Performance Based Seismic Assessment of
Performance Based Seismic Assessment of
Performance Based Seismic Assessment of
- Review Report –
1st Draft
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Table of contents
1 Introduction 4
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6 Bibliography 53
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1 INTRODUCTION
The need to assure a satisfactory behaviour under seismic action of old buildings
designed prior appearance of engineering rules or according to poor seismic
provisions, have become an important task of the civil engineering community. In the
light of recent knowledge regarding seismic motion and structural behaviour many of
existing buildings are obviously substandard and deficient. Older hazardous
buildings are responsible for the thousands of life loss and significant damage. The
existing substandard buildings perhaps are outnumbering the safe building.
Therefore the attention in earthquake engineering should be focus more on existing
buildings than on new ones, in order to provide advanced methodologies for building
assessment. After disastrous hazard event the engineering community silent consent
to upgrade existing buildings at the safety of level new buildings, according to the
limit state procedure provide by standards. The implications of this concept were not
at all rational, first from the technical point of view and second the cost and length of
time. So, a new approach has arisen based on multi-level evaluation together with
differentiate targets [21].
Modern Design Recommendations, like SEAOC's Vision 2000 project and BSSC's
NEHRP Guidelines for Seismic Rehabilitation of Buildings have developed a new
concept in building evaluation and design by introducing design performance
objectives, acceptance criteria tied to performance level, and the use of alternative
analytical techniques for performance evaluation. The proposed 1997 NEHRP
Provisions for Seismic Regulation of Buildings and Other Structures also make an
important contribution, by attempting for the first time to define the margin of safety
inherent in buildings conforming to these provisions, and in the sense of Ultimate
Limits States design philosophy, by directly incorporating this presumed margin in
the definition of the loading function [25].
Key areas of development, required to provide true performance-based capability
in future design and evaluation provisions include the incorporation of a specific
serviceability level performance procedure, verification of the reliability actually
inherent in buildings of different structural systems conforming to the provisions and
the development and refinement of new analytical evaluation (acceptability)
procedures capable of predicting building performance with reduced uncertainty [25].
Retrofitting of all the vulnerable buildings before the next big earthquake is also not a
realistic solution. The highest priority should be on identifying the buildings which
have a high possibility of collapse and identifying those which can ensure life safety
despite being substandard. Seismic rehabilitation of large stocks of buildings
requires engineering approaches different from the traditional approaches of civil
engineering. Methodologies to evaluate the seismic risk of high urbanized area are
emphasis. In last year’s have made important steps in development of quick
methods to establish buildings vulnerability, assess seismic fragility [21].
The Figure 1 presents the relation between Evaluation, Design and Construction
within Conceptual framework of Performance Based Seismic Retrofit (PBSR). It is
important to underline the iterative design process in order to achieve or respect the
desire performance level. In every phase of the rehabilitation process acceptability
criteria plays the decisional role, from the initial evaluation, to design process and
quality assurance of the erection process.
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Evaluation
Performance evaluation
of existing building
Design
Preliminary design
Evaluation of potential
strenghtening solutions
(via conceptual design) NO
NO Acceptability of
preliminay design
(retrofitted building
Acceptability criteria evaluation)
YES
YES Construction
Final design
Selected technique Design review
(preliminary level)
NO
Acceptability of
preliminay design Quality assurance
(detailing impact on YES
fabrication and erection
* Adapted from SEAOC Vision 2000 technology, cost)
Commitee (1995). Performance - based Building maintenance
seismic engineering of building. Report. and function
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Table 1) from strategy, to the concept and detail of the building retrofit work (ATC-
40).
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• Architectural changes
• Voluntary upgrade
Select qualified professionals • Structural Engineer
• Architect
Establish performance objectives • Structural Stability, Limited Safety, Life
Safety, Damage Control, Immediate
Occupancy
Review building conditions • Review Drawings
• Visual Inspection
• Preliminary Calculation
Formulate a strategy • Simplified Procedures
• Inelastic Capacity Methods
• Complex Analyses
Begin the approval process • Building Official
CONCEPT
• Review
Conduct detailed Investigations • Site Analysis
• Material Properties
• Construction Details
Characterize seismic capacity • Modeling Rules
• Force and Displacement
Determinate seismic demand • Seismic Hazard
• Interdependence with Capacity
• Target Displacement
Verify performance • Global Response Limits
• Component Acceptability
• Conceptual Approval
Prepare construction documents • Similarity to New Construction
DETAIL
• Plan Check
• Form of Construction Contract
Monitor construction quality • Submittals, Tests and Inspection
• Verification of Existing Conditions
• Construction Observation by Designer
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A PSBA procedure supposes the collaboration of all the involved parts with a specific
implication in different phase of the process (see Figure 2).
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the functions occurring within the building, economic considerations including costs
related to building damage repair and business interruption, and consideration of the
potential importance of the building as a historical or cultural resource.
Rehabilitation objective
The building owner, in consultation with the designer, shall select a seismic
Rehabilitation Objective but never bellow the code official provision. The selection of
a Rehabilitation Objective shall consist of the selection of a target Building
Performance Level, which intended to represent goals of structural behaviours, from
a range of performance levels and on the selection of an anticipated Earthquake
Hazard Level from a range of seismic hazards [18].
Difficulties in establish performance could be associated with unknown geometry and
member sizes in existing buildings, deterioration of materials, incomplete site data,
variation of ground motion that can occur within a small area, and incomplete
knowledge and simplifications related to modeling and analysis.
