PERFORMANCE POINT EVALUATION OF MASONRY INFILL RC SOFT STOREY BUILDINGS UNDER SEISMIC LOAD USING PUSHOVER ANALYSIS Submitted by Md. Faysal Student No: 0604038 Submitted to the DEPARTMENT OF CIVIL ENGINEERING BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY In partial fulfillment of requirements for the degree of BACHELOR OF SCIENCE IN CIVIL ENGINEERING MARCH, 2012
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Performance Point Evaluation of Masonry Infill Rc Soft Storey Buildings Under Seismic Load Using Pushover Analysis
Due to rapid urbanization to provide sufficient car parking space, open ground story has become a typical feature in the modern multi-storied building. This causes vertical stiffness irregularity and develops soft story mechanism. Soft story mechanism is a potential mode of failure of reinforced concrete structures as experienced during past earthquake. Although some of the national codes do have certain design guide to avoid soft story problem, the Bangladesh National Building Code (BNBC, 1993) does not have any such provision. This thesis has been conducted to investigate the performance of soft story structures. For this purpose, a total of five structures range from six to twelve stories have been considered to evaluate the performance of soft story building under seismic loading. The performances of the structures have been evaluated using the nonlinear static pushover analysis as per the procedure of ATC-40, 1996. From nonlinear inelastic performance based analysis the actual behavior of the structure during earthquake can be found. There are mainly two guidelines of this analysis FEMA-356 and ATC-40, 1996. These analysis procedures have been discussed in this thesis. It has been observed that performances of these structures under seismic loading are highly unsatisfactory. The value of base shear obtained by using Pushover analysis is higher than any other methods like equivalent static force method or response spectrum method. The value of displacement and inter-story drift are very high in soft ground story. Stiffness of open ground story is significantly less than the above. The capacity curve of soft story structure never meets seismic demand. It is seen that the value of base shear increase with the increase in height. Investigation of buildings with soft story shows that soft story mechanism reduces the performance of the structure and makes them vulnerable type of construction in earthquake prone areas. So it is vital for the engineers to provide adequate safety measures to achieve acceptable performance in open ground story structure under seismic action. It is high time to include provisions for soft story structure in Bangladesh National Building Code.
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PERFORMANCE POINT EVALUATION OF MASONRY INFILL
RC SOFT STOREY BUILDINGS UNDER SEISMIC LOAD USING
PUSHOVER ANALYSIS
Submitted by
Md. Faysal Student No: 0604038
Submitted to the
DEPARTMENT OF CIVIL ENGINEERING
BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY
In partial fulfillment of requirements for the degree of
BACHELOR OF SCIENCE IN CIVIL ENGINEERING
MARCH, 2012
ii
ABSTRACT
Due to rapid urbanization to provide sufficient car parking space, open ground story
has become a typical feature in the modern multi-storied building. This causes vertical
stiffness irregularity and develops soft story mechanism. Soft story mechanism is a
potential mode of failure of reinforced concrete structures as experienced during past
earthquake. Although some of the national codes do have certain design guide to
avoid soft story problem, the Bangladesh National Building Code (BNBC, 1993) does
not have any such provision.
This thesis has been conducted to investigate the performance of soft story structures.
For this purpose, a total of five structures range from six to twelve stories have been
considered to evaluate the performance of soft story building under seismic loading.
The performances of the structures have been evaluated using the nonlinear static
pushover analysis as per the procedure of ATC-40, 1996.
From nonlinear inelastic performance based analysis the actual behavior of the
structure during earthquake can be found. There are mainly two guidelines of this
analysis FEMA-356 and ATC-40, 1996. These analysis procedures have been
discussed in this thesis.
It has been observed that performances of these structures under seismic loading are
highly unsatisfactory. The value of base shear obtained by using Pushover analysis is
higher than any other methods like equivalent static force method or response
spectrum method. The value of displacement and inter-story drift are very high in soft
ground story. Stiffness of open ground story is significantly less than the above. The
capacity curve of soft story structure never meets seismic demand. It is seen that the
value of base shear increase with the increase in height. Investigation of buildings
with soft story shows that soft story mechanism reduces the performance of the
structure and makes them vulnerable type of construction in earthquake prone areas.
So it is vital for the engineers to provide adequate safety measures to achieve
acceptable performance in open ground story structure under seismic action. It is high
time to include provisions for soft story structure in Bangladesh National Building
Code.
iii
DECLARATION
It is hereby declared that this thesis work carried out by author and any part of it or
the thesis has not been submitted elsewhere for any other purpose.
March, 2012.
MD. FAYSAL
iv
ACKNOWLEDGEMENT
Foremost, the author would like to express his sincere gratitude to his supervisor Dr.
Khan Mahmud Amanat, Professor of Department of Civil Engineering, BUET for his
encouragement, indispensible guidance and support from the initial to final stage of
this thesis.
The author pays his deepest homage to his parents, sister and friends for their constant
inspiration.
Above all the author thanks the Almighty for all his blessings.
v
TABLE OF CONTENETS
Page No.
