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Al-Nahrain Journal for Engineering Sciences NJES24(1)52-75, 2021
https://doi.org/10.29194/NJES.24010052
NJES is an open access Journal with ISSN 2521-9154 and eISSN 2521-9162
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
52
Seismic Evaluation and Retrofitting of an Existing Buildings-State of
the Art
Haider Ali Abass 1, Husain Khalaf Jarallah 2*
1. Introduction
Buildings are usually designed for seismic
resistance using elastic analysis, most of which
experiences significant inelastic deformations under
large seismic events. Modern performance-based
design methods require ways to define the real
behavior of structures under such conditions. Non-
linear analysis can show an important role in the
design of new and existing buildings [1]. This review
will effort on recent contributions associated with
seismic evaluation and past attempts most closely
associated with the seismic evaluation and
retrofitting of an existing building. With the
improvement of computational techniques, more
difficult methods of seismic evaluation have been
recommended. Analytical methods can be carried
out in absence of past earthquake damage records
for a like type of buildings. It is also used to evaluate
an individual building or type of buildings that has
the same structural characteristics. Based on those
facts, analytical approaches have been used to
evaluate the seismic resistance of existing buildings.
The Capacity Spectrum Method (CSM), A method
for capturing the performance point provides a
graphical statement of the structure's global force-
displacement capacity curve and compares it to the
response spectra representation of the demands of
earthquakes. The inelastic capacity of a building is
then calculating of its capability to scatter earthquake
energy [2]. The Displacement Coefficient Method
Author’s affiliations:
1) Dept. of Civil Eng., Mustansiriyah
University, Baghdad-Iraq.
hiaderaabass@uomustansiriyah.edu.iq
2*) Dept. of Civil Eng., Mustansiriyah
University, Baghdad-Iraq.
khalfdce@uomustansiriyah.edu.iq
Paper History:
Received: 3rd Oct. 2020
Revised: 26th Jan. 2021
Accepted: 31st March 2021
Abstract
In this study, previous researches were reviewed in relation to the
seismic evaluation and retrofitting of an existing building. In recent years, a
considerable number of researches has been undertaken to determine the
performance of buildings during the seismic events. Performance based
seismic design is a modern approach to earthquake resistant design of
reinforcement concrete buildings. Performance based design of building
structures requires rigorous non-linear static analysis. In general, nonlinear
static analysis or pushover analysis was conducted as an efficient instrument
for performance-based design. Pushover analysis came into practice after
1970 year. During the seismic event, a nonlinear static analysis or pushover
analysis is used to analyze building under gravity loads and monotonically
increasing lateral forces. These building were evaluated until a target
displacement reached. Pushover analysis provides a better understanding of
buildings seismic performance, also it traces the progression of damage and
failure of structural components of buildings.
Keywords: Seismic Evaluation, Pushover Analysis, Seismic Retrofitting,
Performance Based Design.
Pushover Test
Pushover Test ,
Pushover Test
Pushover Test
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53
(DCM) affords a direct numerical process for
calculating the displacement demand. It is based on
changing the linear elastic response of the SDOF
system by developing it by chains of the coefficients
to the nonlinear inelastic response of the MDOF
system [3]. The outlines of this study included a
review and discussion of the seismic assessment
codes, a review of previous studies related to the
pushover analysis, procedures for torsional effects,
and a discussion of better ways to retrofit the
existing buildings. The aim of this study is to
indicate that the pushover method is an effective
tool for evaluating and rehabilitation the existing
building.
2. Methodology for Performance
Evaluation
2.1 Structural damage parameters
The choice of appropriate damage parameters is
very important for performance evaluation. Overall
lateral deflection, inter-story drift and plastic hinge
rotation are the most usually used damage
parameters. Overall defection is not always a good
indicator of damage, but the inter-Story drift is quite
helpful because it is typical of the damage to the
lateral load resisting system. Also, the maximum
values of a member or joint rotations, curvature, and
ductility factors are good guides of damage because
they can be directly associated with the element
deformation capacities. However, the maximum
value alone of any of these parameters may not be
sufficient to measure the overall damage caused by a
cyclic reversal of deformation. Damage indicates
which take into account both the maximum
deformation and cyclic effects have been grown for
such cases. Both indices can be used to calculate the
overall damage state of a structure [4].
2.2 Displacement based damage parameters
The vulnerability of many existing structures may
be the reason for structural weaknesses and low
ductility. Common weaknesses in the structural
system are due to lake in the load-path, strength and
stiffness discontinuities, (vertical, horizontal, and
mass) irregularities, weak column and strong beam,
and eccentricities. Low ductility detailing is
considered as insufficient shear reinforcement,
inadequate confinement, and lacking anchorage
length of the beam-reinforcement bars [5].
Commonly used displacement-based damage
parameters are lateral drift or roof displacement;
inter story drift, member or joints rotations,
curvature and ductility factors, etc. Lateral drift and
inter-Story drift are very commonly used parameters
and are part of the direct output of performance
level. Inter-story drift or Inter-Story drift ratio
(IDR), defined as the comparative translational
displacement between two consecutive floors
divided by the story height is an important
engineering response amount and indicator of
structural performance. It shows an important role
in determining the level of damage to columns
during lateral deformation. Inter-story drift can also
be used as a calculate of non-structural damage.
Although the maximum values of the displacement-
based damage parameters offer a good measure of
damage, it does not account for the damage caused
by a cyclic reversal of deformation that happens
during earthquakes. Various energy-based damage
parameters are available [6].
2.3 Review of Displacement based damage
parameters
Biddah et al. [7] found that the inter-story drift
does not account for accumulative damage because
of repeated inelastic deformation. Also, the
relationship between damage and inter-story drift
different relying on the maximum deformation at
collapse which depends on the ductility category of
the structure.
Ghobarah [8] found that the inter-story drift is
associated with different damage levels of different
reinforced concrete components. Two main groups
of drift limits were defined for ductile and non-
ductile structural systems. In ductile structural
system case, the relationship between the roof drift
and the maximum inter-story drift is linear with a
45° slope. For existing non-ductile structures and
poorly designed frames, the maximum inter-story
drift of the soft story may show collapse while the
roof drift will equal to a lower damage level.
Erduran and Yakut. [9] observed that the most
important parameters affecting the damageability of
RC columns are the yield strength of longitudinal
reinforcement, the slenderness of the column and
level of confinement.
2.4 Energy-based damage parameters
2.4.1 Energy dissipation by a structure
It is necessary to assess accurately the cyclic
behavior of structural members which is illustrated
by three primary ingredients: strength, deformability,
and energy dissipation capacity (per load cycle).
Commonly, reinforced concrete members show
compound cyclic behavior with stiffness
degradation. Therefore, the evaluation of the seismic
performance of RC members is usually restricted to
strength and deformability [10]. The estimation of
energy dissipation capacity depends on empirical
equations that are not sufficiently precise. Energy
dissipation can be defined by the sum of the energy
dissipated by concrete and reinforcing steel eq. (1).
concrene steel ….. (1)
Where = the dissipated energy during cyclic
loading,concrene ,steel = the energy dissipated by
concrete and reinforcing steel, respectively.
Concrete is a brittle material composed of aggregates
and matrix. Therefore, if cyclic loading is repeated at
a specific displacement, concrete dissipates
considerably less energy than reinforcing steel
exhibiting plastic behavior does, For the reason, the
overall dissipated energy of the member is equivalent
to the sum of the energy dissipated by flexural rebars
arranged in the member.
….. (2)
Energy dissipation capacity relies on various
parameters such as reinforcement ratio, an
arrangement of reinforcing bars, and the shape and
size of the members’ cross-sections. Thus, such
empirical methods cannot accurately estimate the
energy dissipation capacity, and as a result, they
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decrease the overall accuracy of the evaluation
method [11, 12]. The energy input to the structure
subjected to earthquake ground motion is dissipated
in part by inelastic deformation (hysteretic energy)
and in part by viscous damping. Only hysteretic
energy is assumed to participate in structural
damage. The hysteretic to input energy ratio is an
important response parameter that shows the range
of damage in the structure. Fajfar, et al. [13]
introduced a dimensionless parameter, which
represents the relationship between hysteretic energy
and the maximum displacement. This is an
important energy-based damage indicator.
….. (3)
where EH is the dissipated hysteretic energy, D is the
maximum displacement, m is the mass of the system
and ω is natural frequency. The parameter also
controls the decrease of displacement ductility due
to low cycle fatigue.
2.4.2 Review of Energy-based damage
parameters
Manfredi [14] noted that the definition of
damage is possible, based on the assumption that the
structural collapse occurs when the hysteretic energy
dissipated under seismic actions is equal to the
energy disputed under monotonic load. The
estimation of the input energy appears a first
towards the definition of damage potential capable
of taking into account the effect of the duration of
the ground motions.
Park and Eom [15] found that the concrete
which is a brittle material does not dissipate energy
significantly through repeated cyclic loading. So, the
energy dissipation of the reinforced concrete
member is almost similar to the energy dissipated by
flexural re-bars arranged in the member. It can be
determined by the number of re-bars and the
differential stains that the re-bars practice during
cyclic loading.
Negulescu and Wijesundara [16] found that
no important effects of the number of inelastic
cycles to the damage estimation results for low
ductile structures. It focuses on the importance of
accounting for the effects of the number of inelastic
cycles to the damage assessment for the high ductile
structures.
3. Codal Provisions
It is widely recognized that ground shaking in
existing buildings located in seismic regions may
induce unacceptable levels of damage. Several
reasons have been attributed to this vulnerability,
such as insufficient strength and stiffness, weak
detailing, plan and elevation irregularities, the
dominance of brittle failure modes over ductile ones,
etc. [17]. Various codes display the principle
concepts for finding the performance level.
