DESIGN AND ANALYSIS OF MULTI STORIED STRUCTURES USING STATIC NON LINEAR ANALYSIS

44
International Journal of Research and Innovation (IJRI)
DESIGN AND ANALYSIS OF MULTI STORIED STRUCTURES USING
STATIC NON LINEAR ANALYSIS
P.Swetha1
, K. Mythili2
, G.Venkat Ratnam3
1 Research Scholar, Department Of Civil Engineering, Aurora's Scientific Technological & Research Academy, Hyderabad, India
2 Associate Professor, Department Of Civil Engineering, Aurora's Scientific Technological & Research Academy, Hyderabad, India
3 Associate Professor,Department Of Civil Engineering, Aurora's Scientific Technological & Research Academy, Hyderabad, India
*Corresponding Author:
P.swetha,
Research Scholar, Department of CIVIL Engineering,
Aurora's Scientific Technological & Research Academy,
Hyderabad, India
Published: october 28, 2014
Review Type: peer reviewed
Volume: I, Issue :II
Citation:P.Swetha,(2014)DESIGN AND ANALYSIS OF
MULTI STORIED STRUCTURES USING STATIC NON LIN-
EAR ANALYSIS
INTRODUCTION
GENERAL
Earthquakes in general occur due to intense tec-
tonic activity of earth . In recent times there is a
marked increase in the frequency of occurrence of
earthquakes all over the world .the intensity and lo-
cation of the earthquake is unpredictable even as
on date . structures designed to withstand gravity
loads alone cannot be expected to resist the dam-
ages caused due to seismic effects . structures de-
signed for gravity loads are normally well below the
elastic limiting stage and lie within the service loads
. it is neither practical nor economically viable to de-
sign structures to remain within elastic limits dur-
ing earthquakes . the design approach adopted in
the Indian code IS 1893(Part1): 2002 Criteria for
Earthquake Resistant Design of Structures is to en-
sure that structures possess at least a minimum
strength to withstand minor earthquakes which oc-
cur frequently , without damage ; resist moderate
earthquakes without significant structural damage
through some non-structural damage may occur ;
and aims that structures withstand major earth-
quakes without collapse .
India has experienced many large earthquakes in
the last two decades resulting in heavy loss of life
and property . In fact , more than 50% area in the
country is considered vulnerable to earthquake dis-
asters .Hence there is an urgent need for seismic
evaluation and retrofitting of deficient buildings.
The retrofitting is more so desirable as most of the
majestic structures are designed to resist gravity
loads alone .
A systematic procedure is to be followed while as-
sessing the vulnerability of existing buildings . De-
tailed survey of the buildings under the interest is
to be undertaken. The basic information collected
in the survey should include review of the build-
ing configuration , soil profile and the period of
construction . This is done with the help of quick
checks and evaluation statements .
Abstract
The main objective of the research work presented in this thesis is to provide a systematic procedure to as-
sess the behavior of a structure symmetrical and unsymmetrical
In plan during the seismic excitation using nonlinear static analysis (pushover) have been performed on the
same structure. The literature pertaining to pushover analysis is reviewed. The pushover analysis adopted
in the present study is on similar lines with the procedure presented by Ashraf Habibullah and Stephen
Pyle using ETABS V 9.7 structural analysis software. The effect of earthquake force in a idealized G+4 story
building under maximum earthquake zone, with the help of pushover analysis has been investigated and
the results were compared in terms of base shear, displacement, spectral acceleration, spectral displace-
ment and effective damping and effective time period .to strengthen the symmetric and un symmetric RCC
framed buildings` steel braces are included by using retrofitting method.
The present structure is studied using the evaluation procedures provided in ATC-40 and FEMA-356 docu-
ments and IS 1893:2002.
From the above studies it has been observed that nonlinear pushover analysis provides a good estimate of
in elastic deformation demands and also reveals weakness that may remain hidden in an elastic analysis.
1401-1402

