Study on Seismic Behaviour of RC Frame Vertically Asymmetrical Buildings

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 12 | Dec-2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 6.171 | ISO 9001:2008 Certified Journal | Page 869
STUDY ON SEISMIC BEHAVIOUR OF RC FRAME VERTICALLY
ASYMMETRICAL BUILDINGS
Shalini Verma1, ER. Jainender Sharma2
1Student, M.Tech. Civil Engg. Dept., SAI University , Palumpur, India
2 Assistant Professor, Dept. Of Civil Engg. SAI University, Palumpur, Himachal Pradesh, India
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Abstract : Reinforced concrete framed building may be
balanced and may be irregular. In every type of building
earthquake gives vary bad impact. The balanced building is
more stronger then irregular buildings. RC framed building
consists of frame with flexible joint and bracing member.
As structural design RC multi-storied buildings are very
difficult to model. The latest version of code IS: 1893-2002
say that three – dimensional systems is used to analyzed all
type of building and multi-storied buildings. This is fact that
most of the buildings have asymmetry in plan and elevation,
due to this in seismic performance it gives bad influence and
effect. Vertical irregularity of RC Buildings is discuses in this
paper. ,we study to evaluate the response of all type of
vertical irregular RC Buildings dynamically an and analysed
the persuasion parameters which can control the reaction
on Base shear irregular distribution of mass ,stiffness and
strength or due to irregular geometrical configuration a
structure is called irregular structure. A story in a building
having mass irregularity more than 200% of adjacent story,
we call it irregular building. If stiffness of a storey is 60% of
the adjacent storey; that case we say the storey is ‘weak
storey ’, and if it is less than 70% of the storey it is ‘soft
storey’. Due to functional and aesthetic requirements there
are many building (church, temple, hospital) which contain
different irregularly. There is major function of open space,
if no more open place is there, then we make multi-storey
building. to short out the problem of open space. However,
past earthquake records shows vary bad seismic effect on
these structures. The seismic codes (,IS 4326:1993, IS 1893:
2002,EC8:2004,UBC 1997,NBCC 1989, etc Unawareness of
the asymmetry condition). In reinforced concrete (RC) frame
structures beam and column elements built in such a way
they resist the two seismic and gravity loads. The failure of
this member to take the weight starts to break of the
structure. Collapse capacity of structure under seismic
excitation has always been a essential condition determining
performance of structure. The field of vertically uneven type
of building is now accept a lot of concern in seismic analysis.
Several structures are constructed with vertical irregularity
for architectural appearance. Important change in firmness
and toughness vertical irregularity appear in the buildings.
Open ground storey (OGS) is a case of vertically irregularity.
The common OGS and stepped types of buildings along with
different shape of structure, for designing these structure
different magnification factors are well chosen in process
study adopting Equivalent static Analysis and response
spectrum analysis. For analyzing of the OGS magnification
factors (MF) are advised by the design codes.
Keyword: Seismic performance, RC Building, Vertical
irregularity, soft story, response spectrum analysis.
1. INTRODUCTION:
Structure failure occurs at points of weakness during an
earthquake. This weakness arises due to discontinuity in
mass, stiffness and geometry of structure. All Irregular
structures having this discontinuity. A large portion of
urban infrastructure contributes irregular structures. One
of the major reasons of failures of structures during
earthquakes are vertical irregularities. Soft storey
structures are the example of structures which collapsed.
So, the effect of vertically irregularities in the seismic
performance of structures becomes really important.
Height-wise changes in stiffness and mass render the
dynamic characteristics of these buildings different from
the regular building. IS 1893 definition of Vertically
Irregular structures. The irregularity in the building
structures may be due to irregular distributions in their
mass, strength and stiffness along the height of building.
When such buildings are constructed in high seismic zones
the analysis and design becomes more complicated.
There are two types of irregularities-
1.1 Horizontal Irregularities.
a) Asymmetrical plan shape
b) Re-entrant corners
c) Diaphragm Discontinuity
d) Irregular distribution
1.2. Vertical Irregularities.
a) Stiffness Irregularity
b) Stiffness Irregularity
c) Mass Irregularity
d) Vertical Geometric Irregularity
e) In-Plane Discontinuity in Vertical Elements Resisting
Lateral Force.
f) Discontinuity in Capacity

