=

NRQS=

SWrucWural Analysis of HisWorical ConsWrucWions – Jerzy Jasieńko (ed) © 2012 DPNH ProcławH PolandH ISSN 0860-2395H ISBN 978-83-7125-216-7

mbocloMANCb-BApba pbIpMIC bsAirATIlN ANa obTolcITTINd lc eIpTloIC rNobINcloCba ClNCobTb tAii BrIiaINdp tITe INTboIlo pTbbi coAMbp lguz dunesNI Burcu dunesOI fsmet SozenogluP ABpToACT =

merformanceJbased=seismic=evaluation=of=historical=constructions=is=a=challenge=due=to=the=difficulty=of=their=structural=analysis=that=accurately=captures=their=nonlinear=behaviorK=qhis=paper=focuses=on=the=use=of=PJa=nonlinear= finite=element=method=for=static=pushover=analysis=of=unreinforced=concrete=EroCF=wall= buildings= with= interior= steel= frames= for= seismic= evaluation= and= retrofit= designK= qhree= such=historical=school=buildings=with=different=levels=of=structural=compleñity=were=modeled=in=detail=using=advanced=finite=element=programs=to=obtain= their= linear=and=nonlinear= behavior=under= monotonically=increasing= lateral= loadsK= qhe= capacity= curves= obtained= from= pushover= analyses= were= used= for=performance=evaluation=using= the=Capacity=ppectrum=jethodK=oetrofit= design=verification=for=one=of=the= buildings= was= performed= using= the= same= approachK= qhe= results= show= that= despite= its= involved=modeling= process= and= computational= eñpenseI= pushover= analysis= of= buildings= with= roCLroj=elements= using= PJa= nonlinear= finite= element= method= can= become= a= powerful= practical= tool= for=improved=seismic=performance=evaluation=and=retrofit=designK===heywords: merformance-based designI Seismic evaluationI mushover analysisI oetrofitting NK INTolarCTIlN merformanceJbased=seismic=evaluation=and=design=procedures=are=commonly=used=for=buildings=around=the=world=to=mitigate=the=increasing=seismic=eñposure=and=risk=in=urban=areas=xNJPzK=cor=low=to=midJrise=frame=buildingsI=the=behavior=of=which=are=controlled=by=their=first=mode=shape=vectorI=nonlinear=static=pushover=analysis=has=proven=itself=as=a=fairly=accurate=and=efficient=tool=for=performance=based=design=and= evaluation= xQI= RzK= Buildings= with= roC= or= roj= structural= wallsI= howeverI= continue= to= be=a=challenge= for= researchers= and= practitioners= alike= due= to= difficulties= in= their= nonlinear= pushover=analysisK= eistoric= structures=present= a= special= challenge= due= to= the= limited= information= regarding= the=material =properties =and =the =structural =systemK =oesearch =in =this =area =is =mainly =concentrated =on =roj=buildings= due= to= relatively= modest= number= of= historic= buildings= with= roC= structural= elementsK=eoweverI=the=methods=developed=for=nonlinear=analysis=of=roj=structures=can=be=easily=eñtended=to=roC=structures=due=to=similarities=in=their=macroJscale=behavior=and=failure=modesK==qhe=research=presented=in=this=paper=is=a=comprehensive=PJa=nonlinear=finite=element=modeling=study=performed=for=buildings=with=roC=structural=walls=xSzK=thile=the=general=approach=is=valid=for=most=roC=or=roj=structures=or=their=componentsI= this=study=focused=on=steel=frame=buildings=with=roC=shear= wallsI= classified= as= pQ= type= buildings= by= cbjA= xTI=UzK= Buildings= with= this= type= of= structural=system=were=commonly=built=in=the=late=NVth=and=early=OMth=centuries=in=the=rKpK=and=around=the=worldK=qhose=still=standing=today=have=historical=and=architectural=significance=and=their=seismic=performance=is=a=concern=for=the=ownersK=aamage=eñperienced=by=both=concrete=and=masonry=wall=buildings=during=