45
However , a detailed evaluation is necessary in or-
der to identify the deficiencies associated with the
structural components with regard to the expected
behavior of the building. The code compliance of the
building can be ascertained only when the available
member capacities are compared with the respec-
tive demands due to the earthquake .the demand
in structural members are determined for the seis-
mic forces estimated as per IS 1893-2002 through
linear static analysis . The member capacities are
determined using the procedures prescribed in IS
456-2000 .The deficient members are identified and
the Demand to Capacity Ratio(DCR) exceeds unity
indicating the need for retrofitting in order to estab-
lish compliance with prevailing codes.
NEED FOR THE INVESTIGATION
Low to medium height reinforced concrete frame
buildings with masonry infill are common in ur-
ban India . All these buildings in general designed
to resist gravity loads and hence can’t be expected
to resist the latest seismic provisions . Earthquake
causes shaking of the ground in unspecified direc-
tions . The horizontal shaking along X and Y direc-
tions remain a matter of concern . Structures de-
signed for gravity loads , in general may not be able
to safely sustain the effects of horizontal shaking
due to earthquakes . Hence it is necessary to en-
sure the strength of the structure against horizontal
earthquake effects
OBJECTIVES OF THE STUDY
The primary objective of this work is to study the
seismic response of RC framed building. The ef-
fect of earthquake force on building in a symmetric
and un symmetric building under maximum earth
quake zone ,with the help of push over analysis has
been investigated.
In the present study the main objective is the
investigate the impact of steel bracings in improving
the seismic capacity of RC buildings.
The main objective of undertaking the present study
are as follows :
1)To analyze a RC framed building both symmetric
and un symmetric using pushover analysis proce-
dure , with ETABS v 9.7 for ascertaining the seis-
mic load carrying .
2)To compute the seismic response of building in
terms of base shear , spectral acceleration, spectral
displacement and roof displacements.
3)To study the effect of the steel bracings as a meth-
od of retrofitting .
4)The increasing in base shear .
5)The reduction in amplitude of maximum displace-
ments.
The study is propose to made with ETABS package
on a symmetric and non-symmetric RCC buildings
of five story height , the introduction of steel brac-
ings may be consider as one method of retrofitting.
In the conventional retrofitting technologies adopt-
ed to strength the RCC buildings to begin with the
pushover analysis is carried out on RCC buildings
there after depending on the deficiencies, the retro-
fitting technologies are adopted in the present study
the capacity of the building is increased by the use
of steel braces provided to connect the columns
and beams at the beam columns junction below the
roof. a study is made to access the additional shear
capacity of the building as well as the additional
stiffness for both buildings with both symmetric
and un symmetric plans
SUMMARY
In this chapter, the importance of earthquake and
the post disaster effects of it and some light has been
thrown on the earthquake design philosophy to be
adopted in the construction and the various impor-
tant seismic codes of India. The scope and objective
is also been discussed. Based on the objective of the
present study, research papers were collected and
studied thoroughly. The review of research papers
is discussed in the next chapter named as literature
review.
TERMINOLOGY
The following are the definitions which are most
commonly used in pushover analysis
Performance Point
It is the point where the capacity spectrum inter-
sects the appropriate demand spectrum (capacity
equals demand ). To have desired performance ,
every structure has to be designed for this level of
forces
Representing capacity spectrum , demand spec-
trum , performance point

46
Building Performance Levels
Building performance is a combination of the per-
formance of both structures and non-structural
components . Different buildings performance level,
used to described the performance of building in
pushover analysis are described below
Operational Level (OL):
Building meeting this performances level are ex-
pected to sustain no permanent drift and the struc-
ture substantially retains original strengths and
stiffness .major cracking of facades, partition and
ceilings as well as structural elements are seen . All
the system important to normal operation are func-
tional . Non-structural components are expected to
sustain negligible damage .
Immediate Occupancy Level (IO) :
Building meeting this performances level are ex-
pected to sustain no permanent drift and the struc-
ture substantially retains original strengths and
stiffness . Minor cracking of facades , partition and
ceilings as well as structure elements are seen . El-
evators can be restarted . Fire protection is operable
. Non- structural components such as equipments
and contents stays generally secure , But may not
be operative due to mechanical failure or lack of
utilities.
Life Safety Level (LS):
This level is indicated when some residual strength
and stiffness is left in all stories .Gravity load bear-
ing elements function, no out-of-plane failure of
walls or tripping of parapets occurs . There may
some permanent drift , damage to partitions and
the building may be beyond economical repair .
Among the non-structural components falling haz-
ards mitigated but many architectural , mechanical
and electrical system get damaged
Collapse Prevention Level (CP):
Building meeting this performance level are ex-
cepted to have little residual stiffness and strength
,but load bearing columns and walls function . The
building is expected to sustain large permanent
drifts , some exit blocked , infill and un-braced
parapet failure .Extensive damage to occur to non-
structural component . At this level of performance
, the building remains near collapse state
Building Performance Level’s

