Capacity Spectrum Method for RC Building with Cracked and Uncracked Section

IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE)
e-ISSN: 2278-1684,p-ISSN: 2320-334X, Volume 10, Issue 2 (Nov. - Dec. 2013), PP 58-74
www.iosrjournals.org
www.iosrjournals.org 58 | Page
Capacity Spectrum Method for RC Building with Cracked and
Uncracked Section
Dubal A. C1
, Dr. D.N.Shinde2
M.E Student of PVPIT Institute,Budhgaon.India
M.E. Co-ordinator civil Engineering Dept., PVPIT Institute Budhgaon. India
Abstract: one of the most widespread procedures for the assessment of building behavior, due to earthquake,
is the Capacity Spectrum Method (CSM). In the scope of this procedure, capacity of the structure compares with
the demands of earthquake ground motion on the structure. The capacity of the structure is represented by a
nonlinear force-displacement curve, referred to as a pushover curve. The base shear forces and roof
displacements are converted to equivalent spectral accelerations and spectral displacements, respectively, by
means of coefficients that represent effective modal masses and modal participation factors. These spectral
values define the capacity spectrum. The demands of the earthquake ground motion are represented by response
spectra. A graphical construction that includes both capacity and demand spectra, results in an intersection of
the two curves that estimates the performance of the structure to the earthquake.
In this study, for determination of the performance levels, G+10 R.C.C. Building with cracked and uncracked
section were taken. The structural Capacity of cracked and uncracked section compared with performance point
value, which shows the structural capacity of building having cracked section is lesser than the uncracked
section. Different modeling issues were analyzed to study the effect on Capacity of the structure with cracked
and uncracked section for different position of Shear wall.
Keywords: Non-Linear Static Analysis (CSM), Pushover Analysis, Response Spectra, Performance Point,
Cracked and uncracked Section.
I. Introduction
The damages and the economical losses during the major earthquakes introduced a new approach in
seismic analysis of Structures called ‘Capacity Spectrum Analysis’. In Capacity Spectrum Analysis and
evaluation of structures under earthquake effects, it is necessary to determine the nonlinear behaviour of
structures. The most basic inelastic analysis method, known as the Time History Analysis, is considered very
complex and impractical for general use. For this reason, nonlinear static analysis methods have become
popular.
The central focus of the nonlinear static analysis methods is the generation of the capacity curve or
pushover curve. This curve represents lateral displacement as a function of the force
applied to the structure. The use of nonlinear static analysis methods for design and evaluation helps engineers
to understand better how structures will behave when subjected to major earthquakes, where it is assumed that
the elastic capacity of the structure will be exceeded (ATC 40, 1996).
The most common used nonlinear static analysis procedures for the evaluation of the performance
levels of structures are the Capacity Spectrum Method, which uses the intersection of the capacity curve with a
reduced response spectrum.
In design of reinforced concrete, we adopt two approaches
1) Uncracked section –Whereby the section is considered uncracked & linear stress distribution assumed.
2) Cracked Section – Whereby the section is considered cracked and/ or the stress distribution is non-linear.
The basic principle of elastic theory is that under flexure, concrete area below NA is in tension and cracks, and
hence neglected in design. Tension is taken by steel reinforcement only. However if tensile stresses do not
exceed certain limit as prescribed in IS456 clause B-4, the section may be treated as uncracked and safe without
contribution of reinforcement in strength (however min reinforcement needs to be provided there too.)
OBJECTIVE OF STUDY
The main Objective of this study is to carry out seismic analysis using capacity spectrum method for
RCC multi-story building (Cracked and Uncracked section) to determine the performance level of building by
considering structural capacity obtained from pushover analysis and earthquake demand obtained from response
spectra is intended. Software used for analysis is finite element based software SAP-2000-12.