================================================N=Assistant=mrofessorI=Cankaya=rniversityI=ogunes]cankayaKeduKtr=O=Assistant=mrofessorI=Atilim=rniversityI=bgunes]atilimKeduKtr=P=Chief=AnalystI=qranpystems=CorporationI=TS=testbury=mark=odI=tatertownI=Cq=MSTVR=rKpKAK=

=

NRQT=

recent= earthquakes= and= the= lack= of= consistent= and=accurate= methods= and= criteria= for= their= structural=evaluationI=retrofit=and=repair=is=the=main=motivation=behind=this=researchK=qhe=main=objective=of=this=research=was=to=investigate=the=use=of=PJa=nonlinear=finite=element=modeling=approach=for=static=pushover=analysis=of=pQ=type=buildings=in=order=to=establish=a=practical=procedure=for=improved= seismic= evaluation= and= retrofit= designLverification= practicesK= qhree= pQ= type= buildings= with=different= levels= of= geometric= and= structural= compleñity= were= selected= as= case= studies= for= pushover=analysesK=aetailed=finite=element=models= of= these=buildings=were=constructed=using=two=different= finite=element= programsI= pAmOMMM®= xVz= and= ABAnrp®= xNMzI= to= determine= their= linear= and= nonlinear=behaviorK= konlinear= material=behavior= of=concrete=was=modeled=using=the=Concrete=aamage=mlasticity=ECamF= modelK= mostJcracking= tension= softening= behavior= of= concrete= was= modeled= through= the= stressJcracking=displacement=relationship=approachI=and=an=eñponential=softening=curve=was=used=for=improved=accuracyK=qhe=fracture=energy=value=needed=to=construct=the=softening=curve=was=obtained=from=the=CbBJcfm= jodel= Code= xNNz= using= the= characteristics= of= the= concrete= samples= obtained= from= caseJstudy=buildingsK=qhe=oiks=jethod=xNOz=was=used=as=the=iterative=nonlinear=solution=procedureK=A=viscoplastic=regularization= method= was= used= for= stability= and= convergence= of= the= solution= processK= qhe= capacity=curves=obtained=from=pushover=analyses=were=used=to=determine=the=performance=level=of=buildings=by=implementing=the=Capacity=ppectrum=jethod=xNPI=NQz=described=in=AqCJQM=xNz=and=AqCJRR=xOz=reportsK=cinallyI= retrofit= design= verification= studies= for= one= of= the= buildings= were= performed= using= the= same=approach=outlined=above=to=investigate=the=effectiveness=of=the=selected=retrofit=strategyK== OK abpCoImTIlN ANa cb MlabiINd lc Teb CApb-pTraY BrIiaINdp= =qhe=selected=caseJstudy=buildings=are=located=in=fstanbulI=qurkeyI=and=are=owned=by=an=American=high=schoolK=aesigned=and=built=by=rKpK=companies=in=the=early=OMth=century=Ebetween=NVNP=and=NVOQFI=the=buildings=have=historical=and=architectural=significanceK=All=three=buildings=are=pQ=type=buildings=with=distinct= structural= characteristics= despite= their= common= typeK= cigK=N= shows= the= cb= models= of= the=buildings=constructed=using=pAmOMMM=and=ABAnrp=programs===