A typical force deformation curve
GENERAL
The existing buildings can become seismically de-
ficient since seismic design code requirements are
commonly upgraded and advancement in engineer-
ing knowledge . Future , Indian buildings built over
past two decades are seismically deficient because
of lack of awareness regarding seismic behavior of
structure , The widespread damage especially to
RC buildings during earthquakes exposed the con-
struction practices being adopted around the world
, and generated a great demand for seismic evalu-
ation and retrofitting of existing building stocks
Thus , it leads to the necessary of non-linear static
pushover analysis .
The static pushover analysis is becoming a popu-
lar tool for seismic performance evaluation of ex-
isting and new structures . The expectation is that
the push over analysis will provide adequate system
and its components
The purpose of the study is to summarize the ba-
sic concepts on which the pushover analysis can be
based , assess the accuracy of the pushover predic-
tions, identify conditions under which the pushover
will provide adequate information and perhaps more
importantly , identify causes in which the pushover
predictions will be inadequate or even misleading

47
PRESENT STUDY
INTRODUCTION
In the present study a rectangular building of G+4
stored symmetrical building and unsymmetrical
building with same height are considered, push
over analysis of the buildings is taken up with and
without steel bracings using the package ETABS.
Description And Plan For Symmetrical Building
In the present work, a G+4 storied reinforced con-
crete frame building situated in maximum earth
quack Zone V, is taken for the purpose of study. The
plan area of building is 1200x900mm with 300mm
as height of each typical story. It consists of 4 bays
in X-direction and 4 bays in Y-direction. The total
height of the building is 1500mm. The building is
considered as a Special Moment resisting frame.
The plan of building is shown in while the isometric
view of the buildings Structure with brace and with-
out braces
symmetrical building plan and section in ETABS V
9.7
As the structure is regular and relatively simple the
identification of the differences in results can be
known in easy and can be discuss in depth.
The Structure without braces and Structure with
braces are having same frame properties i.e., same
beam and column properties the only thing that dif-
fer is that the Structure is acquainted with braces
on the top of the slab connected to beams and col-
umns.
Description And Plan For Unsymmetrical Build-
ing
In this present work a G+4 stored rein forced con-
crete frame building situated in maximum earth
quake Zone V, is taken for the purpose of study .
The plan area of building is 1600x1800 mm with
300mm as height of each typical storey. It consists
of 5 bays in X-direction and 7 bays in Y-direction.
The total height of the building is 1500mm. The
building is considered as un symmetrical in plan
as a Special Moment resisting frame. The plan of
building is shown in while the isometric view of the
buildings Structure with brace and with out braces
UN symmetrical building plan and section in ETABS
V9.7
STRUCTURAL SYSTEMS OF THE BUILDING
storey G+4
Slab thickness 125mm
Beam dimensions 230 mm x 450 mm
Column dimensions 230mm x 450 mm
Exterior wall 230 mm
Interior wall 150 mm
Structural dimensions of building
General Data Collection
The building is a G+4 storey building located in
zone V. Tables 5.2, Table 5.3, Table 5.4 present a
summary of the building parameters .The details of
the building are given below.
Variable Type Reference
Type of soil Medium soil IS 1893:2002
Type of founda-
tion
Isolated footing ----
Seismic zone V IS 1893:2002
Geo technical and Geo logical data
Introduction To Load Patterns
Nonlinear static analysis, or pushover analysis,
could be performed directly by a computer program
which can model nonlinear behaviour of lateral load
resisting members of a structure. However, the com-
putational scheme and the assumptions involved in
modelling nonlinear member behaviour could be dif-
ferent that there may be variations in the pushover
results obtained from different software. Therefore,
the underlying principles of any software utilized for
pushover analysis should be well understood to in-
terpret the results of pushover analysis.