Capacity Spectrum Method for RC Building with Cracked and Uncracked Section
V
Roof Disp. ∆
ᵟ
BaseShearV
Fig1 Pushover curve
∆
II. Conceptual Development Of The Capacity Spectrum Method
Simplified nonlinear analysis procedure, such as the capacity spectrum method requires determination
of three primary elements capacity, demand (displacement) and performance. Each of these elements is briefly
discussed below,
Capacity: Structure capacity is represented by a pushover curve. The most convenient way to plot the
force-displacement curve is by tracking the base shear and the roof displacement. A pushover analysis is
performed by subjecting a structure to a monotonically increasing pattern of lateral forces, representing the
inertial forces which would be experienced by the structure when subjected to ground shaking. Under
incrementally increasing loads various structural elements yield sequentially. Consequently, at each event, the
structure experiences a loss in stiffness. Using a pushover analysis, a characteristic nonlinear force-displacement
relationship can be determined. In principle, any force and displacement can be chosen.
Typically the first pushover load case is used to apply gravity load and then subsequent lateral pushover load
cases are specified to start from the final conditions of the gravity. Fig1 Shows the generation of Pushover curve
as below.
In order to use the Capacity Spectrum Method, it is necessary to convert the capacity curve obtained from
pushover analysis in terms of base shear, V and roof displacement ∆, to the capacity spectrum (Fig.2). Capacity
spectrum is the representation of the capacity curve in ADRS (Acceleration Deformation Response Spectrum)
format. This transformation can be done by using Equation 1 and Equation 2.
T
a
V /W
S =
α
1
roof
d
roof
Δ
S =
PF×φ
2
In Equation 1 and Equation 2, the coefficients α and PF are calculated as follows in Equation 3 and 4.
 
 
2
N
i i
i=1
N N
2
i i i
i=1 i=1
Wφ /g
α =
W /g Wφ /g
 
 
 
   
   
   

 
3
 
 
N
i i
i=1
N
2
i i
i=1
Wφ /g
PF =
Wφ /g
 
 
 
 
 
 


4

Sdi
Sa
Sai
Demand: Ground motions 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 use lateral forces to represent a design condition. For a given
structure and ground motion, the displacement demand is an estimate of the maximum expected response of the
building during the ground motion. It is given by spectral acceleration (Sa) Vs. Time period (T) as shown in fig.3
To convert a Response spectrum from the standard Sa vs. T format to ADRS (spectral acceleration vs. Spectral
displacement format which is known as Acceleration-Displacement Response Spectra) format, every point on a
response spectrum curve has associated with it a unique spectral acceleration, Sa spectral velocity, Sv spectral
displacement, Sd and period T.
It is necessary to determine the value of Sdi for each point on the curve, Sai, Ti .
This can be done by Equation 5.
2
i
di ai2
T
S = S ×g
4π
5
Standard demand response spectra contain a range of constant spectral acceleration and a second range of
constant spectral velocity; Sv. Spectral acceleration, Sa and displacement Sd at period Ti are given by equation 6
Fig. 4 shows Demand spectrum curve.
i
di v
T
S S
2π
 ai v
i
2
S S
T

 6
Spectral Displ. (sd)
Spectralacceleration(Sa)
)
Fig.2 Capacity spectrum
AccelerationSa
T
Period T
Fig. 3.Response spectra

Performance point: Performance point can be obtained by
Superimposing capacity spectrum and demand spectrum and the intersection point of these two curves is
performance point. Fig.5. shows superimposition demand spectrum and capacity spectrum.
Check performance level of the structure and plastic hinge formation at performance point. A performance
check verifies that structural and non-structural components are not damaged beyond the acceptable limits of the
performance objective for the force and displacement implied by the displacement demand.
CRACKED AND UNCRACKED SECTION
Uncracked Section
If a structure is subjected to gradually increasing load in the early stages of loading, the applied
moment (at any section) is less than the cracking moment Mcr and the maximum tensile stress fct in the concrete
is less than its flexural tensile strength fcr. This phase is uncracked phase, wherein the entire section is effective
in resisting the moment and is under stress. The uncracked phase reaches its limit when the applied moment
becomes equal to the cracking moment Mcr. In the concrete stress-strain curve the uncracked phase falls within
the initial linear portion.
The Cracking moment is given by the Equation,
t
cr cr
t
I
M f
y
 7
Where, yt is the distance between the neutral axis and the extreme tension fibers, and It is the second moment of
the area of the transformed reinforced concrete section with reference to the N.A.
Cracked Section
As the applied moment exceed Mcr, the maximum tensile stress in concrete exceeds the flexural tensile
strength of concrete and the section begins to crack on the tension side. The cracks are initiated in the bottom
(tensile) fibers of the beam, and with increasing loading, widen and propagate gradually towards the neutral
axis. As the cracked portion of concrete is now rendered ineffective in resisting tensile stresses, the effective
concrete section is reduced.
Fig. 4 Demand spectrum curve.
Spectral displacement (Sd)
Spectral
acceleration(Sa)
Sd
Fig. 5 Performance point representation
Spectral displacement (Sd)
Spectralacceleration(Sa)
Performance point
Demand
spectrum
Sa