ABSTRACT ii
ACKNOWLEDGEMENT iii
LIST OF TABLES viii- ix
LIST OF FIGURES x-xiii
CHAPTER-1 INTRODUCTION
1.1 GENERAL 1
1.2 OBJECTIVE AND SCOPE OF THE STUDY 2
1.3 METHODOLOGY 3
1.4 ORGANIZATION OF THE THESIS 4
CHAPTER-2 LITERATURE REVIEW
2.1 INTRODUCTION 5
2.2 THE SOFT GROUND STORY CONFIGURATION
2.2.1 Definition of Soft Story 6
2.2.2 Behavior of RC Frame under Lateral Load 7
2.3 BEHAVIOR OF SOFT GROUND STORY STRUCTURE 10
2.4 BUILDING DESIGN STRATEGIES IN BUILDING CODE 13
2.4.1 Indian Seismic Code, Is-1893 (2002) 14
2.5 COMPUTATIONAL MODELING AND ANALYSIS OF INFILL
FRAME 15
2.5.1 Equivalent Diagonal Strut Method 15
2.6 PAST RESEARCH ON SOFT STORY BUILDING 17
2.7 REMARKS 19
CHAPTER-3 CONCEPT OF PERFORMANCE BASED DESIGN
3.1 INTRODUCTION 20
vi
3.2 MODELING OF INFILL WALLS 20
3.2.1 Equivalent Strut Method 21
3.2.2 Equivalent Strut Width 22
3.2.1.2 Eccentricity of Equivalent Strut 23
3.2.1.3 Existing infill damage 23
3.2.3 Infill Properties 24
3.2.4 Determination of fm and Em 24
3.2.5 Calculation of Equivalent Strut Width 27
3.3 NON-LINEAR STATIC PROCEDURE
3.3.1 Reduced Demand Spectra 27
3.3.2 Development of Elastic Site Response Spectra 28
3.3.3 Seismic Zone 29
3.3.4 Seismic Source Type 30
3.3.5 Near Source Factor 30
3.3.6 Seismic Coefficients 31
3.3.7 Establishing Demand Spectra 32
3.4 CAPACITY CURVE 36
3.4.1 Capacity Spectrum Method 38
3.5 PERFORMANCE POINT 39
3.5.1 Non linear Static Procedure for Capacity evaluation
As the elastic limit is exceeded, the behavior of masonry infill deteriorates. So it is
important to determine exceeded limit. Existing panel damage must be classified as –
no damage, moderate damage or severe damage. If in doubt to determine the
magnitude of existing panel damage assume severe damage for a conservative
estimate. A reduction factor for existing panel damage (R2 ) must be obtained from
Table (3.1). If the slenderness ratio (hm/t) of the panel is greater than 21, (R2) is not
defined and repair is required. For panels with no existing panel damage, the
reduction factor must be taken as 1.
24
Table 3.1: In-plane damage reduction factor
Type of Damage Type of Damage
hm/t Moderate Severe
<21 0.7 0.4
>21 Repair is required. Repair is required.
3.2.3 Infill Properties
The infill masonry panel will be presented as strut member. The equivalent strut width
shall be determined according to Coul & Smith described earlier. For the modeling of
infill the following properties must be determined.
Modulus of elasticity of concrete Ec value for column and beam materials.
Sectional propertied (i.e. Depth, Width, Moment of Inertia, Center of Gravity)
of the column and beam.
Equivalent width of the masonry infill strut “a”.
fm compressive strength of the masonry assembled units.
Em modulus of elasticity of the masonry unit.
3.2.4 Determination of fm and Em
In this study masonry bricks are considered as infill material. In Bangladesh although
a variety of bricks are used as a building material but most common of them is solid
clay bricks. So, NW type brick, according to ASTM C62, 1994 is considered in this
study. Table 3.2: Specified Compressive Strength of Masonry f’m (psi), based on
specifying the compressive strength of masonry units. (ACI 530, 192/ ASCE 6-92/
TMS 602-92)
25
Compressive Strength of Masonry Units
(psi)
Specified Compressive Strength of Masonry, f'm
Type M or S Mortar (psi)
Type N mortar (psi)
14000 or more 5300 4400 12000 4700 3800 10000 4000 3300
8000 3350 2700 6000 2700 2200 4000 2000 1600
Compressive Strength of Concrete Units
(psi)
Specified Compressive Strength of Masonry, f'm
Type M or S Mortar (psi)
Type N mortar (psi)
4800 or more 3000 2800 3750 2500 2350 2800 2000 1850 1900 1500 1350
NOTE:
1. Compressive strength of solid clay masonry units is based on gross area. Compressive strength of hollow clay masonry units is based on minimum net area. Value may be interpolated.
2. Assumed assemblage. The specified compressive strength of masonry fm is based on gross area strength when using solid units or solid grouted masonry and net area strength when using ungrouted hollow units.
3. Type M, N or S mortar are according to ASTM C270 definition.
From the table for strength of clay masonry unit 4000 psi is chosen and for that fm
1600 psi for N mortar.
Em is the ratio of the stress to the strain of a material or combinations of materials as
in the case for grouted masonry.
To find out the value of Em considering the ACI/ ASCE/ TMS masonry code the
modulus of elasticity is given in the following table-
26
Compressive strength of clay Masonry (psi)
Specific Compressive Strength of
Clay Masonry Assemblage
fm( psi)
Modulus of
Elasticity (psi)
Modular Ratio, n
Modulus of
Rigidity, G = 0.40 Em (psi)
14000 or more 4400 3000000 9.7 1200000
12000 3800 2850000 10.2 1140000
10000 3300 2475000 11.7 990000
8000 2700 2025000 14.3 810000
6000 2200 1650000 17.6 660000
4000 1600 1200000 24.2 480000
Type M or S Mortar
Compressive strength of clay Masonry (psi)
Specific Compressive Strength of
Clay Masonry Assemblage
fm( psi)
Modulus of
Elasticity (psi)
Modular Ratio, n
Modulus of
Rigidity, G = 0.40 Em (psi)
14000 or more 5300 3000000 9.7 1200000
12000 4700 3000000 9.7 1200000
10000 4000 3000000 9.7 1200000
8000 3350 2512500 11.5 1005000
6000 2700 2025000 14.3 810000
4000 2000 1500000 19.3 600000
According to the table, for Em= 1270 ksi
27
3.2.5 Calculation of Equivalent Strut Width
In the following table calculation of some sample strut is shown. In the study due to
various change in geometry several equivalent strut is used. Detail sample calculation
of Equivalent strut width is given below-
Table 3.4: Sample Calculation of equivalent strut width
Column Dimension Beam Dimension θcolumn Strut
Width, a B L B H
mm mm mm mm radian inch
457 457 305 508 0.42 27
508 508 305 508 0.42 27
558 558 305 558 0.46 28
609 609 305 609 0.46 28
Eccentricity is assumed d distance below the column as per advice.
