determine their crashworthiness is described in
Appendix A13. This methodology is based on an
application of the yield line theory. For use beyond the
design of test specimens with expected failure modes
similar to those shown in Figures CA13.3.1-1 and
CA13.3.1-2, a rigorous yield line solution or a finite
element solution should be developed. The procedures of
Appendix A13 are not applicable to traffic railings
mounted on rigid structures, such as retaining walls or
spread footings, when the cracking pattern is expected to
extend to the supporting components.
All bridge traffic barrier systems will be referred to as
railings herein.
The bridge railing performance need not be identical
over the whole highway network. New railing designs
should match site needs leading to a multiple test level
concept, as described in NCHRP Report 350 or
AASHTO’s Manual for Assessing Safety Hardware.
All highway safety hardware accepted prior to the
adoption of AASHTO, Manual for Assessing Safety
Hardware (MASH), using criteria contained in NCHRP
Report 350, may remain in place and may continue to be
manufactured and installed. Highway safety hardware
accepted using NCHRP Report 350 criteria is not required
to be retested using MASH criteria. New highway safety
hardware not previously evaluated must utilize MASH for
testing and evaluation.
With the finite resources available to bridge owners, it
is not reasonable to expect all existing rails to be updated
any more than to expect every existing building to be
immediately updated with the passing of a new building
code. Many existing bridge rails have proven functional
and need only be replaced when removed for bridge
widenings.
13
13.2—DEFINITIONS
Agency—A responsible business or service authorized to act on behalf of others, i.e., a governmental department,
consulting engineering firm, or owner of the facility or feature.
Barrier Curb—A platform or block used to separate a raised pedestrian and/or bicycle sidewalk above the roadway level;
see Figure 13.7.1.1-1.
Bicycle Railing—A railing or fencing system, as illustrated in Figure 13.9.3-1, that provides a physical guide for bicyclists
crossing bridges to minimize the likelihood of a bicyclist falling over the system.
Bridge Approach Railing—A roadside guardrail system preceding the structure and attached to the bridge rail system that
is intended to prevent a vehicle from impacting the end of the bridge railing or parapet.
Combination Railing—A bicycle or pedestrian railing system, as illustrated in Figures 13.8.2-1 and 13.9.3-1, added to a
crashworthy bridge vehicular railing or barrier system.
Concrete Barrier—A railing system of reinforced concrete having a traffic face that usually but not always adopts some
form of a safety shape.
Concrete Parapet—A railing system of reinforced concrete, usually considered an adequately reinforced concrete wall.
Crash Testing of Bridge Railings—Conducting a series of full-scale impact tests of a bridge railing in accordance with the
recommended guidelines in NCHRP Report 350 or AASHTO’s Manual for Assessing Safety Hardware in order to evaluate
the railing’s strength and safety performance.
Crashworthy—A system that has been successfully crash-tested to a currently acceptable crash test matrix and test level or
one that can be geometrically and structurally evaluated as equal to a crash-tested system.
13-1
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
13-2
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Design Force—An equivalent static force that represents the dynamic force imparted to a railing system by a specified
vehicle impacting a railing at a designated speed and angle.
Encroachment—An intrusion into prescribed, restrictive, or limited areas of a highway system, such as crossing a traffic
lane or impacting a barrier system. Also, the occupancy of highway right-of-way by nonhighway structures or objects of
any kind or character.
End Zone—The area adjacent to any open joint in a concrete railing system that requires added reinforcement.
Expressway—A controlled access arterial highway that may or may not be divided or have grade separations at
intersections.
Face of the Curb—The vertical or sloping surface on the roadway side of the curb.
Freeway—A controlled access divided arterial highway with grade separations at intersections.
Longitudinal Loads—Horizontal design forces that are applied parallel to the railing or barrier system and that result from
friction on the transverse loads.
Multiple Use Railing—Railing that may be used either with or without a raised sidewalk.
Owner—An authority or governmental department representing investors and/or taxpayers that is responsible for all the
safety design features and functions of a bridge.
Pedestrian Railing—A railing or fencing system, as illustrated in Figure 13.8.2-1, providing a physical guidance for
pedestrians across a bridge so as to minimize the likelihood of a pedestrian falling over the system.
Post—A vertical or sloping support member of a rail system that anchors a railing element to the deck.
Rail Element—Any component that makes up a railing system. It usually pertains to a longitudinal member of the railing.
Severity—A characterization of the degree of an event. It is usually associated with characterizing accidents as fatal, injury,
or property damage only so that a dollar value can be assessed for economic study. It may also pertain to indexing the
intensity of an accident so that a railing system can be assessed as a preventive or safety measure.
Speeds—Low/High—Vehicle velocities in mph. Low speeds are usually associated with city or rural travel where speeds
are well posted and are under 45 mph. High speeds are usually associated with expressways or freeways where posted
speeds are 45 mph or more.
Traffic Railing—Synonymous with vehicular railing; used as a bridge or structure-mounted railing, rather than a guardrail
or median barrier as in other publications.
Transverse Loads—Horizontal design forces that are applied perpendicular to a railing or barrier system.
Vehicle Rollover—A term used to describe an accident in which a vehicle rotates at least 90° about its longitudinal axis
after contacting a railing. This term is used if the vehicle rolls over as a result of contacting a barrier and not another
vehicle.
Warrants—A document that provides guidance to the Designer in evaluating the potential safety and operational benefits
of traffic control devices or features. Warrants are not absolute requirements; rather, they are a means of conveying
concern over a potential traffic hazard.
13.3—NOTATION
Af
B
=
=
b
=
area of post compression flange (in.2) (A13.4.3.2)
out-to-out wheel spacing on an axle (ft); distance between centroids of tensile and compressive stress
resultants in post (in.) (A13.2) (A13.4.3.2)
length of deck resisting post strength or shear load = h + Wb (A13.4.3.2)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 13: RAILINGS
13-3
C
db
E
FL
Ft
Fv
f c′
G
H
HR
Hw
h
L
Lc
LL
Lt
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
Lv
ℓ
Mb
Mc
Md
Mp
Mpost
Mw
Pp
R
RR
R′R
Rw
=
=
=
=
=
=
=
=
=
=
=
=
=
R′w
=
vertical post capacity or compression flange resistance of post in bending (kip-ft) (CA13.4.3.2)
distance from the outer edge of the base plate to the innermost row of bolts (in.) (A13.4.3.1)
distance from edge of slab to centroid of compressive stress resultant in post (in.) (A13.4.3.2)
longitudinal friction force along rail = 0.33 Ft (kips) (A13.2)
transverse vehicle impact force distributed over a length Lt at a height He above bridge deck (kips) (A13.2)
vertical force of vehicle laying on top of rail (kips) (A13.2)
28-day compressive strength of concrete (ksi) (A13.4.3.2)
height of vehicle center of gravity above bridge deck (in.) (A13.2)
height of wall (ft) (A13.3.1)
height of rail (ft) (13.4)
height of wall (ft) (13.4)
depth of slab (in.) (A13.4.3.2)
post spacing of single span (ft) (A13.3.2)
critical length of wall failure (ft) (A13.3.1)
longitudinal length of distribution of friction force FL , LL = Lt (ft) (A13.2)
longitudinal length of distribution of impact force Ft along the railing located a height of the He above the
deck (ft) (A13.2)
longitudinal distribution of vertical force Fv on top of railing (ft) (A13.2)
length of vehicle impact load on railing or barrier taken as Lt, Lv, or LL, as appropriate (ft) (A13.3.1)
ultimate moment capacity of beam at top of wall (kip-ft) (A13.3.1)
ultimate flexural resistance of wall about horizontal axis (kip-ft/ft) (A13.3.1)
deck overhang moment (kip-ft/ft) (A13.4.3.1)
plastic or yield line resistance of rail (kip-ft) (A13.3.2)
plastic moment resistance of a single post (kip-ft) (A13.3.2)
ultimate flexural resistance of wall about vertical axis (kip-ft) (A13.3.1)
shear force on a single post which corresponds to Mpost and is located Y above the deck (kips) (A13.3.2)
total ultimate resistance, i.e., nominal resistance, of the railing (kips) (A13.3.2)
ultimate capacity of rail over one span (kips) (A13.3.3)
ultimate transverse resistance of rail over two spans (kips) (A13.3.3)
total transverse resistance of the railing (kips); ultimate capacity of wall as specified in Article A13.3.1 (kips)
(A13.3.1) (A13.3.3)
capacity of wall, reduced to resist post load (kips) (A13.3.3)
R
T
Vc
Vn
Vr
Vu
W
Wb
X
Y
βc
φ
=
=
=
=
=
=
=
=
=
=
=
=
sum of horizontal components of rail strengths (kips) (A13.2)
tensile force per unit of deck length (kip/ft) (A13.4.2)
nominal shear resistance provided by tensile stresses in the concrete (kips) (A13.4.3.2)
nominal shear resistance of the section considered (kips) (A13.4.3.2)
factored shear resistance (kips) (A13.4.3.2)
factored shear force at section (kips) (A13.4.3.2)
weight of vehicle corresponding to the required test level, from Table 13.7.2-1 (kips) (13.7.2)
width of base plate or distribution block (ft); width of base plate (in.) (A13.4.3.1) (A13.4.3.2)
length of overhang from face of support to exterior girder or web (ft) (A13.4.3.1)
height of R above bridge deck (in.) (A13.2)
ratio of the long side to the short side of the concentrated load or reaction area (A13.4.3.2)
resistance factor = 1.0 (A13.4.3.2)
13.4—GENERAL
C13.4
The Owner shall develop the warrants for the bridge
site. A bridge railing should be chosen to satisfy the
concerns of the warrants as completely as possible and
practical.
Railings shall be provided along the edges of
structures for protection of traffic and pedestrians. Other
applications may be warranted on bridge-length culverts.
Additional guidance applicable to bridge-length
culverts may be found in the AASHTO Roadside Design
Guide.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
13-4
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
A pedestrian walkway may be separated from an
adjacent roadway by a barrier curb, traffic railing, or
combination railing, as indicated in Figure 13.4-1. On
high-speed urban expressways where a pedestrian
walkway is provided, the walkway area shall be separated
from the adjacent roadway by a traffic railing or
combination railing.
The following guidelines indicate the application of
various types of rails:
•
Traffic railing is used when a bridge is for the
exclusive use of highway traffic;
•
A combination barrier in conjunction with a
raised curb and sidewalk is used only on lowspeed highways;
•
On high-speed highways, the pedestrian or
bicycle path should have both an outboard
pedestrian or bicycle railing and an inboard
combination railing; and
•
Separate pedestrian bridges should be considered
where the amount of pedestrian traffic or other
risk factors so indicate.
For the purpose of this Article, low speed may be
taken as speeds not exceeding 45 mph. High speed may be
taken as speeds in excess of 45 mph.
The walkway faces of combination railings separating
walkways from adjacent roadways serve as pedestrian or
bicycle railings. When the height of such railings above
the walkway surface is less than the minimum height
required for pedestrian or bicycle railings, as appropriate,
the Designer may consider providing additional
components, such as metal rails, on top of the combination
railing. The additional components need to be designed for
the appropriate pedestrian or bicycle railing design forces.
Figure 13.4-1—Pedestrian Walkway
New bridge railings and the attachment to the deck
overhang shall satisfy crash testing requirements to
confirm that they meet the structural and geometric
requirements of a specified railing test level using the test
criteria specified in Article 13.7.2.
Warning devices for pedestrians are beyond the scope
of these Specifications, but they should be considered.
Procedures for testing railing are given in AASHTO’s
Manual for Assessing Safety Hardware.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 13: RAILINGS
13-5
13.5—MATERIALS
C13.5
The requirements of Sections 5, 6, 7, and 8 shall apply
to the materials employed in a railing system, unless
otherwise modified herein.
Factors to be considered in choosing the material for
use in any railing system include ultimate strength,
durability, ductility, maintenance, ease of replacement, and
long-term behavior.
13.6—LIMIT STATES AND RESISTANCE
FACTORS
13.6.1—Strength Limit State
The strength limit states shall apply using the
applicable load combinations in Table 3.4.1-1 and the
loads specified herein. The resistance factors for post and
railing components shall be as specified in Articles 5.5.4,
6.5.4, 7.5.4, and 8.5.2.
Design loads for pedestrian railings shall be as
specified in Article 13.8.2. Design loads for bicycle
railings shall be as specified in Article 13.9.3. Pedestrian
or bicycle loadings shall be applied to combination railings
as specified in Article 13.10.3. Deck overhangs shall be
designed for applicable strength load combinations
specified in Table 3.4.1-1.
13.6.2—Extreme Event Limit State
The forces to be transmitted from the bridge railing to
the bridge deck may be determined from an ultimate
strength analysis of the railing system using the loads
given in Appendix A. Those forces shall be considered to
be the factored loads at the extreme event limit state.
13.7—TRAFFIC RAILING
13.7.1—Railing System
13.7.1.1—General
C13.7.1.1
The primary purpose of traffic railings shall be to
contain and redirect vehicles using the structure. All new
vehicle traffic barrier systems, traffic railings, and
combination railings shall be shown to be structurally and
geometrically crashworthy.
Consideration should be given to:
•
Protection of the occupants of a vehicle in
collision with the railing,
•
Protection of other vehicles near the collision,
•
Protection of persons and property on roadways
and other areas underneath the structure,
•
Possible future rail upgrading,
•
Railing cost-effectiveness, and
•
Appearance and freedom of view from passing
vehicles.
Variations in traffic volume, speed, vehicle mix,
roadway alignment, activities and conditions beneath a
structure, and other factors combine to produce a vast
variation in traffic railing performance requirements.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
13-6
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
A combination railing, conforming to the dimensions
given in Figures 13.8.2-1 and 13.9.3-1, and crash tested
with a sidewalk may be considered acceptable for use with
sidewalks having widths 3.5 ft or greater and curb heights
up to the height used in the crash test installation.
A railing designed for multiple use shall be shown to
be crashworthy with or without the sidewalk. Use of the
combination vehicle-pedestrian rail shown in
Figure 13.7.1.1-1 shall be restricted to roads designated for
45 mph or less and need be tested to Test Level 1 or 2.
Because of more recent tests on sidewalks, an 8.0-in.
maximum height for sidewalk curbs has generally been
accepted.
AASHTO’s A Policy on Geometric Design of
Highways and Streets recommends that a barrier curb be
used only for speeds of 45 mph or less. For speeds of
50 mph or greater, pedestrians should be protected by a
separation traffic barrier.
A railing intended for use only on a sidewalk need not
be tested without the sidewalk.
Figure 13.7.1.1-1—Typical Raised Sidewalk
13.7.1.2—Approach Railings
An approach guardrail system should be provided at
the beginning of all bridge railings in high-speed rural
areas.
A bridge approach railing system should include a
transition from the guardrail system to the rigid bridge
railing system that is capable of providing lateral
resistance to an errant vehicle. The approach guardrail
system shall have a crashworthy end terminal at its nosing.
C13.7.1.2
In urban areas or where city streets and/or sidewalks
prevent installation of approach guardrail transitions or
crashworthy terminals, consideration should be given to:
•
Extending the bridge rail or guard rail in a
manner that prevents encroachment of a vehicle
onto any highway system below the bridge,
•
Providing a barrier curb,
•
Restricting speed,
•
Adding signing of intersections, and
•
Providing recovery areas.
A bridge end drainage facility should be an integral
part of the barrier transition design.
13.7.1.3—End Treatment
In high-speed rural areas, the approach end of a
parapet or railing shall have a crashworthy configuration
or be shielded by a crashworthy traffic barrier.
C13.7.1.3
If the approach railing is connected to a side of road
railing system, it can be continuous with the bridge
approach system, and only a transition from a flexible to a
rigid railing system is required.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 13: RAILINGS
13-7
13.7.2—Test Level Selection Criteria
One of the following test levels should be specified:
•
TL-1—Test Level One—taken to be generally
acceptable for work zones with low posted
speeds and very low volume, low speed local
streets;
•
TL-2—Test Level Two—taken to be generally
acceptable for work zones and most local and
collector roads with favorable site conditions as
well as where a small number of heavy vehicles
is expected and posted speeds are reduced;
•
TL-3—Test Level Three—taken to be generally
acceptable for a wide range of high-speed arterial
highways with very low mixtures of heavy
vehicles and with favorable site conditions;
•
TL-4—Test Level Four—taken to be generally
acceptable for the majority of applications on
high speed highways, freeways, expressways,
and Interstate highways with a mixture of trucks
and heavy vehicles;
•
TL-5—Test Level Five—taken to be generally
acceptable for the same applications as TL-4 and
where large trucks make up a significant portion
of the average daily traffic or when unfavorable
site conditions justify a higher level of rail
resistance; and
•
TL-6—Test Level Six—taken to be generally
acceptable for applications where tanker-type
trucks or similar high center of gravity vehicles
are anticipated, particularly along with
unfavorable site conditions.
It shall be the responsibility of the user agency to
determine which of the test levels is most appropriate for
the bridge site.
The testing criteria for the chosen test level shall
correspond to vehicle weights and speeds and angles of
impact outlined in Table 13.7.2-1.
C13.7.2
The six test levels mentioned herein are intended to
correspond with the six test levels contained in
AASHTO’s Manual for Assessing Safety Hardware and
NCHRP Report 350, “Recommended Procedures for the
Safety Performance Evaluation of Highway Features.”
AASHTO’s A Policy on Geometric Design of Highways
and Streets (2004) and its Roadside Design Guide (2002)
are referred to as aides in the bridge railing selection
process.
The individual tests are designed to evaluate one or
more of the principal performance factors of the bridge
railing, which include structural adequacy, occupant risk,
and postimpact behavior of the test vehicle. In general,
the lower test levels are applicable for evaluating and
selecting bridge railings to be used on segments of lower
service level roadways and certain types of work zones.
The higher test levels are applicable for evaluating and
selecting bridge railings to be used on higher service
level roadways or at locations that demand a special,
high-performance bridge railing. In this regard, TL-4
railings are expected to satisfy the majority of interstate
design requirements.
TL-5 provides for a van-type tractor-trailer that will
satisfy design requirements where TL-4 railings are
deemed to be inadequate due to the high number of this
type of vehicle anticipated, or due to unfavorable site
conditions where rollover or penetration beyond the railing
could result in severe consequences.
TL-6 provides for a tanker-type truck that will satisfy
design requirements where this type vehicle with a higher
center of gravity has shown a history of rollover or
penetration, or unfavorable site conditions may indicate
the need for this level of rail resistance.
Unfavorable site conditions include but are not limited
to reduced radius of curvature, steep downgrades on
curvature, variable cross slopes, and adverse weather
conditions.
Agencies should develop objective guidelines for use
of bridge railings. These guidelines should take into
account factors such as traffic conditions, traffic volume
and mix, cost and in-service performance, and life-cycle
cost of existing railings.
These criteria, including other vehicle characteristics
and tolerances, are described in detail in AASHTO’s
Manual for Assessing Safety Hardware and the NCHRP
Report 350.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
13-8
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
AASHTO MASH
NCHRP Report 350
Table 13.7.2-1—Bridge Railing Test Levels and Crash Test Criteria
Vehicle
Characteristics
W (kips)
B (ft.)
G (in.)
Crash angle, θ
Test Level
TL-1
TL-2
TL-3
TL-4
TL-5
TL-6
W (kips)
B (ft.)
G (in.)
Crash angle, θ
Test Level
TL-1
TL-2
TL-3
TL-4
TL-5
TL-6
Small
Automobiles
1.55
1.8
5.5
5.5
22
22
20°
20°
Pickup
Truck
4.5
6.5
27
25°
30
45
60
60
60
60
2.42
5.5
N/A
25°
30
45
60
60
60
60
3.3
5.5
N/A
N/A
30
45
60
60
60
60
5.0
6.5
28
25°
30
45
60
60
60
60
N/A
N/A
N/A
N/A
N/A
N/A
30
45
60
60
60
60
SingleUnit
Van-Type
Van Truck
Tractor-Trailer
18.0
50.0
80.0
7.5
8.0
8.0
49
64
73
15°
15°
15°
Test Speeds (mph)
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
50
N/A
N/A
N/A
N/A
50
N/A
N/A
N/A
22.0
N/A
79.3
7.5
N/A
8.0
63
N/A
73
15°
N/A
15°
Test Speeds (mph)
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
55
N/A
N/A
N/A
N/A
50
N/A
N/A
N/A
Tractor-Tanker
Trailer
80.0
8.0
81
15°
N/A
N/A
N/A
N/A
N/A
50
79.3
8.0
81
15°
N/A
N/A
N/A
N/A
N/A
50
13.7.3—Railing Design
C13.7.3.1
13.7.3.1—General
A traffic railing should normally provide a smooth
continuous face of rail on the traffic side. Steel posts with
rail elements should be set back from the face of rail.
Structural continuity in the rail members and anchorages of
ends should be considered.
A railing system and its connection to the deck shall
be approved only after they have been shown through
crash testing to be satisfactory for the desired test level.
13.7.3.1.1—Application of Previously Tested
Systems
A crashworthy railing system may be used without
further analysis and/or testing, provided that the proposed
installation does not have features that are absent in the
tested configuration and that might detract from the
performance of the tested railing system.
Protrusions or depressions at rail openings may be
acceptable, provided that their thickness, depth, or
geometry does not prevent the railing from meeting the
crash test evaluation criteria.
Test specimens should include a representative
length of the overhang to account for the effect of deck
flexibility on the distance over which the railing engages
the deck.
C13.7.3.1.1
When a minor detail is changed on or an improvement
is made to a railing system that has already been tested and
approved, engineering judgment and analysis should be
used when determining the need for additional crash
testing.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 13: RAILINGS
13-9
13.7.3.1.2—New Systems
New railing systems may be used, provided that
acceptable performance is demonstrated through full-scale
crash tests.
The crash test specimen for a railing system may be
designed to resist the applied loads in accordance with
Appendix A13.
Provision shall be made to transfer loads from the
railing system to the deck. Railing loads may be taken
from Appendix A13.
Unless a lesser thickness can be proven satisfactory
during the crash testing procedure, the minimum edge
thickness for concrete deck overhangs shall be taken as:
•
For concrete deck overhangs supporting a deckmounted post system: 8.0 in.
•
For a side-mounted post system: 12.0 in.
•
For concrete deck overhangs supporting concrete
parapets or barriers: 8.0 in.
13.7.3.2—Height of Traffic Parapet or Railing
Traffic railings shall be at least 27.0 in. for TL-3,
32.0 in. for TL-4, 42.0 in. for TL-5, and 90.0 in. in height
for TL-6.
The bottom 3.0-in. lip of the safety shape shall not be
increased for future overlay considerations.
The minimum height for a concrete parapet with a
vertical face shall be 27.0 in. The height of other combined
concrete and metal rails shall not be less than 27.0 in. and
shall be determined to be satisfactory through crash testing
for the desired test level.
The minimum height of the pedestrian or bicycle
railing should be measured above the surface of the
sidewalk or bikeway.
The minimum geometric requirements for
combination railings beyond those required to meet crash
test requirements shall be taken as specified in
Articles 13.8, 13.9, and 13.10.
C13.7.3.1.2
Preliminary design for bridge decks should comply
with Article A13.1.2. A determination of the adequacy of
deck reinforcement for the distribution of post anchorage
loads to the deck should be made during the rail testing
program. If the rail testing program satisfactorily models
the bridge deck, damage to the deck edge can be assessed
at this time.
In adequately designed bridge deck overhangs, the
major crash-related damage presently occurs in short
sections of slab areas where the barrier is hit.
C13.7.3.2
These heights have been determined as satisfactory
through crash tests performed in accordance with NCHRP
Report 350 and experience.
For future deck overlays, an encroachment of 2.0 in.,
leaving a 1.0-in. lip, has been satisfactorily tested for
safety shapes.
13.8—PEDESTRIAN RAILING
C13.8.1
13.8.1—Geometry
The minimum height of a pedestrian railing shall be
42.0 in. measured from the top of the walkway.
A pedestrian rail may be composed of horizontal
and/or vertical elements. The clear opening between
elements shall be such that a 6.0 in. diameter sphere shall
not pass through.
When both horizontal and vertical elements are used,
the 6.0 in. clear opening shall apply to the lower 27.0 in. of
the railing, and the spacing in the upper portion shall be
such that a 8.0-in. diameter sphere shall not pass through.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
13-10
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
A safety toe rail or curb should be provided. Rails should
project beyond the face of posts and/or pickets as shown in
Figure A13.1.1-2.
The rail spacing requirements given above should not
apply to chain link or metal fabric fence support rails and
posts. Mesh size in chain link or metal fabric fence should
have openings no larger than 2.0 in.
13.8.2—Design Live Loads
2013 Revision
The design live load for pedestrian railings shall be
taken as w = 0.050 klf, both transversely and vertically,
acting simultaneously. In addition, each longitudinal
element will be designed for a concentrated load of
0.20 kips, which shall act simultaneously with the above
loads at any point and in any direction at the top of the
longitudinal element.
The posts of pedestrian railings shall be designed for a
concentrated design live load applied transversely at the
center of gravity of the upper longitudinal element or, for
railings with a total height greater than 5.0 ft, at a point
5.0 ft above the top surface of the sidewalk. The value of
the concentrated design live load for posts, PLL, in kips,
shall be taken as:
PLL = 0.20 + 0.050 L
The size of openings should be capable of retaining an
average size beverage container.
C13.8.2
These live loads apply to the railing. The pedestrian
live load, specified in Article 3.6.1.6, applies to the
sidewalk.
(13.8.2-1)
where:
L
=
post spacing (ft)
The design load for chain link or metal fabric fence
shall be 0.015 ksf acting normal to the entire surface.
The application of loads shall be as indicated in
Figure 13.8.2-1, in which the shapes of rail members are
illustrative only. Any material or combination of materials
specified in Article 13.5 may be used.
Figure 13.8.2-1—Pedestrian Railing Loads—To be used on
the outer edge of a sidewalk when highway traffic is
separated from pedestrian traffic by a traffic railing.
Railing shape illustrative only.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 13: RAILINGS
13-11
13.9—BICYCLE RAILINGS
13.9.1—General
Bicycle railings shall be used on bridges specifically
designed to carry bicycle traffic and on bridges where
specific protection of bicyclists is deemed necessary.
13.9.2—Geometry
C13.9.2
The height of a bicycle railing shall not be less than
42.0 in., measured from the top of the riding surface.
The height of the upper and lower zones of a bicycle
railing shall be at least 27.0 in. The upper and lower zones
shall have rail spacing satisfying the respective provisions
of Article 13.8.1.
Railings, fences or barriers on either side of a shared
use path on a structure, or along bicycle lane, shared use
path or signed shared roadway located on a highway
bridge should be a minimum of 42.0 in. high. The 42.0-in.
minimum height is in accordance with the AASHTO Guide
for the Development of Bicycle Facilities, Third Edition
(1999).
On such a bridge or bridge approach where high-speed
high-angle impact with a railing, fence or barrier are more
likely to occur (such as short radius curves with restricted
sight distance or at the end of a long descending grade) or
in locations with site-specific safety concerns, a railing,
fence or barrier height above the minimum should be
considered.
The need for rubrails attached to a rail or fence is
controversial among many bicyclists.
If deemed necessary, rubrails attached to the rail or
fence to prevent snagging should be deep enough to
protect a wide range of bicycle handlebar heights.
If screening, fencing, or a solid face is utilized, the
number of rails may be reduced.
13.9.3—Design Live Loads
If the rail height exceeds 54.0 in. above the riding
surface, design loads shall be determined by the Designer.
The design loads for the lower 54.0 in. of the bicycle
railing shall not be less than those specified in
Article 13.8.2, except that for railings with total height
greater than 54.0 in., the design live load for posts shall be
applied at a point 54.0 in. above the riding surface.
The application of loads shall be as indicated in
Figure 13.9.3-1. Any material or combination of materials
specified in Article 13.5 may be used.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
13-12
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure 13.9.3-1—Bicycle Railing Loads—To be used on the
outer edge of a bikeway when highway traffic is separated
from bicycle traffic by a traffic railing. Railing shape
illustrative only.
13.10—COMBINATION RAILINGS
13.10.1—General
The combination railing shall conform to the
requirements of either the pedestrian or bicycle railings, as
specified in Articles 13.8 and 13.9, whichever is
applicable. The traffic railing portion of the combination
railing shall conform to Article 13.7.
13.10.2—Geometry
The geometric provisions of Articles 13.7, 13.8, and
13.9 shall apply to their respective portions of a
combination railing.
13.10.3—Design Live Loads
Design loads, specified in Articles 13.8 and 13.9, shall
not be applied simultaneously with the vehicular impact
loads.
13.11—CURBS AND SIDEWALKS
13.11.1—General
Horizontal measurements of roadway width shall be
taken from the bottom of the face of the curb. A sidewalk
curb located on the highway traffic side of a bridge railing
shall be considered an integral part of the railing and shall
be subject to the crash test requirements specified in
Article 13.7.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 13: RAILINGS
13-13
13.11.2—Sidewalks
C13.11.2
When curb and gutter sections with sidewalks are
used on roadway approaches, the curb height for raised
sidewalks on the bridge should be no more than 8.0 in. If a
barrier curb is required, the curb height should not be less
than 6.0 in. If the height of the curb on the bridge differs
from that off the bridge, it should be uniformly transitioned
over a distance greater than or equal to 20 times the change
in height.
Raised sidewalks on bridges are not usually provided
where the approach roadway is not curbed for pedestrians
or the structure is not planned for pedestrian occupancy.
For recommendations on sidewalk width, see
Figure 13.7.1.1-1 and AASHTO’s A Policy on Geometric
Design of Highways and Streets.
During stage construction, the same transition
considerations will be given to the provision of ramps from
the bridge sidewalk to the approach surface.
13.11.3—End Treatment of Separation Railing
The end treatment of any traffic railing or barrier shall
meet the requirements specified in Articles 13.7.1.2 and
13.7.1.3.
13.12—REFERENCES
AASHTO. 2009. Manual for Assessing Safety Hardware, MASH-1. American Association of State Highway and
Transportation Officials, Washington, DC.
AASHTO. 2011. A Policy on Geometric Design of Highways and Streets, Sixh Edition, GDHS-6. American Association of
State Highway and Transportation Officials, Washington, DC.
AASHTO. 2011. Roadside Design Guide, Fourth Edition, RSDG-4. American Association of State Highway and
Transportation Officials, Washington, DC.
Alberson, D. C., R. A. Zimmer, and W. L. Menges. 1997. NCHRP Report 350 Compliance Test 5-12 of the 1.07-m Vertical
Wall Bridge Railing, FHWA/RD-96/199. Federal Highway Administration, U.S. Department of Transportation,
Washington, DC.
Buth, C. E., W. L. Campise, L. I. Griffin, M. L. Love, and D. L. Sicking. 1986. Performance Limits of Longitudinal
Barriers, FHWA/RD-86/153, Test 4798-13. Federal Highway Administration, U.S. Department of Transportation,
Washington, DC.
Michie, J. D. 1981. NCHRP Report 230: Recommended Procedures for the Safety Performance Evaluation of Highway
Appurtenances. Transportation Research Board, National Research Council, Washington, DC.
Ross, H. E., D. L. Sicking, R. A. Zimmer, and J. D. Michie. 1993. NCHRP Report 350: Recommended Procedures for the
Safety Performance Evaluation of Highway Features. Transportation Research Board, National Research Council,
Washington, DC.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 13: RAILINGS
13-15
APPENDIX A13—RAILINGS
A13.1—GEOMETRY AND ANCHORAGES
A13.1.1—Separation of Rail Elements
CA13.1.1
For traffic railings, the criteria for maximum clear
opening below the bottom rail, cb, the setback distance, S,
and maximum opening between rails, c, shall be based on
the following criteria:
The post setback shown from face of rail for various
post shapes is based upon a limited amount of crash test
data. The potential for wheel snagging involved with a
given design should be evaluated as part of the crash test
program.
The post setback, S, shown for various shape posts in
Figure A13.1.1-2, recognizes the tendency for various
shape posts to snag wheels. The implication of the various
definitions of setback, S, is that all other factors being
equal, the space between a rail and the face of a
rectangular post will be greater than the distance between a
rail and the face of a circular post.
•
The rail contact widths for typical railings may be
taken as illustrated in Figure A13.1.1-1;
•
The total width of the rail(s) in contact with the
vehicle, ΣA, shall not be less than 25 percent of
the height of the railing;
•
For post railings, the vertical clear opening, c,
and the post setback, S, shall be within or below
the shaded area shown in Figure A13.1.1-2; and
•
For post railings, the combination of (ΣA/H) and
the post setback, S shall be within or above the
shaded area shown in Figure A13.1.1-3.
Figure A13.1.1-1—Typical Traffic Railings
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
13-16
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure A13.1.1-2—Potential for Wheel, Bumper, or Hood
Impact with Post
Figure A13.1.1-3—Post Setback Criteria
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2012
Edition
SECTION 13: RAILINGS
13-17
The maximum clear vertical opening between
succeeding rails or posts shall be as specified in
Articles 13.8, 13.9, and 13.10.
A13.1.2—Anchorages
CA13.1.2
The yield strength of anchor bolts for steel railing
shall be fully developed by bond, hooks, attachment to
embedded plates, or any combination thereof.
Reinforcing steel for concrete barriers shall have
embedment length sufficient to develop the yield strength.
Noncorrosive bonding agents for anchor dowels may
be cement grout, epoxy, or a magnesium phosphate
compound. Sulfur or expansive-type grouts should not be
used.
Some bonding agents on the market have corrosive
characteristics; these should be avoided.
Development length for reinforcing bars is specified
in Section 5.
A13.2—TRAFFIC RAILING DESIGN FORCES
CA13.2
Unless modified herein, the extreme event limit state
and the corresponding load combinations in Table 3.4.1-1
shall apply.
Railing design forces and geometric criteria to be used
in developing test specimens for a crash test program
should be taken as specified in Table A13.2-1 and
illustrated in Figure A13.2-1. The transverse and
longitudinal loads given in Table A13.2-1 need not be
applied in conjunction with vertical loads.
The effective height of the vehicle rollover force is
taken as:
Nomenclature for Eqs. A13.2-1 and A13.2-2 is
illustrated in Figure CA13.2-1.
He = G −
12WB
2 Ft
(A13.2-1)
where:
G
=
height of vehicle center of gravity above bridge
deck, as specified in Table 13.7.2-1 (in.)
W =
weight of vehicle corresponding to the required
test level, as specified in Table 13.7.2-1 (kips)
B
=
out-to-out wheel spacing on an axle, as specified
in Table 13.7.2-1 (ft)
Ft
=
transverse force corresponding to the required
test level, as specified in Table A13.2-1 (kips)
Railings shall be proportioned such that:
R ≥ Ft
Y≥
He
12
Figure CA13.2-1—Traffic Railing
If the total resistance, R , of a post-and-beam railing
system with multiple rail elements is significantly greater
than the applied load, Ft, then the resistance, Ri, for the
lower rail element(s) used in calculations may be reduced.
The reduced value of R will result in an increase in
the computed value of Y . The reduced notional total rail
resistance and its effective height must satisfy
Eqs. A13.2-2 and A13.2-3.
(A13.2-2)
(A13.2-3)
in which:
R = Ri
(A13.2-4)
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2012
Edition
13-18
Y=
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Σ(RiYi )
(A13.2-5)
R
where:
Ri
=
resistance of the rail (kips)
Yi
=
distance from bridge deck to the ith rail (ft)
All forces shall be applied to the longitudinal rail
elements. The distribution of longitudinal loads to posts
shall be consistent with the continuity of rail elements.
Distribution of transverse loads shall be consistent with the
assumed failure mechanism of the railing system.
Eq. A13.2-1 has been found to give reasonable
predictions of effective railing height requirements to
prevent rollover.
If the design load located at He falls between rail
elements, it should be distributed proportionally to rail
elements above and below such that Y ≥ He.
As an example of the significance of the data in
Table A13.2-1, the length of 4.0 ft for Lt and LL is the
length of significant contact between the vehicle and
railing that has been observed in films of crash tests. The
length of 3.5 ft for TL-4 is the rear-axle tire diameter of the
truck. The length of 8.0 ft for TL-5 and TL-6 is the length
of the tractor rear tandem axles: two 3.5-ft diameter tires,
plus 1.0 ft between them.
Fv, the weight of the vehicle lying on top of the bridge
rail, is distributed over the length of the vehicle in contact
with the rail, Lv.
For concrete railings, Eq. A13.2-1 results in a
theoretically-required height, H, of 34.0 in. for Test Level
TL-4. However, a height of 32.0 in., shown in
Table A13.2-1, was considered to be acceptable because
many railings of that height have been built and appear to
be performing acceptably.
The minimum height, H, listed for TL-1, TL-2, and
TL-3 is based on the minimum railings height used in the
past. The minimum effective height, He, for TL-1 is an
estimate based on the limited information available for this
test level.
The minimum height, H, of 42.0 in., shown in
Table A13.2-1, for TL-5 is based on the height used for
successfully crash-tested concrete barrier engaging only
the tires of the truck. For post and beam metal bridge
railings, it may be prudent to increase the height by
12.0 in. so as to engage the bed of the truck.
The minimum height, H, shown in Table A13.2-1, for
TL-6 is the height required to engage the side of the tank
as determined by crash test.
Table A13.2-1—Design Forces for Traffic Railings
Design Forces and Designations
Ft Transverse (kips)
FL Longitudinal (kips)
Fv Vertical (kips) Down
Lt and LL (ft)
Lv (ft)
He (min) (in.)
Minimum H Height of Rail (in.)
TL-1
13.5
4.5
4.5
4.0
18.0
18.0
27.0
TL-2
27.0
9.0
4.5
4.0
18.0
20.0
27.0
Railing Test Levels
TL-3
TL-4
54.0
54.0
18.0
18.0
4.5
18.0
4.0
3.5
18.0
18.0
24.0
32.0
27.0
32.0
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TL-5
124.0
41.0
80.0
8.0
40.0
42.0
42.0
TL-6
175.0
58.0
80.0
8.0
40.0
56.0
90.0
2012
Edition
SECTION 13: RAILINGS
13-19
Figure A13.2-1 shows the design forces from
Table A13.2-1 applied to a beam and post railing. This is
for illustrative purposes only. The forces and distribution
lengths shown apply to any type of railing.
Figure A13.2-1—Metal Bridge Railing Design Forces,
Vertical Location, and Horizontal Distribution Length
A13.3—DESIGN PROCEDURE FOR RAILING
TEST SPECIMENS
A13.3.1—Concrete Railings
CA13.3.1
Yield line analysis and strength design for reinforced
concrete and prestressed concrete barriers or parapets may
be used.
The nominal railing resistance to transverse load, Rw,
may be determined using a yield line approach as:
The yield line analysis shown in Figures CA13.3.1-1 and
CA13.3.1-2 includes only the ultimate flexural capacity of the
concrete component. Stirrups or ties should be provided to
resist the shear and/or diagonal tension forces.
The ultimate flexural resistance, Ms, of the bridge deck
or slab should be determined in recognition that the deck is
also resisting a tensile force, caused by the component of the
impact forces, Ft.
In this analysis it is assumed that the yield line failure
pattern occurs within the parapet only and does not extend
into the deck. This means that the deck must have sufficient
resistance to force the yield line failure pattern to remain
within the parapet. If the failure pattern extends into the deck,
the equations for resistance of the parapet are not valid.
The analysis is also based on the assumption that
sufficient longitudinal length of parapet exists to result in the
yield line failure pattern shown. For short lengths of parapet,
a single yield line may form along the juncture of the parapet
and deck. Such a failure pattern is permissible, and the
resistance of the parapet should be computed using an
appropriate analysis.
This analysis is based on the assumption that the
negative and positive wall resisting moments are equal and
that the negative and positive beam resisting moments are
equal.
The measurement of system resistance of a concrete
railing is Rw, which is compared to the loads in Table A13.2-1
to determine structural adequacy. The flexure resistances, Mb,
Mw, and Mc, are related to the system resistance Rw through
the yield line analysis embodied in Eqs. A13.3.1-1 and
A13.3.1-2. In the terminology of these Specifications, Rw is
the “nominal resistance” because it is compared to the
“nominal load” given in Table A13.2-1.
Where the width of the concrete railing varies along the
height, Mc used in Eqs. A13.3.1-1 through A13.3.1-4 for
wall resistance should be taken as the average of its value
along the height of the railing.
•
For impacts within a wall segment:
M c Lc 2
2
Rw =
8M b + 8M w +
H
2 Lc − Lt
(A13.3.1-1)
The critical wall length over which the yield line
mechanism occurs, Lc, shall be taken as:
2
Lc =
Lt
L 8H ( M b + M w )
+ t+
2
Mc
2
•
(A13.3.1-2)
For impacts at end of wall or at joint:
M c Lc 2
2
Rw =
Mb + Mw +
H
2 Lc − Lt
(A13.3.1-3)
2
Lc =
M + Mw
Lt
L
+ t +H b
2
2
Mc
(A13.3.1-4)
where:
Ft
=
transverse force specified in Table A13.2-1
assumed to be acting at top of a concrete wall
(kips)
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2012
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13-20
H
=
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
height of wall (ft)
Lc =
critical length of yield line failure pattern (ft)
Lt
longitudinal length of distribution of impact force
Ft (ft)
=
Rw =
total transverse resistance of the railing (kips)
Mb =
additional flexural resistance of beam in addition
to Mw, if any, at top of wall (kip-ft)
Mc =
flexural resistance of cantilevered walls about an
axis parallel to the longitudinal axis of the bridge
(kip-ft/ft)
Mw =
flexural resistance of the wall about its vertical
axis (kip-ft)
For use in the above equations, Mc and Mw should not
vary significantly over the height of the wall. For other
cases, a rigorous yield line analysis should be used.
Figure CA13.3.1-1—Yield Line Analysis of Concrete
Parapet Walls for Impact within Wall Segment
Figure CA13.3.1-2—Yield Line Analysis of Concrete
Parapet Walls for Impact near End of Wall Segment
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2012
Edition
SECTION 13: RAILINGS
13-21
A13.3.2—Post-and-Beam Railings
CA13.3.2
Inelastic analysis shall be used for design of post-andbeam railings under failure conditions. The critical rail
nominal resistance, R, when the failure does not involve
the end post of a segment, shall be taken as the least value
determined from Eqs. A13.3.2-1 and A13.3.2-2 for various
numbers of railing spans, N.
A basis for applying inelastic analysis is shown in
Figure CA13.3.2-1.
Figure CA13.3.2-1—Possible Failure Modes for Post-andBeam Railings
•
For failure modes involving an odd number of
railing spans, N:
R =
•
16 M p + ( N − 1)( N + 1) Pp L
2 NL − Lt
(A13.3.2-1)
This design procedure is applicable to concrete and
metal post and beam railings.
The post on each end of the plastic mechanism must
be able to resist the rail or beam shear.
For failure modes involving an even number of
railing spans, N:
R=
16 M p + N 2 Pp L
2 NL − Lt
(A13.3.2-2)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
13-22
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
where:
L
=
post spacing or single-span (ft)
Mp
=
inelastic or yield line resistance of all of the
rails contributing to a plastic hinge (kip-ft)
Mpost
=
plastic moment resistance of a single post
(kip-ft)
Pp
=
shear force on a single post which
corresponds to Mpost and is located Y above
the deck (kips)
R
=
total ultimate resistance, i.e., nominal
resistance, of the railing (kips)
Lt , LL
=
transverse length of distributed vehicle
impact loads, Ft and FL (ft)
For multiple rail systems, each of the rails may
contribute to the yield mechanism shown schematically in
Figure CA13.3.2-1, depending on the rotation corresponding
to its vertical position.
For impact at the end of rail segments that causes the
end post to fail, the critical rail nominal resistance, R, shall
be calculated using Eq. A13.3.2-3.
•
For any number of railing spans, N.
N
2M p + 2 Pp L i
i =1
R=
2 NL − Lt
(A13.3.2-3)
A13.3.3—Concrete Parapet and Metal Rail
CA13.3.3
The resistance of each component of a combination
bridge rail shall be determined as specified in
Articles A13.3.1 and A13.3.2. The flexural strength of the
rail shall be determined over one span, RR, and over two
spans, R′R. The resistance of the post on top of the wall, Pp,
including the resistance of the anchor bolts or post shall be
determined.
The resistance of the combination parapet and rail
shall be taken as the lesser of the resistances determined
for the two failure modes shown in Figures A13.3.3-1 and
A13.3.3-2.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 13: RAILINGS
13-23
Figure A13.3.3-1—Concrete Wall and Metal Rail
Evaluation—Impact at Midspan of Rail
Figure A13.3.3-2—Concrete Wall and Metal Rail
Evaluation—Impact at Post
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
13-24
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Where the vehicle impact is at midspan of the metal
rail, as illustrated in Figure A13.3.3-1, the flexural
resistance of the rail, RR, and the maximum strength of the
concrete wall, Rw, shall be added together to determine the
combined resultant strength, R , and the effective height,
Y , taken as:
R = RR + Rw
Y=
(A13.3.3-1)
RR H R + Rw H w
(A13.3.3-2)
R
The commentary to Article CA13.2 applies.
where:
RR =
ultimate capacity of rail over one span (kips)
Rw =
ultimate capacity of wall as specified in
Article A13.3.1 (kips)
Hw =
height of wall (ft)
HR =
height of rail (ft)
Where the vehicle impact is at a post, as illustrated in
Figure A13.3.3-2, the maximum resultant strength, R , shall
be taken as the sum of the post capacity, Pp, the rail strength,
R′R, and a reduced wall strength, R′w, located at a height Y .
R = Pp + RR′ + Rw′
Y =
(A13.3.3-3)
Pp H R + RR′ H R + Rw′ H w
R
(A13.3.3-4)
in which:
Rw′ =
Rw H w − Pp H R
(A13.3.3-5)
Hw
It should also be recognized that a maximum effective
height, Y , equal to the centroid rail height, HR, could be
obtained, but at a reduced resultant strength, R ,equal to
the post capacity, Pp , and rail capacity, R′R , only.
The analysis herein does not consider impacts near
open joints in the concrete wall or parapet. The metal rail
will help distribute load across such joints. Improved rail
resistance will be obtained if the use of expansion and
contraction joints is minimized.
For impact near the end of railing segments, the
nominal resistance may be calculated as the sum of the
wall resistance, calculated using Eq. A13.3.1-3, and the
metal rail resistance over one span, calculated using
Eq. A13.3.2-3.
where:
Pp =
ultimate transverse resistance of post (kips)
R′R =
ultimate transverse resistance of rail over two
spans (kips)
R′w =
capacity of wall, reduced to resist post load (kips)
Rw =
ultimate transverse resistance of wall as specified
in Article A13.3.1 (kips)
A13.3.4—Wood Barriers
CA13.3.4
Wood barriers shall be designed by elastic linear
analysis with member sections proportioned on the basis of
their resistances, specified in Section 8, using the strength
limit states and the applicable load combinations specified
in Table 3.4.1-1.
A limit or failure mechanism is not recommended for
wood railings.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 13: RAILINGS
13-25
A13.4—DECK OVERHANG DESIGN
A13.4.1—Design Cases
Bridge deck overhangs shall be designed for the
following design cases considered separately:
Design Case 1:
the transverse and longitudinal
forces specified in Article A13.2
Extreme Event Load Combination II
limit state
Design Case 2:
the vertical forces specified in
Article
A13.2—Extreme
Event
Load Combination II limit state
Design Case 3:
the loads, specified in Article 3.6.1,
that occupy the overhang—Load
Combination Strength I limit state
For Design Case 1 and 2, the load factor for dead load,
γp, shall be taken as 1.0.
The total factored force effect shall be taken as:
Q = ηi γ i Qi
(A13.4.1-1)
where:
ηi
=
load modifier specified in Article 1.3.2
γi
=
load factors specified in Tables 3.4.1-1 and
3.4.1-2, unless specified elsewhere
Qi =
force effects from loads specified herein
A13.4.2—Decks Supporting Concrete Parapet
Railings
CA13.4.2
For Design Case 1, the deck overhang may be
designed to provide a flexural resistance, Ms in kip-ft/ft
which, acting coincident with the tensile force T in kip/ft,
specified herein, exceeds Mc of the parapet at its base. The
axial tensile force, T, may be taken as:
If the deck overhang capacity is less than that
specified, the yield line failure mechanism for the parapet
may not develop as shown in Figure CA13.3.1-1, and
Eqs. A13.3.1-1 and A13.3.1-2 will not be correct.
The crash testing program is oriented toward survival,
not necessarily the identification of the ultimate strength of
the railing system. This could produce a railing system that
is significantly overdesigned, leading to the possibility that
the deck overhang is also overdesigned.
T=
Rw
Lc + 2 H
(A13.4.2-1)
where:
Rw =
parapet resistance specified in Article A13.3.1
(kips)
Lc =
critical length of yield line failure pattern (ft)
H
=
height of wall (ft)
T
=
tensile force per unit of deck length (kip/ft)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
13-26
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Design of the deck overhang for the vertical forces
specified in Design Case 2 shall be based on the
overhanging portion of the deck.
A13.4.3—Decks Supporting Post-and-Beam Railings
A13.4.3.1—Overhang Design
CA13.4.3.1
For Design Case 1, the moment per ft, Md, and thrust
per ft of deck, T, may be taken as:
Md =
T=
M post
(A13.4.3.1-1)
Wb + db
Pp
Wb + db
Vehicle collision on the beam and post railing
systems, such as a metal system with wide flange or
tubular posts, imposes large concentrated forces and
moments on the deck at the point where the post is
attached to the deck.
(A13.4.3.1-2)
For Design Case 2, the punching shear force and
overhang moment may be taken as:
FL
(A13.4.3.1-3)
Pv = v
Lv
Md =
Pv X
b
(A13.4.3.1-4)
in which:
b = 2X +Wb ≤ L
(A13.4.3.1-5)
where:
Mpost
=
plastic moment resistance of a single post
(kip-ft)
Pp
=
shear force on a single post which
corresponds to Mpost and is located Y above
the deck (kips)
X
=
distance from the outside edge of the post
base plate to the section under investigation,
as specified in Figure A13.4.3.1-1 (ft)
Wb
=
width of base plate (in.)
T
=
tensile force in deck (kip/ft)
db
=
distance from the outer edge of the base
plate to the innermost row of bolts, as shown
in Figure A13.4.3.1-1 (in.)
L
=
post spacing (ft)
Lv
=
longitudinal distribution of vertical force Fv
on top of railing (ft)
Fv
=
vertical force of vehicle laying on top of rail
after impact forces Ft and FL are over (kips)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 13: RAILINGS
13-27
Previous editions of the Standard Specifications
distributed railing or post loads to the slab using similar
simplified analysis, e.g., “The effective length of slab
resisting post loadings shall be equal to E = 0.8x + 3.75 ft
where no parapet is used and equal to E = 0.8x + 5.0 ft
where a parapet is used, where x is the distance in ft from
the center of the post to the point under investigation.”
Figure A13.4.3.1-1—Effective Length of Cantilever for
Carrying Concentrated Post Loads, Transverse or Vertical
A13.4.3.2—Resistance to Punching Shear
For Design Case 1, the factored shear may be taken
as:
Vu = Af Fy
(A13.4.3.2-1)
CA13.4.3.2
Concrete slabs or decks frequently fail in punching
shear resulting from the force in the compression flange of
the post, C. Adequate thickness, h, edge distance, E, or
base plate size (Wb or B or thickness) should be provided
to resist this type failure.
The factored resistance of deck overhangs to punching
shear may be taken as:
Vr = φVn
(A13.4.3.2-2)
B h
Vn = vc Wb + h + 2 E + + h
2 2
(A13.4.3.2-3)
0.1265
vc = 0.0633 +
βc
f c′ ≤ 0.1265 f c′
(A13.4.3.2-4)
B
h
+
≤ B
2
2
(A13.4.3.2-5)
in which:
βc = Wb / db
(A13.4.3.2-6)
where:
Vu =
factored shear force at section (kips)
Af
area of post compression flange (in.2)
=
Fy =
yield strength of post compression flange (ksi)
Vr =
factored shear resistance (kips)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
13-28
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Vn =
nominal shear resistance
considered (kips)
vc
nominal shear resistance provided by tensile
stresses in the concrete (ksi)
=
of
the
section
Wb =
width of base plate (in.)
b
=
length of deck resisting post strength or shear
load = h + Wb
h
=
depth of slab (in.)
E
=
distance from edge of slab to centroid of
compressive stress resultant in post (in.)
B
=
distance between centroids of tensile and
compressive stress resultants in post (in.)
βc =
ratio of the long side to the short side of the
concentrated load or reaction area
f ′c =
28-day compressive strength of concrete (ksi)
φ
resistance factor = 1.0
=
db =
distance from the outer edge of the base plate to
the innermost row of bolts (in.)
The assumed distribution of forces for punching shear
shall be as shown in Figure A13.4.3.2-1.
Test results and in-service experience have shown that
where deck failures have occurred, the failure mode has
been a punching shear-type failure with loss of structural
integrity between the concrete and reinforcing steel. Use of
various types of shear reinforcement may increase the
ultimate strength of the postdeck connection but is
ineffective in reducing shear, diagonal tension, or cracking
in the deck. Shear resistance can be increased by
increasing the slab thickness, base plate width and depth,
or edge distance.