Building performance should be described qualitatively in terms of the safety
afforded building occupants during and after the earthquake; the cost and feasibility
of restoring the building to pre-earthquake condition; the length of time the building is
removed from service to effect repairs and economic, architectural or historic
impacts on the larger community.
Different national’s codes establish various Rehabilitation Objectives. These
Standards treated more or less the same issues and establish Objectives that can be
summarizes according to FEMA 356 [18] as:
• Basic Safety Objective (BSO)
• Enhanced Rehabilitation Objectives (BSE-1, BSE-2)
• Limited Rehabilitation Objectives
o Reduced Rehabilitation Objective
o Partial Rehabilitation Objective
Basic Safety Objective (BSO) is intended to approximate the earthquake risk to life
safety traditionally considered. Buildings meeting the BSO are expected to
experience little damage from relatively frequent, moderate earthquakes, but
significantly more damage and potential economic loss from the most severe and
infrequent earthquakes that could affect them. The level of damage and potential
economic loss experienced by buildings rehabilitated to the BSO may be greater
than that expected in properly designed [18].
Enhanced Rehabilitation Objectives (BSE-1, BSE-2) can be obtained by
designing for higher target Building Performance Levels (method 1), at important
building and facilities, or by designing using higher Earthquake Hazard Levels
(method 2), in case of vital building and facilities, or any combination of these two
methods.
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Seismic hazard due to ground shaking shall be based on the location of the building
with respect to causative faults, the regional and site-specific geologic
characteristics, and a selected Earthquake Hazard Level [18].
Seismic hazard due to ground shaking shall be defined as acceleration response
spectra or acceleration time-histories on either a probabilistic or deterministic basis.
The analysis and evaluation procedures of FEMA 356 are primarily aimed at
improving performance of buildings under loads and deformations imposed by
seismic shaking. However, other seismic hazards could exist at the building site that
could damage the building regardless of its ability to resist ground shaking. This
standard requires hazards due to earthquake shaking to be defined on either a
probabilistic or deterministic basis [18].
Probabilistic hazards are defined in terms of the probability that more severe
demands will be experienced (probability of exceedance) in a 50 year period (see
Table 2) [18].
Deterministic demands are defined within a level of confidence in terms of a specific
magnitude event on a particular major active fault [18].
FEMA 356 defines two basic Earthquake Hazard Levels [18]:
• Basic Safety Earthquake 1 (BSE-1);
• Basic Safety Earthquake 2 (BSE-2).
In addition to the BSE-1 and BSE-2 Earthquake Hazard Levels, Rehabilitation
Objectives may be formed considering ground shaking due to Earthquake Hazard
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In Table 2 are given the medium recurrence interval for frequent, occasional, rare
and very rare according to FEMA 356 356 [18], SEAOC [42], EC8 [16] (only suggest
value for the return period) and P100-3/2003 [35].
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however, for economic reasons this may not be practical. While the damaged
structure is not an imminent collapse risk, it would be prudent to implement structural
repairs or install temporary bracing prior to reoccupancy [18].
Structural Performance, Limited Safety (S-4), shall be defined as the continuous
range of damage states between the Life Safety Structural Performance Level (S-3)
and the Collapse Prevention Structural Performance Level (S-5) [18].
Structural Performance Level Collapse Prevention (S-5), means the post-
earthquake damage state in which the building is on the verge of partial or total
collapse. Substantial damage to the structure has occurred, potentially including
significant degradation in the stiffness and strength of the lateral-force resisting
system, large permanent lateral deformation of the structure, and — to a more
limited extent — degradation in vertical-load-carrying capacity. However, all
significant components of the gravity load-resisting system must continue to carry
their gravity load demands. Significant risk of injury due to falling hazards from
structural debris may exist. The structure may not be technically practical to repair
and is not safe for reoccupancy, as aftershock activity could induce collapse [18].
A building rehabilitation that does not address the performance of the structure shall
be classified as Structural Performance Not Considered (S-6) [18].
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For all this Building Performance Levels referred in standards are associate Damage
Control levels regarding to structural typology and bearing elements.
The following table (see Table 5) presents a qualitative general overview of the
damage, valid for all types of structures, elements and materials, structural and non-
structural [18]:
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Occasional O Performance
Rare O
Very Rare O
Basic Facilities; O Essential/Hazardous Emergency Response Facilities; Safety Critical Facilities
Figure 7. SEAOC Vision 2000 Performance Objective [42]
It is presented an example according to FEMA 356 356 [18] (see Table 8). Having a
non seismic residential reinforced concrete frame, a Basic Safety Objective has been
established by the owner together with the designer. To accomplish this
Performance Objective, using Table 6, are determinate two needed checks situation
k + p. This mean that at a rare earthquake (10%/50 year) the building performance
level should be in Life Safety range and for a very rare earthquake the building
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In first situation Life Safety have been chose Life Safety Level for structural and
nonstructural elements. In second situation Collapse Prevention have been chose
Collapse Prevention Level for structural and Hazards Reduced Level for
nonstructural elements in order to avoid large or heavy items that pose a high risk of
falling hazard to a large number of people — such as parapets, cladding panels,
heavy plaster ceilings are prevented from falling [18].
Frecvent
SEISMIC Occasional
HAZARD Rare
Very rare
SELECTION OF SELECTION OF
STRUCTURAL NONSTRUCTURAL
PERFORMANCE PERFORMANCE
LEVEL LEVEL
Figure 8 Selection of seismic hazard and performance levels for structural and
nonstructural members
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3.1 Introduction
The most important effect of earthquakes on building structures is the inertia forces
produced in the building due to ground shaking. Being a rare event, structures are
usually designed to resist earthquake action in the inelastic range of response. Most
of the existing structures were not designed for seismic action at all, and are
therefore expected to respond beyond the elastic limit under a major earthquake.
