Improved Live Load Deflection Criteria For Steel Bridges
Improved Live Load Deflection Criteria For Steel Bridges
Improved Live Load Deflection Criteria For Steel Bridges
Submitted by:
Charles W. Roeder
University of Washington
Seattle, Washington
Karl Barth
University of West Virginia
Morgantown, West Virginia
Adam Bergman
University of Washington
Seattle, Washington
November 2002
ACKNOWLEDGMENT
This work was sponsored by the American
Association of State Highway and Transportation
Officials (AASHTO), in cooperation with the Federal
Highway Administration, and was conducted in the
National Cooperative Highway Research Program
(NCHRP),
which
is administered by the
Transportation Research Board (TRB) of the National
Academies.
DISCLAIMER
The opinion and conclusions expressed or implied in
the report are those of the research agency. They are
not necessarily those of the TRB, the National
Research Council, AASHTO, or the U.S. Government.
This report has not been edited by TRB.
Contents
Summary
Acknowledgments
Chapter 1 - Introduction
1.1. Problem Statement
1.2. Directions of Research
1.3. Report Content and Organization
1
1
2
3
5
5
9
15
15
19
23
27
27
29
30
31
33
33
34
37
41
41
42
45
50
53
53
54
56
59
5.3.2.
5.3.3.
5.3.4.
5.3.5.
66
72
74
76
77
81
81
81
82
89
90
91
7.4.1.
7.4.2.
7.4.3.
7.4.4.
8.2.1. Conclusions
8.2.2. R ecommended Changes to A A SHTO Specifications
8.3. Recommendations for Further Study
94
97
97
98
99
102
102
107
109
111
112
113
113
115
116
118
120
References
123
129
Summary
This research has examined the AASHTO live-load deflection limit for steel
L
bridges. The AASHTO Standard Specification limits live-load deflections to
for
800
L
ordinary bridges and
for bridges in urban areas that are subject to pedestrian use.
1000
This limit is also incorporated in the AASHTO LRFD Specifications in the form of an
optional serviceability criteria. This limit has not been a controlling factor in most past
bridge designs, but it will play a greater role in the design of bridges built with new HPS
70W steel. This study documented the role of the AASHTO live-load deflection limit of
steel bridge design, determined whether the limit has beneficial effects on serviceability
and performance, and established whether the deflection limit was needed. Limited time
and funding was provided for this study, but an ultimate goal was to establish
recommendations for new design provisions that would assure serviceability, good
structural performance and economy in design and construction.
A literature review was completed to establish the origin and justification for this
deflection limit. This review examined numerous papers and reports, and a
comprehensive reference list is provided. The work shows that the existing AASHTO
deflection limit was initially instituted to control bridge vibration, but deflection limits
are not a good method for controlling bridge vibration. Alternate design methods are
presented. A survey of state bridge engineers was simultaneously completed to examine
how these deflection limits are actually applied in bridge design. The survey also
identified bridges that were candidates for further study on this research issue. Candidate
bridges either:
failed to meet the existing deflection limits,
exhibit structural damage that was attributable to excessive bridge deflection,
were designed with HPS 70W steel, or
had pedestrian or vehicle occupant comfort concerns due to bridge vibration.
The survey showed wide variation in the application of the deflection limit in the
various states, and so a parameter study was completed to establish the consequences of
this variation on bridge design. The effect of different load patterns, load magnitudes,
deflection limits, bridge span length, bridge continuity, and other factors were examined.
There is wide variation in the application of the existing deflection limit, because of the
variation in the actual deflection limits, the variation in the load magnitude and load
pattern used to calculate the deflection, the application of load factors and lane load
distribution factors, and other effects. The difference between the least restrictive and
most restrictive deflection limit may exceed 1,000%. The load pattern and magnitude
have a big impact on this variation. Some states use truck loads, some use distributed
lane loads, and some use combinations of the above. Truck loads provide the largest
deflection for short span bridges. Distributed lane loads provide the largest deflections
for long span bridges.
This analysis showed that a substantial number of bridges are damaged by bridge
deformation. This deformation is related to bridge deflection. The deformations that
cause the damage are relative deflections between adjacent members, local rotations and
deformations, deformation induced by bridge skew and curvature, and similar concerns.
L
None of these deformations are checked with the existing
live-load deflection limit.
800
Additional analyses were performed to examine how the deflection limit interacts
L
with bridge vibration, the span-to-depth ( ) ratio and other design parameters. The
D
study examined the effect these parameters on the economy and performance of bridge
design. The AASHTO live-load deflection limit is less likely to influence the design of
L
ratios and is more likely to control the superstructure member sizes
bridges with small
D
L
as the
ratio increases. Application of the deflection limit with truck load only shows
D
that the existing AASHTO deflection limits will have a significant economic impact on
some steel I-girder bridges built from HPS 70W steel. Simple span bridges are more
frequently affected by this limit than continuous bridges. However, continuous bridges
are also likely to be more frequently affected by existing deflection limits if the span
length, L, is taken as the true span length rather than the distance between inflection
points in the application of the deflection limit. The study shows that many bridges the
satisfy the existing deflection limit are likely to provide poor vibration performance,
while other bridges failing the existing deflection limit will provide good comfort
characteristics.
Lastly, this report summarizes major findings and presents proposed design
recommendations and further research requirements.
Acknowledgments
This research report describes a cooperative research study completed at the University of
Washington and West Virginia University. Funding for this work is provided by the National
Cooperative Research Program under NCHRP 20-07/133 and by the American Iron and Steel
Institute through project entitled "Vibration and Deflection Criteria for Steel Bridges." The
authors gratefully acknowledge this support.
Chapter 1
Introduction
(AASHTO, 1998)
LRFD commentary do not provide detailed explanations or justification for these limits.
Historically, the deflection limit has not affected a significant range of bridge designs.
However, recent introduction of high performance steel (HPS) may change this fact. HPS
has a higher yield stress than other steels commonly used in bridge design (Fy=70 ksi and
higher as opposed to 50 ksi), and the larger yield stress permits smaller cross sections and
moments of inertia for bridge members. As a result, deflections may be larger for HPS
bridges, and deflection limits are increasingly likely to control the design of bridges built
from these new materials. It is therefore necessary to ask:
This research study was jointly funded under the NCHRP 20-7 program and the
American Iron and Steel Institute, and the research was initiated to determine whether the
deflection limits for steel bridges are needed or warranted. The study focuses on steel
bridges, and the particular goals are -
-1-
-2-
research program managers (David Beal for NCHRP and Camille Rubeiz for AISI).
Cooperation between the two research teams were agreed at that time, and the researchers
have had numerous meetings, email exchanges, and conference calls for the duration of
this project. The UW issued a subsequent subcontract to WVU to help balance funding
with the responsibilities. Through these efforts the researchers have exchanged
information throughout the research effort to date. Researchers from both universities are
co-authoring this report and all papers resulting from this coordinated effort.
The research was divided into 6 tasks. The first task provided an initial review of
existing literature and the state of practice for steel bridge deflection control. Task 2
provided an Interim Report, which summarized the results of Task 1, and proposed
directions for the work to be completed during Tasks 3, 4, 5 and 6. The Interim Report
was prepared in March 2001, and was reviewed by an NCHRP Project Panel as well as
being submitted to AISI.
progress, and this guidance was used to direct the research of Tasks 3, 4, and 5. Tasks 3,
4 and 5 consisted of follow up analysis to examine the deflection limits. The range of
variability in the actual professional practice was determined. Bridges, which had reported
damage due to excessive deflection or deformation, were analyzed to determine whether
deflections could or do prevent this damage. Design studies were completed to determine
when and how deflections would affect steel bridge design. Task 6 included preparation
of a final report with the summary and recommendations from the research.
It describes the
introduced the issues of concern. Chapter 2 summarizes the literature review, and Chapter
3 presents the results of a survey of bridge engineering practice. The work in these first 3
chapters was described in somewhat greater detail in the Interim Report submitted to
-3-
NCHRP and AISI in March 2001. This material is summarized in this final report so that
the reader can develop a complete understanding of the issues at hand.
The details of the work in Tasks 3, 4, and 5 were finalized after obtaining feedback
from the Project Panel from the Interim Report. This work is summarized in Chapters 4,
5, 6 and 7 of this report. The survey shows a wide variation of the professional practice,
and Chapter 4 summarizes a parameter study completed at the UW to examine and
understand the impact of this variation on the application of the deflection limit. The
survey of Chapter 3 identified bridges with structural problems that were attributed to
bridge deflections or deformations.
completed at UW, and the results of these specific bridge analyses are provided in Chapter
5. WVU completed a series of evaluations of recent bridge designs to establish how
deflection limits and bridge vibrations affect their performance, this work is summarized in
Chapter 6. WVU also completed a design parameter study to determine the effect and
economic consequences of the deflection limits on actual bridge design.
Chapter 7
provides a summary of this work. Finally, Chapter 8 provides a brief summary of the
work completed and a discussion of the conclusions and recommendations from this
research study.
-4-
Chapter 2
Literature Review
2.1. Overview and Historical Perspective
The original source of the present AASHTO deflection limits was of interest to
this study, as the possible existence of a rational basis for the original deflection limits is
an important consideration. The source of the present limitations is traceable to the 1905
American Railway Engineering Association (AREA) specification where limits to the
span-to-depth ratio,
L
L
, of railroad bridges were initially established. limits indirectly
D
D
control the maximum live-load deflection, and Table 2.1 shows the limiting
L
ratios that
D
(ASCE, 1958)
Although, initially, live load deflections were not directly controlled, the 1935 AASHTO
specification included the following stipulation:
If depths less than these are used, the sections shall be so
increased that the maximum deflection will be not greater
than if these ratios had not been exceeded.
L
, ratios in A.R.E.A. and A.A.S.H.O. (ASCE, 1958).
D
Trusses
Plate Girders
Rolled Beams
1 / 10
1 / 10
1 / 10
1 / 10
1 / 12
1 / 12
1 / 12
1 / 12
1 / 15
1 / 10
1 / 10
1 / 10
1 / 12
1 / 15
1 / 25
1 / 20
1 / 20
1 / 25
- 5 -
L
limits have been employed for many years, the
D
definitions of the span length, L, and the depth, D, have changed over time. Commonly,
engineers have used either the center-to-center bearing distance or the distance between
points of contraflexure to define span length. The depth has varied between the steel
section depth and the total superstructure depth (steel section plus haunch plus concrete
deck in the case of a plate or rolled girder). While these differences may appear to be
small, they have a significant influence on the final geometry of the section, and they
significantly affect the application of the
L
and deflection limits.
D
Actual limits on allowable live-load deflection appeared in the early 1930's when
the Bureau of Public Roads conducted a study that attempted to link the objectionable
vibrations felt on a sample of bridges built in that era
1971; and Fountain and Thunman, 1987)
L
deflection design limit.
800
L
,
800
Some information
regarding the specifics of these studies is lost in history. However, the bridges included
in this early study had wood plank decks, and the superstructure samples were either
pony trusses, simple beams, or pin-connected through-trusses. The
L
deflection limit
1000
for pedestrian brides was set in 1960. Literature suggested that this limit was established
after a baby was awakened on a bridge. The prominent mother's complaint attributed the
babys response to the bridge vibration, and the more severe deflection limit was
established for bridges open to pedestrian traffic (Fountain and Thunman, 1987).
- 6 -
(ASCE, 1958)
reviewed the history of bridge deflection criteria, completed a survey to obtain data on
bridge vibrations, reviewed the field measurements of bridges subjected to moving loads,
and gathered information on human perception to vibration. The committee examined
the effect of the deflection limit on undesirable structural effects including:
The committee also considered the measures needed to avoid undesirable psychological
reactions of pedestrians, whose reactions are clearly consequences of the bridge motion,
and vehicle occupants, whose reactions may be caused by bridge motion or a
combination of vehicle suspension/bridge interaction.
The committee noted that the original deflection limit was intended for different
bridges than those presently constructed. Design changes such as increased highway
live-loads and different superstructure designs such as composite design, pre-stressed
concrete, and welded construction were not envisioned when the limit was imposed. The
limited survey conducted by the committee showed no evidence of serious structural
damage attributable to excessive live-load deflection. The study concluded that human
psychological reaction to vibration and deflection was a more significant issue than that
of structural durability and that no clear structural basis for the deflection limits were
found.
- 7 -
A subsequent study
deflection limits and the effects of slenderness and flexibility on serviceability. They
reviewed literature on human response to vibration and on the effect of deflection and
vibration on deck deterioration. This study suggested that bridge deflections did not have
a significant influence on structural performance, and that deflection limits alone were
not a good method of controlling bridge vibrations or assuring human comfort.
Oehler
(Oehler, 1970)
structures due to a single truck either in the span or in an adjacent span. In no instance
was structural safety perceived as a concern. The survey showed that only pedestrians or
occupants of stationary vehicles objected to bridge vibration.
L
limits in the specifications be altered
D
- 8 -
economy.
determined the
L
in the 1941 AASHTO specifications, which were adopted after the
800
1930 Bureau of Public Roads study, but deflection limits do not limit the vibration and
acceleration that induces the human reaction.
This chapter presents a comprehensive literature review on the dynamic
performance of highway bridges subjected to moving loads. More detailed discussion is
provided on 3 factors that influence or are influenced by, live-load deflection. These
include:
- 9 -
. One study
influence of the AASHTO deflection criteria, because flexural stresses in the deck of
composite bridges are small. Bridge dynamic response changes very little as flexibility
increases, because the lateral distribution of loads to adjacent girders increases with
flexibility. In the negative moment regions of composite spans, the design flexural
stresses in the deck are predictable and reinforcing steel can be provided for crack width
control. They also argue that increased stiffness may increase deck deterioration, because
the effects of volume change on the tensile stresses due to deck/beam interaction increase
as the beam stiffness increases. They examined deck deterioration noted in field survey
data accumulated by the Portland Cement Association (PCA)
(PCA 1970)
in cooperation
- 10 -
climates. The bridges included simple and continuous span concrete T-beams, slabs, box
girders, and pre-stressed beams, as well as steel rolled beams, plate girders, deck and
through trusses. These bridges were systematically and consistently inspected, and the
damage characteristics were noted in detail.
between bridge type and either the amount or degree of deck deterioration.
Others (Krauss and Rogalla, 1996) reviewed literature, surveyed 52 transportation agencies
throughout the U.S. and Canada and conducted analytical, field, and laboratory research.
The survey was sent to develop an understanding of the magnitude and mechanistic basis
of transverse cracking in recently constructed bridge decks. The analytical parametric
study examined stresses in more than 18,000 bridge scenarios.
replacement was monitored in the field, and laboratory experiments examined the effect
of concrete mix and environmental parameters on cracking potential. It was concluded
that cracking is more common among multi-span continuous steel girder structures due to
restraint and that longer spans are more susceptible than shorter spans. It was felt that
reducing deck flexibility may potentially reduce early cracking.