Building=o Building=i Building=CBuilding=o Building=i Building=C

=EaF=pAmOMMM=jodels=

=

= = ==

EbF=ABAnrp=jodels=

cigK N=cinite=element=models=of=the=caseJstudy=buildings=

=

NRQU=

BuildingJo=ErectangularF=is=a=four=storey=building=with=plan=dimensions=of=NRKP=m=˜=PMKR=m=and=floor=heights=of=PKR=m=in=the=basementI=QKNN=m=in=the=ground=floor=and=PKV=m=in=the=upper=floorsK=BuildingJi=EiJshapedF=is=a=four=storey=iJshaped=buildingK=qhe=dimensions=of=the=building=at= the=outer=edges=are=PQKV= m=by= OPKT= mI= and= those= at= the= inner= edges= are= OMKN= m= by= VKS= mI= constituting= a= plan= area= of=approñimately=SPR=mOK=qhe=floor=heights=are=PKR=m=in=the=basement=and=QKNN=m=in=the=remaining=floorsK=BuildingJC= ECJshapedF= is= a= five= storey= symmetric= building= with= plan= dimensions= of= RPKOP= m= by=OQKOR=m=at=the=outer=edgesI=constituting=a=plan=area=of=approñimately=NNNO=mOK=qhe=structural=systems=of=all= three=buildings=are=steel= frames=with=concrete=bearingLshear=wallsK=qhe=interior=steel=framesI=shown=in=cigK=NaI=resist=the=gravity=loadsK=All=steel=frame=members=are=embedded=in= concrete= with= no= transverse= reinforcement= for= fire= protection= and= for= lateral= supportK= qhe= frame=members= are= connected= by= riveted= connections= with= little= moment= resisting= capacityK= qhe= floor=systems=consist=of=reinforced=concrete=slabs=which=are=simply=supported=by=the=eñterior=walls=with=the=help=of=their=reinforcement=embedded=in=the=walls=in=the=form=of=ninety=degree=hooksK=qhe=lateral=load=resisting=systems=of=all=buildings=primarily=consist=of=eñterior=unreinforced=concrete=shear=walls=which=also=carry=part=of=the=floor=loadsK=qhe=fact=that=all=eñterior=walls=are=perforated=shear=walls=with=rather=large= window= and= door= openings= raised= concerns= about= their= seismic= performance= in= view= of= the=compleñ=inJplane=load=behavior=of=perforated=shear=wallsK=cb=modeling=of=the=buildings=was=performed=using=two=different=finite=element=programs=as=shown=in=cigK=NK= All= three= buildings= were= first= modeled= using= pAmOMMMI= a= program= that= enables= pushover=analysis= of= frame= structuresI= however= is= unable= to= consider= material= nonlinearity= for= OJa= or= PJa=elements= used= to= model= wallsK= eenceI= the= same= models= were= also= built= in= ABAnrpI= an= advanced=finite= element=program=with=a=more= involved=modeling=processI= and=pAmOMMM=models= were=used=to=verify= the= ABAnrp= models= through= comparison= of= building= weights= and= dynamic= characteristics=Ehence =the =initial =lateral =stiffnessF =obtained =from =linear =analysesK =ABAnrp =was =used =for =all =the =subsequent=nonlinear=pushover=analysesK=qhe=weight=of=all=buildings=and=their=fundamental=periods=in=two=principal=añes=obtained=from=linear=analyses= performed= using= both= pAmOMMM= and= ABAnrp= are= listed= in= qable= NK= Comparison= of= the=results= obtained=for=both=sets= of=models=was=used=as= a=verification=of= the=models=built= in=ABAnrp=which=paved=the=way=for=subsequent=nonlinear=pushover=analysesK==

Table N=Comparison=of=models=built=using=pAmOMMM=and=ABAnrp==

pAmOMMM Models ABAnrp Models

Building Building=teight=EtonsF=

jode=N=meriod=EsecF=

jode=O=meriod=EsecF=

Building=teight=EtonsF=

jode=N=meriod=EsecF=

jode=O=meriod=EsecF=

o PMPT= MKNQNSS= MKNMMRV= OVNQ= MKNQTVO= MKNMPMN=i QRPM= MKNMOMP= MKMUOO= QQVO= MKNMPPU= MKMUQT=C NMNUP= MKOMTUV= MKNRVM= NMNRU= MKOMNQQ= MKNRVO=

