Non Linear Static Analysis of Dual RC Frame Structure

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 831
NON LINEAR STATIC ANALYSIS OF DUAL RC FRAME STRUCTURE
Sauhardra Ojha1,Arunendra Mishra2 Mohd Firoj3,Dr.K.Narayan4
1,2,3 P.G.student of Civil Engineering department, Institute of Engineering and Technology Lucknow,U.P.INDIA
4Professor, Civil Engineering department, Institute of Engineering and Technology Lucknow,U.P. INDIA
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Abstract- The performance-based modelingandanalysisof
a 10-story building with special moment resisting frame
(SMRF) as seismic force-resistingsystemandSMRFwithshear
wall (Dual System), is presented here. In performance based
seismic analysis, evaluates how building is likely to perform. It
is an iterative process with selection of performance objective
followed by development of preliminary design, anassessment
whether or not the analysis meets the performance objective.
For structural design and assessment of reinforced concrete
members, the non-linear static analysis has become an
important tool, method can be used to study the behaviour of
reinforced concrete structures including force redistribution.
The paper presents a simple computer-based push-over
analysis technique for performance-based design of building
using non-linear static analysis to developed the capacity and
demand curve, push over curve, rotation of hinge for CP
(collapse prevention) performancepoint. Theseismicresponse
of RC building frame and dual system in terms of performance
point and the effect of earthquake forces on multi storey
building frame with the help of pushover analysis is carried
out in this paper. In the present study the building frame is
analyzed using ETAB’S V.16.03, as per IS 456:2000 and IS
1893:2002 and for non-linear parameter ASCE-41-13 and
EC8-2004 is used.
Key Words: Nonlinear-static analysis,Pushoveranalysis,
Performance based assessment, Dual system
1. INTRODUCTION
Many intra-tectonic plate regionsareconsideredtohavelow
to moderate seismic risk. However, after devastating
earthquakes, Bhuj (2001) occur in these regions and result
in high consequences intermsofcasualtiesanddamage.Low
to medium rise reinforced concrete (RC) structures built in
the majority of these regions are analyze and designed
primarily for combinations of gravity loads. Therefore,
during an unpredictable seismic excitation, satisfactory
response of such framed structures relies on their inherent
factors of ductility and overstrength, also the lack of
knowledge regarding site specific earthquake records in
these regions makes it difficult to develop suitable design
spectra for seismic analysis. Venerability to damage of
structures should be identified and an acceptable level of
safety must be determined. To achieve such assessment,
simplified linear-elastic methods are not proportionate.
Thus, the structural engineeringpeoplehasdevelopeda new
method of analysis and design thatincorporateperformance
based analysis of structures and is moving away from
Simplified linear elastic methods and towards a more better
assessment of structure during an earthquake.
The dual system consist combination of the two lateral load
resisting systems i.e. bare frame and structural wall or
bracing as a major lateral [5] load resisting system. In these
systems the shape of the deformation will differ from those
in frames and wall systems, where effecting interlaced force
occur and change the shape of shear and moment diagrams.
A new method based on the nonlinear model of structural
behaviour due to seismic action,broadlycalledtheNonlinear
Static Pushover Analysis or (NSPA), hasbeendevelopingover
the past two decades, and an extensive [7]researchaimedat
its further improvement is still under way. The NSPA
analysis is founded on the modelling of geometrically and
materially non-linear behaviour of structures, whiletreating
seismic actions as a static load, explicitly through forces or
implicitly through displacements. The NSPA analysis is
generally conducted in two phase. The first phase is
performed using the multidegreeoffreedom(MDOF)model,
while in the second phase the targetdisplacementanalysisis
done using the single degree of-freedom (SDOF)system,ora
direct approach is used.
2. NON LINEAR STATIC ANALYSIS
Nonlinear static analysis procedures (pushover analysis)
have been developed for routine application in the practice
of performance-based earthquake engineering due to their
conceptual simplicity and computational effectiveness. A
pushover analysis is performedbysubjectinga structuretoa
monotonically increasing pattern of lateral loads,
representing the inertial forces which wouldbe experienced
by the structure when subjected to ground shaking.Thiswill
lead to development capacity curve. Basedoncapacitycurve
target displacement is determined under incrementally
increasing loads various structural elements may yield
sequentially [8]. Consequently, at each event, the structure
experiences a loss in stiffness. Using a pushover analysis, a
characteristicnon-linearforcedisplacementrelationship can
be determined. Several practical methodologies involving
nonlinear pushover analysis using an invariant height-wise
lateral force distribution, such as the ATC-40, FEMA-356,
FEMA-440, EC8-2004 and ASCE 41-13. Many structural
systems will experience nonlinear response sometime
during their life, any moderate to strong earthquake will