Three studies (Goodpasture and Goodwin, 1971; Wright and Walker, 1971; and Nevels and Dixon, 1973) focus
on the relationship between deck deterioration and live-load deflection. Goodpasture and
Goodwin studied 27 bridges in Phase I of their research to determine which type of
bridges exhibited the most cracking. These bridges including plate girders, rolled beams,
concrete girders, pre-stressed girders, and trusses. The effect of stiffness on transverse
cracking was evaluated for 10 of the continuous steel bridges in Phase II. No correlation
between girder flexibility and transverse cracking intensity could be established.
- 11 -
tension at the top of the deck and possible deck cracking, and were of interest to this
research. The longitudinal deck moments are small. Figure 2.1 shows the influence of
stringer flexibility and span length on transverse moments. The curves give moment per
unit width produced by a dimensionless unit force, M/P. The stiffness parameter, H, is
the ratio of stiffness Eb Ib of the beam and slab stiffness for the span length, L.
H=
Eb I b
E L h3
12 (1 v ) 2
(Eqn. 2.1)
In equation 2.1, E, h, and v are the modulus of elasticity, thickness, and Poissons ratio
for the deck slab, respectively, and h and L are in like units. Flexible structures result in
smaller values of H, and H is varied between 2, 5, 10, 20 and infinity () in the figure,
because this range includes practical extremes of flexibility and stiffness. Span lengths of
40, 80, and 160 ft (12.2, 24.4, and 48.8 m) for both simple and continuous span bridges
are used. Figure 2.1b shows that low values of H (increased girder flexibility) increase
the peak positive transverse moment in the deck. In turn, the peak negative live-load
moments are decreased with increased flexibility, and this subsequently reduces deck
cracking.
Nevels and Hixon (Nevels and Hixon, 1973) completed field measurements on 25 I-girder
bridges to determine the causes of bridge deck deterioration. The total sample of 195
bridges consisted of simple and continuous plate girder and I-girder as well as prestressed
concrete beams with span lengths ranging from 40 to 115 ft (12.2 to 35 m). The work
showed no relationship between flexibility and deck deterioration.
- 12 -
a) Cross-section
b) Variation in Parameters
Figure 2.1 Effect of stringer flexibility on transverse moment in deck
(Wright and Walker, 1971)
- 13 -
An early PCA (PCA 1970) study provides substantial evidence that steel bridges
and bridge flexibility have not greater tendency toward deck cracking damage than other
bridge systems. However, another recent study (Dunker and Rabbat, 1990 and 1995) funded by PCA
appears to contradict earlier PCA results
(PCA 1970)
bridge performance on a purely statistical basis. No bridges are inspected. The condition
assessment and the statistical evaluation are based entirely upon the National Bridge
Inventory data. They show that steel bridges have greater damage levels than concrete
bridges, and imply that this is caused by greater flexibility and deflection. There are
several reasons for questioning this inference. First, the damage scale in the inventory
data is very approximate, and the scale is not necessarily related to structural
performance. Second, the age and bridge construction methods are not considered in the
statistical evaluation. It is likely that the average age of the steel bridges is significantly
older than the prestressed concrete bridges used for comparison.
Therefore, any
increased damage noted with steel bridges may be caused by greater wear and age and
factors such as corrosion and deterioration. Finally, there are numerous other factors that
affect the bridge inventory condition assessment. As a consequence, the results of this
study must be viewed with caution.
The preponderance of the evidence indicates no association between bridge girder
flexibility and poor bridge performance (ASCE, 1958; Wright and Walker, 1971; and Goodpasture and Goodwin,
1971)
. While the literature shows no evidence that bridge deck deterioration is caused by
excessive bridge live-load deflections, other factors are known to influence bridge deck
deterioration. High temperature, wind velocity, and low humidity during placement and
curing accelerate cracking
- 14 -
been found to have a significant effect on the deterioration of concrete at early ages
Mo., 1999; and Issa, Ma. et. al. 2000)
(Issa,
include low shrinkage, low modulus of elasticity, high creep, low heat of hydration, and
the use of shrinkage compensating cement. Variables in the design process that affect
cracking include the size, placement and protective coating of reinforcement bars.
Smaller diameter reinforcement, more closely spaced, is recommended to reduce
cracking
cracking, but the reinforcement must have a sufficient cover, between 1 and 3 inches.
However, a CALTRANS study reported placement as having no effect on transverse
cracking
(Poppe, 1981)
There is considerable evidence that the existing deflection limits are motivated by
vibration control, so research into bridge vibrations is relevant to this study.
2.3.1. Human Response to Vibration
Research
Psychological
discomfort results from unexpected motion, but physiological discomfort results from a
low frequency, high amplitude vibration such as seasickness.
- 15 -
Vertical bridge
(Shahabadi,
1977)
.
In 1931, Reiher and Meister
(Shahabadi, 1977)
(Goldman, 1948)
reviewed the problem and produced from several different sources, including Reiher and
Meister, a set of revised averaged curves corresponding to three tolerance levels
classified as perceptible, unpleasant, and intolerable.
A 1957 study (Oehler, 1957) cites empirical amplitude limits developed by Janeway to
control intolerable levels of vibration amplitude. Janeway's limits recommended that af
equal 2 for bridges with frequency of 1 to 6 cps where a is the amplitude and f is the
frequency of vibration, and af
deflection, vibration amplitude and frequency of vibration were measured for 34 spans of
15 bridges to determine which bridge type was more susceptible to excessive vibrations.
Simple-spans, continuous spans, and cantilever spans of reinforced concrete, steel plate
girder and rolled beam superstructures were investigated. The observed amplitude and
frequency data was compared to Janeways recommended limits. The amplitude of
vibration is shown with the test truck on the span and off the bridge in Fig. 2.3. The test
vehicle produced vibration amplitudes that exceeded Janeways human comfort limits in
7 cantilever-span and 7 simple-span bridges, but this amplitude of vibration never lasted
- 16 -
more than one or two cycles. Reactions from personnel performing the tests disagreed
with the limits set by Janeway.
continuous spans but noted that it was not disturbing. They felt discomfort at high
amplitude, low frequency vibration. It was concluded the cantilever spans were more
prone to longer periods of vibration and larger amplitudes than the simple or continuous
spans. Further, increasing bridge stiffness does not decrease the vibration amplitude
sufficiently to remove it from the perceptible range presented by Reiher and Meister and
Goldman (Oehler, 1970).
Figure 2.2. Six Human Tolerance Levels by Reiher and Meister (Shahabadi 1977)
- 17 -
Figure 2.3. Observed Bridge Amplitude and Frequency with Human Tolerance Limits
Developed by Janeway (Oehler, 1957)
Wright and Green
52 bridges to levels based on Reiher and Meister scale and Goldmans work. They
showed that 25% of the bridges reached the intolerable level indicated by subjects in the
Reiher, Meister, and Goldmans work. They concluded that low natural frequencies, up
to 3 Hz, are not the only parameter that will reduce vibrations.
DeWolf and others
noncomposite continuous bridge with two nonprismatic steel plate girders. This 30-year
old structure had reported objectionable vibrations, when one direction of traffic was
- 18 -
stopped on the bridge while the other lane was moving. Accelerations were determined
and compared to human tolerance limits developed by Bolt, Beranek and Newman, Inc.
The maximum values recorded on the bridge, seen in Fig. 2.4, exceed those accelerations
tolerable by most people. However, the bridge structural performance and the resulting
stresses, based on the initial analysis of the data, are within acceptable limits.
Many factors influence the dynamic behavior of bridges including the following:
vehicle properties,
- 19 -
The
were
monitored under normal commercial traffic, a controlled two-axle truck, and a special
three-axle truck. The Jackson Bridge is an eight-span plate girder bridge with 5 simple
and 3 continuous spans. The Fennville Bridge consists of 6simple-spans of rolled beam
construction of which only one span exhibits composite action. Measured deflections
were compared to theoretical predictions, and the effect of vehicle weight, vehicle type,
axle arrangement, speed, and surface roughness on vibration was studied. Deck surface
irregularities were simulated by boards placed on the bridge deck in the path of the test
vehicle, and they caused increased amplitude of bridge vibration.
Increasing span
Computed
deflections were consistently larger than the measured deflections. Vibrations increased
when the natural period of vibration of the span nearly coincided with the time interval
between axles passing a reference point on the span.
Midspan deflections for all spans due to a 3-axle truck with axle loads of 5.6,
18.1, and 15.5 kips (24.9, 80.5, and 70 kN) were measured (Oehler, 1957) for 15 bridges built
between 1947 and 1957. Several spans showed appreciable vibration although live-load
plus impact deflections were less than
L
. The dynamic behavior of 52 representative
1000
Ontario highway bridges that vibrate under normal traffic were measured
1964)
. Each bridge was inspected to determine traffic conditions, road surface condition
- 20 -
and bridge details. A wide variety of differing types, spans and cross-sectional geometry
were chosen including beam or plate girder and truss systems, simple and continuous
spans. Span lengths ranged from 50 to 320 feet. In all cases, the actual stiffness of the
bridge was larger than that of the calculated stiffness, and as a consequence the measured
frequency was always larger than the computed frequency as shown in Fig. 2.5. One
bridge was selected for further evaluation of the influence of surface roughness on the
dynamic response. A test was performed on that bridge before the final asphalt pavement
was laid and after the pavement was laid while normal traffic operated on the bridge
under both cases. The deck couldnt be considered rough or smooth before the pavement
was placed but was smooth immediately after the pavement was placed. Comparison of
the results of the two tests showed great improvement in the dynamic performance with
the smooth deck.
Figure. 2.5. Measured Bridge National Frequency Versus Calculated Natural Frequency
(Wrignt and Green, 1959)
- 21 -
on 25 bridges with an
HS20 vehicle, with wheel loadings of 7.29 and 32.36 kips (32.4 and 144 kN) and an axle
spacing of 13.25 ft (4.03 m), and compared to calculated deflections. The calculated
deflection was approximately 50 percent larger than the actual values.
Dynamic responses of 40 steel, 19 reinforced concrete and 3 pre-stressed concrete
bridges were measured under normal traffic and loaded with a 21 kip (93.5 kN) test
vehicle
(Kropp, 1977)
predictions made for 900 of the more than 13,000 records accumulated during testing. Of
the 900 records, 65 percent were normal trucks, 30 percent were the test vehicle and 5
percent were light traffic. Only 5% of the measured responses exceeded the comfort
limit proposed by Wright and Walker (Wright and Walker, 1971).
Other field studies of dynamic response of typical bridge structures were carried
out in Ontario, Canada (Green, 1977). For each structure, one of two dominant frequencies of
vibration was generally observed for the free vibration. Many types of bridge geometry,
ages, and conditions were included in the study.
(Eqn. 2.2)
2 L
Eb I b g
w
(Eqn. 2.3)
where Eb is the modulus of elasticity of steel, Ib is the moment of inertial of the beam of
cross-section, g is the acceleration due to gravity, and w is the weight per unit length of
the stringer and its share of deck. Consistent units must be employed for all variables.
This equation was validated for structures with 2 Hz < fcal < 7 Hz.
- 22 -
Haslebacher
(Haslebacher, 1980)
suggested that intolerable dynamic conditions may result if the ratio of forcing frequency
to bridge natural frequency is in the range of 0.5 to 1.5.
He defined intolerable
- 23 -
(Amaraks, 1975)
Surface roughness produced the most significant effect on acceleration for both the
simple and continuous span bridges. The maximum accelerations with a rough roadway
surface were found to be as much as five times those for the same bridge with a smooth
deck.
Maximum
acceleration also increased when the stiffness was reduced, but this increase was
significantly less severe than noted with the surface roughness variations as may be seen
in Fig. 2.6 and 2.7, respectively.
influences peak acceleration. The maximum accelerations were approximately the same
for two and three axle vehicle models, but were about two thirds of the magnitudes
produced by the single axle vehicle model. An investigation of the influence of initial
oscillation of the vehicle suspension on bridge acceleration was also conducted. Initial
oscillation causes a 30 to 50 percent increase in maximum accelerations for the bridge
assumed to have a smooth deck surface.
Aramraks
(Aramraks, 1975)
bridge natural frequency to vehicle frequency, in the range of 0.5 to 2.0, as can be seen in
Fig. 2.8. The vehicle frequency, using an HS20-44 loading, is the tire frequency of the
rear axles.
For the two-span bridge and three-span bridge, the fundamental natural
frequency is 3.53 and 3.0 Hz, respectively. Commonly, the acceleration magnitudes were
approximately the same but increased slightly in the midspan when the vehicle and
bridge had the same natural frequency.
- 24 -
- 25 -
increased with increased vehicle speed. The increase was up to 40 percent in extreme
cases. However, vehicle speed was found to have the greatest effect on the maximum
girder acceleration. Additionally, they showed that initial vehicle oscillation had the
- 26 -
greatest effect on maximum deflections increasing 2.5 times, while the maximum girder
acceleration showed a minimal increase with an increase in oscillations.
Three alternative methods of providing for the serviceability limit state are found
and discussed here.
2.4.1. Canadian Standards and Ontario Highway Bridge Code
Both the Canadian Standard and the Ontario Highway Bridge Code use a
relationship between natural frequency and maximum superstructure static deflection to
evaluate the acceptability of a bridge design for the anticipated degree of pedestrian use
(Ontario Ministry of Transportation, 1991; and Canadian Standards, 1988)
flexural frequency (Hz) versus static deflection (mm) at the edge of the bridge, which the
natural frequency is calculated using Eqn. 2.2
The
This relationship was developed from extensive field data collection and
analytical models conducted by Wright and Green in 1964.
- 27 -
acceleration limits were converted to equivalent static deflection limits to simplify the
design process. For pedestrian traffic, the deflection limit applies at the center of the
sidewalk or at the inside face of the barrier wall or railing for bridges with no sidewalk.
Figure 2.9. First Flexural Frequency versus Static Deflection (Ministry of Transportation, 1991)
More recent studies by Billings conducted over a wide range of bridge types and
vehicle loads, loads ranging from 22.5 kip to 135 kips (100 KN to 600 KN), confirm the
results of the initial study (Ontario Ministry of Transportation, 1991).
For both the Canadian Standards and the Ontario Code, only one truck is placed at
the center of a single traveled lane and the lane load is not considered. The maximum
deflection is computed due to factored highway live-load including the dynamic load
allowance, and the gross moment of inertia of the cross-sectional area is used (i.e. for
composite members, use the actual slab width).
deflection due to flexure is computed at the closest girder to the specified location if the
girder is within 1.5m of that location.