=PK NlNiINbAo MATboIAi Mlabip= mroper=modeling=of=the=nonlinear=behavior=of=concreteI=howeverI= is=essential=for=accurate=analysis=of=roC=buildingsK=Behavior=of=concrete=under=tensionI=generally=ignored=in=linear=analysesI= is=the=most=important= modeling= aspect= in= nonlinear= pushover= analysis= of= roC= buildings= considering= that= the=ultimate =failure =is =most =likely =to =take =place =through =concrete =cracking =under =tensionK =qhere =are =two =commonly=used=models=for=nonlinear=behavior=of=concreteW=Concrete=pmeared=Cracking=ECpCF=jodel=and =Concrete =aamage =mlasticity =ECamF =jodelK =qhe =Cam =jodel =xNRI =NSz =is =more =effective =for =modeling=the=nonlinear=behavior=of=unreinforced=concrete=since=it=can=represent=the=nonlinear=behavior=of= concrete=by= focusing=on= the= stiffness= reduction=due= to=damage=and= failure= rather= than= tracing= the=crack =propagationK =qhe =model =requires =three =sets =of =parameters =that =describe =the =compressive =behaviorI=the=tensile=behaviorI=and=plasticity=as=eñplained=belowK==PKN Concrete Model in Compression jodeling= of= the= compressive= behavior= of= concrete= in= ABAnrp= consists= of= defining=a= stressJstrain=curve=with=a=linearly=elastic=portion=until=an=initial=yield=stress=is=reachedI=followed=by=a=plastic=zone=with=strain=hardening=prior=to=the=ultimate=compressive=stress=and=a=postJpeak=strain=softening=portionK=qhe=initial=yield=of=concrete=is=assumed=to=occur=at=SMB=of=the=ultimate=stressK=qhe=nonlinear=portion=of=

=

NRQV=

the=stressJstrain=curve=in=compression=was=obtained=from=eognestad’s=concrete=model=xNTzI=using=the=characteristic=compressive=strengthI= D NQcf = =jmaI=obtained=from=testing=of=concrete=cores=taken=from=

the=caseJstudy=buildingsI=and=the=elastic=modulusI= DPORM NQMMMc cb f= + =EjmaFI=calculated=from=the=concrete=strength=in=accordance=with=the=qurkish=Concrete=Code=xNUzK===PKO Concrete Model in Compression Tension Concrete=behavior= in= tension=is= linearly=elastic=until=cracking= is= initiatedI=after=which=a= tensile=strain=softening= response= is= observedK= mroper= modeling= of= both= the= tensile= strength= and= the= postJcracking=tensile=softening=response=is=essential=for=predicting=the=lateral=deformation=and=load=capacity=of=roC=buildingsK=cor= the= tensile= strengthI= the= modulus= of= rupture=calculated=as=OKRR=jma=according= to= the=qurkish=Concrete=Code=xNUz=was=used=since=the=observed=failure=mechanism=for=the=analyzed=buildings=was=through=fleñural=cracking=of=concrete=piers=near=the=corners=of=openingsK=mostJcracking=softening=behavior=was=modeled=using=the=cohesive=crack=model=by=eillerborg=et=alK=xNVz=in=whichW==

= E Ff ws = I===== DEMF tf f= I=====M M

E Fcd dw f w dws¥ ¥

= =ò ò = ENF==

whereI=s=is=the=stress=on=the=unit=area=of=the=specimenI=w=represents=the=width=of=crack=openingI=f’t==is=the=tensile=strength=of=concrete=at=which=cracking=is=initiatedI=and=dc=is=the=cohesive=fracture=energy=that=is=necessary=to=create=and=completely=break=a= unit= surface=area=of=cohesive=crackK=qhe=tension= softening=curve=described=by=bqK=ENF=has=an=initial=value=of=f’t==and=the=area=under=the=curve=is=equal=to dcK==peveral=general=eñpressions=were=proposed=to=approñimate=the=softening=behavior=of=concrete=for=use=in= analytical= and= numerical= studiesK= qhe= eñponential= softening= curve= proposed= and= eñperimentally=validated=by=Cornelissen=et=alK=xOMz=was=used=in=this=research=for=improved=accuracyK=lnce=the=shape=of=the=tension=softening=curve=was=selectedI=the=neñt=step=was=to=determine=the=value=of=fracture=energy=which= is= ideally= determined= eñperimentally= by= fracture= tests= such= as= the= work= of= fracture= method=proposed= in=ofibj= xONz= and=by=eillerborg= xOOzK= fn= cases= where= it= was= not= possible= to= eñtract= the=specimens=needed=for=fracture=tests=from=buildingsI=the=fracture=energy=can=be=obtained=from=the=CbBJcfm=jodel=Code=xNNz=eñpressionW==