drive a structure designed by conventional methodsintothe
inelastic range, particularly in certain critical regions.Thisis
very useful numerical integration technique for problems of
structural dynamics is the so called step-by-step integration
procedure.
3. PERFORMANCE OBJECTIVES
A performance objective has two essential parts a damage
state and a level of seismic hazard. Seismic performance is
described by designating the maximum allowable damage
state with drift limit as defined in FEMA-356 [5]. A
performance objective [Fig.1] may include consideration of
damage states for several levelsofgroundmotionand would
then be termed a dual or multiple-level performance
objective. Based on performance objective the capacity and
demand curve is drawn and based on it the suitabledesignis
chosen.
Figure-1: capacity curve of structure
Figure-2: (a) capacity vs. demand curve (Safe design)
Figure-2: (b) capacity vs. demand curve (unsafe design)
4. INELASTIC BEHAVIOUR OF STRUCTURE
The structural elements may themselves comprise of an
assembly of elements such ascolumns,beam, wall piers,wall
spandrels etc. It is important to identify the failure
mechanism for these primarystructural elementsanddefine
their non-linear propertiesaccordingly [7].Thepropertiesof
interest of such elements are relationships between the
forces (axial, bending and shear) and the corresponding
inelastic displacements (displacements, rotations, drifts).
Using the component load-deformation data and the
geometric relationships among components and elements,a
global model of the structure relates the total seismic forces
on a building to it overall lateral displacement to generate
the capacity curve. During the pushover process of
developing the capacity curve as brittle elements degrade,
ductile elements take over the resistance and the result is a
saw tooth shape that helps visualize the performance.
5. HINGE PROPERTIES AND MECHANISM
We may insert plastic hinges at any number of locations
along the clear length of any Frame element or Tendon
object. ETAB’s also admits hinges in vertical Shear wall
elements. Each hinge represents concentrated post-yield
behavior in one or more degrees of freedom. Hinges only
affect the behavior of the structure in nonlinear static and
nonlinear time history analysis. [8]Hingescanbeassignedto
a frame element at any location along the clear length of the
element. Uncoupled moment, torsion, axial force and shear
hinges are available. There are also coupledP-M2-M3hinges
which yield based on the interaction of axial force and bi-
axial bending moments at the hinge location. Sub sets of
these hinges may includeP-M2,P-M3,andM2-M3behaviour.
6. TERMINOLOGY USED IN N.S.P. ANALYSIS
Capacity: The expected ultimate strength (in flexure, shear,
or axial loading) of a structural component excluding the
reduction factors commonly used in design of concrete
members. The capacity usually refers to the strength at the
yield point of the element or structure's [4] capacity curve.
For deformation-controlled components, capacity beyond
the elastic limit generally includes the effects of strain
hardening. Pushover capacity curves approximate how
structure behaves after exceeding the elastic limits.
Demand: A representationoftheearthquakegroundmotion
or shaking that the building is subjected to nonlinear static
analysis procedures, demand is represented by an
estimation of the displacements or deformations that the
structure is expected to undergo. This is in contrast to
conventional, linear elastic analysis procedures in which
demand is represented by prescribed lateral forces applied
to the structure.

