International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 10 - Oct 2013
Non-Linear Static Analysis of Multi-Storied
Building
Srinivasu. A1, Dr. Panduranga Rao. B2
1
PG Student, Department of Civil Engineering, V.R. Siddhartha Engg. College, Vijayawada, A.P, India
2
Professor, Department of Civil Engineering, V.R. Siddhartha Engg. College, Vijayawada, A.P, India
Abstract— In this paper, a method for the
determination of the parameters of plastic hinge
properties (PHP) for structure containing R.C.C
framed structures in the pushover analysis is proposed.
Nonlinear relationship between the lateral shear force
and lateral deformation of RC framed G+5 story
Buiding is calculated first by the static analysis and
then go through the Pushover analysis by using ETABS
Software.
Keywords— Earthquake analysis, Static Analysis,
Pushover Analysis, ETABS.
I. INTRODUCTION
The nonlinear analysis of a structure is an iterative
procedure. It depends on the final displacement, as
the effective damping depends on the hysteretic
energy loss due to inelastic deformations, which in
turn depends on the final displacement. This makes
the analysis procedure iterative. Difficulty in the
solution is faced near the ultimate load, as the
stiffness matrix at this point becomes negative
definite due to instability of the structure becoming a
mechanism. Software available to perform nonlinear
static (pushover) analysis are ETABS, SAP, ADINA,
SC-Push3D Extended Three Dimensional Buildings
Systems (ETABS) and Structural Analysis Program
finite element program that works with complex
geometry and monitors deformation at all hinges to
determine ultimate deformation. It has built-in
defaults for ACI 318 material properties and ATC40and FEMA 273 hinge properties. Also it has
capability for inputting any material or hinge
property. ETABS 9.7 deals with the buildings only.
The analysis in ETABS 9.7 involves the following
four
step.1)
Modeling,,2)
Static
analysis,
3)Designing, 4)Pushover analysis Steps used in
performing.
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Deformation
Fig A. Graph shows the curve Force Vs Deformation





Point A corresponds to unloaded condition.
Point B represents yielding of the element.
The ordinate at C corresponds to nominal
strength and abscissa at C corresponds to the
deformation at which significant strength
degradation begins.
The drop from C to D represents the initial
failure of the element and resistance to
lateral loads beyond point C is usually
unreliable.
The residual resistance from D to E allows
the frame elements to sustain gravity loads.
Beyond point E, the maximum deformation
capacity, gravity load can no longer be
sustained.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 10 - Oct 2013
II. DATA TO BE USED
Ah = Design horizontal seismic coefficient.
W = Seismic weight of the building.
A. Material Properties
In the model, the support condition was assumed to
be fixed and soil condition was assumed as medium
soil. Building was a symmetric structure with respect
to both the horizontal directions.
Modulus of
2
elasticity of steel, Es = 21,0000 N/mm , Modulus of
elasticity of concrete, Ec = 25000 N/mm2.
B. Model Geometry
It was X-direction and Y-direction, each of 4.5m in
length. All the slabs were considered as Membrane
element of 115mm thickness. The model was the bare
frame having beams, columns and slabs. M25 grade
concrete and Fe415.steel were used.
b) Seismic Weight of Building- The seismic
weight of each floor is its full dead load plus
appropriate amount of imposed load as
specified. While computing the seismic
weight of each floor, the weight of columns
and walls in any storey shall be equally
distributed to the floors above and below the
storey. The seismic weight of the whole
building is the sum of the seismic weights of
all the floors. Any weight supported in
between the storey shall be distributed to the
floors above and below in inverse proportion
to its distance from the floors.
c) Fundamental Natural Time Period- The
fundamental natural time period (Ta)
calculates from the expression
Ta = 0.075h0.75 for RC frame building
Ta = 0.085h0.75
for steel frame building
If there is brick filling, then the
fundamental natural period of vibration, may
be taken as
Ta =
d) Distribution of Design Force- The design
base shear, VB computed above shall be
distributed along the height of the building as
per the following expression
C. Plan of The Building
IV. PUSHOVER ANALYSIS