Figure A13.4.3.2-1—Punching Shear Failure Mode
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 14: JOINTS AND BEARINGS
TABLE OF CONTENTS
14
14.1—SCOPE ............................................................................................................................................................. 14-1
14.2—DEFINITIONS ................................................................................................................................................. 14-1
14.3—NOTATION ..................................................................................................................................................... 14-3
14.4—MOVEMENTS AND LOADS......................................................................................................................... 14-6
14.4.1—General ................................................................................................................................................... 14-6
14.4.2—Design Requirements ........................................................................................................................... 14-10
14.4.2.1—Elastomeric Pads and Steel Reinforced Elastomeric Bearings ................................................... 14-11
14.4.2.2—High Load Multirotational (HLMR) Bearings ........................................................................... 14-12
14.4.2.2.1—Pot Bearings and Curved Sliding Surface Bearings ......................................................... 14-12
14.4.2.2.2—Disc Bearings ................................................................................................................... 14-12
14.5—BRIDGE JOINTS .......................................................................................................................................... 14-12
14.5.1—Requirements ....................................................................................................................................... 14-12
14.5.1.1—General....................................................................................................................................... 14-12
14.5.1.2—Structural Design ....................................................................................................................... 14-13
14.5.1.3—Geometry ................................................................................................................................... 14-14
14.5.1.4—Materials .................................................................................................................................... 14-14
14.5.1.5—Maintenance ............................................................................................................................... 14-14
14.5.2—Selection............................................................................................................................................... 14-14
14.5.2.1—Number of Joints ........................................................................................................................ 14-14
14.5.2.2—Location of Joints....................................................................................................................... 14-15
14.5.3—Design Requirements ........................................................................................................................... 14-15
14.5.3.1—Movements during Construction ................................................................................................ 14-15
14.5.3.2—Design Movements .................................................................................................................... 14-16
14.5.3.3—Protection ................................................................................................................................... 14-16
14.5.3.4—Bridging Plates........................................................................................................................... 14-17
14.5.3.5—Armor ......................................................................................................................................... 14-17
14.5.3.6—Anchors ...................................................................................................................................... 14-17
14.5.3.7—Bolts ........................................................................................................................................... 14-18
14.5.4—Fabrication ........................................................................................................................................... 14-18
14.5.5—Installation ........................................................................................................................................... 14-18
14.5.5.1—Adjustment ................................................................................................................................. 14-18
14.5.5.2—Temporary Supports................................................................................................................... 14-19
14.5.5.3—Field Splices............................................................................................................................... 14-19
14.5.6—Considerations for Specific Joint Types............................................................................................... 14-19
14.5.6.1—Open Joints ................................................................................................................................ 14-19
14.5.6.2—Closed Joints .............................................................................................................................. 14-20
14.5.6.3—Waterproofed Joints ................................................................................................................... 14-20
14.5.6.4—Joint Seals .................................................................................................................................. 14-20
14.5.6.5—Poured Seals............................................................................................................................... 14-21
14.5.6.6—Compression and Cellular Seals ................................................................................................ 14-21
14-i
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
14-ii
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
14.5.6.7—Sheet and Strip Seals ..................................................................................................................14-21
14.5.6.8—Plank Seals .................................................................................................................................14-22
14.5.6.9—Modular Bridge Joint Systems (MBJS) ......................................................................................14-22
14.5.6.9.1—General .............................................................................................................................14-22
14.5.6.9.2—Performance Requirements ..............................................................................................14-24
14.5.6.9.3—Testing and Calculation Requirements.............................................................................14-25
14.5.6.9.4—Loads and Load Factors ...................................................................................................14-25
14.5.6.9.5—Distribution of Wheel Loads ............................................................................................14-27
14.5.6.9.6—Strength Limit State Design Requirements ..........................................................................14-28
14.5.6.9.7—Fatigue Limit State Design Requirements ........................................................................14-29
14.5.6.9.7a—General ....................................................................................................................14-29
14.5.6.9.7b—Design Stress Range ...............................................................................................14-31
14.6—REQUIREMENTS FOR BEARINGS ............................................................................................................14-35
14.6.1—General .................................................................................................................................................14-35
14.6.2—Characteristics ......................................................................................................................................14-36
14.6.3—Force Effects Resulting from Restraint of Movement at the Bearing ...................................................14-37
14.6.3.1—Horizontal Force and Movement ................................................................................................14-37
14.6.3.2—Moment ......................................................................................................................................14-38
14.6.4—Fabrication, Installation, Testing, and Shipping ...................................................................................14-40
14.6.5—Seismic and Other Extreme Event Provisions for Bearings .................................................................14-40
14.6.5.1—General .......................................................................................................................................14-40
14.6.5.2—Applicability...............................................................................................................................14-40
14.6.5.3—Design Criteria ...........................................................................................................................14-41
14.7—SPECIAL DESIGN PROVISIONS FOR BEARINGS ..................................................................................14-42
14.7.1—Metal Rocker and Roller Bearings .......................................................................................................14-42
14.7.1.1—General .......................................................................................................................................14-42
14.7.1.2—Materials ....................................................................................................................................14-43
14.7.1.3—Geometric Requirements ............................................................................................................14-43
14.7.1.4—Contact Stresses .........................................................................................................................14-43
14.7.2—PTFE Sliding Surfaces .........................................................................................................................14-44
14.7.2.1—PTFE Surface .............................................................................................................................14-44
14.7.2.2—Mating Surface ...........................................................................................................................14-45
14.7.2.3—Minimum Thickness ...................................................................................................................14-45
14.7.2.3.1—PTFE ................................................................................................................................14-45
14.7.2.3.2—Stainless Steel Mating Surfaces .......................................................................................14-46
14.7.2.4—Contact Pressure .........................................................................................................................14-46
14.7.2.5—Coefficient of Friction ................................................................................................................14-47
14.7.2.6—Attachment .................................................................................................................................14-48
14.7.2.6.1—PTFE ................................................................................................................................14-48
14.7.2.6.2—Mating Surface .................................................................................................................14-48
14.7.3—Bearings with Curved Sliding Surfaces ................................................................................................14-49
14.7.3.1—General .......................................................................................................................................14-49
14.7.3.2—Bearing Resistance .....................................................................................................................14-49
14.7.3.3—Resistance to Lateral Load .........................................................................................................14-50
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
TABLE OF CONTENTS
14-iii
14.7.4—Pot Bearings ......................................................................................................................................... 14-51
14.7.4.1—General....................................................................................................................................... 14-51
14.7.4.2—Materials .................................................................................................................................... 14-51
14.7.4.3—Geometric Requirements............................................................................................................ 14-51
14.7.4.4—Elastomeric Disc ........................................................................................................................ 14-53
14.7.4.5—Sealing Rings ............................................................................................................................. 14-53
14.7.4.5.1—General ............................................................................................................................ 14-53
14.7.4.5.2—Rings with Rectangular Cross-Sections ........................................................................... 14-54
14.7.4.5.3—Rings with Circular Cross-Sections ................................................................................. 14-54
14.7.4.6—Pot .............................................................................................................................................. 14-54
14.7.4.7—Piston ......................................................................................................................................... 14-55
14.7.5—Steel-Reinforced Elastomeric Bearings—Method B ............................................................................ 14-56
14.7.5.1—General....................................................................................................................................... 14-56
14.7.5.2—Material Properties ..................................................................................................................... 14-58
14.7.5.3—Design Requirements ................................................................................................................. 14-59
14.7.5.3.1—Scope ............................................................................................................................... 14-59
14.7.5.3.2—Shear Deformations ......................................................................................................... 14-59
14.7.5.3.3—Combined Compression, Rotation, and Shear ................................................................. 14-60
14.7.5.3.4—Stability of Elastomeric Bearings .................................................................................... 14-63
14.7.5.3.5—Reinforcement.................................................................................................................. 14-64
14.7.5.3.6—Compressive Deflection ................................................................................................... 14-65
14.7.5.3.7—Seismic and Other Extreme Event Provisions.................................................................. 14-66
14.7.5.4—Anchorage for Bearings without Bonded External Plates .......................................................... 14-67
14.7.6—Elastomeric Pads and Steel-Reinforced Elastomeric Bearings—Method A ........................................ 14-67
14.7.6.1—General....................................................................................................................................... 14-67
14.7.6.2—Material Properties ..................................................................................................................... 14-69
14.7.6.3—Design Requirements ................................................................................................................. 14-70
14.7.6.3.1—Scope ............................................................................................................................... 14-70
14.7.6.3.2—Compressive Stress .......................................................................................................... 14-70
14.7.6.3.3—Compressive Deflection ................................................................................................... 14-71
14.7.6.3.4—Shear ................................................................................................................................ 14-73
14.7.6.3.5—Rotation ........................................................................................................................... 14-73
14.7.6.3.5a—General.................................................................................................................... 14-73
14.7.6.3.5b—Rotation of CDP ..................................................................................................... 14-74
14.7.6.3.6—Stability............................................................................................................................ 14-75
14.7.6.3.7—Reinforcement.................................................................................................................. 14-75
14.7.6.3.8—Seismic and Other Extreme Event Provisions.................................................................. 14-75
14.7.7—Bronze or Copper Alloy Sliding Surfaces ............................................................................................ 14-76
14.7.7.1—Materials .................................................................................................................................... 14-76
14.7.7.2—Coefficient of Friction................................................................................................................ 14-77
14.7.7.3—Limit on Load ............................................................................................................................ 14-77
14.7.7.4—Clearances and Mating Surfaces ................................................................................................ 14-77
14.7.8—Disc Bearings ....................................................................................................................................... 14-77
14.7.8.1—General....................................................................................................................................... 14-77
14.7.8.2—Materials .................................................................................................................................... 14-78
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
14-iv
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
14.7.8.3—Elastomeric Disc ........................................................................................................................14-78
14.7.8.4—Shear Resisting Mechanism .......................................................................................................14-79
14.7.8.5—Steel Plates .................................................................................................................................14-79
14.7.9—Guides and Restraints ...........................................................................................................................14-79
14.7.9.1—General .......................................................................................................................................14-79
14.7.9.2—Design Loads..............................................................................................................................14-80
14.7.9.3—Materials ....................................................................................................................................14-80
14.7.9.4—Geometric Requirements ............................................................................................................14-80
14.7.9.5—Design Basis...............................................................................................................................14-80
14.7.9.5.1—Load Location ..................................................................................................................14-80
14.7.9.5.2—Contact Stress...................................................................................................................14-81
14.7.9.6—Attachment of Low-Friction Material ........................................................................................14-81
14.7.10—Other Bearing Systems .......................................................................................................................14-81
14.8—LOAD PLATES AND ANCHORAGE FOR BEARINGS ............................................................................14-82
14.8.1—Plates for Load Distribution .................................................................................................................14-82
14.8.2—Tapered Plates ......................................................................................................................................14-83
14.8.3—Anchorage and Anchor Bolts ...............................................................................................................14-83
14.8.3.1—General .......................................................................................................................................14-83
14.8.3.2—Seismic and Other Extreme Event Design and Detailing Requirements ....................................14-84
14.9—CORROSION PROTECTION .......................................................................................................................14-84
14.10—REFERENCES .............................................................................................................................................14-84
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 14
JOINTS AND BEARINGS
14.1—SCOPE
This Section contains requirements for the design and
selection of structural bearings and deck joints.
Units used in this Section shall be taken as kip, in.,
rad., °F, and Shore Hardness, unless otherwise noted.
14
14.2—DEFINITIONS
Bearing—A structural device that transmits loads while facilitating translation and/or rotation.
Bearing Joint—A deck joint provided at bearings and other deck supports to facilitate horizontal translation and rotation of
abutting structural elements. It may or may not provide for differential vertical translation of these elements.
Bronze Bearing—A bearing in which displacements or rotations take place by the sliding of a bronze surface against a
mating surface.
Cotton-Duck-Reinforced Pad (CDP)—A pad made from closely spaced layers of elastomer and cotton-duck, bonded
together during vulcanization.
Closed Joint—A deck joint designed to prevent the passage of debris through the joint and to safeguard pedestrian and
cycle traffic.
Compression Seal—A preformed elastomeric device that is precompressed in the gap of a joint with expected total range of
movement less than 2.0 in.
Construction Joint—A temporary joint used to permit sequential construction.
Cycle-Control Joint—A transverse approach slab joint designed to permit longitudinal cycling of integral bridges and
attached approach slabs.
Damper—A device that transfers and reduces forces between superstructure elements and/or superstructure and
substructure elements, while permitting thermal movements. The device provides damping by dissipating energy under
seismic, braking, or other dynamic loads.
Deck Joint—A structural discontinuity between two elements, at least one of which is a deck element. It is designed to
permit relative translation and/or rotation of abutting structural elements.
Disc Bearing—A bearing that accommodates rotation by deformation of a single elastomeric disc molded from a urethane
compound. It may be movable, guided, unguided, or fixed. Movement is accommodated by sliding of polished stainless
steel on PFTE.
Double Cylindrical Bearing—A bearing made from two cylindrical bearings placed on top of each other with their axes at
right angles to facilitate rotation about any horizontal axis.
Fiberglass-Reinforced Pad (FGP)—A pad made from discrete layers of elastomer and woven fiberglass bonded together
during vulcanization.
Fixed Bearing—A bearing that prevents differential longitudinal translation of abutting structural elements. It may or may
not provide for differential lateral translation or rotation.
Integral Bridge—A bridge without deck joints.
Joint—A structural discontinuity between two elements. The structural members used to frame or form the discontinuity.
14-1
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
14-2
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Joint Seal—A poured or preformed elastomeric device designed to prevent moisture and debris from penetrating joints.
Knuckle Bearing—A bearing in which a concave metal surface rocks on a convex metal surface to provide rotation
capability about any horizontal axis.
Longitudinal—Parallel with the main span direction of a structure.
Longitudinal Joint—A joint parallel to the span direction of a structure provided to separate a deck or superstructure into
two independent structural systems.
Metal Rocker or Roller Bearing—A bearing that carries vertical load by direct contact between two metal surfaces and that
accommodates movement by rocking or rolling of one surface with respect to the other.
Modular Bridge Joint System (MBJS)—A sealed joint with two or more elastomeric seals held in place by edgebeams that
are anchored to the structural elements (deck, abutment, etc.) and one or more transverse centerbeams that are parallel to
the edgebeams. Typically used for movement ranges greater than 4.0 in.
Movable Bearing—A bearing that facilitates differential horizontal translation of abutting structural elements in a
longitudinal and/or lateral direction. It may or may not provide for rotation.
Multirotational Bearing—A bearing consisting of a rotational element of the pot type, disc type, or spherical type when
used as a fixed bearing and that may, in addition, have sliding surfaces to accommodate translation when used as an
expansion bearing. Translation may be constrained to a specified direction by guide bars.
Neutral Point—The point about which all of the cyclic volumetric changes of a structure take place.
Open Joint—A joint designed to permit the passage of water and debris through the joint.
Plain Elastomeric Pad (PEP)—A pad made exclusively of elastomer, which provides limited translation and rotation.
Polytetrafluorethylene (PTFE)—Also known as Teflon.
Pot Bearing—A bearing that carries vertical load by compression of an elastomeric disc confined in a steel cylinder and
that accommodates rotation by deformation of the disc.
Poured Seal—A seal made from a material that remains flexible (asphaltic, polymeric, or other), which is poured into the
gap of a joint and is expected to adhere to the sides of the gap. Typically used only when expected total range of movement
is less than 1.5 in.
PTFE Sliding Bearing—A bearing that carries vertical load through contact stresses between a PTFE sheet or woven fabric
and its mating surface, and that permits movements by sliding of the PTFE over the mating surface.
Relief Joint—A deck joint, usually transverse, that is designed to minimize either unintended composite action or the effect
of differential horizontal movement between a deck and its supporting structural system.
Restrainers—A system of high-strength cables or rods that transfers forces between superstructure elements and/or
superstructure and substructure elements under seismic or other dynamic loads after an initial slack is taken up, while
permitting thermal movements.
Root Mean Square—RMS
Rotation about the Longitudinal Axis—Rotation about an axis parallel to the main span direction of the bridge.
Rotation about the Transverse Axis—Rotation about an axis parallel to the transverse axis of the bridge.
Sealed Joint—A joint provided with a joint seal.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 14: JOINTS AND BEARINGS
14-3
Shock Transmission Unit (STU)—A device that provides a temporary rigid link between superstructure elements and/or
superstructure and substructure elements under seismic, braking, or other dynamic loads, while permitting thermal
movements.
Single-Support-Bar System (SSB)—A MBJS designed so that only one support bar is connected to all of the centerbeams.
The centerbeam/support bar connection typically consists of a yoke through which the support bar slides.
Sliding Bearing—A bearing that accommodates movement by translation of one surface relative to another.
Steel-Reinforced Elastomeric Bearing—A bearing made from alternate laminates of steel and elastomer bonded together
during vulcanization. Vertical loads are carried by compression of the elastomer. Movements parallel to the reinforcing
layers and rotations are accommodated by deformation of the elastomer.
Strip Seal—A sealed joint with an extruded elastomeric seal retained by edgebeams that are anchored to the structural
elements (deck, abutment, etc). Typically used for expected total movement ranges from 1.5 to 4.0 in., although single
seals capable of spanning a 5.0 in. gap are also available.
Translation—Horizontal movement of the bridge in the longitudinal or transverse direction.
Transverse—The horizontal direction normal to the longitudinal axis of the bridge.
Waterproofed Joints—Open or closed joints that have been provided with some form of trough below the joint to contain
and conduct deck discharge away from the structure.
Welded Multiple-Support-Bar System (WMSB)—A MBJS designed so that each support bar is welded to only one
centerbeam. Although some larger WMSB systems have been built and are performing well, WMSB systems are typically
impractical for more than nine seals or for movement ranges larger than 27.0 in.
14.3—NOTATION
A
AWbot
AWmid
AWtop
acr
Ba
Cα
c
=
=
=
=
=
=
=
=
D
=
Da
Dd
DP
Dr
D1
D2
=
=
=
=
=
=
d
da1
da2
da3
dcb
dsb
Ec
=
=
=
=
=
=
=
Es
=
plan area of elastomeric element or bearing (in.2) (14.6.3.1)
area of weld at the bottom (in.2) (14.5.6.9.7b)
minimum cross-sectional area of weld (in.2) (14.5.6.9.7b)
area of weld at the top (in.2) (14.5.6.9.7b)
creep deflection divided by initial dead load deflection (14.7.5.3.6)
dimensionless coefficient used to determine peak hydrostatic stress (14.7.5.3.3)
parameter used to determine hydrostatic stress (14.7.5.3.3)
minimum vertical clearance between rotating and nonrotating parts (in.); design clearance between piston
and pot (in.) (C14.7.3.1) (14.7.4.7)
diameter of the projection of the loaded surface of the bearing in the horizontal plane (in.); diameter of pad (in.);
diameter of the bearing (in.) (14.7.3.2) (14.7.5.1) (14.7.6.3.6) (14.7.5.3.3) (14.7.5.3.4)
dimensionless coefficient used to determine shear strain due to axial load (14.7.5.3.3)
diameter of the disc element (in.) (14.7.8.1) (14.7.8.5)
internal diameter of pot (in.) (14.7.4.3) (14.7.4.6) (14.7.4.7)
dimensionless coefficient used to determine shear strain due to rotation (14.7.5.3.3)
diameter of the rocker or roller surface (in.) (14.7.1.4)
diameter of the mating surface, positive if the curvatures have the same sign, infinite if the mating surface is
flat (in.) (14.7.1.4)
diameter of rocker or roller (in.); the diameter of the hole or holes in the bearing (in.) (C14.7.1.4) (C14.7.5.1)
dimensionless coefficient used to determine shear strain due to axial load (C14.7.5.3.3)
dimensionless coefficient used to determine shear strain due to axial load (C14.7.5.3.3)
dimensionless coefficient used to determine shear strain due to axial load (C14.7.5.3.3)
depth of the centerbeam (in.) (14.5.6.9.7b)
depth of the support bar (in.) (14.5.6.9.7b)
effective modulus of elastomeric bearing in compression (ksi); uniaxial compressive stiffness of the CDP
bearing pad. It may be taken as 30 ksi in lieu of pad specific test data (ksi) (14.6.3.2) (14.7.6.3.3) (14.7.6.3.5b)
Young’s modulus for steel (ksi) (14.7.1.4)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 14: JOINTS AND BEARINGS
Fy
=
G
=
Hbu
=
Hs
Hu
hp1
hp2
hr
hri
=
=
=
=
=
=
hrt
=
hs
hw
I
K
L
=
=
=
=
=
MH
=
MOT
MV
=
=
Mu
=
m
n
PD
PS
Pu
p
R
RH
Ro
RV
S
=
=
=
=
=
=
=
=
=
=
=
Si
=
SRB
=
SRZ
=
SWbot
=
14-4
specified minimum yield strength of the weakest steel at the contact surface (ksi); yield strength of steel
(ksi); yield strength of steel reinforcement (ksi) (14.7.1.4) (14.7.4.6) (14.7.4.7) (14.7.5.3.5)
shear modulus of the elastomer (ksi); shear modulus of the CDP (14.6.3.1) (C14.6.3.2) (14.7.5.2) (14.7.5.3.3)
(14.7.5.3.4) (C14.7.5.3.6) (14.7.6.2) (14.7.6.3.2) (14.7.6.3.4)
lateral load transmitted to the superstructure and substructure by bearings from applicable strength and
extreme event load combinations in Table 3.4.1-1 (kip) (14.6.3.1)
horizontal load from applicable service load combinations in Table 3.4.1-1 (kip) (14.7.3.3)
lateral load from applicable strength and extreme event load combinations in Table 3.4.1-1 (kip) (14.7.4.7)
pot cavity depth (in.) (C14.7.4.3)
vertical clearance between top of piston and top of pot wall (in.) (C14.7.4.3)
depth of elastomeric disc (in.) (14.7.4.3)
thickness of ith elastomeric layer (in.); thickness of ith internal elastomeric layer (in.); layer thickness for FGP
which equals the greatest distance between midpoints of two double fiberglass reinforcement layers (in.);
thickness of a PEP (in.); mean thickness of two layers of elastomer bonded to the same reinforcement for FGP
when the two layers are of different thicknesses (in.) (14.7.5.1) (14.7.5.3.6) (14.7.5.3.3) (14.7.5.3.5) (14.7.6.3.3)
(14.7.6.3.7) (14.7.6.3.2)
total elastomer thickness (in.); smaller of total elastomer or bearing thickness (in.) (14.6.3.1) (14.6.3.2)
(14.7.5.3.2) (14.7.5.3.3) (14.7.5.3.4) (14.7.6.3.4)
thickness of steel reinforcement (in.) (14.7.5.3.5)
height of the weld (in.); height from top of rim to underside of piston (in.) (14.5.6.9.7b) (C14.7.4.3) (14.7.4.7)
moment of inertia of plan shape of bearing (in.4) (14.6.3.2)
rotational stiffness of CDP (kip-in./rad.); bulk modulus (ksi) (C14.6.3.2) (C14.7.5.3.3)
projected length of the sliding surface perpendicular to the rotation axis (in.); plan dimension of the bearing
perpendicular to the axis of rotation under consideration (generally parallel to the global longitudinal bridge
axis) (in.); length of a CDP bearing pad in the plane of rotation (in.) (14.7.3.3) (14.7.5.1) (14.7.5.3.3)
(14.7.5.3.4) (14.7.6.3.5b) (14.7.6.3.6)
horizontal bending moment range in the centerbeam on the critical section located at the weld toe due to
horizontal force range (kip-in.) (14.5.6.9.7b)
overturning moment range from horizontal reaction force (kip-in.) (14.5.6.9.7b)
vertical bending moment range in the centerbeam on the critical section located at the weld toe due to the
vertical force range (kip-in.); component of vertical bending moment range in the support bar due to the vertical
reaction force range in the connection located on the critical section at the weld toe (kip-in.) (14.5.6.9.7b)
moment transmitted to the superstructure and substructure by bearings from applicable strength and extreme
event load combinations in Table 3.4.1-1 (kip-in.) (14.6.3.2)
modification factor (14.8.3.1) (5.7.5)
number of interior layers of elastomer (14.7.5.3.3) (14.7.5.4) (14.7.6.1)
compressive load at the service limit state (load factor = 1.0) due to permanent loads (kip) (14.7.3.3)
total compressive load from applicable service load combinations in Table 3.4.1-1 (kip) (14.7.1.4) (14.7.3.2)
compressive force from applicable strength and extreme event load combinations in Table 3.4.1-1 (kip) (14.6.3.1)
allowable bearing at the service limit state (kip/in.) (C14.7.1.4)
radius of curved sliding surface (in.) (14.6.3.2) (14.7.3.3)
horizontal reaction force range in the connection (kip) (14.5.6.9.7b)
radial distance from center of pot to object in question (e.g., pot wall, anchor bolt, etc.) (in.) (C14.7.4.3)
vertical reaction force range in the connection (kip) (14.5.6.9.7b)
shape factor of the CDP pad computed based on Eq. 14.7.5.1-1 and based on total pad thickness; shape factor
of an individual elastomer layer; shape factor of PEP (14.6.3.2) (C14.7.5.3.6) (14.7.6.3.2)
shape factor of the ith layer of an elastomeric bearing; shape factor of the ith internal layer of an elastomeric
bearing; shape factor for FGP based upon an hri layer thickness which equals the greatest distance between
midpoints of two double fiberglass reinforcement layers (14.7.5.1) (14.7.5.3.3) (14.7.5.3.4) (14.7.5.4)
(14.7.6.1) (14.7.6.3.2)
combined bending stress range in the centerbeam (ksi); bending stress range in the support bar due to maximum
moment including moment from vertical reaction and overturning at the connection (ksi) (14.5.6.9.7b)
vertical stress range in the top of the centerbeam-to-support-bar weld from the concurrent reaction of the
support beam (ksi); vertical stress range in the bottom of the centerbeam-to-support-bar weld from the
vertical and horizontal reaction force ranges in the connection (ksi) (14.5.6.9.7b)
section modulus of the weld at the bottom for bending in the direction of the support bar axis (in.3)
(14.5.6.9.7b)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 14: JOINTS AND BEARINGS
SWmid
=
SWtop
=
SXcb
SXsb
SYcb
tb
tp
tw
W
=
=
=
=
=
=
=
w
α
γa
γa,cy
γa,st
γr
γr,cy
γr,st
γs
γs,cy
γs,st
β
ΔFTH
=
=
=
=
=
=
=
=
=
=
=
=
=
Δf
=
ΔO
ΔS
=
=
ΔT
Δu
δd
δL
δlt
δu
ε
εa
=
=
=
=
=
=
=
=
εc
=
εdi
εLi
εs
=
=
=
εt
=
θL
=
14-5
section modulus of the weld at the most narrow cross-section for bending in the direction normal to the
centerbeam axis (in.3) (14.5.6.9.7b)
section modulus of the weld at the top for bending in the direction normal to the centerbeam axis (in.3)
(14.5.6.9.7b)
vertical section modulus to the bottom of the centerbeam (in.3) (14.5.6.9.7b)
vertical section modulus of the support bar to the top of the support bar (in.3) (14.5.6.9.7b)
horizontal section modulus of the centerbeam (in.3) (14.5.6.9.7b)
pot base thickness (in.) (14.7.4.6) (14.7.4.7)
total thickness of CDP pad (in.) (14.6.3.2) (14.7.6.3.5b)
pot wall thickness (in.) (14.7.4.6) (14.7.4.7)
roadway surface gap in a transverse deck joint, measured in the direction of travel at the extreme movement
determined using the appropriate strength load combination specified in Table 3.4.1-1 (in.); width of the
bearing (in.); length of cylinder (in.); length of cylindrical surface (in.); plan dimension of the bearing
parallel to the axis of rotation under consideration (generally parallel to the global transverse bridge axis)
(in.) (14.5.3.2) (14.7.1.4) (14.7.3.2) (14.7.3.3) (14.7.5.1) (C14.7.5.3.3) (14.7.5.3.4) (14.7.6.3.6)
height of piston rim (in.) (14.7.4.7)
parameter used to determine hydrostatic stress (1/rad.) (14.7.5.3.3)
shear strain caused by axial load (14.7.5.3.3)
shear strain caused by cyclic axial load (14.7.5.3.3)
shear strain caused by static axial load (14.7.5.3.3)
shear strain caused by rotation (14.7.5.3.3)
shear strain caused by rotation from cyclic loads (14.7.5.3.3)
shear strain caused by rotation from static loads (14.7.5.3.3)
shear strain caused by shear displacement (14.7.5.3.3)
shear strain caused by shear displacement from cyclic loads (14.7.5.3.3)
shear strain caused by shear displacement from static loads (14.7.5.3.3)
angle between the vertical and resultant applied load (rad.) (14.7.3.3)
constant amplitude fatigue threshold taken from Table 6.6.1.2.5-3 for the detail category of interest (ksi);
constant amplitude fatigue threshold for Category A as specified in Article 6.6 (14.5.6.9.7a) (14.7.5.3.5)
force effect, design live load stress range due to the simultaneous application of vertical and horizontal axle
loads specified in Article 14.5.6.9.4 and distributed as specified in Article 14.5.6.9.5, and calculated as
specified in Article 14.5.6.9.7b (ksi) (14.5.6.9.7a) (14.5.6.9.7b)
maximum horizontal displacement of the bridge superstructure at the service limit state (in.) (14.7.5.3.2)
maximum total shear deformation of the elastomer from applicable service load combinations in
Table 3.4.1-1 (in.); maximum total shear deformation of the bearing from applicable service load
combinations in Table 3.4.1-1 (in.); maximum total static or cyclic shear deformation of the elastomer from
applicable service load combinations in Table 3.4.1-1 (in.) (14.7.5.3.2) (14.7.6.3.4) (14.7.5.3.3)
design thermal movement range computed in accordance with Article 3.12.2 (in.) (14.7.5.3.2)
shear deformation from applicable strength and extreme event load combinations in Table 3.4.1-1 (in.) (14.6.3.1)
initial dead load compressive deflection (in.) (14.7.5.3.6)
instantaneous live load compressive deflection (in.) (14.7.5.3.6)
long term dead load compressive deflection (in.) (14.7.5.3.6)
vertical deflection from applicable strength load combinations in Table 3.4.1-1 (in.) (C14.7.4.3)
compressive strain in an elastomer layer (C14.7.5.3.6)
total of static and cyclic average axial strain taken as positive for compression in which the cyclic component
is multiplied by 1.75 from applicable service load combinations in Table 3.4.1-1 (ksi) (14.7.5.3.3) (14.7.5.4)
maximum uniaxial strain due to compression under total load from applicable service load
combinations in Table 3.4.1-1 (14.7.6.3.5b)
initial dead load compressive strain in ith elastomer layer (14.7.5.3.6)
instantaneous live load compressive strain in ith elastomer layer (14.7.5.3.6)
average compressive strain due to total load from applicable service load combinations in Table 3.4.1-1
(14.7.6.3.3)
maximum uniaxial strain due to combined compression and rotation from applicable service load
combinations in Table 3.4.1-1 (14.7.6.3.5b)
maximum rotation of the CDP pad at the service limit state (load factor = 1.0) due to live load (rad.)
(14.7.6.3.5b)
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
14-6
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
θs
=
θu
=
λ
μ
σ
=
=
=
σhyd
σL
=
=
σs
=
σSS
=
φ
φtension
φshear
φA tension
=
=
=
=
φA shear
=
φB tension =
φB shear
=
Ψ
=
maximum service limit state rotation due to total load for bearings unlikely to experience hard contact
between metal components (rad.); maximum service limit state design rotation angle specified in
Article 14.4.2.1 (rad.); maximum rotation of the CDP pad from applicable service load combinations in
Table 3.4.1-1 (rad.); maximum service limit state design rotation angle about any axis of the pad specified in
Article 14.4.2.1 (rad.); maximum static or cyclic service limit state design rotation angle of the elastomer
specified in Article 14.4.2.1 (rad.); total of static and cyclic maximum service limit state design rotation
angles of the elastomer specified in Article 14.4.2.1 in which the cyclic component is multiplied by 1.75
(rad.) (C14.4.2) (14.4.2.1) (14.6.3.2) (14.7.6.3.5b) (14.7.5.3.3) (14.7.5.4)
maximum strength limit state rotation for bearings that may experience hard contact between metal
components (rad.); maximum strength limit state rotation for bearings which are less likely to experience
hard contact between metal components (rad.); design rotation from applicable strength load combinations in
Table 3.4.1-1 or Article 14.4.2.2.1 (rad.); maximum strength limit state design rotation angle specified in
Article 14.4.2.2.1 (rad.); maximum strength limit state design rotation angle specified in Article 14.4.2.2.2
(rad.) (C14.4.2) (14.4.2.2.1) (14.4.2.2.2) (C14.7.3.1) (14.7.3.3) (14.7.4.3) (14.7.4.7) (14.7.8.1)
compressibility index (C14.7.5.3.3)
coefficient of friction; coefficient of friction of the PTFE slider (14.6.3.1) (C14.7.8.4)
instantaneous live load compressive stress or dead load compressive stress in an individual elastomer layer
(ksi) (C14.7.5.3.6)
peak hydrostatic stress (ksi) (14.7.5.3.3)
average compressive stress at the service limit state (load factor = 1.0) due to live load (ksi) (14.7.5.3.5)
(14.7.6.3.2)
average compressive stress due to total load from applicable service load combinations in Table 3.4.1-1 (ksi);
average compressive stress due to total load associated with the maximum rotation from applicable service
load combinations in Table 3.4.1-1 (ksi) ; average compressive stress due to total static or cyclic load from
applicable service load combinations in Table 3.4.1-1 (ksi); total of static and cyclic average compressive
stress in which the cyclic component is multiplied by 1.75 from applicable service load combinations in
Table 3.4.1-1 (ksi) (14.7.4.6) (14.7.5.3.4) (14.7.5.3.5) (14.7.6.3.2) (14.7.6.3.3) (14.7.6.3.4) (14.6.3.2)
(14.7.6.3.5b) (14.7.5.3.3)
maximum average contact stress at the service limit state permitted on PTFE by Table 14.7.2.4-1 or on
bronze by Table 14.7.7.3-1 (ksi) (14.7.3.2) (14.7.3.3)
resistance factor (14.6.1) (14.7.3.2) (C14.7.4.7)
resistance factor for tension for anchors governed by the steel (14.5.6.9.6)
resistance factor for shear for anchors governed by the steel (14.5.6.9.6)
resistance factor for tension for anchors governed by the concrete, Condition A, supplemental reinforcement
in the failure area (14.5.6.9.6)
resistance factor for shear for anchors governed by the concrete, Condition A, supplemental reinforcement in
the failure area (14.5.6.9.6)
resistance factor for tension for anchors governed by the concrete, Condition B, no supplemental
reinforcement in the failure area (14.5.6.9.6)
resistance factor for shear for anchors governed by the concrete, Condition B, no supplemental reinforcement
in the failure area (14.5.6.9.6)
subtended semiangle of the curved surface (rad.) (14.7.3.3)
14.4—MOVEMENTS AND LOADS
14.4.1—General
C14.4.1
The selection and layout of the joints and bearings
shall allow for deformations due to temperature and other
time-dependent causes and shall be consistent with the
proper functioning of the bridge.
Deck joints and bearings shall be designed to resist
loads and accommodate movements at the service and
strength limit states and to satisfy the requirements of the
fatigue and fracture limit state. The loads induced on the
joints, bearings, and structural members depend on the
stiffness of the individual elements and the tolerances
achieved during fabrication and erection. These influences
The joints and bearings should allow movements due
to temperature changes, creep and shrinkage, elastic
shortening due to prestressing, traffic loading, construction
tolerances or other effects. If these movements are
restrained, large horizontal forces may result. If the bridge
deck is cast-in-place or precast concrete, the bearings at a
single support should permit transverse expansion and
contraction. Externally applied transverse loads such as
wind, earthquake, or traffic braking forces may be carried
either on a small number of bearings near the centerline of
the bridge or by an independent guide system. The latter is
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 14: JOINTS AND BEARINGS
shall be taken into account when calculating design loads
for the elements. No damage due to joint or bearing
movement shall be permitted at the service limit state, and
no irreparable damage shall occur at the strength limit
state. At the extreme event limit state, bearings which are
designed to act as fuses or sustain irreparable damage may
be permitted by the Owner provided loss of span is
prevented.
Translational and rotational movements of the bridge
shall be considered in the design of MBJS and bearings.
The sequence of construction shall be considered, and all
critical combinations of load and movement shall be
considered in the design. Rotations about two horizontal
axes and the vertical axis shall be considered. The
movements shall include those caused by the loads,
deformations, and displacements caused by creep,
shrinkage and thermal effects, and inaccuracies in
installation. In all cases, both instantaneous and long-term
effects shall be considered. The influence of dynamic load
allowance shall be included for MBJS, but need not be
included for bearings. The most adverse combination shall
be tabulated for the bearings in a rational form such as
shown in Figure C14.4.1-1.
For determining force effects in joints, bearings, and
adjacent structural elements, the influence of their
stiffnesses and the expected tolerances achieved during
fabrication and erection shall be considered.
The three-dimensional effects of translational and
rotational movements of the bridge shall be considered in
the design of MBJS and bearings.
Both instantaneous and long-term effects shall be
considered in the design of joints and bearings.
The effects of curvature, skew, rotations, and support
restraint shall be recognized in the analysis.
The forces resulting from transverse or longitudinal
prestressing of the concrete deck or steel girders shall be
considered in the design of the bearings.
14-7
likely to be needed if the horizontal forces are large and
fusing or irreparable damage is not permitted.
See Article C14.6.5.3 for discussion concerning
bearings which are designed to act as fuses at the extreme
event limit state.
Distribution of vertical load among bearings may
adversely affect individual bearings. This is particularly
critical when the girders are stiff in bending and torsion and
bearings are stiff in compression, and the construction
method does not allow minor misalignments to be corrected.
Bridge movements arise from a number of different
causes. Simplified estimates of bridge movements,
particularly on bridges with complex geometry, may lead
to improper estimation of the direction of motion and, as a
result, an improper selection of the bearing or joint system.
Curved and skewed bridges have transverse as well as
longitudinal movement due to temperature effects and
creep or shrinkage. Transverse movement of the
superstructure relative to the substructure may become
significant for very wide bridges. Relatively wide curved
and skewed bridges often undergo significant diagonal
thermal movement, which introduces large transverse
movements or large transverse forces if the bridge is
restrained against such movements. Rotations caused by
permissible levels of misalignment during installation
should also be considered, and in many cases they will be
larger than the live load rotations.
The neutral axis of a girder that acts compositely with
its bridge deck is typically close to the underside of the
deck. As a result, the neutral axis of the beam and the
center of rotation of the bearing seldom coincide. Under
these conditions, end rotation of the girder induces either
horizontal movements or forces at the bottom flange or
bearing level. The location of bearings off the neutral axes
of the girders can also create horizontal forces due to
elastic shortening of the girders when subjected to vertical
loads at continuous supports.
The failure of bridge bearings or joint seals may
ultimately lead to deterioration or damage to the bridge.
Each bearing and MBJS should be clearly identified in
design documents, and all requirements should be
identified. One possible format for this information is
shown in Figure C14.4.1-1 for limit states other than
extreme event.
When integral piers or abutments are used, the
substructure and superstructure are connected such that
additional restraints against superstructure rotation are
introduced.
In curved bridges, thermal stresses are minimized
when bearings are oriented such that they permit free
translation along rays from a single point. With bearings
arranged to permit such movement along these rays, there
will be no thermal forces generated when the
superstructure temperature changes uniformly. Any other
orientation of the bearings will induce thermal forces into
the superstructure and substructure. However, other
considerations often make impractical the orientation along
rays from a single point.
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2012
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14-8
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Prestressing of the deck causes changes in the vertical
reactions due to the eccentricity of the forces, which
creates restoring forces. Effects of creep and shrinkage
also should be considered.
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2012
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SECTION 14: JOINTS AND BEARINGS
14-9
Bridge name or ref.
Bearing identification mark
Number of bearings required
Seating material
Upper surface
Lower surface
Permitted average
Service limit state
Upper face
contact pressure
(psi)
Design load
Lower face
Service limit state
Vertical
effects (kip)
max.
perm.
min.
Transverse
Longitudinal
Strength limit state
Vertical
Transverse
Longitudinal
Translation
Service
Irreversible
limit
state
Transverse
Longitudinal
Reversible
Transverse
Longitudinal
Strength
Irreversible
limit
state
Transverse
Longitudinal
Reversible
Transverse
Longitudinal
(continued on next page)
Figure C14.4.1-1—Typical Bridge Bearing Schedule
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14-10
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Rotation (rad.)
Service
Irreversible
Transverse
limit
state
Longitudinal
Reversible
Transverse
Longitudinal
Strength
Irreversible
Transverse
limit
state
Longitudinal
Reversible
Transverse
Longitudinal
Maximum
Upper surface
Transverse
bearing
Longitudinal
dimensions (in.)
Lower surface
Transverse
Longitudinal
Overall height
Tolerable movement of bearing
Vertical
under transient loads (in.)
Transverse
Longitudinal
Permitted resistance to translation
Transverse
under strength or service limit state as applicable (kip)
Longitudinal
Permitted resistance to rotation
Transverse
under strength or service limit state as applicable (kip/ft)
Longitudinal
Type of attachment to structure and substructure
Transverse
Longitudinal
Figure C14.4.1-1 (continued)—Typical Bridge Bearing Schedule
14.4.2—Design Requirements
C14.4.2
The minimum thermal movements shall be computed
from the extreme temperature specified in Article 3.12.2
and the estimated setting temperatures. Design loads shall
be based on the load combinations and load factors
specified in Section 3.
Rotations are considered at the service and strength
limit states as appropriate for different types of bearings.
Bearings must accommodate movements in addition to
supporting loads, so displacements, and in particular
rotations, are needed for design. Live load rotations are
typically less than 0.005 rad., but the total rotation due to
fabrication and setting tolerances for seats, bearings, and
girders may be significantly larger than this. Therefore, the
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2012
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SECTION 14: JOINTS AND BEARINGS
14-11
total design rotation is found by summing rotations due to
dead and live load and adding allowances for profile grade
effects and the tolerances described above. Article 14.8.2
specifies when a tapered plate shall be used if the rotation
due to permanent load at the service limit state (load factor =
1.0) becomes excessive. An Owner may reduce the
fabrication and setting tolerance allowances if justified by a
suitable quality control plan; therefore, these tolerance limits
are stated as recommendations rather than absolute limits.
Failure of deformable components such as elastomeric
bearings is generally governed by a gradual deterioration
under many cycles of load rather than sudden failure under
a single load application. Further, the design limits for
elastomeric bearings were originally developed under ASD
service load conditions rather than the strength limit state
loads considered during development of the high load
multirotational bearing systems. Unless smaller tolerances
can be justified, θs for elastomeric components is the
service limit state rotation plus 0.005 rad.
Metal or concrete components are susceptible to
damage under a single rotation that causes metal-to-metal
contact, and so they must be designed using the strength
limit state rotations. Unless smaller tolerances can be
justified, θu is the strength limit state rotation plus
0.01 rad.
Disc bearings are less likely to experience metal-tometal contact than other High Load Multirotational
(HLMR) bearings because the load element is unconfined.
As a result, the total allowance for rotation is consequently
smaller for a disc bearing than other HLMR bearings;
however, the proof load test, as specified in the AASHTO
LRFD Bridge Construction Specifications, assures against
metal-to-metal contact.
14.4.2.1—Elastomeric Pads and Steel Reinforced
Elastomeric Bearings
The maximum service limit state rotation due to total
load, θs, for bearings unlikely to experience hard contact
between metal components shall be taken as the sum of:
•
The rotations from applicable
combinations in Table 3.4.1-1, and
•
An allowance for uncertainties, which shall be taken
as 0.005 rad. unless an approved quality control plan
justifies a smaller value.
service
load
The static and cyclic components of θs shall be
considered separately when design is according to
Article 14.7.5.3.3.
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14-12
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
14.4.2.2—High Load Multirotational (HLMR)
Bearings
14.4.2.2.1—Pot Bearings and Curved Sliding
Surface Bearings
The maximum strength limit state rotation, θu, for
bearings such as pot bearings and curved sliding surfaces
that may potentially experience hard contact between
metal components shall be taken as the sum of:
•
The rotations from applicable
combinations in Table 3.4.1-1;
•
The maximum rotation caused by fabrication and
installation tolerances, which shall be taken as 0.005
rad. unless an approved quality control plan justifies a
smaller value; and
•
An allowance for uncertainties, which shall be taken
as 0.005 rad. unless an approved quality control plan
justifies a smaller value.
strength
load
14.4.2.2.2—Disc Bearings
The maximum strength limit state rotation, θu, for disc
bearings which are less likely to experience hard contact
between metal components due to their unconfined load
element, shall be taken as the sum of:
•
The rotations from applicable
combinations in Table 3.4.1-1, and
•
An allowance for uncertainties, which shall be taken
as 0.005 rad. unless an approved quality control plan
justifies a smaller value.
strength
load
14.5—BRIDGE JOINTS
14.5.1—Requirements
14.5.1.1—General
C14.5.1.1
Deck joints shall consist of components arranged to
accommodate the translation and rotation of the structure
at the joint.
The type of joints and surface gaps shall accommodate
the movement of motorcycles, bicycles, and pedestrians, as
required, and shall neither significantly impair the riding
characteristics of the roadway nor cause damage to
vehicles.
The joints shall be detailed to prevent damage to the
structure from water, deicing chemicals, and roadway
debris.
Longitudinal deck joints shall be provided only where
necessary to modify the effects of differential lateral
and/or vertical movement between the superstructure and
substructure.
Joints and joint anchors for grid and timber decks and
orthotropic deck superstructures require special details.
To accommodate differential lateral movement,
elastomeric bearings or combination bearings with the
capacity for lateral movement should be used instead of
longitudinal joints where practical.
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SECTION 14: JOINTS AND BEARINGS
14-13
C14.5.1.2
14.5.1.2—Structural Design
Joints and their supports shall be designed to
withstand force effects for the appropriate design limit
state or states over the range of movements for the
appropriate design limit state or states, as specified in
Section 3. Resistance factors and modifiers shall be taken
as specified in Sections 1, 5, 6, 7, and 8, as appropriate.
In snow regions, joint armor, armor connections, and
anchors shall be designed to resist force effects that may
be imposed on the joints by snagging snowplow blades.
The edgebeams and anchorages of strip seals and MBJS
with a skew exceeding 20 degrees in snow regions that do
not incorporate protection methods such as those discussed
in Article 14.5.3.3 shall be designed for the strength limit
state with a minimum snowplow load acting as a
horizontal line load on the top surface of the edgebeam in a
direction perpendicular to the edgebeam of 0.12 kips/in.
for a total length of 10.0 ft anywhere along the edgebeam
in either direction. This load includes dynamic load
allowance.
The following factors shall be considered in
determining force effects and movements:
•
Properties of materials in the structure, including
coefficient of thermal expansion, modulus of
elasticity, and Poisson’s ratio;
•
Effects of temperature, creep, and shrinkage;
•
Sizes of structural components;
•
Construction tolerances;
•
Method and sequence of construction;
•
Skew and curvature;
•
Resistance of the joints to movements;
•
Approach pavement growth;
•
Substructure movements
construction;
•
Foundation movements associated with
consolidation and stabilization of subsoils;
•
Structural restraints; and
•
Static and dynamic structural responses and their
interaction.
due
to
embankment
the
The strength limit state for the edgebeams of strip
seals and MBJS and anchorage to the concrete or other
elements should be checked with this snowplow load if the
skew of the joint exceeds 20 degrees relative to a line
transverse to the traveling direction. For smaller skews, the
blades, which are skewed, will not strike an edgebeam all
at once. Protection methods such as those discussed in
Article 14.5.3.3 may eliminate the need to design for this
snowplow load.
Snowplow blade angles vary regionally. Unless
protection methods such as those discussed in
Article 14.5.3.3 are used, agencies should avoid MBJS
installations with skew that is within three degrees of the
plow angle used in that region, to avoid having the plow
drop into the gap between centerbeams.
The snowplow load was estimated from snowplow
manufacturer information as the force required to deflect a
spring-activated blade with 2.0 in. of compression and
ten degrees of deflection. The snowplow load includes the
effect of impact so the dynamic load allowance should not
be applied. The snowplow load should be multiplied by the
appropriate strength limit state load factor for live load.
Superstructure movements include those due to
placement of bridge decks, volumetric changes, such as
shrinkage, temperature, moisture and creep, passage of
vehicular and pedestrian traffic, pressure of wind, and the
action of earthquakes. Substructure movements include
differential settlement of piers and abutments, tilting,
flexure, and horizontal translation of wall-type abutments
responding to the placement of backfill as well as shifting
of stub abutments due to the consolidation of
embankments and in-situ soils.
Any horizontal movement of a bridge superstructure
will be opposed by the resistance of bridge bearings to
movement and the rigidity or flexural resistance of
substructure elements. The rolling resistance of rocker and
rollers, the shear resistance of elastomeric bearings, or the
frictional resistance of bearing sliding surfaces will oppose
movement. In addition, the rigidity of abutments and the
relative flexibility of piers of various heights and
foundation types will affect the magnitude of bearing
movement and the bearing forces opposing movement.
Rigid approach pavements composed of cobblestone,
brick, or jointed concrete will experience growth or
substantial longitudinal pressure due to restrained growth.
To protect bridge structures from these potentially
destructive pressures and to preserve the movement range
of deck joints and the performance of joint seals, either
effective pavement pressure relief joints or pavement
anchors should be provided in approach pavements, as
described in Transportation Research Record 1113.
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14-14
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The length of superstructure affecting the movement
at one of its joints shall be the length from the joint being
considered to the structure’s neutral point.
For a curved superstructure that is laterally
unrestrained by guided bearings, the direction of
longitudinal movement at a bearing joint may be assumed
to be parallel to the chord of the deck centerline taken from
the joint to the neutral point of the structure.
The potential for unaligned longitudinal and rotational
movement of the superstructure at a joint should be
considered in designing the vertical joints in curbs and
raised barriers and in determining the appropriate position
and orientation of closure or bridging plates.
14.5.1.3—Geometry
The moving surfaces of the joint shall be designed to
work in concert with the bearings to avoid binding the
joints and adversely affecting force effects imposed on
bearings.
14.5.1.4—Materials
When horizontal movement at the ends of a
superstructure is due to volumetric changes, the forces
generated within the structure in resistance to these
changes are balanced. The neutral point can be located by
estimating these forces, taking into account the relative
resistance of bearings and substructures to movement. The
length of superstructure contributing to movement at a
particular joint can then be determined.
C14.5.1.3
For square or slightly skewed bridge layouts,
moderate roadway grades at the joint and minimum
changes in both horizontal and vertical joint alignment
may be preferred in order to simplify the movements of
joints and to enhance the performance of the structure.
C14.5.1.4
The materials shall be selected so as to ensure that
they are elastically, thermally, and chemically compatible.
Where substantial differences exist, material interfaces
shall be formulated to provide fully functional systems.
Materials, other than elastomers, should have a service
life of not less than 75 yr. Elastomers for joint seals and
troughs should provide a service life not less than 25 yr.
Joints exposed to traffic should have a skid-resistant
surface treatment, and all parts shall be resistant to attrition
and vehicular impact.
Except for high-strength bolts, fasteners for joints
exposed to deicing chemicals shall be made of stainless
steel.
14.5.1.5—Maintenance
Deck joints shall be designed to operate with a
minimum of maintenance for the design life of the bridge.
Detailing should permit access to the joints from
below the deck and provide sufficient area for
maintenance.
Mechanical and elastomeric components of the joint
shall be replaceable.
Joints shall be designed to facilitate vertical extension
to accommodate roadway overlays.
Preference should be given to those materials that are
least sensitive to field compounding and installation
variables and to those that can be repaired and altered by
nonspecialized maintenance forces. Preference should also
be given to those components and devices that will likely
be available when replacements are needed.
C14.5.1.5
The position of bearings, structural components, joints
and abutment backwalls, and the configuration of pier tops
should be chosen so as to provide sufficient space and
convenient access to joints from below the deck.
Inspection hatches, ladders, platforms, and/or catwalks
shall be provided for the deck joints of large bridges not
directly accessible from the ground.
14.5.2—Selection
14.5.2.1—Number of Joints
The number of movable deck joints in a structure
should be minimized. Preference shall be given to
continuous deck systems and superstructures and, where
appropriate, integral bridges.
C14.5.2.1
Integral bridges, bridges without movable deck joints,
should be considered where the length of superstructure
and flexibility of substructures are such that secondary
stresses due to restrained movement are controlled within
tolerable limits.
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2012
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SECTION 14: JOINTS AND BEARINGS
The need for a fully functional cycle-control joint
shall be investigated on approaches of integral bridges.
Movable joints may be provided at abutments of
single-span structures exposed to appreciable differential
settlement. Intermediate deck joints should be considered
for multiple-span bridges where differential settlement
would result in significant overstresses.
14-15
Where a floorbeam design that can tolerate differential
longitudinal movements resulting from relative
temperature and live load response of the deck and
independent supporting members, such as girders and
trusses, is not practical, relief joints in the deck slab,
movable joints in the stringers, and movable bearings
between the stringers and floorbeams should be used.
Long-span deck-type structures with steel stringers
that are slightly skewed, continuous, and composite can
withstand substantial differential settlement without
significant secondary stresses. Consequently, intermediate
deck joints are rarely necessary for multiple-span bridges
supported by secure foundations, i.e., piles, bedrock, dense
subsoils, etc. Because the stresses induced by settlement
can alter the point of inflection, a more conservative
control of fatigue-prone detail locations is appropriate.
Guidance on the movements of the substructure can be
found in Articles 10.5.2, 10.6.2, 10.7.2, and 10.8.2.
14.5.2.2—Location of Joints
Deck joints should be avoided over roadways,
railroads, sidewalks, other public areas, and at the low
point of sag vertical curves.
Deck joints should be positioned with respect to
abutment backwalls and wingwalls to prevent the
discharge of deck drainage that accumulates in the joint
recesses onto bridge seats.
Open deck joints should be located only where
drainage can be directed to bypass the bearings and
discharged directly below the joint.
Closed or waterproof deck joints should be provided
where joints are located directly above structural members
and bearings that would be adversely affected by debris
accumulation. Where deicing chemicals are used on bridge
decks, sealed or waterproofed joints should be provided.
For straight bridges, the longitudinal elements of deck
joints, such as plate fingers, curb and barrier plates, and
modular bridge joint system support bars, should be placed
parallel to the longitudinal axis of the deck. For curved and
skewed structures, allowance shall be made for deck end
movements consistent with that provided by the bearings.
Where possible, modular bridge joint systems should
not be located in the middle of curved bridges to avoid
unforeseeable movement demands. Preferably, modular
bridge joint systems should not be located near traffic
signals or toll areas so as to avoid extreme braking forces.
C14.5.2.2
Open joints with drainage troughs should not be
placed where the use of horizontal drainage conductors
would be necessary.
End rotations of deck-type structures occur about axes
that are roughly parallel to the centerline of bearings along
the bridge seat. In skewed structures, these axes are not
normal to the direction of longitudinal movement.
Sufficient lateral clearances between plates, open joints, or
elastomeric joint devices should be provided to prevent
binding due to lack of alignment between longitudinal and
rotational movements.
14.5.3—Design Requirements
14.5.3.1—Movements during Construction
Where practicable, construction staging should be
used to delay construction of abutments and piers located
in or adjacent to embankments until the embankments have
been placed and consolidated. Otherwise, deck joints
should be sized to accommodate the probable abutment
and pier movements resulting from embankment
consolidation after their construction.
C14.5.3.1
Where it is either desirable or necessary to
accommodate settlement or other construction movements
prior to deck joint installation and adjustment, the
following construction controls may be used:
•
Placing abutment embankment prior to pier and
abutment excavation and construction,
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2012
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14-16
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Closure pours in concrete structures may be used to
minimize the effect of prestress-induced shortening on the
width of seals and the size of bearings.
•
Surcharging embankments to accelerate consolidation
and adjustment of in-situ soils,
•
Backfilling wall-type abutments up to subgrade prior to
placing bearings and backwalls above bridge seats, and
•
Using deck slab blockouts to allow placing the major
portion of span dead loads prior to joint installation.
C14.5.3.2
14.5.3.2—Design Movements
A roadway surface gap, W, in in., in a transverse deck
joint, measured in the direction of travel at the maximum
movement determined using the appropriate strength load
combination specified in Table 3.4.1-1 shall satisfy:
•
For single gap:
W ≤ 4.0in.
•
(14.5.3.2-1)
For multiple modular gaps:
W ≤ 3.0in.
(14.5.3.2-2)
For steel and nonprestressed wood superstructures, the
minimum opening of a transverse deck joint and roadway
surface gap therein shall not be less than 1.0 in. for
movements determined using the appropriate strength load
combination specified in Table 3.4.1-1. For concrete
superstructures, consideration shall be given to the opening
of joints due to creep and shrinkage that may require initial
minimum openings of less than 1.0 in. at the strength limit
state.
Unless more appropriate criteria are available, the
maximum surface gap of longitudinal roadway joints shall
not exceed 1.0 in. at the strength limit state.
At the maximum movement determined using the
appropriate strength load combination specified in
Table 3.4.1-1, the opening between adjacent fingers on a
finger plate shall not exceed:
•
2.0 in. for longitudinal openings greater than 8.0 in., or
•
3.0 in. for longitudinal openings 8.0 in. or less.
Safe operation of motorcycles is one of the prime
considerations in choosing the size of openings for finger
plate joints.
The finger overlap at the maximum movement shall be
not less than 1.5 in. at the strength limit state.
Where bicycles are anticipated in the roadway, the use
of special covering floor plates in shoulder areas shall be
considered.
14.5.3.3—Protection
Deck joints shall be designed to accommodate the
effects of vehicular traffic, pavement maintenance
equipment, and other long-term environmentally induced
damage.
Joints in concrete decks should be armored with steel
shapes, weldments, or castings. Such armor shall be recessed
below roadway surfaces and be protected from snowplows.
C14.5.3.3
Snowplow protection for deck joint armor and joint
seals may consist of:
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2012
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SECTION 14: JOINTS AND BEARINGS
Jointed approach pavements shall be provided with
pressure relief joints and/or pavement anchors. Approaches
to integral bridges shall be provided with cycle control
pavement joints.
14-17
•
Concrete buffer strips 12.0 to 18.0 in. wide with joint
armor recessed 0.25 to 0.375 in. below the surface of
such strips,
•
Tapered steel ribs protruding up to 0.50 in. above
roadway surfaces to lift the plow blades as they pass
over the joints,
•
Recesses in flexible pavement to position armor
below anticipated rutting, but not so deep as to pond
water.