3.3 NON-LINEAR STATIC PROCEDURE
Various analysis methods- both elastic and inelastic are available for the analysis of
concrete building. Elastic analysis method available includes code static lateral force
procedure, code dynamic lateral force procedure and elastic procedures using demand
capacity ratios. The most basic inelastic analysis method is the complete non linear
time history analysis, which at this time is considered overly complex and impractical
for general use. Available simplified nonlinear method referred to as nonlinear static
analysis procedure; include the capacity spectrum method (CSM) that uses the
intersection of capacity (pushover) curve and a reduced response spectrum to estimate
maximum displacement. Simplified nonlinear static analysis procedure using
pushover method such as the capacity spectrum method and the displacement
coefficient method requires determination of three primary elements: capacity,
demand (displacement) and performance. Each of these elements is briefly discussed
below
28
Capacity
The overall capacity of a structure depends on the strength and deformation capacities
of the individual components of the structure. In order to determine capacities beyond
the elastic limits, some form of nonlinear analysis such as Pushover Analysis is
required. This procedure uses a series of elastic analysis, superimposed to
approximate a force-displacement capacity diagram of the structure. The
mathematical model of the structure is modified to account for reduced resistance of
yielding components. A force distribution is again applied until the additional
components yields through forming plastic hinges. This process is continued until the
structure becomes unstable or until the predetermined limit is reached. The push over
capacity curve approximates how the structure behaves after exceeding elastic limit.
Demand (Displacement)
Ground motion during an earthquake produce complex horizontal displacement
patterns in structures that may vary with time. Tracking this motion at every time-step
to determine structural design requirements is judged impractical. Traditional linear
analysis methods use lateral forces to represent a design condition. For nonlinear
methods it is easier and more direct to use a set of lateral displacement demand is an
estimate of the maximum expected response of the building during the ground
motion. The displacement demand is established by use of the conventional response
spectra by covering it onto Spectral Acceleration vs. Spectral Displacement.
Performance
Once a capacity curve and demand displacement is defined, a performance check can
be done. A performance check verifies that structural and nonstructural components
are not damaged beyond the acceptable limits of the performance objective for the
forces and displacement imposed by the displacement demand.
3.3.1 Reduced Demand Spectra
The capacity of a particular building and the demand imposed upon it by a given
earthquake motion are not independent. One source of this mutual dependence is
evident from the capacity curve itself. As the demand increases the structure
29
eventually yields and stiffness decreases. Conversion of the capacity curve to spectral
ordinates (ADRS) makes this concept easier to visualize. Since the seismic
acceleration depends on period, demand also changes as the structure yields. Another
source of mutual dependence between capacity and demand is effective damping. As
a building yield in response to seismic demand it dissipates energy with hysteretic
damping. Building that have large, stable hysteresis loops during cyclic yielding
dissipate more energy than those with pinched loops caused by degradation of
strength and stiffness.
Since the energy dissipated need not be stored in the structure, the effective damping
diminishes displacement demand. The reduced displacement demand is shown in
figure above. The equation for the reduced factor SRA and SRv are given by-
SRA = (3.21- 0.681ln βeff) / 2.12 ≥ value in Table Eq.- 3.6
SRv = (2.31-0.41ln βeff)/ 1.65 ≤ value in Table Eq.- 3.7
Table (3.5): Minimum Allowable SRA and SRv values
Structural Behavior Type SRA SRv
Type A 0.33 0.5
Type B 0.44 0.56
Type C 0.56 0.67
Values for SRA and SRv shall not be less than those shown in this table.
Type A, B and C is taken as defined in ATC 40.
3.3.2 Development of Elastic Site Response Spectra
Elastic response spectra for a site are based on estimate of Seismic Co-efficient, CA
which represents the effective peak acceleration (EPA) of the ground and Cv which
represents 5% damped response of a 1- second system. These coefficients for a
particular zone are dependent on the seismicity of the area, the proximity of the site to
active seismic sources and site soil profile characteristics.
3.3.3 Seismic Zone
Bangladesh is divided into three seismic zones as per BNBC (1993). The table below
shows the values of zone coefficients of Bangladesh.
30
Table 3.6: Seismic Zone Factor, Z
Zone 1 2 3
Z 0.075 0.15 0.25
3.3.4 Seismic Source Type
As per ATC- 40 (1996), three types of seismic source may be defined as a shown in
Table below.
Table 3.7: Seismic source type as per ATC- 40, 1996
Seismic Source
Seismic Source Description Maximum Moment
Slip Rate, SR (mm/ yr)
A Faults which are capable of producing large magnitude events.
M> 7 SR> 5
B All faults other than types A and C N/A N/A
C Faults that are not capable of producing large magnitude events and which have a high rate
M< 6.5 SR< 2
3.3.5 Near Source Factor
Currently data pertaining to the active faults close to Dhaka city is not available. It is
not possible to estimate the seismic source distance from a specific site being
considered in this thesis. But it may be safe to assume that all the sources are located
at distance more than 15 km and the Table(3.8) (ATC- 40, 1996) may be used to
consider the Near Source effects for the present study. The near source factor may be
used on the linear interpolation of values for distance other than those shown in the
table. The closest distance of the seismic source shall be taken as the minimum
distance between the site and the area described by the vertical projection of source on
the surface. The surface projecting need not include portions of the source a depth of
10 km or greater. The largest value of the near source factor considering all sources
shall be used in design.
31
Table 3.8: Seismic Source Factor
Seismic Source Type
Closed Distance to Known Seismic Source
< 2km 5km 10km > 15 km
NA Nv NA Nv NA Nv NA Nv
A 1.5 2 1.2 1.6 1 1.2 1 1 B 1.3 1.6 1 1.2 1 1 1 1
C 1 1 1 1 1 1 1 1
3.3.6 Seismic Coefficients
For each earthquake hazard level, the structure is assigned a seismic coefficient CA in
accordance with Table (3.9) (ATC- 40, 1996) and a seismic coefficient Cv in
accordance with Table (3.10) (ATC- 40, 1996). Seismic coefficient CA represents the
effective peak acceleration (EPA) of the ground. A factor of about 2.5 times of CA
represents the average value of peak response of a 5% damped short period system in
acceleration domain. The seismic coefficient Cv represents 5% damped response of 1
sec system. Cv divided by period (T) defines acceleration response in the velocity
domain. These coefficients are dependent on soil profile type and the product of
earthquake zoning coefficient- Z, severity of earthquake- E and near source factor
(ZEN).The soil profile types are taken from the classification of (ATC- 40, 1996).