=MKTD

O PEMKMQSV MKR OSF NMNM

cc a a

fd d d - æ ö= - + ´ ç ÷

è ø===EpfF= EOF=

=

where=dc=is= in=kLmmI= f’c==is=compressive=strengthI=and==da is=the=mañimum=aggregate=size=in=mmK=cor=the=purposes=of=this=researchI=three=different=dc=values=of=NOR=kLmI=ORM=kLmI=and=PTR=kLm=were=used=in=the=pushover=analyses=to=investigate=the=influence=of=dc=values=on=the=analysis=resultsK===QK ANAiYpIp molCbarob= =konlinear= pushover=analyses=of= the=buildings=were=performed=using=the=arcJlength=EoiksF=method=as=the=iterative=solution=procedure=for=the=nonlinear=algebraic=equations=xOPzK=qhe=oiks=jethod=is=based=on= the=kewtonJoaphson= fteration=jethod= with=an= improved=convergence= strategy=by=use=of= an= arc=instead=of=a= line=as=the=constraint=on=the=solution=pathK=eenceI=the=oiks=procedure=is= less=affected=by=the= limit= pointsI= in= the= vicinity= of= which= the= tangent= stiffness= matriñ= becomes= singular= and= causes=divergence=in=the=iteration=procedureI=improving=the=probability=of=obtaining=a=representative=capacity=curve=for=a=given=structureK=fn=the=first=step=of=each=analysisI=the=gravity=loads=were=applied=on=the=structure=instantaneously=and=were=kept=constant=throughout=the=analysisK=fn=the=second=stepI=lateral=loads=defined=at=each=floor=level=in=proportion=with=the=equivalent=lateral=seismic=loads=xOQz=shown=in=qable=O=were=ramped=from=zeroK=mroportioning= the= loads= according= to= equivalent= lateral= seismic= loads= was=preferred= to=using= the=first=mode= shape= since= the= former= produced= more= conservative= resultsK= qhe= load= increments= were=determined=as=part=of=the=oiks=procedure=based=on=the=stability=of=convergence=and=the=solution=was=continued= until= termination= occurred= due= to= computational= instabilityI= or= when= the= load= increments=were= reduced= to= infinitesimal= levelsK= qhe= minimum= and= mañimum= arc= length= increments= were= set=sufficiently=small=and=large=valuesI= respectivelyI=and=the=mañimum=number=of=iterationsI=which=is=the=general=termination=criterionI=was=set=to=a=high=value=to=increase=the=probability=of=convergenceK=

=

NRRM=

jaterial=models= that= display=softening=behavior=and=stiffness= degradation=may=lead=to=computational=problems= in= implicit= programs= such= as= ABAnrpK= fntroduction= of= viscoplasticityI= also= called=viscoplastic=regularizationI=is=commonly=used=to=overcome=some=of=these=difficulties=xORJOTzK=aefining=a= small= viscosity= parameter= in= the= material= model= causes= the= consistent= tangent= stiffness= of= the=softening=material=become=positive=for=sufficiently=small=time=incrementsI=improving=the=convergence=rate=in=the=softening=regimeK==auring=the=pushover=analyses=of=the=caseJstudy=buildingsI=in=cases=where=the=capacity=curve=obtained=from= an= analysis= indicated= that= the= analysis= was= terminated= prematurely= due= to= a= computational=instability=or=a=false=detection=of=unloadingI=both=of=which=became=evident=from=the=loadJdisplacement=curve= and= the= deformed= shapeI= then= viscoplastic= regularization= of= the= constitutive= equations= was=performed=by=introducing=a=small=viscosity=parameter=in=the=Cam=modelK=qhe=influence=of=viscoplastic=regularization=on=the=analysis=results=is=shown=in=the=neñt=section==

Table O=ptory=and=base=shears=calculated=using=the=equivalent=lateral=seismic=load=procedure=xOQz==