Additional precautions to prevent damage by
snowplows should be considered where the skew of the
joints coincides with the skew of the plow blades, typically
30 degrees to 35 degrees.
14.5.3.4—Bridging Plates
Joint bridging plates and finger plates should be
designed as cantilever members capable of supporting
wheel loads at the strength limit state.
The differential settlement between the two sides of a
joint bridging plate shall be investigated. If the differential
settlement cannot be either reduced to acceptable levels or
accommodated in the design and detailing of the bridging
plates and their supports, a more suitable joint should be
used.
Rigid bridging plates shall not be used at elastomeric
bearings or hangers unless they are designed as cantilever
members, and the contract documents require them to be
installed to prevent binding of the joints due to horizontal
and vertical movement at bearings.
14.5.3.5—Armor
C14.5.3.4
Where binding of bridging plates can occur at bearing
joints due to differential vertical translation of abutting
structural elements or due to the longitudinal movement of
bridging plates and bearings on different planes, the plates
can be subjected to the total dead and live load
superstructure reaction. Where bridging plates are not
capable of resisting such loads, they may fail and become a
hazard to the movement of vehicular traffic.
Thick elastomeric bearings responding to the
application of vertical load or short hangers responding to
longitudinal deck movements may cause appreciable
differential vertical translation of abutting structural
elements at bearing joints. To accommodate such
movements, an appropriate type of sealed joint or a
waterproofed open joint, rather than a structural joint with
rigid bridging plates or fingers, should be provided.
C14.5.3.5
Joint-edge armor embedded in concrete substrates
should be pierced by 0.75-in. minimum-diameter vertical
vent holes spaced on not more than 18.0-in. centers.
Vent holes are necessary to help expel entrapped air
and facilitate the attainment of a solid concrete substrate
under joint edge armor.
The contract documents should require hand packing
of concrete under joint armor.
Metal surfaces wider than 12.0 in. that are exposed to
vehicular traffic shall be provided with an antiskid
treatment.
14.5.3.6—Anchors
C14.5.3.6
Armor anchors or shear connectors should be
provided to ensure composite behavior between the
concrete substrate and the joint hardware and to prevent
subsurface corrosion by sealing the boundaries between
the armor and concrete substrate. Anchors for edgebeams
of strip seals and MBJS shall be designed for the
snowplow load as required in Article 14.5.1.2.
Snow plow impact should also be considered in
designing anchors.
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2012
Edition
14-18
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Anchors for roadway joint armor shall be directly
connected to structural supports or extended to effectively
engage the reinforced concrete substrate.
The free edges of roadway armor, more than 3.0 in.
from other anchors or attachments, shall be provided with
0.50-in. diameter end-welded studs not less than 4.0 in.
long spaced at not more than 12.0 in. from other anchors or
attachments. The edges of sidewalk and barrier armor shall
be similarly anchored.
14.5.3.7—Bolts
C14.5.3.7
Anchor bolts for bridging plates, joint seals, and joint
anchors shall be fully torqued high-strength bolts. The
interbedding of nonmetallic substrates in connections with
high-strength bolts shall be avoided. Cast-in-place anchors
shall be used in new concrete. Expansion anchors,
countersunk anchor bolts, and grouted anchors shall not be
used in new construction.
Grouted anchors may be used for maintenance of
existing joints.
14.5.4—Fabrication
C14.5.4
Shapes or plates shall be of sufficient thickness to
stiffen the assembly and minimize distortion due to
welding.
To ensure appropriate fit and function, the contract
documents should require that:
Joint straightness and fit of components should be
enhanced by the use of shapes, bars, and plates 0.50 in. or
thicker.
Construction procedures and practices should be
developed to allow joint adjustment for installation
temperatures without altering the orientation of joint parts
established during shop assembly.
•
Joint components be fully assembled in the shop for
inspection and approval,
•
Joints and seals be shipped to the job-site fully
assembled, and
•
Assembled joints in lengths up to 60.0 ft be furnished
without intermediate field splices.
14.5.5—Installation
14.5.5.1—Adjustment
The setting temperature of the bridge or any
component thereof shall be taken as the actual air
temperature averaged over the 24-hour period immediately
preceding the setting event.
For long structures, an allowance shall be included in
the specified joint widths to account for the inaccuracies
inherent in establishing installation temperatures and for
superstructure movements that may take place during the
time between the setting of the joint width and completion
of joint installation. In the design of joints for long
structures, preference should be given to those devices,
details, and procedures that will allow joint adjustment and
completion in the shortest possible time.
C14.5.5.1
Except for short bridges where installation
temperature variations would have only a negligible effect
on joint width, plans for each expansion joint should
include required joint installation widths for a range of
probable installation temperatures. For concrete structures,
use of a concrete thermometer and measurement of
temperature in expansion joints between superstructure
units may be considered.
An offset chart for installation of the expansion joints
is recommended to account for uncertainty in the setting
temperature at the time of design. The designer may
provide offset charts in appropriate increments and include
the chart on the design drawings. Placement of the
expansion joint hardware during deck forming should
accommodate differences between setting temperature and
an assumed design installation temperature.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
SECTION 14: JOINTS AND BEARINGS
Connections of joint supports to primary members
should allow horizontal, vertical, and rotational
adjustments.
Construction joints and blockouts should be used
where practicable to permit the placement of backfill and
the major structure components prior to joint placement
and adjustment.
14.5.5.2—Temporary Supports
Deck joints shall be furnished with temporary devices
to support joint components in proper position until
permanent connections are made or until encasing concrete
has achieved an initial set. Such supports shall provide for
adjustment of joint widths for variations in installation
temperatures.
14.5.5.3—Field Splices
Joint designs shall include details for transverse field
splices for staged construction and for joints longer than
60.0 ft. Where practicable, splices should be located
outside of wheel paths and gutter areas.
Details in splices should be selected to maximize
fatigue life.
Field splices provided for staged construction shall be
located with respect to other construction joints to provide
sufficient room to make splice connections.
When a field splice is required, the contract
documents should require that permanent seals not be
placed until after joint installation has been completed.
Where practicable, only those seals that can be installed in
one continuous piece should be used. Where field splicing
is unavoidable, splices should be vulcanized.
14-19
Construction procedures that will allow major
structure dead load movements to occur prior to placement
and adjustment of deck joints should be used.
C14.5.5.2
Temporary attachments should be released to avoid
damaging anchorage encasements due to movement of
superstructures responding to rapid temperature changes.
For long structures with steel primary members,
instructions should be included in the contract documents
to ensure the removal of temporary supports or release of
their connections as soon as possible after concrete
placement.
C14.5.5.3
Splices for less critical portions of joints or for lightly
loaded joints should be provided with connections rigid
enough to withstand displacement if joint armor is used as
a form during concrete placement.
14.5.6—Considerations for Specific Joint Types
14.5.6.1—Open Joints
Open deck joints shall permit the free flow of water
through the joint. Open deck joints should not be used
where deicing chemicals are applied. Piers and abutments
at open joints shall satisfy the requirements of Article 2.5.2
in order to prevent the accumulation of water and debris.
C14.5.6.1
Under certain conditions, open deck joints can provide
an effective and economical solution. In general, open
joints are well-suited for secondary highways where little
sand and salt are applied during the winter. They are not
suited for urban areas where the costs of provisions for
deck joint drainage are high.
Satisfactory performance depends upon an effective
deck drainage system, control of deck discharge through
joints, and containment and disposal of runoff from the
site. It is essential that surface drainage and roadway
debris not be permitted to accumulate on any part of the
structure below such joints.
Protection against the deleterious effects of deck
drainage may include shaping structural surfaces to
prevent the retention of roadway debris and providing
surfaces with deflectors, shields, covers, and coatings.
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2012
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14-20
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
14.5.6.2—Closed Joints
Sealed deck joints shall seal the surface of the deck,
including curbs, sidewalks, medians, and, where
necessary, parapet and barrier walls. The sealed deck joint
shall prevent the accumulation of water and debris, which
may restrict its operation. Closed or waterproof joints
exposed to roadway drainage shall have structure surfaces
below the joint shaped and protected as required for open
joints.
Joint seals should be watertight and extrude debris
when closing.
Drainage accumulated in joint recesses and seal
depressions shall not be discharged on bridge seats or
other horizontal portions of the structure.
Where joint movement is accommodated by a change
in the geometry of elastomeric glands or membranes, the
glands or membranes shall not come into direct contact
with the wheels of vehicles.
C14.5.6.2
Completely effective joint seals have yet to be
developed for some situations, particularly where there are
severely skewed joints with raised curbs or barriers, and
especially where joints are subjected to substantial
movements. Consequently, some type of open or closed
joint, protected as appropriate, should be considered
instead of a sealed joint.
Sheet and strip seals that are depressed below the
roadway surface and that are shaped like gutters will fill
with debris. They may burst upon closing, unless the joints
that they seal are extended straight to the deck edges where
accumulated water and debris can be discharged clear of
the structure. To allow this extension and safe discharge, it
may be necessary to move the backwalls and bridge seats
of some abutment types forward until the backwalls are
flush with the wingwalls, or to reposition the wingwalls so
that they do not obstruct the ends of the deck joints.
14.5.6.3—Waterproofed Joints
Waterproofing systems for joints, including joint
troughs, collectors, and downspouts, shall be designed to
collect, conduct, and discharge deck drainage away from
the structure.
In the design of drainage troughs, consideration
should be given to:
•
Trough slopes of not less than 1.0 in./ft;
•
Open-ended troughs or troughs with large discharge
openings;
•
Prefabricated troughs;
•
Troughs composed of reinforced elastomers, stainless
steel, or other metal with durable coatings;
•
Stainless steel fasteners;
•
Troughs that are replaceable from below the joint;
•
Troughs that can be flushed from the roadway surface;
and
•
Welded metal joints and vulcanized elastomeric
splices.
14.5.6.4—Joint Seals
Seals shall accommodate all anticipated movements.
In the choice of a seal type, consideration should be
given to seals that:
•
Are preformed or prefabricated,
•
Can be replaced without major joint modification,
•
Do not support vehicular wheel loads,
•
Can be placed in one continuous piece,
•
Are recessed below joint armor surface,
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2012
Edition
SECTION 14: JOINTS AND BEARINGS
•
Are mechanically anchored, and
•
Respond to joint width changes without substantial
resistance.
14-21
Elastomeric material for seals should be:
•
Durable, of virgin neoprene or natural rubber and
reinforced with steel or fabric laminates;
•
Vulcanized;
•
Verified by long-term cyclic testing; and
•
Connected by adhesives that are chemically cured.
14.5.6.5—Poured Seals
Unless data supports a smaller joint width, the joint
width for poured seals should be at least 6.0 times the
anticipated joint movement determined using the appropriate
strength load combination specified in Table 3.4.1-1.
Sealant bond to metal and masonry materials should
be documented by national test methods.
14.5.6.6—Compression and Cellular Seals
Where seals with heavy webbing are exposed to the full
movement range, joints shall not be skewed more than
20 degrees.
Compression seals for bearing joints shall not be less
than 2.5 in. nor more than 6.0 in. wide when uncompressed
and shall be specified in width increments in multiples of
0.5 in.
Primary roadway seals shall be furnished without
splices or cuts, unless specifically approved by the
Engineer.
In gutter and curb areas, roadway seals shall be bent
up in gradual curves to retain roadway drainage. Ends of
roadway seals shall be protected by securely attached
vented caps or covers. Secondary seals in curbs and barrier
areas may be cut and bent as necessary to aid in bending
and insertion into the joint.
Closed cell seals shall not be used in joints where they
would be subjected to sustained compression, unless seal
and adhesive adequacy have been documented by longterm demonstration tests for similar applications.
C14.5.6.5
Poured seals should be used only for joints exposed to
small movements and for applications where
watertightness is of secondary importance.
C14.5.6.6
Compression seals should be used only in those
structures where the joint movement range can be
accurately predicted.
Performance of compression and cellular seals is
improved when concrete joint recesses are made by sawcutting in a single pass, rather than by being cast with the
aid of removable forms.
14.5.6.7—Sheet and Strip Seals
In the selection and application of either sheet or strip
seals, consideration should be given to:
•
Joint designs for which glands with anchorages not
exposed to vehicular loadings,
•
Joint designs that allow complete closure without
detrimental effects to the glands,
•
Joint designs where the elastomeric glands extend
straight to deck edges rather than being bent up at
curbs or barriers,
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
14-22
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
•
Decks with sufficient crown or superelevation to
ensure lateral drainage of accumulated water and
debris,
•
Glands that are shaped to expel debris, and
•
Glands without abrupt changes in either horizontal or
vertical alignment.
Sheet and strip seals should be spliced only when
specifically approved by the engineer.
14.5.6.8—Plank Seals
Application of plank seals should be limited to
structures on secondary roads with light truck traffic, and
that have unskewed or slightly skewed joints.
Consideration should be given to:
•
Seals that are provided in one continuous piece for the
length of the joint,
•
Seals with splices that are vulcanized, and
•
Anchorages that can withstand the forces necessary to
stretch or compress the seal.
C14.5.6.8
Plank-type seals should not be used in joints with
unpredictable movement ranges.
14.5.6.9—Modular Bridge Joint Systems (MBJS)
14.5.6.9.1—General
C14.5.6.9.1
These Articles of the specifications address the
performance requirements, strength limit state design,
and fatigue limit state design of modular bridge joint
systems (MBJS).
These Specifications were developed primarily for,
and shall be applied to, the two common types of MBJS,
multiple and single support bar systems, including swiveljoist systems.
These MBJS design specifications provide a rational
and conservative method for the design of the main load
carrying steel components of MBJS. These Specifications
do not specifically address the functional design of MBJS
or the design of the elastomeric parts. These Specifications
are based on research described in Dexter et al. (1997),
which contains extensive discussion of the loads and
measured dynamic response of MBJS and the fatigue
resistance of common MBJS details. Fatigue test
procedures were developed for the structural details as
well.
Common types of MBJS are shown in
Figures C14.5.6.9.1-1 through C14.5.6.9.1-3.
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2012
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SECTION 14: JOINTS AND BEARINGS
14-23
Edgebeams
Blockout
Centerbeams
Support box
Spring
Bearing
Support Bars
Figure C14.5.6.9.1-1—Cut-Away View of Typical WeldedMultiple-Support-Bar (WMSB) Modular Bridge Joint
System (MBJS) Showing Support Bars Sliding within
Support Boxes
Edgebeams
Centerbeams
Spring
Blockout
Support Bar
Bearing
Support box
Yoke
Figure C14.5.6.9.1-2—Cross-Section View of Typical
Single-Support-Bar (SSB) Modular Bridge Joint System
(MBJS) Showing Multiple Centerbeams with Yokes
Sliding on a Single Support Bar
Center Beam
Edge Beam
Sealing
Element
Support Bar
Spring
Bearing
Stirrup
Figure C14.5.6.9.1-3—Cut-Away View of a “Swivel Joint,”
i.e., a Special Type of Single-Support-Bar (SSB) Modular
Bridge Joint System (MBJS) with a Swiveling Single
Support Bar
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2012
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14-24
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
14.5.6.9.2—Performance Requirements
C14.5.6.9.2
The required minimum MBJS movement range
capabilities for the six possible degrees of freedom given
in Table 14.5.6.9.2-1 shall be added to the maximum
movement and rotations calculated for the entire range of
seals in the MBJS determined using the appropriate
strength load combination specified in Table 3.4.1-1.
The MBJS should be designed and detailed to
minimize excessive noise or vibration during the passage
of traffic.
A common problem with MBJS is that the seals fill
with debris. Traffic passing over the joint can work the
seal from its anchorage by compacting this debris. MBJS
systems can eject most of this debris in the traffic lanes if
the seals are opened to near their maximum opening.
Therefore, it is prudent to provide for additional movement
capacity.
MBJS should permit movements in all six degrees of
freedom, i.e., translations in all three directions and
rotations about all three axes. While it is mandatory to
provide at least 1.0 in. movement in the longitudinal
direction, as shown in Table 14.5.6.9.2-1, no more than
2.0 in. should be provided in addition to the maximum
calculated movement if feasible. Also, more than 1.0 in.
should not be added if it causes a further seal to be used. In
the five degrees of freedom other than the longitudinal
direction, the MBJS should provide the maximum
calculated movement in conjunction with providing for at
least the minimum additional movement ranges shown in
Table 14.5.6.9.2-1. Half of the movement range shall be
assumed to occur in each direction about the mean
position. Some bridges may require greater than the
additional specified minimum values.
The designer should consider showing the total
estimated transverse and vertical movement in each
direction, as well as the rotation in each direction about the
three principal axes on the contract plans. Vertical
movement due to vertical grade, with horizontal bearings,
and vertical movement due to girder end rotation may also
be considered.
Further design guidelines and recommendations can
be found in Chapter 19 of the AASHTO LRFD Bridge
Construction Specifications and Dexter et al. (1997).
Table 14.5.6.9.2-1—Additional Minimum Movement
Range Capability for MBJS
Type of Movement
Longitudinal Displacement
Transverse Movement
Vertical Movement
Rotation around Longitudinal
Axis
Rotation Around Transverse
Axis
Rotation Around Vertical Axis
*
Minimum Design
Movement Range*
Estimated
Movement + 1.0 in.
1.0 in.
1.0 in.
1°
1°
0.5°
Total movement ranges presented in the table are twice the
plus or minus movement.
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All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 14: JOINTS AND BEARINGS
14-25
14.5.6.9.3—Testing and Calculation Requirements
MBJS shall satisfy all test specifications detailed in
Appendix A of the AASHTO LRFD Bridge Construction
Specifications.
Each configuration of MBJS shall be designed for the
strength and fatigue, and fracture limit states as specified
in Articles 14.5.6.9.6 and 14.5.6.9.7.
14.5.6.9.4—Loads and Load Factors
Edgebeams, anchors, centerbeams, support bars,
connections between centerbeams and support bars,
support boxes, and connections, if any, to elements of the
structure, such as girders, truss chords, crossbeams, etc.,
and other structural components shall be designed for the
strength and fatigue and fracture limit states for the
simultaneous application of vertical and horizontal axle
loads. The edgebeams and anchors of MBJS in snow
regions shall also be designed for the strength limit state
for the snowplow load defined in Article 14.5.1.2. The
design lane load need not be considered for MBJS.
The two wheel loads from each axle shall be centered
72.0 in. apart transversely. Each wheel load shall be
distributed to the various edgebeams and centerbeams as
specified in Article 14.5.6.9.5. The fraction of the wheel
loads applied to each member shall be line loads applied at
the center of the top surface of a member with a width of
20.0 in.
For the strength limit state, the vertical wheel loads
shall be from the design tandem specified in
Article 3.6.1.2.3; the wheel loads from the design truck
in Article 3.6.1.2.2 need not be considered for the
strength limit state of MBJS. Both of the tandem axles
shall be considered in the design if the joint opening
exceeds 4.0 ft. The vertical wheel load shall be increased
by the dynamic load allowance specified for deck joints
in Table 3.6.2.1-1.
The horizontal load for the strength limit state shall be
20 percent of the vertical wheel load (LL + IM), applied
along the same line at the top surface of the centerbeam or
edgebeam. For MBJS installed on vertical grades in excess
of five percent, the additional horizontal component due to
grade shall be added to the horizontal wheel load.
To investigate the strength limit state, the axles shall
be oriented and positioned transversely to maximize the
force effect under consideration.
The vertical wheel load ranges for the fatigue limit
state shall be from the largest axle load from the threeaxle design truck specified in Article 3.6.1.2.2. For
fatigue limit state design of MBJS, this axle load shall be
considered as the total load on a tandem, i.e., the total
load shall be split into two axle loads spaced 4.0 ft apart.
Both of these tandem axles shall be considered in the
design if the joint opening exceeds 4.0 ft. The vertical
load range shall be increased by the dynamic load
allowance specified for deck joints in Table 3.6.2.1-1.
The load factors to consider shall be as specified in
Table 3.4.1-1 for the Fatigue I case.
C14.5.6.9.4
The vertical axle load for fatigue limit state design is
one-half the 32.0-kip axle load of the design truck
specified in Article 3.6.1.2.2 or 16.0 kips. This reduction
recognizes that the main axles of the design truck are a
simplification of actual tandem axles. The simplification is
not satisfactory for MBJS and other expansion joints
because expansion joints experience a separate stress cycle
for each individual axle.
For strength limit state design, there are two load
combinations that could be considered. However,
recognizing that each main axle of the design truck should
actually be treated as 32.0-kip tandems, it is clear the
50.0-kip design tandem, which is not used for fatigue limit
state design, will govern for strength limit state design.
The loads specified for fatigue limit state design
actually represent load ranges. When these loads are
applied to a structural analysis model with no dead load
applied to the model, the moment, force, or stress that is
computed everywhere represents a moment, force or stress
range. In service, these stress ranges are partly due to the
downward load and partly due to upward rebound from the
dynamic impact effect.
The dynamic load allowance (impact factor) specified
for deck joints of 75 percent was developed from field testing
of MBJS conducted in Europe and was confirmed in field
tests described in Dexter et al. (1997). The stress range due to
the load plus this dynamic load allowance represents the sum
of the downward part of that stress range and the upward part
of the stress range due to rebound. Measurements, described
in Dexter et al. (1997), showed that the maximum downward
amplification of the static load is 32 percent, with about
31 percent rebound in the upward direction.
The vertical axle load range with impact for fatigue limit
state design is one-half of the largest axle load of the design
truck specified in Article 3.6.1.2.2, multiplied by 1.75 to
include the dynamic load allowance, multiplied by a load
factor of 1.5 (or 2.0 × 0.75), as specified in Table 3.4.1-1 for
the Fatigue I case, or 42.0 kips. The 0.75 load factor
transforms axles of an HS20 truck to those of an HS15
fatigue truck, which is presumed to represent the effective
stress range. The factor 2.0 amplifies the effective stress
range for the fatigue limit state to the presumed maximum
expected stress range which with impact is required to be
less than the fatigue threshold in Article 14.5.6.9.7a. It is
the intent of the fatigue design specifications that the static
load without impact considered (24.0 kips or
42.0 kips/1.75) should be infrequently exceeded, see
Dexter et al. (1997).
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2012
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14-26
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The horizontal load ranges for the fatigue limit state
shall be at least 20 percent of the vertical wheel load range
(LL + IM) for fatigue. For MBJS installed on vertical
grades in excess of five percent, the additional horizontal
component due to grade shall be added to the horizontal
wheel load range.
To investigate the fatigue limit state, the axles shall be
oriented perpendicular to the travel direction only, but
shall be positioned transversely to maximize the force
effect under consideration. In bridges with a skew greater
than 14 degrees, the two wheel loads from an axle may not
be positioned on a centerbeam simultaneously, and the
maximum stress ranges at a critical detail on the
centerbeam may be the difference between the stresses due
to the application of each wheel load separately.
Field measurements were taken at a variety of
locations; so typical truck excitations should be reflected
in the dynamic load allowance. However, a joint located
on a structure with significant settlement or deterioration
of the approach roadway may be exposed to a dynamic
load allowance 20 percent greater due to dynamic
excitation of the trucks.
MBJS with centerbeam spans less than 4.0 ft are
reported to have lower dynamic effects (Pattis, 1993;
Tschemmernegg and Pattis, 1994). The fatigue limit state
design provisions of Article 14.5.6.9.7 happen to also limit
the spans of typical 5.0 in. deep centerbeams to around
4.0 ft anyway, so there is no need for a specific limitation
of the span.
At sites with a tight horizontal curve (less than 490-ft
radius) the vertical moments could be about 20 percent
higher than would be expected. An increase in the dynamic
load allowance for cases where there is a tight horizontal
curve is not considered necessary if the speed of trucks on
these curves is limited. In this case, the dynamic impact
will be less than for trucks at full speed and the decreased
dynamic impact will approximately offset the increased
vertical load due to the horizontal curve.
The dynamic load allowance is very conservative
when applied to the vertical load for strength limit state
design, since in strength limit state design peak loads, not
load ranges, are of interest. In the measurements made on
MBJS in the field, the maximum downward vertical
moment was only 1.32 times the static moment. There are
usually no consequences of this conservative
simplification since the proportions of the members are
typically governed by fatigue and not strength.
The horizontal loads are taken as 20 percent of the
vertical load plus the dynamic load allowance. In-service
measurements, described in Dexter et al. (1997), indicate
that the 20 percent horizontal load range is the largest
expected from traffic at steady speeds, including the effect
of acceleration and routine braking. The 20 percent
horizontal load range for fatigue limit state design
represents ten percent forward and ten percent backward.
Where strength limit state design is considered, the
20 percent horizontal load requirement corresponds to a
peak load of 20 percent applied in one direction. The
20 percent horizontal peak load is appropriate for strength
limit state design. However, the field measurements,
described in Dexter et al. (1997), show that the horizontal
force effects resulting from extreme braking can be much
greater than at steady speeds. Therefore, the 20 percent
peak horizontal load represents the extreme braking for
strength limit state design. For fatigue limit state design,
these extreme events occur so infrequently that they do not
usually need to be taken into account in most cases.
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2012
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SECTION 14: JOINTS AND BEARINGS
14-27
Special consideration should be given to the horizontal
forces if the MBJS is located near a traffic light, stop sign, or
toll facility or if the centerbeam is unusually wide.
14.5.6.9.5—Distribution of Wheel Loads
Each edgebeam shall be designed for 50 percent of the
vertical and horizontal wheel loads specified in
Article 14.5.6.9.4.
Table 14.5.6.9.5-1 specifies the centerbeam
distribution factor, i.e., the percentage of the design
vertical and horizontal wheel loads specified in
Article 14.5.6.9.4 that shall be applied to an individual
centerbeam for the design of that centerbeam and
associated support bars. Distribution factors shall be
interpolated for centerbeam top flange widths not given in
the table, but in no case shall the distribution factor be
taken as less than 50 percent. The remainder of the load
shall be divided equally and applied to the two adjacent
centerbeams or edgebeams.
Table—14.5.6.9.5-1 Centerbeam Distribution Factors
Width of Centerbeam
Top Flange
Distribution
Factor
2.5 in. (or less)
50%
3.0 in.
60%
4.0 in.
70%
4.75 in.
80%
C14.5.6.9.5
For the convenience of the designer, the vertical axle
load range with impact for fatigue limit state design on one
centerbeam 2.5 in. or less in width is 21.0 kips. On the
centerbeam, each fraction of the wheel load of 10.5 kips is
spaced 72.0 in. apart distributed over a width of 20.0 in.
with a magnitude of 0.525 kips/in.
The distribution factor, i.e., the fraction of the design
wheel load range assigned to a single centerbeam, is a
function of applied load, tire pressure, gap width, and
centerbeam height mismatch. Unfortunately, many of the
factors affecting the distribution factor are difficult to
quantify individually and even more difficult to incorporate
in an equation or graph. Existing methods to estimate the
distribution factor do not incorporate all of these variables
and consequently can be susceptible to error when used
outside the originally intended range. In view of this
uncertainty, a simplified tabular method is used to estimate
the distribution factor. Alternative methods are permitted if
they are based on documented test data.
Wheel load distribution factors shown in
Table 14.5.6.9.5-1 are based on field and laboratory
testing, described in Dexter et al. (1997), and were found
to be in acceptable agreement with the findings of other
researchers. These distribution factors are based on the
worst-case assumption of maximum joint opening
(maximum gap width). Calculating the stress ranges at
maximum gap opening is approximately 21 percent too
conservative for fatigue limit state design. However, as
explained in Dexter et al. (1997), this conservatism
compensates for a lack of conservatism in the AASHTO
fatigue design truck axle load.
For comparison to the fatigue threshold, the factored
static axle load range, without the dynamic load allowance,
would be 24.0 kips (or 42.0 kips/1.75, as discussed in
Article C14.5.6.9.4). The static axle load range at the
fatigue limit state is supposed to represent an axle load that
is rarely exceeded. However, the fatigue limit state design
load is multiplied by a distribution factor that is 21 percent
too large, so in effect, this is equivalent to a static axle load
range at the fatigue limit state of 29.0 kips that should be
rarely exceeded, if correct distribution factors were used.
This is more consistent with the statistics of weigh-inmotion data where axle loads with exceedence levels of
0.01 percent were up to 36.0 kips, see Schilling (1990) or
Nowak and Laman (1995).
A mitigating factor on the impact of these larger axle
loads is that the distribution factor decreases with
increasing axle load. Because of this effect, measurements
reported in Dexter et al. (1997) show that as the axle load
is increased from 24.0 to 36.0 kips, an increase of
50 percent, the load on one centerbeam increases from
12.6 to only 14.6 kips, an increase of only 16 percent.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Even though maximum gap opening occurs only
rarely, it is an appropriate assumption for checking the
Strength-I limit state. No additional conservatism is
warranted in this case, however, because the dynamic load
allowance is about 32 percent too conservative for strength
limit state design only, as discussed in Article C14.5.6.9.
Another advantage of using the conservative
distribution factors is that it may compensate for ignoring
the effect of potential centerbeam height mismatch.
Laboratory studies show that a height mismatch of
0.125 in. resulted in a 24 percent increase in the measured
distribution factor, see Dexter et al. (1997). Although such
mismatch is not common presently, and recent
construction specifications are supposed to preclude this
mismatch, it is prudent to anticipate that it may occur.
14.5.6.9.6—Strength Limit State Design Requirements
Where the MBJS is analyzed for the strength limit
state, the gap between centerbeams shall be assumed to be
at the fully opened position, typically 3.0 in.
The MBJS shall be designed to withstand the force
effects for the strength limit state specified in Article 6.5.4
by applying the provisions of Articles 6.12 and 6.13, as
applicable. All sections shall be compact, satisfying the
provisions of Articles A6.1, A6.2, A6.3.2, and A6.3.3.
MBJS shall be designed to withstand the load combination
for the Strength I limit state that is specified in
Table 3.4.1-1 for the simultaneous application of vertical
and horizontal axle loads specified in Article 14.5.6.9.4.
Dead loads need not be included. Loads shall be
distributed as specified in Article 14.5.6.9.5.
Anchors shall be investigated at the strength limit state
due to vertical wheel loads without the horizontal wheel
loads using the requirements of Article 6.10.10.4.3. The
anchors shall be checked separately for the horizontal
wheel loads at the strength limit state. In snow regions,
another separate analysis shall be performed for the
anchors for the snowplow load defined in Article 14.5.1.2.
Pullout or breakout at the strength limit state under each of
these loads shall be investigated by the latest ACI 318
(Building Code Requirements for Structural Concrete),
using the following resistance factors:
•
For anchors governed by the steel, the resistance
factors are:
φtension = 0.80
φshear = 0.75
•
For anchors governed by the concrete, the load factors
for Condition A, supplemental reinforcement in the
failure area, are:
φA tension = 0.85
φA shear = 0.85
•
C14.5.6.9.6
Anchorage calculations for strength and fatigue limit
states are presented in Dexter et al. (2002). A prescriptive
design was found that satisfies the strength and fatigue
limit state requirements presented in this specification,
including the snowplow load. This design may be adopted
without presenting explicit calculations. This design
consists of a steel edgebeam minimum thickness 0.375 in.
with Grade 50 (50.0 ksi yield) 0.5 in. diameter welded
headed anchors (studs) with length of anchor of 6.0 in.
spaced every 12.0 in. The welded headed anchor shall
have minimum cover depth of 3.0 in., except where over
the support boxes, where the cover depth is 2.0 in.
Analyzing the centerbeam as a continuous beam over
rigid supports has been found to give good agreement with
measured strains for loads in the vertical direction. For
loads in the horizontal direction, the continuous beam
model is conservative. For the loads in the horizontal
direction, more accurate results can be achieved by treating
the centerbeams and support bars as a coplanar frame
pinned at the ends of the support bars.
Maximum centerbeam stresses in interior spans are
typically generated with one of the wheel loads centered in
the span. However, if the span lengths are the same, the
exterior spans (first from the curb) will typically govern
the design. In an optimum design, this exterior span should
be about ten percent less than typical interior spans.
The vertical and horizontal wheel loads are idealized
as line loads along the centerlines of the centerbeams, i.e.,
it is not necessary to take into account eccentricity of the
forces on the centerbeam. The maximum reaction of the
centerbeam against the support bar is generated when the
wheel load is centered over the support bar. This situation
may govern for the throat of the centerbeam/support bar
weld, for design of the stirrup of a single-support-bar
system, or for design of the support bar.
MBJS installed on skewed structures may require
special attention in the design process.
For anchors governed by the concrete, the load factors
for Condition B, no supplemental reinforcement, are:
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SECTION 14: JOINTS AND BEARINGS
14-29
φB tension = 0.75
φB shear = 0.75
14.5.6.9.7—Fatigue Limit State Design
Requirements
14.5.6.9.7a—General
C14.5.6.9.7a
MBJS structural members, including centerbeams,
support bars, connections, bolted and welded splices, and
attachments, shall meet the fracture toughness
requirements in Article 6.6.2. Bolts subject to tensile
fatigue shall satisfy the provisions of Article 6.13.2.10.3.
MBJS structural members, including centerbeams,
support bars, connections, bolted and welded splices, and
attachments, shall be designed for the fatigue limit state as
specified in Article 6.6.1.2 and as modified and
supplemented herein.
Each detail shall satisfy:
Δf ≤ ( ΔF )TH
(14.5.6.9.7a-1)
where:
Δf
=
force effect, design live load stress range due
to the simultaneous application of vertical
and horizontal axle loads specified in
Article14.5.6.9.4 and distributed as specified
in Article 14.5.6.9.5, and calculated as
specified in Article 14.5.6.9.7b (ksi)
ΔFTH
=
constant amplitude fatigue threshold taken
from Table 6.6.1.2.5-3 for the detail category
of interest (ksi)
The fatigue detail categories for the centerbeam-tosupport-bar connection, shop splice, field splice, or other
critical details shall be established by the fatigue testing as
required by Article 14.5.6.9.3. All other details shall have
been included in the test specimen. Details that did not
crack during the fatigue test shall be considered
noncritical. The fatigue detail categories for noncritical
details shall be determined using Table 6.6.1.2.3-1.
Anchors and edgebeams shall be investigated for the
fatigue limit state considering the force effects from vertical
and horizontal wheel loads. Shear connectors and other
anchors shall be designed for the fatigue limit state to resist
the vertical wheel loads according to the provisions of
Article 6.10.10.2 for the Fatigue I case defined in
Article 3.4.1. The force effects from the horizontal wheel
loads need not be investigated for standard welded headed
anchors.
Edgebeams shall be at least 0.375 in. thick.
Edgebeams with standard welded headed anchors spaced
at most every 12.0 in. need not be investigated for in-plane
bending for the fatigue limit state.
The fatigue limit state strength of particular details in
aluminum are approximately one-third the fatigue limit
state strength of the same details in steel and, therefore,
aluminum is typically not used in MBJS.
Yield strength and fracture toughness and weld quality
have not been noted as particular problems for MBJS.
The design of the MBJS will typically be governed by
the stress range at fatigue limit state critical details. The
static strength limit state must also be checked according
to the requirements of Article 14.5.6.9.6, but will typically
not govern the design unless the total opening range and
the support bar span is very large. Alternate design
methods and criteria may be used if such methods can be
shown through testing and/or analysis to yield fatigueresistant and safe designs. The target reliability level for
the fatigue limit state is 97.5 percent probability of no
fatigue cracks over the lifetime of the MBJS.
Provisions are not included for a finite life fatigue
limit state design (Fatigue II case, as defined in
Article 3.4.1). Typically, most structures that require a
modular expansion joint carry enough truck traffic to
justify an infinite-life fatigue limit state design approach
(Fatigue I case, as defined in Article 3.4.1). Furthermore,
uncertainty regarding the number of axles per truck and the
number of fatigue cycles per axle would make a finite life
design approach difficult, and little cost is added to the
MBJS by designing for infinite fatigue life.
The intent of this procedure is to assure that the stress
range from the fatigue limit state load range is less than the
CAFL and thereby ensuring essentially an infinite fatigue life.
Fatigue-critical MBJS details include:
•
The connection between the centerbeams and the
support bars;
•
Connection of any attachments to the centerbeams
(e.g., horizontal stabilizers or outriggers); and
•
Shop and/or field splices in the centerbeams.
MBJS details can in many cases be clearly associated
with analogous details in the bridge design specifications.
In other cases, the association is not clear and must be
demonstrated through full-scale fatigue testing.
The detail of primary concern is the connection
between the centerbeams and the support bars. A typical
full-penetration welded connection, which was shown
previously, can be associated with Category C. Fillet
welded connections have very poor fatigue resistance and
should not be allowed.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Bolted connections should be classified as a Category D
detail, with respect to the bending stress range in the
centerbeam. As in any construction, more than one bolt must
be used in bolted connections.
The bolted connections in single-support-bar MBJS
usually involve a yoke or stirrup through which the support
bar slides and/or swivels. Field-welded splices of the
centerbeams and edgebeams are also prone to fatigue. In
new construction, it may be possible to make a fullpenetration welded splice in the field before the joint is
lowered into the blockout. However, in reconstruction
work, the joint is often installed in several sections at a
time to maintain traffic. In these cases, the splice must be
made after the joint is installed. Because of the difficulty in
access and position, obtaining a full-penetration butt weld
in the field after the joint is installed may be impossible,
especially if there is more than one centerbeam. Partialpenetration splice joints have inherently poor fatigue
resistance and should not be allowed.
Bolted splices have been used and no cracking of
these bolted splice details has been reported. The bolted
splice plates behave like a hinge, i.e., they do not take
bending moments. As a result, such details are subjected
only to small shear stress ranges and need not be explicitly
designed for the fatigue limit state. However, the hinge in
the span creates greater bending moments at the support
bar connection, therefore, the span with the field splice
must be much smaller than the typical spans to reduce the
applied stress ranges at the support bar connection.
Thin stainless-steel slider plates are often welded like
cover plates on the support bars. The fatigue strength of the
ends of cover plates is Category E. However, there have not
been any reports of fatigue cracks at these slider plate details
in MBJS. The lack of problems may be because the support
bar bending stress range is much lower at the location of the
slider plate ends than at the centerbeam connection, which is
the detail that typically governs the fatigue limit state design
of the support bar. Also, it is possible that the fatigue
strength is greater than that of conventional cover plates,
perhaps because of the thinness of the slider plate.
The fatigue limit state of the support bars or centerbeams
should also be checked at the location of welded attachments
to react against the horizontal equidistant devices. In addition
to checking the equidistant device attachments with respect to
the stress range in the support bar, there is also some bending
load in the attachment itself. The equidistant devices take part
of the horizontal load, especially in single-support bar
systems. The horizontal load is also transferred through
friction in the bearings and springs of the centerbeam
connection. However, since this transfer is influenced by the
dynamic behavior of the MBJS, it is very difficult to quantify
the load in the attachments.
These attachments are thoroughly tested in the
Opening Movement Vibration Test required in
Article 14.5.6.9.3. If the equidistant device attachments
have no reported problems in the Opening Movement
Vibration Test, they need not be explicitly designed as a
loaded attachment for the fatigue limit state. If there were a
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SECTION 14: JOINTS AND BEARINGS
14-31
fatigue problem with these attachments, it would be
discovered in the Opening Movement Vibration Test.
14.5.6.9.7b—Design Stress Range
The design stress ranges, Δf, at all fatigue critical
details shall be obtained from structural analyses of the
modular joint system due to the simultaneous application
of vertical and horizontal axle loads specified in
Article 14.5.6.9.4 and distributed as specified in
Article 14.5.6.9.5. The MBJS shall be analyzed with a gap
opening no smaller than the midrange configuration and no
smaller than half of maximum gap opening. For each
detail, the structural analysis shall include the worst-case
position of the axle load to maximize the design stress
range at that particular detail.
The nominal stress ranges, Δf, shall be calculated as
follows for specific types of MBJS:
•
•
Single-Support-Bar Systems
o
Centerbeam: The design bending stress range, Δf,
in the centerbeam at a critical section adjacent to
a welded or bolted stirrup shall be the sum of the
stress ranges in the centerbeam resulting from
horizontal and vertical bending at the critical
section. The effects of stresses in any loadbearing attachments, such as the stirrup or yoke,
need not be considered when calculating the
stress range in the centerbeam. For bolted singlesupport-bar systems, stress ranges shall be
calculated on the net section.
o
Stirrup: The design stress range, Δf, in the stirrup
or yoke shall consider the force effects of the
vertical reaction force range between the
centerbeam and support bar. The stress range
shall be calculated by assuming a load range in
the stirrup that is greater than or equal to 30
percent of the total vertical reaction force range.
The calculation of the design stress range in the
stirrup or yoke need not consider the effects of
stresses in the centerbeam. The effects of
horizontal loads may be neglected in the fatigue
limit state design of the stirrup.
C14.5.6.9.7b
Since the design axle load and distribution factors
represent a “worst case”, the structural analysis for fatigue
limit state design need not represent conditions worse than
average. Therefore, for fatigue loading, the assumed gap
can be equal to or greater than the midrange of the gap,
typically 1.5 in., which is probably close to the mean or
average opening. The gap primarily affects the support bar
span.
See Article C14.5.6.9.6 for guidelines on the structural
analysis. MBJS installed on skewed structures may require
special attention in the design process.
On structures with joint skews greater than
14 degrees, it can be shown that the wheels at either end of
an axle will not roll over a particular centerbeam
simultaneously. This asymmetric loading could
significantly affect the stress range at fatigue sensitive
details, either favorably or adversely. Nevertheless, a
skewed centerbeam span is subjected to a range of
moments that includes the negative moment from the
wheel in the adjoining span, followed or preceded by the
positive moment from the wheel in the span.
The stress states at the potential crack locations in
these connections are multiaxial and very complicated.
Simplified assumptions are used to derive the design stress
range at the details of interest for common types of MBJS.
Experience has shown that these simplified assumptions
are sufficient provided that the same assumptions are
applied in calculating the applied stress range for plotting
the fatigue test data from which the design detail category
was determined.
The design stress range should be estimated at a critical
section at the weld toe. For example, Figure C14.5.6.9.7b-1
shows a typical moment diagram for the support bar
showing the critical section. The support bar design bending
stress range is a result of the sum of the bending moment
created by the applied centerbeam reaction and the
additional overturning moment developed by the horizontal
force applied at the top of the centerbeam.
Welded Multiple-Support-Bar Systems
o
Centerbeam Weld Toe Cracking, i.e., Type A
Cracking: The design stress range, Δf, for Type A
cracking shall include the concurrent effects of
vertical and horizontal bending stress ranges in
the centerbeam, SRB, and the vertical stress ranges
in the top of the weld, SRZ, as shown in Figure
14.5.6.9.7b-1. The design stress range for Type A
cracking shall be determined as:
L
L
RV
Actual Critical Section at
Support Bar Weld Toe
RH
Conservative to use the
moment at this location
Moment Diagram
Figure C14.5.6.9.7b-1—Typical Moment Diagram for a
Support Bar
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Δf = S RB 2 + S RZ 2
(14.5.6.9.7b-1)
in which:
S RB =
MV M H
+
S xcb SYcb
(14.5.6.9.7b-2)
S RZ =
M OT
R
+ V
SWtop AWtop
(14.5.6.9.7b-3)
M OT = RH d cb
(14.5.6.9.7b-4)
where:
SRB =
combined bending stress range in the centerbeam
(ksi)
MV =
vertical bending moment range in the
centerbeam on the critical section located at the
weld toe due to the vertical force range (kip-in.)
MH =
horizontal bending moment range in the
centerbeam on the critical section located at the
weld toe due to horizontal force range (kip-in.)
MOT =
overturning moment range from horizontal
reaction force (kip-in.)
SXcb =
vertical section modulus to the bottom of the
centerbeam (in.3)
SYcb =
horizontal section modulus of the centerbeam
(in.3)
SRZ =
vertical stress range in the top of the centerbeamto-support-bar weld from the concurrent reaction
of the support beam (ksi)
RV =
vertical reaction force range in the connection
(kip)
RH =
horizontal reaction
connection (kip)
dcb =
depth of the centerbeam (in.)
SWtop=
section modulus of the weld at the top for
bending in the direction normal to the centerbeam
axis (in.3)
AWtop=
area of weld at the top (in.2)
force
range
in
It is conservative to estimate the moments at the
centerline of the centerbeam as shown.
For all details except the welded-multiple-support-bar
centerbeam to support bar connection, the design stress
range can be calculated using the design moment at the
location of interest. Special equations for calculating the
stress range are provided for welded multiple-support-bar
MBJS. These special equations are based on cracking that
has been observed in fatigue tests of welded multiplesupport-bar MBJS. For the case of welded multiplesupport bar centerbeam to support bar connections, the
design stress range is obtained by taking the square root of
the sum of the squares of the horizontal stress ranges in the
centerbeam or support bar and vertical stress ranges in the
weld. Note this method of combining the stresses ignores
the contribution of shear stresses in the region. Shear
stresses are ignored in this procedure since they are
typically small and very difficult to determine accurately.
More details are provided in Dexter et al. (1997).
the
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SECTION 14: JOINTS AND BEARINGS
14-33
Mh
RH
Mv
Rv
Mh
M O .T.
Mv
Figure 14.5.6.9.7b-1—Force Effects Associated with
Type A Cracking
o
Support Bar Weld Toe Cracking, i.e., Type B
Cracking: The design stress range, Δf, for Type B
cracking shall include the concurrent effects of
vertical bending stress ranges in the support bar,
SRB, and the vertical stress ranges in bottom of the
weld, SRZ, as shown in Figure 14.5.6.9.7b-2. The
design stress range, Δf, for Type B cracking shall
be determined as:
Δf = S RB 2 + S RZ 2
(14.5.6.9.7b-5)
in which:
S RB
M
1
= V +
S Xsb 2
S RZ =
1
RH d cb + hw + d sb
2
S Xsb
RH ( d cb + hw )
SWbot
+
RV
AWbot
(14.5.6.9.7b-6)
(14.5.6.9.7b-7)
where:
SRB
=
bending stress range in the support bar due
to maximum moment including moment
from vertical reaction and overturning at the
connection (ksi)
MV
=
component of vertical bending moment
range in the support bar due to the vertical
reaction force range in the connection
located on the critical section at the weld toe
(kip-in.)
SXsb
=
vertical section modulus of the support bar to
the top of the support bar (in.3)
hw
=
height of the weld (in.)
dsb
=
depth of the support bar (in.)
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
SRZ
=
vertical stress range in the bottom of the
centerbeam-to-support-bar weld from the
vertical and horizontal reaction force ranges
in the connection (ksi)
SWbot
=
section modulus of the weld at the bottom
for bending in the direction of the support
bar axis (in.3)
AWbot
=
area of weld at the bottom (in.2)
RH
Rv
Mot
Mot+Mv
Figure 14.5.6.9.7b-2—Force Effects Associated with
Type B Cracking
o
Cracking Through the Throat of the Weld, i.e.,
Type C Cracking: The design stress range, Δf, for
Type C cracking is the vertical stress, range, SRZ,
at the most narrow cross-section of the
centerbeam-to-support-bar weld from the vertical
and horizontal reaction force ranges in the
connection, as shown in Figure 14.5.6.9.7b-3.
The design stress range, Δf, for Type C cracking
shall be determined as:
R
Δf = V +
AWmid
1
RH d cb + hw
2
SWmid
(14.5.6.9.7b-8)
where:
SWmid
=
section modulus of the weld at the most
narrow cross-section for bending in the
direction normal to the centerbeam axis (in.3)
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SECTION 14: JOINTS AND BEARINGS
AWmid
=
14-35
minimum cross-sectional area of weld (in.2)
RH
Weld Metal
Rv
MO.T.
Note: Stress Blocks are
Shown Exaggerated
Figure 14.5.6.9.7b-3—Force Effects Associated with
Type C Cracking
14.6—REQUIREMENTS FOR BEARINGS
14.6.1—General
C14.6.1
Bearings may be fixed or movable as required for the
bridge design. Movable bearings may include guides to
control the direction of translation. Fixed and guided
bearings shall be designed to resist all appropriate loads
and restrain unwanted translation.
Unless otherwise noted, the resistance factor for
bearings, φ, shall be taken as 1.0.
Bearings subject to net uplift at any limit state shall be
secured by tie-downs or anchorages.
The magnitude and direction of movements and the
loads to be used in the design of the bearing shall be
clearly defined in the contract documents.
Combinations of different types of fixed or movable
bearings should not be used at the same expansion joint,
bent, or pier, unless the effects of differing deflection and
rotation characteristics on the bearings and the structure
are accounted for in the design.
Multirotational bearings conforming to the provisions
of this Section should not be used where vertical loads are
less than 20 percent of the vertical bearing capacity.
All bearings shall be evaluated for component and
connection strength and bearing stability.
Where two bearings are used at a support of box
girders, the vertical reactions should be computed with
consideration of torque resisted by the pair of bearings.
Bearings support relatively large loads while
accommodating large translation or rotations.
The behavior of bearings is quite variable, and there is
very little experimental evidence to precisely define φ for
each limit state. φ is taken to be equal to 1.0 in many parts
of Article 14.6 where a more refined estimate is not
warranted. The resistance factors are often embedded in
the design equations and based on judgment and
experience, but they are generally thought to be
conservative.
Differing deflection and rotational characteristics may
result in damage to the bearings and/or structure.
Bearings loaded to less than 20 percent of their
vertical capacity require special design (FHWA, 1991).
Bearings can provide a certain degree of horizontal load
resistance by limiting the radius of the spherical surface.
However, the ability to resist horizontal loads is a function
of the vertical reaction on the bearing, which could drop
during earthquakes or other extreme event loadings. In
general, bearings are not recommended for horizontal to
vertical load ratios of over 40 percent unless the bearings are
intended to act as fuses or irreparable damage is permitted.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
14.6.2—Characteristics
C14.6.2
The bearing chosen for a particular application shall
have appropriate load and movement capabilities.
Table 14.6.2-1 and Figure 14.6.2-1 may be used as a guide
when comparing the different bearing systems.
The following terminology shall apply to Table 14.6.2-1:
Practical bearings will often combine more than one
function to achieve the desired results. For example, a pot
bearing may be combined with a PTFE sliding surface to
permit translation and rotation.
Information in Table 14.6.2-1 is based on general
judgment and observation, and there will obviously be
some exceptions. Bearings listed as suitable for a specific
application are likely to be suitable with little or no effort
on the part of the Engineer other than good design and
detailing practice. Bearings listed as unsuitable are likely
to be marginal, even if the Engineer makes extraordinary
efforts to make the bearing work properly. Bearings listed
as suitable for limited application may work if the load and
rotation requirements are not excessive.
S
=
Suitable
U
=
Unsuitable
L
=
Suitable for limited applications
R
=
May be suitable, but requires special
considerations or additional elements such as
sliders or guideways
Long.
=
Longitudinal axis
Trans.
=
Transverse axis
Vert.
=
Vertical axis
Table 14.6.2-1—Bearing Suitability
Type of Bearing
Plain Elastomeric Pad
Movement
Long. Trans.
S
S
Rotation about Bridge
Axis Indicated
Long. Trans. Vert.
S
S
L
Resistance to Loads
Long. Trans.
Vert.
L
L
L
Fiberglass-Reinforced Pad
S
S
S
S
L
L
L
L
Cotton-Duck-Reinforced Pad
U
U
U
U
U
L
L
S
Steel-Reinforced Elastomeric Bearing
S
S
S
S
L
L
L
S
Plane Sliding Bearing
S
S
U
U
S
R
R
S
Curved Sliding Spherical Bearing
R
R
S
S
S
R
R
S
Curved Sliding Cylindrical Bearing
R
R
U
S
U
R
R
S
Disc Bearing
R
R
S
S
L
S
S
S
Double Cylindrical Bearing
R
R
S
S
U
R
R
S
Pot Bearing
R
R
S
S
L
S
S
S
Rocker Bearing
S
U
U
S
U
R
R
S
Knuckle Pinned Bearing
U
U
U
S
U
S
R
S
Single Roller Bearing
S
U
U
S
U
U
R
S
Multiple Roller Bearing
S
U
U
U
U
U
U
S
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 14: JOINTS AND BEARINGS
14-37
Figure 14.6.2-1—Common Bearing Types
14.6.3—Force Effects Resulting from Restraint of
Movement at the Bearing
14.6.3.1—Horizontal Force and Movement
Horizontal forces and moments induced in the bridge
by restraint of movement at the bearings shall be
determined using the movements and bearing
characteristics specified in Article 14.7. For bearings with
elastomeric elements, these characteristics should include,
but are not limited to, the consideration of increased shear
modulus, G, at temperatures below 73°F.
Expansion bearings and their supports shall be
designed in a manner such that the structure can undergo
movements to accommodate the seismic and other extreme
event displacement determined using the provisions in
Section 3 without collapse. Adequate support length shall
be provided for all bearings in accordance with
Article 4.7.4.4.
The Engineer shall determine the number of bearings
required to resist the loads specified in Section 3 with
consideration of the potential for unequal participation due
to tolerances, unintended misalignments, the capacity of
the individual bearings, and the skew.
Consideration should be given to the use of field
adjustable elements to provide near simultaneous
engagement of the intended number of bearings.
C14.6.3.1
Restraint of movement results in a corresponding
force or moment in the structure. These force effects
should be calculated taking into account the stiffness of the
bridge and the bearings. The latter should be estimated by
the methods outlined in Article 14.7. In some cases, the
bearing stiffness depends on time and temperature, as well
as on the movement. For example, the designer should take
note that in cold temperatures which approach the
appropriate minimum specified zone temperatures, the
shear modulus, G, of an elastomer may be as much as four
times that at 73°F. See Article 14.7.5.2 and AASHTO
M 251 for more information.
Expansion bearings should allow sufficient movement
in their unrestrained direction to prevent premature failure
due to seismic and other extreme event displacements.
Often, bearings do not resist load simultaneously, and
damage to only some of the bearings at one end of a span
is not uncommon. When this occurs, high load
concentrations can result at the location of the undamaged
bearings, which should be taken into account. The number
of bearings engaged should be based on type, design, and
detailing of the bearings used, and on the bridge skew.
Skew angles under 15 degrees are usually ignored. Skew
angles over 30 degrees are usually considered significant
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
14-38
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
At the strength and extreme event limit states,
horizontal forces transmitted to the superstructure and
substructure by bearings, Hbu , shall be taken as those
induced by sliding friction, rolling friction, or shear
deformation of a flexible element in the bearing.
Sliding friction force shall be taken as:
H bu = μPu
(14.6.3.1-1)
where:
Hbu =
lateral load transmitted to the superstructure and
substructure by bearings from applicable strength
and extreme event load combinations in
Table 3.4.1-1 (kip)
μ
coefficient of friction
=
Pu =
compressive force from applicable strength and
extreme event load combinations in Table 3.4.1-1
(kip)
and need to be considered in analysis. Skewed bridges
have a tendency to rotate under seismic loading, and
bearings should be designed and detailed to accommodate
this effect.
Horizontal forces transmitted to other bridge elements
by bearings do not include forces associated with the
deformations of stiff bearing elements or hard metal-onmetal contact of bearing components because provisions in
Article 14.7 are intended to avoid such contact.
Maximum extreme event limit state forces should be
considered when the bearing is not intended to act as a
fuse or irreparable damage is not permitted.
Special consideration should be given to bearings that
support large horizontal loads relative to the vertical load
(SCEF, 1991).
Eq. 14.6.3.1-1 is a function of vertical forces and
friction, and is a measure of the maximum horizontal force
which could be transmitted to the superstructure or
substructure before slip occurs. Eq. A13.3.2-2 is also a
measure of the maximum transmitted horizontal force, but
is dependant primarily upon the shear modulus (stiffness)
of the elastomer and applied lateral forces such as braking.
The force due to the deformation of an elastomeric
element shall be taken as:
H bu = GA
Δu
hrt
(14.6.3.1-2)
where:
G
=
shear modulus of the elastomer (ksi)
A
=
plan area of elastomeric element or bearing (in.2)
Δu =
shear deformation from applicable strength and
extreme event load combinations in Table 3.4.1-1
(in.)
hrt =
total elastomer thickness (in.)
