comparative study of reinforced concrete shear wall ... · pdf file183 int. j. struct. &...

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Int. J. Struct. & Civil Engg. Res. 2013 Satpute S G and D B Kulkarni, 2013

COMPARATIVE STUDY OF REINFORCEDCONCRETE SHEAR WALL ANALYSIS IN MULTI-

STOREYED BUILDING WITH OPENINGS BYNONLINEAR METHODS

Satpute S G1* and D B Kulkarni1

1 Department of Civil Engineering, Rajarambapu Institute of Technology, Rajaramnagar, Islampur, Dist. Sangli, Maharashtra, India 415414.

*Corresponding author:Satpute S G, [email protected]

ISSN 2319 – 6009 www.ijscer.comVol. 2, No. 3, August 2013

© 2013 IJSCER. All Rights Reserved

Int. J. Struct. & Civil Engg. Res. 2013

Research Paper

INTRODUCTIONThe reinforced concrete shear wall is importantstructural elements placed in multi-storeybuildings which is situated in seismic zonesbecause they have a high resistance to lateralearthquake loads. RC shear walls must havesufficient ductility to avoid brittle failure underthe action of strong lateral seismic loads. The

adverse effect for tall building is the higherlateral loads due to wind and expectedearthquake. Thus shear walls are introducedinto modern tall buildings to make the structuralsystem more efficient in resisting the horizontaland gravity loads, ground motions as wellthereby causing less damage to the structureduring earthquake. Shear walls in apartment

The reinforced concrete shear wall is one of the most commonly used lateral load resisting inhigh rise building. The reinforced concrete shear wall building is high in plane stiffness andstrength which can be used to simultaneously resist large horizontal load and support gravityload. The scope of the present work was to study seismic responses of the ten storey RC shearwall building with and without opening. Developed mathematical modeling and analyzed thereinforced concrete shear wall building by using different nonlinear methods (time history andpushover method). These methods differ in respect to accuracy, simplicity, transparency andclarity of theoretical background. Non-linear static procedures were developed with the aim ofovercoming the insufficiency and limitations of linear methods, whilst at the same time maintaininga relatively simple application. All procedures incorporate performance-based concepts payingmore attention to damage control. Analysis is carried out by using standard package SAP2000.The comparison of these models for different parameters like displacement, storey drift andbase shear has been presented by RC shear wall building with and without opening.

Keywords: Seismic evaluation, Pushover analysis, Time history analysis, RC shear wallBuilding, Openings

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buildings will be perforated with rows ofopenings that are required for windows inexternal walls or doors ways or corridors ininternal walls. However the opening sizes inthe shear wall building may have an adverseeffect on seismic responses of frame-shearwall structures. Relative stiffness of shear wallsis important since lateral forces are distributedto the individual shear wall according to theirrelative stiffness. Simplified methods forstiffness of shear walls with openings arerecommended in several design guidelines. Itis necessary to know the effects of openingssizes and configurations in shear wall onstiffness as well as on seismic responses andbehavior of structural system so that a suitableconfiguration of openings in shear walls canbe made.

Reinforced concrete shear wall buildingsare designed primarily to serve the needs ofan intended occupancy. One of the dominantdesign requirements is therefore the provisionof an appropriate internal layout of buildings.Once the functional layout is established thento develop a structural system that will satisfythe established design criteria as efficientlyand economically as possible while fitting intothe architectural layout. The vital structuralcriteria are an adequate reserve of strengthagainst failure, lateral stiffness and an efficientperformance during the service life of thebuildings.

SEISMIC ANALYSIS METHODSNonlinear Static Analysis -Pushover Analysis

Pushover analysis is an approximate analysismethod in which the structure is subjected tomonotonically increasing lateral forces with an

invariant height-wise distribution until a targetdisplacement is reached. Pushover analysisconsists of a series of sequential elasticanalysis, superimposed to approximate aforce-displacement curve of the overallstructure. A two or three dimensional modelwhich includes bilinear or trilinear load-deformation diagrams of all lateral forceresisting elements are first created and gravityloads are applied initially. A predefined lateralload pattern which is distributed along thebuilding height is then applied. The lateralforces are increased by some members yield.The structural model is modified to account forthe reduced stiffness of yields members andlateral forces are again increased untiladditional members yield. The process iscontinued until a control displacement at thetop of the building reaches a certain level ofdeformation or structure becomes unstable.The roof displacement is plotted with baseshear to get the global capacity curve.

