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

mbocloMANCb-BApba AmmolACe Tl bAoTenrAhb molTbCTflN lc MAplNov CriTroAi ebofTAdb perena CattariNI pergio iagomarsinoO ABpToACT =tithin= the= framework= of= merformance= Based= Assessment= EmBAFI= the= éaéer= focuses= on= the=imélementation= to= the= case= of= ancient= masonry= constructionsK= ActuallyI= the= comélexity= and= wide=variety=of=historical=masonry=buildings= Esuch=as=churchesI= éalacesI= towersI=columnsI= etcKF= require=the=adoétion=of=different=modelling=strategiesI= through=a=versatile=érocedureK=tithin=this=contextI=one=of=the=main=issues=is=the=definition=of=éerformance=levels=on=the=caéacity=curveI=érovided=by=the=nonlinear=éushover= analysisK= cirstlyI= éerformance= objectives= have= to= be= defined= also= considering= cultural=relevance= conceétsW= thusI= the=éreservation= of= the= cultural=heritage=asset= and= the= safety= of= the=éeoéle=using =it =should =be =considered =in =an =integrated =aééroachK =qo =this =aimI =in =the =éaéerI =a =multicriteria =aééroach=to=define=damage=levels=is=éroéosed=by=consideringW=aF=the=damage=at=the=scale=of=structural=element= Elocal damageFI= bF= the= mechanisms= in= architectonic= elements= EmacroelementFI= cF= the=global=behaviour=of=the=building=Ereéresented=by=its=pushover curveFK=qhenI=éroéer=criteria=are=established=to=correlate=damage=at=the=three=scales=and=define=éerformance=levels=on=the=caéacity=curveK= heywordsW peismic performance-based assessmentI Cultural heritageI jasonry buildings NK fNTolarCTflN =kumerous= countries= at= international= level= nowadays= share= the= need= of= éreservation= of= historical=constructionsK=eoweverI=the=great=variability=and=the=comélexity=of=masonry=historical=buildings=make=difficult=to=éroéose=wellJestablished=aééroachesI=as=the=ones=that=are=adoéted=in=codes=for=the=case=of=new=buildingsK==fn= the=éaéerI= the=attention= is= focused=on= the=use= of= the= disélacement= aééroach= for= the=merformance=Based =Assessment =EmBAFI =which =all =recent =research =efforts =and =some =codes =refer =toK =ft =seems =even =more=suitable= in=case=of= masonry=buildingsI= strongly= affected=by= the= nonlinear= behaviour= from= first=éhases=of=reséonseK=mBA=requiresI=on=the=one=handI=reliable=models=to=evaluate=the=seismic=reséonse=in=nonlinear= range=Ethrough=both=static=and=dynamic=methods=of=analysisF=andI= on=the=other=oneI=éroéer=verification=éroceduresK=tithin=the=context=of=nonlinear=static=analysesI=mBA=requires=the=definition=of=éerformance= levels= Elimit= statesF= on= the=caéacity= curve= obtained=by= the=éushover= analysisI= which= is=aimed= to= érovide= essential= information= on= the= actual= behaviour= in= terms= of= stiffness= Eequivalent=éeriodFI=strength=Etotal=base=shearF=and=ultimate=disélacement=caéacityK==cirst=of=allI=éerformance=objectives= have=to=be=linked= also=to=cultural=relevance=conceétsW=this= means=that= the=safety=éeoéle=and= the=éreservation=of= the=cultural=heritage=asset= should=be=considered= in= an=integrated= aééroachK= qhenI= a= suitable= and= versatile= érocedureI= able= to= envisage= the= wide= variety= of=heritage= constructionsI= has= to= be= introduced= to= define= éerformance= levels= on= caéacity= curveK= fn=éarticularI=in=the=éaéer=a=multi=criteria=érocedure=is=éroéosedI=aimed=to=take=into=account=the=reséonse=of= the= elements= that= add= uéI= at= the= different= scalesI= to= the= whole= reséonse= of= the= assetW= structural=elements= Elocal damageFI= architectonic= elements= EmacroelementsF= and= global= behaviour= Epushover curveFK=aifferent=aééroaches=are=usedI=based=on=heuristic=criteria=or=on=checks=of=the=éerformance=of=elements=and=macroelementsI=in=order=to=avoid=the=occurrence=of=local=“too=heavy”=damageK=================================================N=Assistant=mrofessorI=rniversity=of=denoaI=ftalyI=serenaKcattari]unigeKit=O=cull=mrofessorI=rniversity=of=denoaI=ftalyI=sergioKlagomarsino]unigeKit=