- 28 -
A brief review of the codes and specifications used in other countries were also
examined. Most European Common Market countries base their design specifications
upon the Eurocodes
(Dorka, 2001)
standards. Each country must issue a "national application document (NAD)" which
specifies the details of their procedures. A Eurocode becomes a design standard only in
connection with the respective NAD. Thus, there is considerable variation in the design
specifics from country to country in Europe. If an NAD exists for a specific Eurocode,
then this design standard is enforced when it is applied to a building or bridge. Often, the
old national standards are also still valid and are applied. There is the rule though, that the
designer cannot mix specifications. The designer must make an initial choice and then
use this in all design documents for the structure. However, in general, the full live-loads
are factored with a "vibration factor" to account for extra stresses due to vibrations in
European bridge codes. No additonal checks (frequency, displacements etc.) are then
required. For long span or slender pedestrian bridges, a frequency and mode shape
analysis also is usually performed. Special attention is always paid to cables, since
vibrations are common, and some European bridges have problems with wind induced
cable vibration. Deflection limits are not normally applied in European bridge design.
In New Zealand, the 1994 Transit NZ Bridge Manual limits the maximum vertical
velocity to 0.055 m/s (2.2 in/sec) under two 120 kN (27 kip) axles of one HN unit if the
bridge carries significant pedestrian traffic or where cars are likely to be stationary (Walpole,
2001)
- 29 -
L
and deflection, but
D
A 1971 study conducted by the American Iron and Steel Institute (AISI) reviewed
AASHTO criteria and recommended relaxed design limits based on vertical acceleration
to control bridge vibrations (Wright and Walker, 1971). The proposed criteria requires that:
1. Static deflection,s, is the deflection as a result of live-loads, with a wheel load
distribution factor of 0.7, on one stringer acting with its share of the deck.
2. Natural frequency, f b (cps), is computed for simple or equal spans
fb =
2 L
Eb I b g
w
(Eqn. 2.5)
v
2 fb L
(Eqn. 2.6)
where,
v = vehicle speed, fps.
4. The Impact Factor, DI, is determined as
DI = + 0.15
(Eqn. 2.7)
(Eqn. 2.8)
- 30 -
2.5. Summary
L
for most design situations
800
L
for urban areas where the structure may be used in part by pedestrian traffic
1000
undetermined loads, and the bridges used for this initial limit state development are very
different from those used today. The research has shown that reduced bridge deflections
and increased bridge stiffness will reduce bridge vibrations, but this is clearly not the best
way to control bridge vibration. Bridge vibration concerns are largely based upon human
perception. Human perception of vibration depends upon a combination of maximum
deflection, maximum acceleration and frequency of response. Several models have been
proposed for establishing acceptable limits for perception of vibration, but there does not
appear to be a consensus regarding acceptable limits at this point.
Bridge surface
roughness and vehicle speed interact with the dynamic characteristics of the vehicle and
the bridge (such as natural frequency) to influence the magnitude of bridge response.
Field measurements of bridges show that the actual bridge live-load deflections are often
smaller than computed values for a given truck weight.
- 31 -
L
deflection limit is not typically applied in such a way to control this damage.
800
Within this framework, it is not surprising that the bridge design specifications of
other countries do not commonly employ deflection limits. Instead vibration control is
often achieved through a relationship between natural bridge frequency, acceleration and
live-load deflection.
- 32 -
Chapter 3
Survey of Professional Practice
The
first
general
question established the deflection limits that are applied to steel bridges in that state and
the circumstances under which they are used. The second general question determined the
loads used to compute these deflections for steel-stringer bridges, and the third question
extended this information to other steel bridge types. The fourth question determined the
calculation methods and the stiffness considered in the deflection calculation. Deflection
L
limits and span-to-depth ratio (D ratio) limits appear to accomplish similar objectives in
L
deflection control, and question 5 addressed the role of the D ratio limits in that state.
Questions 6 through 9 identified candidate bridges for more detailed study that
was to be completed in later stages of the research. The economy of HPS bridges may be
adversely affected by the existing deflection limit, and question 6 sought information on
HPS applications. The seventh question identified bridges with structural damage that
engineers attributed to excessive bridge deflections. Question 8 sought information
- 33 -
Bridges
that fail to satisfy the existing deflection limit but still provide good bridge performance
are also strong candidates for further study, because these bridges provide a basis for
modifying present serviceability limits. Question 9 identified these bridges.
Question 10 sought comments on the use and suitability of present live-load
deflection limits and research reports or other information that was relevant to the study.
Field measurements and research reports related to this study were requested.
Of 47 states
- 34 -
L
2 states use a 1200 limit,
L
1 state employs a 1100 limit,
L
39 states use a 1000 limit,
L
3 states employ a 800 limit.
There is very wide variation in these deflection limits, since the largest deflection limit is
twice as large as the smallest deflection limit. Two of the 47 states treat the deflection
limit as a recommendation rather than a design requirement.
The AASHTO Specification indicates that deflections due to live-load plus impact
are to be limited by the deflection limit. Within this context, there is ambiguity in the loads
and load combinations that should be used for the deflection calculations, because design
live-loads are expressed as both individual truck loads and uniform lane loads. The survey
showed that the loads used to compute these deflections have even greater variability than
observed in the deflection limits.
1 state employs the HS (or in some cases LRFD HL) truck load only,
1 state uses truck load plus distributed lane load without impact,
7 states use the larger deflection caused by either truck load plus
impact or the distributed lane load with impact,
17 states use truck load plus distributed lane load plus impact, and
The combination of the variability of the load and the variability of the deflection limit
results in considerable difficulty in directly comparing the various state deflection limits.
For example, Wisconsin uses the smallest deflection limit, but it also employs smaller loads
than most other states. However, the relative importance of the lane load and design truck
- 35 -
L
load are likely to be different for long and short span bridges, and so the 1600 limit used
in Wisconsin may be more restrictive for short span bridges. Conversely, the Wisconsin
limit may be a generous deflection limit for very long span bridges, because the truck load
becomes relatively smaller with longer bridge spans despite the small deflection limit.
The actual methods used to calculate deflections are not defined in the AASHTO
Specification. In typical engineering practice, deflection limits are based upon deflections
caused by service loads under actual service conditions. Load factors or other factors
used to arbitrarily increase design loads are not normally used in these deflection
calculations, and the actual expected stiffness of the full structure is used. The survey
shows that this is a further source of variability in the application of the deflection limits.
Load factors and lane load distribution factors are employed in some states while they are
neglected in others. Lane load distribution factors can significantly affect the magnitude of
the loads used to compute the deflections. The survey shows that 26 states use lane load
distribution factors from the AASHTO Standard Specifications in calculating these
deflections. Three states report that they use the LRFD lane load distribution factors.
Thirteen states indicate that they effectively apply the loads uniformly to the traffic lanes
by the AASHTO multiple presence lane load rules. They then compute the deflections of
the bridge as a system without any increase for load factors, girder spacing or lane load
distribution. These states effectively use an equal distribution of deflection principle. One
state uses its own lane load distribution factor that is comparable to system deflection
calculations. Several states indicate some flexibility in the calculation method, and a few
states indicate a reluctance to permit the bridge deflection limit to control the design. The
effect of the lane load distribution factor can be quite significant. Depending upon the
spacing of bridge girders, the load used for bridge deflection calculations can be 40% to
100% larger than the load used for states where deflections are computed for the bridge as
a system or where the loads are uniformly distributed to girders.
- 36 -
Load factors may also be an issue of concern. Five states report that they apply
load factors to the load used for the deflection calculation.
increase the loads used to compute bridge deflections, and they increase the variability in
the application of the deflection limit between different states.
L
Span-to-depth, D , ratio limits were also examined because they also have
L
interrelation with deflection limits. Seven states indicate that they employ no D limits,
while 34 indicate that they use the AASHTO design limits. Of these 34 states, 6 indicate
that they strictly employ the limit, but 8 indicate that they employ it only as a guideline.
The impact of this observation is not immediately clear, because some states that have no
L
limit or a loose D limit have relatively tight deflection limits. Some states that strictly
L
apply the AASHTO D ratio limits have relatively less restrictive deflection limits.
The combined variability of the deflection limit, the methods of calculating
deflections, and the loads used to calculate deflection indicates that the resulting variability
of the practical deflection limits used in the different states are huge. On the surface, it
appears that variations of at least 200% to 300% are possible. However, the comparison
is neither simple nor precise.
- 37 -
Very few bridges that fail existing deflection limits but still provide good structural
performance were identified in this survey. A small number of bridges with vibration
problems was also identified. A number of HPS bridges were identified and information
regarding these bridges was obtained for possible further evaluation. The identification of
bridges with structural damage that is caused by bridge deflection provided somewhat
confusing results. A number of damaged bridges were identified, but most state bridge
engineers did not believe that they had any bridges with damage due to excessive
deflections. A few states were very clear that they had a significant number of bridges
with structural damage that was apparently associated with large deflections. This damage
was usually deck cracking and steel cracking or other damage due to differential deflection
and out-of-plane bending. However, some of the damage relates to cracking of bolts or
other steel elements. It must be emphasized that even states reporting damage note that
the damaged bridges were a small minority of their total inventory.
Nevertheless, the fact that some engineers felt that they had a significant number of
bridges with the reported damage, while others felt that they had absolutely none was a
source of concern. This contradiction may mean that some states have much better bridge
performance than other state, or it may indicate that bridge engineers may have widely
disparate views as to what constitutes bridge damage. As a result, a limited follow-up
survey was directed toward maintenance and inspection engineers to better understand
and address these results. This survey was limited to 11 states. The states were selected
to represent all geographical parts of the United States, to include populous and lightly
populated states, and to include states with a wide range of vehicle load limits. The
selected states were California
Florida
Illinois
Michigan
Montana
New York
Pennsylvania
Tennessee
- 38 -
Texas
Washington
Wyoming
The results of this follow-up survey showed that the contradictions in reported
bridge behavior are caused by differences in engineer perspective, and there are not likely
to be significant differences in bridge performance from state to state. Most state bridge
engineers are intimately involved in the design and construction of new highway bridges,
but they have limited contact with the repair, maintenance and day to day performance of
most of the bridges in their inventory. Maintenance and inspection engineers often have a
different perspective of bridge performance than the design engineers for their state. They
note a significant number of bridges with cracked steel and cracked concrete decks, and
they are more conscience of the potential causes of this damage. As a result, a number of
damaged bridges were identified from a number of different states, and the damage of
these bridges is usually attributable to some form of bridge deflection. However, none of
this deflection damage can be attributed to the direct deflections that are evaluated in the
AASHTO deflection check. Instead the damage is caused by differential deflections or
relative deflections and other forms of local deformation.
As a result, a significant
number of candidate bridges were located for this category, it must be clearly recognized
that the damage noted in those bridges is often different than what some engineers would
regard as bridge deflection damage.
Bridges that were identified as viable candidates by the above criteria were
investigated in much greater detail. Design drawings, inspection reports, and photographs
were obtained for these candidate bridges, and this information was used for the bridge
analysis discussed in Chapter 5.
- 39 -
- 40 -
Chapter 4
Evaluation of the Variation in Practice
The AASHTO HS and LRFD HL loads are combined, because the geometry and
magnitude of these loads are similar. The AASHTO H truck loading is not discussed here,
because it provides little added insight into the deflection issue.
- 41 -
- 42 -
The second step used the points of maximum influence to apply the appropriate
loading to the same structure with a more refined mesh. The refined mesh permitted
accurate determination of the moment diagram and deflected shape of the structure, since
these were needed to establish the minimum possible moment of inertia required to resist
the loading and pass the various deflection vs. span length, L , check. For this second
step, a structural stiffness model using a 1 ft. (.305 m) element discretization was
assembled. Boundary conditions were applied at the member ends and supports. The
load geometry is selected, the load is applied and deflections are computed for each nodal
point along the bridge length. The axles for the truck loading are spaced at a constant 14
feet and the centroid of the truck load is placed at approximately the point of maximum
influence allowing the axle loads to be placed at the nearest nodes in the structure. This is
done for each span separately and the deflections and bending moments were calculated
for the entire structure due to loading in that span. For HS truck loading the axle loads
had ratios of 0.2, 0.8, and 0.8. This resulted in a total unit load of 1.8. This is done so
that HS truck loading can be directly compared by multiplying the deflections by the gross
weight of the front two axles. For example, the HS20-44 loading can be compared simply
by multiplying the deflection by 40 kips (178 kN).
For distributed lane loading, loading is only applied in spans where it will increase
the deflection in the span of interest. The lane loading is applied using equivalent nodal
loads at all appropriate nodes and the magnitude is also scaled to permit direct comparison
of uniform lane loading and truck loading. Standard HS20-44 lane loads are 0.640 kip/ft
1
(9.34 kN/m) and in the program the lane load has been scaled so that it is 62.5 . If the
deflection results are multiplied by 40 kips (178 kN), the resulting lane load magnitude
would be 0.640 kip/ft (9.34 kN/m), and the resulting deflections will be the same as those
for HS20-44 lane loading. The combination of uniform lane loading and the truck loading
simply combines the truck and lane loading using the same scaling factors and load
positions noted above.
- 43 -
The deflected shape and bending moment diagram are calculated for the maximum
influence in each span, and the ratio of the maximum deflection to the span length is
established. For simple span beams, the span length, L, is determined by taking the
distance between supports, and the maximum deflection is the maximum deflection of
beam span relative to the points of zero moment. If a consistent and comparable measure
is employed for continuous multiple span beams, the span length for the deflection
comparison should be taken as the distance between any points of contraflexure as
illustrated in Fig. 4.1. For continuous bridge girders, the maximum deflection should also
be determined by taking the maximum deflection measured from the chord joining the zero
moment points as shown in the figure.
(Eqn. 4.1)
The parameter, p, represents the load magnitude (in kips), and the load vector, {P},
provides the load pattern. The column matrix or vector, {P}, is assembled using the
methods described earlier. The bending stiffness of the beam, EI, is a constant, and E=
29,000 ksi (201,500 MPa), and [K] is the stiffness matrix. The system of equations can
- 44 -
then be solved by normal matrix inversion or solution techniques, and the deflection
vector, {U}, is determined by
p
{U} = {}E I
(Eqn. 4.2)
The vector, {}, is the deflected shape of the girder resulting from a unit load, p, and EI.
The maximum deflection, , is then
p
=EI
(Eqn. 4.3)
where, , is the maximum value of the shape vector. The deflection is limited by a ratio,
L
R, which is a deflection limit such as 800 . Therefore, the relative stiffness, Irel, may be
computed as follows
Irel = Ibase
p DF IF > p
R
29000 R DF IF.
(Eqn. 4.4)
where IF is an impact factor, Ibase is the base moment of inertia, and DF is the lane load
distribution factor used in the analysis. Ibase is the moment inertia required when R, p,
DF, and IF all equal to 1. It should be noted that several states include load factors in
their bridge deflection evaluation, and if load factors are used they may be incorporated in
the right hand side of Eqn. 4.4. However, load factors are not normally considered in
deflection limit calculations and are not included in this parameter study. Irel can be
calculated for any magnitude of loading or L limit. Irel represents the minimum possible
moment of inertia required in order to satisfy a specific deflection vs. span length value
under a specific load geometry and magnitude.