The soil profile type SE is applicable for Dhaka City. This type includes any soil
profile with more than 10 feet or soft clay defined as a soil with PI > 20, WMC > 40
and Su< 500 psf. Table 3.9: Seismic coefficient, CA
SF Site Specific Geotechnical Investigation required to determine
CA
32
The value of E used to determine the product, ZEN, should be taken to be equal to 0.5 for the serviceability Earthquake, 1.0 for the design earthquake and 1.25 for serviceability earthquake.
Seismic coefficient CA should be determined by liner interpolation for values of the product ZEN other than those shown in the table.
Table 3.10: Seismic coefficient CV (ATC-40, 1996)
Soil profile type
Shaking Intensity, ZEN
ZEN 0.075 0.15 0.2 0.3
SB 0.08 0.15 0.2 0.3
Sc 0.13 0.25 0.32 0.45 SD 0.18 0.32 0.4 0.54 SE 0.26 0.5 0.64 0.84 SF Site Specific Geotechnical Investigation required to determine CA
The value of E used to determine the product, ZEN, should be taken to be equal to 0.5 for the serviceability Earthquake, 1.0 for the design earthquake and 1.25 for serviceability earthquake.
Seismic coefficient CA should be determined by liner interpolation for values of the product ZEN other than those shown in the table.
According to (ATC-40, 1996), Soil profile types for Dhaka city is SE because it
includes any soil profile with more than 10 feet or soft clay defined as a soil with
PI>20, WMC> 40 and Su < 500 psf.
3.3.7 Establishing Demand Spectra
The purpose of subsequent analysis to be made in this thesis, it is necessary to
establish an earthquake demand spectra against which building performance will be
evaluated. The following controlling parameters are considered:
Location of the site : Dhaka City
Soil profile at the site : Soil type SE as per (ATC-40), soft soil with shear wave
velocity Vs< 600 fps, N< 50 and Su < 100 psf
Earthquake source type: A – considering the events similar to the great Indian
Earthquake in Assam in 12 June, 1897
Near Source Factor : > 15 km
33
Calculation of CA
Seismic Zone Factor, Z 0.15 as per BNBC
Earthquake Hazard Level, E 1 Design Earthquake
Near Source Factor, N 1 > 15 km, Table
Shaking Intensity, ZEN 0.15
For soil type, SE 0.3 From Table
Elastic response spectra, for each earthquake hazard level of interest at a site, isbased
on the site seismic coefficients CA and CV calculated above. The coefficient CA
represents the effective peak acceleration (EPA) of the ground. A factor of about 2.5
times CA represents the average value of peak response of a 5% damped short period
system in the acceleration domain. The seismic coefficient CV represents 5% damped
response of a 1 second system and when divided by period defines acceleration
response in velocity domain.
Calculation of CV
Seismic Zone Factor, Z 0.15 as per BNBC
Earthquake Hazard
Level, E 1 Design Earthquake
Near Source Factor, N 1 > 15 km, Table
Shaking Intensity, ZEN 0.15
For soil type, SE 0.5 From Table
The following establishes 5% damped elastic response spectra as shown in figure 3.3.
Effective peak ground acceleration (EPA) = 0.3g
Average value of peak response = 0.75g
Seismic coefficient, CV = 0.5g
Ts = 0.667 sec Ts =Cv / 2.5 CA
34
Ta = 0.133 sec Ta = 0.2Ts
For seismic performance evaluation purpose, this newly constructed site specific 5%
elastic response spectra need to be converted in to ADRS format using relation-
Sd = (T2/ 4π2) Sa g Eqn. – 3.8
Figure 3.3: 5% Damped Elastic Response Spectrum
Calculated spectral acceleration, spectral displacement with respect to the period is
shown in Table 3.11. These values are used to construct the 5% Elastic response
spectrum in Sa vs. Period format (figure: 3.3) and in ADRS format (figure: 3.4).
35
Figure 3.4: 5% Damped elastic response spectrum in ADRS format
Table 3.11: Response quantities for 5% elastic demand
T (sec) Sa, g Sd, cm
0 0.3 0
0.13 0.75 0
0.667 0.75 82.99705
0.8 0.625 99.49694
1 0.5 124.3712
1.2 0.416667 149.2454
1.4 0.357143 174.1196
1.6 0.3125 198.9939
1.8 0.277778 223.8681
2 0.25 248.7423
2.2 0.227273 273.6166
2.4 0.208333 298.4908
2.6 0.192308 323.365
2.8 0.178571 348.2393
3 0.166667 373.1135
3.2 0.1563 397.9877
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 100 200 300 400 500 600
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement, Sd
36
3.4 CAPACITY CURVE
The nonlinear pushover analysis requires development of the capacity curve. The
capacity curve is derived from a nonlinear analysis for the structure. In the process of
performing this incremental nonlinear static analysis, a capacity curve is developed
for the building. The capacity curve is simply the plot of the total lateral seismic
demand “V”, on the structure, at various increment of loading, against the lateral
deflection of the building at the roof level, under that applied lateral force. If a
building had infinite linear capacity, this capacity curve would be a straight line with
a slope equal to the global stiffness of the structure. Since real building do not have
the infinite linear capacities, the capacity curve typically consists of a series of
straight line segments with decreasing slope, representing the progressive degradation
in structural stiffness that occurs as the building is subjected to increased lateral
displacement, yielding and damage. The slope of a straight line drawn from the origin
of the plot for this curve to a point on the curve at any lateral displacement “d”
represent the secant or “effective” stiffness of the structure when pushed laterally to
that displacement. A typical capacity curve of a hypothetical structure is shown-
Figure 3.5: Typical Capacity Curve.