For any further increase in the applied moment the tension component has to contribute solely by the reinforcing
steel. With sudden increase in tension in the steel, there is associated increase in tensile strain in the steel bars at
the cracked section. This relatively large increase in tensile strain at the level of steel results in an upward shift
of the neutral axis and increase in curvature at the cracked section.
Cracked and Uncracked Section Properties:
Properties of concrete cracked section and uncracked section based on Gross section i.e. Gross moment of
inertia Ig,
.
3
g
bd
I
12
 8
Moment of inertia for cracked and uncracked section,
Consider a simple rectangular beam (b x h) reinforced with steel reinforcement of As
E
c
– Modulus of Elasticity – concrete
E
s
– Modulus of Elasticity – steel
As- Area of steel
d – Distance to steel
h- Height
b- Width
Fig.no.6 Cross section of beam
The centroid and moment of inertia is given by the equation,
Uncracked Section
 
 
2
s
i i
si
bh
n 1 A dy A 2y
bh n 1 AA
 
 
 

 9
I    
23 2
s
bh h
y bh d y n 1 A
12 2
 
      
  10
Cracked Section
 
2y
n 2n n
d
 
       
 
11
…..Solve for the centroid by multiplying the result by d
 
3
2
s
by
I d y nA
3
  
12
To check the capacity of Uncracked and cracked section following simple beam problem is taken.
d = 380mm b = 300mm h = 420mm
Es = 200000Mpa Ec = 25000 Mpa
Using 4 bars of 20mm dia. As=1256.63mm2
s
c
E 200000
n 8
E 25000
  
Using above formulae we get the centroid and moment of inertia for Uncracked and cracked section as below
Uncracked section Cracked Section
y = 221.09mm y = 129.428mm
s
c
E
E
n 

I 6 4
2089.98 10 mm  I 6 4
848.006 10 mm 
In above problem it is observed that centroid shifted from 221.09mm to 129.428mm and moment of inertia
decreases from I 6 4
2089.98 10 mm  for uncracked section to I 6 4
848.006 10 mm  for cracked section. The
cracked section loses more than half of its capacity.
Code specification for cracked and uncracked section:
Cracked section are those in which the extreme fiber stresses exceeds the modulus of rupture fcr specified by the
code,
Cracking moment obtained using formula
t
cr cr
t
I
M f
y

Where,
It = second moment of area of transformed RC section and
yt =Dist between NA and extreme tension member
Code IS-456 clause 2.2 suggest formula for
cr ck
f 0.7 f 
Corresponding suggested by code ACI 318 M-05 (American concrete Institute) is,
cr ck
f 0.623 f 
The recent issue of ACI 318-08 gives the following formula,
cr ck
f 0.55 f 
Where, λ is modification factor for light weight concrete for normal weight concrete λ=1.0
For light weight concrete,
ct
ck
f
1.0
0.5 f
 
   
 
 
Where, fct is spalling tensile strength of light weight concrete
Modification factor for cracked section as per the code ACI 318M-05 (Section 10.10.4.1)
1) Moment of Inertia of Columns (Iyy and Izz) = 0.7Ig
No reduction in Ixx (Torsion) and Ax, Ay, Az
2) Moment of Inertia of Beams (Iyy and Izz) = 0.35Ig
No reduction in Ixx (Torsion) and Ax, Ay, Az
Where, Ig is Gross Moment of Inertia given by,
The above section properties are used for modeling of
building in the software SAP-2000.
PROBLEM FORMULATION & MODELING
In this study, for determination of the performance levels, G+10 R.C.C. Building with cracked and
uncracked section were taken. The structural Capacity of cracked and uncracked section compared with
performance point value. Different modeling issues were analyzed to study the effect on Capacity of the
structure in building with cracked and uncracked section for different position of Shear wall.
The example building is G+10 R.C.C. Multi-storey Residential building considered with following details.
1) Plan size 33.40m×12m
2) No of Stories 11(G+10)
3) Floor Height 3m
4) Imposed Load 3kN/m2
5) Materials Concrete (M 30) Reinforcement (Fe 415)
6) Depth of Slab 150mm
7) Thickness of wall 230mm
All beams are of uniform size of 400 × 600mm.