The dynamic nature of earthquake action, which has components along the two
horizontal directions as well as the vertical one, and the possible inelastic structural
response, implies a nonlinear dynamic analysis procedure on a three-dimensional
model of the building structure. Though this type of analysis provides the most
"exact" modelling of structural response under earthquake action, it requires a high
degree of expertise, and can be very time-consuming. In many cases it possible to
adopt more simple analysis procedures. The simplifications may involve the model of
the structure (two plane models instead of a three-dimensional one), time-history
response (static analysis instead of dynamic one), and inelastic structural response
(linear elastic analysis instead of nonlinear analysis) [44].
There are five generally adopted analysis procedures used for seismic analysis of
structures (FEMA 356 356, 2000 [18]; Eurocode 8-1, 2003 [15]) presented bellow in
a hierarchical order:
• lateral force method (linear static procedure);
• response spectrum analysis;
• linear time-history analysis;
• nonlinear static procedure (pushover analysis);
• nonlinear time-history analysis.
The linear procedures maintain the traditional use of a linear stress-strain
relationship, but incorporate adjustments to overall building deformations and
material acceptance criteria to permit better consideration of the probable nonlinear
characteristics of seismic response. The Nonlinear Static Procedure, often called
“pushover analysis,” uses simplified nonlinear techniques to estimate seismic
structural deformations. The Nonlinear Dynamic Procedure, commonly known as
nonlinear time history analysis, requires considerable judgment and experience to
perform [44].
The acceptance criteria for the various performance objectives are prescribed for
each of the analytical procedures and numerical values of the acceptance criteria for
various structural and nonstructural systems are provided in standards.
Guidance on the global model of the structure and criteria for selection of analysis
procedure are available in seismic design codes (FEMA 356 356, 2000[18];
Eurocode 8-1, 2003 [15]; Eurocode 8-3, 2003 [16]). A synthesis of their requirements
is presented hereafter.
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response, their stiffness should be based on the secant stiffness to yield force.
Special attention should be addressed to joints between structural elements, which
need explicit modelling when their stiffness differ significantly from the fully rigid or
pinned assumptions, or when their strength is lower than the one of connected
elements [44].
Horizontal torsion
Horizontal torsion of floor diaphragms is generated by the eccentricity between the
centre of mass and the centre of stiffness. It is not needed to be considered in
structures with flexible floor diaphragms. Beside the actual eccentricity, an accidental
eccentricity of about 5% of building horizontal dimension measured perpendicular to
the direction of lateral load is required by seismic design codes. The accidental
eccentricity is intended to account for uncertainties in the distribution of stiffness and
mass, as well as for the rotational components of the ground motion [44].
A three-dimensional model of the structure accounts directly for torsion due to
eccentricity between the centre’s of mass and stiffness, and need an explicit
consideration of accidental eccentricity only. Effects of torsion can be considered
only approximately in the case of planar structural models. Therefore, planar models
are restricted to structures regular in plan, when the effect o torsion is reduced [44].
Diaphragms
It is generally preferred that floor diaphragms be rigid in their plane. Rigid
diaphragms provide a connection between lateral force resisting systems and the
gravity load resisting systems within a building, and enable for the different lateral
load resisting systems in the building to contribute to the global lateral resistance of
the structure. When horizontal diaphragms can be considered rigid in their plane, the
masses and mass moment of inertia of each floor can be lumped in the centre of
mass of the diaphragm. Structures with rigid diaphragms should account for the
effect of torsion when determining seismic demands in individual lateral force
resisting systems [44].
When diaphragms cannot be considered rigid, structural models should account
explicitly for the in-plane stiffness of the floor diaphragms. Alternatively, for very
flexible diaphragms, lateral force resisting systems can be modelled independently,
with seismic masses determined on the basis of tributary area [44].
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FEMA 356 356 [18] classifies a floor diaphragm as rigid when the maximum
horizontal deformation of the diaphragm along its length is more than twice the
average interstorey drift of the vertical lateral force resisting elements of the storey
immediately below the diaphragm. Accordingly, a floor diaphragm is classified as
rigid when the maximum horizontal deformation of the diaphragm is less than half
the average interstorey drift of the vertical lateral force resisting elements of the
storey immediately below the diaphragm. Floor diaphragms that do not fit into the
above two categories are classified as stiff [44].
According to Eurocode 8-1 [15], a diaphragm can be considered as being rigid, if,
when it is modelled with its actual in-plane flexibility, its horizontal displacements
nowhere exceed those resulting from the rigid diaphragm assumption by more than
10% of the corresponding absolute horizontal displacements in the seismic design
situation [44].
It is proposed to apply acceptance criteria for horizontal diaphragms also. Because
of unknown assessment of performance levels in case of this type of elements and in
order that horizontal diaphragms to be able to perform they role to take and distribute
the horizontal loads to the lateral resisting system, vertical elements, this elements
must be designed to behave in elastic range at the desire building performance level.
With other words, horizontal diaphragm must have a higher capacity than lateral
resisting elements.
Second-order effects
When a structure is very flexible under lateral loads, a first-order analysis may
underestimate substantially forces and deformation. A second-order analysis is
necessary in this case. When a non-linear analysis is used, second-order effects
should be considered directly in the formulation of force-deformation relationships for
all elements subjected to axial forces [44].