The discreet points indicated occurrence of important events in the lateral response
history of the structure. Such an event may be the initiation of yield in a particulars
structural element or a particular type of damage, such as spalling of cover concrete
on a column or shear failure of a spandrel element. Each point is determined by a
37
different analysis sequence. Then by evaluating the cumulative effects of damage
sustained at each of the individual events and the overall behavior of the structure is
increasing lateral displacement, it is possible to determine and indicate on the capacity
curve those total structural lateral displacements that represent limits on the various
structural performance levels, as has been done in Fig.3.5 . The Immediate Occupancy
(IO), the Life Safety level (LS) and the Structural Stability level (SS) are three
performance levels.
The point on the capacity curve at which the first element exceeds the permissible
deformation level for a structural performances level does not necessarily represent
that the structural performance level. Most structures contain many elements and have
considered redundancy. Consequently, the onset of unacceptable damage to a small
percentage of these elements may not represent an unacceptable condition with regard
to the overall performance of the building. When determining the points along the
capacity curve for the structure at which the various structural performance level may
said to be reached, the engineer must view the performance of a building as whole and
consider the importance of damage predicted for the various elements on the overall
behavior of the building.
The methodology described in ATC- 40 (1996), incorporates the concept of
“Primary” and “Secondary” elements to assist the engineers in making these
decisions. Primary elements are those that are required as part of the lateral force
resisting system for the structure. All the other elements are designated as secondary
elements. For a given performance level, secondary elements are generally permitted
to sustain more damage than primary elements since degradation of secondary
elements does not have a significant effect on the lateral load resisting capability of
building. If in the development of the capacity curve it is determined that a few
element fail to meet the acceptance criteria for a given performance level at an
increment of lateral loading and displacement, the engineer has the ability to liberal
acceptance criteria for these few elements. Care is exercised not to designate an
excessive number of elements that are effective in resisting lateral force as secondary.
38
3.4.1 Capacity Spectrum Method
The capacity spectrum method, a nonlinear static procedure, provides a graphical
representation of global force-displacement capacity curve of the structure and
compares it to the response spectra representations of the earthquake demand. This
method is a very useful tool in the evaluation and retrofit design of existing concrete
buildings. Capacity spectrum is the simple representation of the capacity curve in
ADRS domain. A capacity curve is the representation of Base shear to roof
displacement. In order to develop the capacity spectrum from a capacity curve it is
necessary to do a point by point conversion to first mode spectral co ordinates. Figure
3.6 shows a typical spectrum converted from capacity curve of a hypothetical
structure. It is seen that in the capacity spectrum that up to some displacement
corresponding to 1st point while the structure is in elastic deformation. The structure
deflects more to 2nd point. It goes to inelastic deformation. When Sa vs. Sd capacity
Figure: 3.6 Capacity Curve
curve is plotted, radial lines drawn from the origin of the plot through the curve at
various spectral displacements has a slope where ω is the radial frequency of the
effective first mode response of the structure if pushed by an earthquake to that
spectral displacement. Using the relationship T= 2π/ ω, it is possible to calculate, for
each of this radial lines, the effective period of the structure if it is pushed to a given
spectral displacements.
0
0.05
0.1
0.15
0.2
0.25
0 50 100 150 200
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement, Sd (mm)
39
3.5 PERFORMANCE POINT
The capacity spectrum method initially characterizes seismic demand using an elastic
response spectrum. This spectrum is plotted in spectral ordinates (ADRS) format
showing the spectral acceleration as a function of spectral displacement. This format
allows the demand spectra to be “overlaid” on the capacity spectrum for the building.
The intersection of the demand and capacity spectra, if located in the linear range of
the capacity, would define the actual displacement for the structure; however this is
not normally the case as most analysis includes some inelastic behavior. To find the
point where demand and capacity are equal, a point on the capacity spectrum need to
be selected as an initial estimate. Using the spectral acceleration and displacement
defined by this point, reduction factors may be calculated to apply to the 5% elastic
spectrum to account for the hysteretic energy dissipation or effective damping,
associated with the specific point. If the reduced demand spectrum intersects the
capacity spectrum at or near the initial assumed point, then it is the solution for the
unique point where capacity equals demand. If the intersection is not reasonably close
to the initial point, then a new point somewhere between may be assumed and repeat
the process until a solution is reached. This is the performance point where the
capacity of the structure matches the demand or the specific earthquake.
Once the performance point has been determined, the acceptability of a rehabilitation
design to meet the project performance objectives can be judged by evaluating where
the performance points falls on the capacity curve. For the structure and earthquake
represented by the overlay indicated in Figure 3.7, indicating that for this earthquake
this structure would have less damage than permitted for the Life Safety level and
more than would be permitted for the Immediate Occupancy level.
40
Figure 3.7: Determination of performance point
With this information, the performance objective and/ or the effectiveness of the
particular rehabilitation strategy to achieve the project performance objectives can be
judged.
3.5.1 Non linear Static Procedure for Capacity evaluation of Structures
Instead of comparing forces, nonlinear static procedures use displacements to
compare seismic demand to the capacity of a structure. This approach included
consideration of the ductility of the structure on an element by element basis. The
inelastic capacity of a building is then a measure of its ability to dissipate earthquake
energy. The current trend in seismic analysis is toward these simplified inelastic
procedures.