Column Section Properties
Story Column Size(mm)
Base- F2 650 x 650
F3-F6 550 x 550
F7-Roof 450 x 450
Fig. 7 Plan of building
Material Properties
1) Concrete-
M 30, Density-2500 Kg/m3
, Young’s Modulus E- 27386 N/mm2
, Poisson’s Ratio-0.2
2) Steel-
Fe 415, Density-7850 Kg/m3, Young’s Modulus E -2.1 x 105
N/mm2
, Poisson’s Ratio-0.3
Seismic parameters:
Location : Mumbai (zone ш)
Ground condition : Type Medium soil
Importance factor : 1
Response reduction factor : 3
Zone factor : 0.16
Response Spectra : IS 1893(Part1) 2002
Analysis is carried out for Push X and Push Y as shown in Fig no.8 (Pushing Structure in X and Y direction).
Fig no. 8 Directions of Push-X and Push-Y
Capacity Spectrum Analysis is carried out for above G+10 building using Finite Element based software Sap-
2000 for different cases below,
1) Uncracked Section without Shear wall
2) Cracked Section without shear wall
For Different position of shear wall as shown in fig no
Shear wall position in Y-Direction (Fig. No.9)
3) Case 1 4) Case 2 5) Case 3 6) Case 4
Fig. 9 Different position of Shear wall in y-Direction
Shear wall position in X-Direction (Fig. No.10)

7) Case 1 8) Case 2
Fig. 10 Different position of Shear wall in x-Direction
The model created and analyze in SAP-2000 for above cases as shown in fig. Also pushover curve, Hinge
formation and Capacity Spectrum curve as shown in fig. below.
Fig.8 G+ 11 Models in SAP-2000
Fig.12 Pushover Curve
Fig.13 Hinge Formation

Fig.14 Capacity Spectrum Curve
.
III. Results And Discussion:
The Example building is analyze for the performance objective of Life Safety Performance level(
FEMA-273) and the result obtained from the analysis for performance point value using software SAP-2000 is
presented in the form of table as below,
Performance Point values:
a) For uncracked and cracked section without shear wall
For Push-X Direction
Table no.1 Base Shear, Roof Displacement, for Push-X
Analysis cases
Base Shear
Force KN
Displacement mm
Uncracked
without shear
wall
6617.409 43
Cracked
without shear
wall
5498.574 58
For Push-Y Direction
Table no.2Base Shear, Roof Displacement, for Push-Y
Analysis cases
Base Shear Force
KN
Displacement mm
Uncracked
without shear wall
6408.876 47
Cracked
without shear wall
5357.262 56
b) For uncracked section with different position of shear wall in y-direction For Push-X Direction
Table no.3
For Push-X for different position of shear wall in y-direction
Analysis cases
Base Shear
Force KN
Displacement mm
Uncracked without
shear wall
6617.409 43
Shear Wall At Case 1 7034.59 47
Case 2 6922.328 45
Case 3 6907.283 54
Case 4 6868.675 58
Table no.4 for Push-Y different position of shear wall in y-direction
Analysis cases
Base Shear
Force KN
Displacement mm
Uncracked without
shear wall
6408.876 47
Case 2 9942.322 11
Case 3 10454.001 16
Case 4 9963.118 22