When a linear analysis procedure is used, second order effects can be considered
Pδ
by evaluating the stability coefficient θi = i i , where Pi is the total gravity loading
Vi hi
acting at and above storey i in the seismic design situation; Vi is total seismic storey
shear; δi is the interstorey drift at storey i, and hi is the height of storey i. Second
order effects can be neglected when θi ≤ 0.1 in all stories. When the stability
coefficient is between 0.1 and 0.3, second order effects can be considered
approximately by multiplying forces and deformations by in storey i by 1/ (1 − θi ) .
When the stability coefficient is larger than 0.3, the structure is considered unstable,
and measures should be taken to increase the lateral stiffness of the structure [44].
Displacement analysis
If the structure responds mainly in the elastic range under the design seismic action,
lateral displacements can be estimated reliably based on a linear analysis (static or
dynamic). However, if the structure is expected to experience significant yielding
under the design seismic action, lateral deformations can be significantly larger than
the ones estimated based on a linear analysis. The effects that can contribute to
inelastic deformations larger than the elastic ones are: (1) frequency content of the
ground motion, in relation to the fundamental period of vibration of the building, (2)
duration of the ground motion, (3) hysteretic load deformation characteristics of
structural elements, including strength and stiffness degradation [44].
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These effects are accounted directly by a nonlinear dynamic analysis. In the case of
linear analysis procedures, the possibility of inelastic deformation being larger than
the elastic ones can be considered only approximately, by using amplification
coefficients. This strategy is adopted by FEMA 356 356 [18], Eurocode 8-1 [15]
displacement analysis for linear analysis is based on the "equal displacement" rule,
neglecting the effects of frequency content and duration of ground motion, as well as
hysteretic characteristics of the structural elements [44].
Soil-structure interaction
The most important effect of soil-structure interaction is the elongation of period of
vibration of the structure due to flexibility of the foundation-soil interface. Soil-
structure interaction affects mainly rigid structures located on soft soils. It needs to
be considered when the increased period of vibration of the building increases
spectral accelerations [44].
Figure 9 Component Force versus Deformation Curves (FEMA 356 356) [18]
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point 2. Primary and secondary component actions exhibiting this type of behaviour
shall be classified as deformation-controlled if the plastic range is such that e > 2g;
otherwise, they shall be classified as force controlled [18].
The Type 3 curve depicted in Figure 9 is representative of a brittle or nonductile
behaviour where there is an elastic range (point 0 to point 1 on the curve) followed
by loss of strength and loss of ability to support gravity loads beyond point 1. Primary
and secondary component actions displaying Type 3 behaviour shall be classified as
–controlled [18].
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The lateral force method is based on the assumption that seismic response of the
structure is governed by the fundamental mode of vibration. First the base shear
force is determined based on the total mass of the structure, response spectrum
ordinate corresponding to the fundamental period of vibration, and (eventually)
correction coefficients accounting for higher-mode effects, frequency content of the
ground motion and hysteretic characteristics of structural elements. In a second step,
the base shear force is distributed along the height of the structure, according to the
assumed or computed fundamental period of vibration of the structure [44].
In the case of assessment of existing structure (FEMA 356, [18]; Eurocode 8-3, [16]),
the lateral forces are determined based on the elastic response spectrum, and not
on the design one (reduced by the behaviour factor q). This procedure intends to
estimate the design lateral displacements of the structure rather than the design
forces in structural elements, because displacements are better indicator of damage
to the structure in the inelastic range than forces. If the building responds essentially
in the elastic range, the forces estimated using the lateral force method will
approximate reasonable those expected during the seismic event. However, if the
building responds in the inelastic range, actual internal forces that would develop in
the building will be lower than the ones estimated using the lateral force method [44].
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4.1.1 Reversibility
Reversibility is a basic requirement for any type of intervention. Reversible in general
is what can be removed without harming the existing structure. However, it is
generally recognized that full reversibility can never be obtained. A typical example
are holes that are driven in existing elements for placing fasteners, anchors or ties,
which will remain, even if the connection elements are removed. Accordingly, the
use of fasteners is partially a reversible technique, since the fasteners can be
removed, but the holes not without additional measures. Consequently, reference
should be made preferably to the degree of reversibility [47].
Examples for high reversible techniques are [47]:
• Interventions that do not cut walls, but take place below foundation level.
• Use of un-bonded mechanical fasteners
• Use of pre-stress with external tendons, hoops etc.
• Use of additional elements that are mechanically connected to the existing
structure
Examples of low reversible techniques are [47]:
• Use of welding or other monolithic connection
• Use of additional elements that are bonded with the existing structure (FRP’s,
internal tendons etc.)
• Encasing in concrete
4.1.2 Compatibility
4.1.2.1 Material
It is evidently not always possible to find or produce exactly the same materials as
the authentic ones for restorations in historical buildings and monuments. Examples
are old mortars, bricks or metals that cannot be exactly reproduced. Very often,
failures in buildings after restorations are due to lack of knowledge of materials and
construction details that cause a wrong choice of the repair technique and the poor
application of it. Examples are given below [47].
Grout injection in old masonry: Such injections shall fill voids and cracks, as well as
the gaps between two parts of the walls, in order to increase the continuity and
therefore the strength. For that reason, the materials constituting the walls, the crack
distribution, as well as the size, percentage and distribution of voids must be well
documented. Grouts shall be chemically and physically compatible with the existing
material. Walls with low void rations (<4%) or internal fillings with loose materials are
difficult to be injected [47].
FRP composites: Research results and in-situ applications have shown that FRP
composites can be effectively and efficiently used for repair and upgrade of historical
structures. However, this application of FRP composites presents some critical
issues still not sufficiently investigated, like physical and chemical compatibility of the
FRP system with the parent material, which is a key issue for both short- and long-
term performance of the upgraded structure [47].