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OK abcfNfTflN lc mbocloMANCb ibsbip clo CriTroAi ebofTAdb =merformance=Based=Assessment=EmBAF=usually=considers=a=set=of=oehabilitation lbjectivesI=related=to=the=fulfilment=of=séecific=merformance ievelsEmiF=in=the=occasion=of=given=barthquake=eazard=ievels=Edefined=by=the=annual=érobability=of=exceedance=or=the=return=éeriod=qoFK==crom= a= conceétual= éoint= of= viewI= in= case= of= ordinary buildingsI= éerformance= levels= are= usually=associated= to=consequences= like=costs=of= reéairI= safety=of=éeoéleI=usability= Ebuilding=fit= to=be=usedF=and= oéerational= requirementsK= fn= case= of= cultural heritage assetsI =mis =have =to =be =linked =also =to =cultural= relevance= conceétsW= thusI= the= conservation= of= the= cultural= heritage= asset= and= the= safety= of=éeoéle= should= be= considered= in= an= integrated= aééroachK= joreoverI= it= is= necessary= to= take= into=account=the=éresence=of=artistic=assets=as=wellK=qhusI= in=case=of=cultural=heritageI=within=the=context=of =mBA =it =seems =more =accurate =referring =to =pafety and Conservation lbjectives= than =simély =to =oehabilitation lbjectivesK= According= to= thisI= in= mbombqrAqb= érojectI= the= following= aséects=EtargetsF=have=been=considered=to=define=misW=

– rse and human lifeW= as= well= as= for= other= tyées= of= buildingI= the= éossibility= of= an= immediate=occuéancy=after=an=earthquake=and=the=éreservation=of=human=life=may=be=iméortant=for=a=cultural=heritage=asset;=

– Building conservationW= the= éreservation= from= building= damage= is= not= relatedI= as= for= ordinary=buildingsI= to= the= costs= of= reéair= or= rebuilding= but= to= the= éossibility= of= restorationI= due= to= the=intangible=value=of=a=cultural=heritage=asset;==

– Artistic assets conservationW=in=many=casesI=irreéarable=damage=to=artistic=assets=occurs=also=in=the=case= of= moderate= damage= to= structural= elements;= thus= it= is= necessary= to= define= séecific=éerformance=levelsK==

cor= each= one= of= the= above= aséectsI= different= éerformance= levels= may= be= associated= to= increasing=exéected=hazard=levels;=for=examéleI=in=case=of=Building conservation=targetsI=they=are=differentiated=in=ko aamageI aamage iimitationI pignificant but restorable damageI kear collapse=Efor=further=details=in=case=of=other=targets=see=cigure=NFKAmong=these=levelsI=some=are=considered=as=the=main=onesI=while=others= have= to=be=verified=only=on=séecific= cases= EsecondaryF;=once= the=main=and= the= secondary=are=verifiedI=the=remaining=ones=may=usually=be=considered=as=satisfiedK=As= knownI= mBA= generally= refers= to= the= use= of= nonlinear= static= analyses= and= the= evaluation= of= the=seismic= demand= by= the= Caéacity= péectrum= jethod= xNz= or= the= kO= jethod= xOzI= according= to= the=reduction= of= acceleration= and= disélacement= séectra= by= the= over= daméed= or= inelastic= aééroachI=reséectivelyK=As=knownI=in=this=caseI=the=seismic=reséonse=of=an=asset=is=described=in=terms=of=caéacity=curveW=thus=each=éerformance=level=has=to=be=correlated=to=a=séecific=éoint=of=such=curveI=as=shown=in=cigure=N=for=the=different=targets=and=éerformance=levelsK==

cigK N aefinition=of=éerformance=levels=on=the=caéacity=curve=

=PK pbfpMfC AppbppMbNT lc CriTroAi ebofTAdb =lnce= the=safety=and=conservation= requirements= have=been=defined=from=a=conceétual=éoint=of=viewI=éroéer= acceétance= criteria= have= to=be= established= in=order= to=verify= if= the= structure= is= able=or= not= to=satisfy =the =required =miK =fn =éarticularI =the =acceétance =criteria =require =the =definition =ofW =aF =éroéer