Fig 1. Plan of the Building
III. STATIC ANALYSIS OF BUILDINGS USING
IS 1893 (PART 1)-2002
As per IS 1893 (part1)-2002, Seismic Coefficient
analysis Procedure is summarized in following steps
(5).
a)
Design Seismic Base Shear- The total design
lateral force or design seismic base shear (Vb)
along any principal direction of the building
shall be determined by the following
expression
VB= Ah W
Where
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

The program includes several built-in
default hinge properties that are based on
average values from ATC-40 for concrete
members and average values from FEMA273 for steel members. These built in
properties can be useful for preliminary
analyses, but user-defined properties are
recommended for final analyses. This
example uses default properties.
Locate the pushover hinges on the model by
selecting one or more frame members and
assigning them one or more hinge properties
and hinge locations.
Define the pushover load cases. In ETABS
more than one pushover load case can be run
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 10 - Oct 2013
V. METHODOLOGY
in the same analysis. Also a pushover load
case can start from the final conditions of
another pushover load case that was
previously run in the same analysis.
The 6 storied building is shown in Fig 1. The seismic
analysis of building is done by Static Analysis and
then goes through the Pushover Analysis with given
above procedures for Zone III. The obtained results
are shown in Tables.
VI. RESULTS AND GRAPHS
TABLE 1. Data for Pushover Curve
STEP
DISPLACEMENT
BASE
FORCE
0
0.0
1
2
BIO
IOLS
LSCP
CPC
CD
DE
>E
TOTAL
0.0
198
0
0
0
0
0
0
0
198
0.0743
97.12
198
0
0
0
0
0
0
0
198
0.1485
194.42
194
4
0
0
0
0
0
0
198
18
11
14
0
0
0
0
198
3
0.1919
251.37
155
4
0.2705
341.71
150
13
17
16
0
2
0
0
198
5
0.2985
363.96
150
10
9
11
0
0
0
18
198
6
0.2687
359.26
150
8
8
13
0
1
0
18
198
7
0.2847
377.26
150
8
8
9
0
0
0
23
198
220.20
198
0
0
0
0
0
0
0
198
8
Base Shear in KN
AB
0.1572
400.0
350.0
300.0
250.0
200.0
150.0
100.0
50.0
0.0
1
2
3
4
5
6
7
8
9
Displacement in M
Fig 2. Graph shows the curve of Base shear Vs Displacements
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 10 - Oct 2013
Fig 3. Modeling of the structure
Fig 4. Formation of Plastic Hinges at step 4
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 10 - Oct 2013
VII. CONCLUSIONS



The frame behaved linearly elastic up to a
base shear value of around 180 KN at the
value of base shear 360 KN it depicted non
linearity in its behavior. Increase in
deflection has been observed to be drop
down with load increments at base shear of
360 KN.
The frame has shown variety of failures like
beam-column joint failure, flexural failure
and shear failure. Flexural failures have
been seen in beams.
The Pushover Analysis was including 8
steps it has been observed that one sub
sequent push to building, hinges started
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forming in beams first. Initially hinges were
in A-B stage and subsequently proceeding to
B-IO stage. Out of 198 hinges 194 in A-B
stage, 4 in B-IO stage. Overall performance
of building is said to be B-IO stage.
REFERENCES
[1]
[2]
[3]
[4]
[5]
ATC 40-“Seismic Evaluation and Retrofit of Concrete
Buildings”, Applied Technology Council, November 1996.
Chopra AK. Dynamics of Structures: theory and
applications to earthquake engineering. Englewood Cliffs,
NJ; 1995.
FEMA-273-“NEHRP Guidelines for the Seismic
Rehabilitation of Buildings”, Federal Emergency
Management Agency, October 1997.
ETABS User’s Manual, “Integrated Building Design
Software”, Computer and Structures Inc. Berkeley, USA.
IS 1893(Part1):2002, Criteria for earthquake resistant
design of structures, Part 1 General provisions and
buildings, Bureau of Indian Standard, 2002.
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