STATIC LINEAR AND NON-LINEAR (PUSHOVER) ANALYSIS OF
MULTI STOREY RC FRAME WITH AND WITHOUT VERTICAL
IRREGULARITIES
NUTHAN L PATHI1, GURUPRASAD T N2, DHARMESH N3 AND
MADHUSUDHANA Y.B4
Student, 2Assistant Professor, Department of Civil Engineering (CADS), SIET, Tumkur, India.
3,4
Assistant Professors, Department of Civil Engineering, East Point College of Engineering and
Technology, Bangalore.
1PG
Abstract-Earthquakes are most devastating natural hazards in
terms of property loss and life of any region. The response of
structure during earthquake greatly depends on size, geometry
and shape of the structure. The Indian code IS-1893: 2002
(Part-I) has pointed out a variety of structural irregularities
like plan irregularity and vertical irregularity. The study
focuses on the seismic performance of G+6 storey regular and
irregular Reinforced Concrete (RC) buildings. For this
purpose, a finite element computer software ETABS (V. 9.7.1)
has been used. The study as a whole makes an attempt to
evaluate the impact of vertical irregularity on RC buildings in
terms of static linear-Equivalent Static Lateral force Method
(ESLM) and nonlinear analysis (PUSHOVER). Base shear,
Lateral displacement, Storey drift and Performance points are
the response parameters used to quantify the performance of
the structure. The analysis has been carried out for zone II and
zone V of India and soil type III (soft soil) condition. Based on
the above response parameters, the results and conclusions are
drawn.
Keywords: Equivalent Static Lateral Force Method (ESLM),
Pushover analysis, SMRF, OMRF etc.
I.
INTRODUCTION
Earthquake is a phenomenon related to violent shaking
that takes place underneath the earth. Massive strain energy
discharged at the time of an earthquake and travels as
unstable waves called as seismic waves in every directions
through the Earth’s layers, which refracting and reflecting at
every interface. The destruction to structures because of
earthquake depends on the stuff that the structure is formed
out of, the sort of earthquake wave (motion) that is
distressing the structure, and also the ground on that the
structure is constructed. Therefore the dynamic loading
which acts on the structure throughout an earthquake is not
only external loading, but also inertial effect caused by
motion of support. The different factor that causes damage
to the structure throughout earthquake are mass irregularity,
vertical irregularities, torsional irregularity, irregularity in
strength and stiffness, etc. In multi-storied RC framed
buildings, destruction from earthquake ground motion
usually starts at locations of structural weaknesses there in
buildings. In some of the cases, these weaknesses are also
developed by discontinuities in stiffness, strength or mass
between adjacent stories.
Over the past decades it has been recognized that
destruction control has become a more specific design
consideration which will also be carried out most
effectively, by the way of introducing some kind of
nonlinear analysis into the seismic design methodology.
Following this pushover analysis has been developed during
past years and has end up with the preferred method of
analysis for performance-based seismic design (PBSD). It is
the approach by which the ultimate strength and the limit
state can be quite simply investigated after yielding, which
has been researched and utilized in practice for earthquake
engineering and seismic design.
II.
IRREGULARITIES IN BUILDINGS
There are two types of building irregularities, they are
o Plan Irregularities.
o Vertical Irregularities.
In plan irregular building there are of five types, they are





Torsion Irregularity.
Re-entrant Corners.
Diaphragm Discontinuity.
Out-of-Plane Offsets.
Non-parallel Systems.
In vertical irregularity buildings there are also five types,
they are
 Stiffness Irregularity.
 Soft Storey.
 Extreme Soft Storey.
 Mass Irregularity.
 Vertical Geometric Irregularity.
 In-Plane Discontinuity in Vertical Elements
Resisting Lateral Force.
 Discontinuity in Capacity - Weak Storey.
1
III. OBJECTIVE OF THE WORK
The main objectives of this work includes the following,
1) To determine the response of 7 storey RC frame structure
i.e., base shear and lateral displacement by Equivalent static
lateral force method and performance point by pushover
analysis. Modeling and analysis are achieved using ETABS
a finite element software.
2) Equivalent static lateral force method is conducted for
zone-II and zone-V according to IS 1893 2002 (Part 1) for
soft soil type (type III).
3) All the six models are studied and analyzed using
pushover analysis.
IV. PARAMETRIC STUDY
A reinforced concrete frame with 7(G+6) storey of
dimension 19mx31m, has been taken for seismic analysis.
Six building models with different types of irregularities are
considered for comparison:
Model-1: Regular building.
Model-2: Stiffness (Soft storey) irregularity.
Model-3: Mass irregularity.
Model-4: Vertical geometric irregularity.
Model-5: In-Plane Discontinuity in Vertical Elements
Resisting Lateral Force.
Model-6: Combination of all the above irregularities.
These six building models are analyzed for the following
cases
a) Using equivalent static lateral force method for zone-II
and zone-V for soil type-III (soft
soil) as per IS 1893(part 1):2002.
b) Using Pushover analysis.
Grade of
concrete
M35(beams and slabs) & M40
(columns)
Grade of steel
Fe500
Beam sizes
500x850mm
column sizes
600x1200mm
slab thickness
150mm
Live load
2.0kN/m2
Floor finish
1.0kN/m2
Swimming
pool load for
mass and
combination of
irregular
building
10kN/m2
Zone factor
II and V
Soil type
Soft soil
Importance
factor
1
Response
reduction
factor
3.0(OMRF) and 5.0(SMRF)
V. METHOD OF ANALYSIS
The study undertakes the following analysis
 Equivalent Static Lateral Force Method (ESLM).