Deformation Controlled: Refers to components, elements,
actions, or systems which can, and are permitted to, exceed
their elastic limit in a ductile manner. Force or stress levels
for these components are of lesser importance.
Force Controlled: Refers to components, elements, actions,
or systems which are not permitted to exceed their elastic
limits. This category of elements, generally referred to as
brittle or Nonductile, experiences significant degradation
after only limited post-yield deformation.
Target Displacement: The target displacement is intended
to represent the maximum displacement likely to be
experienced for the selected Seismic Hazard Level. In the
displacement coefficient method. The targetdisplacement is
the equivalent of the performance point in the capacity
spectrum method [9]. The target displacement is calculated
by use of a series of coefficients.
7.MATERIALPROPERTIESANDDATADESCRIPTION
In the model, the support condition was assumed to be fixed
Building was a symmetric structure with respect to both the
horizontal directions. soil structure interaction is not
considered during analysis, the data used during analysis
tabulated here.
Table -1 : Modeling Detail of Structure
1 Number of story 10 (G+9)
2 Floor to floor height 3.2m
3 Bottom story height 4.0m
4 Slab thickness 150mm
5 Size of beam 350mm x 500mm
6 Size of column 550mm x 550mm
7 Thickness of shear wall
and it’s grade
150mm, M40
8 Zone and zone factor IV, 0.24
9 Importance factor 1
10 Response factor (R) 5
11 Soil type II ( Medium )
12 Grade of concrete and
rebar in beam
M35, Fe500
13 Grade of concrete (Slab) M35
14 Grade of concrete and
rebar in column
M40, Fe415
15 Grade of shear wall M40
16 Live load and floor finish
load
3kN/ and1kN/m2
kN/
17 Top floor load 2kN/
18 Masonry load Half brick wall, 7.2
kN/m
Figure-3: Plan of bare RC frame
Figure-4: Plan of dual R.C frame with side center
shear wall
Figure-5: 3-D view of bare RC frame structure

Figure-6: 3D view of dual RC frame structure with side
center shear wall.
8.TARGET DISPLACEMENT CALCULATION
a. As Per ASCE 41-13
As per ASCE 41-13 the target displacement is given by
equation
(1.0)
Where is calculated as
(1.1)
is the effective fundamental period in the directionunder
consideration shall be based on the idealized force–
displacement curve.
, is Elastic fundamental period (in seconds) in the
direction under consideration calculated by elastic dynamic
analysis.
, is Elastic lateral stiffness of the building in the direction
under consideration.
, is Effective lateral stiffness of the building in the
direction under consideration.
, is Response spectrum acceleration at the effective
fundamental period and damping ratio of the building in the
direction under consideration.
, is Modification factor to relate spectral displacement of
an equivalent single-degree-of-freedom (SDOF) system to
the roof displacement of the building multi degree of-
freedom (MDOF) system.
, is Modification factor to relate expected maximum
inelastic displacementscalculatedforlinearelasticresponse.
is modification factor to represent the effect of pinched
hysteresis shape, cyclic stiffness degradation, and strength
deterioration on the maximum displacement response.
b. As Per EC 8-2004
The following relation between normalized lateral forces
and normalized displacements is assumed,
(2.0)
Where is mass at ith storey
The mass of an equivalent SDOF system is determined
as:
= (2.1)
And the transformation factor is given by:
= (2.2)
The force and displacement of equivalent SDOF is
computed as:
= and =
Where and are respectively, the base shear force and
the control node displacement of the Multi Degree of
Freedom (MDOF) system.
Based on this assumption, the yield displacement of the
idealized SDOF system is given by:
= 2 (2.3)
Where, is the actual deformation energy up to the
formation of the plastic mechanism.
The period of the idealized equivalent SDOF systen1 is
determined by:
= 2π (2.4)
For the determination of the target displacement for
structures in the short-period rangeandforstructuresin the
medium and long-period ranges different expressions.
= ≥ (2.5)
The target displacement of the MDOF system
corresponding to control node is given by:
= (2.6)

9. RESULT
As per the objective, work methodology and structural
modeling, analysis of both structure bare RC frame and dual
RC frame structure is done with help of ETAB v16.03.The
result of the analyzed structure is presented using codes,
ASCE 41-13, and EC 8-2004. The result is so presented that
we can easily compare both structure for concerned
objectives.
9.1 PUSH OVER DATA
Push over (base shear vs. roof displacaement) data for bare
RC and dual RC frame in X and Y direction
Chart-1: Push over data in X direction
Chart-2: Push over data in Y direction
9.2 SEQUENTIAL HINGE FORMATION
Step1
Step 2

Step 5
Step 6
In Y direction of bare frame out of 2600 hinges only 21 is in
the region of > CP and final roof displacement was 138.91
mm found. Whereas in dual RC frame out of 2640 hinges
none is in the region of > CP and final roof displacement was
60.48mm found
In X direction out of 2600 hinges only 12 is in the region of >
CP and roof displacement was 122.0mm found.whereas in
dual RC frame structure out of 2640 hinges only 1 hinges in
the region of >CP and final roof displacement was 58.41mm
found.