3.1. ATC-40[18]
Capacity Spectrum Method (CSM) has gained
considerable popularity amongst pushover users and
the ATC40 guidelines [18] included it as the
recommended nonlinear static procedure to be
used. The CSM was created to describe a structure's
first mode response based on the assumption that
the main response of the structure is the
fundamental mode of vibration. The results
obtained with the CSM may not be so accurate. The
steps of the capacity spectrum method are described
herein.
Step (1): Seismic Data
A MDOF model of the building must be developed
including the nonlinear force-deformation
relationship for structural elements under monotonic
loadings, Fig. 1a. An elastic acceleration response
spectrum is also required corresponding to the
seismic action under consideration, Fig. 1b.
a) b)
Figure (1): a) MDOF model of the building; b)
Elastic acceleration response spectrum [19].
Step (2): Seismic demand in AD (acceleration
displacement) format.
The seismic demand is defined with a response
spectrum in the format acceleration- displacement
(ADRS). For SDOF, the displacement spectrum can
be computed from the acceleration spectrum using
eq. (4):
…. (4)
Where Sa and Sd are the values for the elastic
acceleration and displacement spectrum,
respectively.
Step (3): Pushover Analysis
A conventional non-adaptive force-based pushover
analysis is performed, applying to the structure a
monotonically increasing pattern of lateral forces. In
CSM the lateral forces applied have a first mode
proportional distribution. Lateral forces are applied
in proportion to the storey masses and the square
height of the floor as per by using eq. (5):
……. (5)
where, mi and hi are the mass and height of
ith floor.
From the pushover analysis one obtains the capacity
curve that represents the base shear and the
displacement at the center of mass of the roof.
Step (4): Equivalent SDOF system
The structural capacity curve expressed in terms
of roof displacement and base shear is then
converted into a SDOF curve in terms of
displacements and accelerations, which is called the
capacity spectrum. The transformations are made
using the following equations:
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…. (6)
…. (7)
…. (8)
roof
roof …. (9)
Fig. Fig. 2. It shows that the participation factor
and modal mass coefficient differ according to the
relative inter-storey displacement over the height of
the building. For example, for a linear distribution of
inter-storey displacement along the height of the
building α1 ≈0.8 and PF1≈ 1.4.
Figure (2): Modal participation factors and
modal mass coefficients [18].
To convert MDOF capacity curve to SDOF
capacity curve in the format (capacity spectrum) of
the Acceleration-Displacement Response Spectra
(ADRS) format (Sa versus Sd), the modal participation
factor PF1 and the modal mass coefficient α must
first be calculated by eq. (7) and eq.(8) Afterwards,
for each point of the MDOF capacity curve (V,
∆roof) calculate the associated point (Sa, Sd) of the
capacity spectrum according to eq.(8) and eq.(9).
Step (5): Estimation of Damping and
Reduction of the Response Spectrum:
ATC-40 defines an equivalent viscous damping to
represent this combination; it can be calculated using
eq. (10): …. (10)
ATC-40 introduces the concept of effective
viscous damping that can be obtained by multiplying
the equivalent damping by a modification factor k by
using eq.(11):
……. (11)
where 5 – 5% viscous damping inherent in the
structure (given to be constant).
The hysteretic damping represented as equivalent
viscous damping can be calculated by using eq. (12):
…. (12)
Figure (3): Derivation of Damping for Spectral
Reduction
The physical meaning of both ED and ES0 is
represented in Fig.3. ED is the energy dissipated by
the structure in a single cycle of motion, that is, the
area bounded by a single hysteresis loop. ES0 is the
maximum strain energy related to that cycle of
motion that is, the area of the hatched triangle. Fig. 4.
Show the derivation of energy dissipated by damping.
Figure (4): Derivation of energy dissipated by
damping, ED.
Therefore, β1 can be written as:
…. (13)
The effective damping can be written as:
…. (14)
The k-factor depends on the structural behavior
of the building, which is related to the seismic
resisting system quality and the ground shaking
duration. ATC40 defines three categories of
structural behavior:
Type A represents stable, reasonably full
hysteresis loops.
Type B represents a moderate reduction of area.
Type C represents poor hysteretic behavior with
a significant reduction of loop area (severely
pinched).
Table 1. indicates the ranges and limits for the values
of k specified to the three structural behavior types.
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Table (1): Modification factor k.
Structural
Behavior
Type
β1
k
Type A
≤ 16.25
1.0
>16.25
Type B
≤ 2.5
0.67
>2.5
Type C
Any
value
0.33
Step (6): Numerical Derivation of Spectral
Reduction
The spectral reduction factors are calculated as
shown in eq. (15) and eq. (16).
……. (15).
……. (16).
Note that the SRA and SRv values should be greater
than or equal to the values referred to in Table 2.
Table (2): The minimum allowable SRA and SRv
values
Structural
Behavior Type
Type A
0.33
0.50
Type B
0.44
0.56
Type C
0.56
0.67
Step (7): Calculation of the target displacement:
The calculation of the target displacement is an
iterative process, where it is necessary to estimate a
first trial performance point. For this purpose, there
are several options one can use:
1. The first trial performance point can be estimated
as the elastic response spectrum displacement
corresponding to the elastic fundamental period. The
response spectrum is defined for the viscous
damping level considered (in buildings one usually
considers 5%);
2. Consider a first trial equivalent damping value, for
example 20%, and calculate the respective reduction
factor. Multiply the elastic spectrum by this reduction
factor and intersect the capacity curve with the
reduced spectrum. The intersection corresponds to
the first trial performance point.
The capacity curve is then bilinearized for this point,
and a new effective damping can be computed and
hence a new reduction factor can be applied. The
new intersection between the capacity curve and the
new reduced spectrum leads to a new performance
point. If the target displacement calculated is within a
tolerable range (for example within 5% of the
displacement of the trial performance point), then
the performance point can be obtained. Fig.5.
represents the process schematically.
Figure (5): General CSM procedure to compute the
target displacement.
Step (8): Determination of MDOF response
parameters in correspondence to the
Performance Point (converted from SDOF to
MDOF)
At this stage of the procedure, one should go back
to the MDOF pushover curve to the point consistent
to the value of the SDOF target displacement
(calculated in the previous step) multiplied by the
transformation factor. For this step, one should take
the building’s performance results, such as
deformations, inter storey drifts and chord rotations.
3.2. FEMA273/356 [20,21]
The Displacement Coefficient Method (DCM) is
the primary nonlinear static procedure presented in
FEMA 356.The target displacement, δ, at each floor
level shall be calculated in accordance with eq. (17):
…… (17)
where:
C0 = Modification factor to associate spectral
displacement of an equivalent SDOF system to the
roof displacement of the building MDOF system
determined using one of the following procedures:
1. The first modal participation factor at the level
of the control node.
2. The appropriate value from Table 3.
Table (3): Values for Modification Factor C0
No. of stories
Modification Factor
1
1.0
2
1.2
3
1.3
5
1.4
+10
1.5
C1= Modification factor to associate with estimated
maximum inelastic displacements to displacements
calculated for linear elastic response:
= 1.0 for Te ≥ TS
= [1.0+(R-1)Ts/Te]/R for Te < TS
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C1 not greater than the values below, and no less
than 1.0.
for
for
Te = Effective fundamental period of the building in
the direction under consideration.
……. (18)
R= Ratio of elastic strength demand to calculated
yield strength coefficient.
…. (19)
C2 = Modification factor to represent the influence
of pinched hysteretic shape, stiffness and strength
degradation on maximum displacement response.
Values of for different framing systems and
Structural Performance Levels shall be calculated
from Table 4.
Table (4): Values for Modification Factor C2
Structural
performance
level
T≤ 0.1 second
T ≥Ts second
Framin
g type
11
Framing
type 22
Framing
type 11
Framing
type 12
Immediate
Occupancy
1.0
1.0
1.0
1.0
Life Safety
1.3
1.0
1.1
1.0
Collapse
Prevention
1.5
1.0
1.2
1.0
1.Structures in which more than 30% of the floor
shear at any level is resisted by any combination of
the following elements, elements, or frames:
ordinary moment-resisting frames, concentrically-
braced frames, frames with partially-restrained
connections, tension-only braces, unreinforced
masonry walls, shear-critical, piers, and spandrels of
reinforced concrete or masonry.
2. All frames not assigned to Framing Type 1.
C3= Modification factor due to dynamic P-∆
effects to represent increased displacements. For
buildings with a positive post-yield stiffness
(maintains its strength during a given deformation
cycle, but loses strength in subsequent cycles, the
effective stiffness also decreases in subsequent cycles
(degradation of cyclic strength)) the value shall be set
at 1.0.For buildings with negative post-yield
stiffness(Note that the degradation happens during
the similar cycle of deformation in which yielding
occurs, resulting in a negative post-elastic stiffness,
(in-cycle strength degradation)), values of shall be
calculated using eq.(20)
…. (20)
Where α is the ratio of post yield stiffness to elastic
stiffness when the nonlinear force-displacement
relation is characterized by a bilinear relation.
3.3. FEMA440 [22]
▪ Improved Procedures for Displacement
Modification
FEMA 440 (2005) [22] advises that the
restrictions (capping) of the C1 coefficient permitted
by FEMA 356 be abandoned. A distinction between
two different types of strength deterioration that have
different effects on system response and performance
is also recognized. This distinction gives rise to
recommendations for the C2 coefficient to account
for cyclic strength and stiffness degradation. It is also
recommended that the coefficient C3 be removed and
replaced with a limitation on strength (R).
a. Maximum Displacement Ratio
(Coefficient C1)
FEMA 356 currently accepts the coefficient C1 to
be restricted (capped) for relatively short-period
structures. FEMA440 suggested that this limitation
not be used. This may increase estimates of
displacement for some structures. For most
structures the following simplified expression may be
used for the coefficient C1:
…. (21)
For periods less than 0.2 s, the value of the
coefficient C1 for 0.2 s may be used. For periods
greater than 1.0 s, C1 may be assumed to be 1.0.
b. Degrading System Response (CoefficientC2)
FEMA 356 suggested that the C2 coefficient
represent the influences of stiffness degradation only.