- 45 -
There are a series of sub-categories within each of these main categories that differ only in
the eventual magnitude of the applied load and deflection limit. This categorization
reduces the number of analyses required for the evaluation, and it permits more direct
comparison of some parameter effects. The analyses were completed for four main
bridge span types:
simply supported,
The nominal spans were varied from 50 ft to 300 ft (15.24 m to 91.44 m) in 50 ft (15.24
m) increments. For each analysis, Ibase was obtained assuming an elastic modulus of
29000 ksi (201,500 MPa) and a R, p, DF, and IF equal to 1.0. The resulting value is in
units of in4 / kip.
Figure 4.2, 4.3, 4.4, and 4.5 show the Ibase for the three load pattern categories for
a simple span bridge, 2 span continuous bridge, a 3 span continuous bridge with equal
span lengths, and a 3 span continuous bridge with the exterior span lengths equal to 80%
of the interior span length, respectively. An increase in span length yields an overall
increase in the base moment of inertia for any bridge geometry or loading, but it is
interesting to note the difference in the base moment of inertia for the different load
patterns. The combined truck and uniform lane loadings require the largest moment of
inertia in all cases. The HS truck load geometry always requires a larger moment of
inertia for short span bridges than does the uniform lane load for all bridge span types.
However, as the span length increases the uniform lane load has a more rapidly increasing
impact on the bridge deflection than does the truck loading. A crossover between the two
load patterns occurs around 175 ft (53.3 m). Comparison of Figs. 4.2 through 4.5 shows
that continuous girders require a smaller Ibase than simple spans. This is partly caused by
- 46 -
the added stiffness due to continuity of the girder, but the more rational method for
defining span length, L, in Fig 4.1 also contributes to this beneficial effect. The difference
between 2 span continuous and 3 span continuous with equal spans is negligible.
As shown in Eqn. 4.4, Ibase can be multiplied by 40 kips (178 kN) to obtain Irel for
HS20-44 loading or multiplied by 50 kips (222.5 kN) to obtain Irel for HS25-44. The
effects of the distribution factor or dynamic impact factor can also be achieved by
- 47 -
multiplying these values by DF and IF in Eqn. 4.4 as appropriate. The effect of individual
deflection limits can be applied by dividing by R as shown in the equation.
Figure 4.4. Ibase for 3 Span Continuous Bridges with Equal Span Length
Figure 4.5. Ibase for 3 Span Continuous Bridge with Unequal Span Lengths
(80%-100%-80%)
Lane load distribution factors play a major role in the application of the deflection
limit. The survey established two widely used methods of determining a lane load
distribution factor. Some states employ lane load distribution factor from the AASHTO
- 48 -
- 49 -
Figure 4.6. Difference in DF Factor for AASHTO Lane Load Distribution Factors as
Compared to the Equal Distribution Method for a Four Lane Bridge
- 50 -
employ combined truck and lane loads are requiring an I value that is nearly twice that
needed for either of the individual load cases. The use of impact factors has a relatively
modest effect on the deflection calculation as shown in Fig. 4.7. Some states use an equal
load distribution model for their deflection check while other states employ the AASHTO
lane load distribution factors. The use of AASHTO lane load distribution factors
invariably increase the minimum required I by approximately 50% over that required with
equal distribution model, and these factors may increase the minimum required moment of
inertia by as much as 350% for some bridge geometry's. The combination of these effects
indicate extreme variation in the application of these deflection limits.
An example of the possible variation in the total deflection limit criteria is useful.
For this example, the same deflection vs. span length limit is used in both cases. The
bridge is a 200 ft (61 m) simply supported bridge. Case A employs HS20-44 truck load
only is used with equal distribution and no dynamic impact factor. For this case the
minimum Irel is 147 in4 (.000061 m4). For Case B an HS25-44 truck plus lane load is
used with AASHTO lane load distribution and the dynamic impact factor. For Case B, the
minimum Irel is 1393 in4(.000579 m4). Case B requires a minimum I, which approximately
950% that required by Case A. This is a huge variation in the deflection limit application.
Normally the L limit would be included in the calculation, but because it was assumed
that both checks would use the same limit, it was unnecessary to include it in this
comparison. Thus, the above I values are relative values rather than absolute
requirements. Larger differences are possible when the variation of the deflection limit are
included in the evaluation. A 200 ft (61 m) bridge is a moderately long span but not
unheard of. These two checks are on extreme opposites of the possible deflection limit
application checks but they are still both possible checks based on survey data obtained
from state bridge offices. They show that there is large possible variation in the
application of deflection limits in various states, and this may have a greater impact upon
steel bridge design in some states than in others.
- 51 -
- 52 -
Chapter 5
Evaluation of Bridges Damaged by Deflection
5.1. Introduction
The survey of Chapter 3 identified a number of bridges, which had structural
damage that engineers attributed to excessive bridge deflection and deformation. Photos,
inspection reports, and design drawings were obtained for these bridges. A more detailed
analysis of some of these bridges was completed, and this chapter summarizes that work.
The damaged bridges identified in the initial study were too numerous for detailed
analysis of each individual bridge within the limited time and funding of this study.
However, careful examination of the candidate bridges showed common attributes among
both the bridge type and the damage characteristics. Bridges with similar design and
construction and similar damage characteristics were grouped. A modest number of
groups were identified, and the detailed analyses of the bridges were greatly simplified,
because only selected candidate bridges from each of these groups were analyzed. The
analyses established whether these selected bridges passed or failed the relevant state
specific deflection criteria and standard deflection criteria, which is proposed in this
chapter. The analyses established whether the damage can rationally be attributed to
bridge deflection, and they examined whether alternate deflection criteria could control or
prevent this damage
This chapter begins with a general description of the modeling and analysis
procedures used in the analyses. The separate bridge type and damage mechanisms are
then discussed, because of the common groups noted earlier. Cumulative results of the
analysis and a discussion of the consequences to this project are then provided.
- 53 -
computer program for each selected bridge. Composite action was assumed only
where shear connectors were present on bridge plans, and the effective concrete flange
width for composite sections was determined as recommended in the AASHTO LRFD
Specification. In the calculation of composite transformed sections, steel reinforcement in
- 54 -
the deck was ignored, and the concrete flange was modeled as a solid concrete section.
The full variation of in-plane flexural properties over the member length were considered.
Support conditions were modeled as pin supports or rollers in all cases.
Modeling began by constructing a MSExcel file that contained the various girder
cross sections provided on the bridge plans. The analysis section properties were
established and a relatively course initial finite element discretization were established in
this spreadsheet to incorporate all section changes encountered in each structure.
Connectivity of members and nodal locations were specified at this point. Haunched
girders were modeled by step function changes to the bridge cross section at 2 ft (610
mm) increments or smaller. The MSExcel file was then loaded into SAP 2000, and the
SAP graphical user interface was used for developing the remainder of the model. Once in
SAP, all elements that were not already in 2 ft (610 mm) or smaller elements were
automatically refined to this mesh. Symmetry was employed to simplify the model where
possible. Support conditions were specified, and the joints and elements were renumbered to aid in the interpretation of results.
Loading was applied in two steps. First, the standard load case was applied to the bridge
using the SAP 2000 built in HS25-44 truck load. A separate load case was used for each
span of continuous bridges, because separate AASHTO dynamic impact factors were
defined for each span. The points of maximum deflection in each span were found, and
influence lines for vertical deflection at those points were used to determine the critical
position of truck loading. Once the points of maximum influence were determined, the
centroid of the HS25-44 truck was placed at the point of maximum influence in each span,
and the maximum deflection and L ratio were determined. This second step was
- 55 -
necessary because SAP 2000 returns only deflection and moment envelopes, when the
automatic truck loading is used. Envelopes are useful for design but they do not
accurately determine the L ratio values for continuous spans. For continuous spans, the
deflected shape and bending moment diagrams for the critical deflection case are required
to correctly determine the L used to establish the deflection limit (see Fig. 4.1). In simply
supported spans, this second step was not necessary, because the maximum overall
deflection is given for the envelope, and L is the distance between supports. The
maximum deflections for the automatically applied trucks and the manually applied trucks
were compared and were always within 1 percent of each other.
Further analyses were completed for some bridges after the initial results were
established. These further analyses attempted to determine if the damage can truly be
attributed to bridge deflection and if a modified deflection check would prevent this bridge
damage. These additional analyses typically evaluated local or system behavior, which is
often a dominant consideration. These individual analyses are very specific to the
individual groups, and they are briefly discussed in the sections that follow.
- 56 -
State
Standard
Evaluation
State
Specific
Comments
California
Pass
Pass
California
Pass
Pass
California
Pass
Pass
Maryland
Pass
Fail
Georgia
Pass
Pass
US-50 By-Pass
Ohio
Fail
Fail
Georgia
Pass
Pass
4-Span continuous truss. Right bridge. Double-angle stringerfloorbeam and floorbeam-truss connections. Floorbeam web
cracking.
- 57 -
Pass
Pass
Simple span truss. Right bridge. Double-angle web stringerfloorbeam connections. Stringer web cracking from cope.
Pass
Pass
Simple span truss. Right bridge. Double-angle web stringerfloorbeam connections. Stringer web cracking.
Washington
Wyoming
Fail
Fail
Wyoming
Pass
Fail
Nevada
Fail
Fail
California
Pass
Pass
- 58 -
- 59 -
- 60 -
bridges are clearly at the point of concern with regard to bridge deflections, and damage is
noted regardless of whether the present AASHTO deflection limit is satisfied or not.
Somewhat more detailed descriptions of these bridges and the resulting damage are
provided.
The bridges pass the proposed standard deflection check with a L ratio of 1534 .
The California deflection limit evaluation uses the HS20-44 truck plus lane plus impact
1
load combination, and the bridge satisfies this deflection limit with a L ratio of 890 if no
lane load distribution factor is employed. The bridge fails this check with a L ratio of
1
339 if AASHTO lane load distribution factors are used with HS20-44 loading.
- 61 -
employed, but it fails the limit with an L ratio of 629 if the AASHTO lane load
distribution factors with HS20-44 loading is employed.
5.3.1.3. SR-99 West Merced Overhead
The SR-99 West Merced Overhead consists of two identical bridges with five
simple spans with lengths between 97.1 and 108 ft (29.6 and 32.91 m). Each bridge has a
skew angle of 61 degrees and consists of five girders spaced at 8.5 ft (2.59 m). The total
- 62 -
bridge width is 39.67 ft (12.09 m) with a roadway width of 37 ft (11.28 m). The bridge
has staggered cross-framing oriented perpendicular to the flow of traffic.
This bridge was built in 1962, and cracking is noted in girder webs at the
diaphragm connections. Most reported damage was on the interior girders near supports.
All spans were analyzed as composite girders with the standard deflection limit evaluation,
1
and the largest L value was 2068 . The state specific deflection limit is again satisfied if
the AASHTO lane load distribution factors are not employed. With AASHTO lane load
1
distribution factors and HS20-44 loads, the most critical span clearly fails the 800
1
- 63 -
these diaphragms transfer more load than may be normally expected because they are
attempting to transfer load directly to interior piers from adjacent bridge girders.
Two single girder models were developed to represent the various bridge girders.
One model simulated the outside girders, and the other model represented interior girders,
which had slightly different dimensional properties. For the standard load check with the
1
HS25-44 loading, the bridges satisfied the deflection limit with a L ratio of 1411 .
Marylands reported deflection limit application case uses the worst of an HS25-44 truck
or HS25-44 lane load and AASHTO distribution factors. No load factors are used, and
the respondent of the phase one survey was unsure of the use of the dynamic impact
factor. As a result, the deflections were checked with and without the AASHTO impact
factor. These bridges clearly failed the state specific deflection limits with deflection ratios
1
in the order of 400 .
- 64 -
The bridge was analyzed as a composite girder. The proposed standard deflection
1
limit evaluation was applied, and the critical L ratio was 808 in the center span.
Georgias reported deflection limit application case uses the worst case of a lane load plus
impact, a truck load plus impact, or a military load plus impact. The military load plus
impact was not defined in the survey, but it is likely heavier than the HS25 truck load.
The deflection limit barely satisfied the standard check, and so the deflections are unlikely
to satisfy the deflection limit with the military vehicle load if multiple lane loads are
applied. In addition, the distributed lane load was also investigated. The second span has
1
the critical deflection under the uniform applied load, and the deflection is 714 of the span
length with the HS20-44 uniform lane load applied to alternate spans of the girder.
However, the survey indicated that Georgia employs only a single lane loading with their
L
state specific deflection check, and with the single lane loading the bridge passes the 800
deflection limit.
- 65 -
are aligned. This bridge differs from the previous examples in that the cross framing is
welded directly to the girder webs. Full depth girder web cracking has occurred in two
girders directly over interior piers. The cracking occurs at a diaphragm connection, which
are also girder splices. The cracks originate from the weld access hole where the girder
was field spliced.
The standard deflection check was applied. The critical deflection occurred in the
1
center span, and it was 385 of the span length. Ohios reported deflection limit uses a lane
load plus impact loading, and they use AASHTO lane load distribution with multiple lane
loading. This state specific loading was applied based upon the HS20-44 loading. The
1
critical deflection was in the center span and was 264 of the span length.
- 67 -
Figure 5.3. Floorbeam Cracking Due to Relative Twist Between Floorbeam and
Superstructure
The AASHTO deflection limit is normally applied to the main bridge structure, and
this deflection limit is evaluated in Table 5.1. In all cases, the global bridge deflections
satisfied both the standard deflection check and the state specific deflection check. The
above comments show that the connection deformations are caused by local deflections of
stringers and floorbeams. The individual deflections of these elements were always closer
L
to the 800 deflection limit than the global checks, but they usually satisfied the deflection
limit. Therefore, the existing AASHTO deflection limits clearly have no benefit in
controlling this damage type. Nevertheless, this damage is caused by connection rotations
(both torsional and flexural) induced by bridge deflection and deformation. Design
engineers commonly treat these connections as pinned connections. They seldom consider
the consequences of member end rotations on the connection or the adjoining members,
and they typically don't consider the effect of the true connection stiffness on the
performance. The relative stiffnesses of these different elements cause this local
- 68 -
deformation, but there is no clear method for controlling this stiffness differential. A more
detailed description of several individual bridges follows.