48
Pushover Analysis Using Etabs V9.7:
The following steps are included in the pushover
analysis. Steps 1 to 4 are to create the computer
model, step 5 runs the analysis, and steps 6 to 10
review the pushover analysis results.
Geometry of symmetric structure
Reinforcement area in the beams and columns ana-
lysed by linear response spectrum
Create the basic computer model (without the
pushover data) as shown in fig 5.6 . The graphical
interface of ETABS v9.7makes this quick and easy
task. Assigned sectional properties & applies all the
gravity loads (i.e. Dead load and Live load) on the
structure respectively.
• In order to know the reinforcement area in the
Beam and Columns the Response Spectra linear
Analysis was done for the zone II with Soil Type-2
and the Building was designed as per IS 456
• Define properties and acceptance criteria for the
pushover hinges. The program includes several
built-in default hinge properties that are based on
average values from ATC-40(3) for concrete members
and average values from FEMA-356(2) for concrete
members. In this analysis, M3 hinges have been de-
fined at both the column ends and M3 hinges have
been defined at both the ends of all the beams.
• Locate the pushover hinges on the model by se-
lecting all the frame members and assigning them
one or more hinge properties and hinge locations as
shown in Fig. 5.9
Frame Hinge Properties Data
Define hinges
Define the pushover load cases, Fig. 5.10, Fig. 5.11
and Fig. 5.12. In ETABS v9.7 more than one pusho-
ver load case can be run in the same analysis. Also
a pushover load case can start from the final condi-
tions of another pushover load case that was previ-
ously run in the same analysis. Typically the first
pushover load case was used to apply gravity load
and then subsequent lateral pushover load cases
were specified to start from the final conditions of
the gravity pushover. Pushover load cases can be
force controlled, that is, pushed to a certain defined
force level, or they can be displacement controlled,
that is, pushed to a specified displacement. Typical-
ly a gravity load pushover is force controlled and lat-
eral pushovers are displacement controlled. In this
case a Gravity load combination of 1.5DL+1.5LL has
been used. This combination has been defined as
GRAV. The lateral loads, have been applied by giv-
ing the displacement to the model to be analysed to
a case called PUSH.

49
Static load case
Run analysis windows for the practical building
Pushover curve for the symmetric structure
steel bracings
Pushover curve for the symmetric structure with
steel bracings

50
Pushover curve for the un symmetric structure
with steel bracings
Capacity spectrum for symmetrical structure
Capacity spectrum for un symmetrical structure
Capacity spectrum for symmetrical structure with
steel bracings
Capacity spectrum for un symmetrical structure
with steel bracings
• The pushover displaced shape and sequence of
hinge information on a step-by-step basis was ob-
tained and is shown in the Fig. 6.1 to 6.4 for the
Structure without steel bracings and in the Fig. 6.5
to 6.8 for the Structure with steel bracings. Output
for the pushover analysis can be printed in a tabu-
lar form for the entire model or for selected elements
of the model. The types of output available in this
form include joint displacements at each step of the
pushover, frame member forces at each step of the
pushover, and hinge force, displacement and state
at each step of the pushover.