Chart-3: Natural time period of the structure
Chart-4: Total no. of hinges in elastic region
9.3 TARGET DISPLACEMENT AS PER ASCE 41-13
Table-2: Target displacement In X direction of bare RC
frame
Table-3: Target displacement In X direction of dual RC
frame
Target
Displacement
(δ)
198.64mm Maximum
Shear (V)
20051.61 kN
Yield
displacement
(
64.10mm Yield base
shear ( )
11771.21 kN
9.4 TARGET DISPLACEMENT AS PER EC-8 2004
Chart-5: Target dispalcement as per EC-8 2004
CONCLUSIONS
The performance of reinforced concretebareanddual frame
with side center shear wall was investigated using the
pushover Analysis in ETAB’s. The conclusions drawn from
the analysis is given here.
(a) We can conclude from the sequential hinge
formation data that when we analyze the structure
for C.P. performance point, collapse hinges formed
in dual RC frame is less as compared to bare RC
frame.
(b) From Pushover data of both structure we can say
that displacement in both X and Y direction is less
for RC dual frame structure and dual RC frame has
more base shear at less displacement which shows
that dual RC frame shows more resistance against
lateral loads.
(c) The critical time period for bare RC frame is 1.305s,
more as compared to dual RC frame which has
0.967s, which shows the stiffness of the dual RC
frame is increased and the dual system behaves
better during lateral load.
(d) Target displacement data shows that shear wall is
more suitable for non-linear range where yield
displacement is not much more affected in case of
dual RC frame.
(e) Target displacement as per EC-8-2004 is more
accurate as compare to ASCE because it is based on
MDOF.
REFRENCES
[1] Limin JIN, Atila ZEKIOGLU And King-Le CHANG
“Performance Based Analysis And Modeling of A
Dual Seismic force-Resisting System” 12 WCEE
2000
Target
Displacement (δ)
182.65mm
Maximum
Shear (V)
21459.73 kN
Yielddisplacement
(
56.15mm
Yield base
shear ( )
12556.76 kN

[2] T. Paulay “Displacement Capacity of Dual
Reinforced Concrete Building Systems” pacific
conference on earthquake engineering 2003.
[3] M.J.N. Priestley, G.M. Calvi and M.J.Kowalsky
“Direct Displacement-Based Seismic Design of
Structures” 2007 NZSEE Conference.
[4] ATC-40 (1996), “Guidelines for Seismic
Rehabilitation of Buildings, Volume 1: seismic
evaluation and retrofit of concrete buildings,”
Applied Technology Council, Redwood City,
California.
[5] FEMA-356 (2000). Pre-standard and Commentary
for the Seismic Rehabilitation of Buildings, Federal
Emergency Management Agency, Washington, DC.
[6] Chopra AK, Goel RK. “A Modal Pushover Analysis
Procedure for Estimating Seismic Demands for
Buildings.” Earthquake Engineering Structural
Dynamics, 2002, 31(3): 561-582.
[7] Naeim F (Ed). “The seismic design
handbook.” Kluwer Academic Publishers,
MA, 2001.
[8] ETAB’s 16.03 and it’s user manual of analysis
Computers and Structures, Inc, CA.
[9] ASCE, 41-13 2000, Standard Methodology for
Seismic Evaluationandretrofitofexisting Buildings.
American Society of Civil Engineers, Reston,
Virginia.
[10] Kadid and A. Boumrkik “Pushover Analysis of
ReinforcedConcreteFrameStructuresAsianJournal
of Civil Engineering (Building And Housing) Vol. 9,
No. 1 (2008) Pages 75-83

Non Linear Static Analysis of Dual RC Frame Structure

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