For the above reasons, the debate on optimal material selection is being opened on
whether inorganic materials could represent a better alternative to organic polymers
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4.1.2.2 Structural
Compatibility problems may arise not only at material, but also at structural level. In
case that the intervention creates stiffness or strength discontinuities, local failures
may result in [47].
Examples are given below.
Wall jacketing: Mesh reinforcement is placed at both sides of the walls and concrete
is injected or grouted subsequently. Incompatibilities may arise from the following: i)
lack of connection between meshes in transverse walls and the floors, ii) insufficient
overlapping between meshes, iii) insufficient transverse connectors between the
mesh and the wall, as well as the two sides of the wall, iv) non-uniform distribution of
the repaired areas over the building. The above incompatibilities result in
discontinuities in the repaired structures that may cause damage after a future
earthquake [47].
Concrete ring beams: They are placed in floors and the roof in order to improve the
diaphragm action. Such ring beams are easier to apply in roofs, after possible
removal of the old roof, but difficult to install in floors due to the fact that the wall
must be partly demolished. For that reason, ring beams do not extend over the
whole width of the wall with the consequence that the walls are eccentrically loaded
and not well tied with the floor beams [47].
The above indicate that any of the aforementioned issues requires an
interdisciplinary effort [47].
In particular, researchers with material-oriented and structural-oriented backgrounds
need to strictly interact with each other for a full understanding of the problems.
While a material knowledge is essential to deal with the topics of durability at the
material level, physical and chemical compatibility, reversibility and optimal selection
of materials, the structural expertise is needed to focus on the macro-scale
behaviour of the strengthened member and structure, and to understand the
structural implications of different material behaviours and micro-scale phenomena.
Moreover, when dealing with historical structures, a third expertise on architectural
restoration will contribute on the issue on minimal invasiveness and reversibility [47].
4.1.3 Durability
Durability is a key issue to all interventions [47]. Examples are given below.
Metals: Metals are subjected to different degrees of corrosion. Lead, aluminium,
stainless steel, or galvanized steel are less prone to corrosion [47].
Timber: The durability of timber is affected by humidity. Best protection is given when
humidity levels are kept constant, or when the material is treated by appropriate
impregnations [47].
Rubber: Rubber is subjected to aging, especially when exhibited to UV-radiation.
FRP composites: This global issue involves durability of FRP and parent material
(concrete, masonry, wood or metal) as stand-alone materials, durability of their
mutual interface, and possibly durability of the devices used for implementation of
the strengthening technology (e.g. anchors, post-tensioning devices, etc.). The
interaction of all these factors affects the durability and structural behaviour of the
upgraded structure as a whole [47].
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4.2.3 Installation/Erection
The design has to consider the way on how to apply for the specific object the
proposed method of intervention. Intermediate states and construction phases have
to be taken into account. The availability of any lifting equipment, if required, has to
be regarded [47].
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freedom (SDOF) system. Inelastic spectra or elastic spectra with equivalent damping
and period are applied. As an alternative representation of inelastic spectrum the
Yield Point Spectrum has been proposed (Aschheim and Black). Some other
simplified procedures based on deformation-controlled design have been developed,
e.g. the approaches developed by Priestley and by Panagiotakos and Fardis.
The essential difference is related to the determination of the displacement demand
(target displacement). If an equivalent elastic spectrum is used, displacement
demand is determined based on equivalent stiffness and equivalent damping, that
depend on the target displacement and, consequently, iteration is needed. The
quantitative values of equivalent damping, suggested by different authors, differ
considerably. On the other side, for the methods using inelastic spectra, bilinear
idealization of the pushover curve is required. If the bilinear idealization depends on
the displacement demand, then the computational procedure becomes iterative,
also. The procedures differ also in the assumed lateral load pattern, used in
pushover analysis, and in the displacement shape, used for the transformation from
the MDOF to the SDOF system (and vice versa). Only if the two vectors are related,
i.e. if the lateral load pattern is determined from the assumed displacement shape,
the transformation from the MDOF to the SDOF system is based on a mathematical
derivation [48].
Related to the organization of evaluation procedure or design of the retrofitted
structure some criteria can be notice [20]:
o Role of the displacement in the design process
o Deformation – calculation based (DCB)
o Iterative deformation – specification based (IDSB)
o Direct deformation – specification based (DDSB)
o Type of analysis used in the design process
o Response spectra – initial stiffness based
o Response spectra – secant stiffness based
o Time history analysis based
o Structural type limitations
o Limit-state or performance objectives limitations
The following matrix (see Table 10) presents a visual representation of various
design procedures, combining the first two criteria.
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The former requires distribution of the floor load to members according to their
rigidities. Evaluation of the building is performed by means of a seismic index, Is,
determined by a ratio between the total allowable lateral load and the probable
lateral seismic load demand, given by
V
I s = all (5)
V
This evaluation is generally performed for ground floor only for savings in time and
labour. In case it is performed for each floor, the most critical index is assigned for
the building. A significant advantage of approximate structural evaluation
methodologies, other than considerable time savings compared to detailed analysis
methods, is the ability to perform a first level prioritization, based on the level of
lateral load resistance, for a detailed analysis or retrofit application [34].
Detailed evaluation through linear analysis methods is the most commonly used
approach since most seismic codes (e.g. [45], [28]) require use of these methods.
Based on detailed structural information, member forces under design loads are
determined and compared with their ultimate strength. With this methodology, it is
possible to accurately determine the overstressed members under design loads;
however, it is difficult to assess the seismic risk of the building at the system level.