= ptory=phears=EtonsF=

cloor= BuildingJo= BuildingJi= BuildingJC=

N= NOUKVT= NUPKN= OVPKP=

O= OQTKVR= PTPKN= RUMKM=

P= PRRKOS= RPOKT= SSVKM=

Q= RQPKPS= UNQKM= VMVKM=

R= J= J= NUORKS=

Base=phear=EtonsF= NOTS= NVMP= QOTT=

=RK ANAiYpIp obpriTp ANa aIpCrppIlN =qhe=capacity=curves=obtained=from=nonlinear=pushover=analyses=of=the=caseJstudy=buildings=are=shown=in=cigK=OK=aue=to=the=high=stiffness=and=vibration=frequencies=of=the=buildingsI=the=seismic=design=loads=are=the=same= in=both=principal=directionsK=eenceI= the=pushover= analyses= were=performed=only= in= the=weaker=directionsI=iKeK=along=the=shorter=plan=dimensions=of=the=buildingsK==cigK=Oa= shows= the= three=capacity= curves= obtained= from= analyses= of= BuildingJo= using= three= different=values=of=the=concrete=fracture=energyI=dcK=thile=the=capacity=curves=that=correspond=to=dc===NOR=kLm=and= dc= = =ORM =kLm =appear =to =be =similarI =dc= == PTR= kLm= produces= a= curve= that= shows= considerably=higher= lateral=load=and=deformation=capacityK=qhe=results=show=that=Efor= the=same=tensile=strengthF=the=value= of= concrete= fracture= energy= may= affect= both= the= load= capacity= and= ductility= of= buildings= with=roC=componentsK=fn=view=of=the=drastically=different=behavior=produced=by=the=conservative=values=of=dcI=there=is=need=for=further=research=focusing=on=the=influence=of=the=concrete=fracture=energy=value=on=building=behavior=and=the=suitability=of=the=CbBJcfm=jodel=Code=eñpression=as=a=conservative=design=eñpressionK=qhe= plan= irregularity= of= BuildingJi= due= to= its= iJshape= geometry= and= the= compleñity= of= its= finite=element=model=resulted= in=premature= termination=of= the=pushover=analyses=performed=using=concrete=fracture= energy= values= of= ORM= kLm= and= PTR= kLm= as= shown= in= cigK=ObK= fn= order= to= improve=computational=stabilityI=the=viscoplastic=regularization=procedure=eñplained=in=pection=PKO=was=applied=by=introducing=a=viscosity=parameter=within=the=plasticity=parameters= in=the=Cam=jodelK=cigK=Ob=also=shows=the=improvement=achieved=by=introducing=a=viscosity=parameter=of=NMJS=secK=in=the=Cam=jodelK=qhe=capacity=curves=obtained=after=viscoplastic=regularization=are=consistent=with=those=obtained=before=the=regularizationI= and=provide=a= more=complete= representation=of= the=building’s= nonlinear= behavior=that=is=supported=by=the=evolution=of=stresses=and=deformations=in=the=buildingK= = qhe= capacity= curves=obtained=for=BuildingJC=using=two=different=values=of=dc=are=shown=in=cigK=OcK=qhe=figure=also=shows=the=effect=of=viscoplastic=regularization=for=two=different=values=of=the=viscosity=parameterK=As=can=be=seen= from= the= figureI= the= magnitude= of= the= viscosity= parameter= has= little= influence= on= the= capacity=curve=provided=that=it=is=sufficiently=small=compared=to=the=time=increments=used=in=the=analysisK=

=

NRRN=

Ea)

Eb)

Ec)

=

cigK O=Capacity=curves=and=deformed=shapes=at=mañimum=base=shear=for=EaF=BuildingJoI=EbF=BuildingJiI==and=EcF=BuildingJC=for=different=values=of=dc=with=or=without=viscoplastic=regularization=