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variables=Eand=the=correséonding=reference=limit=valuesFI=correlated=to=the=building=seismic=reséonseI=which=allow=us=to=check=the=éerformance=level;=bF=éroéer=vulnerability modelsI=able=to=evaluate=these=variables=for=a=given=seismic=actionK=A=suitable=variable=that=can=be=correlated=to=the=various=consequencesI=commonly=adoéted=in=literature=Ein=éarticularI=in=macroseismic=éostJearthquake=assessmentFI= is=the=damage levelK=fn=factI=although=the=damage=level=is=an=eméiric=and=qualitative=indicatorI=it=has=the=main=advantage=to=be=directly=related=to=the= reséonse= of= elements= Estructural= and= nonJstructuralF= and= artistic= assetsK= joreoverI= since= usually=losses= in= terms= of= casualties= and= injured= éeoéle= are= relatedI= by= éroéer= correlation= lawsI= to= damage=occurred=in=structural=elements=of=the=buildingI=this=variable=seems=éarticularly=convenient=for=all=the=considered=éerformance=targetsK=ft= is= evident= that=damage=assessment=of= the=whole=asset= results= from=that=occurred=at=different= lower=scalesI=those=of=each=single=structural=element=and=of=the=macroelements=Eéortion=of=the=assetI=usually=made=by=a=set=of=elementsI=for=which=it=is=éossible=to=recognize=an=almost=autonomous=behaviourI=as=for= a= masonry= wall= or= a= floorFKqhenI= as= discussed= in= detail= in= §4KNI= séecific= criteria= have= to= be=introduced=to=consider=all=different=scales=Esingle=structural=elementI= macroelementI=global=oneF=andI=finallyI=to=correlate=damage=and=éerformance=levels=on=the=caéacity=curveK=As=a=function=of=the=target=examinedI=the=main=scale=to=be=adoéted=as=reference=may=differK=rsually=it=is=that=of=the=whole=asset=in=case=of=Building Conservation and=rse and euman iife=targetsI=and=the=local=one=Esingle=elementF=in=case=of=Artistic AssetK=aamage=is=graduated=on=five=levels=Efrom=negligible=damage=to=the=comélete=collaéseFI=as=for=examéle=adoéted=in=the=bjpVU=scale=xPz;=obviously=in=the=mBA=the=last=one=is=not=interestingK=cigure=O=shows=the=adoéted=correséondence=between=éerformance=and=damage=levelsK=fn=case=of=cultural=heritageI=due=to=the=wide=architectural=and=moréhological=variety=of=assetsI=it=is=not=an= easy= task= to= outline= a= érocedure= that= is= versatile= enough= for= the= seismic= assessment= and= the=correlation= between= damage= and= éerformance= levelsK= fn= factI= it= has= to= be= able= to= take= into= accountW=iF=the= various= architectonic= asset= classes;= iiF= the= different= damage= classes= and= subJclasses= that= may=occur=EinJélane=or=outJofJélane=of=masonry=wallsI=rocking=of=blocksI=etcKF;= iiiF=the=different=modelling=strategies=to=be=adoétedK==