51
SUMMARY
This chapter completely takes care of the case study
of a Structure under consideration and the various
building data surveys done to gather the informa-
tion for modeling of the structure, after carrying
out the pushover analysis , the pushover curves
for both the buildings with and without steel brac-
ings are obtained, based on the performance points
obtained the significant contribution by the use of
steel bracings is noted and found a great achieve-
ment to the field of retrofitting And also illustrates
the step by step procedure followed for the static
non-linear analysis.
DISCUSSION ON RESULTS
GENERAL
The structures has been modelled and the Pushover
analysis of the structures has been carried out ac-
cordingly with the ETABS v9.7
DISCUSSION ON RESULTS OF PUSHOVER ANAL-
YSIS FOR THE SYMMETRICAL STRUCTURE
WITHOUT STEEL BRACINGS AND WITH STEEL
BRACINGS
Observations under Pushover Curve
The Structures has been given in a Pushover curve
for the Structures was graphically generated for
both the symmetric and un symmetric Building i.e.
Structure without steel bracings and Structure With
steel bracings as shown in the Fig. 5.14 and Fig.
5.16 respectively, It has been observe from the Fig.
5.14 and Fig. 5.15 that the base shear was mono-
lithically increasing with the Displacement. And for
the Drift the Maximum Base Shear was observed to
be 796.22 kN and 1560.99 kN respectively.
Table 6.1 and Table 6.2 show the step by
step details for the change in base shear, and the
number of elements falling in different performance
levels like immediate occupancy, life safety and col-
lapse prevention as the roof Displacement changes.
It has been clearly observed from the Table 6.1 for
the symmetric Structure without steel bracings
that the hinges were in the elastic region (i.e. A to
B) up to a displacement of 19.31mm and further
increase in the displacement leads to formation of
56 hinge with this the structure enters into non-
linear stage (i.e. B to IO). The structure remains in
this “Immediate Occupancy” performance level till
the displacement reached 44.3 mm with the Base
shear of 642.7kN at this stage it was observed that
there were around 70 element hinges in this Perfor-
mance Level and further increase in the displace-
ment increases the number of hinge formation in
other Performance Levels. the structure enter the
performance level of “Life Safety” With the formation
of 10 hinges at the displacement of about 73.66 mm
and the building remained in this Life safety’ Per-
formance Level for the entire Drift. It was observed
that the number of element hinges in the ‘life safety’
Performance Level started with the formation of two
Hinges with the Displacement of 106.18 mm and re-
mained in the ‘life safety’ Performance Level for the
entire drift with 400 element hinges in it having the
Displacement and Base shear as 77.622 mm and
796.22 kN respectively.
pushover table for symmetrical structure without
steel bracings
It has been clearly observed from the Table 6.2 that
the for the symmetric Structure with Steel bracings
it started with the Immediate Occupancy stage (i.e.
B to IO) with the formation of 20 element hinges
in this Performance Level.The structure remains
in this “Immediate Occupancy” performance level
till the displacement reached 26.377 mm with the
Base shear of 707.054 kN at this stage it was ob-
served that there were around 280 element hinges
in this Performance Level and further increase in
the displacement makes the structure enters other
Performance Level’s. the structure enter the per-
formance level of “Life Safety” With the formation
of 108 hinges at the displacement of about 80.512
mm and the building remained in this Life safety’
Performance Level for the entire Drift. It was ob-
served that the number of element hinges in the ‘life
safety’ Performance Level started with the formation
of 2 Hinges with the Displacement of 111.372 mm
and remained in the ‘life safety’ Performance Level
for the entire drift with 40 element hinges in it hav-
ing the Displacement and Base shear as 53.316 mm
and 2496.04 kN respectively.
Pushover Curve table for the symmetric structure
with steel bracings