- 69 -
The deflection limit is normally applied to the global bridge deflections, but the
analysis indicates that the damage is caused by relative twisting deformation between the
floorbeam and the truss. The floorbeam twist is largely driven by the stringer end
rotations. Therefore a local application of the deflection limits was applied to the
stringers. The stringers failed the standard deflection check with a deflection that was
1
734 of the stringer span length. The stringers satisfied the state specific deflection limit,
because the HS20-44 load was used for this check.
- 70 -
1
assume multiple lanes loaded with equal distribution. The bridge passed the 1000 limit
1
with a maximum deflection that was 2678 of the span length.
The deflection limits were applied locally to the stringers and floorbeams. The
1
maximum L ratio was 1165 for both the standard and state specific checks, because the
uniform lane loading will not provide the controlling deflection with the short spans. This
bridge passes all relevant deflection limits but is sustaining significant damage.
The standard evaluation procedure was applied and the maximum L ratio was
1
2596 . The state specific deflection limit was also applied to check the global deflections
1
of the bridge, and the maximum deflection was 1987 of the span length. As with prior
examples, the deflection limit was applied to the local deflections for the stringers and
- 71 -
floorbeams. The maximum L ratio for this check was 1020 for both the standard and
state specific evaluation.
- 72 -
provided by joints and bearings. A limit on the tensile strain in the concrete deck as a
result of the expected or inadvertent restraint may be effective in preventing this damage.
ft (33.53, 41.76, 41.76, 41.76, and 33.53 m), respectively, and the total bridge width is
44.67 ft (13.62 m) with a roadway width of 42 ft (12.8 m). The diaphragms were aligned
and placed at a skew with respect to the bridge axis. The bridge was designed in 1969 and
it is experiencing transverse deck cracking, but the cracking is less severe than noted in the
prior example.
The bridge passed the standard deflection limit check with a maximum L ratio of
1
865 in the center span. The state specific deflection limit employs a truck plus uniform
lane load plus impact load case with factored loads. This load combination is significantly
1
larger, and the bridge failed the state specific check with a critical L ratio of 483 .
- 74 -
A single girder model was used to check basic girder stiffness. The beam elements
included composite action. The concrete flange for the girder was taken as 20 ft (6.1 m)
and included the concrete used to embed the girder flanges. Longitudinal WT sections
stiffened the bottom flange over the supports, and these were also included in the
calculation of the moment of inertia of the girder. The standard deflection check was
1
applied. The bridge failed the 1000 limit for bridges with pedestrian access with a
1
maximum L ratio of 829 . Nevada reports that they use an HS 20-44 truck plus impact
load case for non-NHS roads and an HS 25-44 truck plus impact load case for NHS roads
with no load factors, multiple lanes loaded, and AASHTO distribution factors. The bridge
also fails this state specific deflection check. The bridge is quite flexible, and this
flexibility causes the bridge damage. However, more detailed analysis shows that the
system behavior of the combined girders in the wide, skew bridge directly causes the
damage.
There was not adequate time or funding to complete a system analysis of this
bridge, but a somewhat more detailed analysis suggests that the damage is caused by
differential deflections and box girder rotations that are caused by the skewed geometry of
the bridge and the wide bridge deck. Skew bridges deform so that some girders are lightly
loaded under these conditions, and the uplift or unloading causes rotation and twist of
some box girders. The box girder cross-section undergoes slight cross-sectional warping
when subject to this twist, but the bracing diaphragms restrain part this warping, because
they are not normal to the girder axis. The large box girder forces caused by the rotation
induce the local stress and strain that cause the web cracking. It is possible that the
- 75 -
omission of the cross-frames would eliminate this damage but this would make
construction of the box girders nearly impossible.
The bridge passed the standard deflection limit with a maximum L ratio of 1756 .
1
The state specific deflection limit was employed, and the maximum deflection was 819 of
the span length. Analysis suggests that this damage is occurring due to differential
deflection of the two trusses. The damage occurs when one truss deflects relative to the
other, because this causes twisting of the bridge cross-section. The rotation and distortion
are resisted by the top laterals and top chord connections, but these are very light. The
torsional deformation places great demands on the pins in the top chord connections, and
the pins and connections ultimately fracture or sustain other damage.
- 76 -
A deflection check that compares the deflection of individual trusses compared the
spacing or distance between trusses may be a relevant method of controlling this bridge
damage. The bridge is relatively narrow compared to its span length, and so even a
modest vertical truss deflection may cause significant torsional distortion.
- 77 -
control this damage, because local deflection and member end rotation in the stringers and
floorbeams are the driving effect. Local deflection checks based upon stringer and
floorbeam deflections are more relevant, but the AASHTO deflection limit does not
prevent this damage even on this local level. Instead, the engineer must recognize the
local rotations and deformations that occur within the structural system and examine their
consequence on adjacent members and connections if this damage is to be avoided.
Deck cracking caused by bridge deflection was identified in a relatively small
number of bridges. Transverse deck cracking occurs in regions of negative bending and
regions with small positive bending moment. The AASHTO deflection limit is at best an
indirect control of this damage, because the deck cracking is not occurring anywhere near
the location of maximum deflection.
Other damage mechanisms were noted, and these were caused by local
deformations and system behavior rather than global bridge deflections. The AASHTO
deflection limit is applied as a line element check, and it is not effective in controlling this
behavior.
standardize application of the AASHTO deflection check. The state specific deflection
checks are much more variable, but 61% of the bridges were found to pass the state
specific check.
This again suggests that existing deflection limits are not effective in
- 78 -
The bridge designs for these damaged bridges frequently had ill-conceived
details that contributed to or caused the problems, and
Engineers
- 79 -
- 80 -
Chapter 6
Evaluation of Existing Plate Girder Bridges
6.1 Introduction
From the survey of Chapter 3 and from meetings with state bridge engineers
affiliated with the AASHTO T-14 Steel Bridge Committee, the investigators obtained
design drawings for 12 typical plate girder bridges, which are summarized in Table 6.1.
These bridges were recently (approximately last 10 years) constructed by 6 different state
transportation departments. The bridges include simply supported and continuous spans,
and they include structures fabricated from HPS 70W and more conventional steels.
Hence, they are a representative cross-section of I shaped steel plate girder bridge designs
typically employed in present practice. Bridges with haunched girders, box-girders, and
very wide deck widths were obtained but were not considered in the present effort.
This chapter evaluates the live-load deflection performance of these
representative bridges against current AASHTO Specifications and examines the impact
of two alternative serviceability criteria on there performance and design. The alternate
serviceablility criteria included the Walker and Wright (Walker and Wright, 1972) procedures and
the Ontario Highway Bridge Design Codes(Ministry of Transportation, 1991) as discussed in
Chapter 2.
81
. The commercial design package SIMON (SIMON SYSTEMS, 1996) was used for
the Load Factor Design Analyses and CONSYS 2000 by Leap Software (CONSYS 2000) was
used to conduct the moving load analyses based on the Ontario specifications for each of
the bridge. For each analysis, both dead loads and section properties were calculated
based on cross section information provided on the plans. Analyses were conducted
assuming composite action throughout. The analyses accounted for all flange thickness
transitions. The maximum deflection for a given span from the software output was then
recorded and compared to respective limits. The natural frequency for both the Walker
and Wright recommendations and the Ontario Highway Bridge Design Code are
computed using Equation 2.5.
82
Table 6.1 Summary of Typical Plate Girder Bridges Analyzed in this Study
Bridge
Bridge
Number
Identification
Jackson County
State
Standard
Comments
Evaluation
Illinois
Pass
Randolph
Illinois
Pass
County
3
Dodge Street
Pass
Snyder South
Nebraska
Pass
Seneca
New York
Pass
US Route 20
New York
Pass
Ushers Rd
New York
Pass
I-502-2-2
83
Berks County
Pennsylvania
Pass
Northampton
Pennsylvania
Pass
County
10
Clear Fork
Fails
11
Martin Creek
Tennessee
Fails
12
Asay Creek
Utah
Pass
84
#2 - Illinois Route 860 over Old Mississippi River Channel in Randolph County
The Route 860 Bridge is a 4-span continuous steel plate girder with 82.25, 129.5 and
82.25 ft (25.07, 39.47, and 25.07 m) span lengths, respectively. It has a 7.5 in (190.5
mm) reinforced concrete deck and 5 Grade 50 (G345W) steel girders spaced at 5.17 ft
(1.57m) on center. It was designed using the 1996 AASHTO LFD Design Specifications
with the 1997 Interim and the design vehicle is HS20-44.
85
86
87
88
L
Ratio
D
The bridges deflections were computed. Figure 6.1 shows the dependence of span
length to deflection ratio,
larger
L
L
ratio, on the ratio selected by the designer It is clear that
D
L
ratios will normally result in larger live-load deflections. Studies (Clingenpeel, 2001,
D
have shown HPS 70W girders may be very economical where depth
restrictions are mandated due to site restrictions or where it may be advantageous to use
reduces superstructure depths to increase clearances and reduce require substructure
requirements. Present AASHTO deflection limits reduce the economic potential of HPS
may in these applications.
2000
12
1800
9
1600
1
1400
1200
L/
1000
3
800
600
11
400
200
0
15
20
25
30
35
L/D
Figure 6.1
L
L
vs for Typical Highway Bridges
D
89
40
L
L
ratio for each of the 12 bridges, the ratio for each bridge, and the
D
L
L
deflection limit. The calculated ratios
800
D
shown in Table 6.2 are based on the full span length of the span in which the maximum
deflection was calculated divided by the total superstructure depth (i.e. bottom flange +
web + haunch + deck thickness. Table 6.2 shows Bridges 10 and 11 (both the Tennessee
structures) fail the AASHTO deflection limits with
L
ratios of 481 and 456. These
L
values of all the bridges in the study, 38.1 and 33.1
D
respectively.
Table 6.2 Comparisons with AASHTO Standard Specifications
L
Bridge
L
L
max
deflection
Identification Actual D max (in.)
800
21.6
0.872
1430
1.559
26.7
1.436
1082
1.943
32.6
3.232
873
3.525
27.1
1.640
1101
2.258
29.5
1.190
1008
1.500
21.7
0.915
1757
2.010
28.6
1.248
1760
2.745
23.9
1.806
1402
3.165
18.5
0.886
1666
1.845
10
38.1
8.729
481
5.250
11
33.1
6.180
456
3.525
12
19.6
0.465
1961
1.140
90
L
values and vibration performance related
L
of 1760 but is found
L
of 481 (far below the allowable AASHTO limit) is found to be
L
of 873 is categorized as
L
of 1430 (considerably above the require
AASHTO limit) has the same vibration sensitivity. While it is not suggested by the
authors that the Walker and Wright criteria is the most valid measure of superstructure
vibration acceptability, these trends indicate that there is no direct relationship between
superstructure deflections and vibration serviceability.
91
Table 6.3. Comparisons with Wright and Walker Alternative Serviceability Criteria
Bridge
Identification max (in.) f (Hz.)
L
max
a in/sec2
Human Response
0.87
3.12
1430
80.68
Unpleasant to few
1.44
2.10
1082
38.38
Perceptable
3.23
1.11
873
64.82
Unpleasant to few
1.64
1.91
1101
52.80
Unpleasant to few
1.19
2.07
1008
36.14
Perceptable
0.92
2.39
1757
18.38
Perceptable to Most
1.25
1.66
1760
16.90
Perceptible to most
1.81
1.53
1402
29.12
Perceptible
0.89
2.93
1666
32.24
Perceptable
10
8.73
0.65
481
21.11
Perceptible
11
6.18
0.69
456
17.79
Perceptible to most
12
0.47
4.75
1961
63.09
Unpleasant to few
L
ratios (21.6 and 19.6, respectively) and larger
D
92
L
ratios (1430 and 1961, respectively, see Table 6.2) than many of the typical bridges in
this study.
Table 6.4. Comparisons with Ontario Highway Bridge Design Code
Bridge
Indentification max (in.) 1
f (Hz.) 2
Criterion Satisfied
1.169
3.12
Without Sidewalks
2.091
2.10
Without Sidewalks
2.909
1.11
2.085
1.91
Without Sidewalks
1.691
2.07
Without Sidewalks
0.959
2.39
1.198
1.66
0.837
1.53
0.913
2.93
Without Sidewalks
10
3.396
0.65
11
4.169
0.69
12
0.576
4.75
Without Sidewalks
It may also be noted that bridges 10 and 11, which were specifically designed
with disregard for the deflection limit (i.e., in both cases the lane load deflections
exceeded
L
, but all other strength and serviceability criteria were met), were found to
800
almost meet the highest level of bridge vibration criteria. Figure 6.2 suggests that there is
not a clear relationship between the
L
and implied user comfort ratings. For example,
L
ratios, but they do not provide the best performance
93
L
and performance rating.
94
documentation is available to relate this to the actual vibration periods of typical bridge
superstructures.
Bridges 10 and 11 exceed the AASHTO deflection limit requirements, but there
have been no reports of rider discomfort or of structural damage. Results of this study
suggest that there is little relationship between a direct limit state check on live-load
deflection and the suitability of a given structure to provide acceptable levels of user
comfort.
95
96
Chapter 7
Parametric Design Study
7.1 Introduction
A design optimization study to evaluate the impact of bridge deflection limits on
the economy and performance of resulting bridge designs was completed. A matrix of
bridges representing a wide range of steel bridge designs and considering key design
parameters such as span length, girder spacing, and cross-section geometry was
developed. Bridges were designed for combinations of these variables based on a least
weight approach using various commercial bridge design software. Initial designs
disregarded AASHTO live-load deflection limits, but met all other relevant AASHTO
strength and serviceability requirements. Initial designs that failed the deflection criteria
were then redesigned such that the live-load deflections were less than
L
.
800
Comparisons were made between the initial girder weight and that of the redesigned
girder to determine additional steel requirements needed for girders to meet the AASHTO
limits. While it is recognized that the least weight design is not always the most
economical or practical design, this comparison provides evidence of the effect of the
deflection limit on bridge economy.
This parameter study also provided information regarding interaction between
various combinations of design variables and current deflection limits. Additionally,
girder designs generated in this parametric study are compared to two alternative
serviceability criteria provided by Wright and Walker (Wright and Walker, 1972) and the Ontario
97
Highway Bridge Design Code (Ministry of Transportation, 1991). These criteria are presented in
Chapter 2.
7.2. Methodolgy
The majority of the design studies used the AASHTO LFD Specifications
(AASHTO, 1996)
, but a subset used the AASHTO LRFD Specifications (AASHTO, 1998). The
LFD bridge designs were completed using a steel bridge design optimization program,
SIMON (SIMON SYSTEMS, 1996), and the LRFD designs were performed using MDX (MDX
software)
. These are commercially available bridge design packages that perform complete
analysis and design for given input parameters. Extensive hand calculations were
performed to verify program output including shear and moment envelopes as well as
respective strength and serviceability limit state calculations. Several iterations were
typically conducted for a given set of design variables for the initial designs generated by
the software in order to develop a more practical design. For example, sometimes it was
necessary to reduce the number of plate thickness transitions or to make minor changes to
plate widths to produce cleaner designs.