Thus, although this method is useful in prioritizing deficient structures, it may not
yield sufficient information needed for determining the optimum retrofit strategies.
The current trend is to use the nonlinear analysis techniques, which require
approximately the same amount of data, but more engineering effort and expertise
compared to the approaches based on linear analysis techniques [34].
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
Detailed evaluation using nonlinear analysis provides the most accurate and reliable
risk assessment, loss estimation, and retrofit optimization practices at the expense of
detailed site, structural, and material information, longer computation times, and a
higher level of technical expertise. The linear analysis methodology described above
is an integral part of this methodology. By considering the nonlinear inelastic
behaviour of structural members under increasing loads, this methodology can
predict the nonlinear behaviour of the structural system much more realistically
compared to linear analysis techniques [34].
Determining the nonlinear structural behaviour allows for performance-based design,
which results in significant savings in seismic retrofit applications ([4], [18]). Figure
14(a) shows the typical roof displacement vs. base shear curve obtained from
nonlinear pushover analysis of buildings. Using this curve alone, one can perform a
preliminary evaluation of the structure’s seismic safety by comparing its capacity with
the seismic demand determined using the equivalent static load method described in
seismic codes. A better performance evaluation can be performed by converting
both the capacity curve and the seismic demand spectrum to the acceleration-
displacement response spectrum (ADRS) format formed as a relationship of spectral
displacement vs. spectral acceleration as shown in Figure 14b. A further improved
evaluation can be achieved by obtaining a reduced inelastic response spectrum for
the seismic demand to consider the increased damping due to inelastic deformations
in the building [4].
The intersection of the capacity and demand curves shown in Figure 14 is called the
performance point of the building. Based on the location of this performance point,
performance level of the building is determined. The intervals of spectral
displacement that correspond to different performance levels are also shown in
Figure 14. The limits of the performance levels are determined by certain interstory
drift values. If the performance point is located in the initial portion of the capacity
curve where the inelastic deformations are not significant, which corresponds to
interstory drift values less than 0.01, the performance level of the building is
immediate occupancy, which is self explanatory.
For interstory drift values between 0.01-0.02, the limits of which are immediate
occupancy and life safety levels, respectively, the performance level of the building is
damage control. In this region, inelastic deformations are expected in the building
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
that poses no significant threat to the stability of the building and the safety of its
occupants. Between the life safety and structural stability levels, the building
performance level is described as limited safety. Large inelastic deformations are
expected which may result in excessive cracking and failure of some structural
members, which may pose threat to occupants or result in local failures. Beyond the
structural stability level, the collapse of the building is imminent. From this
discussion, it is apparent that nonlinear analysis is a very convenient methodology
for development of realistic fragility curves [34].
Figure 15 Structural vulnerability and damage states for various level of seismic
demand [34]
Figure 15(a) shows the damage states of a building based on the applied base
shear, which can be determined as a function of the seismic demand. The roof
displacement – base shear curve, also called the capacity curve, shown in this figure
represents the nonlinear behaviour of a building under increasing load or
displacement demand. The damage state of the building varies between none to
collapse under increasing levels of demand, which is graphically illustrated in Figure
15(a). A relatively more convenient representation of the damage states is provided
in Figure 15(b) by overlaying both building capacity and seismic demand curves on a
different set of axes showing spectral displacement vs. spectral acceleration. Two
different capacity and seismic demand curves are shown in the figure. Intersection of
the capacity and demand curves represents the damage state likely to be
experienced by the structure. As can be seen from the figure, the strong structure is
likely to suffer from light to moderate damage due to the low seismic demand, and
moderate to extensive damage due to the high seismic demand. On the other hand,
the weak structure is expected to suffer from moderate to extensive damage due to
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
low seismic demand, and collapse during the high seismic demand due to
insufficient seismic resistance [34].
Methods of vulnerability analysis vary based on the exposure information and the
complexity of the approach. Vulnerability of structures to ground motion effects is
often expressed in terms of fragility curves or damage functions that take into
account the uncertainties in the seismic demand and capacity. Fragility functions can
be developed for buildings or its components depending on how detailed the risk
analysis is performed. Early forms of fragility curves were developed as a function of
qualitative ground motion intensities largely based on expert opinion. Recent
developments in nonlinear structural analysis have enabled development of fragility
curves as a function of spectral parameters quantitatively related to the magnitude of
ground motion. Figure 16(a) shows the typical seismic demand and structural
capacity curves together with their uncertainties expressed in terms of probabilistic
distributions. Based on these curves and the associated uncertainties, the fragility
curves shown in Figure 16(b) can be constructed for various damage states. Since
each damage level is associated with a repair/replacement cost, the probabilistic
estimates of the total cost can be estimated using these curves once the hazard is
known. This can be achieved by use of predefined representative fragility curves
developed for structures in the same class, or custom damage curves developed
through nonlinear analysis of individual structures [34].
Construction of the fragility or damage curves is the key element in estimating the
probability of various damage states in buildings or building components as a
function of the magnitude of a seismic event. Thus, development of realistic fragility
curves for the building stock and lifelines in a seismic region constitutes an essential
part of a meaningful seismic risk analysis [34].
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
5.3 Examples
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
Figure 18 Preliminary Design of RC structure endowed with metal shear panel [13]
Based on the evaluation of the damage state of the initial structure as determined by
the examination of the capacity curve, the designer may easily determine the
spectral displacement levels corresponding to the performance levels. For the
examined structures such spectral displacements, corresponding to the Immediate
Occupancy (IO), Life Safety (LS) and Structural Stability (SS) performance levels,
are indicated in Figure 18.