c) For cracked section with different position of shear wall in y-direction For Push-X Direction
Table no.5
For Push-X, different position of shear wall in y-direction
Analysis cases
Base Shear
Force KN
Displacement
mm
cracked without shear
wall
5498.574 58
Case 2 6571.026 60
Case 3 6520.598 59
Case 4 6101.898 62
Table no.6
For Push-Y, different position of shear wall in y-direction
Analysis cases
Base Shear
Force KN
Displacement
mm
cracked without shear
wall
5357.262 56
Case 2 9648.755 11
Case 3 10451.092 18
Case 4 9666.018 23
d) For uncracked section with different position of shear wall in x-direction
Table no.7
For Push-X for different position of shear wall in x-direction
Analysis cases
Base Shear
Force KN
Displacement
z mm
Uncracked without shear
wall
6617.409 43
Case 2 11096.005 11
Table no.8
For Push-Y for different position of shear wall in x-direction
Analysis cases
Base Shear Force
KN
Displacement
mm
Uncracked without
shear wall
6408.876 47
Shear Wall At
Case 1
9618.200 42
Case 2 9382.672 43
e) For cracked section with different position of shear wall in x-direction
Table no.9
For Push-X for different position of shear wall in x-direction
Analysis cases Base Shear Force KN
Displacement
mm
cracked without
shear wall
5498.574 58
Shear Wall At Case
1
10366.327 15
Case 2 10226.381 15
Table no.10 For Push-Y for different position of shear wall in x-direction
Analysis cases
Base Shear Force
KN
Displacement
mm
cracked without
shear wall
5357.262 56
Shear Wall At Case
1
5806.044 54
Case 2 5932.383 54

Interstory Drift
a) For uncracked and cracked section without shear wall
Table No.11 InterStory Drift for Uncracked & Cracked Section without shear wall
Interstory Drift
Push-X Push-Y
Story Uncracked
without shear
wall
Cracked
without
shear wall
Uncracked
without shear
wall
Cracked
without
shear wall
11 0.19667 0.31 0.08333 0.0867
10 0.27333 0.38333 0.13667 0.14
9 0.32 0.43 0.1933 0.2033
8 0.37333 0.48333 0.24667 0.2733
7 0.44333 0.54 0.29667 0.3466
6 0.47 0.55 0.31 0.3766
5 0.52333 0.55333 0.3533 0.4333
4 0.57 0.64333 0.3966 0.49
3 0.59667 0.57 0.39 0.4966
2 0.59667 0.51333 0.3633 0.47
1 0.58333 0.26667 0.19333 0.3333
Fig.15Interstory Drift for uncracked and cracked section for Push-X
.
Fig.16 Interstory Drift for uncracked and cracked section for Push-Y
b) For uncracked section with different position shear wall in y-direction For Push-X Direction
0
2
4
6
8
10
12
0 0.2 0.4 0.6
Story
InterstoryDrift
Cracked section
Uncracked
section
0
2
4
6
8
10
12
0 0.5 1
Uncracked
cracked
Story
InterstoryDrift

Table No.12 InterStory Drift for Uncracked Section with Different Position of Shear Wall in y-direction for
Push-X
Story
Interstory Drift
Uncracked Section
case1 case2 case3 case4
11 0.176667 0.186667 0.213333 0.246667
10 0.236667 0.253333 0.28 0.32
9 0.293333 0.303333 0.34 0.383333
8 0.353333 0.363333 0.41 0.443333
7 0.41 0.42 0.47 0.51
6 0.456667 0.466667 0.513333 0.553333
5 0.503333 0.51 0.563333 0.613333
4 0.553333 0.563333 0.636667 0.676667
3 0.56 0.576667 0.656667 0.7
2 0.6 0.59 0.683333 0.716667
1 0.34 0.326667 0.396667 0.406667
.
Fig.17 Interstory Drift for uncracked section with different position of shear wall in y-direction for Push-X
Table No.13 InterStory Drift for Uncracked Section with Different Position of Shear Wall in y-direction for
Push-Y
Story
Interstory Drift
Uncracked Section
11 0.15667 0.16667 0.16333 0.15667
10 0.15667 0.17 0.17 0.19333
9 0.16 0.17 0.1667 0.22333
8 0.16 0.1667 0.1667 0.25
7 0.15667 0.16 0.16 0.27667
6 0.15333 0.15667 0.15667 0.28333
5 0.15 0.1433 0.14667 0.32
4 0.1333 0.12667 0.13 0.36667
3 0.1233 0.10667 0.1133 0.38667
2 0.09667 0.07667 0.1 0.38
1 0.06667 0.03667 0.0633 0.23667
0
2
4
6
8
10
12
0 0.2 0.4 0.6 0.8
case 1
case2
case3
case4
Story