Strength and extreme event limit states rolling forces
shall be determined by testing.
14.6.3.2—Moment
C14.6.3.2
At the strength and extreme event limit states, both the
substructure and superstructure shall be designed for the
largest moment, Mu, transferred by the bearing.
For curved sliding bearings without a companion flat
sliding surface, Mu shall be taken as:
M u = μPu R
(14.6.3.2-1)
For curved sliding bearings with a companion flat
sliding surface, Mu shall be taken as:
Maximum extreme event limit state forces should be
considered when the bearing is not intended to act as a
fuse or irreparable damage is not permitted.
The tangential force in curved sliding bearings is
caused by friction resistance at the curved surface, and it
acts about the center of the curved surface. Mu is the
moment due to this force that is transmitted by the bearing.
The moment imposed on individual components of the
bridge structure may be different from Mu depending on
the location of the axis of rotation and can be calculated by
a rational method.
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2012
Edition
SECTION 14: JOINTS AND BEARINGS
14-39
M u = 2μPu R
(14.6.3.2-2)
where:
Mu =
moment transmitted to the superstructure and
substructure by bearings from applicable strength
and extreme event load combinations in
Table 3.4.1-1 (kip-in.)
R
radius of curved sliding surface (in.)
=
For unconfined elastomeric bearings and pads, Mu
shall be taken as:
M u = 1.60(0.5Ec I )
θs
hrt
(14.6.3.2-3)
The load-deflection curve of an elastomeric bearing is
nonlinear, so Ec is load dependent. One acceptable
approximation for the effective modulus is:
Ec = 4.8GS 2
(C14.6.3.2-1)
where:
where:
=
moment of inertia of plan shape of bearing (in.4)
S
=
shape factor of an individual elastomer layer
Ec =
effective modulus of elastomeric bearing in
compression (ksi)
G
=
shear modulus of the elastomer (ksi)
I
θs
=
hrt =
maximum service limit state design rotation
angle specified in Article 14.4.2.1 (rad.)
total elastomer thickness (in.)
For CDP, Mu shall be taken as:
M u = 1.25 ( 4.5 − 2.2 S + 0.6σ s )
Ec I
tp
θs
(14.6.3.2-4)
where:
Ec =
uniaxial compressive stiffness of the CDP
bearing pad. It may be taken as 30 ksi in lieu of
pad-specific test data (ksi)
K = ( 4.5 − 2.2 S + 0.6σ s )
The moment, Mu, may be crucial for the design of
CDP, because movable CDP are normally designed with
PTFE sliding surfaces to develop the translational
movement capacity. Mu in the bearing pad results in edge
bearing stress on the PTFE in addition to the average
compressive stress. The PTFE on CDP pads is unconfined,
and this moment may limit the bearing stress on the PTFE
to a stress somewhat smaller than permitted on the CDP
alone.
tp
=
total thickness of CDP pad (in.)
S
=
shape factor of the CDP pad computed based on
Eq. 14.7.5.1-1 and based on total pad thickness
σs =
average compressive stress due to total load
associated with the maximum rotation from
applicable service load combinations in
Table 3.4.1-1 (ksi)
θs
maximum rotation of the CDP pad from
applicable service load combinations in
Table 3.4.1-1 (rad.)
=
For a more precise approximation of effective
modulus, the denominator of Eq. 14.7.5.3.3-15 may be
used along with a calculated Ba from Eq. C14.7.5.3.3-7 or
Eq. C14.7.5.3.3-8.
The factor 1.60 in Eq. 14.6.3.2-3 is an average
multiplier on total load on the bearing to estimate a
strength limit state load, Mu, based on a service limit state
rotation, θs.
The factor 1.25 in Eq. 14.6.3.2-4 is a multiplier on
total load on the bearing to estimate a strength limit state
load, Mu, based on a service limit state rotation, θs, and
stress, σs.
The rotational stiffness, K, of CDP is provided by:
Ec I
tp
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
(C14.6.3.2-2)
2012
Edition
14-40
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
14.6.4—Fabrication, Installation, Testing, and
Shipping
C14.6.4
The provisions for fabrication, installation, testing,
and shipping of bearings, specified in Section 18, “Bearing
Devices,” of the AASHTO LRFD Bridge Construction
Specifications, shall apply.
Some jurisdictions have provided additional guidance
beyond that provided in the AASHTO LRFD Bridge
Construction Specifications with respect to the fabrication,
installation, testing, and shipping of multirotational-type
bearings (SCEF, 1991).
Setting temperature is used in installing expansion
bearings.
An offset chart for girder erection and alignment of
the bearings is recommended to account for uncertainty in
the setting temperature at the time of design. Offset charts
should be defined in appropriate increments and included
in the design drawings so that the position of the bearing
can be adjusted to account for differences between setting
temperature and an assumed design installation
temperature.
The setting temperature of the bridge or any
component thereof shall be taken as the actual air
temperature averaged over the 24-hour period immediately
preceding the setting event.
14.6.5—Seismic and Other Extreme Event Provisions
for Bearings
14.6.5.1—General
C14.6.5.1
This Article shall apply to the analysis, design and
detailing of bearings to accommodate the effects of
earthquakes and, as appropriate, other extreme events for
which the horizontal loading component is very large.
These provisions shall be applied in addition to all
other applicable code requirements. The bearing-type
selection shall consider the criteria described in
Article 14.6.5.3 in the early stages of design.
14.6.5.2—Applicability
These provisions shall apply to pin, roller, rocker,
and bronze or copper-alloy sliding bearings, elastomeric
bearings, spherical bearings, and pot and disc bearings in
common slab-on-girder bridges but not to isolation-type
bearings or structural fuse bearings designed primarily
for the effects of extreme event dynamic horizontal
loadings.
Although the strategy taken herein assumes that
inelastic action is confined to properly detailed hinge areas
in substructures, alternative concepts that utilize
movement at the bearings to dissipate extreme event
horizontal and/or vertical forces may also be considered.
Where alternate strategies may be used, all ramifications
of the increased movements and the predictability of the
associated forces and transfer of forces shall be considered
in the design and details.
Extreme events other than earthquakes for which the
horizontal loading component is very large include vehicle
collisions, ship collisions, and high-velocity winds.
C14.6.5.2
2013 Revision
Provisions for the design, specification, testing, and
acceptance of isolation bearings are given in AASHTO
(1999).
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 14: JOINTS AND BEARINGS
14-41
14.6.5.3—Design Criteria
The selection, and the seismic or other extreme event
horizontal loading design of bearings shall be related to
the strength and stiffness characteristics of both the
superstructure and the substructure.
Bearing design shall be consistent with the intended
seismic or other extreme event response of the whole
bridge system.
Where rigid-type bearings are used, the seismic or
other horizontal extreme event forces from the
superstructure shall be assumed to be transmitted through
diaphragms or cross-frames and their connections to the
bearings and then to the substructure without reduction
due to local inelastic action along that load path. However,
forces may be reduced in situations where the enddiaphragms in the superstructure have been specifically
designed and detailed for inelastic action, in accordance
with generally accepted provisions for ductile enddiaphragms.
As a minimum, bearings, restraints, and anchorages
shall be designed to resist the forces specified in
Article 3.10.9.
C14.6.5.3
2013 Revision
The commentary provided below specifically
addresses seismic design considerations. However, it is
also applicable to other extreme event horizontal loadings
such as vehicle and ship collisions which are dynamic in
nature but can have a very short duration. Accounting for
the effects of other extreme events such as wind or waves
may require special considerations that are not fully
addressed in these specifications for bearing design.
Bearings have a significant effect on the overall
seismic response of a bridge. They provide the seismic
load transfer link between a stiff and massive
superstructure and a stiff and massive substructure. As a
result, very high (and difficult-to-predict) load
concentrations can occur in the bearing components. The
primary functions of the bearings are to resist the vertical
loads due to dead load and live load and to allow for
superstructure movements due to live load and temperature
changes. Allowance for translation is made by means of
rollers, rocker, or shear deformation of an elastomer, or
through the provision of a sliding surface of bronze or
copper alloy or PTFE. Allowance for rotation is made by
hinges, confined or unconfined elastomers, or spherical
sliding surfaces. Resistance to translation is provided by
bearing components or additional restraining elements.
Historically, bearings have been very susceptible to
seismic loads. Unequal loading during seismic events and
much higher loads than anticipated have caused various
types and levels of bearing damage. To allow movements,
bearings often contain elements vulnerable to high loads
and impacts.
The performance of bearings during past earthquakes
needs to be evaluated in context with the overall
performance of the bridge and the performance of the
superstructure and substructure elements connected to the
bearings. Rigid bearings have been associated with
damage to the end cross-frames and the supporting pier or
abutment concrete. In some cases, bearing damage and
slippage has prevented more extensive damage.
The criteria for seismic design of bearings should
consider the strength and stiffness characteristics of the
superstructure and substructure. To minimize damage, the
seismic load resisting system made of the end cross-frame
or diaphragms, bearings, and substructure should allow a
certain degree of energy dissipation, movement, or plastic
deformation even if those effects are not quantified as they
would be for seismic isolation bearings or structural fuses.
Based on their horizontal stiffness, bearings may be
divided into four categories:
•
Rigid bearings that transmit seismic loads without any
movement or deformations;
•
Deformable bearings that transmit seismic loads
limited by plastic deformations or restricted slippage
of bearing components;
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
14-42
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Elastomeric bearings having less than full rigidity, but
not designed explicitly as seismic isolators or fuses, may
be used under any circumstance. If used, they shall either
be designed to accommodate imposed seismic or other
horizontal extreme event loads, or, if survival of the
elastomeric bearing itself is not required, other means such
as restrainers, STUs, widened support lengths, or dampers
shall be provided to prevent unseating of the
superstructure.
•
Seismic isolation type bearings that transmit reduced
seismic loads, limited by energy dissipation; and,
•
Structural fuses that are designed to fail at a
prescribed load.
For the deformable-type bearing, limited and
reparable bearing damage and displacement may be
allowed for the design earthquake.
When both the superstructure and the substructure
components adjacent to the bearing are very stiff, a
deformable-type bearing should be considered.
Seismic isolation-type bearings are not within the
scope of these provisions, but they should also be
considered.
Elastomeric bearings have been demonstrated to result
in reduced force transmission to substructure.
A bearing may also be designed to act as a “structural
fuse” that will fail at a predetermined load changing the
articulation of the structure, possibly changing its period
and hence seismic response, and probably resulting in
increased movements. This strategy is permitted as an
alternative to these provisions under Article 14.6.5.2. Such
an alternative would require full consideration of forces
and movements and of bearing repair/replacement details.
It also requires the designer to address the inherent
difficulty of detailing a structural element to fail reliably at
predetermined load.
14.7—SPECIAL DESIGN PROVISIONS FOR
BEARINGS
14.7.1—Metal Rocker and Roller Bearings
14.7.1.1—General
C14.7.1.1
The rotation axis of the bearing shall be aligned with
the axis about which the largest rotations of the supported
member occur. Provision shall be made to ensure that the
bearing alignment does not change during the life of the
bridge. Multiple roller bearings shall be connected by
gearing to ensure that individual rollers remain parallel to
each other and at their original spacing.
Metal rocker and roller bearings shall be detailed so
that they can be easily inspected and maintained.
Rockers should be avoided wherever practical and,
when used, their movements and tendency to tip under
seismic actions shall be considered in the design and
details.
Cylindrical bearings contain no deformable parts and
are susceptible to damage if the superstructure rotates
about an axis perpendicular to the axis of the bearing.
Thus, they are unsuitable for bridges in which the axis of
rotation may vary significantly under different situations,
such as bridges with a large skew. They are also unsuitable
for use in seismic regions because the transverse shear
caused by earthquake loading can cause substantial
overturning moment.
Good maintenance is essential if mechanical bearings
are to perform properly. Dirt attracts and holds moisture,
which, combined with high local contact stresses, can
promote stress corrosion. Metal bearings, in particular,
must be designed for easy maintenance.
Rockers can be suitable for applications in which the
horizontal movement of the superstructure, relative to the
substructure, is well within the available movement range
after consideration of other applicable movements.
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All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 14: JOINTS AND BEARINGS
14-43
14.7.1.2—Materials
C14.7.1.2
Rocker and roller bearings shall be made of stainless
steel conforming to ASTM A240, as specified in
Article 6.4.7, or of structural steel conforming to AASHTO
M 169 (ASTM A108), M 102M/M 102 (ASTM
A668/A668M), or M 270M/M 270 (ASTM A709/A709M),
Grades 36, 50, or 50W. Material properties of these steels
shall be taken as specified in Table 6.4.1-1 and
Table 6.4.2-1.
14.7.1.3—Geometric Requirements
C14.7.1.3
The dimensions of the bearing shall be chosen taking
into account both the contact stresses and the movement of
the contact point due to rolling.
Each individual curved contact surface shall have a
constant radius. Bearings with more than one curved
surface shall be symmetric about a line joining the centers
of their two curved surfaces.
If pintles or gear mechanisms are used to guide the
bearing, their geometry should be such as to permit free
movement of the bearing.
Bearings shall be designed to be stable. If the bearing
has two separate cylindrical faces, each of which rolls on a
flat plate, stability may be achieved by making the
distance between the two contact lines no greater than the
sum of the radii of the two cylindrical surfaces.
14.7.1.4—Contact Stresses
For cylindrical surfaces:
PS ≤ 8
•
Fy 2
D1 Es
1 −
D2
(14.7.1.4-1)
F3
y
Es 2
(14.7.1.4-2)
WD1
For spherical surfaces:
D
1
PS ≤ 40
D1
1− D
2
2
where:
D1 =
The choice of radius for a curved surface is a
compromise: a large radius results in low contact stresses
but large rotations of the point of contact and vice versa.
The latter could be important if, for example, a rotational
bearing is surmounted by a PTFE slider because the PTFE
is sensitive to eccentric loading.
A cylindrical roller is in neutral equilibrium. The
provisions for bearings with two curved surfaces achieves
at least neutral, if not stable, equilibrium.
C14.7.1.4
At the service limit state, the contact load, PS, shall
satisfy:
•
Carbon steel has been the traditional steel used in
mechanical bearings because of its good mechanical
properties. Surface hardening may be considered.
Corrosion resistance is also important. The use of stainless
steel for the contact surfaces may prove economical when
life-cycle costs are considered. Weathering steels should
be used with caution as their resistance to corrosion is
often significantly reduced by mechanical wear at the
surface.
diameter of the rocker or roller surface (in.)
The service limit state loads are limited so that the
contact causes calculated shear stresses no higher than
0.55 Fy or surface compression stresses no higher than 1.65
Fy. The maximum compressive stress is at the surface, and
the maximum shear stress occurs just below it.
The formulas were derived from the theoretical value
for contact stress between elastic bodies (Roark and
Young, 1976). They are based on the assumption that the
width of the contact area is much less than the diameter of
the curved surface.
If two surfaces have curves of the opposite sign, the
value of D2 is negative. This would be an unusual situation
in bridge bearings.
If careful inspection indicates that existing bearings
which do not satisfy these provisions are performing well
and there is no evidence of rutting or ridging, which may
be evidence of local yielding, then reuse of the bearing
may be viable. Evaluation of roller and rocker bearings
with flat mating surfaces may proceed using the following
historical provision:
Bearing per linear in. on expansion rockers and rollers
at the service limit state shall not exceed the values
obtained by the following formulas:
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
14-44
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Diameters up to 25.0 in.
p=
Fy − 13
20
(0.6 d )
(C14.7.1.4-1)
Diameters 25.0 to 125.0 in.
p=
Fy −13
20
3 d
(C14.7.1.4-2)
where:
p
=
allowable bearing at the service limit state
(kip/in.)
d
=
diameter of rocker or roller (in.)
Fy =
D2 =
diameter of the mating surface (in.) taken as:
•
Positive if the curvatures have the same sign, and
•
Infinite if the mating surface is flat.
Fy =
specified minimum yield strength of the weakest
steel at the contact surface (ksi)
Es =
Young’s modulus for steel (ksi)
W =
width of the bearing (in.)
specified minimum yield strength of the weakest
steel at the contact surface (ksi)
If loads are increased significantly by the rehabilitation or
the mating surface is curved, complying with the current
provisions may be more appropriate.
The two diameters have the same sign if the centers of
the two curved surfaces in contact are on the same side of
the contact surface, such as is the case when a circular
shaft fits in a circular hole.
14.7.2—PTFE Sliding Surfaces
C14.7.2
PTFE may be used in sliding surfaces of bridge
bearings to accommodate translation or rotation. All PTFE
surfaces other than guides shall satisfy the requirements
specified herein. Curved PTFE surfaces shall also satisfy
Article 14.7.3.
PTFE, is also known as TFE and is commonly used in
bridge bearings in the United States. This Article does not
cover guides. The friction requirements for guides are less
stringent, and a wider variety of materials and fabrication
methods can be used for them.
14.7.2.1—PTFE Surface
The PTFE surface shall be made from pure virgin
PTFE resin satisfying the requirements of ASTM D4894
or D4895. It shall be fabricated as unfilled sheet, filled
sheet, or fabric woven from PTFE and other fibers.
Unfilled sheets shall be made from PTFE resin alone.
Filled sheets shall be made from PTFE resin uniformly
blended with glass fibers, carbon fibers, or other chemically
inert filler. The filler content shall not exceed 15 percent for
glass fibers and 25 percent for carbon fibers.
C14.7.2.1
PTFE may be provided in sheets or in mats woven
from fibers. The sheets may be filled with reinforcing
fibers to reduce creep, i.e., cold flow, and wear, or they
may be made from pure resin. The friction coefficient
depends on many factors, such as sliding speed, contact
pressure, lubrication, temperature, and properties such as
the finish of the mating surface (Campbell and Kong,
1987). The material properties that influence the friction
coefficient are not well understood, but the crystalline
structure of the PTFE is known to be important, and it is
strongly affected by the quality control exercised during
the manufacturing process.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 14: JOINTS AND BEARINGS
Sheet PTFE may contain dimples to act as reservoirs
for lubricant. Unlubricated PTFE may also contain
dimples. Their diameter shall not exceed 0.32 in. at the
surface of the PTFE, and their depth shall be not less than
0.08 in. and not more than half the thickness of the PTFE.
The reservoirs shall be uniformly distributed over the
surface area and shall cover more than 20 percent but less
than 30 percent of the contact surface. Dimples should not
be placed to intersect the edge of the contact area.
Lubricant shall be silicone grease, which satisfies Society
of Automotive Engineers Specification SAE-AS8660.
Woven fiber PTFE shall be made from pure PTFE
fibers. Reinforced woven fiber PTFE shall be made by
interweaving high-strength fibers, such as glass, with the
PTFE in such a way that the reinforcing fibers do not
appear on the sliding face of the finished fabric.
14.7.2.2—Mating Surface
The PTFE shall be used in conjunction with a mating
surface. Flat mating surfaces shall be stainless steel, and
curved mating surfaces shall be stainless steel or anodized
aluminum. Flat surfaces shall be stainless steel, Type 304,
conforming to either ASTM A167 or A264, and shall be
provided with a surface finish of 8.0 μ-in. RMS or better.
Finishes on curved metallic surfaces shall not exceed 16.0
μ-in. RMS. The mating surface shall be large enough to
cover the PTFE at all times.
14-45
Unfilled dimples can act as reservoirs for
contaminants (dust, etc.) which can help to keep these
contaminants from the contact surface.
C14.7.2.2
Stainless steel is the most commonly used mating
surface for PTFE sliding surfaces. Anodized aluminum has
been sometimes used in spherical and cylindrical bearings
produced in other countries and may be considered if
documentation of experience, acceptable to the Owner, is
provided. The finish of this mating surface is extremely
important because it affects the coefficient of friction.
ASTM A240, Type 304, stainless steel, with a surface
finish of 16.0 μ-in. RMS or better, is appropriate, but the
surface measurements are inherently inexact, and hence it
is not a specified alternative. Friction testing is required for
the PTFE and its mating surface because of the many
variables involved.
14.7.2.3—Minimum Thickness
14.7.2.3.1—PTFE
C14.7.2.3.1
For all applications, the thickness of the PTFE shall
be at least 0.0625 in. after compression. Recessed sheet
PTFE shall be at least 0.1875 in. thick when the maximum
dimension of the PTFE is less than or equal to 24.0 in.,
and 0.25 in. when the maximum dimension of the PTFE is
greater than 24.0 in. Woven fabric PTFE, which is
mechanically interlocked over a metallic substrate, shall
have a minimum thickness of 0.0625 in. and a maximum
thickness of 0.125 in. over the highest point of the
substrate.
A minimum thickness is specified to ensure uniform
bearing and to allow for wear.
During the first few cycles of movement, small
amounts of PTFE transfer to the mating surface and
contribute to the very low friction achieved subsequently.
This wear is acceptable and desirable.
PTFE continues to wear with time (Campbell and Kong,
1987) and movement; wear is exacerbated by deteriorated or
rough surfaces. Wear is undesirable because it usually causes
higher friction and reduces the thickness of the remaining
PTFE. Unlubricated, flat PTFE wears more severely than the
lubricated material. The evidence on the rate of wear is
tentative. High travel speeds, such as those associated with
traffic movements, appear to be more damaging than the
slow ones due to thermal movements. However, they may be
avoided by placing the sliding surface on an elastomeric
bearing that will absorb small longitudinal movements. No
further allowance for wear is made in this Specification due
to the limited research available to quantify or estimate the
wear as a function of time and travel. However, wear may
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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14-46
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
ultimately cause the need for replacement of the PTFE, so it
is wise to allow for future replacement in the original design.
C14.7.2.3.2
14.7.2.3.2—Stainless Steel Mating Surfaces
The thickness of the stainless steel mating surface
shall be at least 16 gage when the maximum dimension of
the surface is less than or equal to 12.0 in. and at least
13 gage when the maximum dimension is larger than
12.0 in.
Backing plate requirements shall be taken as specified
in Article 14.7.2.6.2.
14.7.2.4—Contact Pressure
The minimum thickness requirements for the mating
surface are intended to prevent it from wrinkling or
buckling. This surface material is usually quite thin to
minimize cost of the highly finished mating surface. Some
mating surfaces, particularly those with curved surfaces,
are made of carbon steel on which a stainless steel weld is
deposited. This welded surface is then finished and
polished to achieve the desired finish. Some jurisdictions
require a minimum thickness of 0.094 in. for welded
overlay after grinding and polishing.
C14.7.2.4
The contact stress between the PTFE and the mating
surface shall be determined at the service limit state using
the nominal area.
The average contact stress shall be computed by
dividing the load by the projection of the contact area on a
plane perpendicular to the direction of the load. The
contact stress at the edge shall be determined by taking
into account the maximum moment transferred by the
bearing assuming a linear distribution of stress across the
PTFE.
Stresses shall not exceed those given in
Table 14.7.2.4-1. Permissible stresses for intermediate
filler contents shall be obtained by linear interpolation
within Table 14.7.2.4-1.
The average contact stress shall be determined by
dividing the load by the projection of the contact area onto
a plane perpendicular to the direction of the load. The edge
contact stress shall be determined based on the service
limit state load and the maximum service limit state
moment transferred by the bearing.
The contact pressure must be limited to prevent
excessive creep or plastic flow of the PTFE, which causes
the PTFE disc to expand laterally under compressive stress
and may contribute to separation or bond failure. The
lateral expansion is controlled by recessing the PTFE into a
steel plate or by reinforcing the PTFE, but there are
adverse consequences associated with both methods. Edge
loading may be particularly detrimental because it causes
large stress and potential flow in a local area near the edge
of the material in hard contact between steel surfaces. The
average and edge contact pressure in Table 14.7.2.4-1 are
in appropriate proportions to one another relative to the
currently available research. Better data may become
available in the future. These are in the lower range of
those used in Europe.
Table 14.7.2.4-1—Maximum Contact Stress for PTFE at the Service Limit State (ksi)
Material
Unconfined PTFE:
Unfilled Sheets
Filled Sheets with
Maximum Filler Content
Confined Sheet PTFE
Woven PTFE Fiber over a Metallic
Substrate
Reinforced Woven PTFE over a
Metallic Substrate
Average Contact Stress (ksi)
Permanent
Loads
All Loads
Edge Contact Stress (ksi)
Permanent
Loads
All Loads
1.5
2.5
2.0
3.0
3.0
3.0
4.5
4.5
3.5
3.5
5.5
5.5
3.0
4.5
3.5
5.5
4.0
5.5
4.5
7.0
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2012
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SECTION 14: JOINTS AND BEARINGS
14.7.2.5—Coefficient of Friction
The service limit design coefficient of friction of the
PTFE sliding surface shall be taken as specified in
Table 14.7.2.5-1. Intermediate values may be determined
by interpolation. The coefficient of friction shall be
determined by using the stress level associated with the
applicable load combination specified in Table 3.4.1-1.
Lesser values may be used if verified by tests.
Where friction is required to resist nonseismic loads,
the design coefficient of friction under dynamic loading
may be taken as not more than ten percent of the values
listed in Table 14.7.2.5-1 for the bearing stress and PTFE
type indicated.
The coefficients of friction in Table 14.7.2.5-1 are
based on a 8.0 μ-in. finish mating surface. Coefficients of
friction for rougher surface finishes must be established by
test results in accordance with the AASHTO LRFD Bridge
Construction Specifications, Chapter 18.
The contract documents shall require certification
testing from the production lot of PTFE to ensure that the
friction actually achieved in the bearing is appropriate for
the bearing design.
14-47
C14.7.2.5
The friction factor decreases with lubrication and
increasing contact stress but increases with sliding velocity
(Campbell and Kong, 1987). The coefficient of friction
also tends to increase at low temperatures. Static friction is
larger than dynamic friction, and the dynamic coefficient
of friction is larger for the first cycle of movement than it
is for later cycles. Friction increases with increasing
roughness of the mating surface and decreasing
temperature. The friction factors used in the earlier
editions of the AASHTO Standard Specifications are
suitable for use with dimpled, lubricated PTFE. They are
too small for the flat, dry PTFE commonly used in the
United States. These Specifications have been changed to
recognize this fact. Nearly all research to date has been
performed on dimpled, lubricated PTFE. The coefficients
of friction given in Table 14.7.2.5-1 are not applicable to
high-velocity movements such as those occurring in
seismic events. Seismic velocity coefficients of friction
must be determined in accordance with the AASHTO
Guide Specifications for Seismic Isolation Design.
Coefficients of friction, somewhat smaller than those given
in Table 14.7.2.5-1, are possible with care and quality
control.
Certification testing from the production lot is
essential for PTFE sliding surfaces primarily to ensure that
the friction actually achieved in the bearing is appropriate
for the bearing design. Testing is the only reliable method
for certifying the coefficient of friction and bearing
behavior.
Contamination of the sliding surface with dirt and dust
increases the coefficient of friction and increases the wear
of the PTFE. To prevent contamination, the bearing should
be sealed by the manufacturer and not separated at the
construction site. To prevent contamination and gouging of
the PTFE, the stainless steel should normally be on top and
should be larger than the PTFE, plus its maximum travel.
Woven PTFE is sometimes formed by weaving pure
PTFE strands with a reinforcing material. These
reinforcing strands may increase the resistance to creep
and cold flow and can be woven so that reinforcing strands
do not appear on the sliding surface. This separation is
necessary if the coefficients of friction provided in
Table 14.7.2.5-1 are to be used.
If there is no lubricant in the dimples, the dimples tend
to flatten out filling the dimples, resulting in a surface
much like unfilled PTFE.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Table 14.7.2.5-1—Design Coefficients of Friction—Service Limit State
Type PTFE
Dimpled Lubricated
Coefficient of Friction
Pressure
(ksi)
Temperature
(°F)
68
−13
−49
0.5
1.0
2.0
>3.0
0.04
0.06
0.10
0.030
0.045
0.075
0.025
0.040
0.060
0.020
0.030
0.050
68
−13
−49
68
−13
−49
68
−13
−49
0.08
0.20
0.20
0.24
0.44
0.65
0.08
0.20
0.20
0.070
0.180
0.180
0.170
0.320
0.550
0.070
0.180
0.180
0.050
0.130
0.130
0.090
0.250
0.450
0.060
0.130
0.130
0.030
0.100
0.100
0.060
0.200
0.350
0.045
0.100
0.100
Unfilled or Dimpled
Unlubricated
Filled
Woven
14.7.2.6—Attachment
14.7.2.6.1—PTFE
C14.7.2.6.1
Sheet PTFE confined in a recess in a rigid metal
backing plate for one-half its thickness may be bonded or
unbonded.
Sheet PTFE that is not confined shall be bonded to a
metal surface or an elastomeric layer with a Shore A
durometer hardness of at least 90 by an approved method.
Woven PTFE on a metallic substrate shall be attached
to the metallic substrate by mechanical interlocking that
can resist a shear force no less than 0.10 times the applied
compressive force.
14.7.2.6.2—Mating Surface
The mating surface for flat sliding surfaces shall be
attached to a backing plate by welding in such a way that it
remains flat and in full contact with its backing plate
throughout its service life. The weld shall be detailed to
form an effective moisture seal around the entire perimeter
of the mating surface to prevent interface corrosion. The
attachment shall be capable of resisting the maximum
friction force that can be developed by the bearing under
service limit state load combinations. The welds used for
the attachment shall be clear of the contact and sliding area
of the PTFE surface.
Recessing is the most effective way of preventing creep
in unfilled PTFE. The PTFE discs may also be bonded into
the recess, but this is optional and the benefits are debatable.
Bonding helps to retain the PTFE in the recess during the
service life of the bridge, but it makes replacement of the
disc more difficult. If the adhesive is not applied uniformly it
can cause an uneven PTFE sliding surface that could lead to
premature wear. Some manufacturers cut the PTFE slightly
oversize and pre-cool it before installation because this
results in a tighter fit at room temperature.
Sometimes PTFE is bonded to the top cover layer of
an elastomeric bearing. This layer should be relatively
thick and hard to avoid rippling of the PTFE (Roeder et al.,
1987). PTFE must be etched prior to epoxy bonding in
order to obtain good adhesion. However, ultra-violet light
attacks the etching and can lead to delamination, so PTFE
exposed to ultra-violet light should not be attached by
bonding alone.
C14.7.2.6.2
The restrictions on the attachment of the mating
surface are primarily intended to ensure that the surface is
flat and retains uniform contact with the PTFE at all times,
without adversely affecting the friction of the surface or
gouging or cutting the PTFE.
The mating surface of curved sliding surfaces should
be machined to the required surface finish from a single
piece.
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SECTION 14: JOINTS AND BEARINGS
14-49
14.7.3—Bearings with Curved Sliding Surfaces
14.7.3.1—General
C14.7.3.1
Bearings with curved sliding surfaces shall consist of
two metal parts with matching curved surfaces and a low
friction sliding interface. The curved surfaces may be
either cylindrical or spherical. The material properties,
characteristics, and frictional properties of the sliding
interface shall satisfy the requirements specified in
Articles 14.7.2 and 14.7.7.
The two surfaces of a sliding interface shall have
equal nominal radii.
These provisions are directed primarily toward
spherical or cylindrical bearings with bronze or PTFE
sliding surfaces.
Some jurisdictions require that the minimum center
thickness of concave spherical surfaces be at least 0.75 in.
and that a minimum vertical clearance between the
rotating and nonrotating parts be as given by
Eqs. C14.7.3.1-1 or C14.7.3.1-2 but not less than 0.125 in.
•
For rectangular spherical or curved bearings:
c = 0.7 Dθu + 0.125
•
(C14.7.3.1-1)
For round spherical or round bearings:
c = 0.5 Dθu + 0.125
(C14.7.3.1-2)
where:
θu =
design rotation from applicable strength
load combinations in Table 3.4.1-1 or
Article 14.4.2.2.1 (rad.)
Similarly, the minimum edge thickness on the convex
surface has sometimes been limited to 0.75 in. for bearing
on concrete and 0.50 in. for bearing on steel.
14.7.3.2—Bearing Resistance
C14.7.3.2
The radius of the curved surface shall be large enough
to ensure that the total compressive load at the service
limit state on the horizontal projected area of the bearing,
Ps, is less than or equal to the average allowable load as
computed from the service stress specified in
Articles 14.7.2.4 or 14.7.7.3.
•
For cylindrical bearings:
Ps ≤ φDW σ SS
•
(14.7.3.2-1)
For spherical bearings:
Ps ≤ φ
πD 2 σ SS
4
(14.7.3.2-2)
The geometry of a spherical bearing controls its
ability to resist lateral loads, its moment-rotation behavior,
and its frictional characteristics. The geometry is relatively
easy to define, but it has some consequences that are not
widely appreciated. The stress may vary over the contact
surface of spherical or cylindrical bearings. Cylindrical
and spherical surfaces cannot be machined as accurately
as a flat smooth surface. It is important that the radius of
the convex and concave surfaces be within appropriate
limits. If these limits are exceeded the bronze may crack
due to hard bearing contact, or there may be excessive
wear and damage due to creep or cold flow of the PTFE.
The stress limits used in this Section are based on average
contact stress levels.
where:
Ps =
total compressive load from applicable service
load combinations in Table 3.4.1-1 (kip)
D
diameter of the projection of the loaded surface
of the bearing in the horizontal plane (in.)
=
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
σSS =
maximum average contact stress at the service
limit state permitted on PTFE by
Table 14.7.2.4-1
or
on
bronze
by
Table 14.7.7.3-1 (ksi)
W =
length of cylinder (in.)
φ
resistance factor taken as 1.0
=
14.7.3.3—Resistance to Lateral Load
C14.7.3.3
Where bearings are required to resist horizontal loads
at the service limit state, an external restraint system shall
be provided or:
•
For a cylindrical sliding surface, the horizontal load
shall satisfy:
H s ≤ 2 RW σ SS sin(ψ − β − θu ) sin β (14.7.3.3-1)
•
For a spherical surface, the horizontal load shall
satisfy:
H s ≤ πR 2 σ SS sin(ψ − β − θu ) sin β
(14.7.3.3-2)
The geometry of a curved bearing combined with
gravity loads can provide considerable resistance to lateral
load. An external restraint is often a more reliable method
of resisting large lateral loads at the service and strength
limit states, and at the extreme event limit state when the
bearing is not intended to act as a fuse or irreparable
damage is not permitted.
The applied loads for determination of the angle β and
the applied load check are at the service limit state because
the stress limits, σss, are service-based. The rotation at the
strength limit state is utilized because bearings with curved
sliding surfaces are susceptible to more serious
consequences if overloaded or over rotated.
The geometry of a cylindrical sliding bearing is shown
in the deformed position in Figure C14.7.3.3-1.
in which:
H
β = tan −1 s
PD
(14.7.3.3-3)
and
L
ψ = sin −1
2R
(14.7.3.3-4)
where:
Hs =
horizontal load from applicable service load
combinations in Table 3.4.1-1 (kip)
L
projected length of the sliding
perpendicular to the rotation axis (in.)
=
PD =
R
=
surface
compressive load at the service limit state (load
factor = 1.0) due to permanent loads (kip)
Figure C14.7.3.3-1—Bearing Geometry
radius of curved sliding surface (in.)
W =
length of cylindrical surface (in.)
β
=
angle between the vertical and resultant applied
load (rad.)
θu =
maximum strength limit state design rotation
angle specified in Article 14.4.2.2.1 (rad.)
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2012
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SECTION 14: JOINTS AND BEARINGS
14-51
σSS =
maximum average contact stress at the
service limit state permitted on PTFE
by Table 14.7.2.4-1 or on bronze by
Table 14.7.7.3-1 (ksi)
Ψ
subtended semiangle of the curved surface (rad.)
=
14.7.4—Pot Bearings
14.7.4.1—General
Where pot bearings are provided with a PTFE slider to
provide for both rotation and horizontal movement, such
sliding surfaces and any guide systems shall be designed in
accordance with the provisions of Articles 14.7.2 and 14.7.9.
The rotational elements of the pot bearing shall consist
of at least a pot, a piston, an elastomeric disc, and sealing
rings.
For the purpose of establishing the forces and
deformations imposed on a pot bearing, the axis of rotation
shall be taken as lying in the horizontal plane at midheight
of the elastomeric disc.
The minimum vertical load on a pot bearing should
not be less than 20 percent of the vertical design load.
14.7.4.2—Materials
C14.7.4.2
The elastomeric disc shall be made from a
compound based on virgin natural rubber or virgin
neoprene conforming to the requirements of Section 18.3
of the AASHTO LRFD Bridge Construction
Specifications. The nominal hardness shall lie between
50 and 60 on the Shore A scale.
The pot and piston shall be made from structural steel
conforming to AASHTO M 270M/M 270 (ASTM
A709/A709); Grades 36, 50, or 50W; or from stainless
steel conforming to ASTM A240. The finish of surfaces in
contact with the elastomeric pad shall be smoother than 60
μ-in. The yield strength and hardness of the piston shall
not exceed that of the pot.
Brass sealing rings satisfying Articles 14.7.4.5.2 and
14.7.4.5.3 shall conform to ASTM B36 (half hard) for
rings of rectangular cross-section, and Federal
Specification QQB626, Composition 2, for rings of
circular cross-section.
14.7.4.3—Geometric Requirements
C14.7.4.3
The depth of the elastomeric disc, hr, shall satisfy:
hr ≥ 3.33D p θu
Softer elastomers permit rotation more readily and are
preferred.
Corrosion resistant steels, such as AASHTO
M 270M/M 270 (ASTM A709/A709), Grade 50W, are not
recommended for applications where they may come into
contact with saltwater or be permanently damp, unless
their whole surface is completely corrosion protected. Most
pot bearings are machined from a solid plate, so use of
high-strength steel to decrease the wall thickness results in
only a very small reduction in volume of material used.
Other properties, such as corrosion resistance, ease of
machining, electrochemical compatibility with steel
girders, availability, and price should also be considered.
The provision on relative hardness is mentioned to avoid
wear or damage on the inside surface of the pot and the
consequent risk of seal failure.
The choice of brass for sealing rings reflects present
practice.
(14.7.4.3-1)
where:
Dp =
internal diameter of pot (in.)
θu =
maximum strength limit state design rotation
angle specified in Article 14.4.2.2.1 (rad.)
The requirements of this Article are intended to
prevent the seal from escaping and the bearing from
locking up even under the most adverse conditions. Use of
the design rotation, θu, means that the designer should
account for both the anticipated movements due to loads
and those due to fabrication and installation tolerances,
including the rotation imposed on the bearing due to
out-of-level of other bridge components, such as
undersides of prefabricated girders, and permissible
misalignments during construction. Vertical deflection
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14-52
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The dimensions of the elements of a pot bearing shall
satisfy the following requirements under the least
favorable combination of strength limit state displacements
and rotations:
•
The pot shall be deep enough to permit the seal and
piston rim to remain in full contact with the vertical
face of the pot wall, and
•
Contact or binding between metal components shall
not prevent further displacement or rotation.
caused by compressive load should also be taken into
account because it will reduce the available clearance.
Anchor bolts projecting above the base plate should be
taken into consideration when clearance is determined.
Rotation capacity can be increased by using a deeper
pot, a thicker elastomeric pad, and a larger vertical
clearance between the pot wall and the piston or slider. The
minimum thickness of the pad specified herein results in
edge deflections due to rotation no greater than 15 percent
of the nominal pad thickness. Figure C14.7.4.3-1 and
Eqs. C14.7.4.3-1 and C14.7.4.3-2 may be used to verify
clearance.
Figure C14.7.4.3-1—Pot Bearing—Critical Dimensions for
Clearances
The pot cavity depth, hp1, may be determined as:
(
)
hp1 ≥ 0.5D p θu + hr + hw
(C14.7.4.3-1)
where:
hr
=
hw =
depth of elastomeric disc (in.)
height from top of rim to underside of piston (in.)
The vertical clearance between top of piston and top of
pot wall, hp2 may be determined as:
hp2 ≥ Ro θu + 2δu + 0.125
(C14.7.4.3-2)
where:
=
vertical deflection from applicable strength load
combinations in Table 3.4.1-1 (in.)
Ro =
radial distance from center of pot to object in
question (e.g., pot wall, anchor bolt, etc.) (in.)
δu
Note that Eq. C14.7.4.3-1 does not contain any allowance
for vertical deflection δu. This omission is conservative.
The design rotation, θu, already represents an extreme
rotation for use with the strength limit state and requires no
further factoring.
δu and θu may also be considered at the extreme event
limit state.
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SECTION 14: JOINTS AND BEARINGS
14-53
Thicker pads with deeper pots cause smaller strains in
the elastomer, and they appear to experience less wear and
abrasion. Recessing of the rings into the pad is necessary
for satisfactory pad performance, but it also decreases the
effective thickness of the pad at that location. Further, the
recess has sometimes been cut into the pad, and this cut
appears to make the pad susceptible to additional damage.
Therefore, it is generally better to use a deeper pot and
thicker pad even though this leads to greater material and
machining costs.
14.7.4.4—Elastomeric Disc
The average stress on the elastomer at the service
limit state should not exceed 3.5 ksi.
To facilitate rotation, the top and bottom surfaces of
the elastomer shall be treated with a lubricant that is not
detrimental to the elastomer. Alternatively, thin PTFE
discs may be used on the top and bottom of the elastomer.
C14.7.4.4
The average stress on the elastomeric disc is largely
limited by the seal’s ability to prevent escape of the
elastomer. The 3.5 ksi level has been used as a practical
upper limit for some years, and most bearings have
performed satisfactorily but a few seal failures have
occurred. The experimental research of NCHRP 10-20A
showed that greater wear and abrasion due to cyclic
rotation occurred when higher stress levels are employed,
but this correlation is not strong. As a result, the 3.5 ksi
stress limit is retained as a practical design limit.
Lubrication helps prevent abrasion of the elastomer
during cyclic rotation, however, research has shown that
the beneficial effect of the lubrication tends to be lost with
time. Silicon grease has been used with success. It
performed well in experiments and is recommended. Thin
sheets of PTFE have also been used. These sheets
performed quite well in experimental studies, but they are
less highly recommended because there is a concern that
they may wrinkle and become ineffective. Powdered
graphite has been used but has not performed well in
rotation experiments. As a result, silicon grease is the
preferred lubricant, and powdered graphite is not
recommended. PTFE discs are permitted as a method of
lubrication, but the user should be aware that some
problems have been reported.
14.7.4.5—Sealing Rings
C14.7.4.5.1
14.7.4.5.1—General
A seal shall be used between the pot and the piston.
At the service limit state seals shall be adequate to prevent
escape of elastomer under compressive load and
simultaneously applied cyclic rotations. At the strength
limit state, seals shall also be adequate to prevent escape
of elastomer under compressive load and simultaneously
applied static rotation.
Brass rings satisfying the requirements of either
Articles 14.7.4.5.2 or 14.7.4.5.3 may be used without
testing to satisfy the above requirements. The Engineer
may approve other sealing systems on the basis of
experimental evidence.
Failure of seals has been one of the most common
problems in pot bearings. Multiple flat brass rings, circular
brass rod formed and brazed into a ring, and proprietary
plastic rings have been found to be successful.
Experimental research suggests that solid circular brass
rings provide a tight fit and prevent leakage of the
elastomer, but they experience severe wear during cyclic
rotation. Experiments suggest that flat brass rings are
somewhat more susceptible to elastomer leakage and
fracture, but they are less prone to wear. PTFE rings should
not be used. The rings should preferably be recessed into
the elastomer or vulcanized to it in order to minimize
distortion of the elastomer.
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2012
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14-54
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Cyclic rotation of the bearing due to temperature
variations or traffic loading can cause chafing of the
elastomer against the pot wall, which can give rise to some
loss of elastomer past the seal. The detail design of the
sealing system is important in preventing this. The details
of the tests for alternative sealing systems are left to the
discretion of the Engineer. However, tests should include
cyclic rotation.
14.7.4.5.2—Rings with Rectangular Cross-Sections
Three rectangular rings shall be used. Each ring shall
be circular in plan but shall be cut at one point around its
circumference. The faces of the cut shall be on a plane at
45 degrees to the vertical and to the tangent of the
circumference. The rings shall be oriented so that the cuts
on each of the three rings are equally spaced around the
circumference of the pot.
The width of each ring shall not be less than either
0.02 Dp or 0.25 in. and shall not exceed 0.75 in. The depth
of each shall not be less than 0.2 times its width.
14.7.4.5.3—Rings with Circular Cross-Sections
One circular closed ring shall be used with an outside
diameter of Dp. It shall have a cross-sectional diameter not
less than either 0.0175 Dp or 0.15625 in.
14.7.4.6—Pot
C14.7.4.6
The pot shall consist at least of a wall and base. All
elements of the pot shall be designed to act as a single
structural unit.
The minimum thickness of a base bearing directly
against concrete or grout shall satisfy:
•
tb ≥ 0.06 D p and
•
tb ≥ 0.75in.
(14.7.4.6-1)
(14.7.4.6-2)
The thickness of a base bearing directly on steel
girders or load distribution plates shall satisfy:
•
tb ≥ 0.04 D p and
•
tb ≥ 0.50in.
(14.7.4.6-3)
(14.7.4.6-4)
The minimum pot wall thickness, tw, for an unguided
sliding pot bearing shall satisfy:
tw ≥
Dp σs
1.25 Fy
(14.7.4.6-5)
and:
tw ≥ 0.75in.
(14.7.4.6-6)
Pots are constructed most reliably by machining from
a single plate. For very large bearings, this may become
prohibitively expensive, so fabrication by welding a ring to
a base plate is implicitly accepted. However, the ring must
be attached to the plate by a full penetration weld because
the wall is subject to significant bending moments where it
joins the base plate. The quality of welding should be
assured by quality control. The finished inside profile of
the pot must satisfy the required shape and tolerances.
Straightening and machining may be needed to rectify
welding distortions.
The lower bounds on the thickness of the base plate
are intended to provide some rigidity to counteract the
effects of uneven bearing. If the base plate was to deform
significantly, the volume of elastomer would be inadequate
to fill the space in the pot, and hard contact could occur
between some elements.
Eqs. 14.7.4.6-5 and 14.7.4.6-6 define minimum wall
thickness requirements for unguided pot bearings.
Eq. 14.7.4.6-5 is based upon hoop strength of the pot walls
with the elastomeric disc under hydrostatic compressive
stress. This equation is conservative for this application,
because it neglects the beneficial effect of the bending
strength and stiffness at the pot wall-base interface.
However, this equation provides no lateral (horizontal)
resistance to the bearing, and it is limited to unguided
bearings (Stanton, 1999).
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SECTION 14: JOINTS AND BEARINGS
14-55
where:
tw
=
pot wall thickness (in.)
Fy =
yield strength of the steel (ksi)
Dp =
internal diameter of pot (in.)
σs
average compressive stress due to total load from
applicable service load combinations in
Table 3.4.1-1 (ksi)
=
The wall thickness (tw) and base thickness (tb) of
guided or fixed pots shall also satisfy the requirements of
Eq. 14.7.4.7-1 for applicable strength and extreme event
load combinations specified in Table 3.4.1-1 which are
transferred by the piston to the pot wall.
14.7.4.7—Piston
C14.7.4.7
The piston shall have the same plan shape as the
inside of the pot. Its thickness shall be adequate to resist
the loads imposed on it, but shall not be less than
six percent of the inside diameter of the pot, Dp, except at
the rim.
The perimeter of the piston shall have a contact rim
through which horizontal loads may be transmitted. In
circular pots, its surface may be either cylindrical or
spherical. The body of the piston above the rim shall be set
back or tapered to prevent binding. The height, w, of the
piston rim shall be large enough to transmit the strength
and extreme event limit states horizontal forces between
the pot and the piston.
Where a mechanical device is used to connect the
superstructure to the substructure, it shall be designed to
resist the greater of Hu at the support for the strength and
extreme event limit states, or 15 percent of the maximum
vertical load at the service limit state at that location.
Pot bearings subjected to lateral loads shall be
proportioned so that the thickness of the pot wall (tw) and
the pot base (tb) shall satisfy:
tw , tb ≥
25 H u θu
Fy
(14.7.4.7-1)
Pot bearings that transfer load through the piston shall
satisfy:
hw ≥
1.5H u
D p Fy
hw ≥ 0.125 in., and
The limitation of Eq. 14.7.4.6-6 is based upon past
manufacturing practice (SCEF, 1991).
The surface finish on the inside of the pot may have
considerable impact on bearing performance. A smooth
finish reduces rotational resistance and wear and abrasion
of the elastomer. It may also improve the performance of
the sealing rings, but at present there are no definitive
limits as to what the surface finish should ideally be for
good bearing performance. Metalization on the inside of
the pot tends to cause a rougher surface finish, which leads
to significant increases in damage under cyclic rotation; as
a result, metalization may not be a good method of
protection.
Maximum extreme event limit state forces should be
considered when the bearing is not intended to act as a fuse
or irreparable damage is not permitted.
(14.7.4.7-2)
(14.7.4.7-3)
The required piston thickness is controlled by rigidity
and strength. A central internal guide bar fitted in a slot in
the piston causes bending moments that are largest where
the piston is weakest. In this case, the piston must also be
thick enough to supply an adequate grip length for any
bolts used to secure the guide bar.
If the piston rotates while a horizontal load is acting,
the piston rim will be subject to bearing stresses due to
horizontal load and to shear forces. If the rim surface is
cylindrical, contact between it and the pot wall will
theoretically be along a line when the piston rotates. In
practice, some localized yielding is inevitable. If the rim
surface forms part of a sphere, the contact area will be
finite, providing less potential for local damage. Damage to
the pot wall should be avoided because it will jeopardize
the effectiveness of the seal. The dimensions of the rim
depend on the contact area, and because this is uncertain,
the rim should be designed conservatively. Eq. 14.7.4.7-4
is based on consideration of bearing stresses alone, using a
strength limit state horizontal force of 0.15 times the
vertical service limit state load, Fy = 50.0 ksi and φ = 0.9.
The 15 percent factor applied to the service limit state
vertical load, embedded in Eq. 14.7.4.7-4 and used in the
design of mechanical devices that connect the
superstructure to the substructure, approximates a strength
limit state horizontal design force.
Maximum extreme event limit state forces should be
considered when the bearing is not intended to act as a fuse
or irreparable damage is not permitted. θu may also be
considered at the extreme event limit state.
The clearance between piston and pot is critical to the
proper functioning of the bearing. In most bearings the
finished clearance, after anticorrosion coatings have been
applied, should be about 0.02 to 0.04 in., a range that is
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
hw ≥ 0.03D p
(14.7.4.7-4)
where:
Hu =
lateral load from applicable strength and extreme
event load combinations in Table 3.4.1-1 (kip)
=
maximum strength limit state design rotation
angle specified in Article 14.4.2.2.1 (rad.)
θu
Fy =
yield strength of steel (ksi)
Dp =
internal diameter of pot (in.)
hw =
height from top of rim to underside of piston (in.)
tw
=
pot wall thickness (in.)
tb
=
pot base thickness (in.)
easily achievable. The equation for minimum clearance is
based on geometry. Eq. 14.7.4.7-5 may occasionally
produce a negative number; however, in these instances the
minimum value of 0.02 in. controls.
The diameter of the piston rim shall be the inside
diameter of the pot less a clearance, c. The clearance, c,
shall be as small as possible in order to prevent escape of
the elastomer but not less than 0.02 in. If the surface of the
piston rim is cylindrical, the clearance shall satisfy:
D p θu
c ≥ θu hw −
2
(14.7.4.7-5)
where:
Dp =
internal diameter of pot (in.)
hw =
height from top of rim to underside of piston (in.)
θu =
maximum strength limit state design rotation
angle specified in Article 14.4.2.2.1 (rad.)
14.7.5—Steel-Reinforced Elastomeric Bearings—
Method B
14.7.5.1—General
C14.7.5.1
Steel-reinforced elastomeric bearings may be
designed using either of two methods commonly referred
to as Method A and Method B. Where the provisions of
this Article are used, the component shall be taken to meet
the requirements of Method B. Where the provisions of
Article 14.7.6 are used, the component shall be taken to
meet the requirements of Method A.
Steel-reinforced elastomeric bearings shall consist of
alternate layers of steel reinforcement and elastomer
bonded together. In addition to any internal reinforcement,
bearings may have external steel load plates bonded to
either or both the upper or lower elastomer layers.
The stress limits associated with Method A usually
result in a bearing with a lower capacity than a bearing
designed using Method B. This increased capacity
resulting from the use of Method B requires additional
testing and quality control.
Steel-reinforced elastomeric bearings are treated
separately from other elastomeric bearings because of their
greater strength and superior performance in practice
(Roeder et al., 1987; Roeder and Stanton, 1991). The
critical parameter in their design is the shear strain in the
elastomer at its interface with the steel plates. Axial load,
rotation, and shear deformations all cause such shear
strains. The design method (Method B) described in this
Section accounts directly for those shear strains and
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SECTION 14: JOINTS AND BEARINGS
14-57
Tapered elastomer layers shall not be used. All
internal layers of elastomer shall be of the same thickness.
The top and bottom cover layers shall be no thicker than
70 percent of the internal layers.
The shape factor of a layer of an elastomeric bearing,
Si, shall be taken as the plan area of the layer divided by
the area of perimeter free to bulge. Unless noted
otherwise, the values of Si and hri to be used in
Articles 14.7.5 and 14.7.6 for steel-reinforced elastomeric
bearing design shall be that for an internal layer. For
rectangular bearings without holes, the shape factor of a
layer may be taken as:
Si =
LW
2hri ( L + W )
(14.7.5.1-1)
provides a versatile means of allowing for different
combinations of loadings.
Tapered layers cause larger shear strains and bearings
made with them fail prematurely due to delamination or
rupture of the reinforcement. All internal layers should be
the same thickness because the strength and stiffness of the
bearing in resisting compressive load are controlled by the
thickest layer.
The shape factor, Si, is defined in terms of the gross
plan dimensions of layer i. Refinements to account for the
difference between gross dimensions and the dimensions
of the reinforcement are not warranted because quality
control on elastomer thickness has a more dominant
influence on bearing behavior. Holes are strongly
discouraged in steel-reinforced bearings. However, if holes
are used, their effect should be accounted for when
calculating the shape factor because they reduce the loaded
area and increase the area free to bulge. Suitable shape
factor formulae are:
•
where:
L
=
plan dimension of the bearing parallel to the axis
of rotation under consideration (generally parallel
to the global transverse bridge axis) (in.)
hri =
thickness of ith elastomeric layer (in.)
For circular bearings without holes, the shape factor
of a layer may be taken as:
Si =
D
4hri
π 2
d
4
Si =
hri [2 L + 2W + Σπd ]
LW − Σ
plan dimension of the bearing perpendicular to
the axis of rotation under consideration
(generally parallel to the global longitudinal
bridge axis) (in.)
W =
For rectangular bearings:
•
(C14.7.5.1-1)
For circular bearings:
Si =
D 2 − Σd 2
4hri ( D + Σd )
(C14.7.5.1-2)
where:
d
=
the diameter of the hole or holes in the bearing
(in.)
(14.7.5.1-2)
where:
D
=
diameter of the projection of the loaded surface
of the bearing in the horizontal plane (in.)
Large steel-reinforced elastomeric bearings (defined as
those which are thicker than 8 in. or having a plan area
greater than 1,000 in.2) are more difficult to fabricate than
small ones. The consequences of failure are also likely to
be more severe in a large bearing. As such, large bearings
should be designed according to Method B, which requires
additional testing and quality control.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
14.7.5.2—Material Properties
The shear modulus of the elastomer at 73°F shall be
used as the basis for design.
The elastomer shall have a specified shear modulus
between 0.080 and 0.175 ksi. It shall conform to the
requirements of Section 18.2 of the AASHTO LRFD
Bridge Construction Specifications and AASHTO
M 251.
The acceptance criteria in AASHTO M 251 shall be
followed which:
•
Permits a variation of ±15 percent from the value
specified for shear modulus according to the first and
second paragraphs of this Article, and
•
Does not permit a shear modulus below 0.080 ksi.