II PRESENT RESEARCH STATUS
Open ground storey building frames designed with various
MFs (Magnification factor) and stepped irregular frames
with different infill configurations, and having heights (3
stories) are considered for the present study. We take for
observation non-ductile RC frame having a 3 storey 2 bay
open ground- storey building. We observed that in the
presence of masonry infill at the upper floor of the building
the stiffness of the building increases as the total storey
shear force increases. Because formation of hinges the
failure is formed due to soft storey mechanism occur in
ground storey columns and the bending moments in the
ground floor columns increase. Base shear for OGS
building a multiplication factor was proposed. The
modelling the stiffness of the infill walls in the analysis was
focused. The effect of in Multiplication factor with the
increase in storey height was studied. We observed as the
number of storey increases from three to six the
multiplication factor ranging from 1.5to1.86. We observed
for load transferring assemblies the steel cage-to-RC
footing connection and brace-to-steel cage connection
exhibited excellent performance under lateral cyclic
loading without any sign of failures. Whereas compared to
the non-ductile frame only steel caging RC frame
strengthened and improved lateral strength, movement
capacity and energy dissipation potential but it could not
avoid collapse completely. For OGS buildings the effect of
the infill wall is studied considering the Indian standard
code IS 1893 2002 criteria Equivalent Static Analysis and
Response Spectrum Analysis is used to study. We observed
that both method gives same result and if time history is
not present response spectrum gives fairly results.
III EXPERIMENTAL PROCEDURE SEISMIC
ANALYSIS:
Seismic analysis:
Is a major tool in earthquake engineering which is used to
understand the response of buildings due to seismic
excitations in a simpler manner. In the past the buildings
were designed just for gravity loads and seismic analysis is
a recent development. It is a part of structural analysis and
a part of structural design where earthquake is prevalent.
There are different types of earthquake analysis methods.
Some of them used in the project are-
1. OGS Building
2 Equivalent Static Analyses
1.1 Calculation of design horizontal seismic
coefficient
The total design seismic base shear (VB along any principal
direction shall be determined by following expression.
V A W B h = * (1)
Where, W is the total weight of the building calculated
using the structural
Details and Ah is calculated as shown below:
( ) ( ) ( )
Where, Z is zone factor, I is Importance factor, R is
response reduction factor and Sa/g is spectral acceleration
coefficient.
1.2 Design lateral force at each floor i
The design lateral force, Vb shall be distributed along the
height of the building
∑
Where, Q i = Design lateral force at floor i
W i = Seismic weight of floor i
h i = Height of floor I measured from base and
n = Number of storeys in the building
3. Response Spectrum Analysis Outline:
 Building Detail
 Mass, Stiffness and Damping Matrix
 Dynamic Equilibrium Equation
 Decoupling of Equation of Motion
 Modal Response From Spectrum
 Total Response at Floor
Generation of Mass Matrix, Stiffness Matrix,
Damping Matrix

Mass Matrix:
[ ]
Stiffness Matrix:
[ ]
Damping Matrix:
[ ]
Dynamic Equilibrium Equation
̈ ̈
̈̇̈
U=U(x,t)
For decoupling the equation
U(x,t) =
̈̇̈
Pre multiply with
̈ ̇ ̈
Due to modal orthogonality, M, C, K matrices will become
diagonal matrices
[ ] {
̈
̈
̈
[ ] {
̇
̇
̇
+[ ] { ={ ̈
The decoupled equations are
̈ + ̇ + = ̈
̈ + ̇ + = ̈
̈ + ̇ + = ̈
Divide the equation by mass,
̈ ̇ ̈
̈ ̇ ̈
Generalizing,
̈ ̇ ̈
̈ ̇ ̈ i=1,2,3........n
Where Pi is participation factor
P
Modal Response from Spectrum
Maximum displacement is more important for calculating
the Design forces.
Hence from Response Spectrum.
̈ ̇ ̈
| | ( )
Spectral Displacement (SD) is for complete earthquake but
the particular participation in the total response of the
building. Therefore, the amount of displacement in one
mode is given by:
`| | ( )
Where j represent the floor and i represent the mode.