.
Fig.18Interstory Drift for uncracked section with different position of shear wall in y-direction for Push-Y
c) For cracked section with different position shear wall in y-direction For Push-X Direction
Table No.14 InterStory Drift for Cracked Section with Different Position of shear Wall in y-direction for Push-
X
Story
Interstory Drift
Cracked
11 0.123333 0.293333 0.233333 0.263333
10 0.163333 0.366667 0.296667 0.326667
9 0.19 0.423333 0.346667 0.373333
8 0.226667 0.486667 0.393333 0.423333
7 0.256667 0.55 0.443333 0.47
6 0.276667 0.613333 0.463333 0.496667
5 0.296667 0.633333 0.5 0.526667
4 0.306667 0.706667 0.52 0.543333
3 0.283333 0.733333 0.496667 0.516667
2 0.24 0.746667 0.456667 0.466667
1 0.113333 0.393333 0.23 0.233333
.
Fig.19 Interstory Drift for Cracked section with different Position of shear wall in y-direction for Push-X
Table No.15 InterStory Drift for Cracked Section with Different Position of shear Wall in y-direction for Push-
Y
Story
Interstory Drift
Cracked
11 0.19667 0.25667 0.24 0.17
10 0.2033 0.25333 0.24 0.22
9 0.2033 0.25333 0.23667 0.24667
8 0.2033 0.25 0.2233 0.2733
0
2
4
6
8
10
12
0 0.2 0.4 0.6
Story
InterstoryDrift
case1
Case2
Case3
Case4
0
2
4
6
8
10
12
0 0.5 1
cracked
case1
case2
case3
case4
story

7 0.2033 0.2433 0.21667 0.2933
6 0.1933 0.2333 0.20333 0.3
5 0.19 0.22 0.19 0.33667
4 0.17667 0.1933 0.17667 0.39
3 0.15667 0.17333 0.17 0.42667
2 0.13 0.13333 0.18333 0.45667
1 0.09 0.0733 0.13667 0.29
.
Fig.20 Interstory Drift for Cracked section with different Position of shear wall in y-direction for Push-Y
d) For uncracked section with different position shear wall in x-direction
Table No.16 InterStory Drift for Uncracked Section with Different Position of shear Wall in x-direction
Story
Uncracked Section
Push-X Push-Y
11 0.19333 0.13 0.13333 0.10667
10 0.20333 0.14 0.18 0.17333
9 0.20333 0.13667 0.20333 0.22333
8 0.20333 0.14 0.22667 0.25667
7 0.20333 0.13667 0.24 0.29
6 0.19667 0.13 0.24333 0.30667
5 0.19 0.12667 0.25 0.32667
4 0.17 0.11667 0.25 0.33
3 0.15 0.10333 0.22667 0.31667
2 0.12333 0.10667 0.19333 0.29667
1 0.07 0.1 0.09 0.1
(a)
0
2
4
6
8
10
12
0 0.1 0.2 0.3 0.4 0.5
case1
Case2
Case3
Case4
0
2
4
6
8
10
12
0 0.1 0.2 0.3
Story
Interstorydrift
case1
Case2

.
(b)
Fig.21Interstory Drift for Uncracked section with different Position of shear wall in x-direction for Push-X (a)
Push-Y (b)
e) For cracked section with different position shear wall in x-direction
Table No.17 InterStory Drift for Cracked Section with Different Position of shear Wall in x
Direction
(a)
0
2
4
6
8
10
12
0 0.1 0.2 0.3 0.4Story
Interstory Drift
case1
Case2
Story
Cracked Section
Push-X Push-Y
11 0.15333 0.22 0.16 0.14
10 0.15667 0.22 0.21 0.19667
9 0.15667 0.22333 0.24667 0.24333
8 0.15667 0.22 0.29 0.29333
7 0.15333 0.21667 0.33333 0.34333
6 0.14667 0.20667 0.36 0.37667
5 0.14 0.19333 0.39667 0.41667
4 0.12333 0.17667 0.41667 0.44667
3 0.10667 0.15333 0.4 0.44
2 0.08 0.12333 0.35333 0.39
1 0.04333 0.07 0.16333 0.18667
0
2
4
6
8
10
12
0 0.1 0.2 0.3
Story
Interstory drift
case1
Case2