FEMA440 recommended that the displacement
prediction be modified to account for cyclic
degradation of stiffness and strength. It
recommended that the C2 coefficient be as follows:
……. (22)
For periods less than 0.2 s, the value of the
coefficient C2 for 0.2 s may be used. For periods
greater than 0.7 sec. C2 may be assumed equal to 1.0
for assumption would include buildings with modern
concrete or steel special moment-resisting frames,
steel eccentrically braced frames, and buckling-
restrained braced frames as either the original system
or the system added during seismic retrofit.
c. P-∆ Effects (Coefficient C3)
Because of dynamic P- effects, the displacement
modification factor C3 is intended to account for
increased displacements. FEMA 440 proposed
removing the current coefficient of C3 and replacing
it with the maximum strength ratio, R, intended to
calculate dynamic instability. Where the value for
Rmax is exceeded, a Nonlinear Dynamic Procedures
(NDP) analysis is recommended to capture strength
degradation and dynamic P-Δ effects to confirm
dynamic stability of the building. Nonlinear static
procedures are not capable of distinguishing
completely between cyclic and in-cycle strength
losses. However, insight can be obtained by
separating the in-cycle P-∆ effects from α2, Fig.6.
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Figure (6): Idealized Force-Displacement Curves.
An effective post-elastic stiffness can then be
determined as
…. (23)
Where 0≤ λ ≤1.0
FEMA 440 recommended that λ be assigned a
value of 0.2 for sites not subject to near field effects
and 0.8 for those that are. Displacement
amplifications increase as the post-yield negative
stiffness (caused by in-cycle strength degradation)
ratio α decreases (becomes more negative), as R
increases. Minimum strength (maximum R) required
avoiding dynamic instability. The recommended
limitation on the design force reduction, Rmax, is as
follows max
… (24)
Where
t=1+0.15lnT …. (25)
The structural model must appropriately model
the strength degradation characteristics of the
structure and its components.
▪ Improved Procedures for Equivalent
Linearization
An improved equivalent linearization procedure
as adjustment to the Capacity-Spectrum Method
(CSM) of ATC-40[18]. When equivalent linearization
is used as a part of a nonlinear static procedure that
models the nonlinear response of a building with a
SDOF oscillator, the objective is to evaluate the
maximum displacement response of the nonlinear
system with an “equivalent” linear system using an
effective period, Teff , and effective damping, βeff ,
Fig.7.
Figure (7): Effective period and damping parameters
of the equivalent linear system
a. Effective damping
The formulas herein presented apply to any
capacity curve, independent of hysteretic model type
or post-elastic stiffness value (α) used. The effective
damping is calculated using Equations below
depending on the structure’s level of ductility µ.
For µ < 4.0:
…. (26)
For 4.0 ≤ µ ≤ 6.5:
…. (27)
For µ > 6.5:
… (28)
b. Effective period
The following equations apply to any capacity
spectrum independent of hysteretic model form or
post-elastic stiffness value. The effective period
depends on the ductility level and is calculated using
Equations below:
For µ < 4.0:
eff
……. (29)
For 4.0 ≤ µ ≤ 6.5:
. (30)
For µ > 6.5:
... (31)
Where α is the post-elastic stiffness and µ the
ductility, calculated as follows
… (32)
and
… (33)
c. Spectral reduction factor for effective damping
The spectral reduction factor is a function of the
effective damping and is called the damping
coefficient, B(βeff ) and is calculated using Equation
…. (34)
It is used to adjust spectral acceleration ordinates as
shown in eq.35.
…. (35)
3.4. ASCE 41-06 [23]
ASCE41-06 depends on the displacement
coefficient method to capture the target
displacement. The target displacement, δ at each
floor level shall be determined in accordance with
eq.36.
…. (36)
where Co = modification factor to relate spectral
displacement of an equivalent single-degree of
freedom (SDOF) system to the roof displacement of
the building. Multi-Degree Of Freedom (MDOF)
system determined using one of the following
procedures:
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1. The first mode mass participation factor
multiplied by me ordinate of the first mode
shape at the control node.
2. The mass participation factor calculated Using a
shape vector corresponding to the deflected
shape of the building at the target displacement
multiplied by ordinate of the shape vector at the
control node.
3. The appropriate value from Table.5.
Table (5): Values for Modification Factor Co
Shear Buildings1
Other
Buildings
No. of
stories
Triangular
load
pattern
Uniform
load pattern
Any load
pattern
1
1.0
1.0
1.0
2
1.2
1.15
1.2
3
1.2
1.2
1.3
5
1.3
1.2
1.4
+10
1.3
1.2
1.5
1Buildings in which, for all stories, story drift
decreases with increasing height.
C1 = factor of modification to relate the estimated
maximum inelastic displacements to the linear elastic
response displacements calculated. For periods less
than 0.2 sec, C, need not be taken greater than the
value at T = 0.2 sec. For periods greater than 1.0 sec,
C1 = 1.0.
…. (37)
where
a = site class factor:
= 130 site Class A, B;
= 90 site Class C;
= 60 site Class D, E, F;
C2 = modification factor to represent the influence of
pinched hysteresis shape, cyclic stiffness degradation,
and strength deterioration on maximum displacement
response. For periods greater than 0.7 sec, C2 =1.0;
……. (38)
• The strength ratio R shall be calculated in
accordance with eq.39.
……. (39)
▪ Cm taken as the effective modal mass participation
factor determined for the fundamental mode using
an Eigenvalue analysis shall be acceptable. Cm shall
be taken as 1.0 if the fundamental period, T, is
greater than 1.0 sec.
For buildings with negative post-yield stiffness,
the maximum strength ratio, Rmax shall be calculated
in accordance with eq.41.
war
…. (40)
where
∆d = lesser of target displacement, or displacement at
maximum base shear defined in Figure (7)
∆y = displacement at effective yield strength defined
in Fig. (7).
h = 1 + 0.15. In T, and
αe= effective negative post-yield slope ratio defined
in eq.41.
…. (41)
where
α2 = negative post-yield slope ratio defined in Figure
(6). This contains P-A effects, in-cycle degradation,
and cyclic degradation;
α p-∆ = negative slope ratio caused by P-∆ effects;
and
λ = near field effect factor:
= 0.8 if S1≤0.6 (Maximum Considered Earthquake,
MCE); = 0.2 if S1 < 0.6 (MCE).
3.5. Euro code 8 [24]
N2 method, first proposed by Fajfar and
Fischinger [24] and subsequently developed by
Fajfar[25][26, 27], is the Nonlinear Static Procedures
(NSP) adopted by Euro code 8[23] and is a modified
version of the CSM. Indeed, the estimation of seismic
demand is based on the use of inelastic spectra in the
N2 method instead of highly damped elastic spectra,
as per the CSM. The steps of the capacity spectrum
method are defined herein.
Step (1) and Step (2) are the same steps of capacity
spectrum method with ATC-40[18].
Step (3): Pushover analysis
A pushover analysis is performed, applying to the
structure a monotonically increasing pattern of lateral
forces, Fig.8. These forces represent the inertial
forces induced in the structure by the ground motion.
Any reasonable distribution of lateral loads can be
used in the N2 method. The Euro code 8
recommends the use of at least two distributions: a
first mode proportional load pattern and a uniform
load pattern.
The vector of the lateral loads used in the
pushover analysis proportional to the first mode is
determined as:
…. (42)
The lateral force in the i-th level is proportional to
the component Φ of the assumed displacement
shape Φi , weighted by the story mass mi
…. (43)
The vector of the lateral loads used in the
pushover analysis with a uniform distribution is
determined as:
uni …. (44)
.... (45)
Figure (8): Pushover analysis of the MDOF model
The N2 method prescribes that this curve should
represent the base shear (Fb) and the displacement at
the center of mass of the roof (dn).
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Step (4): Equivalent SDOF system
The MDOF structure should be transformed into
an equivalent SDOF system. The definition of the
transformation factor Γ is based on the equation of
motion of a MDOF system.
.... (46)
Where, U is the displacement vector, is the
acceleration vector, M is a diagonal mass matrix, R is
the internal forces vector, 1 is a unit vector and a is
the ground acceleration as a function of time. The
deformed pattern Φ is assumed to be constant during
the structural response to the earthquake. The
displacement vector is then written as eq.47.
.... (47)
where the time dependent top displacement. The
Φ is normalized in order to have its component at
the top equal to 1. The internal forces R are equal to
the statically applied external loads.
=R .... (48)
Equations (42 and 47) into Equation (46) and
multiplying the equation by Φ , it follows:
... (49)
The equation of motion of the SDOF system can be
written as:
.... (50)
where is the equivalent mass of the SDOF system
and it is calculated using eq.51.:
.... (51)
The transformation of the MDOF to the SDOF
system is made in the N2 method using eq.52 and
eq.53.
.... (52)
.... (53)
where , are the displacement and base shear of
the SDOF system. The transformation factor Γ from
the MDOF to the SDOF model is defined according
eq.54:
...(54)
The transformation factor Γ is usually called the
modal participation factor. The SDOF capacity curve
is defined by the displacement of the SDOF () and
base shear of this system () as shown in Fig.9.
Figure (9): Equivalent SDOF system.
Euro code 8 prescribes a simplified elastic-perfectly
plastic bilinear approximation of the SDOF capacity
curve.