Pushover analysis can be performed asforce-controlled or displacement-controlled. Inforce-controlled pushover procedure, the fullload combination is applied as specified, i.e.,force-controlled procedure should be usedwhen the load is known (such as gravityloading). Also, in force-controlled pushoverprocedure some numerical problems thataffect the accuracy of results occur since targetdisplacement may be associated with a verysmall positive or even a negative lateralstiffness because of the development ofmechanisms and P-delta effects.

Pushover analysis has been the preferredmethod for seismic performance evaluation ofstructures by the major rehabilitation guidelines

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and codes because it is conceptually andcomputationally simple. Pushover analysisallows tracing the sequence of yielding andfailure on member and structural level as wellas the progression of the overall capacity curveof the structure.

Nonlinear Dynamic Analysis – TimeHistory Analysis

Nonlinear dynamic analysis is most accuratemethod to determine the seismic responsesof structures. In this method the structure issubjected to actual ground motion which is therepresentation of the ground accelerationversus time. The ground acceleration isdetermined at small time step to give theground motion record. Then the structuralresponse is calculated at every time instant toknow its time history and the peak value of thistime history is chosen to be design demand.Hence, “A mathematical model directlyincorporating the nonlinear characteristic ofindividual component and element of thebuilding shall be subjected to earthquakeshaking represented by ground motion timehistory to obtain forces and the displacement”.Since numerical model directly accounts forthe effect of material nonlinearity, inelasticresponses and calculated internal forces willbe reasonably approximate to those expectedduring the design earthquake. There are twomethods by which the time history analysis iscarried out (a) Nonlinear Modal Time HistoryAnalysis; and (b) Nonlinear Direct IntegrationTime History Analysis.

Nonlinear Modal Time HistoryAnalysis

As mentioned earlier, from the fundamental ofstructural dynamics it is clear that the response

of the MDOF system can be estimated fromits modal responses. In this analysis, also calledas Response history Analyses, the modal loadvectors are determined for the predefined noof modes. For the selected mode, the staticanalysis of the structure is carried out toestimate its modal static responses, thestructure being subjected to correspondingmodal load vector. Then the dynamic analysisof the corresponding ESDOF system iscarried out to get its spectral ordinates at everytime step. This spectral ordinate at each timestep is multiplied with the corresponding modalstatic response to get the actual Time historyof that response for that modal quantity. Thesame procedure is carried out to other modesand corresponding modal response history isdetermined. These modal responses are thenadded at each time step to get the time historyof the selected response for the design groundmotion record.

Nonlinear Direct Integration TimeHistory Analysis-

The fundamental equation governing theresponse of MDOF system subjected to ground

acceleration is given by ( )u t

.sin ( )s gmu cu f u u mtu t

The only unknown quantity in the aboveexpression is the displacement vector u. In thismethod the above equation is formulated forthe entire structure at every time step at whichthe ground acceleration is determined. Thisequation is then solved by any of the well knownmethods to get directly the displacement ateach time step. The other response quantitytime history is then calculated from knowndisplacement time history. The peak from the

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particular response time history is thenselected as the design demand.

STRUCTURAL MODELINGAND ANALYSISThe finite element analysis software SAP2000,Nonlinear is utilized to create 3D models andrun all analyses. The software is able to predictthe geometric nonlinear behavior of spaceframes under static or dynamic loadings,taking into account both geometric nonlinearityand material inelasticity. The software acceptsstatic loads (either forces or displacements)as well as dynamic (accelerations) actions andhas the ability to perform eigenvalues,nonlinear static pushover and nonlineardynamic analyses.