(b)
Fig.22 Interstory Drift for Cracked section with different Position of shear wall in x-direction for Push-X (a)
Push-Y (b)
IV. Discussion:
From The problem solved it is observed that centroid shifted from 221.09mm to 129.428mm and
moment of inertia decreases from 6 4
2089.98 10 mm for uncracked section to 6
848.006 10 mm for cracked
section. The cracked section looses more than half of its capacity.
In Cracked section Neutral Axis is shifted upwards as compared to uncracked section. Effective cross-section is
reduced in case of cracked section due to Reduction in cross-section of cracked section its moment of inertia is
reduced as compared to uncracked section hence cracked section loses its strength (Capacity).
Comparison of base shear and Roof displacement
From the tables no.1 it shows that the base shear at performance point for Push-X increases from
5498.574KN for cracked section to 6617.409KN for uncracked section, the roof displacement at performance
point is decreases from 58mm for cracked section to 43mm for uncracked section. Also From the tables no.2 it
shows that the base shear at performance point for Push-Y increases from 5357.262KN for cracked section to
6408.876KN for uncracked section, the roof displacement at performance point is decreases from 56mm for
cracked section to 47mm for uncracked section. For both Uncracked and Cracked section the base shears
increases and roof displacement is reduced in Push-X direction compared to Push-Y direction.
From table no.3 for uncracked section with shear wall in y-direction for Push-X the base shear at
performance point for position of shear wall at case 1 is7034.59KN which is more than all other cases and roof
displacement 47mm which is less than all other cases. And also from table no.4 for Push Y base shear for case1
and case2 is 9522.756KN and 9942.322KN and roof displacement is 12mm and 11mm which are good result
compared to all other cases. But considering both Push-X and Push-Y shear wall position Case1gives better
result than the all other case. Similarly from table no.5 and 6 for cracked section shear wall position case1 result
better than all other cases. For both Uncracked and cracked section with shear wall in y-direction the base shears
increases and roof displacement is reduced in Push-Y direction compared to Push-X direction.
From table no.7 for uncracked section with shear wall in x-direction for Push-X the base shear at performance
point for position of shear wall at case1 and case2 is 10497.671KN and 11096KN and roof displacement is
11mm for both cases1 and case2. And also from table no. 8 for Push-Y base shear for case1 and case2 is
9618.200KN and 9382.672KN and roof displacement is 42mm and 43mm. considering both Push-X and Push-Y
result the case1 is having good result. Similarly from table no.9 and 10 for cracked section shear wall position
case1 result good than all other cases. For both Uncracked and cracked section with shear wall in x-direction the
base shears increases and roof displacement is reduced in Push-X direction compared to Push-Y direction.
Comparison of Drift
From table no.11 and fig.no.15 and 16 it is observed that the building interstory drifts with uncracked
section is less than the cracked section for Push-X and Push-Y. From table no. 12 and 13 and from fig.no.17 and
18 for uncracked section with shear wall in y-direction for Push-X and Push-Y for position of shear wall at case
1 shows less interstory drifts than all other position of shear wall cases. Also from table no.14 and 15 and from
fig.no.19 and 20 for cracked section with shear wall in y-direction for Push-X and Push-Y for case 1 less
interstory drift. Similarly for uncracked and cracked section for shear wall in x-direction for both Push-X and
Push-Y giving less interstory drift results for case1.
From above discussion it is also observe that cracked section with shear wall in y-direction for case1
gives good result for Push-Y i.e. base shear 8848.061KN and roof displacement 12mm and for cracked section
without shear wall base shear is 5357.262KN and roof displacement 56mm. In case of cracked section with
0
2
4
6
8
10
12
0 0.2 0.4 0.6Stoty
Interstorydrift
case1
Case2