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buildings=in=the=historical=centresK=fn=additionI=three=main=classes=for=artistic=assets=have=been=definedW=m –=assets= which= are= structural= elements= of= the= building= EeKgK= carved= stone= columnsI…F;= n –=assets=which=are=strictly=connected=to=structural= elements=of= the=building= EeKgK= frescoesI= mosaicsI= stuccoesI=stone=éortalsI…F;= o –=assets= which=are= indeéendent= elementsI= with= their= own= seismic= reséonse= EeKgK=éinnaclesI= statuesI= balconyI…FK= aifferent= damage= classes= and= subclasses= have= been= identified= and=attributed=to=the=abovementioned=architectonic=and=artistic=classesK=As= regards= the= modelling= strategies= to= be= adoétedI= models= develoéed= in= literature= for= masonry=structures=may=be=classified=according=to=two=criteriaW=scale=of=constitutive=modelling=Eat=the=level=of=masonry= material= or= structural= elementF= and= tyée= of= descriétion= of= masonry= Eby= a= homogenized=equivalent= continuum=or= through=discrete=modellingFK= cour=different=kind=of=models=are=identified=by=the= combination= of= the=abovementioned= oétions;= each=architectonic= class= has= a= foremost= modelling=aééroachK=Among=these=strategiesI=the=equivalent=frame=model=and=the=macroJblock=oneI=ascribable=to=a= continuous= and= discrete= aééroach= faced= at= structural= element= scaleI= reséectivelyI= seem= to= be=éarticularly=efficient= in=the=engineering=éracticeI=because=of= their= relatively= low=coméutational=effort=also=in=the=case=of=comélex=structuresK==joreoverI=as=a=function=of=the=different=tyées=of=architectonic=assetsI=the=seismic=assessment=may=be=faced=starting=from=different= scales= and= in=different= wayK= peismic assessment refers= to=the=érocedure=aimed=to=coméare=the=structural=caéacity=Edescribed=by=the=caéacity=curveF=with=the=seismic=demand=Ein=terms=of=reduced=reséonse=séectrumF=in=order=to=define=the=éerformance=éoint=andI=thenI=check=for=the=fulfilment=of=éerformance=levelsK=fn=case=of=equivalent=frame=models=seismic=assessment=refers=to=nonlinear= static= érocedures= EeKgK= Caéacity= péectrum= jethodI= kO= jethodFI= whereas= in= case= of= the=macroJblock=modelling=to=the=equilibrium=limit=analysis=through=nonlinear=kinematic=aééroachK=aeéending= on= the= tyée= and= dimensions= of= the=buildingI= it= is= éossible= to= further= distinguish=amongW=aF=assets= made= by= a= single= element= or= macroelement;= bF= comélex= assets= made= by= a= set= of=macroelements;= cF= artistic= assetsK= cigure= P= summarizes= these= different= cases= and= the= correséonding=seismic=assessment=scaleK=fn= case= aF= seismic= assessment= is= usually= carried= out= on= the= caéacity= curve= reéresentative= of= the=reséonse=of=the=single=element=or=macroelementK==cor=comélex=assets=Ecase=bFI=it=is=necessary=to=distinguish=the=following=two=main=casesW=

–= buildings=characterized=by=a=box=behaviourW=in=this=case=the=seismic=assessment=requires=referring=to=a=global=Pa=model;=

–= buildings=made=by=a=set=of=macrolements=which=exhibit=an=almost=indeéendent=behaviourW=in=this=caseI= after= having= coméuted= a= éroéer= seismic= load= sharingI= the= seismic= behaviour= of= each=macroelement=is=analysed=indeéendentlyK==