For design purposes, the shear modulus shall be taken
as the least favorable of the values in the ranges described
above.
Other properties, such as creep deflection, should be
obtained from Table 14.7.6.2-1 or from tests conducted
using AASHTO M 251.
For the purposes of bearing design, all bridge sites shall
be classified as being in temperature Zones A, B, C, D, or E
for which design data are given in Table 14.7.5.2-1. In the
absence of more precise information, Figure 14.7.5.2-1 may
be used as a guide in selecting the zone required for a given
region.
Bearings shall be made from AASHTO lowtemperature grades of elastomer as defined in Section 18
of the AASHTO LRFD Bridge Construction Specifications
and AASHTO M 251. The minimum grade of elastomer
required for each low-temperature zone shall be taken as
specified in Table 14.7.5.2-1.
Any of the three design options listed below may be
used:
•
Specify the elastomer with the minimum lowtemperature grade indicated in Table 14.7.5.2-1 and
determine the shear force transmitted by the bearing
as specified in Article 14.6.3.1;
•
Specify the elastomer with the minimum lowtemperature grade for use when special force provisions
are incorporated in the design and provide a low friction
sliding surface, in which case the bridge shall be
designed to withstand twice the design shear force
specified in Article 14.6.3.1; or
•
Specify the elastomer with the minimum lowtemperature grade for use when special force provisions
are incorporated in the design but do not provide a low
C14.7.5.2
Shear modulus, G, is the most important material
property for design, and it is, therefore, the primary means of
specifying the elastomer. Hardness has been widely used in
the past, and is still permitted for Method A design, because
the test for it is quick and simple. However, the results
obtained from it are variable and correlate only loosely with
shear modulus.
Materials with a specified shear modulus greater
than 0.175 ksi are prohibited because they generally have
a smaller elongation at break and greater stiffness and
greater creep than their softer counterparts. This inferior
performance is generally attributed to the larger amounts
of filler present. Their fatigue behavior does not differ in
a clearly discernible way from that of softer materials.
The least favorable value for the shear modulus used
in design calculations is dependent upon whether the
parameter being calculated is conservatively estimated by
over- or under-estimating the shear modulus. The forgiving
nature of elastomers tends to compensate for service and
installation conditions which are less than ideal. (See
Article 14.7.5.3.2.) Despite this, the designer should be
cautious about specifying a shear modulus which is at or
near the specified upper or lower bounds of 0.175 ksi and
0.080 ksi, respectively.
The zones are defined by their extreme low
temperatures or the largest number of consecutive days
when the temperature does not rise above 32°F, whichever
gives the more severe condition.
Shear modulus increases as the elastomer cools, but
the extent of stiffening depends on the elastomer
compound, time, and temperature. It is, therefore,
important to specify a material with low-temperature
properties that are appropriate for the bridge site. In order
of preference, the low-temperature classification should be
based on:
•
The 50-yr temperature history at the site,
•
A statistical analysis of a shorter temperature history,
or
•
Figure 14.7.5.2-1.
Table 14.7.5.2-1 gives the minimum elastomer grade
to be used in each zone. A grade suitable for a lowertemperature may be specified by the Engineer, but
improvements in low-temperature performance can often
be obtained only at the cost of reductions in other
properties. This low-temperature classification is intended
to limit the force on the bridge substructure to 1.5 times
the service limit state design force under extreme
environmental conditions.
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SECTION 14: JOINTS AND BEARINGS
14-59
friction sliding surface, in which case the components
of the bridge shall be designed to resist four times the
design shear force as specified in Article 14.6.3.1.
Figure 14.7.5.2-1—Temperature Zones
Table 14.7.5.2-1—Low-Temperature Zones and Minimum Grades of Elastomer
Low-Temperature Zone
50-yr low temperature (°F)
Maximum number of consecutive days when the temperature
does not rise above 32°F
Minimum low-temperature elastomer grade
Minimum low-temperature elastomer grade when special force
provisions are incorporated
A
0
3
B
−20
7
C
−30
14
D
−45
N/A
E
<−45
N/A
0
0
2
0
3
2
4
3
5
5
14.7.5.3—Design Requirements
14.7.5.3.1—Scope
C14.7.5.3.1
Bearings designed by the provisions herein shall be
tested in accordance with the requirements for steelreinforced elastomeric bearings as specified in Article 18.2
of the AASHTO LRFD Bridge Construction Specifications
and the AASHTO M 251.
14.7.5.3.2—Shear Deformations
The maximum horizontal displacement of the bridge
superstructure, ΔΟ, shall be taken as 65 percent of the
design thermal movement range, ΔT, computed in
accordance with Article 3.12.2, combined with movements
caused by creep, shrinkage, and post-tensioning.
The maximum shear deformation of the bearing, at the
service limit state, ΔS, shall be taken as ΔO, modified to
account for the substructure stiffness and construction
procedures. If a low friction sliding surface is installed, ΔS
Steel-reinforced bearings are designed to resist
relatively high stresses. Their integrity depends on good
quality control during manufacture, which can only be
ensured by rigorous testing.
C14.7.5.3.2
The shear deformation is limited to ±0.5 hrt in order to
avoid rollover at the edges and delamination due to fatigue.
Generally, the installation temperature is within
±15 percent of the average of the maximum and minimum
design temperatures. Consequently, 65 percent of the
thermal movement range is used for design purposes
(Roeder, 2002). The forgiving nature of elastomeric bearings
more than accounts for actual installation temperatures
greater than or less than the likely approximated installation
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
need not be taken to be larger than the deformation
corresponding to first slip.
The bearing shall satisfy:
hrt ≥ 2Δ S
(14.7.5.3.2-1)
where:
hrt =
total elastomer thickness (in.)
ΔS =
maximum total shear deformation of the
elastomer from applicable service load
combinations in Table 3.4.1-1 (in.)
14.7.5.3.3—Combined Compression, Rotation, and
Shear
Combinations of axial load, rotation, and shear at the
service limit state shall satisfy:
( γ a,st + γ r ,st + γ s,st ) + 1.75 ( γ a,cy + γ r ,cy + γ s,cy ) ≤ 5.0
(14.7.5.3.3-1)
The static component of γa shall also satisfy:
γ a , st ≤ 3.0
(14.7.5.3.3-2)
where:
γa
=
shear strain caused by axial load
γr
=
shear strain caused by rotation
γs
=
shear strain caused by shear displacement
Subscripts “st” and “cy” indicate static and cyclic
loading, respectively. Cyclic loading shall consist of loads
induced by traffic. All other loads may be considered
static. In rectangular bearings, the shear strains shall be
evaluated for rotation about the axis which is parallel to
the transverse axis of the bridge. Evaluation of shear
strains for rotation about the axis which is parallel to the
longitudinal axis of the bridge should also be considered.
For circular bearings, the rotations about two primary
temperature. Additionally, if the bearing is originally set or
reset at the average of the design temperature range,
50 percent of the design thermal movement range computed
in accordance with Article 3.12.2 may be substituted for
65 percent as specified.
Fatigue tests that formed the basis for this provision
were conducted to 20,000 cycles, which represents one
expansion/contraction cycle per day for approximately
55 yr (Roeder et al., 1990). The provisions will, therefore,
be unconservative if the shear deformation is caused by
high-cycle loading due to braking forces or vibration. The
maximum shear deformation due to these high-cycle
loadings should be restricted to no more than ±0.10 hrt,
unless better information is available. At this strain
amplitude, the experiments showed that the bearing has an
essentially infinite fatigue life.
If the bridge girders are lifted to allow the bearings to
realign after some of the girder shortening has occurred,
that may be accounted for in design.
Pier deflections sometimes accommodate a significant
portion of the bridge movement, and this may reduce the
movement that must be accommodated by the bearing.
Construction methods may increase the bearing movement
because of poor installation tolerances or poor timing of
the bearing installation.
C14.7.5.3.3
Elastomers are almost incompressible, so when a steellaminated bearing is loaded in compression, the elastomer
expands laterally due to the Poisson effect. That expansion is
partially restrained by the steel plates to which the elastomer
layers are bonded, and the restraint results in bulging of the
layers between the plates. The bulging creates shear stresses
at the bonded interface between the elastomer and steel. If
they become large enough, they can cause shear failure of
the bond or the elastomer adjacent to it. This is the most
common form of damage in steel-laminated elastomeric
bearings and is the reason why limitations on the shear strain
in the elastomer dominate the design requirements.
The cyclic components of the loading are multiplied by
an amplification factor of 1.75 in Eq. 14.7.5.3.3-1. This
reflects the results of tests that showed that cyclic shear strain
causes more debonding damage than a static shear strain of
the same amplitude. This approach of using an explicit
summation of the shear strain components coupled with an
amplification factor on cyclic components is found in other
specifications, such as the European EN 1337.
In some cases, the rotations due to dead and live load
will have opposite signs, in which case use of the
amplification factor of 1.75 could lead to an amplified
rotation that is artificially low. This is clearly not
consistent with the intent of the amplification factor. In
cases where the sense of the loading components in the
critical combination is unclear, the sum of the absolute
value should be used.
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SECTION 14: JOINTS AND BEARINGS
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orthogonal axes shall be added vectorially, and the shear
strains shall be evaluated using the largest sum.
The shear strains γa, γr, and γs, shall be established by
rational analysis, in lieu of which the following
approximations are acceptable.
The shear strain due to axial load may be taken as:
σs
GSi
γ a = Da
(14.7.5.3.3-3)
in which, for a rectangular bearing:
Da = 1.4
and, for a circular bearing:
(14.7.5.3.3-4)
Da = 1.0
(14.7.5.3.3-5)
where:
Da =
dimensionless coefficient used to determine shear
strain due to axial load
G
=
shear modulus of the elastomer (ksi)
Si
=
shape factor of the ith internal layer of an
elastomeric bearing
σs =
average compressive stress due to total static or
cyclic load from applicable service load
combinations in Table 3.4.1-1 (ksi)
The shear strain due to rotation for a rectangular
bearing may be taken as:
For rectangular bearings, separate evaluations about
each primary rotation axis (parallel to the transverse global
axis and parallel to the longitudinal global axis of the
bridge) may be necessary and appropriate, such as for
structures with significant skew. Where rectangular
bearings are evaluated about an axis parallel to the global
longitudinal axis of the bridge, the definitions of L and W
should be interchanged.
For highly skewed or curved bridges, the girder ends
will significantly rotate in both bending and torsion.
Circular bearings offer a good alternative.
The constants 1.4 assigned to Da and 0.5 assigned to
Dr for rectangular bearings represent simplified values
for determining shear strains which are evaluated for
rotation about an axis which is parallel to the transverse
axis of the bridge. They were derived from procedures
suggested by Stanton et al. (2007). Da and Dr may
alternatively be determined with Eqs. C14.7.5.3.3-1
through C14.7.5.3.3-6 about either primary orthogonal
axis for rectangular bearings.
L
Da = max d a1 , d a 2 + d a 3 ×
W
Dr =
1.552 − 0.627 λ
2.233 + 0.156λ +
L
W
≤ 0.5
(C14.7.5.3.3-1)
(C14.7.5.3.3-2)
in which:
d a1 = 1.06 + 0.210λ + 0.413λ 2
(C14.7.5.3.3-3)
d a 2 = 1.506 − 0.071λ + 0.406λ 2
(C14.7.5.3.3-4)
d a 3 = −0.315 + 0.195λ − 0.047 λ 2
(C14.7.5.3.3-5)
2
L θ
γ r = Dr s
hri n
(14.7.5.3.3-6)
in which:
λ = Si
(C14.7.5.3.3-6)
where:
Dr = 0.5
(14.7.5.3.3-7)
and, for a circular bearing:
K
=
bulk modulus (ksi)
L
=
plan dimension of the bearing perpendicular to
the axis of rotation under consideration (generally
parallel to the global longitudinal bridge axis)
(in.)
W =
plan dimension of the bearing parallel to the axis of
rotation under consideration (generally parallel to
the global transverse bridge axis) (in.)
λ
compressibility index
2
D θ
γ r = Dr s
hri n
(14.7.5.3.3-8)
in which:
Dr = 0.375
3G
K
(14.7.5.3.3-9)
=
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
where:
D
=
diameter of the bearing (in.)
Dr =
dimensionless coefficient used to determine shear
strain due to rotation
hri =
thickness of ith internal elastomeric layer (in.)
L
=
plan dimension of the bearing perpendicular to
the axis of rotation under consideration (generally
parallel to the global longitudinal bridge axis)
(in.)
n
=
number of interior layers of elastomer, where
interior layers are defined as those layers which are
bonded on each face. Exterior layers are defined as
those layers which are bonded only on one face.
When the thickness of the exterior layer of
elastomer is equal to or greater than one-half the
thickness of an interior layer, the parameter, n, may
be increased by one-half for each such exterior
layer.
θs
=
maximum static or cyclic service limit state
design rotation angle of the elastomer specified in
Article 14.4.2.1 (rad.)
In the absence of better information, the bulk
modulus, K, may be taken as 450 ksi for all elastomers
permissible under this specification for use in steelreinforced elastomeric bearings.
The compressibility index, λ, represents the effect of
finite bulk stiffness of the rubber. For conventional
bearings it makes little difference, but in high shape factor
bearings it reduces the stiffness below the value that would
be computed using an incompressible model (i.e. with
λ = 0).
The shear strain due to shear deformation of any
bearing may be taken as:
γs =
Δs
hrt
(14.7.5.3.3-10)
where:
hrt =
total elastomer thickness (in.)
Δs =
maximum total static or cyclic shear deformation
of the elastomer from applicable service load
combinations in Table 3.4.1-1 (in.)
In each case, the static and cyclic components of the
shear strain shall be considered separately and then
combined using Eq. 14.7.5.3.3-1.
In bearings with externally bonded steel plates on both
top and bottom, the peak hydrostatic stress shall satisfy:
σ hyd ≤ 2.25G
(14.7.5.3.3-11)
in which:
σ hyd = 3GSi3
θs
Cα
n
(14.7.5.3.3-12)
Previous editions of these Specifications contained
provisions to prevent net upward movement of any point
on the bearing. Recent research (Stanton et al., 2007) has
shown that, if the bearing is not equipped with bonded
external plates, the sole plate can lift away from the
bearing without causing any tension in the elastomer.
Furthermore, the compression effects are slightly less
severe than in a bearing that is identical except for the
presence of bonded external plates, and is subjected to the
same loading combination. Thus the “no-lift-off”
provisions have been removed.
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2012
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SECTION 14: JOINTS AND BEARINGS
4 2 1
α +
3
3
Cα =
1.5
− α 1 − α2
(
εa n
Si θ S
α=
εa =
)
14-63
(14.7.5.3.3-13)
(14.7.5.3.3-14)
σs
(14.7.5.3.3-15)
3Ba GSi2
for rectangular bearings:
Ba = 1.6
(14.7.5.3.3-16)
and, for circular bearings:
Ba = 1.6
(14.7.5.3.3-17)
where:
Ba =
dimensionless coefficient used to determine peak
hydrostatic stress
εa
total of static and cyclic average axial strain taken as
positive for compression in which the cyclic
component is multiplied by 1.75 from applicable
service load combinations in Table 3.4.1-1 (ksi)
θs
=
=
σs =
total of static and cyclic maximum service limit
state design rotation angles of the elastomer
specified in Article 14.4.2.1 in which the cyclic
component is multiplied by 1.75 (rad.)
total of static and cyclic average compressive
stress in which the cyclic component is
multiplied by 1.75 from applicable service load
combinations in Table 3.4.1-1 (ksi)
For values of α greater than one third, the hydrostatic
stress is compressive, so Eq. 14.7.5.3.3-11 is
satisfied automatically and no further evaluation
is necessary.
14.7.5.3.4—Stability of Elastomeric Bearings
Bearings shall be investigated for instability at the
service limit state load combinations specified in
Table 3.4.1-1.
Bearings satisfying Eq. 14.7.5.3.4-1 shall be considered
stable, and no further investigation of stability is required.
2A ≤ B
in which:
(14.7.5.3.4-1)
However, in a bearing equipped with external plates,
upward movement of part of the plate can cause internal
rupture due to hydrostatic tension. Provisions have been
added to address this case. It is expected to control only
rarely, and when it does, it is likely to do so during
construction, when the axial load is light and the rotation, due
to pre-camber, is large. For the construction load case, the
cyclic components of the loading will be zero. For bearings
with external plates, Eqs. 14.7.5.3.3-1 and 14.7.5.3.3-11
should be checked under all critical loading conditions,
including construction, and about both strong and weak axes
of rectangular bearings when necessary and appropriate.
The constant 1.6 assigned to Ba for rectangular and
circular bearings represents a simplified value for
determining compressive strain due to a purely axial load
(Eq. 14.7.5.3.3-15). This also applies to hydrostatic tension
which is evaluated for rotation about an axis, which is
parallel to the transverse axis of the bridge. It was derived
from procedures suggested by Stanton et al. (2007). A
more precise value of Ba (and consequently more precise
value of E and axial strain) may alternatively be
determined with Eqs. C14.7.5.3.3-7 or C14.7.5.3.3-8 about
either primary orthogonal axis.
For rectangular bearings:
Ba = ( 2.31 − 1.86λ ) + ( −0.90 + 0.96λ )
L W
× 1 − min ,
W L
2
(C14.7.5.3.3-7)
and, for circular bearings:
Ba =
2
1 + 2λ 2
(C14.7.5.3.3-8)
Tests have shown that sharp edges on the internal steel
reinforcement layers cause stress concentrations in the
elastomer and promote the onset of debonding. The
internal steel reinforcement layers should be deburred or
otherwise rounded prior to molding the bearing. The
design values in Eq. 14.7.5.3.3-1 are consistent with this
procedure.
C14.7.5.3.4
The average compressive stress is limited to half the
predicted buckling stress. The latter is calculated using the
buckling theory developed by Gent, modified to account
for changes in geometry during compression, and
calibrated against experimental results (Gent, 1964;
Stanton et al., 1990). This provision will permit taller
bearings and reduced shear forces compared to those
permitted under previous editions of the AASHTO
Standard Specifications.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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14-64
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
h rt
L
2.0 L
1+
W
1.92
A =
B=
(14.7.5.3.4-2)
2.67
( Si + 2.0) 1 + 4.0LW
(14.7.5.3.4-3)
where:
G
=
shear modulus of the elastomer (ksi)
hrt =
total elastomer thickness (in.)
L
=
plan dimension of the bearing perpendicular to
the axis of rotation under consideration (generally
parallel to the global longitudinal bridge axis)
(in.)
Si
=
shape factor of the ith internal layer of an
elastomeric bearing
W =
plan dimension of the bearing parallel to the axis of
rotation under consideration (generally parallel to
the global transverse bridge axis) (in.)
For a rectangular bearing where L is greater than W,
stability shall be investigated by interchanging L and W in
Eqs. 14.7.5.3.4-2 and 14.7.5.3.4-3.
For circular bearings, stability may be investigated by
using the equations for a square bearing with
W = L = 0.8D.
For
rectangular
bearings
not
satisfying
Eq. 14.7.5.3.4-1, the stress due to the total load shall
satisfy Eq. 14.7.5.3.4-4 or 14.7.5.3.4-5.
•
If the bridge deck is free to translate horizontally:
σs ≤
•
GSi
2A − B
Eq. 14.7.5.3.4-4 corresponds to buckling in a sideway
mode and is relevant for bridges in which the deck is not
rigidly fixed against horizontal translation at any point.
This may be the case in many bridges for transverse
translation perpendicular to the longitudinal axis. If one
point on the bridge is fixed against horizontal movement,
the sideway buckling mode is not possible, and Eq.
14.7.5.3.4-5 should be used. This freedom to move
horizontally should be distinguished from the question of
whether the bearing is subject to shear deformations
relevant to Articles 14.7.5.3.2 and 14.7.5.3.3. In a bridge
that is fixed at one end, the bearings at the other end will
be subjected to imposed shear deformation but will not be
free to translate in the sense relevant to buckling due to the
restraint at the opposite end of the bridge.
A negative or infinite limit from Eq. 14.7.5.3.4-5
indicates that the bearing is stable and is not dependent on
σs.
If the value A−B ≤ 0, the bearing is stable and is not
dependent on σs.
(14.7.5.3.4-4)
If the bridge deck is fixed against horizontal
translation:
σs ≤
GSi
A− B
(14.7.5.3.4-5)
14.7.5.3.5—Reinforcement
The minimum thickness of steel reinforcement, hs,
shall be .0625 in., as specified in Article 4.5 of AASHTO
M 251.
The thickness of the steel reinforcement, hs, shall
satisfy:
C14.7.5.3.5
The reinforcement should sustain the tensile stresses
induced by compression of the bearing. With the present
load limitations, the minimum steel plate thickness
practical for fabrication will usually provide adequate
strength.
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2012
Edition
SECTION 14: JOINTS AND BEARINGS
•
At the service limit state:
hs ≥
•
14-65
3hri σ s
Fy
(14.7.5.3.5-1)
At the fatigue limit state:
hs ≥
2hri σ L
ΔFTH
(14.7.5.3.5-2)
where:
ΔFTH
=
constant amplitude fatigue threshold for
Category A as specified in Article 6.6 (ksi)
hri
=
σL
=
thickness of ith internal elastomeric layer
(in.)
average compressive stress at the service
limit state (load factor = 1.0) due to live load
(ksi)
σs
=
average compressive stress due to total load
from applicable service load combinations in
Table 3.4.1-1 (ksi)
Fy
= yield strength of steel reinforcement (ksi)
If holes exist in the reinforcement, the minimum
thickness shall be increased by a factor equal to twice the
gross width divided by the net width.
14.7.5.3.6—Compressive Deflection
C14.7.5.3.6
Deflections of elastomeric bearings due to dead load
and to instantaneous live load alone shall be considered
separately.
Loadings considered in this Article shall be at the
service limit state with all load factors equal to 1.0.
Instantaneous live load deflection shall be taken as:
δ L = ε Li hri
(14.7.5.3.6-1)
where:
εLi =
instantaneous live load compressive strain in ith
elastomer layer
hri =
thickness of ith elastomeric layer (in.)
Initial dead load deflection shall be taken as:
δ d = ε di hri
(14.7.5.3.6-2)
where:
εdi =
Holes in the reinforcement cause stress concentrations.
Their use should be discouraged. The required increase in
steel thickness accounts for both the material removed and
the stress concentrations around the hole.
initial dead load compressive strain in ith
elastomer layer
Limiting instantaneous live load deflections is
important to ensure that deck joints and seals are not
damaged. Furthermore, bearings that are too flexible in
compression could cause a small step in the road surface at
a deck joint when traffic passes from one girder to the
other, giving rise to additional impact loading. A
maximum relative live load deflection across a joint of
0.125 in. is suggested. Joints and seals that are sensitive to
relative deflections may require limits that are tighter than
this.
Long-term dead load deflections should be considered
where joints and seals between sections of the bridge rest
on bearings of different design and when estimating
redistribution of forces in continuous bridges caused by
settlement.
Laminated elastomeric bearings have a nonlinear load
deflection curve in compression. In the absence of
information specific to the particular elastomer to be used,
Eq. C14.7.5.3.6-1 or Figure C14.7.6.3.3-1 may be used as
an approximate guide for calculating dead and live load
compressive strains for Eqs. 14.7.5.3.6-1 and 14.7.5.3.6-2.
It should be noted that as shape factors become higher
(greater than ≈6), the correlation of results between
Eq. C14.7.5.3.6-1 and Figure C14.7.6.3.3-1 diverges.
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2012
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14-66
hri =
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
thickness of ith elastomeric layer (in.)
Long-term dead load deflection, including the effects
of creep, shall be taken as:
δ lt = δ d + acr δ d
(14.7.5.3.6-3)
Eq. C14.7.5.3.6-1 provides a linear solution for a material
that exhibits nonlinear behavior in compression. A
bearing-specific value of axial strain may be found using
Eqs. 14.7.5.3.3-15, C14.7.5.3.3-7 and C14.7.5.3.3-8.
ε=
where:
acr =
creep deflection divided by initial dead load
deflection
Values for εLi and εdi shall be determined from test
results or by analysis. Creep effects should be determined
from information relevant to the elastomeric compound
used. If the engineer does not elect to obtain a value for the
ratio, acr, from test results using Annex A2 of AASHTO
M 251, the values given in Table 14.7.6.2-1 may be used.
σ
4.8GS 2
(C14.7.5.3.6-1)
where:
σ
=
instantaneous live load compressive stress or
dead load compressive stress in an individual
elastomer layer (ksi)
S
=
shape factor of an individual elastomer layer
G
=
shear modulus of the elastomer (ksi)
Eq. C14.7.5.3.6-1 or Figure C14.7.6.3.3-1 may also be
used as an approximate guide for specifying an allowable
value of compressive strain at the design dead plus live
service limit state compressive load when employing
Section 8.8.1 of AASHTO M 251.
Guidance for specifying an allowable value for creep
when Annex A2 of AASHTO M 251 is employed may be
obtained from NCHRP Report 449 or from Table 14.7.6.2-1
Reliable test data on total deflections are rare because
of the difficulties in defining the baseline for deflection.
However, the change in deflection due to live load can be
reliably predicted either by design aids based on test
results or by using theoretically based equations (Stanton
and Roeder, 1982). In the latter case, it is important to
include the effects of bulk compressibility of the
elastomer, especially for high-shape factor bearings.
14.7.5.3.7—Seismic and Other Extreme Event
Provisions
Elastomeric expansion bearings shall be provided with
adequate seismic and other extreme event resistant
anchorage to resist the horizontal forces in excess of those
accommodated by shear in the pad unless the bearing is
intended to act as a fuse or irreparable damage is
permitted. The sole plate and the base plate shall be made
wider to accommodate the anchor bolts. Inserts through the
elastomer should not be allowed, unless approved by the
Engineer. The anchor bolts shall be designed for the
combined effect of bending and shear for seismic and other
extreme event loads as specified in Article 14.6.5.3.
Elastomeric fixed bearings shall be provided with
horizontal restraint adequate for the full horizontal load.
C14.7.5.3.7
The seismic and other extreme event demands on
elastomeric bearings exceed their design limits. Therefore,
positive connection between the girder and the
substructure concrete is needed. If the bearing is intended
to act as a fuse or irreparable damage is permitted, the
positive connection need not be designed for the maximum
extreme event limit state forces.
Holes in elastomer cause stress concentrations that can
lead to tearing of the elastomer during earthquakes.
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SECTION 14: JOINTS AND BEARINGS
14-67
14.7.5.4—Anchorage for Bearings without
Bonded External Plates
In bearings without externally bonded steel plates, a
restraint system shall be used to secure the bearing against
horizontal movement if:
θ s 3ε a
≥
n
Si
(14.7.5.4-1)
where:
n
=
number of interior layers of elastomer, where
interior layers are defined as those layers which are
bonded on each face. Exterior layers are defined as
those layers which are bonded only on one face.
When the thickness of the exterior layer of
elastomer is equal to or greater than one-half the
thickness of an interior layer, the parameter, n, may
be increased by one-half for each such exterior
layer.
Si
=
shape factor of the ith internal layer of an
elastomeric bearing
εa
=
total of static and cyclic average axial strain
taken as positive for compression in which the
cyclic component is multiplied by 1.75 from
applicable service load combinations in
Table 3.4.1-1 (ksi)
θs
=
total of static and cyclic maximum service limit
state design rotation angles of the elastomer
specified in Article 14.4.2.1 in which the cyclic
component is multiplied by 1.75 (rad.)
14.7.6—Elastomeric Pads and Steel-Reinforced
Elastomeric Bearings—Method A
14.7.6.1—General
C14.7.6.1
The provisions of this Article shall be taken to apply
to the design of:
•
Plain elastomeric pads, PEP;
•
Pads reinforced with discrete layers of fiberglass,
FGP;
•
Steel-reinforced elastomeric bearings in which Si2 n
< 22, and for which the primary rotation is about the
axis parallel to the transverse axis of the bridge; and
•
Cotton-duck pads (CDP) with closely spaced layers of
cotton duck and manufactured and tested under
compression in accordance with Military
Specification MIL-C-882E except where superseded
by these Specifications.
Elastomeric pads have characteristics different from
those of steel-reinforced elastomeric bearings. Plain
elastomeric pads are weaker and more flexible because they
are restrained from bulging by friction alone (Roeder and
Stanton, 1986, 1983). Slip inevitably occurs, especially
under dynamic loads, causing larger compressive deflections
and higher internal strains in the elastomer.
In the fourth edition of the Specifications, the stress
limits for steel elastomeric bearing pads designed by
Method A were increased by 25 percent. This increase was
based on the application of Method B equations with an
assumed service limit rotation of 0.02 radians to determine
the strain effects of rotation and the resulting reserve
capacity for axial stresses (Stanton et al., 2007). Therefore,
design for rotation in Method A is implicit in the geometric
and stress limits given. Since Method A is restricted to
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
where:
n
=
number of interior layers of elastomer, where
interior layers are defined as those layers which
are bonded on each face. Exterior layers are
defined as those layers which are bonded only on
one face. When the thickness of the exterior layer
of elastomer is equal to or greater than one-half
the thickness of an interior layer, the parameter,
n, may be increased by one-half for each such
exterior layer.
Si
=
shape factor of the ith internal layer of an
elastomeric bearing
Layer thicknesses in FGP may be different from one another.
For steel-reinforced elastomeric bearings designed in
accordance with the provisions of this Section, internal layers
shall be of the same thickness, and cover layers shall be no
more than 70 percent of the thickness of internal layers.
The shape factor for PEP, FGP pads and steelreinforced elastomeric bearings covered by this Article
shall be determined as specified in Article 14.7.5.1. The
shape factor for CDP shall be based upon the total pad
thickness.
bearings pads rotated about their strong axis, a square
bearing pad provided the conservative case for determining
the increased stress limit. A Si2/n ratio of 16 was selected
for the calculation and resulted in the compressive stress
limits of Eqs. 14.7.6.3.2–6 and 14.7.6.3.2–7. For
rectangular bearing pads, the specified limit of 22 for Si2/n
is appropriate except that a limiting value of 20 for Si2/n
should be considered when the value of n is greater than or
equal to 3. A limiting value of 16 should be considered
when the bearing pad is circular or nearly square.
In pads reinforced with layers of fiberglass, the
reinforcement inhibits the deformations found in plain pads.
However, elastomers bond less well to fiberglass, and the
fiberglass is weaker than steel, so the fiberglass pad is unable
to carry the same loads as a steel-reinforced bearing (Crozier
et al., 1979). FGP has the advantage that it can be cut to size
from a large sheet of vulcanized material.
CDP are preformed pads that are produced in large
sheets and cut to size for specific bridge applications. CDP
are reinforced with closely spaced layers of cotton-duck
and typically display high compressive stiffness and
strength, obtained by the use of very thin elastomeric layers.
However, the thin layers also give rise to very high shear and
rotational stiffness, which could easily lead to edge loading
and a higher shear stiffness than that to be found in layered
bearings. These increased shear and rotational stiffnesses lead
to larger moments and forces in the bridge and reduced
movement and rotational capacity of the bearing pad. As a
consequence, CDP is often used with a PTFE slider on top of
the elastomer pad (Nordlin et al., 1970).
It is essential that CDP bearing pads be tested and
verified to meet the test requirements of Military
Specification MIL-C-882E which can be found at:
http://assist.daps.dla.mil. Note that there is no AASHTO
equivalent to this Military Specification. A summary of
testing and acceptance criteria for CDP is given below.
These criteria require that:
•
A lot of preformed CDP be defined as a single sheet
that is continuously formed to a given thickness
except that a single lot not exceed 2500 lbs of
material;
•
A minimum of two samples from each lot shall be
tested;
•
The samples be 2 in. × 2 in. with the full sheet
thickness;
•
The test specimens be cured for four hours at room
temperature (70°F ± 10°F);
•
Each specimen is then to be loaded in compression,
perpendicular to the direction of lamination;
•
The origin of deflection and compressive strain
measurements be taken at a compressive stress of
5 psi;
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2012
Edition
SECTION 14: JOINTS AND BEARINGS
14.7.6.2—Material Properties
The elastomeric-type materials for PEP, FGP, and
steel reinforced elastomeric bearings shall satisfy the
requirements of Article 14.7.5.2, except as noted below:
•
Hardness on the Shore A scale may be used as a basis
for specification of bearing material,
•
The specified shear modulus for PEP, FGP, and steelreinforced elastomeric bearings with a PTFE or
equivalent slider on top of the bearing shall be
between 0.080 ksi and 0.250 ksi or the nominal
hardness shall be between 50 and 70 on the Shore A
scale, and
•
The specified shear modulus for steel-reinforced
elastomeric bearings without a PTFE or equivalent
slider on top of the bearing designed in accordance
with the provisions of Article 14.7.6 shall be between
0.080 and 0.175 ksi or the nominal hardness shall be
between 50 and 60 on the Shore A scale.
14-69
•
The load be increased at a steady rate of 500 lbs/ min.
and the deflection be recorded;
•
The specimen be loaded to a compressive stress of
10,000 psi without fracture or other failure; and
•
The entire lot of CDP be rejected if any of the CDP
specimens fail to satisfy either of these test criteria: The
average compressive strain of the specimens for that lot
is not to be less than 0.075 in./in. nor shall it be greater
than 0.175 in./in. at an average compressive stress of
2,000 psi. CDP bearing pads which fail to achieve the
10,000 psi stress limit here fall outside the specified
strain range and will not develop the deformation limits
permitted in later parts of Article 14.7.
C14.7.6.2
The elastomer requirements for PEP and FGP are the
same as those required for steel-reinforced elastomeric
bearings. The ranges given in Table 14.7.6.2-1 represent
the variations found in practice. If the material is specified
by hardness, a safe and presumably different estimate of G
should be taken for each of the design calculations,
depending on whether the parameter being calculated is
conservatively estimated by over- or under-estimating the
shear modulus. Creep varies from one compound to
another and is generally more prevalent in harder
elastomers or those with a higher shear modulus but is
seldom a problem if high-quality materials are used. This
is particularly true because the deflection limits are based
on serviceability and are likely to be controlled by live
load, rather than total load. The creep values given in
Table 14.7.6.2-1 are representative of neoprene and are
conservative for natural rubber.
PEP, FGP, and steel reinforced elastomeric bearings with
or without a PTFE or equivalent slider on top of the
bearing shall conform to the requirements of Article 18.2
of the AASHTO LRFD Bridge Construction Specifications
and AASHTO M 251. If the material is specified by its
hardness, the shear modulus for design purposes shall be
taken as the least favorable value from the range for that
hardness given in Table 14.7.6.2-1. Intermediate values
may be obtained by interpolation. If the material is
specified by shear modulus, it shall be taken for design
purposes as the least favorable from the value specified
according to the ranges given in Article 14.7.5.2. Other
properties, such as creep deflection, are also given in
Table 14.7.6.2-1.
The shear force on the structure induced by
deformation of the elastomer in PEP, FGP and steelreinforced elastomeric bearings shall be based on a G
value not less than that of the elastomer at 73°F. Effects of
relaxation shall be ignored.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
CDP shall be manufactured to Military Standards
MIL-C-882E except where the provisions of these
Specifications supersede those provisions. The
elastomeric-type materials for CDP shall have a nominal
hardness between 50 and 70 on the Shore A scale and meet
the requirements of Article 14.7.5.2 as appropriate. The
finished CDP shall have a nominal hardness between 85
and 95 on the Shore A scale. The shear modulus for CDP
may be estimated using Eq. 14.7.6.3.4-3. The cotton-duck
reinforcement shall be either a two-ply cotton yarn or a
single-ply 50-50 blend cotton-polyester. The fabric shall
have a minimum tensile strength of 150 lb./in. width when
tested by the grab method. The fill shall be 40 ± 2 threads
per in., and the warp shall be 50 ± 1 threads per in. The
CDP provisions included herein shall be taken as only
applicable to bearing pads up to 2 in. in total thickness.
CDP is made of elastomers with hardness and
properties similar to that used for PEP and FGP. However,
the closely spaced layers of duck fabric reduce the
indentation and increase the hardness of the finished pad to
the 85 to 95 durometer range. Appendix X1 of AASHTO
M 251 contains provisions for hardness of elastomers, but
not finished CDP. The acceptable range from the specified
value for hardness of elastomers is ±5 points on the
Shore A scale. The acceptable range criteria for elastomers
in AASHTO M 251 may also be considered for finished
CDP. The cotton-duck requirements are restated from the
military specification because the reinforcement is
essential to the good performance of these pads.
Table 14.7.6.2-1—Correlated Material Properties
Shear Modulus @ 73°F (ksi)
Creep deflection @ 25 yr
divided by initial deflection
1
50
0.095–0.130
0.25
Hardness (Shore A)
60
0.130–0.200
0.35
70 1
0.200–0.300
0.45
Only for PEP, FGP, and steel-reinforced elastomeric bearings with a PTFE or equivalent slider on top of the bearing.
14.7.6.3—Design Requirements
C14.7.6.3.1
14.7.6.3.1—Scope
Steel-reinforced elastomeric bearings may be designed
in accordance with this Article, in which case they qualify
for the test requirements appropriate for elastomeric pads.
For this purpose, they shall be treated as FGP.
The provisions for FGP apply only to pads where the
fiberglass is placed in double layers 0.125 in. apart.
The physical properties of neoprene and natural
rubber used in these bearings shall conform to AASHTO
M 251.
14.7.6.3.2—Compressive Stress
C14.7.6.3.2
At the service limit state, the average compressive
stresses, σs and σL, in any layer shall satisfy:
•
The design methods for elastomeric pads are simpler and
more conservative than those for steel-reinforced bearings, so
the test methods are less stringent than those of Article 14.7.5.
Steel-reinforced elastomeric bearings may be made eligible
for these less stringent testing procedures by limiting the
compressive stress as specified in Article 14.7.6.3.2.
The three types of pad, PEP, FGP, and CDP behave
differently, so information relevant to the particular type of
pad should be used for design. For example, in PEP, slip at
the interface between the elastomer and the material on
which it is seated or loaded is dependent on the friction
coefficient, and this will be different for pads seated on
concrete, steel, grout, epoxy, etc.
For PEP:
σ s ≤ 1.00GS and
(14.7.6.3.2-1)
σ s ≤ 0.80 ksi
(14.7.6.3.2-2)
In PEP, the compressive stress is limited to G times
the shape factor and an absolute limit of 0.80 ksi. A stress
check incorporating G times the shape factor limits the use
of a proportionately thick PEP with a high compressive
stress. In FGP, the compressive stress is limited to 1.25G
times the effective shape factor and an absolute limit of
1.0 ksi. The CDP stress limits were developed to provide
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SECTION 14: JOINTS AND BEARINGS
•
•
14-71
For FGP:
σ s ≤ 1.25GSi and
(14.7.6.3.2-3)
σ s ≤ 1.0 ksi
(14.7.6.3.2-4)
For CDP:
σ s ≤ 3.0 ksi and
(14.7.6.3.2-5)
σ L ≤ 2.0 ksi
(14.7.6.3.2-6)
where:
σs =
average compressive stress due to total load
from applicable service load combinations in
Table 3.4.1-1 (ksi)
S
shape factor for PEP
=
σL =
average compressive stress at the service limit
state (load factor = 1.0) due to live load (ksi)
In FGP, the value of Si used shall be based upon an hri
layer thickness which equals the greatest distance between
midpoints of two double fiberglass reinforcement layers.
For steel-reinforced elastomeric bearings designed in
accordance with the provisions of this Article:
σ s ≤ 1.25GSi and
(14.7.6.3.2-7)
σ s ≤ 1.25 ksi
(14.7.6.3.2-8)
long-term serviceability and durability. CDP stiffness
and behavior is less sensitive to shape factor. The total
maximum compressive stress is limited to 3.0 ksi
because experiments showed that CDP does not fail
under monotonically compressive stress values
significantly larger than this stress limit. CDP, which is
subject to compressive stress levels larger than 3.0 ksi,
may delaminate under dynamic loadings typical of those
experienced by bridge bearings. CDP may experience
dramatic failure when maximum compressive strains
exceed approximately 0.25. However, bearing pads
which meet the strain and stiffness limits which are
required by the military specification will not achieve
this failure strain under pure compressive load.
The live load stresses are limited to 2.0 ksi, because
research shows that delamination is caused by the
compressive stress range as well as the maximum
compressive level. Live loads control the maximum
compressive stress range under repeated loading, and this
limit controls the adverse effects of this delamination.
Larger compressive strains would result in increased
damage to the bridge and the bearing pad and reduced
serviceability of the CDP (Lehman et al., 2003).
The reduced stress limit for steel-reinforced
elastomeric bearings designed in accordance with these
provisions is invoked in order to allow these bearings to be
eligible for the less stringent test requirements for
elastomeric pads.
where the value of Si used shall be that of an internal layer
of the bearing.
These stress limits may be increased by ten percent
where shear deformation is prevented.
In FGP, the value of Si used shall be based upon an hri
layer thickness that equals the greatest distance between
midpoints of two double fiberglass reinforcement layers.
14.7.6.3.3—Compressive Deflection
In addition to the provisions of Article 14.7.5.3.6, the
following shall also apply.
In lieu of using specific product data, the compressive
deflection of a FGP should be taken as 1.5 times the
deflection estimated for steel-reinforced bearings of the
same shape factor in Article 14.7.5.3.6.
The compressive deflection under instantaneous live
load and initial dead load of a PEP or an internal layer of a
steel-reinforced elastomeric bearing at the service limit
state without impact shall not exceed 0.09hri, where hri is
the thickness of a PEP, or the thickness of an internal layer
of a steel-reinforced elastomeric bearing (in.).
C14.7.6.3.3
The compressive deflection with PEP, FGP, and CDP
will be larger and more variable than those of steelreinforced elastomeric bearings. Appropriate data for these
pad types may be used to estimate their deflections. In the
absence of such data, the compressive deflection of a PEP
and FGP may be estimated at 3 and 1.5 times, respectively,
the deflection estimated for steel-reinforced bearings of the
same shape factor in Article 14.7.5.3.6.
Figure C14.7.6.3.3-1 provides design aids for
determining the strain in an elastomer layer for steel
reinforced bearings based upon durometer hardness and
shape factor. It should also be noted that initial dead load
compressive deflection does not include deflections
associated with long-term creep.
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure C14.7.6.3.3-1—Stress-Strain Curves
For CDP, the computed compressive strain, εs, may be
taken as:
εs =
σs
Ec
(14.7.6.3.3-1)
where:
Ec =
uniaxial compressive stiffness of the CDP
bearing pad. It may be taken as 30 ksi in lieu of
pad-specific test data (ksi)
σs =
average compressive stress due to total load from
applicable service load combinations in
Table 3.4.1-1 (ksi)
CDP is typically very stiff in compression. The shape
factor may be computed, but it has a different meaning and
less significance to the compressive deflection than it does
for FGP and PEP (Roeder et al., 2000). As a result, the
maximum compressive deflection for CDP can be based
upon an average compressive strain, εs , for the total
bearing pad thickness as computed in Eq. 14.7.6.3.3-1.
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SECTION 14: JOINTS AND BEARINGS
14-73
C14.7.6.3.4
14.7.6.3.4—Shear
The maximum horizontal superstructure displacement
shall be computed in accordance with Article 14.4. The
maximum shear deformation of the pad at the service limit
state, ΔS, shall be taken as the maximum horizontal
superstructure displacement, reduced to account for the pier
flexibility and modified for construction procedures. If a low
friction sliding surface is used, ΔS need not be taken to be
larger than the deformation corresponding to first slip.
The provisions of Article 14.7.5.3.2 shall apply,
except that the pad shall be designed as follows:
•
For PEP, FGP and steel-reinforced elastomeric
bearings:
hrt ≥ 2Δ S
•
(14.7.6.3.4-1)
For CDP:
hrt ≥ 10Δ S
(14.7.6.3.4-2)
where:
hrt =
smaller of total elastomer or bearing
thickness (in.)
ΔS =
maximum total shear deformation of the
bearing from applicable service load
combinations in Table 3.4.1-1 (in.)
The deformation in PEP and FGP are limited to
±0.5 hrt because these movements are the maximum
tolerable for repeated and long-term strains in the
elastomer. These limits are intended to ensure serviceable
bearings with no deterioration of performance and they
limit the forces that the pad transmits to the structure.
In CDP, the shear deflection is limited to only onetenth of the total elastomer thickness. There are several
reasons for this limitation. First, experiments show that
CDP may split and crack at larger shear strains. Second,
CDP has much larger shear stiffness than that noted with
steel-reinforced elastomeric bearings, PEP and FGP, and
so the strain limit assures that CDP pads do not cause
dramatically larger bearing forces to the structure than do
other bearing systems. Third, the greater shear stiffness
means that relative slip between the CDP and the bridge
girders is likely if the deformation required of the bearing
is too large. Slip may lead to abrasion and deterioration of
the pads, as well as other serviceability concerns. Slip may
also lead to increased costs because of anchorage and other
requirements. Finally, CDP pads are harder than PEP and
FGP, and so they are very suitable for the addition of
PTFE sliding surfaces to accommodate the required bridge
movements. As a result, CDP with large translational
movements is invariably designed with PTFE sliding
surfaces.
The shear modulus, G, for CDP for determination of
the bearing force in Article 14.6.3.1 may be conservatively
estimated as:
G = 2σ s ≥ 2.0 ksi
(14.7.6.3.4-3)
where:
σs =
average compressive stress due to total load from
applicable service load combinations in
Table 3.4.1-1 (ksi)
14.7.6.3.5—Rotation
14.7.6.3.5a—General
The provisions of these Articles shall apply at the
service limit state. Rotations shall be taken as the
maximum sum of the effects of initial lack of parallelism
and subsequent girder end rotation due to imposed loads
and movements. Stress shall be the maximum stress
associated with the load conditions inducing the maximum
rotation.
C14.7.6.3.5a
In the fourth edition of the Specifications, rotation of
steel-reinforced elastomeric bearings and elastomeric pads
was, in part, controlled by preventing uplift between the
bearing and the structure. Research (Stanton et al., 2007)
has shown that lift-off is not a concern for elastomeric
bearings and the “no lift-off” provisions were removed
from Method B as described in Article C14.7.5.3.3.
Furthermore, as explained in Article C14.7.6.1, design for
rotation in Method A is implicit in the geometric and stress
limits given. Therefore, the “no lift-off” provisions have
been removed from Method A in order to provide
consistency between the two procedures. Additionally, it
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2012
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
has been shown that the Method A limit on Si2/n
(Article 14.7.6.1) prevents the build-up of any significant
hydrostatic tension in bearings with bonded external
plates.
C14.7.6.3.5b
14.7.6.3.5b—Rotation of CDP
The maximum compressive strain due to combined
compression and rotation of CDP at the service limit state,
εt, shall not exceed:
εt = ε c +
θs L
2t p
< 0.20
(14.7.6.3.5b-1)
where:
εc =
σs
(14.7.6.3.5b-2)
Ec
Maximum rotation shall be limited to:
θ s ≤ 0.80
θ L ≤ 0.20
2t p ε c
L
and
(14.7.6.3.5b-3)
2t p ε c
(14.7.6.3.5b-4)
L
where:
Ec =
uniaxial compressive stiffness of the CDP
bearing pad. It may be taken as 30 ksi in lieu of
pad-specific test data
L
=
length of a CDP bearing pad in the plane of
rotation (in.)
tp
=
total thickness of CDP pad (in.)
εc
=
maximum uniaxial strain due to compression
under total load from applicable service load
combinations in Table 3.4.1-1
εt
=
maximum uniaxial strain due to combined
compression and rotation from applicable service
load combinations in Table 3.4.1-1
σs =
average compressive stress due to total load
associated with the maximum rotation from
applicable service load combinations in
Table 3.4.1-1 (ksi)
θL =
maximum rotation of the CDP pad at the service
limit state (load factor = 1.0) due to live load (rad.)
Rotation, and combined compression and rotation of
CDP are controlled by shear strain limits and delamination
requirements. Experiments show that CDP that meets the
testing requirements of MIL-C-882E will not fracture or
fail until a combined compressive strain exceeds 0.25.
Creep strains do not contribute to this fracture potential.
Design Eq. 14.7.6.3.5b-1 limits this compressive strain to
0.20, because the design is made with service loads, and
research shows that the 0.20 strain limit is sufficiently far
from the average failure strain to assure a β factor of 3.5
for LRFD design. Delamination due to rotation is
associated with uplift or separation between the bearing
pad and the load surface. Delamination does not result in a
fracture or immediate failure of the bearing pad, but it
results in a significant reduction in the bearing service life.
Cyclic rotation associated with live loads represents the
more severe delamination problem, and Eq. 14.7.6.3.5b-4
provides this design limit. However, research also shows
that delamination is also influenced by maximum rotation
level. CDP do not recover all of their compressive
deformation after unloading, and Eq. 14.7.6.3.5b-3
recognizes approximately 20 percent residual compressive
strain and limits uplift due to the maximum rotation in
recognition of the delamination potential. Shear strains of
the elastomer are a less meaningful measure for CDP than
for steel reinforced elastomeric bearings, because shape
factor has a different meaning for CDP than for other
elastomeric bearing types. CDP is known to have relatively
large compressive load capacity, and it is generally
accepted that it can tolerate relatively large compressive
strains associated with these loads. It should be noted that
these compressive strains in CDP are larger than those
tolerated in steel reinforced bearings, but they have been
justified by experimental results for CDP that meets the
requirements of these Specifications. This does not suggest
that CDP is generally superior to steel reinforced
elastomeric bearings. A well designed steel-reinforced
bearing is likely to provide superior long-term
performance, but CDP can be designed and manufactured
quickly and may provide good performance under a range
of conditions.
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SECTION 14: JOINTS AND BEARINGS
θs
=
maximum rotation of the CDP pad from the
applicable service load combinations in
Table 3.4.1-1 (rad.)
C14.7.6.3.6
14.7.6.3.6—Stability
To ensure stability, the total thickness of the pad shall
not exceed the least of L/3, W/3, or D/4.
where:
L
=
plan dimension of the bearing perpendicular to
the axis of rotation under consideration (generally
parallel to the global longitudinal bridge axis)
(in.)
n
=
number of interior layers of elastomer, where
interior layers are defined as those layers that are
bonded on each face. Exterior layers are defined
as those layers that are bonded only on one face.
When the thickness of the exterior layer of
elastomer is more than one half the thickness of
an interior layer, the parameter, n, may be
increased by one half for each such exterior layer.
W =
plan dimension of the bearing parallel to the axis
of rotation under consideration (generally parallel
to the global transverse bridge axis) (in.)
D
diameter of pad (in.)
=
14-75
14.7.6.3.7—Reinforcement
The reinforcement in FGP shall be fiberglass with a
strength in each plan direction of at least 2.2 hri in kip/in.
For the purpose of this Article, if the layers of elastomer
are of different thicknesses, hri shall be taken as the mean
thickness of the two layers of the elastomer bonded to the
same reinforcement. If the fiberglass reinforcement
contains holes, its strength shall be increased over the
minimum value specified herein by twice the gross width
divided by net width.
Reinforcement for steel-reinforced elastomeric
bearings designed in accordance with the provisions of
this Article shall conform to the requirements of
Article 14.7.5.3.5.
The stability provisions in this Article are unlikely to
have a significant impact upon the design of PEP, since a
plain pad which has this geometry would have such a low
allowable stress limit that the design would be uneconomical.
The buckling behavior of FGP and CDP is complicated
because the mechanics of their behavior is not well
understood. The reinforcement layers lack the stiffness of
the reinforcement layers in steel-reinforced bearings and so
stability theories developed for steel-reinforced bearings do
not apply to CDP or FGP. The geometric limits included
here are simple and conservative.
C14.7.6.3.7
The reinforcement should be strong enough to sustain
the stresses induced in it when the bearing is loaded in
compression. For a given compression, thicker elastomer
layers lead to higher tension stresses in the reinforcement.
It should be possible to relate the minimum reinforcement
strength to the compressive stress that is allowed in the
bearing in Article 14.7.6.3.2. The relationship has been
quantified for FGP. For PEP and CDP, successful past
experience is the only guide currently available.
For steel-reinforced elastomeric bearings designed in
accordance with the provisions of Article 14.7.6, the equations
from Article 14.7.5.3.5 are used. Although these equations are
intended for steel-reinforced bearings with a higher allowable
stress, the thickness of reinforcing sheets required is not
significantly greater than those required by the old Method A.
14.7.6.3.8—Seismic and Other Extreme Event
Provisions
Expansion bearings designed according to
Article 14.7.6 shall be provided with adequate seismic and
other extreme event resistant anchorage to resist the
horizontal forces in excess of those accommodated by
shear in the pad unless the bearing is intended to act as a
fuse or irreparable damage is permitted. The provisions of
Article 14.7.5.3.7 shall also apply as applicable.
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14-76
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
14.7.7—Bronze or Copper Alloy Sliding Surfaces
14.7.7.1—Materials
C14.7.7.1
Bronze or copper alloy may be used for:
•
Flat sliding surfaces to accommodate translational
movements,
•
Curved sliding surfaces to accommodate translation
and limited rotation, and
•
Pins or cylinders for shaft bushings of rocker bearings
or other bearings with large rotations.
Bronze sliding surfaces or castings shall conform to
AASHTO M 107 (ASTM B22) and shall be made of Alloy
C90500, C91100, or C86300, unless otherwise specified.
The mating surface shall be structural steel, which has a
Brinell hardness value at least 100 points greater than that
of the bronze.
Bronze or copper alloy sliding surfaces have a long
history of application in the United States with relatively
satisfactory performance of the different materials.
However, there is virtually no research to substantiate the
properties and characteristics of these bearings. Successful
past experience is the best guide currently available.
Historically these bearings have been built from
sintered bronze, lubricated bronze, or copper alloy with no
distinction between the performance of the different
materials. However, the evidence suggests otherwise.
Sintered bronze bridge bearings have historically been
included in the Standard Specifications. Sintered bronze is
manufactured with a metal powder technology, which
results in a porous surface structure that is usually filled
with a self-lubricating material. There do not appear to be
many manufacturers of sintered bronze bridge bearings at
this time, and there is some evidence that past bridge
bearings of this type have not always performed well. As a
result, there is no reference to sintered bronze herein.
Lubricated bronze bearings are produced by a number
of manufacturers, and they have a relatively good history
of performance. The lubrication is forced into a pattern of
recesses, and the lubrication reduces the friction and
prolongs the life of the bearing. Plain bronze or copper
lacks this self-lubricating quality and would appear to have
poorer bearing performance. Some jurisdictions use the
following guidelines for lubricant recesses (FHWA, 1991):
•
The bearing surfaces should have lubricant recesses
consisting of either concentric rings, with or without
central circular recesses with a depth at least equal to
the width of the rings or recesses.
•
The recesses or rings should be arranged in a
geometric pattern so that adjacent rows overlap in the
direction of motion.
•
The entire area of all bearing surfaces that have
provision for relative motion should be lubricated by
means of the lubricant-filled recesses.
•
The lubricant-filled areas should comprise not less
than 25 percent of the total bearing surface.
•
The lubricating compound should be integrally
molded at high pressure and compressed into the rings
or recesses and project not less than 0.010 in. above
the surrounding bronze plate.
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SECTION 14: JOINTS AND BEARINGS
14-77
Bronze or copper alloy sliding expansion bearings
shall be evaluated for shear capacity and stability under
lateral loads.
The mating surface shall be made of steel and be
machined to match the geometry of the bronze surface so
as to provide uniform bearing and contact.
14.7.7.2—Coefficient of Friction
The coefficient of friction may be determined by
testing. In lieu of such test data, the design coefficient of
friction may be taken as 0.1 for self-lubricating bronze
components and 0.4 for other types.
Bronze or copper-alloy sliding expansion bearings
should be evaluated for stability. The sliding plates inset into
the metal of the pedestals or sole plates may lift during high
horizontal loading. Guidelines for bearing stability
evaluations may be found in Gilstad (1990). The shear
capacity and stability may be increased by adding anchor
bolts inserted through a wider sole plate and set in concrete.