The recommended central methodology is on the formulation of inelastic capacity
curve for the structure. This curve is a plot of the horizontal movement of a structure
as it is pushed to one side. Initially the plot is a straight line as the structure moves
linearly. As the parts of the structure yield the plot begins to curve as the structure
softens. This curve is generated by building a model of the entire structure from
nonlinear representation of all of its elements and components. Most often this is
accomplished with a computer and structural analysis software. The specific forces
and displacement characteristics are specified for each piece of the structure resisting
the earthquake demand. These pieces are assembled geometrically to represent the
Performance Point
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 100 200 300 400 500 600
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement, Sd (mm)
41
complete lateral load resisting system. The resulting model is subjected to increasing
increment of load in a pattern determined by its dynamic properties. The
corresponding displacements define the inelastic capacity curve of the building. The
generation of capacity curve defines the capacity of the building uniquely and
independently of any specific demand. When an earthquake displaces the building
laterally, its response is represented by a point on this curve. A point on the curve
defines a specific damage state of the building. The deformation of its entire
components can be related to the global displacement of the structure.
Building capacity and demand requires from earthquake are mutually dependent
which is depicted by capacity curve. As the demand increases the structure eventually
yields and stiffness decreases. Its period lengthens. Since the seismic accelerations
depend on period, demand also changes as the structure yields. Another source of
mutual dependence between capacity and demand is effective damping. As building
yields in response to seismic demand, it dissipates energy with yielding dissipate
more energy than those with pinched loops caused by degradation of strength and
stiffness. Since the energy that is dissipated need not be stored in the structure, the
damping has the effect of diminishing displacement demand.
3.5.2 Structural Performance Levels and Ranges
The performance of a building under any particular event is dependent on a wide
range of parameters. These parameters are defined (ATC-40, 1996; FEMA 356, 2000)
qualitatively in terms of the safety afforded by the building to the occupants during
and after the event; 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. These
performance characteristics are directly related to the extent of damage that would be
sustained by the building.
The Federal Emergency Management Agency in its report ‘pre-standard and
Commentary for the Seismic Rehabilitation of Buildings, (FEMA-356, 2000) defines
the structural performance levels and two intermediate structural performance ranges.
42
The discrete Structural Performance Levels are –
Immediate Occupancy (S-1)
Life Safety (S-3)
Collapse Prevention (S-5) and
Not Considered (S-6)
The Intermediate Structural Performance Ranges are-
Damage Control Range (S-2) and
Limited Safety Range (S-4)
The definition of these performance ranges are given by FEMA (FEMA-356, 2000)
Acceptance criteria for performance within the Damage Control Structural
Performance Range may be obtained by interpolating the acceptance criteria provided
for the Immediate Occupancy and Life Safety Levels. The performance levels and
ranges. As per FEMA (FEMA-356, 2000), are described in the sections that follow.
After analysis in case where structure collapses before reaching performance
point, the value of βeff is taken from the step where base shear reaches its
maximum i.e. from the collapse state.
In case of soft story structure, if fails to meet performance point, base shear
and hinge status are considered from collapse state for comparison.
4.8.1 Performance Evaluation of the Structure 1
Table 4.2: Effective damping and spectral reduction factor for structure 1
Frame Type Bare Frame Soft Story (40%
infill)
Effective Damping, βeff 10.40% 10.80%
Spectral Reduction Factor, SRA 0.762 0.749
Spectral Reduction Factor, SRv 0.818 0.809 Seismic State Co-efficient, CA 0.3 Seismic State Co-efficient, CV 0.5
Figure 4.2: Comparison of capacity spectrum of structure 1 for different infill
condition
0
0.1
0.2
0.3
0.4
0.5
0.6
0 50 100 150 200 250 300
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement, Sd mm
CC 40% infill
EDRS 40% infill
EDRS Bare Frame
CC Bare Frame
57
Table 4.3: Effective damping and spectral reduction factor for structure 1
Frame Type Bare Frame Soft Story (60%
infill)
Effective Damping, βeff 10.40% 10.90% Spectral Reduction Factor, SRA 0.762 0.747 Spectral Reduction Factor, SRv 0.818 0.808 Seismic State Co-efficient, CA 0.3 Seismic State Co-efficient, CV 0.5
Figure 4.3: Comparison of capacity spectrum of structure 1 for different infill condition
Table 4.4: Effective damping and spectral reduction factor for structure 1
Frame Type Bare Frame Soft Story
(80% infill)
Effective Damping, βeff 10.40% 11.30%
Spectral Reduction Factor, SRA 0.762 0.735
Spectral Reduction Factor, SRv 0.818 0.795
Seismic State Co-efficient, CA 0.3
Seismic State Co-efficient, CV 0.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0 50 100 150 200 250 300
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement. Sd (mm)
CC 60% infill
EDRS 60% infill
CC 60% infill
EDRS Bare Frame
58
Figure 4.4: Comparison of capacity spectrum of structure 1 for different infill
condition
Structure 1 is a six storied structure. Detailed configuration is given in section 4.7
under this chapter. The capacity spectrum of the structure is shown in figure 4.2 to 4.4
and table 4.2 to 4.4. From evaluation, it has been found that capacity of bare frame
meets demand but structure has to deform a considerable amount to meet the demand
curve. As a result some of its elements are stressed above their elastic limit and
elements become nonlinear. Fig. 4.2 to 4.4 describes the fact more clearly. It has also
been observed in case of soft storied structure with the increase in infill the value of
βeff increases but capacity spectrum never meets the demand curve. Columns of the
ground floor collapse before reaching the demand result the failure of the structure.
Table 4.5: Base Shear Comparison among different methods for structure 1
Base Shear (KN) Bare Frame 40% infill 60% infill 80% infill
ESFM Method 2104 2104 2104 2104
RSM Method 3299 3760 4234
Push Over Method 3797 5570 5789 5958
Table above shows, the more the presence of infill above the ground story the more is
the value of base shear because story above are stiffer than the ground floor.
0
0.1
0.2
0.3
0.4
0.5
0.6
0 50 100 150 200 250 300
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement. Sd mm
CC 80% infill
EDRS 80% infill
CC Bare Frame
EDRS Bare Frame
59
Figure 4.5: Comparison of story shear observed from different method
From table 4.6, it is found that for bare frame structure develops limited number of
hinges beyond life safety performance level at performance point. The base shear
developed at performance point is less than that of the soft story structure because of
no active member in form of diagonal strut.