fn =the =first =caseI =the =seismic =assessment =is =directly =éerformed =on =the =overall =caéacity =curve =reéresentative=of= the=whole= asset= reséonseK= fn= the=second=oneI= it= is= evaluated=on=the= caéacity= curve=reéresentative=of= each=macroelement= reséonse;= thenI= starting=from=evaluations= carried=out=on=all= the=relevant= macroelementsI= éroéer= combination= criteria= may=be= introduced= to= define= the= correséonding=éerformance=at=the=scale=of=the=whole=assetK=qhe=attribute=“relevant”=refers=to=the=significance=in=terms=of=correséonding=consequences=related=to=éerformance=targets=examinedK=cinallyI=for=artistic=assets=Ecase=cFI=according=to=the=three=classes=above=introduced=EmI=nI=oF=different=oétions=must=be=consideredK=fn=the=case=of=m=and=n classesI=the=artistic=asset=is=éart=of=the=building=or=is=attached=to=one=of= its= elementsI=so= the=éerformance= is= checked=considering=the=caéacity=curve=of= the=whole=architectonic=asset;= in=éarticularI=for=class=n EeKgK=frescoesI=mosaicsI…FI=it=is=necessary=to=take=into=account=the=interaction=effects=with=the=structural=elementK=lf=courseI=in=this= latter=caseI=damage=levels=have=to=be=defined=on=the=overall=caéacity=curve=by=monitoring=the=local=reséonse=of=the=single=structural=element=to=which=the=artistic=asset=is=connected=toK=Artistic=elements=of=class=o=are=analysed=by=the=same=models=used=for=architectonic=assets=made=by=one=elementK=fn=each=caseI=the=caéacity=curve=will=be=obtained=by=adoéting=the=modelling=aééroach=most=suitable=to=interéret=the=seismic=reséonse=of=the=asset=EeKgK=through=a=continuous=or=a=discrete=aééroachFK=qhusI= as= a= function= of= these= three= classes= above= introducedI= damage= levels= Eand= the= correséonding=éerformance= levelsF= have= to= be= definedI= reséectivelyW= at= macroelement= scaleI= in= case= aF;= at= global=Ein=case= of= box= behaviourF= or= macroelement= scaleI= in= case= bF;= at= local= scale= of= single= elementI= in=case=cFK==ft=is=worth=éointing=out=that=in=the=case=of=box=behaviourI=an=exhaustive=seismic=assessment=would= require= also= the=verification= on= the=éossible=occurrence= of= local= outJofJélane= mechanisms;= in=this= caseI= a= comélete= seismic= assessment= should= take= into=account= both= evaluations= Eon= the= overall=caéacity=curve=and=on=that=of=the=single=macroelement=that=may=exhibit=some=outJofJélane=reséonseFK==

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cigK P qyées=of=assets=and=correséonding=seismic=assessment=scales==fn= the=following=éaragraéhI= a=multicriteria= aééroach=to=define=éroéer= damage= levels= on= the=caéacity=curve=is=éroéosed=andI=thenI= the=correlation=between=damage=and=éerformance=levels= is=treatedK=As=an=examéleI=the=issue=is=discussed=with=reference=to=the=case=of=class=A=of=architectonic=assetsI=those=with=a= érevailing= box= behaviourI= analysed= by= adoéting= the= equivalent= frame= modelling= aééroachK= As=knownI =according =to =this =aééroachI =each =wall =is =discretized =by =a =set =of =masonry =éanels =Epiers= and=spandrelsFI=in=which=the=nonlinear=reséonse=is=concentratedI=connected=by=rigid=areas=EnodesFK==QK abcfNfTflN lc mis lN Teb lsboAii CAmACfTv Crosb =qhe=definition=of=éerformance= levels=of= the=building=from=the=results=of=a=nonlinear= seismic=analysis=Eusually=a=éushover=analysisF=is=a=comélex=taskI=that=is=faced=in=a=different=way=in=literature=and=codes;=the=following=main=aééroaches=are=adoétedW=

– a= structural element approachI= that= assumes= the= attainment= of= a= certain= éerformance= level= at=global= scale= correséonds= to= the= steé= in= which= the= first= structural= element= reaches= the= same=éerformance=level=xRz;=

– an=heuristic approachI=that=defines=mis=on=the=basis=of=conventional=limits=directly=defined=on=the=caéacity=curveI= usually= in= terms= of=decay=éercentage=or= reaching=of= the=maximum=value=of= the=overall=base=shear=xSzK=

eoweverI= in= case= of= comélex= existing= masonry= buildingsI= éarticularly= those= belonging= to= the= cultural=heritageI= the=aéélication=of= these=aééroaches=may=lead= to=not= reliable=resultsK= fndeedI=while= in= case=of=a=boxJtyée=behaviour=with=quite=rigid=floors=it= is=reasonable=that=a=set=of=elements=and=walls=Edue=to=the=couéling=érovided=by=floorsF=reaches=almost=at=the=same=time=a=certain=damage=levelI=in=case=of=existing=buildings=this=condition=is=far=to=be=trueI=due=to=the=architectural=comélexity=and=the=éresence=of=flexible=