The mating surface is commonly manufactured by a
steel fabricator rather than by the bearing manufacturer
who produces the bronze surface. This contractual
arrangement is discouraged because it can lead to a poor fit
between the two components. The bronze is weaker and
softer than the steel, and fracture and excessive wear of the
bronze may occur if there is inadequate quality control.
C14.7.7.2
The best available experimental evidence suggests that
lubricated bronze can achieve a coefficient of friction on the
order of 0.07 during its early life, while the lubricant projects
above the bronze surface. The coefficient of friction is likely
to increase to approximately 0.10 after the surface
lubrication wears away and the bronze starts to wear down
into the recessed lubricant. Copper alloy or plain bronze
would cause considerably higher friction. In the absence of
better information, conservative coefficients of friction of
0.1 and 0.4, respectively, are recommended for design.
14.7.7.3—Limit on Load
The nominal bearing stress due to combined dead and
live load at the service limit state shall not exceed the
values given in Table 14.7.7.3-1.
Table 14.7.7.3-1—Bearing Stress at the Service Limit State
AASHTO M 107
(ASTM B22)
Bronze Alloy
C90500—Type 1
C91100—Type 2
C86300—Type 3
Bearing Stress
(ksi)
2.0
2.0
8.0
14.7.7.4—Clearances and Mating Surfaces
The mating surface shall be steel that is accurately
machined to match the geometry of the bronze surface and
to provide uniform bearing and contact.
14.7.8—Disc Bearings
14.7.8.1—General
C14.7.8.1
The dimensions of the elements of a disc bearing shall
be such that hard contact between metal components,
which prevents further displacement or rotation, will not
occur under the least favorable combination of design
displacements and rotations at the strength limit state.
A disc bearing functions by deformation of a
polyether urethane disc, which should be stiff enough to
resist vertical loads without excessive deformation and yet
be flexible enough to accommodate the imposed rotations
without liftoff or excessive stress on other components,
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The disc bearing shall be designed for the maximum
strength limit state design rotation, θu, specified in
Article 14.4.2.2.2.
For the purpose of establishing the forces and
deformations imposed on a disc bearing, the axis of
rotation may be taken as lying in the horizontal plane at
midheight of the disc. The urethane disc shall be held in
place by a positive location device.
Limiting rings may be used to partially confine the
elastomer against lateral expansion. They may consist of
steel rings welded to the upper and lower plates or a
circular recess in each of those plates.
If a limiting ring is used, the depth of the ring should
be at least 0.03Dd , where Dd is the diameter of the disk
element.
14.7.8.2—Materials
such as PTFE. The urethane disc should be positively
located to prevent its slipping out of place.
The primary concerns are that clearances should be
maintained and that binding should be avoided even at
extreme rotations. The vertical deflection, including creep,
of the bearing should be taken into account.
θu may also be considered at the extreme event
limit state.
The depth of the limiting ring should be at least
0.03Dd to prevent possible overriding by the urethane disc
under extreme rotation conditions.
C14.7.8.2
The elastomeric disc shall be made from a compound
based on polyether urethane, using only virgin materials. The
hardness shall be between 45 and 65 on the Shore D scale.
The metal components of the bearing shall be made
from structural steel conforming to AASHTO
M 270M/M 270 (ASTM A709/A709M), Grade 36, 50, or
50W or from stainless steel conforming to ASTM A240.
14.7.8.3—Elastomeric Disc
The elastomeric disc shall be held in location by a
positive locator device.
At the service limit state, the disc shall be designed so
that:
•
Its instantaneous deflection under total load does not
exceed ten percent of the thickness of the unstressed
disc, and the additional deflection due to creep does
not exceed eight percent of the thickness of the
unstressed disc;
•
The components of the bearing do not lift off each
other at any location; and
•
The average compressive stress on the disc does not
exceed 5.0 ksi. If the outer surface of the disc is not
vertical, the stress shall be computed using the
smallest plan area of the disc.
AASHTO LRFD Bridge Construction Specifications,
Article 18.3.2, provides material specifications for
polyether urethane compounds.
Polyether urethane can be compounded to provide a
wide range of hardnesses. The appropriate material
properties must be selected as an integral part of the design
process because the softest urethanes may require a
limiting ring to prevent excessive compressive deflection,
whereas the hardest ones may be too stiff and cause too
high a resisting moment. Also, harder elastomers generally
have higher ratios of creep to elastic deformation.
AASHTO M 270M/M 270 (ASTM A709/A709M),
Grades 100 and 100W steel should be used only where
their reduced ductility will not be detrimental.
C14.7.8.3
The primary concerns are that clearances should be
maintained and that binding should be avoided even at
extreme rotations. The vertical deflection, including creep,
of the bearing should be taken into account.
Design of the urethane disc may be based on the
assumption that it behaves as a linear elastic material,
unrestrained laterally at its top and bottom surfaces. The
estimates of resisting moments, so calculated, will be
conservative, because they ignore creep, which reduces the
moments. However, the compressive deflection due to
creep should also be accounted for. Limiting rings stiffen
the bearing in compression because they make the bearing
behave more like a confined elastomeric bearing, i.e., a pot
bearing. Their influence is conservatively ignored in the
linear elastic design approach. Subject to the approval of
the Engineer, design methods based on test data are
permitted.
No liftoff of components can be tolerated; therefore,
any uplift restraint device should have sufficiently small
vertical slack to ensure the correct location of all
components when the compressive load is reapplied.
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2012
Edition
SECTION 14: JOINTS AND BEARINGS
If a PTFE slider is used, the stresses on the PTFE
slider shall not exceed the values for average and edge
stresses given in Article 14.7.2.4 for the service limit state.
The effect of moments induced by the urethane disc shall
be included in the stress analysis.
14.7.8.4—Shear Resisting Mechanism
In fixed and guided bearings, a shear-resisting
mechanism shall be provided to transmit horizontal forces
between the upper and lower steel plates. It shall be
capable of resisting a horizontal force in any direction
equal to the larger of the design shear force at the strength
and extreme event limit states or 15 percent of the design
vertical load at the service limit state.
The horizontal design clearance between the upper
and lower components of the shear-restricting mechanism
shall not exceed the value for guide bars given in
Article 14.7.9.
14.7.8.5—Steel Plates
The provisions of Sections 3, 4, and 6 of these
Specifications shall apply as appropriate.
The thickness of each of the upper and lower steel
plates shall not be less than 0.045 Dd , where Dd is the
diameter of the disk element, if it is in direct contact with a
steel girder or distribution plate, or 0.06 Dd if it bears
directly on grout or concrete.
14-79
Rotational experiments have shown that uplift occurs
at relatively small moments and rotations in disc bearings.
There are concerns that this could lead to edge loading on
PTFE sliding surfaces and increase the potential for
damage to the PTFE. Bearings passing the test
requirements of Article 18.3.4.4.4 of the LRFD Bridge
Construction Specification should assure against any
damage to the PTFE.
C14.7.8.4
The shear resisting device may be placed either inside
or outside the urethane disc. If shear is carried by a
separate transfer device external to the bearing, such as
opposing concrete blocks, the bearing itself may be
unguided.
In unguided bearings, the shear force that should be
transmitted through the body of the bearing is μP, where μ
is the coefficient of friction of the PTFE slider and P is the
vertical load on the bearing. This may be carried by the
urethane disc without a separate shear-resisting device,
provided that the disc is held in place by positive locating
devices, such as recesses in the top and bottom plates.
The 15 percent factor applied to the service limit state
vertical load approximates a strength limit state horizontal
design force.
Maximum extreme event limit state forces should be
considered when the bearing is not intended to act as a
fuse or irreparable damage is not permitted.
C14.7.8.5
The plates should be thick enough to uniformly
distribute the concentrated load in the bearing. Distribution
plates should be designed in accordance with Article 14.8.
14.7.9—Guides and Restraints
14.7.9.1—General
C14.7.9.1
Guides may be used to prevent movement in one
direction. Restraints may be used to permit only limited
movement in one or more directions. Guides and restraints
shall have a low-friction material at their sliding contact
surfaces.
Guides are frequently required to control the direction
of movement of a bearing. If the horizontal force becomes
too large to be carried reliably and economically on a
guided bearing, a separate guide system may be used.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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14-80
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
14.7.9.2—Design Loads
Guides or restraints shall be designed at the strength
limit state for:
•
The horizontal force from applicable strength load
combinations specified in Table 3.4.1-1, but shall not
be taken less than
•
15 percent of the total vertical force from applicable
service load combinations specified in Table 3.4.1-1
acting on all the bearings at the bent divided by the
number of guided bearings at the bent.
C14.7.9.2
The 15 percent factor applied to the service limit state
vertical load approximates a minimum strength limit state
horizontal design force. This design force is intended to
account for responses that cannot be calculated reliably,
such as horizontal bending or twisting of a bridge deck
caused by nonuniform or time-dependent thermal effects.
Large ratios of horizontal to vertical load can lead to
bearing instability, in which case a separate guide system
should be considered.
Maximum extreme event limit state forces should be
considered when the bearing is not intended to act as a
fuse or irreparable damage is not permitted.
Guides and restraints shall be designed for applicable
seismic or other extreme event forces using the extreme
event limit state load combinations of Table 3.4.1-1 and, in
the case of seismic, the provisions in Article 3.10.9.
14.7.9.3—Materials
C14.7.9.3
For steel bearings, the guide or restraint shall be made
from steel conforming to AASHTO M 270M/M 270
(ASTM A709/A709M), Grades 36, 50, or 50W or stainless
steel conforming to ASTM A240. For aluminum bearings,
the guide may also be aluminum.
The low-friction interface material shall be approved
by the Engineer.
14.7.9.4—Geometric Requirements
Guides shall be parallel, long enough to accommodate
the full design displacement of the bearing in the sliding
direction, and shall permit a minimum of 0.03125-in. and a
maximum of 0.0625-in. free slip in the restrained direction.
Guides shall be designed to avoid binding under all design
loads and displacements, including rotation.
Many different low-friction materials have been used
in the past. Because the total transverse force at a bent is
usually smaller than the total vertical force, the guides may
contribute less toward the total longitudinal friction force
than the primary sliding surfaces. Thus, material may be
used that is more robust but causes higher friction than the
primary material. Filled PTFE is common, and other
proprietary materials, such as PTFE-impregnated metals,
have proven effective.
C14.7.9.4
Guides must be parallel to avoid binding and inducing
longitudinal resistance. The clearances in the transverse
direction are fairly tight and are intended to ensure that
excessive slack does not exist in the system. Free
transverse slip has the advantage that transverse restraint
forces are not induced, but if this is the objective a
nonguided bearing is preferable. On the other hand, if
applied transverse loads are intended to be shared among
several bearings, free slip causes the load to be distributed
unevenly, possibly leading to overloading of one guide.
14.7.9.5—Design Basis
14.7.9.5.1—Load Location
The horizontal force acting on the guide or restraint
shall be assumed to act at the centroid of the low-friction
interface material. Design of the connection between the
guide or restraint and the body of the bearing system shall
consider both shear and the overturning moments so
caused.
C14.7.9.5.1
Guides are often bolted to the slider plate to avoid
welding distortions. Horizontal forces applied to the guide
cause some overturning moment, which must be resisted
by the bolts in addition to shear. The tension in the bolt
can be reduced by using a wider guide bar. If high-strength
bolts are used, the threaded hole in the plate should be
deep enough to develop the full tensile strength of the bolt.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
SECTION 14: JOINTS AND BEARINGS
The design and detailing of bearing components
resisting lateral loads, including seismic and other extreme
event loads determined as specified in Article 14.6.3.1,
shall provide adequate strength and ductility. Guide bars
and keeper rings or nuts at the ends of pins and similar
devices shall either be designed to resist all imposed loads
or an alternative load path shall be provided that engages
before the relative movement of the substructure and
superstructure is excessive.
14.7.9.5.2—Contact Stress
The contact stress on the low-friction material shall
not exceed that recommended by the manufacturer. For
PTFE, the stresses at the service limit state shall not
exceed those specified in Table 14.7.2.4-1 under sustained
loading or 1.25 times those stresses for short-term loading.
14.7.9.6—Attachment of Low-Friction Material
The low-friction material shall be attached by at least
any two of the following three methods:
•
Mechanical fastening,
•
Bonding, and
•
Mechanical interlocking with a metal substrate.
14-81
Some press-fit guide bar details in common use have
proven unsatisfactory in resisting horizontal loads. When
analyzing such designs, consideration should be given to
the possibility of rolling the bar in the recess (SCEF,
1991).
Where guide bars are recessed into a machined slot,
tolerances should be specified to provide a press fit. The
guide bar should also be welded or bolted to resist
overturning.
Past earthquakes have shown that guide and keeper
bars and keeper rings or nuts at the ends of pins and other
guiding devices have failed, even under moderate seismic
loads. In an experimental investigation of the strength and
deformation characteristics of rocker bearings (Mander et
al., 1993), it was found that adequately sized pintles are
sometimes capable of providing the necessary resistance to
seismic loads.
C14.7.9.5.2
Appropriate compressive stresses for proprietary
materials should be developed by the Manufacturer and
approved by the Engineer on the basis of test evidence.
Strength, cold flow, wear, and friction coefficient should
be taken into consideration.
On conventional materials, higher stresses are allowed
for short-term loading because the limitations in
Table 14.7.2.4-1 are based partly on creep considerations.
Short-term loading includes wind, earthquake, etc., but not
thermal or gravity effects.
C14.7.9.6
Some difficulties have been experienced where PTFE
is attached to the metal backing plates by bonding alone.
Ultra-violet light attacks the PTFE surface that is etched
prior to bonding, and this has caused bond failures. Thus,
at least two separate methods of attachment are required.
Mechanical fasteners should be countersunk to avoid
gouging the mating surface.
14.7.10—Other Bearing Systems
C14.7.10
Bearing systems made from components not specified
in Articles 14.7.1 through 14.7.9 may also be used, subject
to the approval of the Engineer. Such bearings shall be
adequate to resist the forces and deformations imposed on
them at the service and strength limit states without
material distress and without inducing deformations
detrimental to their proper functioning. At the extreme
event limit state, bearings which are designed to act as
fuses or sustain irreparable damage may be permitted by
the Owner provided loss of span is prevented.
Tests cannot be prescribed unless the nature of the
bearing is known. In appraising an alternative bearing
system, the Engineer should plan the test program
carefully because the tests constitute a larger part of the
quality assurance program than is the case with more
widely used bearings.
In bearings that rely on elastomeric components,
aspects of behavior, such as time-dependent effects,
response to cyclic loading, temperature sensitivity, etc.,
should be investigated.
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2012
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14-82
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The dimensions of the bearing shall be chosen to
provide for adequate movements at all times. Materials
shall have sufficient strength, stiffness, and resistance to
creep and decay to ensure the proper functioning of the
bearing throughout the design life of the bridge.
The Engineer shall determine the tests that the bearing
shall satisfy. The tests shall be designed to demonstrate
any potential weakness in the system under individual
compressive, shear, or rotational loading or combinations
thereof. Testing under sustained and cyclic loading shall
be required.
Some bearing tests are very costly to perform. Other
bearing tests cannot be performed because there is no
available test equipment in the United States. At the
present time, the largest U.S. facility for testing bearings in
combined axial load and shear is the Seismic Response
Modification Device Test Facility at the University of
California, San Diego constructed by Caltrans. This
facility can test bearings of all kinds up to 12,000-kip axial
load capacity and 2,000-kip transverse load capacity
(HITEC, 2002). Nevertheless, the following test
requirements should be carefully considered before
specifying them (SCEF, 1991):
•
Vertical loads exceeding 5,000 kips,
•
Horizontal loads exceeding 500 kips,
•
The simultaneous application of horizontal and
vertical load where the horizontal load exceeds
75 percent of the vertical load,
•
Triaxial test loading,
•
The requirement for dynamic rotation of the test
bearing while under vertical load, and
•
Coefficient of friction test movements with normal
loads greater than 250 kips.
14.8—LOAD PLATES AND ANCHORAGE FOR
BEARINGS
14.8.1—Plates for Load Distribution
C14.8.1
The bearing, together with any additional plates, shall
be designed so that:
Large forces may be concentrated in a bearing that
must be distributed so as not to damage the supporting
structure. In general, metal rocker and roller bearings
cause the most concentrated loads, followed by pots,
discs, and sphericals, whereas elastomeric bearings
cause the least concentrated loads. Masonry plates may
be required to prevent damage to concrete or grout
surfaces.
Many simplified methods have been used to design
masonry plates, some based on strength and some on
stiffness. Several studies have indicated that masonry
plates are less effective in distributing the load than these
simplified methods would suggest, but the cost of heavy
load distribution plates would be considerable (McEwen
and Spencer, 1981; Saxena and McEwen, 1986). The
present design rules represent an attempt to provide a
uniform basis for design that lies within the range of
traditional methods. Design based on more precise
information, such as finite element analysis, is preferable
but may not be practical in many cases.
•
The combined system is stiff enough to prevent
distortions of the bearing that would impair its proper
functioning when subjected to service and strength
limit state loadings, and maximum extreme event
loadings when required;
•
The stresses imposed on the supporting structure
satisfy the limits specified by the Engineer and
Sections 5, 6, 7, or 8; and
•
The bearing can be replaced within the jacking height
limits specified by the Engineer without damage to the
bearing, distribution plates, or supporting structure. If
no limit is given, a height of 0.375 in. shall be used.
Resistance of steel components shall be determined in
accordance with Section 6.
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SECTION 14: JOINTS AND BEARINGS
14-83
In lieu of a more refined analysis, the load from a
bearing fully supported by a grout bed may be assumed to
distribute at a slope of 1.5:1, horizontal to vertical, from
the edge of the smallest element of the bearing that resists
the compressive load.
The use and design of bearing stiffeners on steel
girders shall comply with Section 6.
Sole plate and base plate connections shall be
adequate to resist lateral loads at the strength limit state.
These connections shall also be adequate to resist the
maximum seismic and other extreme event lateral loads
unless the bearings are designed to act as fuses or sustain
irreparable damage. Sole plates shall be extended to allow
for anchor bolt inserts, when required.
Some types of bearings were only developed in the last
20 or 30 yr, so their longevity has yet to be proven in the
field. Hence the requirement for bearing replaceability.
One common way to provide for replacement is to use a
masonry plate, attached to the concrete pier head by
embedded anchors or anchor bolts. The bearing can then be
attached to the masonry plate by seating it in a machined
recess and bolting it down. The bridge needs then to be lifted
only through a height equal to the depth of the recess in order
to replace the bearing. The deformation tolerance of joints
and seals, as well as the stresses in the structure, should be
considered in determining the allowable jacking height.
14.8.2—Tapered Plates
C14.8.2
If, under full permanent load at the mean annual
temperature for the bridge site (at the service limit state
with all load factors equal to 1.0), the inclination of the
underside of the girder to the horizontal exceeds 0.01 rad.,
a tapered plate shall be used in order to provide a level
surface.
Tapered plates may be used to counteract the effects
of end slope in a girder. In all but short-span bridges, the
dead load will dominate the forces on the bearing, so the
tapered plate should be designed to provide zero rotation
of the girder under this condition. The limit of 0.01 rad.
out of level corresponds to the 0.01 rad. component, which
is required in the design rotation in Article 14.4.
14.8.3—Anchorage and Anchor Bolts
14.8.3.1—General
C14.8.3.1
All load distribution plates and bearings with external
steel plates shall be positively secured to their associated
superstructure or substructure element by bolting or
welding.
All girders shall be positively secured to supporting
bearings by a connection that can resist the horizontal
forces that may be imposed on it unless fusing or
irreparable damage is permitted at the extreme event limit
state. Separation of bearing components shall not be
permitted at the strength limit state. Connections shall
resist the least favorable combination of loads at the
strength limit state and shall be installed wherever deemed
necessary to prevent separation.
Trusses, girders, and rolled beams shall be securely
anchored to the substructure. Where possible, anchor bolts
should be cast in substructure concrete, otherwise anchor
bolts may be grouted in place. Anchor bolts may be
swedged or threaded to secure a satisfactory grip upon the
material used to embed them in the holes.
The resistance of the anchor bolts shall be adequate
for loads at the strength limit state and for the maximum
loads at the extreme event limit state unless the bearings
are designed to act as fuses or sustain irreparable damage.
The tensile resistance of anchor bolts shall be
determined as specified in Article 6.13.2.10.2.
Bearings should be anchored securely to the support
to prevent their moving out of place during construction or
over the life of the bridge. Elastomeric bearings may be
left without anchorage if adequate friction is available. A
design coefficient of friction of 0.2 may be assumed
between elastomer and clean concrete or steel.
Girders may be located on bearings by bolts or pintles.
The latter provide no uplift capacity. Welding may be
used, provided that it does not cause damage to the bearing
or difficulties with replacement.
Uplift should be prevented both among the major
elements, such as the girder, bearing, support, and between
the individual components of a bearing. If uplift occurs,
some parts of the structure could be misaligned when
contact is regained, causing damage.
Anchor bolts are very susceptible to brittle failure
during earthquakes or other extreme events. To increase
ductility, it has been recommended in Astaneh-Asl et al.
(1994) to use upset anchor bolts placed inside hollow
sleeve pipes and oversized holes in the masonry plate.
Thus, deformable bearing types may use the anchor bolts
as the ductile element (Cook and Klingner, 1992).
Bearings designed for rigid load transfer, especially at
the extreme event limit state, should not be seated on grout
pads or other bedding materials that can create a sliding
surface and reduce the horizontal resistance.
Seismic loading of the anchor bolts has often resulted
in concrete damage, especially when they were too close to
the edge of the bearing seat. Guidelines for evaluating
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14-84
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
The shear resistance of anchor bolts and dowels shall
be determined as specified in Article 6.13.2.12.
The resistance of anchor bolts in combined tension
and shear shall be determined as specified in
Article 6.13.2.11.
The bearing resistance of the concrete shall be taken
as specified in Article 5.7.5. The modification factor, m,
shall be based on a nonuniformly distributed bearing
stress.
edge distance effects and concrete strength requirements
may be found in Ueda et al. (1990), among others.
For global design of anchorages to concrete, refer to
Building Code Requirements for Structural Concrete
(ACI 318-05), Appendix D.
As an approximation, the bearing stress may be
assumed to vary linearly from zero at the end of the
embedded length to its maximum value at the top surface
of concrete.
14.8.3.2—Seismic and Other Extreme Event
Design and Detailing Requirements
Sufficient reinforcement shall be provided around the
anchor bolts to develop the level of horizontal forces
considered at the extreme event limit state and anchor
them into the mass of the substructure unit. Potential
concrete crack surfaces next to the bearing anchorage shall
be identified and their shear friction capacity evaluated as
required.
14.9—CORROSION PROTECTION
C14.9
All exposed steel parts of bearings not made from
stainless steel shall be protected against corrosion by zinc
metalization, hot-dip galvanizing, or a paint system
approved by the Engineer. A combination of zinc
metalization or hot-dip galvanizing and a paint system may
be used.
The use of stainless steel is the most reliable protection
against corrosion because coatings of any sort are subject to
damage by wear or mechanical impact. This is particularly
important in bearings where metal-to-metal contact is
inevitable, such as rocker and roller bearings. Weathering
steel is excluded because it forms an oxide coating that may
inhibit the proper functioning of the bearing.
When using hot-dip galvanizing for corrosion
protection, several factors must be considered.
Embrittlement of very high-strength fasteners, such as
AASHTO M 253 (ASTM A490) bolts, may occur due to
acid cleaning (pickling) before galvanizing, and quenched
and tempered material, such as Grade 70W and 100W,
may undergo changes in mechanical properties, so
galvanizing these should be avoided (see ASTM A143 on
avoiding embrittlement). With good practice, commonly
used steels, such as Grades 36, 50, and 50W, should not be
adversely affected if their chemistry and the assembly’s
details are compatible (see ASTM A385 on ensuring highquality coating). Certain types of bearings, such as
intricate pot or spherical bearings, are not suitable for hotdip galvanizing.
14.10—REFERENCES
2013 Revision
AASHTO. 2002. Standard Specifications for Highway Bridges, 17th Edition, HB-17. American Association of State
Highway and Transportation Officials, Washington, DC.
AASHTO. 2010. Guide Specifications for Seismic Isolation Design, Second Edition, GSID-3. American Association of
State Highway and Transportation Officials, Washington, DC.
ACI. 1999. Building Code Requirements for Structural Concrete, 318-99 and Commentary, 318R-99. American Concrete
Institute, Farmington Hills, MI.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 14: JOINTS AND BEARINGS
14-85
ACI. 2005. Building Code Requirements for Structural Concrete, 318-05. American Concrete Institute, Farmington Hills, MI.
Astaneh-Asl, A., B. Bolt, K. M. McMullin, R. R. Donikian, D. Modjtahedi, and S. Cho. 1994. Seismic Performance of
Steel Bridges during the 1994 Northridge Earthquake, Report No. UCB/CE-STEEL-94/01. Report to the California
Department of Transportation, April 1994.
Campbell, T. I., and W. L. Kong. 1987. TFE Sliding Surfaces in Bridge Bearings, Report ME-87-06. Ontario Ministry of
Transportation and Communications, Downsview, ON.
Cook, A.R., and R. E. Klingner. 1992. “Ductile Multiple-Anchor Steel-to-Concrete Connections,” Journal of Structural
Engineering. American Society of Civil Engineers, New York, NY, Vol. 118, No. 6, June 1992, pp. 1645–1665.
Crozier, W. F., J. R. Stoker, V. C. Martin, and E. F. Nordlin. 1979. A Laboratory Evaluation of Full-Size Elastomeric Bridge
Bearing Pads, Research Report CA DOT, TL-6574-1-74-26. Highway Research Report, Washington, DC, June 1979.
Dexter, R. J., R. J. Connor, and M. R. Kaczinski. 1997. Fatigue Design of Modular Bridge Joint Systems, NCHRP
Report 402. Transportation Research Board, National Research Council, Washington, DC.
Dexter, R. J., M. J. Mutziger, and C. B. Osberg. 2002. Performance Testing for Modular Bridge Joint Systems, NCHRP
Report 467. Transportation Research Board, National Research Council, Washington, DC.
Gent, A. N. 1964. “Elastic Stability of Rubber Compression Springs,” Journal of Mechanical Engineering Science.
Abstract, Vol. 86, No. 3, p. 86.
Gilstad, D. E. 1990. “Bridge Bearings and Stability,” Journal of Structural Engineering. American Society of Civil
Engineers, New York, NY, Vol. 116, No. 5, May 1990.
HITEC. 2002. Guidelines for Testing Large Seismic Isolator and Energy Dissipation Devices, HITEC/CERF
Report 40600. American Society of Civil Engineers, Washington, DC.
Jacobsen, F. K., and R. K. Taylor. 1971. TFE Expansion Bearings for Highway Bridges, Report No. RDR-31. Illinois
Department of Transportation, Springfield, IL.
Lehman, D. E., C. W. Roeder, R. Larson, and K. Curtin. 2003. Cotton Duck Bearing Pads: Engineering Evaluation and
Design Recommendations, Research Report No. WA-RD 569.1. Washington State Department of Transportation,
Olympia, WA.
McEwen, E. E., and G. D. Spencer. 1981. “Finite Element Analysis and Experimental Results Concerning Distribution of
Stress under Pot Bearings.” In Proc., 1st World Congress on Bearings and Sealants, Publication SP-70. American
Concrete Institute, Farmington Hills, MI.
Mander, J. B, J. H. Kim, and S. S. Chen. 1993. “Experimental Performance and Modeling Study of a 30-Year-Old Bridge
with Steel Bearings,” Transportation Research Record 1393. Transportation Research Board, National Research Council,
Washington, DC.
Nordlin, E. F., J. F. Boss, and R. R. Trimble. 1970. “Tetrafluorethylene. TFE as a Bridge Bearing Material,” Research
Report No. M and R 64642-2. California Department of Transportation, Sacramento, CA.
Nowak, A. S., and J. A. Laman. 1995. “Monitoring Bridge Load Spectra,” IABSE Symposium, Extending the Lifespan of
Structures. San Francisco, CA.
Pattis, A. 1993. “Dynamische Bemessung von Wasserdichten Fahrbahnubergangen-Modulsysteme (Dynamic Design of
Waterproof Modular Expansion Joints).” Ph.D. Dissertation. Civil Engineering and Architecture, University of Innsbruck,
Austria, December 1993.
Roark. R. J., and W. C. Young. 1976. Formulas for Stress and Strain, Fifth Edition. McGraw Hill, New York, NY.
Roeder, C. W. 2000. LRFD Design Criteria for Cotton Duck Pad Bridge Bearing, NCHRP Web Doc 24. Available online:
http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_w24.pdf
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
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AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Roeder, C. W. 2002. Thermal Design Procedure for Steel and Concrete Bridges, Final Report for NCHRP 20-07/106.
Transportation Research Board, National Research Council, Washington, D.C.
Roeder, C. W., and J. F. Stanton. 1983. “Elastomeric Bearings: A State of the Art,” Journal of the Structural Division.
American Society of Civil Engineers, New York, NY, Vol. 109, No. 12, December 1983, pp. 2853–2871.
Roeder, C. W., and J. F. Stanton. 1986. “Failure Modes of Elastomeric Bearings and Influence of Manufacturing
Methods.” In Vol. 1, Proc. of 2nd World Congress on Bearings and Sealants, Publication SP-94-17. 84-AB. American
Concrete Institute, Farmington Hills, MI.
Roeder, C. W., and J. F. Stanton. 1991. “State of the Art Elastomeric Bridge Bearing Design,” ACI Structural Journal.
American Concrete Institute, Farmington Hills, MI, Vol. 88, No. 1, pp. 31–41.
Roeder, C. W., J. F. Stanton, and T. Feller. 1990. “Low Temperature Performance of Elastomers,” Journal of Cold
Regions. American Society of Civil Engineers, New York, NY, Vol. 4, No. 3, September 1990, pp. 113–132.
Roeder, C. W., J. F. Stanton, and A. W. Taylor. 1987. Performance of Elastomeric Bearings, NCHRP Report 298.
Transportation Research Board, National Research Council, Washington, DC, October 1987.
Roeder, C. W., J. F. Stanton, and A. W. Taylor. 1990. “Fatigue of Steel-Reinforced Elastomeric Bearings,” Journal of
Structural Division. American Society of Civil Engineers, New York, NY, Vol. 116, No. 2, February 1990.
Saxena, A., and E. E. McEwen. 1986. “Behavior of Masonry Bearing Plates in Highway Bridges.” In Proc. of 2nd World
Congress on Bearings and Sealants, ACI Publication SP-94-31. 84-AB. American Concrete Institute, Farmington Hills, MI.
Schilling, C. G. 1990. Variable Amplitude Load Fatigue, Task A—Literature Review: Volume I—Traffic Loading and Bridge
Response, FHWA/RD/87-059. Federal Highway Administration, U.S. Department of Transportation, Washington, DC, July 1990.
Stanton, J. F., and C. W. Roeder. 1982. Elastomeric Bearings Design, Construction, and Materials, NCHRP Report 248.
Transportation Research Board, National Research Council, Washington, DC, August 1982.
Stanton, J. F., C. W. Roeder, and T. I. Campbell. 1999. High-Load Multi-Rotational Bridge Bearings, NCHRP Report 432.
Transportation Research Board, National Research Council, Washington DC.
Stanton, J. F., G. Scroggins, A. W. Taylor, and C. W. Roeder. 1990. “Stability of Laminated Elastomeric Bearings,” Journal of
Engineering Mechanics. American Society of Civil Engineers, New York, NY, Vol. 116, No. 6, June 1990, pp. 1351–1371.
Stanton, J. F., C. W. Roeder, P. Mackenzie-Helnwein, C. White, C. Kuester, and B. Craig. 2008. Rotation Limits for
Elastomeric Bearings, NCHRP Report 596. Transportation Research Board, National Research Council, Washington, DC,
February 2008.
Subcommittee for High Load Multi-Rotational Bearings, FHWA Region 3 Structural Committee for Economical
Fabrication. 1991. Structural Bearing Specification. Federal Highway Administration, U.S. Department of Transportation,
Washington, DC, October 1991.
Tschemmernegg, F. 1991. “The Design of Modular Expansion Joints.” Proceedings of the 3rd World Congress on Joint
Sealing and Bearing Systems for Concrete Structures. Toronto, ON.
Tschemmernegg, F., and A. Pattis. 1994. “Using the Concept of Fatigue Test to Design a Modular Expansion Joint.”
Transportation Research Board 73rd Annual Meeting, January 1994.
Ueda, T., S. Kitipornchai, and K. Ling. 1990. “Experimental Investigation of Anchor Bolts under Shear,” Journal of
Structural Engineering. American Society of Civil Engineers, New York, NY, Vol. 116, No. 4, April 1990, pp. 910–924.
U.S. Department of Defense. 1989. Cloth, Duck, Cotton or Cotton-Polyester Blend, Synthetic Rubber, Impregnated, and
Laminated, Oil Resistant, Military Specification MIL-C-882E. Available online at: http://assist.daps.dla.mil. (Requires site
registration.)
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2012
Edition
SECTION 15: DESIGN OF SOUND BARRIERS
TABLE OF CONTENTS
15.1—SCOPE ............................................................................................................................................................. 15-1
15.2—DEFINITIONS................................................................................................................................................. 15-1
15.3—NOTATION ..................................................................................................................................................... 15-1
15.4—GENERAL FEATURES .................................................................................................................................. 15-2
15.4.1—Functional Requirements ....................................................................................................................... 15-2
15.4.1.1—General......................................................................................................................................... 15-2
15.4.1.2—Lateral Clearance ......................................................................................................................... 15-2
15.4.2—Drainage................................................................................................................................................. 15-2
15.4.3—Emergency Responders and Maintenance Access ................................................................................. 15-2
15.4.4—Differential Settlement of Foundations .................................................................................................. 15-3
15.5—LIMIT STATES AND RESISTANCE FACTORS ......................................................................................... 15-3
15.5.1—General ................................................................................................................................................... 15-3
15.5.2—Service Limit State................................................................................................................................. 15-3
15.5.3—Strength Limit State ............................................................................................................................... 15-3
15.5.4—Extreme Event Limit State ..................................................................................................................... 15-4
15.6—EXPANSION DEVICES ................................................................................................................................. 15-4
15.6.1—General ................................................................................................................................................... 15-4
15.6.2—Structure-Mounted Sound Barriers ........................................................................................................ 15-4
15.6.3—Ground-Mounted Sound Barriers........................................................................................................... 15-5
15.7—SOUND BARRIERS INSTALLED ON EXISTING BRIDGES .................................................................... 15-5
15.8—LOADS ............................................................................................................................................................ 15-5
15.8.1—General ................................................................................................................................................... 15-5
15.8.2—Wind Load ............................................................................................................................................. 15-5
15.8.3—Earth Load ............................................................................................................................................. 15-9
15.8.4—Vehicular Collision Forces .................................................................................................................... 15-9
15.9—FOUNDATION DESIGN .............................................................................................................................. 15-12
15.9.1—General ................................................................................................................................................. 15-12
15.9.2—Determination of Soil and Rock Properties ......................................................................................... 15-12
15.9.3—Limit States .......................................................................................................................................... 15-12
15.9.4—Resistance Requirements ..................................................................................................................... 15-12
15.9.5—Resistance Factors................................................................................................................................ 15-13
15.9.6—Loading ................................................................................................................................................ 15-13
15.9.7—Movement and Stability at the Service Limit State.............................................................................. 15-13
15.9.7.1—Movement .................................................................................................................................. 15-13
15.9.7.2—Overall Stability ......................................................................................................................... 15-13
15.9.8—Safety against Geotechnical Failure at the Strength Limit State .......................................................... 15-13
15.9.9—Seismic Design .................................................................................................................................... 15-13
15.9.10—Corrosion Protection .......................................................................................................................... 15-13
15.9.11—Drainage............................................................................................................................................. 15-14
15.10—REFERENCES ............................................................................................................................................ 15-14
15-i
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 15
DESIGN OF SOUND BARRIERS
15.1—SCOPE
C15.1
This Section applies to the structural design of
sound barriers which are either ground-mounted or
structure-mounted and the design of the foundations of
ground-mounted sound barriers.
This Section specifies the design forces and the
design requirements unique to sound barriers constructed
along highways. This Section does not cover sound
barriers constructed adjacent to railroad tracks or the
acoustical requirements for sound barriers.
These provisions are largely based on the
requirements of the Guide Specifications for Structural
Design of Sound Barriers (1989).
15.2—DEFINITIONS
Clear Zone—The total roadside border area, starting at the edge of the traveled way, available for safe use by errant
vehicles.
Crashworthy—A traffic railing system that has been successfully crash-tested to a currently acceptable crash test
matrix and test level or one that can be geometrically and structurally evaluated as equal to a crash-tested system.
Ground-Mounted Sound Barriers—Sound barriers supported on shallow or deep foundations.
Post-and-Panel Construction—Type of sound barrier construction consisting of vertical posts supported on a structure
or on the foundations and panels spanning horizontally between adjacent posts.
Right-of-Way—The land on which a roadway and its associated facilities and appurtenances are located. The highway
right-of-way is owned and maintained by the agency having jurisdiction over that specific roadway.
Right-of-Way Line—The boundary of the right-of-way.
Sound Barrier—A wall constructed along a highway to lower the highway noise level in the area behind the wall.
Sound Barrier Setback—The distance between the point on the traffic face of the sound barrier wall that is closest to
traffic and the closest point on the traffic face of the traffic railing the sound barrier is mounted on or located behind
as defined in Article 15.8.4.
Structure-Mounted Sound Barriers—Sound barrier supported on bridges, crashworthy traffic railings, or retaining
walls.
Traffic Railing—Synonymous with vehicular railing; used as a bridge or structure-mounted railing rather than as a
guardrail or median barrier, as in other publications.
Vehicular Railing—Synonymous with traffic railing; used as a bridge or structure-mounted railing rather than as a
guardrail or median barrier, as in other publications.
15.3—NOTATION
S
=
setback distance of sound barrier (15.8.4)
V0 =
friction velocity; a meteorological wind characteristic for various upwind surface characteristics (mph)
(15.8.2)
V30 =
wind speed at 30.0 ft above low ground or water level (mph) (15.8.2)
Z0 =
friction length of upstream fetch; a meteorological wind characteristic (ft) (15.8.2)
φ
=
soil angle of internal friction (degrees) (C15.4.2)
p
=
load factor for permanent loads (15.9.9)
15-1
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
15-2
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
15.4—GENERAL FEATURES
15.4.1—Functional Requirements
15.4.1.1—General
Consult a roadway professional for sight-distance
and sound barrier height and length requirements.
15.4.1.2—Lateral Clearance
C15.4.1.2
Unless dictated by site conditions and approved by
the Owner, sound barriers shall be located outside the
clear zone or, when the clear zone is wider than the
distance between the edge of the traffic lanes and the
edge of the available right-of-way, just inside the rightof-way.
Locating the sound barrier farther from the edge of
the traffic lanes reduces the possibility of vehicular
collision with the barrier. The most desirable location for
a sound barrier is outside the clear zone, which
minimizes the possibility of vehicular collision. In many
cases, because sound barriers are typically used in urban
areas, the width of available right-of-way is less than the
width of the clear zone.
When conditions make it impractical to locate the
sound barrier at adequate distance from the edge of
traffic lanes and the sound barrier is mounted on a traffic
barrier, the recommended minimum clearance from the
edge of traffic lanes to the face of the traffic barrier is
10.0 ft. Lateral clearances greater than 10.0 ft should be
used when feasible. Guardrail or other traffic barriers
should be considered for use when the sound barrier is
located inside the clear zone.
In addition to safety considerations, maintenance
requirements should be considered in deciding sound
barrier locations. Sound barriers placed within the area
between the shoulder and right-of-way line complicate
the ongoing maintenance and landscaping operations and
lead to increased costs, especially if landscaping is
placed on both sides of the sound barrier. Special
consideration should be given to maintaining the
adjoining land behind the sound barrier and adjacent to
the right-of-way line.
15.4.2—Drainage
C15.4.2
Adequate drainage shall be provided along sound
barriers.
It is important to have drainage facilities along
sound barriers to ensure soil stability. Soils with an angle
of internal friction, φ, of 25 degrees or less may develop
flowing characteristics when saturated. Limits on fines,
especially clay and peat, should be specified.
15.4.3—Emergency Responders and Maintenance
Access
C15.4.3
Provisions for emergency and maintenance access
shall be provided. Local fire department requirements for
fire hose and emergency access shall be satisfied.
Provisions may be necessary to allow firefighters
and hazardous material clean-up crews access to fire
hydrants on the opposite side of the sound barrier. The
designer should consult with local fire and emergency
officials regarding their specific needs.
Shorter barriers may be traversed by throwing the
fire hose over the wall. Taller barriers may require an
opening through which the hose is passed. Such an
opening can consist of a formed or cored hole, a hollow
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
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SECTION 15: DESIGN OF SOUND BARRIERS
15-3
masonry block turned on its side, a maintenance access
gate, etc. A small sign may be placed adjacent to the
emergency access location on the traffic side of the
sound barrier. This sign would bear the street name on
which the hydrant is located, thus aiding emergency
crews in identifying the hydrant nearest the opening.
Access to the back side of the sound barrier must be
provided if the area is to be maintained. In subdivision
areas, access can be via local streets, when available. If
access is not available via local streets, access gates or
openings are essential at intervals along the sound
barrier. Offset barriers concealing the access opening
must be overlapped a minimum of 2.5 times the offset
distance in order to maintain the integrity of the main
barrier’s sound attenuation. Location of the access
openings should be coordinated with the appropriate
agency or land owner.
15.4.4—Differential Settlement of Foundations
C15.4.4
For long masonry sound barriers supported on
spread footings, provisions should be made to
accommodate differential settlement.
Provisions should be made to accommodate
differential settlement when sound barriers are supported
on continuous spread or trench footings or cap beams.
15.5—LIMIT STATES AND RESISTANCE
FACTORS
C15.5.1
15.5.1—General
Structural components shall be proportioned to
satisfy the requirements at all appropriate service,
strength, and extreme event limit states.
Limit states applicable to sound barrier foundations
design shall be in accordance with Article 15.9. Limit
states applicable to the structural design of sound barrier
components shall be as presented herein.
The limit states shall apply using the applicable load
combinations in Table 3.4.1-1 and the loads specified
herein.
Where masonry or other proprietary walls are
utilized, the Owner shall approve the design
specifications to be used.
These Specifications do not include design
provisions for masonry structures. Design provisions for
masonry structures should be taken from other
specifications.
15.5.2—Service Limit State
The resistance factors for the service limit states for
post, wall panel and foundation components shall be as
specified in Article 1.3.2.1. Design for service limit
states shall be in accordance with the applicable
requirements of Articles 5.5.2, 6.5.2, 7.5.1, and 8.5.1.
15.5.3—Strength Limit State
The resistance factors for the strength limit states for
post, wall panel and foundation components shall be as
specified in Articles 5.5.4, 6.5.4, 7.5.4, and 8.5.2.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
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15-4
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
15.5.4—Extreme Event Limit State
The resistance factors for the extreme event limit
states for post, wall panel, and foundation components
shall be as specified in Article 1.3.2.1.
15.6—EXPANSION DEVICES
15.6.1—General
Adequate noise sealant material shall be placed at
expansion joints of sound barriers.
15.6.2—Structure-Mounted Sound Barriers
C15.6.2
Except for post-and-panel construction, as a
minimum, expansion joints shall be provided in the
sound barriers at the location of expansion joints in the
supporting structure, at bridge intermediate supports, and
at the centerline of bridge spans.
When the type of construction utilized for sound
barriers does not inherently allow movements between
the sound barrier components, allowance should be made
to accommodate the movement and deformations of the
supporting structure. Therefore, expansion devices are
required in the sound barriers at expansion joint locations
in order not to restrict the movement of the expansion
joints of the supporting structures.
Sound barriers mounted on bridges stiffen the
supporting bridge superstructures, resulting in
longitudinal stresses developing in the sound barriers.
The higher curvature of bridge girders at high moment
locations near midspans and, for continuous bridges, at
intermediate supports increases the magnitude of these
stresses. Providing expansion joints in the sound barriers
at these locations reduces the effect of the stiffness of the
sound barrier on the deformations of the girders and the
stresses in the barrier due to live load deflection of the
bridge.
When mounted on bridges, additional expansion
devices in the sound barrier may be utilized as required
to further minimize the stresses on the barrier due to the
live load deflection of the bridge.
Post-and-panel sound barriers inherently provide an
expansion joint at either end of each wall panel. Typical
posts are made of steel rolled I-shapes or concrete
I-sections. Characteristically, the seat width of the wall
panels on the posts is relatively small as it corresponds to
the width of the post flange overhang on either side of
the post web. These typical seat widths provide for
dimensional and installation tolerances and dimensional
changes caused by panel deformations due to applied
loads and temperature changes. For smaller post flange
widths, unless a post is provided on either side of an
expansion joint in the supporting structure, the change in
the opening of the structure expansion joint may be
larger than the panel seat width on the post and may
cause the failure of the panel straddling the structure
expansion joint due to the loss of panel seat width.
When post-and-panel construction is utilized, wall
panels may be allowed to bridge the expansion joints in,
or at the ends of, the deck of the supporting structure
where the panels seat width on the posts is sufficient to
accommodate the expansion joint movements and the
dimensional and installation tolerances; otherwise, posts
shall be placed on either side of any expansion joint in
the supporting structure.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 15: DESIGN OF SOUND BARRIERS
15-5
15.6.3—Ground-Mounted Sound Barriers
C15.6.3
Except for post-and-panel construction, expansion
devices shall be provided at adequate spacing to allow
for thermal expansion of the sound barriers. For sound
barriers prone to vehicular collision, relative deflection
between the sound barriers on either side of an expansion
joint shall be restricted.
For sound barriers not utilizing post-and-panel
construction, minimizing the relative deflection between
the wall sections on either side of an expansion joint
improves the performance of the barrier during vehicular
collision near the expansion joint. This can be
accomplished by installing a sliding dowel-and-sleeve
connection, similar to the one shown in Figure C15.6.3-1,
near the top of the wall.
Figure C15.6.3-1—Sliding Dowel-and-Sleeve Connection
15.7—SOUND BARRIERS INSTALLED ON
EXISTING BRIDGES
C15.7
When sound barriers are installed on existing
bridges, the effects of the sound barrier forces on existing
bridge components shall be investigated, including the
effect of unbalanced mass.
Sound barrier forces transmitted to the bridge
include the weight of the barrier, wind loads, seismic
loads, vehicular collision forces, and any other forces
that may act on the sound barriers. These forces affect
railings, bridge deck overhangs, floorbeams, and girders.
When sound barriers are added on an existing
bridge, the bridge should be reanalyzed to determine its
load rating taking into account the forces applied to the
sound barriers. The stiffening effect of the sound barriers
may be considered when determining the load rating of
the bridge.
15.8—LOADS
15.8.1—General
Unless explicitly modified below, all applicable
loads shall be applied in accordance with the provisions
of Section 3.
C15.8.2
15.8.2—Wind Load
Except as modified below, the provisions of
Article 3.8.1 shall apply.
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All rights reserved. Duplication is a violation of applicable law.
2012
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15-6
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Wind load shall be applied to the entire surface of
sound barriers as a uniformly distributed load. Where
post-and-panel construction is utilized, the wind load
effects on the posts shall be determined by applying the
resultant wind loads from the uniformly loaded panels as
concentrated loads to the posts at the mid-height
elevation of the exposed portion of the sound barrier.
For sound barriers, wind velocity at 30.0 ft above
low ground or above design water level, V30, shall be
taken as 1.07 times the wind velocity at the sound barrier
location determined from Figure 15.8.2-1.
For sound barriers, the factors Vo and Zo shall be
taken from Table 15.8.2-1.
The wind velocities in Figure 15.8.2-1 have a 50-yr
return period. The 1.07 multiplier is meant to convert the
wind speed return period from the 50-yr period that
Figure 15.8.2-1 is based on to a 75-yr return period to be
consistent with the design life span assumed in these
Specifications.
The Guide Specifications for Structural Design of
Sound Barriers (1989) included four upstream surface
conditions; B1, B2, C, and D; based on a limited study by
Washington State Department of Transportation (2006).
Upstream Surface Conditions B1 and C are
approximately equivalent to the Suburban and Country
upstream surface conditions shown in Table 3.8.1.1-1 and
described in Article C3.8.1.1. The description of these
categories is repeated below. Table 15.8.2-1 includes two
upstream surface conditions, designated as Sparse
Suburban and Coastal, that do not exist in Table 3.8.1.1-1.
The values of V0 and Z0 for these two upstream surface
conditions were selected to yield wind pressures
approximately equal to those obtained for Upstream
Surface Conditions B2 and D in the Guide Specifications
for Structural Design of Sound Barriers (1989).
Coastal—Flat, unobstructed areas and water surfaces
directly exposed to wind. This category includes
large bodies of water, smooth mud flats, salt flats,
and unbroken ice.
Open Country—Open terrain with scattered
obstructions having heights generally less than
30.0 ft. This category includes flat open country and
grasslands.
Sparse Suburban—Areas with fewer obstructions
than described for Suburban conditions but still
more than described for Open Country conditions.
Suburban—Urban and suburban areas, wooded
areas, or other terrain with numerous closely spaced
obstructions having the size of single-family or
larger dwellings. Use of this category shall be
limited to those areas for which representative
terrain prevails in the upwind direction at least
1,500 ft.
City—Large city centers with at least 50 percent of
the buildings having a height in excess of 70.0 ft.
Use of this category shall be limited to those areas
for which representative terrain prevails in the
upwind direction at least one-half mile. Possible
channeling effects of increased velocity pressures
due to the bridge or structure’s location in the wake
of adjacent structures shall be taken into account.
© 2012 by the American Association of State Highway and Transportation Officials.
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2012
Edition
SECTION 15: DESIGN OF SOUND BARRIERS
Wind loads on structure-mounted sound barriers
located in areas that can be characterized as City,
Suburban, Sparse Suburban, and Open Country shall be
determined using the values for V0 and Zo specified for
Open Country conditions in Table 15.8.2-1.
15-7
Typically, the collapse of structure-mounted sound
barriers poses higher danger to life and property than
ground-mounted sound barriers. Therefore, in areas with
low wind pressure, structure-mounted sound barriers are
designed to a higher minimum wind load than groundmounted sound barriers having the same upwind surface
characteristics. This is accomplished by designing
structure-mounted sound barriers to Open Country
conditions as a minimum.
Table 15.8.2-1—Values of V0 and Z0 for Various Upstream Surface Conditions
Condition
V0 (mph)
Z0 (ft)
Coastal
7
0.025
Open Country
8.20
0.23
Sparse
Suburban
9.4
0.98
Suburban
10.90
3.28
City
12.00
8.20
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2012
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15-8
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
Figure 15.8.2-1—Isotach .02 quantiles, in mph: Annual extreme-mile 30.0 ft above ground, 50 yr mean recurrence intervals
2012
Edition
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All rights reserved. Duplication is a violation of applicable law.
SECTION 15: DESIGN OF SOUND BARRIERS
15.8.3—Earth Load
15-9
C15.8.3
The provisions of Article 3.11 shall apply.
The possibility of difference between the actual
finished grade and that shown on the contract documents
should be considered in the design.
15.8.4—Vehicular Collision Forces
Sound barrier systems consisting of a traffic railing
and a sound barrier that have been successfully crashtested may be used with no further analysis.
The depth of aesthetic treatments into the traffic face
of sound barrier that may be subjected to vehicular
collision shall be kept to a minimum.
Sound barrier materials shall be selected to limit
shattering of the sound barrier during vehicular collision.
In lieu of crash-testing, the resistance of components
and connections to Extreme Event II force effects may be
determined based on a controlled failure scenario with a
load path and sacrificial elements selected to ensure
desirable performance of a structural system containing
the soundwall. Vehicular collision forces shall be applied
to sound barriers located within the clear zone as
follows:
Case 1: For sound barriers on a crashworthy traffic
railing and for sound barriers mounted behind a
crashworthy traffic railing with a sound barrier
setback no more than 1.0 ft: vehicular collision
forces specified in Section 13 shall be applied to
the sound barrier at a point 4.0 ft above the
surface of the pavement in front of the traffic
railing for Test Levels 3 and lower and 6.0 ft
above the surface of the pavement in front of the
traffic railing for Test Levels 4 and higher.
Case 2: For sound barriers behind a crashworthy traffic
railing with a sound barrier setback of 4.0 ft:
vehicular collision force of 4.0 kips shall be
Article 3.11.5.10 contains specific requirements for
the determination of earth pressure on sound barrier
foundation components.
Soil build-up against sound barriers has been
observed in some locations. Owners may determine the
earth loads for the worst load case assuming an
allowance in the finished grade elevation.
C15.8.4
Minimizing the depth of aesthetic treatment into the
traffic face of sound barriers that may be in contact with
a vehicle during a collision reduces the possibility of
vehicle snagging.
Sound barrier systems may contain sacrificial
components or components that could need repair after
vehicular collision. Limiting shattering of sound barriers
is particularly important for sound barriers mounted on
bridges crossing over other traffic. When reinforced
concrete panels are utilized for structure-mounted sound
barriers, it is recommended that two mats of
reinforcement are used to reduce the possibility of the
concrete shattering during vehicular collision. Restraint
cables placed in the middle of concrete panels may be
used to reduce shattering while avoiding the increased
panel thickness required to accommodate two layers of
reinforcement.
The bridge overhang or moment slabs need not to
be designed for more force effects than the resistance of
the base connection of the sound barrier.
The design strategy involving a controlled failure
scenario is similar in concept to the use of capacity
protected design to resist seismic forces. Some damage
to the soundwall, traffic barrier, or connections is often
preferable to designing an overhang or moment slab for
force effects due to vehicular collision. The bridge
overhang or moment slabs need not be designed for more
force effects than the resistance of the base connection of
the sound barriers.
Some guidance on desirable structural performance
of sound barriers can be found in European Standard
EN1794-2 (2003).
Very limited information is available on crashtesting of sound barrier systems. The requirements of this
Article, including the magnitude of collision forces, are
mostly based on engineering judgment and observations
made during crash-testing of traffic railings without
sound barriers.
In the absence of crash test results for sound barrier
systems, sound barriers that have not been crash-tested
are often used in conjunction with vehicular railings that
have been crash-tested as stand-alone railings, i.e.
without sound barriers. The collision forces specified
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2012
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15-10
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
applied. The collision force shall be assumed to
act at a point 4.0 ft above the surface of the
pavement in front of the traffic railing for Test
Levels 3 and lower and 14.0 ft above the surface
of the pavement in front of the traffic railing for
Test Levels 4 and higher.
Case 3: For sound barriers behind a crashworthy traffic
railing with a sound barrier setback between
1.0 ft and 4.0 ft: vehicular collision forces and
the point of application of the force shall vary
linearly between their values and locations
specified in Case 1 and Case 2 above.
Case 4: For sound barriers behind a crashworthy traffic
railing with a sound barrier setback more than
4.0 ft: vehicular collision forces need not be
considered.
herein are meant to be applied to the sound barriers
portion of such systems.
Crash Test Levels 3 and lower are performed using
small automobiles and pick-up trucks. Crash Test Levels
4 and higher include single unit, tractor trailer trucks, or
both. The difference in height of the two groups of
vehicles is the reason the location of the collision force is
different for the two groups of sound barriers.
For crash Test Levels 3 and lower, the point of
application of the collision force on the sound barriers is
assumed to be always 4.0 ft above the pavement.
During crash-testing of traffic railings for crash Test
Level 4 and higher, trucks tend to tilt above the top of the
railing and the top of the truck cargo box may reach
approximately 4.0 ft behind the traffic face of the traffic
railing. For such systems, the point of application of the
collision force is expected to be as high as the height of
the cargo box of a truck, assumed to be 14.0 ft above the
pavement surface.