Table 4.6: Base shear at performance point and number and number of hinges
developed up to performance point
In-fill Condition of Frame
Base Shear (KN)
Status of Hinge Formation at Different Performance Stages
A-B B-IO IO-LS LS-CP CP-C C-D
D-E
>E Total
Bare Frame
3797 1020 205 68 175 0
2 0 1470
Soft story (40% infill)
5570 1049 300 35 85 0 0 1 0 1470
Soft story (60% infill)
5788 1072 292 21 81 0 0 4 0 1470
Soft story (80% infill)
5958 1105 261 19 79 0 2 4 0 1470
0
1000
2000
3000
4000
5000
6000
7000
Base
She
ar, K
N
No infill 40% 60% 80%
ESFM
RSM Method
Push Over Method
60
The following figure 4.6 shows the displacement of structure 1 at different percentage
of infill present. The deformation of soft story is not uniform and also maximum.
Figure 4.6: Comparison of displacement (mm) in X direction
The following figure 4.7 shows the drift at different story level of structure 1 having
different infill percentage.
Figure 4.7.1: Comparison of maximum total drift ratio in X direction of structure 1
0
1
2
3
4
5
6
7
0 50 100 150 200 250 300
No
of s
tory
Displacement (mm)
60% infill
80% infill
40% infill
Bare Frame
0
1
2
3
4
5
6
7
0 0.005 0.01 0.015 0.02 0.025
No.
of S
tory
Drift in X
40% infill
Bare Frame
IO
LS
61
Figure 4.7.2: Comparison of maximum total drift ratio in X direction of structure 1
Figure 4.7.3: Comparison of maximum total drift ratio in X direction of structure 1
Figure 4.7 shows that the drift of the soft ground story is above the level of immediate
occupancy and also non uniform along both directions. Difference of performance
level in bare and soft story is due to stiffness irregularity.
0
1
2
3
4
5
6
7
0 0.005 0.01 0.015 0.02 0.025
No.
of S
tory
Drift , X
60% infill
Bare Frame
IO
LS
0
1
2
3
4
5
6
7
0 0.005 0.01 0.015 0.02 0.025
No
of S
tory
Drift in X
80% infill
bare frame
IO
LS
62
a) Exterior Frame (Bare) b) Interior Frame (Bare)
c) Exterior Frame (Bare) d) Interior Frame (Bare)
Figure 4.8: Deformation pattern of structure 1 at performance point
4.8.2 Performance Evaluation of the Structure 2 Table 4.7: Effective damping and spectral reduction factor for structure 2
Frame Type Bare Frame Soft Story (40% infill)
Effective Damping, βeff 11.50% 11.90% Spectral Reduction Factor, SRA 0.727 0.718 Spectral Reduction Factor, SRv 0.791 0.785 Seismic State Co-efficient, CA 0.3 Seismic State Co-efficient, CV 0.5
63
Figure 4.9: Comparison of capacity spectrum of structure 2 for different infill condition
Table 4.8: Effective damping and spectral reduction factor for structure 2
Frame Type Bare Frame Soft Story
(60% infill)
Effective Damping, βeff 11.50% 12.20%
Spectral Reduction Factor, SRA 0.727 0.71
Spectral Reduction Factor, SRv 0.791 0.746
Seismic State Co-efficient, CA 0.3
Seismic State Co-efficient, CV 0.5
Figure 4.10: Comparison of capacity spectrum of structure 2 for different infill condition
0
0.1
0.2
0.3
0.4
0.5
0.6
0 50 100 150 200 250 300
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement, Sd (mm)
SS 40% infill
EDRS SS 40% infill
EDRS Bare Frame
CC Bare Frame
0
0.1
0.2
0.3
0.4
0.5
0.6
0 50 100 150 200 250 300
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement, Sd (mm)
CC SS 60% infill
EDRS 60% infill
EDRS Bare Frame
CC Bare Frame
64
Table 4.9: Effective damping and spectral reduction factor for structure 2
Frame Type Bare Frame Soft Story (80%
infill)
Effective Damping, βeff 11.50% 12.20%
Spectral Reduction Factor, SRA 0.727 0.71
Spectral Reduction Factor, SRv 0.791 0.746
Seismic State Co-efficient, CA 0.3
Seismic State Co-efficient, CV 0.5
Figure 4.11: Comparison of capacity spectrum of structure 2 for different infill
condition
Structure 2 is an eight storied structure. Detailed configuration is given in section 4.7
under this chapter. The capacity spectrum of the structure is shown in figure 4.9 to
4.11 and table 4.7 to 4.9. From evaluation, it has been found that capacity of bare
frame meets demand but structure has to deform a considerable amount to meet the
demand curve. As a result some of its elements are stressed above their elastic limit
and elements become nonlinear. Fig. 4.9 to 4.11 describes the fact more clearly. It has
also been observed in case of soft storied structure with the increase in infill the value
of βeff increases but capacity spectrum never meets the demand curve. Columns of the
ground floor collapse before reaching the demand result the failure of the structure.
0
0.1
0.2
0.3
0.4
0.5
0.6
0 50 100 150 200 250 300
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement, Sd (mm)
SS 80% infill
EDRS 80% infill
EDRS Bare Frame
CC Bare Frame
65
Table 4.10: Base Shear Comparison among different methods
Base Shear (KN) Bare Frame 40% infill 60% infill 80% infill
ESFM Method 1823 1823 1823 1823
RSM Method 4494 5021 5566
Push Over Method 5570 7420 7816 8136
Table above shows, the more the presence of infill above the ground story the more is the value of base shear because story above are stiffer than the ground floor.
Figure 4.12: Comparison of story shear observed from different method
From table 4.11, it is found that for bare frame structure develops limited number of
hinges beyond life safety performance level at performance point. The base shear
developed at performance point is less than that of the soft story structure because of
no active member in form of diagonal strut.