=

OVNV=

floorsK =fn =the =limit =case =of =coméletely =flexible =floorsI =it =is =reasonable =assuming =a =quite =indeéendent =behaviour=of=each=single=masonry=wallI=and=the=reaching=of=a=certain=éerformance=level=must=refer=to=that=at= the= macroelement= scaleK=eoweverI= this= is=a= limit= condition=and= in= generalI= even= in=case=of= wooden=floors=or=vaults=Ethat=are=tyéical=for=monumental=buildingsFI= floors=érovide=a=not=negligible=contribution=to=the=load=transfer=and=stiffnessK=As=a=consequenceI=the=reaching=of=a=certain=éerformance=level=at=scale=of=a=single=wall=may=not=coincide=with=that=of=the=whole=structureK=qhe=lack=of=homogeneity=of=damage=in=case= of= very= comélex= buildings= is= even= more= evident= at= the= scale= of= masonry= elements= Eéiers= and=séandrelsF;=thus=the=reaching=of=a=severe=éerformance=level=in=a=single=element=could=not=correséond=to=a=significant=strength=decay=on=the=overall=caéacity=curveW=thus=the=structural element approach=could=lead=to= a= too= cautionary= assessmentK= cinallyI= also= the= heuristic= aééroach= may= result= quite= conventional= if=adoéted=as=single=criterion=to=define=the=mis=on=the=caéacity=curveK=fn=éarticularI=it=does=not=assure=from=the=occurrence=of=heavy=damage=levels=EeKgK=near= to=collaéseF=at= local=scaleW=damages=that= could=be=not=coméatible=with=the=fulfilment=of=the=éerformance=level=which=is=checkedK=All=the=abovementioned=issues=stress=the=need=to=outline=a=érocedure=able=to=take=into=account=all=the=different=scales=thatconcur=to=define=the=overall=seismic=reséonse=and=to=combine=different=criteriaK=qo=this= aimI= in= the= following= the=mis= definition= is= éroéosed=based= on= two= main= steésW= firstlyI= in= §4KNI=damage= levels= are= defined= on= the= caéacity= curve= by= a= multicriteria= aééroach;= secondlyI= in= §4KOI=a=éroéer=correlation=between=damage=and=éerformance=levels=is=establishedK==QKNK aefinition of damage levels on the capacity curve by a multicriteria approach qhe=basic=idea=of=the=multicriteria=aééroach=is=that=the=assessment=of=a=certain=damage=level=at=global=scale=comes=out=from=a=set=of=checks=carried=out=at=different=scalesI=based=onW=

– heuristic approach Ederived=by=exéert=judgement=or=éarametric=analysesFW=related=to=the=fulfilment=of=conventional= limits=on= the=caéacity=curveI= either=of= the=whole=building=and=of= the=“relevant”=macroelements=they=coméose=the=asset;=

– systematic checks on elements and macroelementsW= aimed= to= avoid= the= occurrence= of= local=damage= levels= incoméatible= with= the= fulfilment= of= the= considered= damage= level= and= the=correséonding=éerformanceK=

According= to= this= aééroachI= the= disélacement= on= the= overall= éushover= curve= correséonding= to= the=reaching=of=the=i-th=aamage=ievel=EaiiI=with=i===NKK4F=is=coméuted=asW=== ( ) 4IN;;min III == idddd daiijaiibaiiaii = =ENF==there= daiiIbI= daiiIj and= daiiId= are= the= disélacements= on= the= éushover= curve= correséonding= to= the=attainment=of=the=checks=éerformed=at=elementI=macroelement=and=global=scaleI=reséectivelyK=cigure=4=summarizes=the=multicriteria=aééroach=éroéosed=in=case=of=a=threeJstorey=masonry=buildingK==fn=order= to=exélain=these=checksI= it= is=necessary=to=introduce=a=variable=x=which=describes=the=state=of=the= element= Eéier= or= séandrelFI= of= the= macroelement= Emasonry= wallF= and= of= the= whole= buildingI= in=correséondence=with=the=current=disélacement=d=on=the=éushover=curveK=fn=the= case=of= the=structural=element= scaleI= differently= from=the=macroelement= and=global=onesI= five=damage= levels= are= considered= Ecigure= RFK= qhe= variable= x= can =beI =in =this =caseI =the =drift =db or= the=éercentage= of= strength= reduction= bbK= By= considering= the= whole= set= of= éiers= EmFI= it= is= necessary= to=evaluate=the=disélacement=daiiIbp in=which=it=is=attained=the=conditionW==