shear wall in x-direction for case 1 gives good result for Push-X i.e. 10366.327KN and roof displacement 15mm
and for without shear wall base shear is 5498.574KN and roof displacement 58mm. It shows that by providing
shear wall at periphery (case1) of building capacity of cracked section is increases compared to uncracked
section.
V. CONCLUSION
The based on above result and discussion, the following conclusion can be drawn.
1) Capacity spectrum method gives graphically clear
Picture of how a building responds to Earthquake Ground motion.
2) Pushover analysis can be effectively used in assessing the seismic performance evaluation of buildings.
3) According to the performance evaluation with the capacity spectrum method, the eleven story (G+10)
reinforced concrete building without shear wall having lesser lateral load capacity (performance point value) in
Push-Y direction than Push-X direction. The given type of rectangular building is stiffer in Push-X direction
than Push-Y direction. The depth (no. of bays) in x direction of building is greater compared to y direction
hence number of bays in x direction is more it provide high stiffness in Push-X. The number bays increases the
lateral load capacity of structure.
4) Considering the result obtained from G+10 reinforced concrete building with shear wall in y direction having
more lateral load capacity(performance point value) for Push-Y compared to Push-X. The shear walls in y
direction are plane elements made of R.C. thin wall having length and thickness providing lateral stiffness to the
structure. Due to high stiffness of shear wall in y direction strength (capacity) of structure is more in Push-Y
direction. Similarly result obtained for shear wall in x direction having more lateral load capacity for Push-X
than Push-Y.
5) From the result obtained and discussion of G+10 R.C building for different position of shear wall, the
position of shear wall at case1 (periphery of building) improve the lateral load capacity (performance pint value
i.e. displacement, drift, hinges formation) compared to all other position of shear wall which is inside the
building for both shear wall in x and y direction. Shear wall close to centre of building are less efficient hence
shear wall along perimeter (case1) are more efficient because shear wall along perimeter of building improves
resistance twist (torsional effect).
Exterior wall like a cage established outside to lateral forces. Shear wall should be provided in both direction
x and y at perimeter of building improves the capacity, if it is provided in one direction a proper moment
resistance frame must be provided in other direction.
6) Based on the result obtained for uncracked and cracked section of G+10 reinforced concrete building at
performance point value, cracked section having lesser lateral load capacity than uncracked section. The
reduction in moment of inertia in cracked section, stiffness of cracked section is reduced compared to uncracked
section this reduction in stiffness looses half of its strength (capacity) of cracked section.
7) From result and discussion the cracked section looses it’s more than half of its capacity than uncracked
section. By providing shear wall at periphery of building the capacity of cracked section is improves more than
uncracked section. Capacity of cracked section less than uncracked section is increases by providing shear wall.
Shear wall behave like rigid diaphragm to resist lateral load in their plane.
Acknowledgement
I deem it my proud privilege to express my heartfelt gratitude to Dr. D.N. Shinde, M.E. Co-ordinator in
civil Engineering Department, PVPIT Institute, Budhgaon. I take this opportunity to express my profound
gratitude to them for their invaluable guidance, continuous encouragement, suggestions, and discussions at
various stages of work. These words are formal thanks, which cannot express the real depth of feeling and
affection that I have towards them.
References
[1]. Taner, Mustafa “Seismic Performance Assessment of Reinforced Concrete Structures” Journal of Engineering Science Cilt: 9 Sayı:
2 sh. 63-76 May 2007
[2]. Mrugesh D. Shah “Performance Based Analysis of R.C.C. Frames” National Conference on Recent Trends in Engineering &
Technology 13-14 May 2011
[3]. Applied Technology Council ATC 40 (1996): “ATC 40 Seismic Evaluations and Retrofit of Concrete Buildings” (V.1) Washington
DC.
[4]. Federal Emergency Management Agency (FEMA) (1997), NEHRP “Guidelines for the Seismic Rehabilitation of Buildings”,
FEMA-273.
[5]. Computers And Structures Inc. (CSI), video tutorials, Berkeley, California
[6]. IS: 1893 (Part 1) 2002- Indian standard- “Criteria for earthquake resistant design of structures”, Bureau of Indian Standards, New
Delhi.

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