52
Observations under Capacity spectrum curve
The Fig. 5.18 and Fig. 5.20 shows the capacity
spectrum curve for a drift, obtained the intersection
of pushover curve with response spectrum curve.
Firstly both these curves are converted in terms of
spectral acceleration and spectral displacement i.e.
in the ADRS format, and then they are superim-
posed to give the performance point of the structure.
The green colour curve seen in the Fig. 5.18 and
Fig. 5.20 is the pushover curve for the symmetric
Structure without steel bracings and the symmetric
Structure with steel bracings respectively and the
curve in yellow color is the response spectrum curve
in terms of spectral acceleration and spectral dis-
placement.
At the performance point for the symmetric Struc-
ture without steel bracings the base shear is 796.22
KN at a displacement of 77.622 mm, we can observe
that the hinges are still in the state of “Immediate
Occupancy” Performance level. Hence, the struc-
ture is still safe at this performance point for design
based earthquake for the Zone V. Table 6.3 shows
the demand, capacity details in terms of single de-
mand spectrum ADRS (variable Damping) and ca-
pacity spectrum at various steps during the pusho-
ver analysis for Drift. The effective time period at
the performance point is 0.978 sec and the effective
Damping was 0.185 which can be seen between the
steps 2nd and 3rd (refer Fig. 5.18 and Table 6.3).
Capacity Spectrum Curve table for the symmetric
Structure without steel bracings
At the performance point for the symmetric Struc-
ture with steel bracings the base shear is 1560.99
kN at a displacement of 70.237mm, which was ob-
tained between steps 1st and 2nd (refer Table 6.4),
we can observe that the hinges are still in the state of
“Immediate Occupancy” Performance level. Hence,
the structure is still safe at this performance point
for design based earthquake for the Zone V. Table
6.4 shows the demand, capacity details in terms of
single demand spectrum ADRS (variable Damping)
and capacity spectrum at various steps during the
pushover analysis for Drift. The effective time period
at the performance point is 0.639 and the effective
Damping was0.077. which can be seen between the
steps 2nd and 3rd (refer Fig. 5.20 and Table 6.4).
DISCUSSION ON RESULTS OF PUSHOVER ANAL-
YSIS . FOR THE UN SYMMETRIC STRUCTURE
WITHOUT STEEL BRACINGS AND THE UN SYM-
METRIC STRUCTURE WITH STEEL BRACINGS
Observations under Pushover curve
The Modelled un symmetrical Structures has been
given a initial Drift . The Pushover curve for the un
symmetrical Structures was graphically generated
for both the Building i.e. un symmetrical Structure
without steel bracings and Structure With steel
bracings as shown in the Fig. 5.15 and Fig5.17
respectively. It has been observe from the Fig5.15
and Fig. 5.17 that the base shear was monolithi-
cally increasing with the Displacement. And for the
.Drift the Maximum Base Shear was observed to be
1561.499 kN and2496.045 kN respectively.
Table 6.5 and Table 6.6 show the step by step de-
tails for the change in base shear, and the number
of elements falling in different performance levels
like immediate occupancy, life safety and collapse
prevention as the roof Displacement changes.
When the un symmetrical Structure without steel
bracings was given a Drift the further Deformation
Performance of the Building was graphically repre-
sented in the Fig. 5.15. It has been clearly observed
from the Table 6.5 that from the Step 7th the build-
ing enter in the ‘Collapse Prevention’ Performance
Level (i.e. from LS to CP) with the formation of 114
element hinges in it with the Base shear and Dis-
placement as 710.770 kN and 19.50mm respec-
tively and further increase in the Displacement at
about 44.04mm the building entered in the ‘Resid-
ual Strength zone’ with the Base Shear as 1288.160
kN and there are 31 element hinges in this Resid-
ual strength zone. It has been observed that the
Base shear has increased down from 1288.16kN to
1515.75KN in the Total Failure Zone and the no of
element hinges in this zone are 13 with Displace-
ment of about 99.34mm this was observed. The
Building was Totally Elapsed at the Displacement
of about 99.34mm so there is no need for assessing
the . Drift of the building.

53
Pushover curve table for un symmetrical structure
without steel bracings
When the un symmetrical Structure with steel
bracings was given a Drift the further Deformation
Performance of the Building was graphically repre-
sented in the Fig. 5.17. It has been clearly observed
from the Table 6.6 that the building enter in the
‘Collapse Prevention’ Performance Level (i.e. from LS
to CP) with the formation of 31 element hinges in it
with the Base shear and Displacement as 1288.162
kN and 44.04mm respectively and further increase
in the Displacement at about 71.77mm the build-
ing entered in the ‘Residual Strength zone’ with the
Base Shear as 1542.697 kN and there are 27 ele-
ment hinges in this Residual strength zone .At .the
building has entered the ‘Total Failure Zone’ with
Base shear, Displacement and number of element
hinges as 16207.036kN, 99.34mm and 4 respec-
tively. It has been observed that the Base shear has
increased from 1561.499kN to 2496.045kN .and no
of element hinges in this zone are with Displace-
ment of about 77.919mm. The Building was Total-
ly Elapsed at the Displacement is decreased from
77.919 to 53.316.
Pushover Curve table for the un symmetrical Struc-
ture with steel bracings
Observations under Capacity spectrum curve
The Fig. 5.19 and Fig. 5.21 shows the capacity spec-
trum curve, obtained the intersection of pushover
curve with response spectrum curve.
At the performance point for the un symmetric
Structure without steel bracings the base shear is
1245.475 kN at a displacement of 26 mm, which
was obtained between steps 1st and 2nd (refer Ta-
ble 6.7), we can observe that the hinges are still in
the state of “Immediate Occupancy” Performance
level. Hence, the structure is still safe at this per-
formance point for design based earthquake for
the Zone V Table 6.7 shows the demand, capacity
details in terms of single demand spectrum ADRS
(variable Damping) and capacity spectrum at vari-
ous steps during the pushover analysis. The effec-
tive time period at the performance point is 1.030sec
and the effective Damping was 0.201 which can be
seen between the steps 1st and 2nd (refer Fig 5.19
and Table 6.7).
Capacity Spectrum Curve table for the un symmet-
ric Structure without steel bracings.
At the performance point for the un symmetric Struc-
ture with steel bracings the base shear is 2496.045
kN at a displacement of 53.316 mm, which was ob-
tained between steps 1st and 2nd (refer Table 6.8),
we can observe that the hinges are still in the state of
“Immediate Occupancy” Performance level. Hence,
the structure is still safe at this performance point
for design based earthquake for the Zone V. Table
6.8 shows the demand, capacity details in terms of
single demand spectrum ADRS (variable Damping)
and capacity spectrum at various steps during the
pushover analysis. The effective time period at the
performance point is 0.599 and the effective Damp-
ing was 0.077 which can be seen between the steps
2th and 3th (refer Fig. 5.21 Table 6.8).
Capacity Spectrum Curve table for the un symmet-
ric Structure with steel bracings
HINGE PATTERNS FOR SYMMETRIC STRUCTURE
WITHOUT STEEL BRACINGS AND UN SYMMETRIC
STRUCTURE WITH STEEL BRACINGS
Fig. 6.1 to 6.4represent the sequence of formation
of hinges from the initial stage i.e. from the elastic
stage to the total collapse stage for the symmetric
Structure without Steel bracings and the symmetric
Structure with steel bracings respectively. These are
color coded and are represented by respective color
at different pushover steps. These hinges are essen-
tial to closely study the behavior of the structure.