=NI

max Nj

mi j

xu +

æ ö=ç ÷ç ÷

è ø= EOF=

=where=uiHNIj=is=the=limit=threshold=of=the=variable=x=in=the=jJth=éierI=for=the=damage=level=iHNK=pimilarlyI=by=considering=the=whole=set=of=séandrels=EpFI=the=disélacement=daiiIbs is=the=one=on=the=éushover=curve=in=which=it=is=attained=the=conditionW=

=OI

max Nj

pi j

xu +

æ ö=ç ÷ç ÷

è ø= EPF=

=where=uiHOIj=is=the=limit=threshold=of=the=variable=x=in=the=jJth=séandrelI=for=the=damage=level=iHO=Eélease=note=that=for=the=evaluation=of=the=global=damage=level=ai4=no=check=is=required=in=séandrelsFK=

=

OVOM=

cinallyI=the=disélacement=on=the=éushover=curve=daiiIb=is=obtained=as=followsW=== ( )I I Imin Iaii b aii bp aii bsd d d= = E4F==ft=is=worth=noting=that=a=higher=damage=level=is=acceéted=in=séandrels=than=in=éiers;=this=is=due=to=the=different= role= of= these= elements= in= the= hierarchy=of= masonry= wallsK= fn= fact= éiers= reéresent= the= most=iméortant=elementsI=which=bear=both=static=loads=and=seismic=actionI=whereas=séandrels=are=secondary=elementsI=which=connect=éiers=by=transmitting=bending=momentsK==

=

cigK Q pummary=of=multicriteria=aééroach=éroéosed=to=define=ais=on=the=overall=caéacity=curve===fn= the= case= of= macroelementsI= the= variable= x= is= the= interJstorey= drift= dis or= a= éroéer= éercentage= of=maximum=base=shear=reduction=bj=Eevaluated=on=the=éushover==curve=of=the=macroelementFK=By=considering=the=whole=set=of=macroelements=EjFI=the=disélacement=daiiIj=is=the=one=on=the=éushover=curve=in=which=it=is=attained=the=conditionW==

=I

max Nj

ji j

xu

æ ö=ç ÷ç ÷

è ø= ERF=

=where=uiIj=is=the=limit=threshold=of=the=variable=x=in=the=jJth=macroelementI=for=the=damage=level=iK=At= the=global= scaleI= daiiId= is= evaluated= Eonly= for= f ==PI4F= by=considering= for= the=variable= x= a =éroéer =éercentage=of=reduction=of=the=maximum=overall=base=shear=bdK=salues=of=the=limit=thresholds=of=the=variables=x=are=éroéosed=in=qable=NI=as=a=function=of=the=damage=levels=and=scales=consideredK=As=regard=the=structural=elementsI=drift=and=strength=decay=limits=have=to=be=differentiated=as=a= function=of=the=different= failure=modes=that=may=occur=EeKgK=oockingI=aiagonal=CrackingI= Bed= goint= pliding= or= mixed= modes= as= wellF;= moreoverI= in= the= case= of= séandrelsI= as=highlighted=by=some=recent=exéerimental=caméaigns=and=for=examéle=discussed=in=xTzI=these=values=are=also=function=of=the=architrave=tyée=EeKgK=masonry=archI=stone=lintel=or=woodenLsteel=beamF=and=of= the=éresence=of=another=tensile=resistant=element=couéled=to=it=EeKgK=tieJrod=or=rKcK=ringJbeamFK=As=regard=the=masonry=éanels=constitutive=modelsI= a=bilinear= forceJdrift=relationshié=without=hardening=and= residual= caéacity= is= usually= éroéosed= in= various= codes= xSI= Uz;= howeverI= in= order= to= get= a= reliable=éushover=curve=on=which=define=ais=reéresentative=till=to=near=collaése=conditionI=more=accurate=models=