For sound barriers mounted on crashworthy traffic
barriers or with a small setback assumed to be less than
1.0 ft, the full crash force is expected to act on the sound
barrier. The point of application of this force is assumed
to be at the level of the cargo bed, taken as 6.0 ft above
the surface of the pavement.
For a sound barrier mounted with a setback more
than 1.0 ft behind the traffic face of the traffic railing, it
is expected that the truck cargo box, not the cargo bed,
will impact the sound barrier. It is expected that the top
of the cargo box will touch the sound barrier first. Due to
the soft construction of cargo boxes, it is assumed that
they will be crushed and will soften the collision with the
sound barrier. The depth of the crushed area will increase
with the increase of the collision force, thus lowering the
location of the resultant of the collision force. The
magnitude of the collision force and the degree to which
the cargo box is crushed are expected to decrease as the
setback of the sound barrier increases.
In the absence of test results, it is assumed that a
collision force of 4.0 kips will develop at the top of the
cargo box when it impacts sound barriers mounted with a
setback of 4.0 ft.
The collision force and the point of application are
assumed to vary linearly as the sound barrier setback
varies between 1.0 ft and 4.0 ft.
The setback of the sound barrier, S, shall be taken as
shown in Figure 15.8.4-1.
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SECTION 15: DESIGN OF SOUND BARRIERS
15-11
Figure 15.8.4-1—Sound Barrier Setback Distance
Collision forces on sound barriers shall be applied as
a line load with a length equal to the longitudinal length
of distribution of collision forces, Lt, specified in
Appendix A13.
For sound barriers prone to vehicular collision
forces, the wall panels and posts and the post connections
to the supporting traffic barriers or footings shall be
designed to resist the vehicular collision forces at the
Extreme Event II limit state.
For post-and-panel construction, the design collision
force for the wall panels shall be the full specified
collision force placed on one panel between two posts at
the location that maximizes the load effect being
checked. For posts and post connections to the
supporting components, the design collision force shall
be the full specified collision force applied at the point of
application specified in Cases 1 through 3 above.
The vehicular railing part of the sound barrier/railing
system does not need to satisfy any additional
requirements beyond the requirements specified in
Section 13 of the Specifications for the stand-alone
railings, including the height and resistance
requirements.
Unless otherwise specified by the Owner, vehicular
collision forces shall be considered in the design of
sound barriers.
In some cases, the wall panel is divided into a series
of horizontal elements. In these situations, each
horizontal strip should be designed for the full design
force.
Owners may select to ignore vehicular collision
forces in the design of sound barriers at locations where
the collapse of the sound barrier or portions of thereof
has minimal safety consequences.
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2012
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15-12
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
15.9—FOUNDATION DESIGN
15.9.1—General
C15.9.1
Unless otherwise specified by the Owner, the
geotechnical resistance of materials supporting sound
barrier foundations shall be estimated using the
procedures presented in Article 10.6 for spread footings,
Article 10.7 for driven piles, and Article 10.8 for drilled
shafts.
Although sound barriers may be supported on spread
footing or driven pile foundations, drilled shafts are more
commonly used because drilled shafts facilitate
controlling the vertical alignment of sound barrier
structural wall supports and the lateral spacing between
them.
15.9.2—Determination of Soil and Rock Properties
The provisions of Articles 2.4 and 10.4 shall apply.
15.9.3—Limit States
Sound barriers shall be designed to withstand lateral
wind and earth pressures, self weight of the wall,
vehicular collision loads, and earthquake loads in
accordance with the general principles specified in this
Section and in Sections 10 and 11.
Sound barriers shall be investigated for vertical and
lateral displacement and for overall stability at the
Service I Limit State. Tolerable deformation criteria shall
be developed based on maintaining the required barrier
functionality, achieving the anticipated service life, and
the consequences of unacceptable movements.
Sound barrier foundations shall be investigated at
the strength limit states using Eq. 1.3.2.1-1 for:
•
•
•
Bearing-resistance failure,
Overall stability, and
Structural failure.
Sound barrier foundations shall be investigated at
the extreme event limit states using the applicable load
combinations and load factors specified in Table 3.4.1-1.
15.9.4—Resistance Requirements
The factored resistance, RR, calculated for each
applicable limit state shall be the nominal resistance, Rn,
multiplied by an appropriate resistance factor, φ,
specified in Articles 10.5.5.1, 10.5.5.2, 10.5.5.3, 11.5.6,
or 11.5.7.
C15.9.4
Procedures for calculating nominal geotechnical
resistance of footings, driven piles, and drilled shafts are
provided in Articles 10.6, 10.7, and 10.8. These methods
are generally accepted for barriers supported on spread
footings or footings on two or more rows of driven piles
or drilled shafts. The nominal geotechnical resistance of
a single row of driven piles or drilled shafts or by a
continuous embedded foundation wall (commonly
referred to as a “trench footing”) is more appropriately
calculated using the provisions in Article 11.8 for
nongravity cantilever walls.
Procedures for calculating nominal structural
resistance for concrete and steel components are
provided in Sections 5 and 6.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 15: DESIGN OF SOUND BARRIERS
15-13
15.9.5—Resistance Factors
The resistance factors for geotechnical design of
foundations shall be as specified in Table 10.5.5.2.2-1 for
spread footing foundations, Table 10.5.5.2.3-1 for driven
pile foundations, Table 10.5.5.2.4-1 for drilled shaft
foundations, and Table 11.5.7-1 for permanent retaining
walls.
If methods other than those prescribed in these
Specifications are used to estimate geotechnical resistance,
the resistance factors chosen shall provide reliability equal
or greater than those given in Tables 10.5.5.2.2-1,
10.5.5.2.3-1, 10.5.5.2.4-1, and 11.5.7-1.
15.9.6—Loading
The provisions of Section 3, as modified by
Article 15.8, shall apply.
15.9.7—Movement and Stability at the Service Limit
State
15.9.7.1—Movement
The provisions of Articles 10.6.2, 10.7.2, 10.8.2, or
11.8.3, as appropriate, shall apply.
15.9.7.2—Overall Stability
The provisions of Article 11.6.2.3 shall apply.
15.9.8—Safety against Geotechnical Failure at the
Strength Limit State
Spread footings or footings supported on two or
more rows of driven piles or drilled shafts shall be
designed in accordance with the provisions of Articles
10.6.3, 10.7.3, or 10.8.3, respectively.
Footings supported on a single row of driven piles or
drilled shafts or on a continuous embedded foundation
wall (“trench footing”) shall be designed in accordance
with the provisions of Article 11.8.4 using the earth
pressure diagrams provided in Article 3.11.5.10.
15.9.9—Seismic Design
The effect of earthquake loading shall be
investigated using the Extreme Event I limit state of
Table 3.4.1-1 with load factor γp = 1.0, and an accepted
methodology.
15.9.10—Corrosion Protection
The provisions of Article 11.8.7 shall apply.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
15-14
AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS
15.9.11—Drainage
Where sound barriers support earth loads or can
impede water flow, the provisions of Article 11.8.8 shall
apply.
15.10—REFERENCES
AASHTO. 1989 with 1992 and 2002 interims. Guide Specifications for Structural Design of Sound Barriers, GSSB1-M. American Association of State Highway and Transportation Officials, Washington, DC.
Bullard, Jr. D. L., N. M. Sheikh, R. P. Bligh, R. R. Haug, J. R. Schutt, and B. J. Storey. 2006. Aesthetic Concrete
Barrier Design, NCHRP Report 554. Transportation Research Board, National Research Council, Washington, DC.
Washington State Department of Transportation. 2006. Wind Loading Comparison. Washington State Department of
Transportation, Olympia, WA.
White, M., J. Jewell, and R. Peter. 2002. Crash Testing of Various Textured Barriers, FHWA/CA/TL-2002/03.
California Department of Transportation, Sacramento, CA.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
CHANGED AND DELETED ARTICLES, 2012
SUMMARY OF AFFECTED SECTIONS
The revisions included in the AASHTO LRFD Bridge Design Specifications, Sixth Edition affect the following sections:
2.
3.
4.
5.
6.
7.
9.
10.
11.
12.
13.
14.
15.
General Design and Location Features
Loads and Load Factors
Structural Analysis and Evaluation
Concrete Structures
Steel Structures
Aluminum Structures
Decks and Deck Systems
Foundations
Abutments, Piers, and Walls
Buried Structures and Tunnel Liners
Railings
Joints and Bearings
Design of Sound Barriers
SECTION 2 REVISIONS
Changed Articles
The following Articles in Section 2 contain changes or additions to the specifications, the commentary, or both:
2.5.2.6.3
Deleted Articles
No Articles were deleted from Section 2.
SECTION 3 REVISIONS
Changed Articles
The following Articles in Section 3 contain changes or additions to the specifications, the commentary, or both:
3.3.2
3.4.1
3.4.4
3.6.1.2.5
3.6.1.4.1
3.6.5.1
3.8.1.1
3.8.1.2.1
3.10.2.1
3.10.9.2
3.11.5.10
3.15
3.16
Deleted Articles
No Articles were deleted from Section 3.
SECTION 4 REVISIONS
Changed Articles
The following Articles in Section 4 contain changes or additions to the specifications, the commentary, or both:
4.2
4.6.1.1
4.6.1.2.1
4.6.1.2.2
4.6.1.2.3
4.6.2.1.8
4.6.2.2.3c
4.6.2.5
4.6.2.6.4
4.6.3.2.4
4.7.6
4.9
xi
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
Deleted Articles
No Articles were deleted from Section 4.
SECTION 5 REVISIONS
Changed Articles
The following Articles in Section 5 contain changes or additions to the specifications, the commentary, or both:
5.2
5.3
5.4.2.6
5.5.3.1
5.5.4.2.1
5.7.3.3.2
5.8.1.5
5.9
5.9.1.1
5.9.1.6
5.9.4.2.2
5.10.4.3
5.10.4.3.1
5.10.4.3.1a
5.10.4.3.1b
5.10.4.3.1c
5.10.4.3.1d
5.10.4.3.2
5.10.5
5.10.9.3.7
5.13.2.2
5.14.2.3.2
5.14.2.3.4a
5.14.2.3.4b
5.15
Deleted Articles
5.9.4.3
SECTION 6 REVISIONS
Changed Articles
The following Articles in Section 6 contain changes or additions to the specifications, the commentary, or both:
6.3
6.5.4.2
6.5.5
6.6.1.2.1
6.6.1.2.3
6.6.1.2.4
6.6.1.2.5
6.6.1.3.1
6.6.1.3.2
6.7.3
6.7.4.1
6.9.4.2.2
6.9.4.4
6.10.1.7
6.10.6.2.3
6.10.10
6.10.11.1.3
6.11.1.1
6.11.5
6.11.8.2.2
6.11.11.2
6.12.2.2.1
6.14.3
6.14.3.1
6.14.3.3
6.14.3.4
6.14.3.2.1
6.14.3.2.2
6.14.3.2.3
6.14.4.2
6.16
6.16.1
6.16.2
6.16.3
6.16.4
6.16.4.1
6.16.4.2
6.16.4.3
6.16.4.4
6.17
Deleted Articles
6.14.3.4
6.14.3.5
SECTION 7 REVISIONS
Changed Articles
The following Articles in Section 7 contain changes or additions to the specifications, the commentary, or both:
7.6.1.2.1
Deleted Articles
No Articles were deleted from Section 7.
xii
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 9 REVISIONS
Changed Articles
The following Articles in Section 9 contain changes or additions to the specifications, the commentary, or both:
9.8.3.4
9.8.3.4.1
9.8.3.4.2
9.8.3.4.3
9.8.3.4.3a
9.8.3.4.3b
9.8.3.4.3c
9.8.3.4.4
9.8.3.6.2
9.8.3.6.2a
9.8.3.6.2b
9.8.3.6.2c
9.8.3.6.2d
9.8.3.7.1
9.8.3.7.2
9.8.3.7.3
9.8.3.7.4
9.10
Deleted Articles
9.8.3.5
9.8.3.5.1
9.8.3.5.2
9.8.3.5.3
SECTION 10 REVISIONS
Changed Articles
The following Articles in Section 10 contain changes or additions to the specifications, the commentary, or both:
10.6.3.3
10.8.3.6.3
Deleted Articles
No Articles were deleted from Section 10.
SECTION 11 REVISIONS
Changed Articles
The following Articles in Section 11 contain changes or additions to the specifications, the commentary, or both:
11.3.1
11.4.1
11.5.3
11.5.4
11.5.4.1
11.5.4.2
11.5.5
11.5.6
11.5.7
11.5.8
11.6.3.3
11.6.5
11.6.5.1
11.6.5.2
11.6.5.2.1
11.6.5.2.2
11.6.5.3
11.6.5.4
11.6.5.5
11.6.5.6
11.8.1
11.8.6
11.8.6.1
11.8.6.2
11.8.6.3
11.8.6.4
11.9.6
11.10.1
11.10.2.1
11.10.4.2
11.10.6.3.2
11.10.6.4.2a
11.10.6.4.2b
11.10.6.4.3b
11.10.6.4.4b
11.10.7
11.10.7.1
11.10.7.2
11.10.7.3
11.10.7.4
11.10.10.1
11.11.6
11.12
A11
A11.1
A11.2
A11.3
A11.3.1
A11.3.2
A11.3.3
A11.4
A11.5
A11.6
Deleted Articles
No Articles were deleted from Section 11.
xiii
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
SECTION 12 REVISIONS
Changed Articles
The following Articles in Section 12 contain changes or additions to the specifications, the commentary, or both:
12.3
12.5.5
12.6.6.3
12.7.2.2
12.7.2.5
12.8.9.1
12.8.9.2.2
12.8.9.3.1
12.8.9.3.2
12.8.9.4
12.8.9.5
12.14.5.6
Deleted Articles
No Articles were deleted from Section 12.
SECTION 13 REVISIONS
Changed Articles
The following Articles in Section 13 contain changes or additions to the specifications, the commentary, or both:
A13.4.3.1
Deleted Articles
No Articles were deleted from Section 13.
SECTION 14 REVISIONS
Changed Articles
The following Articles in Section 14 contain changes or additions to the specifications, the commentary, or both:
14.3
14.6.3.2
14.7.5.3.3
14.7.5.3.6
14.7.6.1
14.7.6.3.2
14.7.6.3.3
14.7.6.3.5a
14.7.6.3.5b
14.7.6.3.6
Deleted Articles
14.7.6.3.5d
SECTION 15
Section 15 is completely new.
AASHTO Publications Staff
January 2012
xiv
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
Kirk T. Steudle, P.E., President
Director, Michigan Department of Transportation
John Horsley, Executive Director
444 North Capitol Street NW, Suite 249, Washington, DC 20001
(202) 624-5800 Fax: (202) 624-5806 • www.transportation.org
ERRATA
June 2012
Dear Customer:
Recently, we were made aware of some technical revisions that need to be applied to the AASHTO LRFD
Bridge Design Specifications, 6th Edition.
Please replace the existing text with the corrected text to ensure that your edition is both accurate and
current.
AASHTO staff sincerely apologizes for any inconvenience.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
Page
Existing Text
Corrected Text
Section 3
3-13
The last row of Table 3.4.1-1, column 1, reads
“Fatigue I II”
Change “Fatigue I II” to “Fatigue II”.
Eq. C4.6.2.5-3 reads:
Revise denominator to read:
§E I ·
Σ¨ c c ¸
L
G= © c ¹
§ Eg I c ·
Σ¨
¨ Lg ¸¸
©
¹
§E I ·
Σ¨ c c ¸
L
G= © c ¹
§ Eg I g ·
Σ¨
¨ Lg ¸¸
©
¹
4-60
through
4-61
Article includes the following extra content:
Table 4.6.2.6.4-1, Figure 4.6.2.6.4-1, four
specification paragraphs, and two commentary
paragraphs.
In Article 4.6.2.6.4, delete the table, figure and last
four paragraphs in the Article. In the commentary
to Article 4.6.2.6.4, delete the last two paragraphs.
4-70
In Article 4.6.3.2.4, the second sentence of the
first paragraph reads “The structural model should
include all components and connections and
consider local structural stress at fatigue prone
details as shown in Table 6.6.1.2.3-3.”
Change table number from “6.6.1.2.3-3” to
“6.6.1.2.3-1”.
In Article C4.6.3.2.4, FHWA citation is shown as
pending.
Update to “2012”.
FHWA (2012) is cited (see above) but the
reference is missing from Article 4.9.
Add the following reference:
The first bullet in Article 5.5.4.2.1 reads:
Delete bullet.
Section 4
4-51
4-93
FHWA. 2012. Manual for Design, Construction,
and Maintenance of Orthotropic Steel Bridges.
Federal Highways Administration, U.S.
Department of Transportation, Washington, DC.
Section 5
5-26
• For shear and torsion:
normal weight concrete……………. 0.90
lightweight concrete………………...0.80
5-39
The fourth bullet reads:
Change second value so bullet reads:
• For shear and torsion:
normal weight concrete……………. 0.90
lightweight concrete………………...0.70
• For shear and torsion:
normal weight concrete……………. 0.90
lightweight concrete………………...0.80
In Eqs. 5.7.3.1.1-3 and 5.7.3.1.1-4, the subscript
in “ β1 ” runs into the next variable in the
expression.
Reformat the subscript so that it isn’t overlooked.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
Page
5-46
Existing Text
The second to last paragraph of Article 5.7.3.4
reads:
The maximum spacing of the skin reinforcement
shall not exceed either de /6 or 12.0 in.
Corrected Text
Correct subscript from “e” to “Ɛ” to read:
The maximum spacing of the skin reinforcement
shall not exceed either dƐ /6 or 12.0 in.
5-80
through
5-82
Most equations in Article 5.8.4.2 have the “u”
symbol.
Reset in standard algebraic notation.
5-81
Eq. 5.8.4.2-2 reads:
Revise to read:
Vui = vui Acv = vui 12bv
Vui = vui Acv = vui 12bvi
5-84
The second bullet of Article 5.8.4.4 includes the
phrase “…provisions of Article 5.8.1.1 is…”
Revise the article number to read “…provisions of
Article 5.8.2.5 is…”
5-108
Eq. 5.9.5.4.3b-1 reads:
Revise flat bracket placement to read:
∆f pCD =
5-121
(
)
Ep
f ȥ ª t , t − ȥb ( td , ti ) º» K df
¼
Eci cgp b ¬« f i
Ep
+
∆f ȥ §¨ t , t ·¸ K
Ec cd b © f d ¹ df
Eq. C5.10.8-1 reads:
As ≥
1.3 Ag
Perimeter ( fy )
∆f pCD =
(
)
Ep
f ª ȥ t , t − ȥb ( td , ti ) º» K df
¼
Eci cgp ¬« b f i
Ep
+
∆f ȥ §¨ t , t ·¸ K
Ec cd b © f d ¹ df
Format the “Format the “y” as a subscript to read:
As ≥
1.3 Ag
Perimeter
(f )
y
Section 6
6-32
6-34
6-34 and
6-45
In Article 6.6.1.2.1, the second sentence of the
third paragraph reads:
Revise to read:
In regions where the unfactored permanent loads
produce compression, fatigue shall be considered
only if the compressive stress is less than twice
the maximum tensile live load stress resulting
from the fatigue load combination specified in
Table 3.4.1-1.
In regions where the unfactored permanent loads
produce compression, fatigue shall be considered
only if the compressive stress is less than the
maximum live load tensile stress caused by the
Fatigue I load combination specified in
Table 3.4.1-1.
In Article 6.6.1.2.3, a paragraph after the second
paragraph is missing.
Insert the following:
Last paragraph of C6.6.1.2.3 is misplaced.
Move paragraph just after the fifth paragraph.
For components and details on fracture-critical
members, the Fatigue I load combination specified
in Table 3.4.1-1 should be used in combination
with the nominal fatigue resistance for infinite life
specified in Article 6.6.1.2.5.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
Page
Existing Text
Corrected Text
6-35
through
6-36
In Table 6.6.1.2.3-1, the descriptions for
Conditions 2.1 through 2.3 are incomplete.
Add the following to the condition descriptions:
6-36
In Table 6.6.1.2.3-1, Condition 2.5 is missing.
Add Condition 2.5.
6-42
In Table 6.6.1.2.3-1, the description for
Condition 7.1 is incomplete.
Add the following to the condition description:
In Table 6.6.1.2.3-1, Condition 7.2 is missing.
Add Condition 7.2.
6-43
through
6-44
In Table 6.6.1.2.3-1, the figures for
Conditions 8.1 through 8.9 display “∆σ”.
Replace with figures that display “∆f”.
6-46
through
6-47
Table 6.6.1.2.3-3 is redundant.
Delete table.
6-93
In the where list for Eq. 6.9.4.2.2-9, the definition
of Aeff ends with “ ¦ ( b − be ) t ”.
Revise the definition for Aeff as follows:
(Note: see Condition 2.5 for bolted angle or tee
section member connections to gusset or
connection plates.)
(Note: see Condition 7.2 for welded angle or tee
section member connections to gusset or
connection plates.)
summation of the effective areas of the crosssection based on a reduced effective width for
each slender stiffened element in the cross-section
A − ¦ ( b − be ) t (in.2)
6-95
In the open-circle bullet immediately above
A
≤ 80 ” is too
Eq. 6.9.4.4-1, the expression “
rx
small.
6-108
The last sentence of the first paragraph of
Article 6.10.1.7 reads as follows:
Reword to read:
The reinforcement used to satisfy this requirement
shall have a specified minimum yield strength not
less than 60.0 ksi and a size not exceeding No. 6
bars.
The reinforcement used to satisfy this requirement
shall have a specified minimum yield strength not
less than 60.0 ksi; the size of the reinforcement
should not exceed No. 6 bars.
The last sentence of the second paragraph of
Article 6.10.1.7 reads as follows:
Reword to read:
The individual bars shall be spaced at intervals
not exceeding 12.0 in.
The individual bars should be spaced at intervals
not exceeding 12.0 in.
6-109
Remove the subscripting of “
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
A
≤ 80 ”.
rx
2012
Edition
LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
Page
6-134
through
6-140
Existing Text
Corrected Text
The last sentence of the third paragraph of
Article C6.10.6.2.3 reads as follows:
Revise the sentence and add to the end of the
paragraph to read as follows:
Research has not yet been conducted to extend the
provisions of Appendix A6.
Research has not yet been conducted to extend the
provisions of Appendix A6 either to sections in
kinked (chorded) continuous or horizontally
curved steel bridges or to bridges with supports
skewed more than 20 degrees from normal.
Severely skewed bridges with contiguous crossframes have significant transverse stiffness and
thus already have large cross-frame forces in the
elastic range. As interior-pier sections yield and
begin to lose stiffness and shed their load, the
forces in the adjacent cross-frames will increase.
There is currently no established procedure to
predict the resulting increase in the forces without
performing a refined nonlinear analysis. With
discontinuous cross-frames, significant lateral
flange bending effects can occur. The resulting
lateral bending moments and stresses are
amplified in the bottom compression flange
adjacent to the pier as the flange deflects laterally.
There is currently no means to accurately predict
these amplification effects as the flange is also
yielding. Skewed supports also result in twisting
of the girders, which is not recognized in plasticdesign theory. The relative vertical deflections of
the girders create eccentricities that are also not
recognized in the theory. Thus, until further
research is done to examine these effects in greater
detail, a conservative approach has been taken in
the specification.
6-174
The text immediately under the where list for
Eq. 6.11.1.1-1 is shown as a new paragraph rather
than a continuation.
Remove the indent at the beginning of the
paragraph immediately under the where list for
Eq. 6.11.1.1-1.
6-183
The text immediately under the bullet items in
Article 6.11.5 is shown as a new paragraph rather
than a continuation.
Remove the indent at the beginning of the
paragraph immediately under the bullet items in
Article 6.11.5.
The third sentence of the text immediately under
the bullet items in Article 6.11.5 is incomplete.
Reword to read:
In Article 6.11.8.2.2, the first paragraph reads:
Add variable to read:
The nominal flexural resistance of the
compression flange shall be taken as:
The nominal flexural resistance of the
compression flange, Fnc, shall be taken as:
6-190
The allowables specified for nonredundant
members are arbitarily reduced from those
specified for redundant members due to the more
severe consequences of failure of a nonredundant
member.
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
Page
6-191
Existing Text
Eq. 6.11.8.2.2-1 reads:
Fnc = φ f Fcb
§ f ·
1− ¨ v ¸
© φv Fcv ¹
Corrected Text
Remove “φf” just after equal sign to read:
2
Fnc = Fcb
§ f ·
1− ¨ v ¸
© φv Fcv ¹
2
In Article 6.11.8.2.2, the variable description
under “in which” reads:
Add missing phrase to read:
Fcb = nominal axial compression buckling
resistance of the flange calculated as
follows:
Fcb = nominal axial compression buckling
resistance of the flange under compression
alone calculated as follows:
Eq. 6.11.8.2.2-3 reads:
Replace “1” with “∆” in two places to read:
ª
§
∆ − 0.3 · § λ f − λ p · º
Fcb = Rb Rh Fyc «1 − ¨ 1 −
¸»
¸¨
Rh ¹ ©¨ λ r − λ p ¹¸ ¼»
©
¬«
ª
Fcb = Rb Rh F yc «∆ −
«¬
The variable description following
Eq. 6.11.8.2.2-4 reads:
Add missing phrase to read:
Fcv = nominal shear buckling resistance of the
flange calculated as follows:
Fcv = nominal shear buckling resistance of the
flange under shear alone calculated as
follows:
In the second paragraph of Article C6.11.8.2.2,
the sentence following Eq. C6.11.8.2.2-1 reads as
follows:
Revise to show the complete equation number as
follows:
Rearranging Eq. C6.11.8.2.2-1 in terms of fc and
substituting Fnc for fc facilitates the definition of
the nominal flexural resistance of the compression
flange as provided in Eq. 6.11.8.2.2.
Rearranging Eq. C6.11.8.2.2-1 in terms of fc and
substituting Fnc for fc facilitates the definition of
the nominal flexural resistance of the compression
flange as provided in Eq. 6.11.8.2.2-1.
In Article C6.11.8.2.2, the first sentence of the
third paragraph reads as follows:
Revise to include omitted phrase as follows:
The nominal axial compression buckling resistance
of the flange, Fcb, is defined for three distinct
regions based on the slenderness of the flange.
The nominal axial compression buckling
resistance of the flange under compression alone,
Fcb, is defined for three distinct regions based on
the slenderness of the flange.
§
∆ − 0.3 ·§¨ λ f − λ p
¨∆ −
¸
¨
Rh ¸¹¨© λ r − λ p
©
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
·º
¸»
¸»
¹¼
2012
Edition
LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
Page
6-191
(cont’d.)
6-192
6-202
Existing Text
Corrected Text
In Article C6.11.8.2.2, the fifth paragraph reads:
Revise to include omitted phrase as follows:
The equations for the nominal shear buckling
resistance of the flange, Fcv, are determined from
the equations for the constant, C, given in
Article 6.10.9.3.2, where C is the ratio of the
shear buckling resistance to the shear yield
strength of the flange taken as Fyc / 3 .
The equations for the nominal shear buckling
resistance of the flange under shear alone, Fcv, are
determined from the equations for the constant, C,
given in Article 6.10.9.3.2, where C is the ratio of
the shear buckling resistance to the shear yield
strength of the flange taken as Fyc / 3 .
Eq. 6.11.8.2.2-13 reads:
Revise to read:
( ∆ − 0.3 ) Fyc ≤ Fyw
( ∆ − 0.3 ) Fyc
In Eq. 6.12.2.2.1-4, there is an extra zero in the
first term of equation, reading “0.038”.
Delete zero to right of decimal point to read
“0.38”.
In the where list for Eq. 6.12.2.2.2-1, there are
separate definitions for b and t instead of one for
b/t.
Replace definitions for b and t with the following:
b/t = width of any flange or depth of any web
component divided by its thickness
neglecting any portions of flanges or
webs that overhang the box perimeter
6-225
First paragraph of Article 6.13.2.10.3 is not
indented.
Indent paragraph.
6-263
The second FHWA reference reads as follows:
Revise year and title to read:
FHWA. 2011. Manual for Design, Construction,
and Maintenance of Orthotropic Steel Bridges.
Federal Highway Administration, U.S.
Department of Transportation, Washington, DC.
FHWA. 2012. Manual for Design, Construction,
and Maintenance of Orthotropic Steel Deck
Bridges. Federal Highway Administration, U.S.
Department of Transportation, Washington, DC.
6-304
In Figure C6.4.5-1, the decision branch on the right
side involving “Shored Construction” is incorrect.
Replace with a singular box in flowchart reading
“Concrete compressive stress ≤ 0.6f ac”.
6-315
The figure immediately below Table D6.1-2 is
incorrect.
Replace figure.
Articles 9.8.3.6 and 9.8.3.7 need revisions.
After moving three paragraphs of Article C9.8.3.6
to Article C9.8.3.7, delete the rest of Article
9.8.3.6, renumber Article 9.8.3.7 as 9.8.3.6, and
renumber object references and article cross
references as needed.
Section 9
9-26
through
9-30
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
LRFDUS-6-E1: June 2012 Errata to LRFD Design, Sixth Edition
Page
9-28
Existing Text
Corrected Text
Article 9.8.3.6.4, item d reads:
Revise to read:
Combined fillet-groove welds may have to be
used in cases where the required size of fillet
welds to satisfy the fatigue resistance
requirements would be excessive, if used alone.
Combined fillet-groove welds may have to be used
1) in cases where the required size of fillet welds
to satisfy the fatigue resistance requirements
would be excessive if used alone or 2) to
accomplish a ground termination.
Eq. 12.12.2.2-2 is missing parentheses.
Revise to read:
9-44
Section 12
12-72
∆t =
12-74
Eq. 12.12.3.5-1 is missing parentheses.
(
)
K B DL Psp + CL PL Do
(
1000 E p I p R + 0.061 M s
3
)
+ ε sc D
Revise to read:
(
Pu = ηEV γ EV K γE K 2VAF P sp + γWA P w
+ ηLL γ LL P L C L
12-80
Eq. 12.12.3.9-1 is missing parentheses.
Revise to read:
PL =
12-83
Eq. 12.12.3.10.1e-2 is missing parentheses.
)
P (1 + IM /100 ) m
[ L0 + (12 H + K 1) LLDF ][W0 + (12 H + K1 ) LLDF ]
Revise to read:
εbck =
(
1.2Cn E p I p
Aeff E p
)
1
3
2
ª φ M (1 − 2ν ) º 3
« s s
» Rh
2
«¬ (1 − ν )
»¼
© 2012 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2012
Edition
2013 INTERIM REVISIONS TO THE AASHTO LFRD
BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
INSTRUCTIONS AND INFORMATION
INSTRUCTIONS AND INFORMATION
General
AASHTO has made interim revisions to the AASHTO LRFD Bridge Design Specifications, Sixth Edition (2012). This
packet contains the revised pages. They are not designed to replace the corresponding pages in the book but rather to be
kept with the book for quick reference.
Affected Articles
Underlined text indicates revisions that were approved in 2012 by the AASHTO Highways Subcommittee on Bridges
and Structures. Strikethrough text indicates any deletions that were likewise approved by the Subcommittee. A list of
affected articles is included below.
All interim pages have a page header displaying the section number affected and the interim publication year. Please
note that these pages may also contain nontechnical (e.g., editorial) changes made by AASHTO publications staff; any
changes of this type will not be marked in any way so as not to distract the reader from the technical changes.
Please note that in response to user concerns, page breaks are now being added within sections between
noncontiguous articles. This change makes it an option to insert the changes closer to the affected articles.
Table i—2012 Changed or Deleted Articles
SECTION 3: LOADS AND LOAD FACTORS
3.3
3.4.1
C3.4.1
3.6.1.1.1
3.6.1.2.6
3.6.1.2.6a
3.6.1.2.6b
3.6.1.2.6c
C3.6.1.2.6
3.16
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
4.3
4.6.2.2.1
4.6.2.2.2a
4.6.2.2.2b
4.6.2.2.2c
4.6.2.2.2d
4.6.2.2.2e
4.6.2.2.2f
4.6.2.2.3a
4.6.2.2.3b
4.6.2.2.3c
C4.6.3.2.4
4.9
SECTION 5: CONCRETE STRUCTURES
5.2
5.3
5.4.3.1
C5.4.3.1
5.4.3.2
5.4.3.3
C5.4.3.3
5.5.3.2
C5.5.3.2
5.5.4.2.1
C5.5.4.2.1
5.7
C5.7
5.7.2.1
C5.7.2.1
5.7.3.2.5
C5.7.3.3.1
5.7.3.4
C5.7.3.4
5.7.3.5
C5.7.3.5
C5.7.4.4
5.7.4.6
5.8.2.4
C5.8.2.4
5.8.2.4
5.8.2.5
C5.8.2.7
5.8.2.8
C5.8.2.8
iii
© 2013 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2013
Revision
2013 INTERIM REVISIONS TO THE AASHTO LFRD
BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
INSTRUCTIONS AND INFORMATION
C5.8.3.3
5.8.3.5
C5.8.3.5
5.8.4.1
5.8.6.2
5.10.2.1
5.10.2.2
C5.10.2.2
5.10.6.1
C5.10.6.1
5.10.11.1
5.11.1
C5.11.1
5.11.1.1
C5.11.1.1
5.11.2
C5.11.2
5.11.2.1
C5.11.2.1
5.11.2.4
5.11.2.4.3
5.11.4.1
C5.11.4.1
5.11.5
C5.11.5
5.11.5.3
C5.11.5.3
5.11.5.3.1
C5.11.5.3.1
5.12.3
5.15
APPENDIX C5
APPENDIX D5
SECTION 6: STEEL STRUCTURES
6.2
6.3
6.4.1
C6.4.1
6.6.1.2.1
6.6.1.2.3
6.6.1.2.5
C6.6.1.2.5
C6.9.4.1.3
C6.10.1
C6.10.1.1.1a
C6.10.1.6
C6.10.4.2.2
C6.10.6.1
C6.10.10.2
6.10.11.1.1
C6.10.11.1.1
C6.13.6.1.4a
6.13.6.1.4c
C6.13.6.1.4c
9.8.3.4.4
9.10
11.12
A11.3.1
6.17
SECTION 7: ALUMINUM STRUCTURES
This Section has been replaced in its entirety due to extreme revisions.
SECTION 9: DECKS AND DECK SYSTEMS
9.3
9.8.3.4.1
C9.8.3.4.1
SECTION 11: WALLS, ABUTMENT, AND PIERS
11.6.1.3
11.10.5.5
C11.10.5.5
SECTION 12: BURIED STRUCTURES AND TUNNEL LINERS
12.1
C12.1
12.3
12.4.1.3
C12.4.1.3
12.4.2.8
12.4.2.9
C12.4.2.9
12.4.2.10
12.5.1
C12.5.1
12.5.2
12.5.3
12.7
12.7.2.1
C12.7.2.1
12.7.2.2
12.7.2.4.1
12.7.2.7
C12.7.2.7
12.10.4.3.2C
C12.10.4.3.2C
C12.11.2.1
12.11.4.3.2
C12.11.4.3.2
12.11.4.4
12.12.1
C12.12.1
12.12.2.2
12.12.3.3
C12.12.3.3
12.12.3.5
C12.11.4.3.2
12.11.4.4
12.12.1
iv
© 2013 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2013
Revision
2013 INTERIM REVISIONS TO THE AASHTO LFRD
BRIDGE DESIGN SPECIFICATIONS, SIXTH EDITION 2012
INSTRUCTIONS AND INFORMATION
C12.12.1
12.12.2.2
12.12.3.3
C12.12.3.3
12.12.3.5
12.12.3.9
12.12.3.10.1b
C12.12.3.10.1b
12.12.3.10.1c
C12.12.3.10.1c
12.15
12.15.1
12.15.1
12.15.2
12.15.3
12.15.3.1
C12.15.3.1
12.15.3.2
C12.15.3.2
12.15.4
C12.15.4
12.15.5
12.15.5.1
12.15.5.2
C12.15.5.2
12.15.6
12.15.6.1
12.15.6.2
12.15.6.3
12.15.6.4
12.15.7
12.16
SECTION 13: RAILINGS
13.8.2
SECTION 14: JOINTS AND BEARINGS
C14.6.5.2
C14.6.5.3
14.10
v
© 2013 by the American Association of State Highway and Transportation Officials.
All rights reserved. Duplication is a violation of applicable law.
2013
Revision
INDEX
Index Terms
Links
A
Abutments and retaining walls
backfill
11-5
bearing resistance
11-8
11-15
conventional walls and abutments
11-16
11-18
drainage
11-33
expansion and contraction joints
11-18
extreme event limit state
11-7
free-standing abutments
11-110
integral abutments
11-18
load combinations and load factors
11-10
loading
11-17
movement and stability
11-19
overturning
11-64
passive resistance
11-23
reinforcement
11-18
resistance factors
11-6
safety against structural failure
11-23
seismic design
11-23
service limit state
11-103
11-10
11-6
11-19
11-23
11-65
strength limit state
11-7
11-20
subsurface erosion
11-22
wingwalls
11-18
sliding
11-102
Aeroelastic instability
aeroelastic phenomena
3-43
control of dynamic responses
3-44
wind tunnel tests
3-44
Alkali-silica reactive aggregates
5-175
Aluminum
minimum thickness
7-21
Aluminum orthotropic decks
See: Orthotropic aluminum decks
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Anchor bolts
bearings
14-83
deck joints
14-17
Anchorages
bearings
14-67
deck joints
14-17
elastomeric bearings
14-63
footings
10-53
post-tensioned anchorage zones
5-122
post-tensioning
14-82
5-21
railings
13-17
tension ties
5-33
Anchored walls
11-43
anchor pullout capacity
11-46
anchor stressing and testing
11-53
anchors
11-49
bearing resistance
11-45
construction and installation
11-53
corrosion protection
11-52
drainage
11-54
dynamic load allowance
3-30
3-23
earth pressure
3-99
3-113
facing
11-51
loading
11-44
movement
11-44
overall stability
11-45
passive resistance
11-49
safety against soil failure
11-45
safety against structural failure
11-49
seismic design
11-51
ultimate unit bond stress for anchors
11-46
vertical wall elements
11-51
Angles
flexural resistance
6-205
6-209
3-138
3-141
Annual frequency of collapse
geometric probability
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Annual frequency of collapse (Cont.)
probability of aberrancy
3-143
probability of collapse
3-147
vessel frequency distribution
3-142
Approximate methods of analysis
analysis of segmental concrete bridges
4-65
beam-slab bridges
4-29
decks
4-22
effective flange width
4-54
effective length factor
4-49
equivalent strip widths for box culverts
4-67
equivalent strip widths for slab-type
bridges
4-48
lateral wind load distribution in
multibeam bridges
4-62
moment magnification
4-14
4-15
orthotropic decks
9-20
9-27
seismic lateral load distribution
4-63
stress analyses and design
truss and arch bridges
5-137
4-49
Arch bridges
refined analysis
4-70
Arch structures
See: Metal pipe, pipe arch, and arch
structures
Arches
5-231
aluminum structures
7-56
arch ribs
5-231
load distribution
4-49
moment magnification
4-15
steel, diaphragms
6-60
4-73
B
Backfill
See: Abutments and retaining walls
Barriers
See: Railings
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Basic requirements of structural dynamics
damping
4-77
distribution of masses
4-77
natural frequencies
4-77
stiffness
4-77
Batter piles
10-82
Beam columns
moment magnification
Beam ledges
4-14
5-182
design for bearing
5-186
design for flexure and horizontal force
5-184
design of hanger reinforcement
5-185
design for punching shear
5-184
design for shear
5-183
Beam-slab bridges
application
4-29
distribution factor method for moment
and shear
4-35
distribution factor method for shear
4-42
refined methods of analysis
4-68
special loads with other traffic
4-47
Bearing area
concrete
5-57
Bearing pressure
spread footings
10-52
Bearing resistance
abutments and retaining walls
11-10
anchored walls
11-45
buried structures
12-18
fastener holes
7-53
flat surfaces and pins
7-53
MSE walls
11-64
prefabricated modular walls
reinforced concrete pipe
at rivet and bolt holes
spread footings
11-20
11-102
12-61
7-53
10-64
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Bearing stiffeners
6-165
axial resistance
6-166
bearing resistance
6-165
projecting width
6-165
steel
6-285
Bearings
14-1
See also: Disc bearings, Elastomeric
bearings, Pot bearings
anchor bolts
14-82
applicability
14-40
bearing resistance
14-49
bronze or copper alloy sliding surfaces
14-76
characteristics
14-36
corrosion protection
14-84
curved sliding surfaces
14-12
design criteria
14-41
design requirements
14-10
14-49
fabrication, installation, testing, and
shipping
14-40
force effects resulting from restraint of
movement at the bearing
14-37
guides and restraints
14-79
horizontal force and movement
14-37
launching
5-211
metal rocker and roller bearings
14-42
moment
14-38
movements and loads
14-6
other bearing systems
14-81
plates for load distribution
14-82
PTFE sliding surfaces
14-44
resistance to lateral load
14-50
seismic design
14-84
seismic provisions
14-40
special design provisions
14-42
tapered plates
14-83
Bicycle railings
5-228
5-232
13-11
design live loads
13-11
geometry
13-11
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Bolted connections
6-214
See also: Bolted splices, Bolts
bearing resistance at fastener holes
bearing-type
7-53
6-215
block shear or end rupture
7-54
bolts and nuts
7-50
combined tension and shear
6-226
edge distance
6-220
7-52
end distance
6-219
7-52
factored resistance
6-215
holes
6-217
maximum pitch for sealing fasteners
maximum pitch for stitch bolts
7-51
6-219
maximum pitch for stitch fasteners
7-52
maximum spacing for sealing bolts
6-218
minimum edge distance
6-220
minimum pitch and clear distance
minimum spacing and clear distance
nuts
7-51
6-218
6-26
shear resistance
6-220
shear resistance of fasteners
7-52
size of fasteners
7-51
slip-critical
6-214
slip-critical connections
slip resistance
7-53
6-221
spacing of fasteners
7-51
stitch fasteners at the end of compression
members
7-52
tension
7-53
washers
6-26
6-216
Bolted splices
compression members
6-233
fillers
6-241
flange splices
6-238
flexural members
6-233
tension members
6-232
web splices
6-243
welded splices
6-242
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Bolts
bearing resistance
6-224
materials
6-25
minimum required bolt tension
6-221
prying action
6-225
size
6-218
spacing
6-218
tensile resistance
6-225
Boundary conditions
mathematical modeling
4-10
Box culverts
equivalent strip widths
4-67
live loads
3-27
4-27
Box girders
effective flange width
4-54
wind load distribution
4-62
Bracing
See also: Diaphragms and cross-frames,
Lateral bracing
box sections
4-63
glued laminated timber girders
8-37
portal bracing
6-246
sawn wood beams
7-56
8-36
sway bracing
6-246
7-56
trusses
6-246
8-37
Brackets and corbels
5-179
alternative to strut-and-tie model
5-181
Braking force
3-32
Bridge aesthetics
2-16
Bridge joints
See: Deck joints
Bridge scour
See: Scour
Bridge site arrangement
traffic safety
Bridge testing
2-4
2-4
4-90
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Bridges composed of simple span precast
girders made continuous
5-201
age of girder when continuity is
established
5-203
continuity diaphragms
5-209
degree of continuity at various limit states
5-204
material properties
5-203
negative moment connections
5-206
positive moment connections
5-206
restraint moments
5-202
service limit state
5-205
strength limit state
5-206
Bronze or copper alloy sliding surfaces
14-76
clearances and mating surfaces
14-77
coefficient of friction
14-77
limit on load
14-77
materials
14-76
Builtup members
6-78
perforated plates
6-78
Bundled reinforcement
development length
5-162
number of bars in a bundle
5-112
spacing
5-112
ties
5-120
Buried structures
bearing resistance and stability
12-18
corner backfill for metal pipe arches
12-19
corrosive and abrasive conditions
12-23
cross-section properties
12-91
differential settlement between structure
and backfill
12-14
embankment installations
12-19
end treatment
12-22
flexibility limits and construction
stiffness
12-13
flexible culverts constructed on skew
12-22
footing settlement
12-14
hydraulic design
12-19
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Buried structures (Cont.)
load modifiers and load factors
12-9
loading
12-13
longitudinal differential settlement
12-14
mechanical properties
12-73
minimum longitudinal seam strength
12-90
minimum soil cover
12-20
12-100
12-101
minimum spacing between multiple lines
of pipe
12-21
resistance factors
12-10
safety against soil failure
12-18
scour
12-19
service limit state
12-9
settlement
12-14
soil envelope
12-19
strength limit state
12-9
tolerable movement
12-14
trench installations
12-19
unbalanced loading
12-15
uplift
12-18
12-14
C
Cable-stayed bridges
refined analysis
4-72
Cables
bridge strand
6-29
bright wire
6-28
epoxy-coated wire
6-29
galvanized wire
6-28
Caissons
See: Drilled shafts
Camber
aluminum structures
7-18
glued laminated timber girders
8-37
heat-curved rolled beams and welded
plate girders
6-70
6-71
This page has been reformatted by Knovel to provide easier navigation.
12-103
Index Terms
Links
Camber (Cont.)
steel structures
6-57
stress laminated timber deck bridge
8-37
trusses
6-245
8-37
Cantilever slabs
design
9-8
segmental construction
5-211
wheel load position
3-25
Cantilevered retaining walls
11-34
corrosion protection
11-42
drainage
11-43
earth pressure
3-99
facing
11-36
loading
11-34
movement
11-34
overall stability
11-35
safety against soil failure
11-35
safety against structural failure
11-36
seismic design
11-38
vertical wall elements
11-36
Cast-in-place box culverts and arches
12-65
cast-in-place structures
12-70
construction and installation
12-71
design moment for box culverts
12-70
distribution of concentrated loads in
skewed box culverts
12-69
distribution of concentrated loads to
bottom slab of culvert
12-69
earth load modification
12-66
embankment and trench conditions
12-66
loads and live load distribution
12-66
minimum cover for precast box
structures
12-71
minimum reinforcement
12-71
other installations
12-69
precast box structures
12-70
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Cast-in-place box culverts and arches (Cont.)
safety against structural failure
12-70
service limit state
12-69
soil-structure interaction
12-66
Cast-in-place girders and box and T-beams
bottom flange
5-210
bottom slab reinforcement in box girders
5-211
deck slab reinforcement cast-in-place in
T-beams and box girders
effective flange width
5-210
4-54
flange and web thickness
5-210
reinforcement
5-210
top flange
5-210
web
5-210
4-55
Cast-in-place piles
See: Concrete piles
Cast-in-place solid slab superstructures
5-231
Cast-in-place voided slab superstructures
5-232
compressive zones in negative moment
area
5-234
cross-section dimensions
5-232
drainage of voids
5-234
general design requirements
5-233
minimum number of bearings
5-233
solid end sections
5-233
Cast metal
cast iron
6-28
cast steel and ductile iron
6-28
malleable castings
6-28
Cellular and box bridges
refined analysis
Centrifugal forces
4-72
3-32
Charpy V-notch test
requirements
6-48
temperature zones
6-49
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Clearances
drilled shafts
10-124
highway horizontal
2-6
highway vertical
2-6
navigational
2-6
piles
10-81
railroad overpass
2-6
Coefficient of thermal expansion
concrete
5-15
Collision force
See: Vehicular collision force, Vessel
collisions
Combination railings
13-12
design live loads
13-12
geometry
13-12
Combined force effects
aluminum
7-48
Compact sections
nominal flexural resistance
6-136
6-187
Composite box girders
See also: Box girders
diaphragms
6-59
fatigue
6-157
lateral bracing
6-65
wind effects
4-79
Composite sections
aluminum
7-19
concrete-encased shapes
6-99
6-212
concrete-filled tubes
6-99
6-212
nominal shear resistance
6-212
sequence of loading
6-102
steel
6-102
stresses
6-102
Compression flange flexural resistance
6-142
6-284
lateral torsional buckling resistance
6-144
6-279
local buckling resistance
6-143
6-278
Compression flange proportions
6-196
6-213
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Compression members
aluminum
7-24
axial resistance
5-51
biaxial flexure
5-52
compressive resistance
6-77
concrete
5-53
hollow rectangular
5-38
limiting slenderness ratio
6-81
splices
7-54
steel composite members
6-98
steel noncomposite members
6-82
subjected to torsion
7-45
wood
8-33
5-53
5-54
7-27
7-29
Compressive resistance
aluminum
7-26
axial compression
6-81
combined axial compression and flexure
6-81
concrete
5-53
steel
6-81
steel composite members
6-98
steel noncomposite members
6-82
steel piles
6-252
Compressive struts
effective cross-sectional area of strut
5-32
limiting compressive stress in strut
5-33
reinforced strut
5-33
strength of unreinforced strut
5-31
Concrete
basic steps for concrete bridges
5-247
classes
5-13
coefficient of thermal expansion
5-15
cohesion factor
5-83
compressive strength
5-13
creep
5-15
effects of imposed deformation
5-29
friction factor
5-82
modulus of elasticity
5-21
modulus of rupture
5-18
This page has been reformatted by Knovel to provide easier navigation.
7-31
7-35
Index Terms
Links
Concrete (Cont.)
Poisson’s ratio
5-18
properties
5-20
shrinkage
3-133
strut-and-tie model
5-29
tensile strength
5-18
unit weight
3-16
Concrete box girders
bridges composed of simple span precast
girders made continuous
cross-section dimensions and details
5-201
5-220
effective flange width
4-54
girder segment design
5-200
joints between segments
5-205
length of top flange cantilever
5-199
live load distribution factors
4-30
minimum flange thickness
5-220
minimum web thickness
5-220
overlays
5-222
post-tensioning
5-201
prestress losses
5-105
spliced precast girders
5-198
torsional resistance
5-200
5-77
Concrete deck slabs
See: Concrete slabs
Concrete formwork
bedding of panels
9-14
creep and shrinkage control
9-14
depth
9-13
reinforcement
9-14
Concrete piles
5-192
cast-in-place piles
5-194
pile dimensions
5-192
precast prestressed
5-192
precast reinforced
5-192
reinforcing steel
5-192
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Concrete piles (Cont.)
seismic requirements
5-194
splices
5-112
structural resistance
10-117
Concrete slabs
application of empirical design
9-9
composite action
9-7
design conditions
9-10
design of cantilever slabs
9-8
distribution reinforcement
9-12
edge support
9-8
effective length
9-9
empirical design
9-8
minimum depth and cover
9-7
precast deck slabs on girders
9-14
reinforcement requirements
9-11
segmental construction
9-15
shear
5-57
skewed bridges
4-40
skewed decks
9-7
stay-in-place formwork
9-12
traditional design
9-12
Concrete stress limits
partially prestressed components
5-98
service limit state after losses
5-95
temporary stresses before losses
5-93
Connections
See also: Bolted connections, Splices,
Welded connections
block shear or end rupture
7-54
block shear rupture resistance
6-230
elements
6-231
rigid frame
6-243
rigid frame connections
6-243
Constructibility
dead load deflections
6-120
6-179
6-126
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Constructibility (Cont.)
deck placement
6-124
design objectives
2-7
2-20
flexure
6-121
6-179
shear
6-124
6-182
Continuous beam bridges
approximate method of analysis
4-22
refined method of analysis
4-68
Continuously braced flanges in tension
6-190
Continuously braced flanges in tension or
compression
6-123
6-141
Corrosion
buried structures
12-23
piles
10-119
Corrosion protection
alternative coating
8-23
anchored walls
11-52
bearings
14-84
cantilevered retaining walls
11-42
metallic coating
8-23
Corrugated metal decks
composite action
9-30
distribution of wheel loads
9-30
Cover plates
6-170
end requirements
6-170
yield moment
6-317
Creep effect
3-135
5-15
6-119
6-178
Cross-frames
See: Diaphragms and cross-frames
Cross-section proportion limits
flange proportions
special restrictions on use of live load
distribution factor for multiple box
sections
6-178
web proportions
6-118
6-177
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Culverts
See also: Long-span structural plate
structures
design for flexure
5-236
design for shear in slabs of box culverts
5-236
live loads
3-25
location, length, and waterway area
2-23
segmental construction
Curbs
5-211
13-12
end treatment of separation railing
13-13
Curved structures
concrete cover, prestressing tendons
5-118
multicell concrete box girders
4-32
multiple beam superstructures
4-20
single girder superstructures
4-18
torsionally stiff superstructures
4-18
Curved tendons
effects of curved tendons
5-114
in-plane force effects
5-115
out-of-plane force effects
5-118
D
Dead loads
load factors
3-16
MSE walls
11-96
steel structures
6-57
unit weight of materials
6-126
3-7
Deck analysis
deck slab design table
4-97
loading
9-6
methods
4-22
methods of analysis
9-6
Deck joints
adjustment
14-18
anchors
14-17
armor
14-17
bolts
14-18
bridging plates
14-17
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Deck joints (Cont.)
closed joints
14-20
compression and cellular seals
14-21
design requirements
14-10
fabrication
14-18
field splices
14-19
geometry
14-14
installation
14-18
joint seals
14-20
location
14-15
maintenance
14-14
materials
14-14
modular bridge joint systems
14-22
movements and loads
14-15
14-6
movements during construction
14-15
movements in service
14-16
number of joints
14-14
open joints
14-19
plank seals
14-22
poured seals
14-21
protection
14-16
requirements
14-12
segmental construction
9-15
selection
14-14
sheet and strip seals
14-21
specific joint type considerations
14-19
structural design
14-13
temporary supports
14-19
waterproofed joints
14-20
Deck overhang design
13-25
decks supporting concrete parapet
railings
13-25
decks supporting post-and-beam railings
13-26
design cases
13-25
overhang design
13-26
resistance to punching shear
13-27
stay-in-place formwork
Deck overhang load
9-5
3-28
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Decks
See also: Deck joints, Deck overhang
design
applicability
4-22
concrete appurtenances
cross-sectional frame action
deck drainage
9-5
4-27
9-4
distribution of wheel loads
4-26
edge supports
9-5
edges of slabs
4-25
equivalent strips
4-23
force effects
4-24
inelastic analysis
4-29
interface action
9-4
live load effects on grids
4-27
live loads
3-25
longitudinal edges
4-25
stay-in-place formwork
transverse edges
9-5
4-25
Deep beams
detailing requirements
5-178
Deflection
aluminum
7-9
criteria
2-11
Deformations
axial
5-48
concrete
5-59
criteria for deflection
2-11
criteria for span-to-depth ratios
2-13
force effects due to superimposed
deformations
3-133
permanent
6-127
steel
6-127
Deformed bars and deformed wire in tension
tension development length
5-160
Deformed bars in compression
compressive development length
5-162
modification factors
5-162
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Depth of the web in compression
in the elastic range
6-317
at plastic moment
6-318
Design lane load
3-24
Design lanes
number of
3-17
Design objectives
bridge aesthetics
2-16
constructibility
2-14
economy
2-15
safety
2-7
serviceability
2-8
Design philosophy
ductility
1-5
limit states
1-3
operational importance
1-7
redundancy
1-6
Design tandem
3-24
Design truck
3-23
Design vessel
3-138
Development of reinforcement
basic requirements
5-157
bonded strand
5-168
bundled bars
5-112
deformed bars and deformed wire in
tension
5-160
deformed bars in compression
5-162
development by mechanical anchorages
5-167
flexural reinforcement
5-167
footings
5-187
modification factors
5-161
partially debonded strands
5-169
prestressing strand
5-166
shear reinforcement
5-185
standard hooks in tension
5-163
welded wire fabric
5-164
5-162
5-163
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Diaphragms and cross-frames
aluminum structures
6-59
7-21
concrete structures
5-174
orthotropic deck superstructures
6-247
steel arches
6-64
steel box section members
6-62
steel I-section members
6-60
steel trusses
6-64
Disc bearings
5-211
5-220
6-246
14-77
See also: Bearings
elastomeric disc
14-78
materials
14-78
movements and loads
14-12
shear resistance mechanism
14-79
steel plates
14-79
Distortion-induced fatigue
7-17
lateral connection plates
6-52
orthotropic decks
6-53
transverse connection plates
6-52
7-18
7-18
Distribution of load
concrete slabs
4-27
curved steel bridges
4-46
exterior beams
4-39
4-44
4-46
interior beams
4-35
4-38
4-42
4-46
skewed bridges
4-40
4-46
wheel loads through earth fills
3-25
Dowels
concrete columns
5-187
Downdrag
3-131
10-83
10-89
10-95
10-128
10-126
10-130
10-147
10-148
Drainage
See also: Roadway drainage
abutments and retaining walls
11-33
anchored walls
11-54
cantilevered retaining walls
11-43
cast-in-place voided slab superstructures
5-232
MSE walls
11-94
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Drainage (Cont.)
prefabricated modular walls
sound barrier
11-105
15-2
steel box-section flexural members
Drilled shafts
15-14
6-177
10-123
battered shafts
10-124
buckling
10-143
clearance
10-124
combined side and tip resistance
10-138
concrete
10-144
diameter
10-124
downdrag
10-126
embedment
10-124
enlarged bases
10-124
extreme event limit state
10-144
groundwater table and buoyancy
10-130
group resistance
10-140
horizontal movement
10-130
horizontal resistance
10-143
lateral squeeze
10-130
lateral stability
10-143
load test
10-139
reinforcement
10-143
10-144
resistance in cohesionless soils
10-134
10-140
resistance in cohesive soils
10-131
10-141
resistance in rock
10-136
scour
10-130
service limit state
10-126
settlement
10-126
shaft loads
10-126
shaft resistance
10-125
10-130
10-144
10-130
shaft resistance in intermediate geo
materials
10-139
shafts in strong soil overlying weaker
compressible soil
10-136
side resistance
10-132
spacing
10-124
strength limit state
10-130
10-134
10-137
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Drilled shafts (Cont.)
structural resistance
10-143
tip resistance
10-133
tolerable movements
10-126
transverse reinforcement
10-144
uplift
10-126
uplift resistance
10-142
10-135
10-138
Driven piles
See: Piles
Ductility
1-5
Ductility requirements
steel I-section flexural members
6-140
Ducts
at deviation saddles
5-23
size of
5-22
spacing
5-112
Durability
5-113
5-174
alkali-silica reactive aggregates
5-175
concrete cover
5-175
materials
2-8
protection for prestressing tendons
5-176
protective coatings
5-176
self-protecting measures
2-8
Dynamic analysis
Analysis of blast effects
4-90
analysis for collision loads
4-90
analysis for earthquake loads
4-77
basic requirements
4-79
elastic dynamic responses
4-76
inelastic dynamic responses
4-80
Dynamic load allowance
buried components
3-31
wood components
3-32
E
Earth loads
sound barrier
3-17
15-9
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Earth pressure
3-99
active
3-103
anchored walls
3-113
at-rest
3-103
cantilevered walls
3-109
compaction
3-100
downdrag
3-131
effect of earthquake
3-101
equivalent-fluid method of estimating
3-107
friction angle for dissimilar materials
3-105
lateral earth pressure
3-101
mechanically stabilized earth walls
3-116
passive
3-105
prefabricated modular walls
3-118
presence of water
3-100
reduction due to earth pressure
3-131
surcharge loads
3-123
3-109
Earthquake effects
See: Seismic loads
Economy
alternative plans
2-15
Edge distance
6-220
Edge support
slabs
9-8
Effective area
aluminum
7-23
steel
6-57
welds
6-229
Effective flange width
4-54
cast-in-place multicell superstructures
4-59
orthotropic steel decks
4-59
analysis of segmental concrete bridges
4-65
segmental concrete box beams and single
cell cast-in-place box beams
4-55
Effective length
columns
4-49
span
6-57
7-19
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Effective plastic moment
all other interior-pier sections
6-290
interior-pier sections with enhanced
moment-rotation characteristics
6-289
Elastic dynamic responses
vehicle-induced vibration
4-79
wind-induced vibration
4-79
Elastic stress analysis
5-136
Elastomeric bearings
See also: Bearings
combined compression, rotation, and
shear
14-60
compressive deflection
14-65
14-71
compressive stress
14-70
design method A
14-67
design method B
14-56
extreme event provisions
14-66
14-75
material properties
14-58
14-69
movements and loads
14-11
reinforcement
14-64
rotation
14-73
seismic provisions
14-66
shear
14-73
shear deformation
14-59
stability
14-63
14-75
14-75
14-75
Elastomeric pads
See: Elastomeric bearings
Emergency responder access to sound
barriers
15-2
End requirements
cover plates
6-170
Environment
2-7
Equivalent members
mathematical modeling
Erosion control
4-10
11-22
11-95
11-103
Existing bridges, sound barrier installation
for
15-5
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Expansion
See: Coefficient of thermal expansion
Expansion devices for sound barriers
Extreme event limit states
15-4
1-5
abutments and retaining walls
11-7
concrete structures
5-44
decks
11-16
9-6
drilled shafts
10-144
foundations
10-31
10-50
3-11
3-13
load combinations
piles
10-118
railings
13-5
spread footings
10-80
steel structures
6-31
vessel collision damage
wood structures
3-138
8-31
Eyebars
factored resistance
6-78
minimum size pin for
6-69
packing
6-80
proportions
6-80
F
Fasteners
See also: Bolts
alternative
6-27
shear resistance of
7-52
spacing of
7-51
Fatigue
distortion-induced
6-46
load-induced
6-31
Fatigue and fracture limit states
aluminum structures
1-4
7-9
concrete structures
decks
5-23
5-35
9-6
9-18
modular bridge joint systems
14-29
orthotropic aluminum decks
9-26
prestressing tendons
5-25
This page has been reformatted by Knovel to provide easier navigation.