Figure (10): SDOF capacity curve and its bi
linearization
The elastic period of the idealized bilinear SDOF
system T* is computed according to eq.55:
.... (55)
N2 method assumes that in the medium/long
period range (T*≥Tc) the equal displacement rule
applies, i.e. the displacement of the inelastic system Sd
is equal to the displacement of the associated elastic
system Sde characterized by the same period T*,
where Tc is the characteristic period of the ground
motion, which is defined as the transition period
between the constant acceleration section of the
response spectrum (corresponding to the short
period range) and the constant velocity segment of
the response spectrum (corresponding to the medium
period range) Fig.11.
Figure (11): Long period range.
This means Rμ= μ in the above-mentioned
period range. Seismic demand in terms of inelastic
displacement can be obtained by intersecting the
radial line with the elastic demand spectrum
corresponding to the SDOF system period. In the
case of short-period structures (T*< TC) the inelastic
displacement is larger than the elastic one and the
equal displacement rule does not apply anymore
Fig.12. Consequently < μ and it can be calculated
as the ratio between the elastic acceleration demand
capacity Sae and the inelastic acceleration Say. The
inelastic displacement demand is, in this case, equal to
Sd= μ ·D*y being D*y the yielding displacement of the
SDOF system. The ductility factor can be derived
from the reduction factor by the relation:
.... (56)
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Figure (12): Short period range.
In both cases (T*≥Tc and T*<TC) the inelastic
acceleration demand Sa is equal to the elastic one Sae
and it can be verified at the intersection of the radial
line corresponding to the period of the SDOF system
with the elastic demand spectrum.
3.6 Japanese Standard [25]
Three screening levels have been introduced in
the Japanese standard (2001) for seismic capacity
evaluation. Seismic index of the structure for each
story
Is =Eo.SD.T ……(57)
where Eo is the primary seismic index of
screening levels. The primary seismic index of
structure Eo of the i-th story in an n-story building is
given as a product of strength index. C, ductility
index F and α is the effective strength factor,
differently in each screening levels as shown in table
below.
SD is introduced to adjust the basic seismic index
by measuring the effects of horizontal and vertical
shapes, and the mass and stiffness irregular
distribution of the structure.
T is a modification factor of the basic seismic
index which evaluates the effects of cracks,
deflection, and aging of building. T value will be at
range 0.7 to 0.9 but if there is no defect, the T value
is 1. Building older than 30 years have a T value of
0.8, but for newer buildings less than 19 years old the
T value should be equals to 1.
Table (6): Values of primary seismic index (Eo)
Screening
primary seismic index (Eo)
First
Screening
Second
Screening
Third
Screening
Forth
Screening
Seismic demand index(Iso) regardless of the
number of stories in the building:
sо …… (58)
where
is the basic seismic demand index of the structure,
standard values of which shall be selected as 0.8 for
the first level screening and 0.6 for the second and
third level screenings.
Z is zone index, namely the modification factor
accounting for the seismic activities and intensities
expected in the region of the site.
G is a ground index, namely the modification factor
accounting for the effects of the amplification of the
surface soil, geological conditions and soil-and-
structure interaction on the expected earthquake
motions.
U is the usage index, namely the modification factor
accounting for the building.
If
Is≥Iso … (59)
If eq.59 is satisfied, the building may be assessed to
be “safe”. Otherwise, the building should be assessed
to be “an uncertainty” in seismic safety and need to
retrofit.
3.7 ZS1170.5 2004[26]
The target displacement of NZS1170.5 2004is
calculated by using the coefficient method as
described in FEMA-356.
……. (60)
where the coefficients take the same roles in
modifying the expected elastic displacement
Expressions for them are redefined here to better
reflect the intent of NZS1170.5.
C0 will equal “1” as we plot the deflection of the
dynamic center of mass.
C1 accounts for the variation between the response of
an elasto-plastic and elastic SDF systems and can be
obtained from clauses 5.2 and 7.2.1.1 of the Standard
expressed as
……. (61)
C2 will equal “1” as there is no account made in
NZS1170.5 for differences in response of systems
with a pinched hysteretic shape and stiffness and
strength degradation.
C3 is to account for the increased displacements
resulting from dynamic P-delta effects. This can be
derived from the Standard as
……… (62)
NZS1170.5 provides limitations as to which
buildings require P-delta effects included in the
analyses. This is a pragmatic approach to allow
simple regular buildings to be quickly designed with
the knowledge that other conservative clauses in the
Standard will provide for the shortfall in strength. It
is recommended here, that where the NSP procedure
is used in aseismic assessment procedure and the
building has not been designed to modern Standards,
C3 as per Eq.8 be included in the analysis of all
buildings(T) is the ordinate of the elastic hazard
spectrum as per clause 3.1.1 of the Standard.
3.8 IS-15988(2013) [27]
Recommendation for Detailed Evaluation:
A building is recommended to undergo a detailed
evaluation, if any of the following conditions are met:
a) Building fails to comply with the requirements of
the preliminary evaluation;
b) A building is 6 stories and higher;
c) Buildings located on incompetent or liquefiable
soils and/or located near (less than 15 km) active
faults and/or with inadequate foundation details; and
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d) Buildings with inadequate connections between
primary structural members, such as poorly designed
and/or constructed joints of pre-cast elements.
If acceptability criteria satisfied, the retrofit not
recommended.
Detailed Evaluation (for primary lateral-force
resisting system):
a) Evaluation Procedures
1. Probable Flexure and Shear Demand and
Capacity
Estimate the probable flexural and shear strengths
of the critical sections of the members and joints of
vertical lateral force resisting elements. These
calculations shall be performed as per respective
codes for various building types and modified with
knowledge factor K.
2. Design Base Shear
Calculate the total lateral force (design base shear)
in accordance with [IS 1893 (Part 1)] and multiply it
with U, a factor for the reduced useable life (equal to
0.70).
3. Analysis Procedure
Perform a linear equivalent static or a dynamic
analysis of the lateral load resisting system of the
building in accordance with IS 1893 (Part 1) for the
modified base shear determined in the previous step
and determine resulting member actions for critical
components.
a) Mathematical model: The physical structure's
mathematical model is designed to represent the
spatial distribution of the mass and the stiffness of
the structure to the extent that it is adequate to
calculate the significant characteristics of its lateral
force distribution. Both elements of concrete as well
as masonry must be used in the model.
b) Component stiffness: Component stiffness shall
be determined based on some rational procedure
4. It must compare probable component strength
with expected seismic demands.
Acceptability Criteria
A building is said to be acceptable if one of the
following two requirements, along with additional
criteria for a specific form of building, are met:
a) All critical elements of lateral force resisting
elements have strengths greater than computed
actions and drift checks are satisfied.
b) Except a few elements, all critical elements of the
lateral force resisting elements have strengths greater
than computed actions and drift checks are satisfied.
The engineer has to ensure that the failure of these
few elements shall not lead to loss of stability or
initiate progressive collapse. This needs to be verified
by a non-linear analysis such as pushover analysis,
carried out up to the collapse load.
3.9 Review of Codes Procedures for Seismic
Assessment of Existing Buildings
Mahaylov and Petrini [28] studied five codes for
evaluating existing buildings (Italian Seismic Code
[29], EC8 [24], FEMA356 [21], ATC40 [18] and
FEMA440 [22] were analyzed by looking at the
theoretical basis of the problems. It found that the
dynamic P-∆ effect is not considered by the Italian
seismic code and the EC8. According to FEMA440
[22], the procedures implemented in FEMA356 and
ATC-40 [21] are not able to adequately capture the
dynamic instability phenomenon. The non-linear
static procedure in the Italian seismic code and EC8
[24] is based on the Equivalent SDOF system's
elastic-perfectly plastic nature. Degradation effects
of strength and stiffness are not considered. This
simplification may lead to underestimation of the
target displacement.
Moshref et al. [30] used two main guidance
documents, the New Zealand Guideline [31] and
FEMA 440 [22], on the evaluation of existing
buildings currently available for concrete frame
resistance. The main aim of the study was to trace
the differences between the results provided by these
two guidelines. Under the two guidelines, the Peak
Ground Acceleration (PGA) values that cause the
collapse are calculated and compared with their
similar values, which are determined from a non-
linear dynamic analysis. The outcome of the force-
based approach suggested by the New Zealand
Guideline was found to be more consistent with
nonlinear dynamic analysis. Appropriate results were
given by the New Zealand displacement method and
FEMA440 [22], but their results are not
conservative.
Alwashali and Maeda [32] investigated the
damage caused by the Great East Japan earthquake
in Sendai City-Japan in 2011 to many low-rise RC
buildings. Using the Japanese Standard for Seismic
Evaluation of Existing RC Buildings, the chosen
building is assessed to have a high seismic capacity.
On those buildings, pushover analysis was
performed. The pushover analysis was found to
predict the degree of damage well, but there were
some variations in the position of the plastic hinge
compared to the actual damage. Plastic hinges were
expected to occur in beams and not in columns, but
this wasn’t the case in the actual damage.
Xiaoguang et al. [33] studied the seismic design
code for buildings in Japan (Japanese standard Code)
[34], India (IS 1893-2002) [35], Turkey [36], China
(GB 50011-2010) [37], Korea [38], Nepal
(NBC105)[39], Indonesia (SNI-02-1726-2002)[40],
and Iran (Iranian code) [41], in detail. These
countries' seismic fortification parameters are
contrasted by evaluating the classification of the site,
the seismic effective coefficient, and the seismic
spectral design. The findings indicate that China and
Japan have the highest horizontal seismic activity. So
in China and Japan, the seismic fortification level is
high. In Turkey and Korea, the seismic fortification
level is low. In most Asian countries, except the
seismic design code of Korea [38], the response
spectrum principle was used in the seismic design of
buildings.
Araujo et al. [42] conducted a comparative
analysis of the European and American seismic
safety assessment procedures as described in
Eurocode 8-Part3 (EC8-3) [24] and ASCE41-06 [23].