54
hing pattern for symmetrical without steel bracings
hing pattern for symmetrical with steel bracings
hing pattern for un symmetrical without steel brac-
ings
hingpattern for un symmetrical with steel bracings
Performance of different structures under the
zones V
The Capacity Spectrum Curves for The symmetric
Structure without Steel bracings under maximum
Earthquake Zones V. The performance point of the
building in terms of Base shear, Roof Displacement,
Spectral Acceleration, Spectral Displacement, ef-
fective Time Period, and Effective Damping of the
structure.
The symmetric Structure without Steel bracings
and The Structure With Steel bracings were first
analysis by the Non Linear Static analysis and were
Designed accordingly to the Indian IS 456-2000.
Pushover Analysis on these building was performed
accordingly under the different Zone’s. The Perfor-
mance point of the Structures was tabulated in the
Table 6.9 and Table 6.10 accordingly to the change
in the Earthquake Zones
Summary
This chapter copes with the numerical study and
presentation of results of pushover analysis method
for the current buildings under study and the re-
sults are tabulated and are represented in the form
of graphs. The results were studied and based on
the study, the conclusions were drawn. The con-
clusions for the present study are given in the next
chapter.
CONCLUSIONS
After having perform the pushover analysis on two
different buildings with and without steel bracings
following conclusions are drawn
• In symmetrical building based an the per-
formance point obtained from pushover curve (fig no
page no )and the same building with steel bracings
(fig no page no) the value of base share is found in-
creased by % and the amplitude and displacement
found by reduced %
• In un symmetrical building based on the
performance point obtained from pushover curve
(fig no page no )and the same building with steel
bracings (fig no page no) the value of base share is

55
found increased by % and the amplitude and dis-
placement found by reduced %
• Based on the above study it is felt that introduc-
tion of steel bracings is one proven method of struc-
tural retro fitting
SCOPE FOR FURTHER STUDY
• In the present study, the pushover analysis has
been carried out for the G+4 storey buildings. This
study can further be extended for tall buildings.
• In the present study, the conceptual design i.e.,
the sizes of beams and columns are kept common.
Work can be done to optimize the sizes of various
frame elements using pushover analysis.
• Further studies can be done to compare the accu-
racy of non-linear pushover analysis and non-linear
time history analysis taking the displacement as a
common parameter.
• Laboratory tests on the structures should be car-
ried out to backup the numerical results so that
these results can be more informative and valuable.
• More studies are required to carried out before
generalized conclusions can be drawn
• A retrofitting of frames with weak storey and un
symmetrical elevations are also needed to be stud-
ied.
SUMMARY
This chapter, details the discussions drawn based
on the present work and the scope for the further
study and Investigation based on the present study
was discussed.
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56
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author
P.SWETHA
Research Scholar, Department of CIVIL Engineering,
Hyderabad, India
MRS. K. MYTHILI
Associate Professor, Department of CIVIL Engineering,
Hyderabad, India
MR. G.VENKAT RATNAM
Associate Professor, Department of CIVIL Engineering,
Hyderabad, India

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