To begin a design, a preliminary superstructure depth based on the targeted
L
D
was calculated. Once the preliminary superstructure depth, D, was calculated, the
structural thickness of the deck, the haunch, and the bottom flange was subtracted to
achieve the web depth, h. From this web depth, an initial flange width was selected such
that web depth to compression flange width,
h
, ratio fell in the range of 3.00 to 4.5.
bf
h
ratios resulted from previous research (Barth and White 2000). It
bf
98
was not possible to remain with this range for all designs, and the maximum permitted
variation was between 2 and 5. After a preliminary girder was chosen, the appropriate
noncomposite and composite dead loads were calculated. The preliminary information
was input into the respective design package to obtain an optimized section.
For the simple span designs, a flange thickness transition was included 20% away
from each abutment if a weight savings of 900 lbs or more was achieved. In the negative
moment region of the two-span continuous bridges, a flange thickness transition was
included 15-ft away from the pier if a weight savings of more than 900 lbs was achieved.
The web thickness, tw, was initially based on the thickness required such that no
transverse stiffeners are needed. This initial thickness was then reduced by 1/16-in. to
1/8-in., depending upon the resulting stiffener layout and weight savings. The resulting
web thickness was held constant for full length of a given girder.
The haunch (which includes the top flange thickness) was assumed to be 2 in.
unless section requirements mandated that the top flange thickness be greater than 2 in.
In these cases, the haunch was increased to the thickness of the top flange.
7. 3. Design Parameters
Table 7.1 shows a matrix of design variables that were selected for four
representative bridge cross sections. Figure 7.1 shows each of the four cross sections
selected to investigate the influence of both the number of lanes and the number of
girders.
99
2 Haunch
(typ.)
11-6
11-6
11-6
4-1/4
4-1/4
a. Cross-Section # 1
8 1/2 Slab (Including 1/2 WS)
2 Haunch
(typ.)
9-0
9-0
9-0
9-0
3-3 1/4
3-3 1/4
b. Cross-Section # 2
8 1/2 Slab (Including 1/2 WS)
40-0 (Out-to-Out Deck)
37-6 (Roadway Width)
2 Haunch
(typ.)
10-4
10-4
10-4
4-6
4-6
c. Cross-Section # 3
8 1/2 Slab (Including 1/2 WS)
2 Haunch
(typ.)
8-6
8-6
2-6 1/4
8-6
2-6 1/4
d. Cross-Section # 4
Figure 7.1 Cross-sectional Geometry for 4 Bridge Arrangements
100
Span Length, L
(ft.)
1
2
3
Steel
Strength,
Fy (ksi.)
50, 70
50, 70
50, 70
50, 70
L
Ratio
D
15, 20, 25, 30
15, 20, 25, 30
151, 201, 251, 301
Girder
Spacing,
S
9-0
11-6
10-4
Span
Configuration
Simple, 2-span
Simple, 2-span
Simple, 2-span
8-6
Simple, 2-span
A number of parameters were held constant throughout the study. These include:
HS25 live loading for LFD or HL93 live loading for LRFD,
Parameters that describe the cross-section of the bridge and the members and material
parameters were varied throughout the study as illustrated in Fig. 7.1 and Table 7.1. The
study considered simple and two-span continuous bridges with span lengths ranging from
100 to 300 ft (30.5 to 91.4 m). Four
L
ratios between 15 and 30 were investigated. L
D
was defined as the total span length for simple spans and the length between dead load
101
L
ratios. Bridges
D
were designed with HPS70W and conventional Grade 50W (G345W) steels.
7.4. Results
The combinations of material and geometric parameters described above and
summarized in Table 7.1 and Fig. 7.1 yield an initial set of 272 girder designs. Twenty
nine of these initial 272 LFD designs did not satisfy the AASHTO live-load deflection
limit.
Tables 7.2 through 7.5 present design summary information for initial girder
designs that failed to meet the AASHTO deflection limit. For the LFD designs, two HS25
trucks were placed on the bridge and impact was I=50/(L+125). For the LRFD examples,
an HS20 trucks and IM=1.33 was used. The full width of the deck slab was used to
compute the girder section properties with n=8, and all girders were assumed to carry the
live load equally for analysis in this chapter. For each initial girder design shown in these
tables, the following line (shown in italics) presents information for the redesigned
performed to meet the deflection limit. This table also presents the Walker and Wright
vibration classification for both the initial designs as well as the girder redesigns.
L
of either 15 or 20 satisfied the AASHTO deflection
D
L
ratio is increased to 25 and 30, an increasing number of
D
structures fail to meet the AASHTO limits. This can be illustrated by noting:
102
Table 7.2 Comparison of Initial Girder Designs with Girders Not Meeting the Deflection
Criteria for Cross-section # 1
L
Span
Fy
f b2
Weight1
L
(ft)
(ksi)
(tons)
(Hz)
D
simple spans
100
70
30.4
629
15.0
2.07
100
70
30.0
815
26.5
2.22
200
70
30.1
711
50.0
1.22
200
70
30.0
808
58.9
1.27
300
70
29.6
774
126.0
0.91
300
70
25.3
806
144.7
0.90
Notes:
1
weight is for one steel girder
2
natural frequency computed using Eqn. 6.1
3
parametric based on Wright and Walker (Wright and Walker, 1971)
a3
(in/sec2)
44.680
38.076
26.502
24.714
19.764
18.658
Classification 3
Perceptible
Perceptible
Perceptible
Perceptible
Perceptible to Most
Perceptible to Most
Table 7.3 Comparison of Initial Girder Designs with Girders Not Meeting the Deflection
Criteria for Cross-section # 2
L
fb 2
Weight 1
Span
Fy
L
(Hz)
(tons)
(ft)
(ksi)
D
simple span
100
70
30.1
615
11.0
2.22
100
70
25.1
806
19.7
2.39
200
70
30.1
671
38.0
1.27
200
70
25.0
802
48.9
1.34
300
70
29.9
716
102.0
0.92
300
70
25.6
815
130.6
0.93
100
50
30.3
657
12.0
2.28
100
50
30.1
821
19.5
2.41
200
50
30.0
768
44.0
1.33
200
50
30.0
802
46.2
1.35
2 span continuous
300
70
29.6
774
184.6
0.67
300
70
29.7
801
188.6
0.68
Notes:
1
weight is for one steel girder
2
natural frequency computed using Eqn. 6.1
3
parametric based on Wright and Walker (Wright and Walker, 1971)
103
a3
in/sec2
Classification 3
63.116
53.542
37.229
33.711
27.143
56.838
61.337
53.210
34.821
34.072
Unpleasant to Few
Unpleasant to Few
Perceptible
Perceptible
Perceptible
Perceptible
Unpleasant to Few
Unpleasant to Few
Perceptible
Perceptible
15.863
15.658
Perceptible to Most
Perceptible to Most
Table 7.4 Comparison of Initial Girder Designs with Girders Not Meeting the Deflection
Criteria for Cross-section # 3
Span
Fy
Design
method
(ft)
(ksi)
simple spans
100
50
LFD
100
50
LFD
100
50
LFD
100
50
LFD
100
50
LRFD
100
50
LRFD
100
70
LFD
100
70
LFD
100
70
LRFD
100
70
LRFD
100
70
LFD
100
70
LFD
100
70
LRFD
100
70
LRFD
150
50
LFD
150
50
LFD
150
70
LFD
150
70
LFD
150
70
LFD
150
70
LFD
150
70
LRFD
150
70
LRFD
200
50
LFD
200
50
LFD
200
70
LFD
200
70
LFD
200
70
LFD
200
70
LFD
250
70
LFD
250
70
LFD
250
70
LFD
250
70
LFD
2 span continuous
150
150
150
150
150
150
50
50
50
50
50
50
LFD
LFD
LFD
LFD
LRFD
LRFD
L
D
Weight1
f b2
a3
(tons)
(Hz)
in/sec2
Classification 3
25.3
25.1
30.0
29.7
30.5
30.0
25.1
25.1
25.3
25.1
30.0
29.7
30.5
30.0
30.2
29.5
24.9
24.9
29.8
29.8
29.7
29.5
29.9
29.9
25.0
25.0
30.0
29.9
24.9
25.1
30.0
29.9
726
811
628
808
638
802
734
800
752
864
548
806
582
824
711
817
723
810
567
840
731
819
716
801
729
803
571
801
777
804
578
802
11.42
14.06
14.93
26.25
11.90
15.40
10.86
12.19
8.00
9.00
12.72
25.45
9.50
15.0
26.27
37.52
20.17
23.83
21.10
41.14
16.9
19.2
48.95
65.66
36.82
44.51
37.48
65.66
69.24
74.59
63.34
101.85
2.54
2.64
2.27
2.44
2.10
2.28
2.57
2.66
2.36
2.51
2.19
2.45
2.05
2.35
1.72
1.73
1.77
1.82
1.57
1.70
1.55
1.65
1.38
1.36
1.43
1.44
1.27
1.36
1.21
1.19
1.07
1.13
51.991
49.237
51.036
44.051
44.954
40.206
52.254
50.460
45.052
42.909
55.584
44.374
47.629
40.902
37.430
32.830
38.410
35.687
41.068
32.333
31.307
30.563
31.519
27.585
32.669
30.064
35.003
26.783
27.164
28.831
30.371
26.752
Unpleasant to Few
Perceptible
Unpleasant to Few
Perceptible
Perceptible
Perceptible
Unpleasant to Few
Unpleasant to Few
Perceptible
Perceptible
Unpleasant to Few
Perceptible
Perceptible
Perceptible
Perceptible
Perceptible
Perceptible
Perceptible
Perceptible
Perceptible
Perceptible
Perceptible
Perceptible
Perceptible
Perceptible
Perceptible
Perceptible
Perceptible
Perceptible
Perceptible
Perceptible
Perceptible
24.9
24.9
30.0
30.0
30.1
30.0
765
900
623
845
710
818
56.88
75.39
76.88
111.65
62.3
67.4
1.27
1.29
1.07
1.15
1.01
1.07
22.539
19.580
21.870
17.788
17.755
16.662
Perceptible
Perceptible to Most
Perceptible
Perceptible to Most
Perceptible to Most
Perceptible to Most
104
Fy
Design
method
L
D
f b2
a3
(Hz)
in/sec2
1.34
1.35
1.12
1.16
1.09
1.15
0.96
0.99
0.86
0.92
0.97
1.02
0.84
0.92
0.71
0.75
0.78
0.83
0.66
0.75
25.155
23.144
25.235
18.820
17.893
18.423
18.395
17.376
17.185
13.946
21.013
17.738
21.337
15.466
19.641
12.029
17.699
14.701
17.773
13.127
Weight1
(ft)
(ksi)
(tons)
2 spans Continuous (Cont)
150
70
LFD
24.8
739
43.78
150
70
LFD
24.9
812
54.38
150
70
LFD
30.0
575
55.68
150
70
LFD
30.0
845 111.65
150
70
LRFD
30.0
781
53.6
150
70
LRFD
30.0
816
55.4
200
50
LFD
24.9
728 100.27
200
50
LFD
24.9
805 109.20
200
50
LFD
29.5
669 132.12
200
50
LFD
29.5
905 179.77
200
70
LFD
25.0
647
75.97
200
50
LFD
25.7
822 107.72
200
70
LFD
29.7
522
90.45
200
70
LFD
29.5
816 157.38
250
50
LFD
30.0
720 224.77
250
50
LFD
30.0
804 165.60
250
70
LFD
25.1
630 126.35
250
70
LFD
25.5
827 178.75
250
70
LFD
30.0
498 148.23
250
70
LFD
30.0
804 239.59
Notes:
1
weight is for one steel girder
2
natural frequency computed using Eqn. 6.1
3
parametric based on Wright and Walker (Wright and Walker, 1971)
Classification 3
Perceptible
Perceptible
Perceptible
Perceptible to Most
Perceptible to Most
Perceptible to Most
Perceptible to Most
Perceptible to Most
Perceptible to Most
Perceptible to Most
Perceptible
Perceptible to Most
Perceptible
Perceptible to Most
Perceptible to Most
Perceptible to Most
Perceptible to Most
Perceptible to Most
Perceptible to Most
Perceptible to Most
Table 7.5 Comparison of Initial Girder Designs with Girders Not Meeting the Deflection
Criteria for Cross-section # 4
Span
(ft)
Fy
(ksi)
L
D
Weight
1
fb
(Hz)
(tons)
simple spans
100
70
29.2
743
12.3
2.37
100
70
29.1
802
14.6
2.42
200
70
29.5
732
35.5
1.33
200
70
29.4
801
38.9
1.38
300
70
29.3
781
105.1
0.95
300
70
29.8
812
107.8
0.96
Notes:
1
weight is for one steel girder
2
natural frequency computed using Eqn. 6.1
3
parametric based on Wright and Walker (Wright and Walker, 1971)
105
a3
(in/sec2)
68.844
65.773
43.803
42.268
31.306
30.620
Classification 3
Unpleasant to Few
Unpleasant to Few
Perceptible
Perceptible
Perceptible
Perceptible
L
L
of approximately 25 (i.e.
between 24 and 26), 9.8%
D
D
L
of approximately 30, 45% failed the AASHTO
D
deflection limit.
Simple span girders were found to be more likely to fail the AASHTO
deflection limit than 2-span continuous girders, since 82% of those failing the
AASHTO deflection limit were simple span girders. This may be partially
attributed to the procedure used to establish the
L
ratio for continuous
D
girders.
It is relevant to note that plots of girder weight versus
L
ratio would show the optimum
D
This
L
ratio is also the
D
L
ratios are the most
D
weight to be developed at an
L
of approximately 25.
D
severely affected by the deflection limits. However, these structures are routinely used in
depth restricted applications.
Span length may also be an issue of concern. Simple span bridges with ratios in
the range of 24 and above were evaluated separately, since these are the bridges more
susceptible to failing the AASHTO deflection limit. This comparison shows that:
79% of bridges with a 100 ft (30.5 m) span length failed the AASHTO
deflection limit,
106
40% of bridges with a 200 ft (71 m) span length failed the AASHTO
deflection limit, and
25% of bridges with a 250 ft (76.2 m) or longer span length failed the
AASHTO deflection limit.
Also, the yield strength of the steel was found to have a clear impact upon the deflection
limit. This is illustrated by noting:
75% of the bridges that failed the AASHTO deflection limit were designed of
HPS 70W steel, but
continuous 2 span bridges with grade 50W steel failed the deflection limit
with approximately the same frequencey as HPS 70W steel.
L
limit were re800
performance ratio of the girder and the demand/capacity ratio for all other design criteria.