Details of the Model

The model which has been adopted for thestudy are ten storeys (G+9) RC shear wallbuilding. The buildings consist of wall thickness230 mm. The floor slabs are taken as 125 mmthick. The height of all the ten stories is 3 m..The live load is taken as 3.5 KN/m2 and 2 KN/m2 for floor and terrace, respectively from IS1893-2002 (Part-I) (Figure 1).

Rectangular shear walls building with andwithout opening were modeled using shellelements available in structural analysisprogram SAP2000. For the parametric study,the percentage of centered opening in theexternal face of the building was increased from0%, 14%, 25%, 33%, and 42% model. Thefollowing models have been considered.

Dimensions of Proposed Model

Plan dimension of structure = 20 m × 12 m

No of bays in X-direction = 5

No of bays in Y-direction = 4

Spacing of bays in X-direction = 4.0 m

Spacing of bays in Y-direction = 3.0 m

Height of all typical floors (including groundfloor) = 3.0 m

Height of parapet wall = 1 m (all around theperiphery of roof floor)

RESULTS AND DISCUSSIONAnalyze the reinforced concrete shear wallbuildings with and without opening by usingthe nonlinear dynamic method-Time Historyanalysis

The time history procedure is used if it isimportant to represent inelastic responsecharacteristics or to incorporate time

Figure 1: Model Plan Consideredin the Study

Table 1: Opening in Percentage

Model Opening %

1 0

2 14

3 25

4 33

5 42

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85.91%, 87.09%, 90.05%, respectively whichis considerable when compared to the valuesof model 1. The percentage variation of topdisplacements for all the models shown inTable 2.

Storey Drift

Storey drift is the displacement of one levelrelative to the other level above or below.Figure 3 shows the comparison of curves fordifferent storey height and storey drift.

From Figure 3 observed that storey driftincreases as the height of storey increased

Figure 2: Shows the Comparisonof Storey Height and Displacement

Curves for Different Storey Height WiseDistributions for all the Models

dependent effects when computing thestructures dynamic response. The realearthquake ground motions are taken timehistory analysis of koyana earthquake (xdirection), damping of 5% is taken forearthquake ground motions

Lateral Displacements

Figure 2 shows the comparison of storeyheight and displacement curves for differentstorey height wise distributions for all themodels.

From Figure 2 observed that the displacementof model 2, 3, 4, 5 is increased to 84.97%,

Figure 3: Shows the Comparisonof Storey Height and Storey Drift Curves

for Different Storey Height WiseDistributions for all the Models

Table 2: Percentage Variation inDisplacement for all the Models

Model No. Variations of Top Displacement (%)

1 0

2 84.97

3 85.91

4 87.09

5 90.05

Table 3: Percentage Variation in StoreyDrift for all the Models

Model No. Variations of Story Drift (%)

1 0

2 75.27

3 85.43

4 66.50

5 79.00

0

3000

6000

9000

12000

15000

18000

21000

24000

27000

30000

33000

0 1 2 3 4 5 6 7Displacement (mm)

Sto

rey

heig

ht (

mm

)

Model 1Model 2 Model 3Model 4 Model 5

0

3000

6000

9000

12000

15000

18000

21000

24000

27000

30000

33000

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1Storey drift (mm)

Sto

rey

heig

ht (

mm

)

Model 1Model 2 Model 3Model 4 Model 5

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and reduced at the top floor. The percentagevariation of model 2, 3, 4, 5 is variable to75.27, 85.43, 66.50, 79, respectively which isconsiderable when compared to the values ofmodel 1 shown in Table 3.

Time History Curves of Base Shearand Time

The base shear and time of all the building asobtained from time history analysis inSAP2000. From Figures 4 to 8 shows themaximum and minimum base shear and time.

Max. Base shear = 1212 KN at time 3.76 s

Min. Base shear = –1468 KN at time 3.44 s

Figure 4: Shows the BaseShear Vs. Time for Model 1

Max. Base shear = 2724 kN at time 3.96 s

Min. Base shear = –2553 kN at time 4.16 s



Min. Base shear = –2304 KN at time 4.20s



Min.Base shear = -1668 KN at time 3.44 s


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to 71.14%, 78.32%, 81.21%, 82.63%respectively which is considerable whencompared to the values of model 1. Thepercentage variation of top displacement forall the models shown in Table 4.