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Base
She
ar (K
N)
NO infill 40% 60% 80%
ESFM
RSM
Push over
66
Table 4.11: Base shear at performance point and number and number of hinges
developed up to performance point
Infill Condition of Frame
Base Shear (KN)
Status of Hinge Formation at Different Performance Stages
A-B B-IO
IO-LS LS-CP CP-C C-D
D-E
>E Total
Bare Frame
5570 1491 94 54 246 0 0 5 0 1890
Soft Story (40% infill)
7420 1544 216 33 96 0 1 0 0 1890
Soft Story (60% infill)
7816 1548 234 18 88 0 0 2 0 1890
Soft Story (80% infill)
8136 1578 207 22 79 0 2 2 0 1890
The following figure 4.13 shows the displacement of structure 2 at different
percentage of infill present. The deformation of soft story is not uniform and also
maximum.
Figure 4.13: Comparison of displacement (mm) in X direction
0
1
2
3
4
5
6
7
8
9
0 50 100 150 200 250 300 350 400
No.
of S
tore
y
Displacement (mm)
SS 40% infill
SS 80% infill
SS 60% infill
Bare Frame
67
The following figure 4.14.1 - 3 shows the drift at different story level of structure 2
having different infill percentage.
Figure 4.14.1: Comparison of maximum total drift ratio in X direction of structure 2
Figure 4.14.2: Comparison of maximum total drift ratio in X direction of structure 2
0
1
2
3
4
5
6
7
8
9
0 0.005 0.01 0.015 0.02 0.025
No.
of S
tory
Drift in X direction
SS 40% infill
Bare Frame
IO
LS
0
1
2
3
4
5
6
7
8
9
0 0.005 0.01 0.015 0.02 0.025
No.
Sto
ry
Drift in X
SS 60% infill
Bare Frame
IO
LS
68
Figure 4.14.3: Comparison of maximum total drift ratio in X direction of structure 2
Figure 4.14.1- 3, shows that the drift of the soft ground story is above the level of
immediate occupancy and also non uniform along both directions. Difference of
performance level in bare and soft story is due to stiffness irregularity.
4.8.3 Performance Evaluation of the Structure 3
Table 4.12: Effective damping and spectral reduction factor for structure 3
Frame Type Bare Frame Soft Story (40% infill)
Effective Damping, βeff 11.20% 11.60%
Spectral Reduction Factor, SRA 0.738 0.727
Spectral Reduction Factor, SRv 0.799 0.791
Seismic State Co-efficient, CA 0.3
Seismic State Co-efficient, CV 0.5
0
1
2
3
4
5
6
7
8
9
0 0.005 0.01 0.015 0.02 0.025
No.
of S
tory
Drift in X
SS 80% infill
Bare Frame
IO
LS
Linear (LS)
69
Figure 4.15: Comparison of capacity spectrum of structure 3 for different infill
condition
Table 4.13 Effective damping and spectral reduction factor for structure 3
Frame Type Bare Frame Soft Story (40% infill)
Effective Damping, βeff 11.20% 11.60%
Spectral Reduction Factor, SRA 0.738 0.727
Spectral Reduction Factor, SRv 0.799 0.791
Seismic State Co-efficient, CA 0.3
Seismic State Co-efficient, CV 0.5
Figure 4.16: Comparison of capacity spectrum of structure 3 for different infill
condition
0
0.1
0.2
0.3
0.4
0.5
0.6
0 100 200 300 400
Spec
tral
Acc
elar
atio
n, S
a (g
)
Spectral Displacement, Sd mm
CC SS 40% infill
EDRS 40% infill
EDRS Bare Frame
CC Bare Frame
0
0.1
0.2
0.3
0.4
0.5
0.6
0 100 200 300 400
Spec
tral
Acc
elar
atio
n, S
a (m
m)
Spectral Displacement, mm
CC SS 60% infill
EDRS 60% infill
CC Bare Frame
EDRS Bare Frame
70
Table 4.14 Effective damping and spectral reduction factor for structure 3
Frame Type Bare Frame Soft Story (80% infill)
Effective Damping, βeff 11.20% 11.7
Spectral Reduction Factor, SRA 0.738 0.724
Spectral Reduction Factor, SRv 0.799 0.788
Seismic State Co-efficient, CA 0.3 Seismic State Co-efficient, CV 0.5
Figure 4.17: Comparison of capacity spectrum of structure 3 for different infill condition
Structure 3 is a ten storied structure. Detailed configuration is given in section 4.7
under this chapter. The capacity spectrum of the structure is shown in figure 4.15 to
4.17 and table 4.12 to 4.14. From evaluation, it has been found that capacity of bare
frame meets demand but structure has to deform a considerable amount to meet the
demand curve. As a result some of its elements are stressed above their elastic limit
and elements become nonlinear. Fig. 4.15 to 4.17 describes the fact more clearly. It
has also been observed in case of soft storied structure with the increase in infill the
value of βeff increases but capacity spectrum never meets the demand curve. Columns
of the ground floor collapse before reaching the demand result the failure of the
structure.
0
0.1
0.2
0.3
0.4
0.5
0.6
0 100 200 300 400
Spec
tral
Acc
elar
atio
n, S
a
Spectral Displacement, Sd
SS CC 80% infill
EDRS 80% infill
EDRS Bare Frame
CC Bare Frame
71
Table 4.15: Base Shear Comparison among different methods
Base Shear (KN) Bare Frame 40% infill 60% infill 80% infill
ESFM Method 2104 2104 2104 2104
RSM Method
3299 3760 4234
Push Over 5033 7828 9402 9543
Table above shows, the more the presence of infill above the ground story the more is
the value of base shear because story above are stiffer than the ground floor.
Figure 4.18: Comparison of story shear observed from different method
From table 4.17, it is found that for bare frame structure develops limited number of
hinges beyond life safety performance level at performance point. The base shear
developed at performance point is less than that of the soft story structure because of
no active member in form of diagonal strut.
Table 4.16: Base shear at performance point and number and number of hinges
developed up to performance point
In-fill Condition of
Frame
Base Shear (KN)
Status of Hinge Formation at Different Performance Stages