The performance ratios were larger than 0.985 (but less than 1.0) for all initial designs.
However, these ratios fell as low as 0.887 for the redesigns.
Figure 7.2 shows a plot of the deflections for a 150 ft simple span bridge for cross
section 3 for a range of
L
limits for both 50 and 70 ksi designs. This figure shows values
D
for the LFD studies. Again, this figure shows that no initial girder design with
107
L
of 15
D
L
= 25, the 70 ksi design fails
D
L
= 30 both the 50 and 70 ksi design fails to meet the limits.
D
Figure 7.3 shows a plot of the total girder weight for both the initial and redesigns for the
same example. While the increase in required steel weight at
L
= 25 was negligible, at
D
L
= 30 a substantial increase in steel weight was required for a given girder to meet the
D
deflection limit.
L
for 150 ft/ Simple Span Bridge with Cross-section # 3
D
108
L
for 150 ft/ Simple Span Bridge with Cross-section # 3
D
Again, Tables 7.2 through 7.5 show design summary values for both the original
design failing to meet the AASHTO criteria as well as the associate redesigns. On
average, 36% more steel was required to meet the given deflection limits. This increase
was the highest for the continuous span structures and lowest for the longer span simplespan bridges. Naturally, these numbers may vary based on design input, but it is clear
that substantial cost savings may be possible with the incorporation of alternate
serviceability criteria.
109
unpleasant to few.
Figures 7.4 and 7.5 show plots for the Ontario specifications
1991)
(Ministry of Transporation,
with data points plotted for those girders initially failing to meet the
L
limit for
800
simple and two span continuous bridges respectively. The Ontario Highway Bridge code
limits the static deflection as a function of the first flexural frequency and the intended
use. While the majority of bridges were found to fall within the limits for having
sidewalks and little pedestrian use, all designs were found to fall within the acceptable
range for bridges with no sidewalks.
Figure 7.4. Comparison with OHBD Code for Simple Span Girders Failing the
AASHTO Deflection Limit
110
L
800
Figure 7.5. Comparison with OHBD Code for 2 Span Continuous Girders Failing the
L
AASHTO Deflection Limit
800
L
deflection limit, but
800
only 6 of the LRFD designs exceeded this limit. This is partly due to the design vehicle
used for evaluation of the limits. In LFD, it is specified that the vehicle used to evaluate
strength must also be used to evaluate serviceability; hence, the HS25 truck loading was
used in this evaluation. In LRFD, it is specified that the deflection criteria are to be
evaluated using the design truck only, which is the HS20-44. Also, differences in
resistance equations, distribution factors, and design loadings produce different
111
geometries for LFD and LRFD. Both methods incorporate the same live-load deflection
distribution factor, which is determined by assuming that only any load placed on the
structure after deck placement may be assumed to be carried equally by all girders.
L
ratios, simple span bridges, and bridges
D
designed with HPS70W steel appear to be more seriously influenced by the deflection
limit. However, it should be noted that other superstructure geometries may not be as
dramatically influenced by the existing criteria.
112
Chapter 8
Summary, Conclusions and Recommendations
8.1 Summary
This research has examined the AASHTO live-load deflection limits for steel
bridges. The AASHTO Standard Specification limits live-load deflections to
L
for
800
L
for bridges in urban areas that are subject to pedestrian use.
1000
While these limits are also given in the AASHTO LRFD specifications, they are posed in
the form of an optional serviceability criteria in this document. This limit has not been a
controlling factor in most past bridge designs, but it will play a greater role in the design
of bridges built with new HPS 70W steel. This study documented the role of the
AASHTO live-load deflection limit of steel bridge design, determined whether the limit
has beneficial effects on serviceability and performance, and established whether the
deflection limit was needed. Limited time and funding was provided for this study, but an
ultimate goal was to establish recommendations for new design provisions that would
assure serviceability, good structural performance and economy in design and
construction.
A literature review was completed to establish the origin and justification for the
deflection limits. This review examined numerous papers and reports, and a
comprehensive reference list is provided. A survey of state bridge engineers was
completed to examine how these deflection limits are actually applied in bridge design.
The survey also identified bridges that were candidates for further study on this research
issue. Candidate bridges either:
113
The survey showed wide variation in the application of the deflection limit in the
various states, and so a parameter study was completed to establish the consequences of
this variation on bridge design. The effect of different load patterns, load magnitudes,
deflection limits, bridge span length, bridge continuity, and other factors were examined.
The survey identified a number of bridges which were experiencing structural damage
and reduced service life associated with bridge deflections. Design drawings, inspection
reports, photographs, and other information was collected on these bridges. They were
grouped and analyzed to:
114
L
ratio. The study examined the effect these parameters on the
D
L
ratios where D
D
is the total superstructure depth (i.e. girder depth plus haunch and slab thickness). In
addition, span length based deflection limits (i.e.
L
) are based upon the actual span
800
length and maximum deflection for the specified load for simple span bridges. For
continuous bridges, the span length is the length between inflection points and the
deflection is the chord deflection as illustrated in Fig. 4.1. It is recognized that this span
length and deflection require additional engineering calculation, but it provides a more
consistent serviceability measure between simple span and continuous bridges.
Engineers may choose to use an alternate procedure for continuous bridges where the
total maximum deflection and the total span length are employed.
The alternate
procedure uses a larger span length and a larger deflection, but it is easier to compute.
115
However, it must be recognized that this alternate method will provide a significantly
more restrictive serviceability criteria for many continuous bridges.
8.2.1. Conclusions
Several conclusions are worthy of particular note.
1) The existing AASHTO deflection limit was initially instituted to control bridge
vibration. Deflection control is not a good method for controlling bridge vibration.
Alternate design methods have been developed and are more rational, but there is
variability in these methods. Several practical limitations reduce the full design
effectiveness of the alternate procedures.
2) There is wide variation in the application of the existing deflection limit. This occurs
because of the variation in the actual limits used in evaluation, the variation in the
load magnitude and load pattern used to calculated the deflection, the application of
load factors and lane load distribution factors, and other effects. The difference
between the least restrictive and most restrictive deflection limit may exceed 1,000%.
Live-load deflections do not affect many steel bridge designs, but the huge variation
reported by the various states show that the effect will be much greater in some states
than in others.
3) The load pattern and magnitude have a big impact on the variation noted above.
Some states use truckloads, some use distributed lane loads, and some use
combinations of the above. Truck loads provide the largest deflection for short span
bridges. Distributed lane loads provide the largest deflections for long span bridges.
116
4) Application of the deflection limit with truck load only shows that the existing
AASHTO deflection limits will have a significant economic impact on some steel Igirder bridges built from HPS 70W steel. Simple span bridges are more frequently
affected by this limit than continuous bridges. However, continuous bridges are also
likely to be more frequently affected by existing deflections if the span length, L, is
taken as the true span length rather than the distance between inflection points in the
application of the deflection limit.
5) The AASHTO live-load deflection limit is less likely to influence the design of
bridges with small
sizes as the
L
ratios and is more likely to control the superstructure member
D
L
ratio increases.
D
This
L
live-load deflection limit is a
800
poor means of controlling this deformation. The deformations that cause the damage
are relative deflections between adjacent members, local rotations and deformations,
deformation induced by bridge skew and curvature, and similar concerns. None of
these deformations are checked in the existing live-load deflection evaluation. Bridge
serviceability is an important design consideration, and other methods of assuring
serviceability are needed.
7) Many bridges that satisfy the existing deflection limit are likely to provide poor
vibration performance, and they may experience structural damage due to excessive
deformation. Other bridges, which fail the existing deflection limit, will provide
good comfort characteristics and good serviceability.
117
recommended changes to the AASHTO Specifications. The second type reflects research
or additional study that is required to bring these changes to their full fruition. This
second type of recommendations are provided in Section 8.3.
The live-load deflection requirements of the AASHTO Standard Specifications
require a relatively few words.
should not be included because they have a very detrimental effect on the design of
long span bridges and cause the large variability observed in the application of the
deflection limit. Load factors and lane load distribution factors should not be used,
because the deflection check is a serviceability check. It is recommended that the
span length for the
L
deflection limit be the total span length for simple span
800
bridges and the distance between inflection points (or points of contraflexure) for
continuous bridges. It should be noted that this recommendation is essentially the
118
standard criteria used in Chapters 5, 6 and 7. It will significantly reduce the adverse
effect of the deflection limit on the economy of steel bridge design. However, it will
not completely eliminate this adverse effect. This interim change is desirable because
the existing deflection limit is the primary serviceability criteria in AASHTO
Specifications.
and this study shows that structural damage due to deformation does occur. The
AASHTO live-load deflection limit is not a good serviceability criteria, but at present
sufficient documentation is not available to warrant removal of this limit.
2) As another immediate change, the
L
deflection limit for bridges with pedestrian
1000
access should be removed from the specification. This report is recommending that
the deflection limit be used as an interim serviceability criteria. The sole goal of the
L
deflection limit for bridges with pedestrian access is vibration control. There is
1000
no reason why pedestrian bridges should have more restrictive serviceability criteria
than other bridges.
vibration control. Other better methods of vibration control are presently available,
and these methods can be approximately employed with tools presently available to
the design engineer. Until improved vibration control procedures are developed, the
method proposed by Walker and Wright
recommended. The
(1971)
L
deflection limit is not warranted in view of these factors.
1000
119
control. There are some limitations that must be addressed to completely accomplish
this goal that are discussed in Section 8.3.
4) As a longer-term recommendation, it is recommended that a direct vibration
frequency and amplitude control be inserted into the AASHTO Specifications as a
method of assuring pedestrian and vehicle occupant comfort and structural damage
control. Several tools are needed to fully achieve this goal as discussed in Section
8.3.
120
It is also
unclear how well existing equations approximate the actual frequency with the flange
transitions and member size changes commonly used in bridge design.
3) The structural problems associated with bridge deformation are invariably local
effects. Much of this damage occurred in skewed bridges, and the local effects are
usually attributable to the system behavior resulting from bridge skew. Skew and
curved bridge girders do not behave as the line elements commonly assumed by
bridge engineers. This system behavior needs to be better understood if the damage
observed on these bridges is to be avoided.
121
122
References
AASHTO. (1996). Load Factor Design: Bridge Design Specifications, (16th ed.).
American Association of State Highway and Transportation Officials , Washington,
D. C.
AASHTO. (1996, 1997). Interim Revisions for LFD: Bridge Design Specifications, (1st
ed.). American Association of State Highway and Transportation Officials,
Washington D.C.
AASHTO. (1998). Load Resistance and Factor Design: Bridge Design Specifications,
(2nd ed.). American Association of State Highway and Transportation Officials,
Washington, D. C.
AASHTO. (2000). Interim Revisions for LRFD: Bridge Design Specifications, (2nd ed.).
American Association of State Highway and Transportation Officials , Washington
D.C.
AASHTO (1997, August). Guide Specifications for the Design of Pedestrian Bridges.
American Association of State Highway and Transportation Officials , Washington,
D. C.
AASHTO, (1991). Guide Specifications for Alternate Load Factor Design Procedures
for Steel Beam Bridges Using Braced Compact Sections. American Association of
State Highway and Transportation Officials , Washington, D. C.
Aramraks, T., Gaunt, J. T., Gutzwiller, M. J., & Lee, R. H. (1977). Highway Bridge
Vibration Studies. Transportation Research Record. Transportation Research Board,
645, 15-20.
Aramraks, T. (1975, February). Highway Bridge Vibration Studies. Joint Highway
Research Project (Report No. JHRP 75-2). Purdue University & Indiana State
Highway Commission.
Biggs, J.M., Suer, H.S., and Louw, J.M., (1959). Vibration of Simple Span Highway
Bridges, Transactions, ASCE, Vol. 124, New York.
Billing, J. R. (1979). Estimation of the natural frequencies of continuous multi-span
bridges. Research Report 219, Ontario Ministry of Transportation and
Communications, Research and Development Division, Ontario, Canada.
Cantieni, R., (1983). Dynamic Load Testing of Highway Bridges, Transportation
Research Record 950, Vol. II, TRB, Washington, D.C.
123
Clingenpeel, Beth F. (2001). The economical use of high performance steel in slab-onsteel stringer bridge design. Master Thesis, Department of Civil and Environmental
Engineering, West Virginia University, Morgantown, WV.
CONSYS 2000 USERS MANUAL (1997). LEAP Software, Inc., Tampa, Florida.
CSA (1990). CSA S6- 88 and Commentary. Design of Highway Bridges. Canadian
Standards Association, Rexdale, Ontario, Canada.
Deflection Limitations of a Bridge: Proceedings of the American Society of Civil
Engineers. (1958, May). Journal of the Structural Division, 84, (Rep. No. ST 3).
DeWolf, J. T., Kou, J-W., & Rose, A. T. (1986). Field Study of Vibrations in a
Continuous Bridge. Proceedings of the 3rd International Bridge Conference in
Pittsburgh, PA, 103-109.
Dorka, Ewe, (2001, February). Personal communcation with Charles Roeder. University
of Rostock, Wismar, Germany.
Dunker, K. F., and Rabbat, B.G., (1990). Performance of Highway Bridges, Concrete
Interational: Design and Construction, Vol. 12, No. 8.
Dunker, K.F., and Rabbat, B.G., (1995). Assessing Infrastructure Deficiencies: The Case
of Highway Bridges, ASCE, Journal of Infrastructure Systems, Vol. 1, No. 2.
Dusseau, R. A . (1996). Natural Frequencies of Highway Bridges in the New Madrid
Region (Final Report). Detroit, MI: USGS and Wayne State University Civil
Engineering Department.
Fisher, J.W., (1990). Distortion-Induced Fatigue Cracking in Steel Bridges, NCHRP
Report 336, TRB, National Research Council, Washington, D.C..
FHWA Report. (1998). High Performance Steel Bridges: Tennessee State Route 53
Bridge over Martin Creek, Jackson County (Report RD-98-112).
Foster G. M., & Oehler, L. T. (1954). Vibration and Deflection of Rolled Beam and
Plate Girder Type Bridges (Progress Report No. 219). Michigan State Highway
Department.
Fountain, R. S., & Thunman, C. E. (1987). Deflection Criteria for Steel Highway
Bridges. Proceedings of the AISC National Engineering Conference in New Orleans,
20-1:20-12.
French, C., Eppers, L. J., Le, Q. T., & Hajjar, J. F. (1999). Transverse Cracking in
Bridge Decks. University of Minnesota Department of Civil Engineering.
124
Gaunt, J. T., & Sutton, D. C. (1981). Highway Bridge Vibration Studies (Final Report).
West Lafayette, IN: Purdue University, Indiana State Highway Commission, U. S.
Department of Transportation.