In the seismic evaluation of four separate steel
buildings built according to different requirements,
these two principles are used. The main results in the
study are no safety checks could be performed as
Eurocode 8-Part3 (EC8-3) [24] requires the analyst
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to evaluate the safety of each ductile element by
checking its plastic rotation capacity based on the
demand obtained from a linear elastic structural
model.
Hakim et al. [43] evaluated the performance of
buildings that were built using pushover analysis by
the Saudi Building Code (SBC 301) [44]. It examines
four typical RC frame structures. To produce the
ultimate building capacity, pushover analysis is
performed. Building performance levels are defined
by ATC-40 [18], FEMA-356[21], and FEMA-440
[22]. The findings show that all three methods
suggest that the safety margin against collapse is
high, adequate reserves of strength, and
displacements are available. It found that the design
of SBC buildings usually meets the acceptance
requirements for these methods.
Cavdar and Bayraktar [45] included several
performance evaluation procedures. Four main
guidelines/codes describe the most common
evaluation procedures: ATC-40 [18], FEMA 356
[21], FEMA 440 [22], and TEC-2007[46]. The static
pushover and nonlinear time history studies analyze
the nonlinear seismic behavior of a collapsed
reinforced concrete (RC) residential building in
Turkey. It found that the current structural structure
of residential buildings did not meet the ATC-40
[18], FEMA 356 [21], FEMA 440 [22], and TEC-
2007[46] predicted standards of performance (LS).
According to both nonlinear static pushover analysis
and time history analysis under earthquake loads, the
building constructed according to TEC-1975[47]
presents the level of CO performance through two-
direction results.
Kurniawandy and Nakazawa [48] explained
the seismic assessment of existing buildings based on
a Japanese standard [25] using the seismic index
method. Based on the intensity and ductility
parameters, the fundamental seismic index is
determined. Two existing buildings were assessed.
For each story, the seismic index of the structure has
a different value. The minimum seismic index exists
on the ground floor, and as the number of floors
increases, the index increases. If the seismic index
(Is) is higher than the seismic demand index (Iso), the
structure is evaluated for seismic safety. It was found
that the correlation between the results of the
measurement of the seismic index based on the
Japanese standard and the drift requirements
according to the ASCE41-06 [23] was consistent, it a
good method to evaluate existing structures.
4. Analytical techniques of performance
evaluation
To assess the seismic performance of any structure,
it is important to estimate its dynamic characteristics
and to predict its response to the ground motion to
which it may be exposed during its service life.
Dynamic characteristics, namely periods and mode
shapes, are obtained through an eigenvalue analysis
[49]. As it is exposed to different levels of ground
motion, the nonlinear dynamic time-history analysis
provides the damage states of the building. The
nonlinear study of time history can be divided into
two methods; one is based on the dynamic response
of a multi-degree of freedom (MDOF) system
similar to a single degree of freedom system [50], the
other is based on an equivalent response directly
derived from the MDOF system's nonlinear dynamic
response [51]. To assess the lateral load resisting
capacity of a structure and the maximum damage
level to the structure at the ultimate load, nonlinear
static procedure (push-over) analysis may be used. It
is also possible to divide the static pushover analysis
into two methods; one is based on the first
(fundamental mode) pushover analysis [18], the
other based on the Modal Pushover Analysis (MPA)
where higher mode effects are taken into account.
[52].
4.1 Nonlinear Static Analysis
4.1.1 Capacity Spectrum Method (CSM)
A performance-based seismic analysis
methodology, the Capacity Spectrum Method
(CSM), may be used for several purposes, such as
rapid assessment of a large inventory of buildings,
design verification for new construction of
individual buildings, assessment of an existing
structure to identify damage states, and correlation
of damage states of buildings to different ground
motion amplitudes. The method compares the
structure's capacity (in the form of a pushover curve)
with the structure's demands (in the form of a
response spectrum). The graphic intersection of the
two curves approximates the structure's response.
Effective viscous damping values are applied to
linear-elastic response spectra similar to inelastic
response spectra to account for the non-linear
inelastic behavior of the structural system [53]. This
approach is often referred to as a pushover analysis.
Fig.13.Shows the principle of the capacity spectrum
method.
Figure (13): Demand& Capacity Curves [53].
4.1.2 Displacement Coefficient Method (DCM)
The nonlinear static procedure is introduced
through the Displacement Coefficient Method. This
approach modifies the SDOF system's linear elastic
response by multiplying it by many coefficients from
C0 to C3. To achieve this equivalence, these four
coefficients are required to take account of the
structure's inelastic behavior as well as the increase
in the number of degrees of freedom. The first one
(C0) is related to the spectral displacement
equivalence between both systems, the second one
(C1) takes into account the inelastic deformation, the
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third one (C2) corresponds to the effect of pinched
hysteretic shape and the fourth one (C3) is due to the
dynamic (P-∆) effects [54]. Fig.14.Show the Process
Schematic of the Displacement Coefficient Method.
Figure (14): Process Schematic of the Displacement
Coefficient Method [22].
4.2 Review of Pushover Analysis
4.2.1 Review of Pushover Analysis of an Existing
Hospital Buildings
Singh et al. [55] studied the eight story ward
building of GTB hospital located at Delhi-India. The
brick masonry infills were modeled as strut
components, the slabs were assumed as a rigid
diaphragm, the plastic hinge rotation values
corresponding to different performance levels were
taken according to FEMA 356[21], taking into
account the relations between axial force moment
and shear force moment. Using both the Capacity
Spectrum Method (CSM) and the Displacement
Coefficient Method (DCM), with the value of
coefficients as per FEMA 440[20], the performance
point of the building was calculated. The result
showed that the plastic deformations in beams and
columns were found to be within the level of IO
performance while those in masonry infills exceeded
the level of CP performance. The beams and
columns have been checked and found safe at the
performance point for the predicted shear force. The
columns were also tested for the shear caused by
diagonal masonry struts and found safe.
Ismaeil [56] studied the seismic performance of
Sudan's existing hospital buildings. Using SAP2000
software [56], the pushover analysis was approved
on the building. To govern the analysis, the
principles of Performance-Based Seismic
Engineering are used. The assessment showed that
the three-story hospital building is seismically safe.
Jarallah [57] studied the effects of the soil-
structure relationship on the building's seismic
assessment when a framed building is supported on
a raft base. The foundation-soil interaction effect
was considered by replacing it with equivalent
springs. The Capacity Spectrum Method of ATC-40
[18] has been used to conduct nonlinear static
pushover studies of eight-story reinforced concrete
hospital buildings. The findings show that the
interaction of the soil-structure has a pronounced
effect on the displacement of the roof, story drift,
effective damping, and crack pattern for beams and
columns while the torsional behavior of the building
is minorly affected.
Jarallah et al. [58], studied the eight story RC
building is the eight-story building. Using the
patented software ETABS [62], the nonlinear
pushover analysis of the building is predicted. The
performance-based analysis has also been performed
as per FEMA 356/273[21,20] and ATC40 [18]. To
capture the performance level of the building, the
target displacement method and the capability
spectrum method were used. In the nonlinear
pushover analysis, it was observed that the
unreinforced masonry (URM) infills collapsed before
the Maximum Considered Earthquake (MCE)
performance point of the building. Whether it was
possible to protect the infills by stiffening the
building by having external buttresses has been
explored. Two instances of retrofitting systems in
the transverse direction of 1.2m wide and 3m wide
buttresses were used and analyzed.
4.2.2 Review of Pushover Analysis of an Existing
Other Buildings
Korkmaz et al. [59] studied the effect of infill
walls on earthquake response is considered to be
examined by a 3-story RC frame structure with
different amounts of masonry infill walls. For
modeling masonry infill walls, the diagonal strut
method is adopted. For structures, pushover curves
are obtained using the nonlinear analysis option of
SAP2000 [60] commercial software. Besides,
findings are presented and the effects of an irregular
configuration of the masonry infill wall on the
structural performance are presented. It was found
the current study show that structural infill walls
have very significant effects on structural behavior
due to earthquake effects, to a large extent the global
seismic behavior of framed buildings, and improved
stability and integrity of reinforced concrete frames.
Irregular distributions of masonry infill walls in
elevation can result in unacceptably elastic
displacement in the soft story frame.
Goel [61] used the non-linear static procedures
set out in the documents FEMA-356 [21],
ASCE/SEI 41-06 [23], ATC-40[18], and FEMA-440
[22] for the seismic analysis and assessment of
building structures using strong-motion records of
reinforced concrete structures. The maximum roof
displacement predicted by the nonlinear static
procedure is compared directly with the value
derived" from the recorded movements, It is shown
that: 1) for many of the buildings considered in this
investigation, the nonlinear static procedures either
overestimate or underestimate the peak roof
displacement; 2) The ASCE/SEI 41-06 [23]
Coefficient Method (CM), which is based on the
recent FEMA-356 [20] (CM) proposed changes in
the FEMA-440 [22] document, does not necessarily
provide a better estimate of the displacement of
roofs., and 3) Compared to the ATC-40 CSM, the
improved FEMA-440 [22] Capacity Spectrum
System (CSM) usually offers better estimates of roof
displacement.
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Singh et al. [62] presented an analytical review
with and without Unreinforced Masonry Wall
(URM) infills on the seismic performance and
vulnerability (or fragility) analysis (fragility analysis of
a structure is described as its susceptibility to damage
by the ground shaking of a given intensity) of Indian
code-designed RC frame buildings. As per ASCE 41
guidelines, infills are modeled as diagonal struts and
different modes of failure are considered. The
seismic vulnerability of bare and infilled frames is
contrasted with nonlinear static analysis. The
comparative study indicates that URM infills lead to
a substantial increase in the seismic vulnerability of
RC frames and that their influence needs to be
better integrated into design codes.