=SK mbocloMANCb bsAirATIlN rpINd CAmACITY pmbCTorM MbTela =merformance= evaluation= of= the= caseJstudy= buildings= were= performed= using= the= Capacity= ppectrum=jethod=xNPI=NQz=in=the=accelerationJdisplacement=response=spectrum=EAapoF=format= xOUz=as= initially=described= in= the= AqCJQM= report= xNz= and= later= improved= in= AqCJRR= xOzK= qhis= simplified= nonlinear=procedure=provides=a=clear=graphical=representation=of=a=building’s=performance=level=and=the=impact=of= various= retrofit= strategies=by=comparing=the=capacity=spectrum=with=spectral=acceleration=response=spectra= representations= of= earthquake= demands= xNzK= A= performance= level= is= associated= with= the=intersection=of=the=capacity=and=demand=curvesI=the=soJcalled=performance=pointK==As= an= initial= assessment= of= the= performance= levelI= the= capacity= curves= of= the= caseJstudy= buildings=shown= in= cigK=Pa= were= converted= to= Aapo= format= and= were= compared= with= the= elastic= response=spectrum=with=RB=damping=as=shown=in=cigK=PbK=As=can=be=seen=from=the=figureI=the=capacity=spectra=of= Buildings= i= and= C= intersect= the= elastic= response=spectrumI= which= represents= the= highest= level= of=design= seismic= demandI= at= the= constant= acceleration= regionK= qhe= capacity= spectrum= for= BuildingJi=intersects=the=elastic=response=spectrum=at=Sd ==MKMMPR=m=which=corresponds=to=a=roof=displacement=of=Droof ===MKMMQQ=m=and=a=drift=ratio=of=MKMPBK=pimilarlyI=the=capacity=spectrum=for=BuildingJC=intersects=the=elastic=spectrum=at=Sd===MKMNQU=m=which= corresponds= to=a= roof= displacement= of=Droof ===MKMNUU=m=and=a=drift=ratio=of=MKMVBK=qhe=drift=ratios=for=both=buildings=are=significantly=lower=than=the=MKPB=limit=given=in=cbjAJPRS=xOVz=for=immediate=occupancy=EpJNF=performance=level=for=noninfill=roj=wallsK=Considering= that= a= nonlinear= performance= evaluation= will= reduce= the= demand= spectrum= due= to=increased=dampingI=one=can=conclude=without=further=analysis=that=the=eñpected=performance=level=for=both=BuildingJi=and=BuildingJC=are=immediate=occupancyK==

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merformance=point=at:pd=0.0048=m EDroof=0.00S2=m)pa=0.SS8=Eg) Es=1PSR=tons)

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====EcF=performance=evaluation=before=retrofitting=== =======EdF=performance=evaluation=after=retrofitting= =

=

cigK Q=oetrofitting=of=BuildingJo=and=comparison=of=capacity=curves=and=building=performance==before=and=after=retrofitting=