Goldman, D.E. (1948). A Review of Subjective Responses to Vibratory Motion of the
Human Body in the Frequency Range 1 to 70 Cycles per Second. Naval Medical
Research Institute National Naval Medical Center. Bethesda, Maryland.
Goodpasture, D. W., & Goodwin, W. A. (1971). Final Report on the Evaluation of
Bridge Vibration as Related to Bridge Deck Performance. The University of
Tennessee and Tennessee Department of Transportation.
Green, R. (1977). Dynamic Response of Bridge Superstructures - Ontario Observations.
TRRL Supplemental Report SR 275, Crawthorne, England, 40-55.
Haslebacher, C. A. (1980). Engineering: Limits of Tolerable Movements for Steel
Highway Bridges. (Thesis, West Virginia University, 1980).
Horton, R., Power E., Van Ooyen, K., Azizinamini, A. (2000). High performance steel
cost comparison study. Steel bridge design and construction for the new millennium
with emphasis on high performance steel, Conference proceeding, 120-137.
Issa, Mahmoud, A., Yousif, A. A., & Issa, M. A. (2000, August). Effect of Construction
Loads and Vibration on New Concrete Bridge Decks. Journal of Bridge Engineering,
5(3), 249-258.
Issa, Mohsen, A. (1999, May). Investigation of Cracking in Concrete Bridge Decks at
Early Ages. Journal of Bridge Engineering, 4(2), 116-124.
Janeway, R. N. (1948, April).
Automotive Industries.
Kou, J-W. (1989). Continuous Span Highway Bridge Vibrations (Doctoral Dissertation,
The University of Connecticut, 1989). UMI Dissertation Abstracts.
Kou, J-W., & DeWolf J. T. (1997). Vibrational Behavior of Continuous Span Highway
Bridge-Influencing Variables. Journal of Structural Engineering, 123(3), 333-344.
Krauss, P. D., & Rogalla, E. A. (1996). Transverse Cracking in Newly Constructed
Bridge Decks (National Cooperative Highway Research Program Report No. 380).
Washington, DC: Transportation Research Board. National Research Council.
Kropp, P. K. (1977, March). Experimental Study of Dynamic Response of Highway
Bridges. Joint Highway Research Project (Report No. JHRP 77-5). Purdue
University & Indiana State Highway Commission.
125
Leland, A.. (2000, October) Toutle River Tied Arches (Bridge No. 5/140 E & W, Internal
Report, Bridge and Structures Office, WSDOT, Olympia, WA.
MDX Software , (2000) Curved & Straight Steel Bridge Design & Rating for Windows
95/98/NT. 2000 MDX Software, Inc.
Mertz, D. R. (1999). High-Performance Steel Bridge Design Issues. Structural
Engineering of the 21st Century: Proceedings of the 1999 Structures Congress, 749752.
Ministry of Transportation: Quality and Standards Division. (1991). Ontario Highway
Bridge Design Code/Commentary, (3rd ed.). Toronto, Ontario, Canada.
Nevels, J. B., & Hixon, D. C. (1973). A Study to Determine the Causes of Bridge Deck
Deterioration. Research and Development Division. (Final Report). State of
Oklahoma Department of Highways. Oklahoma City, Oklahoma.
Nowak, A. S., & Grouni, H. N. (1988). Serviceability Considerations for Guideways
and Bridges. Canadian Journal of Civil Engineering, 15(4), 534-537.
Nowak, A.S., & Kim, S. (1998, June) Development of a Guide for Evaluation of Existing
Bridges Part I, Project 97-0245 DIR, University of Michigan, Ann Arbor, MI.
Nowak, A.S., Sanli, A.K., Kim, S, Eamon, C., & Eom, J. (1998, June) Development of a
Guide for Evaluation of Existing Bridges Part II, Project 97-0245 DIR, University of
Michigan, Ann Arbor, MI.
Nowak, A.S., Sanli, A.K., & Eom, J. (2000, January) Development of a Guide for
Evaluation of Existing Bridges Phase 2, Project 98-1219 DIR, University of
Michigan, Ann Arbor, MI.
Nowak, A.S., and Saraf, V.K. (1996, October) Load Testing of Bridges, Research Report
UMCEE 96-10, University of Michigan, Ann Arbor, MI.
Oehler, L. T. (1957). Vibration Susceptibilities of Various Highway Bridge Types.
Michigan State Highway Department (Project 55 F-40 No. 272).
Oehler, L. T. (1970, February). Bridge Vibration Summary of Questionnaire to State
Highway Departments. Highway Research Circular. Highway Research Board (No.
107).
PCA (1970). Durability of Concrete Bridge Decks: A Cooperative Study, Final Report,
Portland Cement Association (PCA), Skokie, IL.
126
Poppe, J. B. (1981). Factors Affecting the Durability of Concrete Bridge Decks (Final
Report SD-81/2). Sacramento, CA: California Department of Transportation;
Division of Transportation Facilities Design.
Roeder, C.W., MacRae, G.A., Arima, K., Crocker, P.N., and Wong, S.D. (1998) Fatigue
Cracting of Riveted Steel Tied Arch and Truss Bridges, Report WA-RD447.1,
WSDOT, Olympia, WA 1998.
Schultz, A. (2001) Report in progress at the University of Minnesota, Minneapolis, MN.
Shahabadi, A. (1977, September). Bridge Vibration Studies. Joint Highway Research
Project (Report No. JHRP 77-17). Purdue University & Indiana State Highway
Commission.
SIMON SYSTEMS USER MANUAL, Version 8.1 (1996). The National Steel Bridge
Alliance, AISC, Chicago, Illinois.
Walker, W. H., & Wright, R. N. (1971, November). Criteria for the Deflection of Steel
Bridges. Bulletin for the American Iron and Steel Institute, No. 19.
Walker, W. H., & Wright, R. N. (1972). Vibration and Deflection of Steel Bridges.
AISC Engineering Journal, 20-31.
Walpole, W. (2001, March). Personal communcation with Charles Roeder. University of
Canterbury, New Zealand.
Wilson. E.H., and Habibullah. (2001). "Integrated Structural Design and Analysis",
Computers and Structures, Inc., Berkeley, CA.
Wright, D. T. & Green, R. (1964, May). Highway Bridge Vibrations. Part II: Report
No. 5. Ontario Test Programme. Ontario Department of Highways and Queen's
University. Kingston, Ontario.
Wright, D. T., & Green, R. (1959, February). Human Sensitivity to Vibration (Report
No.7). Ontario Department of Highways and Queen's University. Kingston, Ontario.
127
128
Appendix A
Sample Survey
and
Summarized State by State Results
129
L
?
800
2. For steel girder-concrete deck bridges, what loads do you use for application of
this deflection limit?
a) Load magnitude?
Lane Live Load Only?
Including Impact?
Without Impact?
Factored Loads?
Unfactored Loads?
Other? Explain_______________________________________________
b) Lane application?
Single Lane Only?
S
? Explain ______________
5.5
130
Yes?
No?
No?
No?
131
7. Does your state have any steel bridge which have experienced structural damage
(excessive deck cracking, cracking of steel or etc) due to excessive deflection or
vibration?
Yes?
No?
If so, please identify the bridges with the most severe damage and note the type of
damage observed on these bridges?______________________________________
________________________________________________________________________
______
If so, please identify an engineer (and phone number if possible) who can be contacted
for more detailed information on that bridge?_____________________
__________________________________________________________________
(Contact this person and complete the more detailed information sheet for specific
bridges after the statements have been evaluated)
8. Does your state have any steel bridge which have objectionable deflection or
vibration? (deformations that do not cause structural damage but that are
objectionable to drivers or pedestrians)
Yes?
No?
If so, please identify the bridges with the most severe response and note the response
observed on these bridges?_____________________________________
________________________________________________________________________
______
If so, please identify an engineer (and phone number if possible) who can be contacted
for more detailed information on that bridge?_____________________
_________________________________________________________________
(Contact this person and complete the more detailed information sheet for specific
bridges after the statements have been evaluated)
9. Does your state have any steel bridge which did not satisfy your state deflection
limit but that appear to provide satisfactory performance?
Yes?
No?
132
________________________________________________________________________
______
If so, please identify an engineer (and phone number if possible) who can be contacted
for more detailed information on that bridge?_____________________
__________________________________________________________________
(Contact this person and complete the more detailed information sheet for specific
bridges after the statements have been evaluated)
133
whether the stiffness of curbs, railings and sidewalks were included in the
calculation.
Individual answers to these individual questions varied widely, but the total effects of the
different state responses were often quite similar. This occurred because different states
compensated for the various issues at different steps in their evaluation process. The last
column of Table A.1 summarizes the consensus of the final effect regarding this issue
rather than the individual answers to specific questions.
134
State
Lane Application
Alabama
L / 1000
L / 800
loose AASHTO
HS 20 44 Truck
No
Alaska
L / 1000
L / 800
loose AASHTO
HS 20 Truck + I
No
Evaluated as a system
Arizona
L / 1000
L / 800
AASHTO
No
Arkansas
L / 1000
L / 800
AASHTO
HS 20 Truck + I or
Lane; whichever
governs
Truck + Lane + I
Yes
California
L / 800
L / 800
Truck + Lane + I
No
Colorado
L / 1000
L / 800
non-composite beams
or girders are D/S >
0.04 and composite
girders are D/S > 0.045
for simple and 0.04 for
continuous
strict AASHTO
Truck + Lane + I
No
Connecticut
L / 1000
L / 800
No
Truck + Lane + I
No
Delaware
L / 1000
L / 800
AASHTO
HS 25 Truck + I
before, now HL 93
Truck + I;
No
135
Florida
L / 1000
L / 800
Truck + I
No
Georgia
L / 1000
L / 800
AASHTO
Lane + I or Truck
+ I or Military
Load + I;
whichever governs
No
Truck + I
No
Hawaii
Idaho
Effectively system
analysis with equal
distribution
Effectively system
analysis with equal
distribution
Illinois
L / 1000
L / 800
No
Lane + I or Truck
+ I; whichever
governs
No
Indiana
Iowa
L / 1000
L / 800
No
Truck + Lane + I
No
Evaluated as a single
girder with lane load
distribution
Kansas
L / 1000
L / 800
No
Truck + I
No
Kentucky
L / 1000
L / 800
AASHTO
HS 20 Truck +
Lane + I
No
Effectively system
analysis with equal
distribution
Start with girder analysis
but move to system
analysis but use lane load
distribution
Louisiana
L / 1000
L / 800
strict AASHTO
Truck + Lane + I
No
Evaluated as a single
girder with lane load
distribution
Maine
L / 1000
L / 800
strict AASHTO
HS 20 Truck +
Lane + I
No
Evaluated as a single
girder with lane load
distribution
136
Maryland
L / 1000
L / 800
AASHTO
HS 25 Truck or
Lane; whichever
governs
(respondent did not
know if impact was
included)
Truck + Lane + I
No
Evaluated as a single
girder with lane load
distribution
Massachusetts
L / 1000
strict AASHTO
Michigan
L / 1000
L / 800 as an
upper limit but
L / 1000 is
preferred
L / 800
No
Evaluated as a single
girder with lane load
distribution
HS 25 Truck + I
No
Minnesota
L / 1200
L / 1000
AASHTO as a
preliminary
Truck + I
No
Mississippi
L / 1000
L / 800
AASHTO
Missouri
L / 1000
L / 800
AASHTO
Truck + Lane + I
No
Evaluated as a single
girder with lane load
distribution
Montana
L / 1000
L / 1000
loose AASHTO
Truck + Lane
Yes
Nebraska
L / 1000
L / 800
AASHTO
Lane + I or HS 25
Truck + I;
whichever governs
No
Effectively system
analysis with equal
distribution
137
Effectively system
analysis with equal
distribution
Truck + I or Lane
No
Start with single girder
+ I or Military + I; Response and advance to system
whichever governs
analysis if needed but
with lane load distribution
Nevada
L / 1000
L / 800
AASHTO
HS 20 Truck + I
for non-NHS roads
and HS 25 Truck +
I for NHS Roads
New Hampshire
New Jersey
L / 1000
L / 1000
No
New Mexico
L / 1000
New York
L / 1000
recommended
North Carolina
L / 1000
North Dakota
L / 1000
L / 800
AASHTO
Truck + Lane + I
Ohio
L / 800
L / 800
ratio of 10 to 20
Lane + I
Oklahoma
L / 1000
L / 800
AASHTO
Truck + Lane + I
Oregon
L / 800
L / 800
AAHSTO
Truck + I
No
Evaluated as a single
girder with lane load
distribution
HL 93 Truck + I
No
Evaluated as system with
and a Permit
lane distribution factors
Vehicle
L / 800
AASHTO
No set policy, up to No set
Evaluated as a single
design engineer policy, up
girder with lane load
to design
distribution
engineer
L / 800
AASHTO as a guideline Truck + I or Lane
No
Effectively system
recommended
+ I; whichever
analysis with equal
governs
distribution
L / 800
AASHTO
Truck + Lane + I
No
Evaluated as a single
recommended
girder with lane load
distribution
138
No
Effectively system
analysis with equal
distribution
No
Evaluated as single girder
Response
with lane distribution
factors
Yes
Evaluated as a single
girder with lane load
distribution
No
Pennsylvania
L / 1000
L / 800
strict AASHTO
Truck + I
No
Rhode Island
L / 1100
L / 1100
30 to 1
Truck + Lane + I
Yes
South Carolina
L / 1000
L / 800
AASHTO
Yes
Evaluated as a single
girder with lane load
distribution
South Dakota
L / 1200
L / 1000
No
Evaluated as a single
girder with lane load
distribution
Tennessee
L / 1000
recommended
L / 800
recommended
AASHTO
HS 20 44 Truck + I
No
Texas
L / 1000
L / 800
Truck + I or Lane
+I
No
Effectively system
analysis with equal
distribution
Evaluated as a single
girder with lane load
distribution
Utah
L / 1000
L / 800
AASHTO
Truck or Lane
Vermont
L / 1000
L / 1000
AASHTO
HS 25 Truck + I
Virginia
L / 1000
L / 800
strict AASHTO
Truck + Lane + I
No
Washington
L / 1000
L / 800
HS 25 Truck + or
Lane +I
No
Equal distribution
139
Effectively system
analysis with equal
distribution
Evaluated as a single
girder with lane load
distribution
No
Evaluated as single girder
Response
with lane distribution
factors
No
Evaluated as a single
girder with lane load
distribution
West Virginia
L / 1000
L / 800
No limit.
HS 25 Truck + or
Lane +I
No
Wisconsin
L / 1600
L / 1600
HS 25 Truck + I
No
Wyoming
L / 1000
L / 800
Truck + Lane + I
Yes
140
Equal distribution
including all stiffness
contributing elements
such as curbs and railings
Evaluated as system with
lane distribution factors
Start with single girder
and advance to system
analysis if needed but
with lane load distribution