Ahmed [63] analysed ten stories-five bays of
reinforced concrete frame (two-dimensional beams
and columns system) subject to the seismic risk of
Mosul city/Iraq. When the member yields, the
plastic hinge is used to reflect the failure mode in the
beams and columns. The study of nonlinear static
(Pushover) was introduced by ATC-40 [18]. The
results showed that the frame is capable of resisting
the presumed seismic force with many beams with
some substantial yield. Only in the beams can the
sequence of the creation of plastic hinges (yielding)
in the frame members be seen. The building works
as a weak beam mechanism with a strong column.
Total overall drift, maximum inelastic drift, and
structural stability do not exceed the performance
level limitations, so the current building is
considered safe against the seismic force for citizens.
Sabu and, Pajgade [64] focused on seismic
assessment and retrofitting of existing RC buildings.
Bare frame modeling, brick infill frame modeling,
and soil effect interaction model are all three
modeling formats. Results show that infill panels
have a substantial influence on frame behavior
during earthquake excitation. In general, infill panels
increase the structure's stiffness, while deflection in a
bare frame is very high compared to the infilled
frame. The strength of the current structure can be
increased to the necessary level and the building's
seismic resistance capacity can be improved, the
concrete jacketing method is a simple, effective, and
economical way to improve the member's and
building's seismic resistance capacity as well as.
Babu et al. [65] used non-linear study of
different symmetric and asymmetric systems built on
plain and sloping grounds subjected to different load
forms. The study was carried out Using SAP2000
[60] and ETABS [66]. The paper concluded that the
vertical irregularity structure is important relative to
a plan irregularity structure.
Tamboli and Karadi [67] performed seismic
analysis for various reinforced concrete (RC) frame
construction models, including the bare frame,
infilled frame, and open first Storey frame, using the
Equivalent Lateral Force procedures. It examines the
effects of the bare frame, infilled frame, and open
first story frame, and conclusions drawn. The
Equivalent Diagonal Strut system is used to model
the masonry infill panels and the ETABS program
[66] is used for the study of all frame models.
Golghate [68] determined the actions of the
G+3 reinforced concrete frame system in Zone IV
subjected to earthquake forces. The reinforced
concrete structures are analyzed using SAP2000
software [60] by nonlinear static analysis (Pushover
Analysis). The frame was exposed to the design of
earthquake forces along the X-direction as defined.
In the beams and columns showing the 3 stages of
immediate occupancy, life safety, collapse
prevention, the outcomes hinges have created. The
column hinges have limited the damage.
Neethu and Saji [69] analyzed a symmetric
construction is a portion of a four-story educational
building. It was checked the type of performance
that a building can provide when designed by Indian
standards. The hinge length is measured as half of
their effective depth for every beam and column.
Using SAP2000 [60], a static non-linear (pushover)
study of the current educational building was
performed. The results showed that the demand
curve intersects the capacity curve near the elastic
range, the structure has good resistance and high
collapse protection, the properly detailed behavior of
reinforced concrete frame design is adequate as
indicated by the demand and capacity curves
intersection.
Azaz [70] used the pushover analysis on a
reinforced concrete structure is emphasized in this
article. In which the building of G+10 was revealed
to push in x and push in the direction of y. In
SAP2000 [60], the analysis was done. Nearly 6
elements exceed the limit level between life safety
(LS) and collapse prevention (CP) from the results
obtained in x-direction and y-direction. The study
showed that the building requires retrofitting.
Daniel and John [71] studied a ten-storeyed
reinforced concrete building is analyzed by
displacement-controlled pushover analysis using
SAP2000 software [59]. It was developed to model
the beam and column sections of the user-defined
hinges. The lateral forces were connected to the
building. Pushover analysis is carried out in the
direction of +x and +y by vertical loading (gravity
load) followed by a gradually increasing
displacement-controlled lateral load. The results
showed that the maximum base shear capacity was
greater than the base shear design, and the hinge
formation sequence showed that localized collapse
occurs before columns in beams.
Sangeetha and, Sathyapyiya [72] analyzed a
four-story building construction is planned and
evaluated according to the Indian standard in the
report. Structural analysis and design software SAP
2000 [60] conducts the pushover analysis of the RC
building frame. The frame was subjected to the X-
directions of design earthquake forces. In the beams
and columns showing the 3 stages of immediate
occupancy, life safety, collapse prevention, the
results showed that hinges have grown. The damage
has been limited by the column hinges. It proposed
some retrofitting, buckled longitudinal
reinforcement, broken ties, and crushed concrete by
replacing new reinforcement welded with existing
bars and supplying new additional closed ties.
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Ning, N.et al. [73] presented a pushover study
using ABAQUS. The influence of the infills on the
RC frames' failure patterns was studied. An RC
frame with completed infills, half-filled infills, and
without infills is considered to be the Finite Element
Method (FEM) model. Research findings suggest
that because of the influence of infills, the position
of the inflection point differed. The effective slab
width and the required ratio of a column to beam
strength are found to be reduced due to the infill
effects. The actual effective width of the slab should
be considered in the required ratio of a column to
beam strength.
Cavdar et al. [74] studied a building that
collapsed in the Turkish earthquake in 2003;
pushover analysis and nonlinear dynamic analysis
were carried out. To test the reliability and usability
of performance levels, their purpose was to perform
the pushover analysis and NDA for various
earthquakes. The present Turkish Earthquake Code,
TEC (2007) [46] was used to conduct a performance
assessment. It is concluded that when a reinforced-
concrete shear-wall building is not severely damaged,
pushover will provide a fairly reliable measurement
of performance level. Pushover analysis
underestimates the building efficiency, regardless of
the lateral load distributions, if the building is
severely collapsed.
Al-jassim and Husssain [75] used a nonlinear
static analysis (Pushover analysis based on the
ATC40 capacity spectrum approach to analyze an
existing G + 5 story reinforced concrete building. In
three instances, the building is evaluated (regular,
irregular in plan, and irregular in height). The default
plastic hinge in the SAP2000 program [60] is built.
Results clearly illustrate that during the design
earthquake, all buildings perform very well (nearly
elastic), which means that the buildings are over-
designed. At an output level below the immediate
occupancy level, all the plastic hinges are both
buildings behave almost elastically, with no
noticeable difference between their activities, except
that the irregular plan building shows less Y-
direction displacements and drifts than the other
buildings.
Abhilash and Vijayanand [76] carried out
pushover analysis by using ETABS software [65] to
understand the conduct of G+8 multistoried
building in two separate areas in India. From the
results of the study, maximum lateral load, story
displacement, and monitored displacement were
found to be increased in Zone III compared to
Zone II. Although in Zone II, the maximum base
force is higher than in Zone III. The hinges between
IO (Immediate Occupancy) and LS (Life Safety) are
established here, indicating the building. Hence the
structural model analyzed in this state is safe.
Ingale and Kalurkar [77], studied the effect of
Push over analysis for G+15 story RC structure with
and without the Zipper frame using SAP2000 [60]
software. For the rising efficiency of RC, Framed
structure types of bracing systems, such as zipper
braced frame, are used in framed structures for
seismic design. The displacement values for regular
RC construction (without the zipper brace frame)
were found to increase compared to the zipper brace
frame displacement. The pushover analyses are
helping to understand the model behavior and its
demand as well as capacity as shown in the above
results.
5. Torsional Effects in Pushover
Analysis
Studies on the torsion effects of irregular
buildings date back to the 30s of the last century
[78]. There can be several and varying types of
causes of irregularity in a building configuration and
they are usually classified into two key categories:
plan and elevation irregularities [79]. Among the two
aforementioned types of structural irregularity, in-
plan irregularity appears to have the most adverse
effects on the applicability of classical nonlinear
static procedures (NSPs), precisely because such
methods have been developed for seismic
assessment of structures whose activity is primarily
translational [80]. This explains why the
improvement of NSPs in recent years has centered
mainly on the contribution of higher vibration
modes, which are intended to account for the effects
of vertical and in-plan irregularities. Two main
approaches can be identified among the many
proposed methods developed in this research field:
the first one aims to take into account the
contribution of more eigen modes called model
pushover analysis (MPA), in addition, a similar
approach, an extended version of the N2 method
has been proposed by Fajfar et al. [81] for the
application to plan irregular building structures.
5.1 Analytical techniques of torsional effect
in pushover analysis
5.1.1 Model Pushover Analysis (MPA)
One of the main approaches in the developing of
NSPs for the analysis of irregular building structures
involves the evaluation of the contribution of more
Eigen modes in the analysis. Within this approach,
the major contribution has been given by Chopra
and Goel [82] who extended the previously defined
MPA to asymmetric-plan buildings.
5.1.1.1 Brief Description of MPA Procedures [83]
To better understand the method proposed in
this research, it is summarized below:
1. Compute the structural natural frequencies ωn and
modes n. In practical applications, only the first
two or three modes are needed.
2. For the nth mode, develop the pushover curve
(base shear-top displacement curve) using force
distribution
defined as
……. (63)
where M is the mass matrix of the structure.
3. Idealize the pushover curve as a bilinear curve as
shown in Fig.15.
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Figure (15): Pushover curve and the idealized
bilinear curve
4. Convert the idealized pushover curve to the force-
deformation relationship (Fsn/Ln -D) of nth mode
inelastic SDF system as shown in Fig.16.
…. (64)
where n is the nth modal participation factor, and
is the effective modal mass and determine the
initial elastic vibration period Tn and yielding
deformation Dny.
Figure (16): Converted force-displacement
relationship for equivalent SDF system.
5. Compute the peak deformation Dn of the nth
mode inelastic SDF system by nonlinear history
analysis, or using inelastic design spectrum.
6. Calculate the peak roof displacement urn
associated with the nth-mode inelastic SDF
system from
…. (65)
7. From the pushover database, extract values of any
desired responses rn at the peak roof displacement
urn.