For the sake of example, the performance point occurs for this structure at a spectral
displacement of about 5 cm, resulting in a Structural Stability (SS) performance level.
Since the structure has to be retrofitted, let us assume that the “Life Safety” is set by
the designer sets as a performance objective for the building. According to the
procedure and based on the “equal displacements” simplifying assumption, the initial
stiffness for the retrofitted structure is defined starting from the knowledge of the
corresponding period, leading to the following relationship:
2
T
K r = Ki i (6)
Tr
Where Ki and Ti are the stiffness and the period of the initial structure, respectively,
and Kr is the stiffness required for the retrofitted one. Therefore, considering that the
retrofitted structure will be able to provide at least the same level of damping of the
initial structure, the “desired performance point” is defined and the required ultimate
base shear capacity for the retrofitted structure can be obtained by the following
equation:
S
Vr = a r Vi (7)
S ai
where Vi is the ultimate base shear capacity of the initial structure, Vr is the required
ultimate shear capacity of the retrofitted structure, Sai and Sar are the ultimate
spectral acceleration for the unretrofitted and retrofitted structures, respectively.
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
Therefore, once Vr and Kr have been determined, the contribution provided by shear
panels in terms of both strength and stiffness can be achieved through the following
relationships:
K p = K r − Ki (8)
V p = Vr − Vi (9)
Once the required stiffness and strength of shear panels have been determined, it is
possible to develop a preliminary design for selecting the panel geometry. However,
it should be emphasized, that while the presented approach is suitably accurate to
lead to a preliminary design solution, it is extremely important that the actual demand
and capacity spectra for the retrofitted structure are formally computed as part of the
final design process.
Evaluation of the bare RC structure [13]
In this example, according to the results of the performed preliminary test the
performance point of the bare RC structure subjected to horizontal forces applied in
longitudinal direction to the first storey only has to be evaluated. To this purpose the
pushover curve of the structure must be converted into the capacity spectrum one
(Figure 19).
According to the seismic classification provided by the new seismic Italian code [2],
the structure under study is located in a second category seismic zone,
characterized by peak ground acceleration equal to 0.25 g. Besides, sub-soil
conditions type B can be assumed. In Figure 20, the design elastic response
spectrum is plotted in the Sa-Sd plane, considering the spectral acceleration
reduction obtained by accounting for different damping ratios (β). As a first step, by
the comparison with the capacity curve of the examined structure, the performance
point can be estimated by means of the equal displacement approximation method,
which provides ai = 0.128 g and di = 0.072 m.
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
Then, the effect of a damping modification factor κ can be accounted for, it being
equal to 0.33 according to the ATC-40 provisions for existing structures
characterized by poor dissipative capacity.
Therefore, based on two iteration procedures only, a performance point
characterized by ai = 0.130 g, di = 6.4 cm and βeq = 37% can be determined. Such
performance values are not compatible with the base structure, whose plastic hinges
fail at a displacement of 5.6 cm. Therefore, a seismic retrofitting intervention is
necessary.
In order to evaluate the initial stiffness of the retrofitted structure, the target design
displacement of the first level of the RC structure at collapse (LS) has been fixed
equal to 2.5 cm, corresponding to an inter-storey drift (∆/H) of about 1%. By applying
Equation (1) a stiffness Kr = 15.53 kNmm-1 is obtained, corresponding to a stiffness
contribution provided by shear panels Kp = 11.5 kNmm-1.
By assuming a viscous damping coefficient for the bare RC structure equal to 20%,
the global shear strength of the structure has been determined as Vr = 275.10 kN,
leading to a required shear panel strength Vp = 192 kN.
Finally, the capacity curve of the reinforced structure may be represented in the
spectral acceleration – spectral displacement (ADRS) plane, as shown in Figure 21.
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
plates characterized by a b/t ratio less than 80 should behave as compact shear
panels. Being the minimum panel dimension (namely the distance between
succeeding stiffeners) equal to 400 mm, a plate thickness of 5 mm ensures the
satisfaction of the above requirement.
The selected panels have been installed in a reaction steel frame composed by
UPN180 members with an intermediate UPN240 beam and positioned on both sides
of the structure at the first floor. At this aim the reinforcing of both the RC beam and
the foundation beam has been carried out by means of UPN220 profiles and M16
threaded bars. A global view of the adopted system is illustrated in Figure 22.
a) b)
Figure 22 Global view of the structure retrofitted by means of steel (a) and aluminium
(b) shear panels [13]
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
7. Repeat steps 2 - 6 for each performance level using the actual stiffness ratios
of the selected shear walls. Revise the design if drift limits are exceeded at
any performance levels.
8. Compute design base shear, story shear and uplift force using the actual
nonlinear backbone curves of shear walls.
Figure 23 Global view of the structure retrofitted by means of steel (a) and aluminium
(b) shear panels [37]
3.0 [m] B B B B
B B B B
3.0 [m]
A B C D E D C B A
A B C D E D C B A
]
3.0 [m] A B B A [m
6
3.