Total Response at Floor:
As the maximum values do not occur at a same time
instant, the cannot be added. There are two methods for
obtaining total response.
 CQC method ( Complete Quadratic combination)
 SRSS Method (Square root of sum of square)
We use SRSS Method
SRSS Method:
This method is used when first Eigen value is 30 and
second value may be 40, 50, 60.
√( ) ( ) ( )
√( ) ( ) ( )
√ ( )
√ ( )
√ ( )
Data we assume:
 3Storeyed building
 Location- Himachal Pradesh (Zone IV)
 Soil Type- Medium Soil
 Purpose: Residential
 Structure type- Ordinary Moment Resisting Frame
Without Infill.
 Storey Height- 3m
 Column Dimensions : 230mm X230mm
 Beam Dimensions : 230mmX230mm
 Slab Dimensions : 6mX6m
 Number of column : 9
 Number of Beam: 6
 Unit Weight of Concrete: 25KN/m3
 Live Load is 2KN/ m3
 Thickness of slab 100mm
That data is used for Equivalent Static Analysis and
Response Spectrum Analysis.
IV RESULTS
Equivalent Static Analysis
1.000 1.000 1.000
Since natural frequencies are distinct, SRSS method of
modal combination can be used. In such case, maximum
displacement response of the structure is 0.357m
Response spectrum analysis
In such case, maximum displacement response of the
structure is 3.100m
CONCLUSION
 The Response spectrum may give fairly good results,
when maximum displacement and maximum forces
might occur on the structure.
 If time history is available Time history Response is
done for critical structure,.
 In multi-storey buildings maximum displacement
occur in topmost storey.
 In multi-storey buildings torsion moment also exist.
 Vertical stiffness irregularity at a storey in a building
causes increase in storey movement, while buildings
without stiffness irregularity perform well for
lateral loads.
 Base shear will increase when the zones changes
from II to V and soil stratum III to I in Equivalent
Static method as well as Response Spectrum
method.
LIST OF PUBLICATION
 Varadharajan, S., Sehgal, V.K., and Saini, B.(2012),
“Seismic response of multistory reinforced concrete
frame with vertical mass and stiffness irregularities”,
The structural design of tall and special buildings,
Wiley publications , DOI: 10.1002/tal.1045.

 Mohaiminul Haque, Sourav Ray, Amit Chakraborty,
Mohammad Elias, Iftekharul Alam. Seismic
Performance Analysis of RCC Multi-Storied Buildings
with Plan Irregularity. American Journal of Civil
Engineering. Vol. 4, No. 3, 2016, pp. 68-73.
doi: 10.11648/j.ajce.20160403.11
 Bholebhavi Rahul D.1, Inamdar V.M.2 “An Evaluation
of Seismic Response Reduction Factor for Irregular
Structures Using Non Linear Static Analysis”IJIRSET
Vol. 5, Issue 5, May 2016
 Shaikh Abdul Aijaj Abdul Rahman1,* and Ansari
Ubaidurrahman Salik2 “Seismic analysis of vertically
irregular buildings “Received 6 February 2015;
revised accepted 19 July 2016 doi:
10.18520/cs/v111/i10/1658-1663
 C.M. Ravi Kumar1, K.S. Babu Narayan2, M.H.
Prashanth3, H.B Manjunatha4 and D. Venkat “Seismic
Performance Evaluation Of Rcbuildings With Vertical
Irregularity “October 20-21, 2012
 Gowthami.V1 Satheesh V.S2 Dr.SureshBabu.S3 “An
Epitome on 3D Plan Irregularities of RC Buildings
with Seismic Analysis” IJSRD - International Journal
for Scientific Research & Development| Vol. 4, Issue 1,
2016
 Mario De Stefano · Barbara Pintucchi “A review of
research on seismic behaviour of irregular building
structures since 2002”Received: 26 July 2006 /
Accepted: 27 September 2007 / Published online: 23
November 2007

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