=

NRRP=

oetrofitting= of= roj= and= roC= buildings= can= be= performed= using= several= methods= such= as= base=isolationI=bonding=com=polymer=sheets=or=stripsI=grouted=reinforcement= in=drilled=coresI= or=reinforced=shotcrete=overlays= xPMzK= Considering= the=historical= and=architectural= character= of=BuildingJoI= several=feasible= retrofit= alternatives= were= evaluated= from= engineeringI= economicsI= completion= timeI= and=aesthetics=viewpointsK=fn=view=of=the=collapse=mechanism=observed=from=nonlinear=pushover=analysesI=installation=of= steel=channel= sections= around= the= openings= in= the= eñterior= walls= was= found= to=be= the=optimum= retrofit= strategyK= tindow= and= door= openings= in= the= eñterior= walls= along= the= width= of= the=building=were=framed=with=O=cmJthick=channel=sections=with=NT=cm=flange=widthK=cigK=Qa=shows=one=of=the=eñterior=walls=of=BuildingJo=after=retrofit=applicationK==oetrofit=design=and=verification=for=BuildingJo=was=performed=using=the=same=approach=described=in=the=previous= sectionsK= qhe= finite= element= model= of= BuildingJo= was= modified= to= include= the= retrofit=application= as= shown= in= cigK=QaK= Capacity= curves= obtained= from= nonlinear= pushover= analyses= of=BuildingJo= before= and= after= retrofitting= are= compared= in= cigK=QbI= cigK=Qc= and= Qd= show= the= capacity=spectrum=solutions=for=before=and=after=retrofittingI=respectivelyI=using=the=eñact=procedures=described=in=AqCJQM=and=AqCJRRK=Both=procedures=essentially=gave=the=same=resultsI=eñcept=for=the=jump=in=the=AqCJQM=curve=in=cigK=QcI=which=was=caused=by=the=difference=in=the=acceleration=and=velocity=response=reduction= factors= as= the= secant= period= of= the= structure= shifts= from= constant= acceleration= region= to=constant= velocity= region= on= the= RB= damped= elastic= spectrumK= qhis= problem= does= not= appear= in= the=improved=procedure=described=in=AqCJRRK=bñamination=of=cigK=Q=shows=that=while=the=capacity=spectrum=solutions=show=no=performance=point=for=BuildingJo= before= retrofittingI= indicating= potential= collapse= of= the= building= under= design= seismic=demandI= the= eñpected= performance= level= after= retrofitting= is= immediate= occupancy= with= hardly= any=nonlinear= deformation=demand= on= the=buildingK=qhis= shows= the= effectiveness= of= the= retrofit= strategy=through=an=objective=performance=evaluationK===UK ClNCirpIlNp =As= the= first= comprehensive=PJa=nonlinear= finite=element= study=performed= for= buildings= with= roC=wallsI= this= study=demonstrates= the= feasibility= of= the= method= for=use= in=practical= applications= as= an=improved= pushover= analysis= tool= compared= to= currently= used= and= actively= investigated= equivalent=frame=methodsK=thile=the=value=of=such=approñimate=methods=to=the=practicing=engineer=cannot=be=deniedI=there=is=also=a=need=for=comprehensive=nonlinear=finite=or=discrete=element=analysis=studies=to=build=a=collective=body= of=knowledge=and=eñperience= that= will= serve=as=a=practical=or= research= tool=that= can= replaceI= complementI= or= verify= the= results= obtained= from= simplified= methodsK= qhis= is=especially= necessary= in= view= of= the= fact= that= the= finite= or= discrete= element= solutions= that= are=sometimes=used=to=validate=the=simplified=methods=are=not=problemJfree=themselves=when=it=comes=to=analysis=of=buildings=with=roCLroj=structural=componentsK=cracture=mechanics=concepts=can=be=used= to= describe= the= post= cracking= tensile= behavior= of= concreteI= with= the= fracture= energy= value=obtained= from= the= CbBJcfm= jodel= Code= through= an= inherently= conservative= design= eñpressionK=qopics=such=as=eñperimental=verification=of=this=approach=for=a=simple=wall=configurationI=potential=meshJdependency= of= analysis= resultsI= optimum= meshing= strategies= and= mesh= sizes= etcK= that= were=beyond= the= scope= of= this= research= are= among= the= topics= of= additional= research= need= to= build= the=aforementioned= body= of= knowledge= and= eñperienceK= aespite= the= current= popularity= of= simplified=nonlinear= analysis=methodsI= future=demand=for= improved=performanceJbased=design=and=evaluation=tools=for=roCLroj=buildings=is=likely=to=necessitate=use=of=advanced=nonlinear=analysis=methods=at=least= for= those= buildings= that= have= functionalI= historicalI= or= architectural= significanceK= eenceI= the=authors= view= parallel= research= on= advanced= and= simplified= methods= that= can= be= used= in=a=complimentary=fashion=as=the=optimum=strategyI=and=consider=the=research=presented=in=this=paper=as= an= intermediate= step= in= an= ongoing= research= that= aims= to= perform= PJa= nonlinear= timeJhistory=analysis= of= roC= buildings= to= achieve= improved= accuracy= and= objectivity= in= performanceJbased=design=and=evaluationK===ACKNltibadbMbNTp =qhis =research =was =partly =performed =at =rniversity =of =jassachusetts =iowell =ErjiFI =iowellI =jAI =during= the= first= author’s= tenure= as= an= assistant= professorK= qhe= authors= gratefully= acknowledge= the=support=provided=by=rji=in=the=form=of=startup=fundsK==

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