8. Repeat steps 3-7 for the first few “modes”.
9. Determine the total seismic demand rtotal with
Square Root of Sum of Squares (SRSS) rule
total …. (66)
5.1.2 Extended N2 Method
The extension to plan-asymmetric buildings of
the N2 method, where torsional effects are
significant, it was established by assuming that the
torsional effects in the inelastic range are Just like in
the elastic range, the torsional effects are determined
by the standard elastic modal analysis. The
displacements taken by pushover analysis are
amplified through a corrective factor, given by the
ratio of the normalized displacement gained by
modal analysis and that incoming from pushover
analysis. It is assumed that the structure stays in the
elastic range when vibrating in higher modes, and
that the seismic demands can be calculated as an
envelope of demands determined by a pushover
analysis, which does not take into account the higher
mode effects, and normalized demands determined
by an elastic modal analysis, which involves higher
mode effects [84].
5.1.2.1 Brief Description of Extended N2
Procedures [85]
The following procedure can be applied to
predict the structural response for a building with a
non-negligible effect of higher modes along the
elevation:
1. Perform the basic N2 analysis and find out the
target roof displacement.
2. Perform the standard elastic modal analysis of the
MDOF model considering all relevant modes.
Identify floor drifts for each floor. Normalize the
results in such a way that the top displacement is
equal to the target top displacement.
3. Determine the envelope of the results obtained in
Steps 1 and 2.
4. For each floor, determine the correction factor
CHM, which are defined as the ratio between the
results obtained by elastic modal analysis (Step 2)
and the results obtained by pushover analysis (Step
1). If the ratio is larger than 1.0, the correction factor
CHM is equal to this ratio, otherwise it amounts to
1.0. The correction factors for storey drifts are
important.
5. The resulting floor drifts (and displacements, if
applicable) are obtained by multiplying the results
determined in Step 1 with the corresponding
correction factors CHM.
6. Determine other local amounts. The resulting
correction factors for floor drifts CHM apply to all
local deformation amounts (e.g. rotations).
Correction factors CHM for floor drifts also apply to
internal member forces, provided that the resulting
internal forces do not exceed the load-bearing
capacity of the structural member.
5.2 Criteria of Seismic Codes on
Applicability of NSPs to Torsional Effects
In spite of the large tries of researchers to better
understand the seismic behavior of irregular building
structures and to improve the current NSPs, it
appears that most regulatory forms have not still
translated the research improvements achieved into
seismic codes.
ASCE7-10 [86] specific prescriptions for the use of
NSPs are not included. The only constraint on the
option of the form of study with respect to torsional
irregularity is that similar lateral force analysis is not
required for torsionally irregular structures.
ASCE 41-06 [23] defines limitations in the use of
linear analyses centered on the presence of structural
irregularities evaluated by static or dynamic linear
analysis. If there is some form of structural
irregularity (in-plane and out-of-plane
discontinuities, weak story, torsional
strength/stiffness irregularity) defined by one or
more structural components, then linear procedures
are not applicable and should not be used.
FEMA 273 [20] It advises that the effects of torsion
cannot be used to reduce the demands on
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components and elements for force and
deformation.
EC8-1 [24] provides for the application of the N2
method, although it meets the absence of a full
suitability for irregular building structures.
Japanese Guidelines [25] provides a numerical
method to take the irregular building effects in to
account by using the factor SD in seismic index.
6. Acceptance Criteria
Response quantities from the nonlinear static
analysis are compared with limits for acceptable
performance levels to decide whether a building
meets a specified performance level. The limits of
response fall into two groups [18]:
1. Global building acceptability limits: These
response limits include requirements for the vertical
load capacity, lateral load resistance, and lateral drift.
2. Element and component acceptability limits:
Each element (frame, wall, diaphragm, or
foundation) must be checked to determine if its
components respond within acceptable limits.
6.1 Global building acceptability limits
Lateral deformations at the performance point
displacement are to be checked against the
deformation limits. Deformation limits for various
performance levels and for various seismic
assessment codes were presented below.
6.1.1 ATC-40[18]
Table (7): Limits of global building according to
ATC-40[18]
Inter-story
Drift
Limit
Immediate
Occupancy
Life
Safety
Structural
Stability
Maximum
Total drift
0.01
0.02
0.33Vi/Pi
Maximum
Inelastic
drift
0.005
No limit
No limit
6.1.2 Japanese Standard [25]
Seismic index of the structure for each story
Is =Eo.SD.T
Seismic demand index(Iso) regardless of the
number of stories in the building:
Isо =Es.Z.G.U
If ………. (63)
If eq.63 was fulfilled, the building is safe. If eq.63
was not fulfilled, the building is unsafe and it needs
to retrofit
6.1.3 TEC-2007[46]
Table (8): Boundaries of Relative Story Drift
according to TEC-2007
Ratio of Relative
Story Drift
Damage Boundary
MN1
GV2
GC3
δji/ hji4
0.01
0.03
0.04
1. MN is Minimum Damage Region.
2. GV is Safety Limit.
3. GC is Collapsing Limit.
4. δji / hji4, δji The relative drift of the story is
measured as a substitute difference between the
bottom and top ends of the jth column or wall in the
ith storey, while hji indicates the height of the related
element.
Table (9): Performance criteria used in analyses
(TEC-2007)
Damage
Level
Limited value for
confined
concrete
Limited
values for
steel bar
Minimum
Damage Limit
(MN)
()
=0.0035
()
=0.010
Safety Damage
Limit
(GV)
()=0.040
Collapse
Damage
Limit
(GC)
)=0.060
6.1.4 TEC-2018[87]
Table (10): Performance criteria used in analyses
(TEC-2018)
Damage
Level
Limit Values
Confined Concrete
Steel Bar
Limited
Damage
(SH)
Boundary
Controlled
Damage
(KH)
Boundary
Collapse
Prevention
(GO)
Boundary
6.2 Element and component acceptability
limits
To determine if its components meet
acceptability criteria under performance point forces
and deformations, each part must be examined.
Primary and secondary elements and provides
general information on checks for strength and
deformability. Each element and component is
classified as primary or secondary, depending on its
importance at or near the performance point for the
lateral load resisting system. Plastic hinge properties
can be characterized by a typical elastic-plastic force-
deformation relationship with strength degradation
at high ductility demands as shown in Fig.17.
Figure (17): Component modeling and
acceptability.
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Point A identify to the unloaded condition; Point B
has a resistance equal to the nominal yield strength,
taken as 10% total strain hardening for steel, the
abscissa at C identify to the deformation at which
considerable strength degradation begins, point
defining the maximum deformation capacity [88].
6.2.1 Review of plastic hinge properties in
nonlinear analysis
Inel and Ozmen [89] studied the effect of
default and user-defined nonlinear component
properties in the results of pushover analysis. For
this analysis, four- and seven-story structures were
observed to reflect low- and medium-rise buildings.
Pushover analysis is carried out in many programs
based on the FEMA-356[21] and ATC-40[18]
guidelines for either user-defined nonlinear hinge
properties or default-hinge properties. Observations
show that the length of the plastic hinge and the
spacing of the transverse reinforcement have little
effect on the base shear capacity, while these
parameters have a significant impact on the frame
displacement capacity.
Eslami and Ronagh [90] demonstrated the
effects of pushover studies of modeled RC
structures based on the nonlinear FEMA hinges and
identified hinges. The force-deformation curves of
the specified hinges are calculated following the
validation of the adopted models in a rigorous
approach taking into account the material inelastic
behavior, reinforcement details, and members'
dimensions. Concerning the inter-story drift, hinging
pattern, failure mechanism, and the pushover curve,
nonlinear responses of both models are elaborated.
FEMA hinges have been confirmed to
underestimate the strength and more importantly,
the displacement capacity, especially for frames with
low ductility.
Jadhav and Patil [91] studied the variations in
pushover analysis results by reason SAP2000 [59]
default and user-defined hinge properties. The
amount of transverse reinforcement is the parameter
assumed to affect the frame's base shear ability and
displacement capacity. The comparison points out
that the displacement capacity is increased by a raise
in the quantity of transverse reinforcement. But
because it takes average values, the capacity curve
for the default hinge model is reasonable.
Compassion demonstrates that the user-defined
hinge model is better at capturing the hinge
mechanism than the default hinge model. However,
the default hinge model is preferred due to simplicity
but the user should be aware of what is provided in
the program.
LOPEZ et al. [92], studied the influence on the
nonlinear behavior of reinforced concrete structures
of various plastic hinge models. Considering the
FEMA-356[21] plastic hinge model and two
additional models, several nonlinear analyses were
carried out using empirical expressions calibrated
with different experimental data. The results show
that plastic hinges modeled with empirical
expressions can be used to model the behavior of
structural components more precisely, besides, to
compare the results of the models included in
seismic building design codes.
7. Seismic Retrofit
The strengthening and enhancement of the
performance of deficient structural elements in a
structure or the structure as a whole is referred to as
retrofitting. Retrofitting of a building is not the
same as repair or rehabilitation. Repair refers to the
partial improvement of the degraded strength of a
building after an earthquake [93]. The approaches
considered for the existing buildings such as
Jacketing of existing beams, columns. Several
authors carried out numerical and experimental
campaigns on the behavior of concrete structural
elements before and after the Carbon Fiber
Reinforced Polymer (CFRP) wrapping [94]. Another
retrofitting technique is steel bracing, Steel Bracings
Systems modify the structural response in seismic or
collapse scenarios maintaining the before mentioned
advantages and reducing the cost [95].