9-19
Index Terms
Links
Fatigue and fracture limit states (Cont.)
reinforcing bars
5-24
steel box-section flexural members
6-183
steel I-section flexural members
6-130
steel structures
6-29
welded or mechanical splices of
reinforcement
5-25
Fatigue design
cycles
6-49
orthotropic steel decks
6-83
6-51
Fatigue load
approximate methods
3-25
frequency
3-29
load distribution for fatigue
3-29
magnitude and configuration
3-28
refined methods
3-29
Fatigue resistance
shear connectors
6-157
Filled and partially filled grid decks
design requirements
9-17
fatigue and fracture limit state
9-18
Fillers
bolted splices
6-241
Fillet-welded connections
6-228
size
6-229
Flange proportions
6-178
Flange-strength reduction factors
hybrid factor
6-113
web load-shedding factor
6-114
Flexibility limits and construction stiffness
corrugated metal pipe and structural plate
structures
12-12
spiral rib metal pipe and pipe arches
12-12
steel tunnel liner plate
12-13
thermoplastic pipe
12-13
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Flexural members
aluminum
7-30
concrete
5-39
splices
7-54
wood
8-28
5-121
8-31
Flexural resistance
based on tension flange yielding
6-282
based on the compression flange
6-277
box flanges in compression
6-190
compact sections
6-136
compression-flange flexural resistance
6-142
concrete
6-187
5-44
continuously braced flanges in tension
6-190
continuously braced flanges in tension or
compression
6-141
discretely braced flanges in compression
6-141
discretely braced flanges in tension
6-141
ductility requirement
6-140
interior-pier I-sections in straight
continuous-span bridges
6-286
lateral torsional buckling
resistance
6-144
6-279
local buckling resistance
6-143
6-278
noncompact sections
6-139
6-187
straight composite I-sections in negative
flexure
6-271
straight noncomposite I-sections with
compact or noncompact webs
6-271
tension-flange flexural resistance
6-150
Flexure
composite sections in negative flexure
and noncomposite sections
6-134
composite sections in positive flexure
6-132
concrete deck
6-123
continuously braced flanges in tension or
compression
6-123
discretely braced flanges in compression
6-121
discretely braced flanges in tension
6-123
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Footings
5-187
development of reinforcement
5-190
distribution of moment reinforcement
5-188
loads and reactions
5-187
moment in
5-187
reactions
5-187
resistance factors
5-187
shear in slabs and footings
transfer of force at base of column
Foundation design
5-59
12-30
5-188
5-190
10-163
Foundation investigation
2-7
topographic studies
10-163
2-7
Fracture
aluminum
7-18
steel
6-53
toughness requirements
6-53
Free-standing abutments
design for displacement
11-120
Mononobe-Okabe analysis
11-110
nonyielding abutments
Friction forces
11-30
3-138
G
General zone
5-124
application of the strut-and-tie model
5-132
blister and rib reinforcement
5-130
design methods
5-125
design principles
5-126
deviation saddles
5-132
diaphragms
5-131
intermediate anchorages
5-129
multiple slab anchorages
5-131
responsibilities
5-125
special anchorage devices
5-144
tie-backs
5-130
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Geometry
bicycle railings
13-11
combination railings
13-12
deck joints
14-14
large deflection theory
4-12
pedestrian railings
13-9
small deflection theory
4-12
traffic railings
13-15
Geophysical tests
soil and rock
10-12
Glued laminated decks
9-32
deck tie-downs
9-32
interconnected decks
9-32
noninterconnected decks
9-33
Glued laminated timber
See also: Wood
bracing
8-36
camber
8-37
dimensions
8-13
reference design values
8-14
volume factor
8-27
Gravel
unit weight
3-16
Gravity loads
design vehicular live load
3-19
vehicular live load
3-17
Groove-welded connections
complete penetration
6-227
partial penetration
6-228
Grout
steel tunnel liner plate
12-88
Guides and restraints
14-79
attachment of low-friction material
14-81
contact stress
14-81
design basis
14-80
design loads
14-80
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Guides and restraints (Cont.)
geometric requirements
14-80
load location
14-80
materials
14-80
Gusset plates
6-246
H
Heat-curved rolled beams and welded plate
girders camber
6-70
minimum radius of curvature
6-70
High load multirotational (HLMR) bearings
curved sliding surface bearings
14-12
disc bearings
14-12
pot bearings
14-12
Holes
long-slotted
6-217
7-51
maximum hole size
6-217
oversize
6-217
7-51
short-slotted
6-217
7-51
size
6-217
type
6-217
Hollow rectangular compression members
hoops
5-157
limitations on the use of the rectangular
stress block method
5-54
reinforcement
5-156
splices
5-156
ties
5-156
wall slenderness ratio
5-53
Hooks and bends
basic hook development length
5-163
hooked-bar tie requirements
5-164
minimum bend diameters
5-110
modification factors
5-162
seismic hooks
5-110
standard hooks
5-110
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Horizontal wind pressure
on structures
3-41
on vehicles
3-42
Hydraulic analysis
bridge foundations
2-20
bridge waterway
2-20
roadway approaches to bridge
2-23
stream stability
2-17
Hydrology and hydraulics
culvert location, length, and waterway
area
2-23
hydraulic analysis
2-19
hydrologic analysis
2-18
roadway drainage
2-24
site data
2-18
I
Ice loads
adhesion
3-50
combination of forces
3-49
crushing and flexing
3-47
dynamic ice forces on piers
3-46
effective ice strength
3-46
hanging dams and ice jams
3-50
ice accretion and snow loads on
superstructures
3-51
slender and flexible piers
3-50
small streams
3-48
static ice loads on piers
3-50
Idealization
See: Mathematical modeling
Impact
See: Dynamic load allowance
In-situ tests
See: Soil properties
Inelastic dynamic responses
plastic hinges and yield lines
4-80
4-80
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Influence of plan geometry
curved structures
4-17
plan aspect ratio
4-17
Instantaneous losses
anchorage set
5-98
elastic shortening
5-101
friction
5-99
Interaction systems
See: Culverts
Interconnected decks
panels parallel to traffic
9-32
panels perpendicular to traffic
9-32
Interface shear transfer—shear friction
cohesion and friction factors
5-82
computation of factored interface shear
force
5-80
minimum area of interface shear
reinforcement
5-83
Interior beams
distribution of load
4-35
4-38
L
Laboratory tests
rock properties
10-11
soil properties
10-11
Lap splices
in compression
5-172
general requirements
5-170
in tension
5-171
Large deflection theory
4-12
approximate methods
4-13
refined methods
4-16
Lateral bracing
See also: Bracing, Diaphragms and cross-frames
aluminum structures
7-22
I-section members
6-65
7-55
This page has been reformatted by Knovel to provide easier navigation.
4-42
Index Terms
Links
Lateral bracing (Cont.)
through-spans
7-22
trusses
6-68
tub section members
6-66
Lateral buckling
equations for
6-319
Lateral clearance, sound barrier
Lateral torsional buckling resistance
15-2
6-144
6-279
Lightweight concrete
coefficient of thermal expansion
5-15
compressive strength
5-13
creep
5-15
modifications for
5-59
modulus of elasticity
5-17
modulus of rupture
5-18
Poisson’s ratio
5-18
shrinkage
5-17
tensile strength
5-19
unit weight
3-16
Limit states
See: Extreme event limit states, Fatigue
and fracture limit states, Service limit
states, Strength limit states
Live loads
application
3-25
braking force
3-32
centrifugal forces
3-32
deck overhang load
3-28
decks, deck systems, top slabs of box
culverts
3-27
design lane load
3-24
design tandem
3-24
design truck
3-23
4-68
distribution of wheel loads through earth
fills
3-25
gravity loads
3-17
live load deflection
3-26
multiple box sections
6-178
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Live loads (Cont.)
multiple presence
3-18
reinforced concrete pipe
12-52
steel tunnel liner plate
12-88
tire contact area
3-24
vehicular collision force
3-35
Load factors
3-8
buried structures
12-9
combinations
construction loads
definition
3-8
3-15
3-15
5-213
5-226
1-2
jacking
3-16
modular bridge joint systems
14-25
post-tensioning
3-16
Load indicator devices
6-27
Load-induced fatigue
application
6-32
7-12
design criteria
6-33
7-12
detail categories
6-34
7-12
detailing to reduce constraint
6-48
fatigue resistance
6-48
7-16
steel
6-143
6-278
Local zone
5-124
Local buckling
bearing resistance
5-143
dimensions of
5-142
responsibilities
5-125
special anchorage devices
5-129
Location features
bridge site arrangement
2-4
clearances
2-6
environment
2-7
route location
2-3
Long-slotted holes
6-217
Long-span structural plate structures
12-26
acceptable special features
12-29
backfill protection
12-38
balanced support
12-35
7-51
This page has been reformatted by Knovel to provide easier navigation.
5-229
Index Terms
Links
Long-span structural plate structures (Cont.)
concrete relieving slabs
12-36
construction and installation
12-37
construction requirements
12-31
continuous longitudinal stiffeners
12-29
cross-section
12-27
cut-off (toe) walls
12-36
end treatment design
12-33
footing design
12-31
footing reactions in arch structures
12-30
foundation design
12-29
hydraulic protection
12-35
hydraulic uplift
12-36
mechanical and chemical requirements
12-28
reinforcing ribs
12-29
safety against structural failure
12-25
scour
12-36
seam strength
12-29
section properties
12-27
service limit state
12-27
service requirements
12-32
settlement limits
12-29
shape control
12-28
soil envelope design
12-31
standard shell end types
12-33
thrust
12-29
wall area
12-29
Longitudinal stiffeners
12-27
12-29
6-166
limiting slenderness ratio
6-82
long-span structural plate structures
12-29
moment of inertia and radius of gyration
6-169
projecting width
6-169
Loss of prestress
approximate estimate of time-dependent
losses
5-103
creep
5-108
instantaneous losses
5-114
5-98
losses for deflection calculations
5-109
This page has been reformatted by Knovel to provide easier navigation.
12-33
Index Terms
Links
Loss of prestress (Cont.)
refined estimate
5-104
relaxation
5-106
shrinkage
5-105
total
5-108
5-98
M
Maintenance access to sound barriers
15-2
Materials
adjustment factors for reference design
values
8-24
alternative fasteners
6-27
aluminum castings
7-7
aluminum forgings
7-7
aluminum pipe and structural plate
structures
12-7
aluminum sheet, plate, and shapes
bolts, nuts, and washers
bronze or copper alloy sliding surfaces
7-3
6-25
14-76
cables
6-28
cast metal
6-28
concrete
5-12
deck joints
14-14
disc bearings
14-77
fasteners—rivets and bolts
glued laminated timber
7-6
8-12
guides and restraints
14-79
load indicator devices
6-25
metal fasteners and hardware
8-21
pins, rollers, and expansion rockers
pins, rollers, and rockers
pot bearings
12-7
7-6
6-25
14-51
precast concrete pipe
12-7
precast concrete structures
12-7
precast reinforced concrete three-sided
structures
12-91
preservative treatment
8-23
prestressing steel
5-22
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Materials (Cont.)
railings
13-5
sawn lumber
8-5
stainless steel
6-28
steel pipe and structural plate structures
12-8
steel reinforcement
12-7
structural steels
6-22
stud shear connectors
6-27
thermoplastic pipe
12-7
weld metal
6-27
wood products
7-7
8-5
Mathematical modeling
4-10
equivalent members
4-16
geometry
4-12
modeling boundary conditions
4-16
structural material behavior
4-11
Mechanically stabilized earth walls
See: MSE walls
Metal decks
corrugated
9-29
filled and partially filled grid decks
9-17
limit states
9-25
metal grid decks
9-16
open grid floors
9-16
orthotropic aluminum decks
9-28
orthotropic steel decks
9-20
superposition of local and global effects
9-25
Metal fasteners and hardware
8-21
corrosion protection
8-23
drift pins and bolts
8-22
fasteners
8-21
minimum requirements
8-21
nails and spikes
8-22
prestressing bars
8-21
shear plate connectors
8-22
spike grids
8-22
split ring connectors
8-22
toothed metal plate connectors
8-22
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Metal pipe, pipe arch, and arch structures
12-24
construction and installation
12-26
corner backfill for corner pipe arches
12-19
flexibility limits and construction
stiffness
12-12
handling and installation requirements
12-25
resistance to buckling
12-25
safety against structural failure
12-24
seam resistance
12-25
section properties
12-24
smooth lined pipe
12-26
stiffening elements for structural plate
structures
12-26
thrust
12-24
Methods of analysis
See: Dynamic analysis, Mathematical
modeling, Physical model analysis, Static
analysis
Modular bridge joint systems (MBJS)
14-22
design stress range
14-31
distribution of wheel loads
14-27
fatigue limit state design requirements
14-29
loads and load factors
14-25
performance requirements
14-24
strength limit state design requirements
14-28
testing and calculation requirements
14-25
Modulus of elasticity
concrete
5-18
reinforcing steel
5-19
wood piles
8-21
Modulus of rupture
5-18
Moment redistribution
concrete
5-47
from interior-pier I-sections in straight
continuous-span bridges
Mononobe-Okabe analysis
6-283
6-287
11-110
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Index Terms
Links
MSE walls
11-54
abutments
11-99
bearing resistance
11-64
boundary between active and resistant
zones
11-70
concentrated dead loads
11-95
corrosion issues for facing
11-60
design life considerations
11-76
design tensile resistance
11-80
drainage
11-94
dynamic load allowance
3-31
earth pressure
3-117
external stability
11-62
facing
11-58
facing reinforcement connections
11-82
flexible wall facings
11-59
geosynthetic reinforcements
11-78
hydrostatic pressures
11-98
internal stability
11-65
lateral displacement
11-61
loading
11-60
maximum reinforcement loads
11-66
minimum front face embedment
11-58
minimum length of soil reinforcement
11-57
obstructions in the reinforced soil zone
11-98
overall stability
11-61
overturning
11-64
11-86
11-80
11-82
11-87
11-63
11-65
reinforcement/facing connection design
strength
11-82
reinforcement loads at connection to wall
face
11-70
reinforcement pullout
11-70
reinforcement strength
11-74
safety against soil failure
11-62
safety against structural failure
11-65
seismic design
11-86
settlement
11-60
sliding
11-64
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
MSE walls (Cont.)
special loading conditions
11-95
steel reinforcements
11-76
11-80
11-82
stiff or rigid concrete, steel, and timber
facings
11-59
structure dimensions
11-56
subsurface erosion
11-94
traffic loads and barriers
11-96
Multimode spectral analysis method
4-85
Multiple presence of live load
3-18
Multispan bridges
multimode spectral method of analysis
4-85
selection of method
4-81
single-mode method of analysis
4-82
single-mode spectral method of analysis
4-82
time-history method of analysis
4-85
uniform load method of analysis
4-83
N
Net area
aluminum
7-24
steel
6-77
Noncompact sections
nominal flexural resistance
6-140
6-188
Noncomposite sections
box-shaped members
6-202
builtup members
6-78
channels, angles, tees, and bars
6-205
circular tubes
6-204
I- and H-shaped members
6-201
nominal compressive resistance
6-82
rectangular bars and solid rounds
6-210
tees and double angles
6-205
6-207
6-209
Nondestructive testing
aluminum
7-19
Nonyielding abutments
11-100
Nordlund/Thurman method
10-103
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Index Terms
Links
Nuts
grade and finish of
7-50
materials
6-26
O
Operational importance
1-7
Orthotropic aluminum decks
approximate analysis
9-29
limit states
9-29
Orthotropic deck superstructures
6-247
decks in global compression
6-247
effective width of deck
6-249
superposition of global and local effects
6-249
Orthotropic decks
See: Orthotropic aluminum decks;
Orthotropic steel decks
Orthotropic steel decks
approximate analysis
9-21
closed ribs
9-24
deck and rib details
9-27
design
9-23
detailing requirements
9-26
effective flange width
4-54
load-induced fatigue
6-32
minimum plate thickness
9-26
refined analysis
9-21
unauthorized welding
9-27
wearing surface
9-20
wheel load distribution
9-20
Oversize holes
6-217
9-26
7-51
P
Parapets
See: Railings
PE pipes
See: Plastic
Pedestrian loads
3-30
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Pedestrian railings
design live loads
13-10
geometry
13-9
Perforated plates
6-78
Permanent loads
3-16
dead loads
3-16
earth loads
3-17
6-94
Physical model analysis
bridge testing
4-90
scale model testing
4-90
Piers
barge collision force
3-154
collision protection
11-34
collision walls
11-34
facing
11-34
ice loads
3-44
load combinations and load factors
11-10
load effects
11-33
3-50
longitudinal reinforcement of hollow
rectangular precast segmental
piers
5-230
protection
11-34
scour
11-34
seismic design
5-147
service limit state
11-6
ship collision force
3-151
Pile bents
3-97
Piles
See also: Concrete piles, Steel piles,
Wood piles
α-method
10-101
axial resistance change after pile driving
10-93
batter piles
10-82
β -method
10-102
buckling and lateral stability
10-118
buoyancy
10-94
corrosion and deterioration
design requirements
10-119
10-82
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Piles (Cont.)
10-121
determination of Rndr
downdrag
10-83
drivability analysis
10-121
driven to hard rock
10-90
driven to soft rock
10-90
dynamic formula
10-99
dynamic testing
10-97
extreme event limit state
10-118
λ -method
10-102
groundwater effects
10-94
horizontal pile foundation movement
10-87
length estimates for contract documents
10-91
load determination
10-83
minimum pile penetration
10-95
10-120
minimum pile spacing, clearance, and
embedment into cap
nearby structures
10-81
10-84
Nordlund/Thurman method in
cohesionless soils
10-103
piles through embankment fill
10-82
point bearing piles on rock
10-90
relaxation
10-93
resistance factors
10-38
resistance of pile groups in compression
10-112
scour
10-94
service limit state
10-84
settlement
10-84
setup
10-93
special requirements
10-167
static analysis
10-100
static load test
10-97
strength limit state
10-29
structural resistance
10-117
test piles
10-123
tip resistance in cohesive soils
10-103
tolerable movements
uplift
10-89
10-84
10-114
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Piles (Cont.)
uplift due to expansive soil
using SPT or CPT in cohesionless soils
wave equation analysis
Pin-connected plates
10-83
10-108
10-98
6-79
packing
6-80
pin plates
6-79
proportions
6-80
Pins
location
6-68
materials
6-25
minimum size pin for eyebars
6-69
pins and pin nuts
6-70
resistance
6-69
Pipe arch structures
See: Metal pipe, pipe arch, and arch
structures
Pipes
flexibility factor
12-12
Plank decks
See: Wood decks and deck systems
Plastic
polyethylene (PE) pipes
12-8
12-102
polyvinyl chloride (PVC) pipes
12-8
12-103
Plastic hinges
4-80
Plastic moment
6-313
6-318
Portal and sway bracing
6-246
7-56
deck truss spans
6-246
through-truss spans
6-246
Post-and-beam railings
13-21
Post-tensioned anchorage zones
5-122
Polytetrafluorethylene sliding surfaces
See: PTFE sliding surfaces
13-26
application of the strut-and-tie model to
the design of general zone
5-132
approximate stress analyses and design
5-137
bursting forces
5-140
compressive stresses
5-138
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Post-tensioned anchorage zones (Cont.)
design of general zone
5-125
design of local zones
5-142
edge tension forces
5-141
elastic stress analysis
5-136
general zone and local zone
5-123
limitations of application
5-137
Pot bearings
14-51
elastomeric disc
14-53
geometric requirements
14-51
materials
14-51
movements and loads
14-15
piston
14-55
pot
14-54
sealing rings
14-53
14-16
Precast beams
bridges composed of simple span precast
girders made continuous
5-201
concrete strength
5-198
detail design
5-197
extreme dimensions
5-197
lifting devices
5-197
preservice conditions
5-197
Precast deck bridges
5-234
cast-in-place closure joint
5-236
design
5-235
longitudinal construction joints
5-235
longitudinally post-tensioned precast
decks
9-15
post-tensioning
5-235
shear-flexure transfer joints
5-236
shear transfer joints
5-235
structural overlay
5-236
transversely joined precast decks
9-14
Precast prestressed piles
concrete quality
5-192
pile dimensions
5-192
reinforcement
5-193
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Index Terms
Links
Precast reinforced concrete three-sided
structures
12-91
concrete
12-91
concrete cover for reinforcement
12-91
crack control
12-93
deflection control at the service limit
state
12-93
design
12-91
distribution of concentrated load effects
in top slab and sides
12-92
distribution of concentrated loads in
skewed culverts
12-92
footing design
12-93
geometric properties
12-91
materials
12-91
minimum reinforcement
12-93
reinforcement
12-91
resistance factors
12-93
scour protection and waterway
considerations
12-93
shear transfer in transverse joints
between culvert sections
12-92
span length
12-92
structural backfill
12-93
Precast reinforced piles
pile dimensions
5-192
reinforcing steel
5-192
Prefabricated modular walls
11-102
See also: Earth pressure
abutments
11-105
bearing resistance
11-102
drainage
11-105
dynamic load allowance
3-31
loading
11-102
module members
11-103
movement at the service limit state
11-102
overturning
11-103
passive resistance and sliding
11-103
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Prefabricated modular walls (Cont.)
safety against soil failure
11-102
safety against structural failure
11-103
seismic design
11-104
sliding
11-102
subsurface erosion
11-103
11-103
Preservative treatment for wood
fire retardant treatment
8-24
inspection and marking
8-24
requirement for
8-23
treatment chemicals
8-23
Prestressed concrete
See also: Prestressing steel
buckling
5-91
crack control
5-91
loss of prestress
5-98
section properties
5-91
specified concrete strengths
5-91
stress limitations for prestressing tendons
5-92
stresses due to imposed deformation
5-92
tendons with angle points or curves
5-91
Prestressing steel
concrete cover
5-175
materials
5-20
modulus of elasticity
5-21
post-tensioning anchorages and couplers
5-21
stress at nominal flexural resistance
5-40
Prestressing strand
bonded
5-168
partially debonded
5-169
Prestressing tendons
protection for
5-176
Pretensioned anchorage zones
confinement reinforcement
5-146
factored bursting resistance
5-149
Probability of aberrancy
approximate method
3-143
statistical method
3-143
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Protective coatings
5-176
See: Corrosion protection
Provisional post-tensioning ducts and
anchorages
5-219
bridges with internal ducts
5-219
provision for future dead load or
deflection adjustment
5-219
Provisions for structure types
arches
5-231
beam and girder framing
7-55
beams and girders
5-196
culverts
5-236
floor system
7-55
lateral bracing
7-55
orthotropic deck superstructures
6-247
segmental construction
5-211
slab superstructures
5-232
solid web arches
6-249
through-girder spans
6-250
trusses
6-244
PTFE sliding surfaces
7-56
7-55
14-44
attachment
14-48
coefficient of friction
14-47
contact pressure
14-46
mating surface
14-45
minimum thickness
14-45
PTFE surface
14-44
stainless steel mating surfaces
14-46
14-48
PVC pipes
See: Plastic
R
Railing design
protection of users
railing test specimens
2-5
13-19
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Railings
13-3
See also: Bicycle railings, Combination
railings, Pedestrian railings, Traffic
railings
concrete parapet and metal rail
13-22
extreme event limit state
13-5
materials
13-5
post-and-beam railings
strength limit state
13-21
13-26
13-5
wood barriers
13-24
Railroads
rail transit load
3-30
Rectangular stress block method
Redundancy
5-54
1-6
Refined methods of analysis
4-16
arch bridges
4-73
beam-slab bridges
4-70
cable-stayed bridges
4-73
cellular and box bridges
4-72
decks
4-67
fatigue load
3-28
nominal moment-rotation curves
4-68
6-292
orthotropic steel decks
9-21
suspension bridges
4-74
truss bridges
4-72
Reinforced concrete pipe
12-47
bearing resistance
12-61
bedding factor
12-62
circumferential reinforcement
12-55
concrete cover
12-58
construction and installation
12-65
crack width control
12-57
development of quadrant mat
reinforcement
12-65
direct design method
12-53
flexural resistance
12-55
indirect design method
12-61
live loads
12-52
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Reinforced concrete pipe (Cont.)
loading
12-48
loads and pressure distribution
12-53
maximum flexural reinforcement without
stirrups
12-56
minimum reinforcement
12-55
pipe fluid weight
12-52
pipe ring analysis
12-54
process and material factors
12-55
safety against structural failure
12-52
service limit state
12-52
shear resistance
12-58
standard installations
12-48
stirrup anchorage
12-61
stirrup embedment
12-61
stirrup reinforcement anchorage
12-61
12-60
Reinforcement
See also: Spacing of reinforcement
abutments and retaining walls
11-18
approximate stress analyses and design
5-137
cast-in-place girders and box and T-beams
5-210
compression members
5-48
concrete cover
5-110
5-175
crack control
5-34
5-91
drilled shafts
10-142
10-143
elastic stress analysis
5-136
elastomeric bearings
14-64
external tendon supports
5-119
14-75
hollow rectangular compression
members
5-156
hooks and bends
5-110
longitudinal
5-75
materials
5-18
maximum reinforcement
5-43
minimum reinforcement
5-43
post-tensioned anchorage zones
5-122
pretensioned anchorage zones
5-144
shrinkage and temperature
5-121
5-77
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Reinforcement (Cont.)
spacing of
5-111
special applications
5-20
spirals and ties
5-53
tendon confinement
5-114
torsional
5-88
transverse
5-62
5-77
5-150
5-151
5-119
Reinforcing steel
See: Reinforcement
Relaxation losses
after transfer
5-107
at transfer
5-106
Relieving slabs
long-span structural plate structures
12-86
structural plate box structures
12-46
Resistance factors
abutments, piers, and walls
11-6
aluminum structures
7-10
buried structures
11-13
11-16
12-10
compression members
5-51
concrete structures
5-147
conventional construction
5-26
drilled shafts
10-47
driven piles
10-39
footings
5-187
foundations
10-38
precast reinforced concrete three-sided
structures
12-93
segmental construction
5-28
seismic zones 3 and 4
5-149
spread footings
10-39
steel
6-30
Retaining walls
See: Abutments and retaining walls
Rigid frame connections
6-243
This page has been reformatted by Knovel to provide easier navigation.
5-121
Index Terms
Links
Roadway drainage
design storm
2-24
discharge from deck drains
2-25
drainage of structures
2-25
type, size, and number of drains
2-24
Rock bearing resistance
10-77
analytic method
10-78
load test
10-78
semiempirical procedures
10-78
Rock properties
erodability
10-27
geophysical tests
10-12
in-situ tests
10-11
informational needs
10-7
laboratory tests
10-11
mass deformation
10-25
mass strength
10-21
selection of design properties
10-13
Rocker bearings
14-42
contact stresses
14-43
geometric requirements
14-43
materials
6-25
Roller bearings
14-42
contact stresses
14-43
geometric requirements
14-43
materials
6-25
Route location
14-43
14-43
2-3
waterway and floodplain crossings
2-3
S
Safety
See also: Traffic safety
abutments and retaining walls
11-23
anchored walls
11-45
11-49
cantilevered retaining walls
11-35
11-36
design objective
2-7
MSE walls
prefabricated modular walls
11-62
11-65
11-102
11-103
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Sawn lumber
See also: Wood
bracing
8-36
dimensions
8-6
moisture content
8-6
reference design values
8-6
size factor
8-26
Scale model testing
4-90
Scour
2-21
buried structures
12-19
change in foundations
3-39
drilled shafts
10-130
piers
11-34
piles
10-94
Sealing rings
rings with circular cross-sections
14-53
rings with rectangular cross-sections
14-53
Sectional design model
combined shear and torsion
5-77
longitudinal reinforcement
5-75
nominal shear resistance
5-67
5-77
procedures for determining shear
resistance
5-68
sections near supports
5-65
Segmental bridge analysis
analysis of the final structural system
5-212
effective flange width
4-65
erection analysis
4-66
final structural system
4-66
longitudinal analysis
4-66
strut-and-tie models
4-65
transverse analysis
4-66
Segmental bridge design
deck joints
9-15
principal stresses in webs
5-84
Segmental bridge substructures
design
5-235
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Segmental construction
5-211
alternative construction methods
5-228
analysis of segmental bridges
5-212
box girder cross-section dimensions and
details
5-220
cantilever construction
5-225
construction analysis
5-225
construction loads
5-213
creep and shrinkage
5-217
design
5-213
design details
5-227
design of construction equipment
5-228
details for cast-in-place construction
5-225
details for precast construction
5-223
5-215
5-226
force effects due to construction
tolerances
5-226
incrementally launched construction
5-226
plan presentation
5-219
prestress losses
5-218
provisional post-tensioning ducts and
anchorages
5-219
seismic design
5-222
span-by-span construction
5-225
substructures
5-217
thermal effects during construction
5-217
types of segmental bridges
5-223
Seismic design
abutments and retaining walls
11-23
anchored walls
11-51
bearings
14-40
cantilevered retaining walls
11-23
column connections
5-155
concrete piles
5-191
construction joints in piers and columns
5-155
elastomeric bearings
14-66
hold-down devices
3-98
lateral load distribution
4-63
MSE walls
14-75
5-192
11-86
This page has been reformatted by Knovel to provide easier navigation.
5-229
Index Terms
Links
Seismic design (Cont.)
prefabricated modular walls
11-104
segmental construction
5-211
seismic zone1
5-148
seismic zone 2
5-148
seismic zones 3 and 4
5-149
wall-type piers
5-154
Seismic loads
acceleration coefficient
3-54
combination of seismic force effects
3-92
design of bridge components
3-167
dynamic analysis
4-77
elastic seismic response coefficient
3-90
forces resulting from plastic hinging
3-91
longitudinal restrainers
3-98
minimum support length requirements
4-85
multispan bridges
4-78
operational classification
3-90
P-∆ requirements
4-86
requirements for temporary bridges and
stage construction
3-98
response modification factors
3-91
seismic hazard
3-54
seismic zone 1
3-93
seismic zone 2
3-94
seismic zones 3 and 4
3-94
single-span bridges
4-78
site effects
3-84
3-89
Seismic zone 1
3-93
5-148
Seismic zone 2
3-94
5-148
Seismic zones 3 and 4
column and pile bent design forces
3-97
column connections
5-155
column requirements
5-149
concrete piles
5-191
construction joints in piers and columns
5-155
foundation design forces
3-97
inelastic hinging forces
3-94
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Seismic zones 3 and 4 (Cont.)
modified design forces
3-94
pier design forces
3-97
piers with two or more columns
3-96
resistance factors
5-26
single columns and piers
3-95
wall-type piers
5-154
Service limit states
1-3
abutments and retaining walls
aluminum structures
11-6
11-19
7-7
bridges composed of simple span
precast girders made continuous
buried structures
5-201
12-9
12-14
cast-in-place box culverts and
arches
12-71
concrete structures
5-23
decks
5-35
5-95
10-28
10-29
9-5
drilled shafts
10-126
flexure
6-286
foundations
10-27
interior-pier I-sections in straight
continuous-span bridges
6-286
lateral squeeze
10-89
long-span structural plate structures
12-27
orthotropic aluminum decks
9-26
piers
11-6
piles
10-84
redistribution moments
6-287
reinforced concrete pipe
12-52
sound barriers
15-3
steel box-section flexural members
6-182
steel I-section members
6-127
steel structures
6-29
structural plate box structures
wood structures
12-41
8-33
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Serviceability
deformations
2-10
durability
2-8
inspectability
2-9
maintainability
2-9
rideability
2-9
utilities
2-9
widening
2-14
Settlement
buried structures
12-14
cohesionless soils
10-58
cohesive soils
10-58
downdrag
10-95
due to downdrag
10-86
10-130
equivalent footing analogy
10-84
force effects
3-138
group settlement
10-130
intermediate geo materials
10-129
on rock
10-63
single-drilled shaft
10-127
Shear and torsion
aluminum
7-40
beam ledges
7-45
5-177
concrete
5-56
design and detailing requirements
5-62
development of reinforcement
interface shear transfer—shear friction
5-63
5-160
5-78
interior-pier I-sections in straight
continuous-span bridges
6-285
longitudinal reinforcement
5-77
modifications for lightweight concrete
5-59
nominal shear resistance
5-67
sectional design model
5-64
segmental box girder bridges
5-85
shear in slabs and footings
skewed bridges
steel
torsional resistance
5-188
4-40
6-151
5-77
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Shear and torsion (Cont.)
transfer and development lengths
5-60
transverse reinforcement
5-60
in tubes
7-49
warping torsion
7-47
Shear connectors
6-136
cover and penetration
6-157
fatigue resistance
6-157
permanent load contraflexure
6-158
pitch
6-155
steel box-section flexural members
6-194
strength limit state
6-158
studs
5-77
6-154
6-27
transverse spacing
6-156
Shear resistance
aluminum
7-40
bolted connections
6-220
disc bearings
14-73
reinforced concrete pipe
12-58
steel box-section flexural members
6-194
steel I-section flexural members
6-151
wood
12-60
8-31
Ship collision force
See: Vessel collisions
Short-slotted holes
6-217
7-51
Shrinkage
3-137
5-17
Sidewalks
13-12
end treatment of separation railing
13-13
Skewed bridges
live load distribution
4-32
4-47
Slab superstructures
cast-in-place solid slab superstructures
5-231
cast-in-place voided slab
superstructures
precast deck bridges
5-232
5-234
Slabs
See: Concrete slabs
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Slenderness effects and limits
compression members
5-51
ice loads, piers
3-50
Slenderness ratios
aluminum
7-20
steel
6-77
6-82
6-214
7-53
Slip-critical connections
Slip resistance
bolted connections
6-221
Small deflection theory
4-12
Soil bearing resistance
10-66
basic formulation
10-67
considerations for footings in slopes
10-71
considerations for punching shear
10-70
considerations for two-layer soil
systems—critical depth
10-73
plate load tests
10-77
semiempirical procedures
10-76
theoretical estimation
10-67
two-layered soil system in drained
loading
10-76
two-layered soil system in undrained
loading
10-74
Soil properties
determination of
11-5
envelope backfill soils
12-6
foundation soils
12-6
geophysical tests
10-12
in-situ tests
10-11
informational needs
12-6
15-12
10-7
laboratory tests
10-11
selection of design properties
10-13
soil deformation
10-18
soil strength
10-15
subsurface exploration
10-8
unit weight
3-17
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Soil strength
drained strength of cohesive soils
10-16
drained strength of granular soils
10-16
undrained strength of cohesive soils
10-15
Soil-structure interaction systems
See: Culverts
Solid web arches
flange stability
6-250
moment amplification for deflection
6-249
web slenderness
6-249
Sound barriers
corrosion protection
15-13
design limit states
15-12
drainage
15-2
earth load
15-9
extreme event limit state
15-4
foundation design
15-12
loading
15-13
resistance factors
15-13
safety against geotechnical failure
15-13
seismic design
15-13
service limit state
15-3
soil and rock properties
15-14
15-13
15-12
strength limit state
15-3
wind load
15-5
vehicle collision forces
15-9
15-13
Spacing of reinforcement
bundled bars
5-112
cast-in-place concrete
5-111
couplers in post-tensioning tendons
5-114
curved post-tensioning ducts
5-113
hollow rectangular compression
members
5-156
maximum spacing of reinforcing bars
5-112
minimum spacing of prestressing tendons
and ducts
5-112
minimum spacing of reinforcing bars
5-111
multilayers
5-111
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Spacing of reinforcement (Cont.)
post-tensioning ducts straight in plan
5-113
precast concrete
5-111
pretensioning strand
5-112
splices
5-112
Spike laminated decks
9-38
deck tie-downs
9-39
panel decks
9-39
Splices
See also: Bolted splices, Splices of bar
reinforcement, Splices of welded
wire fabric
compression members
7-54
flexural members
7-54
tension members
7-54
welded
6-248
welding
7-55
Splices of bar reinforcement
See also: Lap splices
bars in compression
5-172
detailing
5-170
end-bearing splices
5-173
general requirements
5-170
mechanical connections
5-171
mechanical connections or welded
splices in compression
5-172
mechanical connections or welded
splices in tension
5-172
reinforcement in tension
5-171
tension tie members
5-172
welded splices
5-171
Splices of welded wire fabric
deformed wire in tension
5-173
smooth wire in tension
5-173
Spread footings
10-51
anchorage of inclined footings
10-53
bearing depth
10-51
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Spread footings (Cont.)
bearing resistance at the service limit
state
10-64
bearing stress distributions
10-52
eccentric load limitations
10-81
effective footing dimensions
10-52
extreme event limit state
10-80
failure by sliding
10-79
groundwater
10-53
loads
10-54
nearby structures
10-53
overall stability
10-64
resistance factors
10-38
service limit state
10-53
settlement on cohesionless soils
10-55
settlement on cohesive soils
10-58
settlement on rock
10-63
strength limit state
10-38
structural design
10-81
tolerable movements
10-53
uplift
10-53
10-66
St. Venant torsion
aluminum
7-46
Stability
buried structures
12-17
elastomeric bearings
14-63
14-75
MSE walls
11-60
11-62
sound barriers
15-13
static analysis
4-75
Stainless steel
11-65
6-28
Static analysis
analysis for temperature gradient
4-75
approximate methods
4-19
axial pile resistance in compression
influence of plan geometry
10-93
4-17
redistribution of negative moments in
continuous beam bridges
4-74
This page has been reformatted by Knovel to provide easier navigation.
11-86
11-87
Index Terms
Links
Static analysis (Cont.)
refined methods
4-68
stability
4-75
Stay-in-place formwork
concrete
9-13
deck overhangs
9-5
steel
9-13
Steel
basic steps for steel bridge
superstructures
6-295
coefficient of thermal expansion
6-22
minimum mechanical properties by
shape, strength, and thickness
6-25
modulus of elasticity
6-22
thickness of metal
6-22
Steel box-section flexural members
6-171
access and drainage
6-177
bearings
6-176
compact sections
6-187
constructibility
6-179
cross-section proportion limits
6-177
fatigue and fracture limit state
6-183
flange-to-web connections
6-176
flexural resistance—sections in negative
flexure
6-189
flexural resistance—sections in positive
flexure
6-187
noncompact sections
6-187
service limit state
6-182
shear connectors
6-194
shear resistance
6-194
stiffeners
6-195
strength limit state
6-185
stress determination
6-173
Steel dimension and detail requirements
dead load camber
6-57
diaphragms and cross-frames
6-57
effective length of span
6-57
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Steel dimension and detail requirements (Cont.)
heat-curved rolled beams and welded
plate girders
6-70
lateral bracing
6-65
minimum thickness of steel
6-59
pins
6-68
Steel I-girders
See: Steel I-section flexural members
Steel I-section flexural members
compact sections
6-136
composite sections
6-102
constructibility
6-120
cover plates
6-170
cross-section proportion limits
6-118
diaphragms or cross-frames
6-59
ductility requirement
6-140
fatigue and fracture limit state
6-130
flange-strength reduction factors
6-113
flange stresses and member bending
moments
6-106
flexural resistance
6-136
6-141
flexural resistance—composite sections
in negative flexure and
noncomposite sections
6-139
flexural resistance—composite sections
in positive flexure
6-136
flowcharts for design
6-300
fundamental calculations
6-313
hybrid sections
6-104
lateral bracing
6-60
minimum negative flexure concrete deck
reinforcement
6-108
moment redistribution from interior-pier
I sections in straight continuousspan bridges
6-283
net section fracture
6-110
noncompact sections
6-139
noncomposite sections
6-103
6-140
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Steel I-section flexural members (Cont.)
service limit state
6-127
shear connectors
6-154
shear resistance
6-151
stiffeners
6-161
stiffness
6-106
strength limit state
6-131
variable web depth members
6-104
web bend-buckling resistance
6-110
Steel I-section proportioning
flange proportions
6-119
web proportions
6-118
Steel orthotropic decks
See: Orthotropic steel decks
Steel piles
6-250
axial compression
6-252
buckling
6-252
combined axial compression and flexure
6-252
compressive resistance
6-252
maximum permissible driving stresses
6-252
structural resistance
6-250
Steel tension members
6-71
builtup members
6-78
eyebars
6-78
limiting slenderness ratio
6-77
net area
6-77
pin-connected plates
6-79
tensile resistance
6-72
Steel tunnel liner plate
10-117
12-87
buckling
12-89
construction stiffness
12-89
earth loads
12-87
flexibility limits and construction
stiffness
12-13
grouting pressure
12-88
live loads
12-88
loading
12-87
safety against structural failure
12-88
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Steel tunnel liner plate (Cont.)
seam strength
12-89
section properties
12-88
wall area
12-88
Stiffened webs
nominal resistance
6-152
Stiffeners
See also: Longitudinal stiffeners,
Transverse intermediate stiffeners
bearing stiffeners
6-165
design of
7-42
longitudinal compression-flange
6-196
web
6-195
Stirrups
See: Transverse reinforcement
Stream pressure
lateral
3-38
longitudinal
3-37
Strength limit states
1-3
abutments and retaining walls
11-7
aluminum structures
7-10
11-20
bridges composed of simple span precast
girders made continuous
buried structures
5-201
12-9
combined flexure and axial load
concrete structures
6-199
5-44
decks
9-6
drilled shafts
10-130
flexure
6-131
6-185
foundations
10-29
10-38
interior-pier I-sections in straight
continuous-span bridges
modular bridge joint systems
6-288
14-28
railings
13-5
resistance factors
5-26
6-30
shear
6-136
6-186
6-200
shear connectors
6-136
6-158
6-186
spread footings
10-66
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Strength limit states (Cont.)
stability
5-29
steel box-section flexural members
6-185
steel structures
6-29
wood structures
8-30
6-199
Stress analyses and design
bursting forces
5-140
compressive stresses
5-138
edge tension forces
5-141
limitations of application
5-137
Stress laminated decks
9-33
camber
8-37
deck tie-downs
9-34
holes in lamination
9-34
nailing
9-33
staggered butt joints
9-34
stressing
9-34
Stressing
corrosion protection
9-38
design requirements
9-37
prestressing materials
9-36
prestressing system
9-34
railings
9-38
Structural analysis
4-1
acceptable methods
4-9
dynamic
4-77
mathematical modeling
4-10
by physical models
4-90
static analysis
4-17
Structural material behavior
elastic behavior
4-11
elastic versus inelastic behavior
4-11
inelastic behavior
4-11
Structural plate box structures
12-40
concrete relieving slabs
12-46
construction and installation
12-47
crown soil cover factor
12-45
footing reactions
12-45
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Structural plate box structures (Cont.)
loading
12-41
moments due to factored loads
12-42
plastic moment resistance
12-44
safety against structural failure
12-41
service limit state
12-41
Structure-mounted sound barriers
15-4
Strut-and-tie model
crack control reinforcement
general zone
5-34
5-132
proportioning of compressive struts
5-31
proportioning of node regions
5-34
proportioning of tension ties
5-33
structural modeling
5-30
Substructures
construction load combinations
5-230
design
5-222
longitudinal reinforcement of hollow
rectangular precast segmental piers
vessel collisions
5-230
2-5
3-156
Superimposed deformations
creep
3-133
design thermal movements
3-136
differential shrinkage
3-137
settlement
3-138
temperature gradient
3-133
uniform temperature
3-130
Superstructure design
5-222
Surcharge loads
live load surcharge
3-129
point line and strip loads
3-124
reduction of surcharge
3-130
strip loads—flexible walls
3-127
uniform surcharge
3-123
Suspension bridges
refined analysis
4-72
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
T
Temperature gradients
3-136
4-75
Temporary stresses before losses
compression stresses
5-93
tension stresses
5-93
Tendon confinement
effects of curved tendons
5-114
wobble effect in slabs
5-114
Tensile resistance
aluminum
7-23
combined tension and flexure
6-76
fatigue resistance
6-225
MSE walls
11-62
nominal
6-225
prying action
6-225
reduction factor
7-30
6-73
Tension-flange flexural resistance
6-193
Tension members
aluminum
7-23
concrete
5-58
splices
7-54
Tension ties
anchorage of tie
5-34
proportioning
5-33
strength of tie
5-33
Test piles
10-123
Thermal forces
temperature gradient
3-136
temperature range for procedure A
3-133
temperature range for procedure B
3-134
uniform temperature
3-133
Thermoplastic pipes
12-71
bending strain
12-84
buckling
12-81
chemical and mechanical requirements
12-73
combined strain
12-84
12-83
flexibility limits and construction
stiffness
12-13
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
Thermoplastic pipes (Cont.)
handling and installation requirements
materials
12-83
12-8
resistance to local buckling of pipe
wall
12-81
safety against structural failure
12-73
section properties
12-73
service limit state
12-71
slenderness and effective width
12-82
thrust
12-83
wall resistance
12-81
Through-girder spans
6-247
Timber
See: Wood
Timber floors
See: Wood decks and deck systems
Time-history method
4-85
Tire contact area
3-24
Torsion
See: Shear and torsion
Traffic railings
13-5
application of previously tested systems
13-8
approach railings
13-6
design forces
13-17
end treatment
13-6
height of traffic parapet or railing
13-9
new systems
13-9
railing design
13-8
railing system
13-5
separation of rail elements
13-15
test level selection criteria
13-7
Traffic safety
geometric standards
2-5
protection of structures
2-4
protection of users
2-5
road surfaces
2-5
vessel collisions
2-5
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Index Terms
Links
Transverse intermediate stiffeners
moment of inertia
6-162
projecting width
6-162
Transverse reinforcement
compression members
5-122
concrete
5-120
5-60
drilled shafts
10-144
flexural members
5-121
Truss bridges
refined analysis
4-71
Trusses
6-244
bracing
8-37
camber
6-245
8-37
6-59
6-245
diaphragms
factored resistance
6-247
gusset plates
6-256
half-through
6-257
lateral bracing
6-64
load distribution
4-47
portal and sway bracing
6-246
secondary stresses
6-245
truss members
6-245
working lines and gravity axes
6-245
7-56
Tub-section members
lateral bracing
6-66
U
Unfilled grid decks composite with
reinforced concrete slabs
design
9-19
fatigue limit state
9-19
Unstiffened webs
nominal resistance
6-152
Uplift
aluminum
buried structures
7-19
12-18
drilled shafts
10-126
load test
10-139
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Index Terms
Links
Uplift (Cont.)
pile group uplift resistance
piles penetrating expansive soil
10-114
10-83
resistance
10-142
single-pile uplift resistance
10-114
spread footings
10-143
10-53
V
Vehicle-induced vibration
4-79
Vehicular collision force
protection of structures
3-35
vehicle collision with barriers
3-36
Vehicular live load
multiple presence of live load
3-18
number of design lanes
3-17
Vertical wind pressure
3-43
Vessel collisions
3-138
annual frequency of collapse
3-140
barge bow damage length
3-155
barge collision force on pier
3-154
damage at extreme limit state
3-155
design collision velocity
3-150
design vessel
3-140
impact force
3-147
impact force, substructure design
3-156
impact force, superstructure design
3-157
owner’s responsibility
3-140
protection against
2-5
protection of substructures
3-157
ship bow damage length
3-153
ship collision force on pier
3-151
ship collision force on superstructure
3-153
ship collision with bow
3-153
ship collision with deck house
3-153
ship collision with mast
3-154
vessel collision energy
3-150
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Index Terms
Links
W
Warping torsion
7-47
Washers
6-216
materials
6-26
Water loads
buoyancy
3-37
drag coefficient
3-37
scour
3-39
static pressure
3-37
stream pressure
3-37
wave load
3-39
Wearing surface
chip seal
9-40
orthotropic steel decks
9-20
plant mix asphalt
9-40
wood decks
9-40
Web bend-buckling resistance
webs with longitudinal stiffeners
6-86
webs without longitudinal stiffeners
6-86
Web crippling
aluminum
7-9
steel
6-321
Web local yielding
6-321
Web plastification factors
compact web sections
6-274
noncompact web sections
6-275
Web proportions
webs with longitudinal stiffeners
6-119
6-178
webs without longitudinal stiffeners
6-118
6-178
Webs
nominal resistance of stiffened webs
6-152
nominal resistance of unstiffened webs
6-152
Welded connections
6-227
complete penetration groove-welded
connections
6-227
effective area
6-229
factored resistance
6-227
fillet weld end returns
6-230
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Index Terms
Links
Welded connections (Cont.)
fillet-welded
6-228
minimum effective length of fillet welds
6-230
partial penetration groove-welded
connections
6-228
seal welds
6-230
size of fillet welds
6-229
Welded wire fabric
deformed
5-164
plain
5-165
quadrant mat reinforcement
12-64
Welding
procedures for aluminum
7-18
requirements for aluminum
7-18
splices
7-55
weld metal
6-27
Wheel loads
corrugated metal decks
9-30
decks
4-27
distribution through earth fills
3-25
modular bridge joint systems
14-27
orthotropic steel decks
9-20
Widening
exterior beams
2-14
substructure
2-14
Wind-induced vibration
4-79
Wind load
aeroelastic instability
3-43
horizontal wind pressure
3-39
multibeam bridges
4-59
sound barriers
15-5
vertical wind pressure
3-43
Wind pressure on structures
3-41
box sections
4-63
construction
4-63
I-sections
4-62
loads from superstructures
3-41
Wind pressure on vehicles
3-42
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Index Terms
Links
Wood
bracing
8-36
camber
8-37
components in combined flexure and
axial loading
8-35
components in compression
8-33
components in flexure
8-31
components in tension parallel to grain
8-35
components under shear
8-33
connection design
8-37
deck factor
8-29
flat-use factor
8-28
format conversion factor
8-25
glued laminated timber
8-12
incising factor
8-29
metal fasteners and hardware
8-21
preservative treatment
8-21
sawn lumber
8-5
wet service factor
8-26
Wood barriers
railing design
13-23
Wood decks and deck systems
9-30
deck tie-downs
9-32
deformation
9-31
design requirements
9-30
glued laminated decks
9-32
interconnected decks
9-32
load distribution
9-30
nailing
9-33
noninterconnected decks
9-33
plank decks
9-40
shear design
9-31
skewed decks
9-31
spike laminated decks
9-38
stress laminated decks
9-33
thermal expansion
9-31
wearing surfaces
9-31
9-34
9-40
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9-39
9-40
Index Terms
Links
Wood piles
base resistance and modulus of elasticity
structural resistance
8-14
10-118
Y
Yield lines
4-80
Yield moment
6-315
composite sections in negative flexure
6-316
composite sections in positive flexure
6-316
noncomposite sections
6-315
sections with cover plates
6-317
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