Pushover Analysis.
VI. DESCRIPTIONS OF BUILDING
Description of building
Structure type
Ordinary Moment Resisting
Frame[OMRF] & Special Moment
Resisting Frame[SMRF]
Plan
dimension
19x31m
Storey height
3.5m
Height of
building
G+6=7 storeys
Fig 1: plan of regular building
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VII. RESULTS AND DISCUSSION
A. Base Shear
Table 1: Base Shear of OMRF and SMRF building models
in Zone-II and Zone-V along both x-x and y-y direction
zone II X-X
COMBIN…
INPLANE
zone II Y-Y
VERTICAL
5000
4000
3000
2000
1000
0
MASS
Fig 3: Elevation of mass irregular building
Base shear in kN
REGULAR
STIFF
MASS
VERTI
INPLANE
COMBI
REGULAR
Fig 2: Elevation of stiffness irregular building
Base shear in kN
zone II
zone V
X-X
Y-Y
X-X
Y-Y
1572.82 1572.82 3397.29 3397.29
1514.08 1514.08 3270.42 3270.42
1910.22 1910.22 4126.08 4126.08
1144.17 1144.17 2471.42 2471.42
1578.3
1578.3
3409.12 3409.12
1438.38 1438.38 3106.89 3106.89
STIFFNESS
MODELS
zone V X-X
zone V Y-Y
Fig 7: Base Shear of OMRF and SMRF building models
in Zone-II and Zone-V along both x-x and y-y direction
Fig 4: Elevation of vertical irregular building
B. Lateral Displacement
Table 2: Lateral displacement of OMRF and SMRF building
models in Zone-II and Zone-V along both x-x and y-y
direction
MODELS
REGULAR
STIFF
MASS
VERTI
INPLANE
COMBI
Displacement in mm
zone II
zone V
X-X
Y-Y
X-X
Y-Y
4.4
5.6
9.4
12.2
4.7
6.3
10.1
13.6
5.3
6.8
11.4
14.7
3.9
5.1
8.4
10.9
4.1
5.8
8.8
12.6
4.1
6.5
8.9
14
Displacement in
mm
Fig 5: Elevation of in-plane discontinuity building
Fig 6: Elevation of combination of irregular building
15
10
zone II X-X
5
zone II Y-Y
0
zone V X-X
zone V Y-Y
Fig 8: Lateral displacement of OMRF and SMRF
building models in Zone-II and Zone-V along both x-x
and y-y direction
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C. Pushover Results
Fig 9: Capacity spectrum curve for regular building in
zone II
Fig 10: Capacity spectrum curve for stiffness irregular
building in zone II
Fig 13: Capacity spectrum curve for in-plane
discontinuity irregular building in zone II
Fig 14: Capacity spectrum curve for combination of
irregular building in zone II
Fig 11: Capacity spectrum curve for mass irregular
building in zone II
Fig 13: Capacity spectrum curve for regular building in
zone V
Fig 12: Capacity spectrum curve for vertical geometric
irregular building in zone II
Fig 14: Capacity spectrum curve for stiffness irregular
building in zone V
4
D. Performance Point
Table 3: Comparison of base shear for all models in zone II
and V
Performance point of base shear
Models
Zone V
Zone II
REGULAR
10576.67 10712.06
STIFFNESS 10149.12 10279.11
MASS
10723.91 8436.621
VERTICAL 7973.329 8086.673
IN-PLANE
11309.64 11574.07
COMBI
9949.022 10389.48
Fig 16: Capacity spectrum curve for vertical geometric
irregular building in zone V
15000
10000
5000
Zone II
COMBI
INPLANE
VERTICAL
MASS
STIFFNESS
0
REGULAR
Base shear (kN)
Fig 15: Capacity spectrum curve for mass irregular
building in zone V
Zone V
Fig 19: Comparison of base shear for all models in zone
II and V
Table 4: Comparison of displacement for all models in zone
II and V
Performance point of displacement
Models
Zone V
Zone II
REGULAR
69
69
STIFFNESS
76
76
MASS
82
95
VERTICAL
59
58
IN-PLANE
62
60
COMBI
64
60
100
50
Zone II
COMBI
INPLANE
VERTICAL
MASS
STIFFNESS
0
REGULAR
Displacement
(mm)
Fig 17: Capacity spectrum curve for in-plane
discontinuity irregular building in zone V
Zone V
Fig 20: Comparison of displacement for all models in
zone II and V
Fig 18: Capacity spectrum curve for combination of
irregular building in zone V
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DISCUSSION:

base shear and displacement is more in mass
irregular building for both zone II and V from
ESLM analysis.
Capacity spectrum curves are obtained from
Pushover analysis and it is shown in above figs.
At performance point base shear is more in inplane discontinuity building and displacement is
more in mass irregular building for both zone II
and zone V.


VIII. CONCLUSIONS AND FUTURE SCOPE
A. Conclusions
1.
2.
3.
4.
Maximum base shear occurs in the mass
irregularity building when compared to other
models because of heavy mass are provided in
mass irregularity building along X-X and Y-Y
direction considering zone II and zone V.
Maximum lateral displacement is obtained mass
irregular building and less in vertical geometric
irregularity building shows less displacement.
Hence vertical irregularity building shows better
performance in zone II and zone V.
Performance point of base shear is more in in-plane
discontinuity building when compared to all
models both zone II and zone V.
Performance point of displacement is more in mass
irregular building and less in vertical geometrical
buildings when compared to other models in both
zone II and zone V.
B. Future Scope


[4]. Santhosh.D “Pushover analysis of RC frame structure
using ETABS 9.7.1” IOSR Journal of Mechanical and
Civil Engineering (IOSR-JMCE) e-ISSN: 2278-1684, pISSN: 2320-334X, Volume 11, Issue 1 Ver. V (Feb.
2014), PP 08-16.
[5]. Mohommed Anwaruddin
Md. Akberuddin and Mohd.
Zameeruddin Mohd. Saleemuddin “Pushover Analysis
of Medium Rise Multi-Story RCC Frame With and
Without Vertical Irregularity” Int. Journal of Engineering
Research and Applications Vol. 3, Issue 5, Sep-Oct 2013,
pp.540-546.
[6]. N.K. Manjula Praveen Nagarajan and T.M. Madhavan
Pillai “A Comparison of Basic Pushover Methods”
International Refereed Journal of Engineering and
Science (IRJES) ISSN (Online) 2319-183X, (Print)
2319-1821 ,Volume 2, Issue 5(May 2013), PP. 14-19.
[7]. Ankesh Sharma and Biswobhanu Bhadra (2013) “seismic
analysis and design of vertically irregular rc building
frames”
[8]. C.M. Ravi Kumar, Babu Narayan, M.H. Prashanth, H.B
Manjunatha and D. Venkat Reddy “Seismic Performance
Evaluation Of Rc Buildings With Vertical Irregularity”
ISET GOLDEN JUBILEE SYMPOSIUM Indian Society
of Earthquake Technology Department of Earthquake
Engineering Building IIT Roorkee, Roorkee October 2021, 2012, Paper No. E012.
Codes:
[1]. BIS, IS 456:2000, - Plain and reinforced concrete code of
practice‖ Bureau of Indian Standards, Fourth revision.
[2]. BIS, IS 1893 (Part 1): 2002, - Criteria for Earthquake
Similar studies can be carried out for lateral load
resisting systems like masonry infill and bracings.
In the present study fixed base is considered for the
structure, further study can be carried out for using
soil structure interaction.
Resistant Design of Structures Part-I General Provisions
and Buildings‖, Bureau of Indian Standards, Fifth
revision.
[3]. ATC 40, Applied Technology Council, “Seismic
Evaluation and Retrofitting of Concrete Building”,
Volume 1, Redwood City, CA, U.S.A.
REFERENCES
[1]. Dr. Mohd. Hamraj “Performance Based Pushover
Analysis of R.C.C Frames for Plan Irregularity”
International Journal of Science, Engineering and
Technology Volume 2, Issue 7, Sep-Oct 2014.
[2]. Gayathri.H,
Dr.H.Eramma, C.M.RaviKumar, and
Madhukaran “A Comparative Study On Seismic
Performance Evaluation Of Irregular Buildings With
Moment Resisting Frames And Dual Systems”
International Journal of Advanced Technology in
Engineering and Science, Volume No.02, Issue No. 09,
September 2014.
[3]. Mr. Gururaj B. Katti and Dr. Basavraj S. Balapgol
“Seismic Analysis of Multistoried RCC Buildings Due to
Mass Irregularity by Time History Analysis”
International Journal of Engineering Research &
Technology (IJERT) ISSN: 2278-0181 Vol. 3 Issue 7,
July - 2014.
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