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
6.0
Acceleration Se(T) [m/s2]
5.0
4.0
3.0
2.0
1.0
0.0
0 1 2 3 4
Period T [s]
Performance assessment
• Moment resisting frame (MRF) [43]
Analysis of the original MRF showed an unsatisfactory seismic response. First
plastic hinge appears in the column. Plastic mechanism involves mostly columns
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
from the first and second floors (Figure 26 a), but also some beams from the first
storey. Lateral drifts at the ultimate limit state also indicate concentration of damage
in first two storeys (Figure 28). Ultimate rotations in plastic hinges corresponding to
collapse prevention limit state are first reached in columns (Figure 18). It can be
observed the structure has a limited global ductility, because columns attain collapse
prevention limits state at a top displacement roughly four times smaller than the top
displacement demand due to design earthquake action. Fundamental period of
vibration and target displacements at the ultimate limit state for the original
reinforced concrete frame and several alternative strengthening solutions are
presented in Table 11.
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
Strengthening of the reinforced concrete frame by means of BRB only did not
eliminated failure of reinforced concrete members. Therefore, a consolidation by
both FRP and BRB systems was considered.
a) MRF
b) MRF+BRB(q=6) c)MRF+FRP
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
Pushover Curves
MRF+FRP+BRB(q=3)
250
200
150
MRF+BRB
..
MRF+FRP
100
MRF
50
0
0 0.1 0.2 0.3 0.4
BRB-CP Beam-CP Top Displacement
Column-CP [m]
N2-Target Displacement
3
Story number
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
a) b)
Figure 29 Strengthening solutions proposed in frame of FP6 PROHITECH
For the experimental tests was chosen a 25x1500x1500 mm masonry panel in order
represent an entire wall or a critical pier zone between openings. The Figure 30
shows the way to determinate the characteristic strength of the tested shear wall Rk .
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
SSP_PT_1
500.00
400.00
FORCE [kN]
300.00
200.00
100.00
0.00
-1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00
DISPLACEMENTS [mm]
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
6 BIBLIOGRAPHY
[1] Albanesi T., Nuti C., Vanzi I. – A simplified procedure to assess the seismic
response of nonlinear structures, Earthquake Spectra 16(4), 2000
[2] Arzhang Alimoradi, Performance Performance-Based Seismic Design
Application of New Developments, West Tennessee Structural Engineers
Meeting, May 27, 2004
[3] Aschheim M.A., Black E.F. – Yield point spectra for seismic design and
rehabilitation, Earthquake Spectra, vol.16, no.2, 2000
[4] ATC 40 – Seismic evaluation and retrofit of concrete buildings – volume 1,
November 1996
[5] ATC, Development of Performance-based Earthquake Design Guidelines,
ATC-58, Redwood City, 2002.
[6] Browning J.P. – Proportioning of Earthquake-Resistant RC Building
Structures, Journal of the structural division AISC, vol. 127, no.2, 2001
[7] Buyukozturk O., Gunes O., Karaca E. – Advances in Earthquake Risk
Assessment and Hazard Reduction for Large Inventory of Structures with
High Characteristic Variability, MIT - IST – Infrastructure Science and
Technology Group – Department of Civil and Environmental Engineering
[8] CEB Fastenings for Seismic Retrofitting - State-of-the-art Report (Bulletin 226
part 2, Telford, London, 1996)
[9] Chopra A.K., Goel R.K. – Capacity Demand Diagram Methods based on
Inelastic design spectrum, Earthquake Spectra 15(4), 1999
[10] Chopra A.K., Goel R.K. – Direct-displacement based design: Use of inelastic
vs. elastic design spectra, Earthquake Spectra, vol.17 no.1, 2001
[11] Chopra, A.K. "Estimating seismic demands for performance-based
engineering of buildings". 13th World Conf. on Earthquake Engineering,
Vancouver, B.C., Canada. Paper no. 5007, 2004
[12] Coburn A.W., Spence R.J.S. and Pomonis A. – Vulnerability Risk
Assessment, DMTP of UNDP, Cambridge 1994
[13] De Matteis G., Formisano A., Mazzolani F.M. - SEISMIC RETROFITTING
METHODOLOGY OF EXISTING RC BUILDINGS BASED ON METAL
SHEAR PANELS, Earthquake Engineering and Structural Dynamics (in print)
[14] Earthquake Engineering Research Centre, Performance-based Seismic
Design of Buildings: An Action Plan, U.C., Berkeley, 1995.
[15] Eurocode 8-1/2003 "Eurocode 8: Design of structures for earthquake
resistance. Part 1: General rules, seismic actions and rules for buildings".
CEN - European Committee for Standardization.
[16] Eurocode 8-3/2003. "Eurocode 8: Design of structures for earthquake
resistance. Part 3: Strengthening and repair of buildings". CEN - European
Committee for Standardization.
[17] Fajfar P. – A nonlinear analysis method for performance-based seismic
design, Earthquake Spectra, vol. 16, no. 3, 2000
[18] FEMA 356, Guidelines for Seismic Rehabilitation of Buildings, Vol. 1:
Guidelines, FEMA 356, Washington DC, 2002 (formerly FEMA 273).
[19] FEMA 356/EERI, Action Plan for Performance-Based Seismic Design, FEMA
349, Washington DC, 2000.
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
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Performance based seismic assessment of buildings for evaluation of retrofitting systems efficiency
List of figures
List of tables
[49]
[50]
[51]
[52]
[53]
Table 1 Phases in PBSA process [4]
Table 2 Earthquake hazard level
Table 3 Building performance level
Table 4 Target Building Performance Levels and Ranges [18]
Table 5 Damage Control and Building Performance Levels [18]
Table 6 Rehabilitation Objectives (FEMA 356) [18]
Table 7 Rehabilitation Objectives (P100-3) [35]
Table 8 Performance Objective accomplish
Table 9 Data Collection Requirements (FEMA 356) [18]
Table 10 Matrix of design procedures [20]
Table 11 Fundamental period of vibration and target displacements for the considered structures
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