Figure 9: Shows the Comparison ofPushover Curves for Different

Displacements and Storey Height



Min. Base shear = –1154 KN at time 3.48 s

Analyze The Reinforced ConcreteShear Wall Buildings With AndWithout Opening By Using TheNonlinear Static Method- PushoverAnalysis

Lateral Displacement

Lateral Displacement of models at each storeyheight for all the models is shown in Figure 9.

From Figure 9 observed that thedisplacement of model 2, 3, 4, 5 is increased

Table 4: Percentage Variation in TopDisplacement for all the Models

Model No. Variations of Top Displacement (%)

1 0

2 71.14

3 78.32

4 81.21

5 82.63

Storey Drift

Storey drift is the displacement of one levelrelative to the other level above or below. Figure10 shows the comparison of curves fordifferent storey height and storey drift.

From Figure 10 observed that storey driftis increased as the height of storey increasedand reduced at the top floor. The percentagevariation of model 2, 3, 4, 5 is variable to44.53, 32.74, 58.83, 47.32, respectively whichis considerable when compared to the valuesof model 1 shown in Table 5.

Figure 10: Shows the Comparisonof Curves For Different Storey Height

and Storey Drift

0

3000

6000

9000

12000

15000

18000

21000

24000

27000

30000

33000

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30Storey drift (mm)

Stor

ey h

eigh

t (m

m)

Model 1Model 2Model 3Model 4Model 5

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Capacity SpectrumCapacity spectrum is the capacity curvetransformed from base shear vs. roofdisplacement coordinates into spectralacceleration vs. spectral displacement (Sa vs.S

d) coordinates. The performance point is

obtained by superimposing demand spectrumon capacity curve transformed into spectralcoordinates. To have desired performance,every structure has to be designed for thespectral acceleration corresponding to theperformance point.

The reduced demand spectra intersectedthe capacity spectra. The performance pointcalculated is within 5% of the assumed value.The calculated spectral displacement is theinelastic displacement that the equivalentsingle degree of freedom structure willexperience for the given level of earthquake.

A roof displacement that the structure willundergo = 5.142 mm

Drift ratio =5.142*100/30000=0.44 % <1%(Immediate occupancy state)

Table 5: Percentage Variation in StoreyDrift for all the Models

Model No. Variations of storey drift (%)

1 0

2 44.53

3 32.74

4 58.83

5 47.32

Figure 11: Shows The CapacitySpectrum For Model 1


A roof displacement that the structure willundergo = 42 mm

Drift ratio =42*100/30000=0.14 % <1%(Immediate occupancy state)


Drift ratio = 64*100/30000 = 0.21 % <1%(Immediate occupancy state)


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Evaluation of Seismic Performanceof Buildings

The seismic performance of a building ismeasured by the state of damage under acertain level of seismic hazard. The state ofdamage is quantified by the drift of the roofand the displacement of the structuralelements. Initially, gravity push is carried outusing the force control method. It is followedby a lateral push with displacement controlusing SAP2000. For carrying outdisplacement based pushover analysis, targetdisplacement needs to be defined. Pushoveranalysis gives an insight into the maximumbase shear that the structure is capable ofresisting. A building performance level is acombination of the performance levels of thestructure and the nonstructural components. Aperformance level describes a limitingdamage condition which may be consideredsatisfactory for a given building with specificground motion. The structural performancelevels as per FEMA 356 are; (1) Operational,(2) Immediate Occupancy (IO), (3) Life Safety(LS), (4) Structural Stability and (5) CollapsePrevention (CP). Typical values of roof driftsfor the three performance levels (FEMA356)are; (i) Immediate Occupancy: Transient driftis about 1% or negligible permanent drift, (ii)Life Safety: Transient drift is about 2% or 1%permanent drift, (iii) Collapse Prevention: 4%transient drift or permanent drift.