7.1 Retrofitting of Existing Buildings under
Seismic Loading
Fahmi and, Faraj [96] concerned with the
seismic evaluation of existing reinforced concrete
buildings. The methodology includes linear elastic
analysis based on equivalent static lateral load
according to the 1988 Uniform Building Code and
the Draft Iraqi Seismic Code. Six-story moment-
resisting frame structure with shear wall located in
Baghdad. The results indicate that the stress ratio of
some members (beams, columns) of the existing
building are determined using the stresses due to the
vertical and seismic forces divided by the allowable
stresses more than one. These critical elements are
inadequate and need strengthening. The mechanism
of strengthening by using shotcrete and
reinforcement on the outside of the original cross-
sectional area of the element. The stress ratio
indicates that after strengthening each element in the
existing building has adequate strength to resist the
vertical and seismic forces.
Dhiman et al. [97] studied the response of a
braced and unbraced structure subjected to seismic
loads was evaluated and the appropriate bracing
system was identified to effectively resist seismic
loads. After analyzing the structure with different
types of structural systems, it was concluded that
after the application of the bracing system, the
displacement of the structure decreases. The
maximum reduction in lateral displacement occurs
after the cross-bracing system has been applied. In
the columns, the bracing system decreases bending
moments and shear forces. The lateral load is
transferred through axial action to the foundation.
The cross-bracing system performance is better than
the other bracing systems specified, Steel bracings
can be used to retrofit the existing structure. The
total weight of the existing structure will not change
significantly after the application of the bracings.
Bhojkar and Bagade [98] analyzed reinforced
concrete (RC) structures with different bracing types
are studied in this paper. By using STAAD Pro
software [99], a G+9 building is analyzed. In this
paper, lateral displacement, story drift, axial force,
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70
base shear are the main parameters considered to
compare the seismic analysis of buildings. The X
type of steel bracing has been found to significantly
contribute to the structural stiffness and reduce the
maximum inter-story drift of the frames. The
bracing system improves not only the lateral stiffness
and strength capacity but also the displacement
capacity of the structure.
Hyderuddin et al. [100] investigated the seismic
efficiency of reinforced concrete (RC) buildings
rehabilitated using concentrated steel bracing. For
peripheral columns, bracing is provided. By using
ETABS 2015 [62] Software, a ten-story building is
analyzed. For models with Diagonal bracing,' V'
form bracing, inverted 'V' form bracing, inverted 'V'
form bracing,' X' form bracing,' K' form bracing, the
design is evaluated and compared to an unbraced
frame bracing. Lateral displacement, story drift, axial
forces in the columns, base shear are the main
parameters in this study to compare the seismic
analysis of buildings. It was found that the 'X' type
of steel bracing contributes greatly to the structural
stiffness and decreases the frames' overall story
drifts. The bracing systems increase not only the
lateral stiffness but also the structure's displacement
strength.
Basereh et al. [100] introduced a new retrofit
method for code-deficient reinforced concrete shear
walls which, due to improper detailing or lack of
well-confined boundary elements, are vulnerable to
non-ductile failure modes. To define working
specifics of the retrofit process, three-dimensional
finite element models of pre-and post-retrofit shear
walls under cyclic lateral loading have been used.
Results of the analysis showed that rocking is the
governing behavior for the retrofitted walls and the
contribution of shear to displacements decreased
due to retrofit. Changes in residual displacements,
energy dissipation, strength, and secant stiffness due
to retrofit were documented.
8. Conclusions
From the previous review on evaluation and
retrofitting of an existing building and their
procedures, it can be noted that the researcher aimed
to investigate the behavior of buildings under
seismic loads, assess the level of an existing building
state under loads, in addition, retrofitting the weak
links in an existing building. From literature, the
following prominent remarks concerning the seismic
evaluation and retrofit of buildings:
1. The improvement of capacity spectrum method
(CSM) and displacement coefficient method
(DCM) in FEMA 440 focused on the effect of
stiffness degradation and changes in dynamic
properties associated with progressive damage
but doesn't take the effect of irregularity in plan
or in elevation into account, on the other hand
the Japan Standard relied on a numerical method
taking the stiffness degradation and the torsional
effect in the seismic evaluation.
2. ATC-40, FEMA273/356, FEMA440, and ASCI
41-06 are considered the most important than
Euro code 8 – Part 3 and Italian Seismic Code,
Italian seismic code and EC8 do not consider the
dynamic P-∆ effects. Also, according to
FEMA440, the procedures implemented in
FEMA273/356 and ATC-40 are not able to
adequately capture the dynamic instability
phenomenon.
3. Nonlinear static analysis (Pushover analysis)
Procedures are deemed to be a very practical tool
to assess the nonlinear seismic performance of
structures, it introduced in this context are a
powerful tool for performance evaluation.
4. Unreinforced Masonry Wall (URM) infills have a
significant increase in the seismic vulnerability of
RC frames compare with the bare frame and
their effect needs to be properly incorporated in
design codes.
5. The soil-structure interaction has a marked effect
on the global acceptability limits as a roof
displacement and story drift. Most researchers
don’t take this effect into account.
6. For SAP2000 and ETAPS, the user-defined
hinge model is better than the default hinge
model in displaying nonlinear behavior
consistent with element properties.
7. Despite the large efforts of researchers aimed at
the improvement of NSPs for a reliable
application to irregular buildings, these
developments have not yet transposed to Both
European and American codes. For this reason,
these cods are still in need of improvement
regarding specific prescriptions concerning the
seismic analysis of irregular structures.
8. The retrofitting by adding steel braces enhance
greatly the strength capacity of the buildings on
the dynamic characteristic of the building. The
zipper (vertical structural member, connected at
the top and down to the beams at the vertical
strut) bracing systems are found the most
efficient.
Abbreviations
A list of symbols should be inserted before the
references if such a list is needed
CSM
Capacity Spectrum Method.
DCM
Displacement Coefficient Method.
Te
Effective fundamental period of the
building in the direction under
consideration.
Ti
Elastic fundamental period (in seconds) in
the direction under consideration
calculated by elastic dynamic analysis.
Ki
Elastic lateral stiffness of the building in
the direction under consideration
Ke
Effective lateral stiffness of the building
in the direction under consideration.
TS
Characteristic period of the response
spectrum, defined as the period associated
with the transition from the constant
acceleration segment of the spectrum to
the constant velocity segment of the
spectrum.
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R
Ratio of elastic strength demand to
calculated yield strength coefficient.
Sa
Response spectrum acceleration.
S1
Response spectrum acceleration at
period,1 sec.
Vy
Yield strength calculated using results of
the NSP for the idealized nonlinear force-
displacement curve developed for the
building.
W
Effective seismic weight.
Cm
Effective mass factor.
α
The ratio of post yield stiffness to elastic
stiffness when the nonlinear force-
displacement relation is characterized by a
bilinear relation.
αe
Effective negative post-yield slope ratio.
α p-∆
Negative slope ratio caused by P-∆
effects.
λ
Near field effect factor.
PF1
Modal participation factor for the first
natural mode.
α1
Modal mass coefficient for the first
natural mode.
V
Base shear.
∆ roof
Roof displacement (V and the associated
∆roof make up points on the capacity
curve).
βeq
Equivalent viscous damping.
βeff
Effective viscous damping.
k
Damping modification factor
β1
Hysteretic damping represented
as equivalent viscous damping.
ED
Energy dissipated by damping.
ES0
Maximum strain energy.
ES0
Maximum strain energy.
Spectral Acceleration Reduction.
Spectral Velocity Reduction.
T*
Elastic Period.
Reducing Factor.
Characteristic Period.
α2
Negative post-yield slope ratio.
∆d
Displacement at maximum base shear.
∆y
Displacement at effective yield strength.
Teff
Effective period.
µ
Ductility factor.
βeff
Effective damping.
β0
Initial viscous damping (5% - concrete
buildings).
T0
Fundamental period in the direction
under consideration.
api
Trail Spectral Acceleration.
dpi
Trail Spectral Displacement.
ay
Bilinear curve yielding spectral
Acceleration.
dy
Bilinear curve yielding spectral
Displacement.
dy
Bilinear curve yielding spectral
Displacement.
SDOF
Single Degree of Freedom.
MDOF
Multi Degree of Freedom.
RC
Reinforcement Concrete.
ATC
Applied Technology Council.
FEMA
Federal Emergency Management Agent.
ASCI
American Society of Civil Engineers.
EC
Euro Code.
IO
Immediate Occupancy.
LS
Life Safety.
CP
Collapse Prevention.
9. References
[1] G. G. Deierlein, A. M. Reinhorn and M. Willford
(2010), “Non-Linear Structural Analysis for
Seismic Design, A guide for practicing engineer”,
National Institute of Standards and Technology
NEHRP Seismic Design Technical Brief No. 4,
Gaithersburg, MD, USA.
[2] S. E. Abdel Raheem and T. Hayashikawa (2003),
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International Workshop on Structural Health
Monitoring of Bridges/Colloquium on Bridge
Vibration, Kitami, Hokkaido, Japan.
[3] A. Mechaala, C.Benazouz, H. Zedira, and M.
Benbouras (2018), “Evaluation of the
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demands assessment of structures”, 14th ASEC
conference in Jordan 12-15 April 2018 Jordan
University of Science &Technology.
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Performance of Reinforced Concrete Buildings”,
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Damage Assessment for RC Structures Based on
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[6] R. Dumaru (2018), “Seismic Performance
Assessment and Strengthening Techniques for
Existing Reinforced Concrete in Nepal”, Ph.D.,
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[7] A. Biddah, A. Ghobarah and H. ABOU-
ELFATH (2000), “Response Based Damage
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with different damage levels”, M.Sc., thesis
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[9] E. Erduran and, A. Yakut (2004), “Drift Based
Damage Functions for Components of RC
Structures”, 13th World Conference on
Earthquake Engineering, Vancouver, B.C.,
Canada.
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[10] M. Seckin (1981), “Hysteretic behavior of cast-
in-place exterior beam-column sub-assembles”,
Ph. D. Thesis, University of Toronto, 266 pp,
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