CONCLUSIONIn this work, by performing of RC shear wallsbuilding with openings ten storey building wascarried out to compare the different sizes ofthe opening analysis by nonlinear static andnonlinear dynamic method. The analysis of RCshear walls with openings building was carried





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out using the SAP2000 nonlinear software tool.The following conclusions are drawn on thebasis of the numerical results obtained bysoftware.

1. The values of seismic responses namelybase shear, storey displacement and storeydrift for the both methods are found to beincreasing order for model 1, 2, 3, 4, and 5.

2. The variation in the height-wise distributionof top displacement increase by 84.97%,85.91%, 87.09%, 90.05% in time historyanalysis and 71.14%, 78.32%, 81.21%, and82.63% in pushover analysis for model 2,3, 4, 5, respectively as compared to valueof model 1.

3. As a percentage of opening increases withincreases displacements.

4. The distribution of the story drift ratio overthe frame height becomes non uniform asframe height increases for both themethods. Storey drift ratios for differentdamage states of class of buildingsdesigned as per IS1893-2002.

5. The capacity spectrum method givesdemand curve intersects the capacity curveat event IO (immediate occupation), soplastic hinges occurred in the structureremains stable.

ACKNOWLEDGMENTThe authors sincerely thank for staff of CivilEngineering Department, RajarambapuInstitute of Technology, Shivaji University,Maharashtra, India.

REFERENCES1. ATC-40 (1996), “Seismic Evaluation And

Retrofit Of Concrete Buildings”, Vol. 1,

Applied Technology Council, SeismicSafety Commission, State of California.

2. Balkaya C and Kalkan E (2004), “Three-Dimensional Effects on Openings ofLaterally Loaded Pierced Shear Walls”,Journal of Structural Engineering, Vol.130, No. 10, ©ASCE, ISSN 0733-9445.

3. Golghate K, Baradiya V and Sharma A(2013), “Pushover Analysis of 4 Storey’sReinforced Concrete Bui lding”,International Journal of Latest Trends inEngineering and Technology (IJLTET),Vol. 2, No. 3, ISSN: 2278-621X.

4. Husain M A (2011), “Analysis of ShearWall with Openings using Brick Element”,European Journal of Scientific ResearchISSN 1450-216X, Vol. 51, No. 3, pp. 359-371 © Euro Journals Publishing.

5. Indian Standard Criteria for EarthquakeResistant Design of Structures, Part 1:General Provisions and Buildings, IS:1893 (Part 1) – 2002.

6. Indian Standard Plain and ReinforcedConcrete – Code of Practice IS: 456 –2000.

7. IS: 13920- 1993 Indian Standard- “DuctileDetail ing of Reinforced ConcreteStructures Subjected To Seismic Forces”,Bureau of Indian Standards, New Delhi.

8. Kima H, Lee D and Kim C (2005),“Efficient three-dimensional seismicanalysis of a high-rise building structurewith shear walls”, Engineering Structures,pp. 963-976.

9. Parvathaneni S and Elavenil S (2012),“Time History Response Prediction ForMulti-Storey Buildings Under Earthquake

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Ground Motions”, Journal of Civil,Structural, Environmental, Waterresources and InfrastructureEngineering Research (JCSEWIER),Vol. 2, No. 2.

10. Rahman M K, Ajmal M, Baluch M H andCelep Z (2012), “Nonlinear StaticPushover Analysis of Eight Storey RCFrame Shear Wall Building In SaudiArabia”, 15 WCEE.

11. Romy M and Prabha C (2011), “Dynamic

Analysis of RCC Buildings with ShearWall”, International Journal of EarthSciences and Engineering, ISSN 0974-5904, Vol. 4, No. 6 SPL, pp. 659-662.

12. Sakurai M, Kuramoto H, Matsui T andAkita T (2008), “Seismic Performance OfRC Shear Walls With Multi-Openings”,The 14th World Conference onEarthquake Engineering, Beijing, China.

13. SAP 2000 Nonlinear Version 15 SoftwarePackage.

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