Control node

Non linear static analysis

global

inWerVWory_1

inWerVWory_2

inWerVWory_3

Pall 8 aiPaiO

aiN

ai4

pta

te=v

aria

bles

and=

Xa

iifo

ra

iP=a

nd=a

i4

smax

bM,3smax

bM,4smax

pta

te=v

aria

bles

and=

Xa

iifo

ra

i1=a

nd=a

i2

dis,2

dis,1

MAColbibMbNT pCAib : daiiIM

aiP

ai4

bd,3stotImax

bd,4stotImax

stotImax

dilBAi pCAib : daiiId

global

Pall 1

Pall 7

Pall 8

Pall 3

The worst condition among those evaluated at dif ferent scales isassumed as reference to def ine the ai W min Edai3IE I dai3IMI dai3Id F

aiPMN aiPMP aiPMU

aiP

bibMbNT pCAib : daiiIb

÷÷

ø

ö

çç

è

æ÷÷ø

öççè

æ=÷

÷ø

öççè

æ=

++

Nmax;NmaxminII ON jai

j

pjai

j

mii

ux

ux

0

0,2

0,4

0,6

0,8

1

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

sLs

u

ari ft [B]

aiP

ai4 aiR

bquivalent frame idealisation of tall U

Checks at level of each elementWkode

mier

ppandrel

dwallU

dwallU

s wal

lUfn

ters

tory

drif

t wal

lU

d

s tot

d

s

dai3Id

dai3IM dai3IE

=

OVON=

are=necessaryK= fn=éarticularI= it= is=éroéosed=to=assume=multiJlinear=constitutive=laws=like=those=shown=in=cigure= R;= in= case= of= éiersI= it= should= be= reéresentative= of= a= érevailing= shear= reséonse= EeKgK= aiagonal=CrackingFI=whereas=in=case=of=séandrels=of=a=tyéical=failure=in=éresence=of=a=wooden=architraveK===

Table N aefinition=of=variables=x=at=the=different=scales=and=limit=thresholds=Eall=limits=are=in=BF==

aii=ptructural element scale

Macroelement scale dlobal scale miers ppandrels

N – – disIN EMKMRIMKNRF= –

O oeaching=of=maximum=strength= –

jaximum=base=shear=EsjF=disIO EMKNRIMKPF=

–

P bseIP EMIOMF;==

dseIP EMKPIMKSF=bseIP EMIRMF;==dseIP EMKRINF=

bjIP EPMI4MF bdIP ENMIOMF

Q bseIQ EOMISMF;=dseIQ EMK4INKOF=

bseIQ EOMITMF;==dseIQ ENIOF=

bjIQ ERMITMF bdIQ EPMI4MF

R dseIR EMKSINKRF= dseIR ENKRIOKRF= – –

=

=

cigK R jultiJlinear=constitutive=laws=for=éier=EleftF=and=séandrels=ErightF=elements== =QKOK Correlation between damage levels and performance levels lnce=damage=levels=have=been=defined=on=basis=of=the=éroéosed=multicriteria=aééroachI=it=is=necessary=to=establish=“acceétability=thresholds”=in=order=to=define=the=disélacements=associated=to=the=fulfilment=of=the=various=éerformance=levelsK=qhe=definition=of=mis=on=the=caéacity=curve=may=be=done=directly=from=the=damage=levels=or=introducing=a=érobabilistic=aééroach=Eby=means=of=fragility=curvesFK=qhe =basic =assumétion =is =to =assume =as =“acceétability =criteria” =that =mis =are =coincident =with =the =correséonding= aisK= fn= éarticularI= this= criterion= seems= consistent= in= case= of= assets= constituted= by=a=single=element=or=macroelementK=aeséite=this=general=criterionI=at=global=scaleI=as=a= function=of= the=éerformance= target= examinedI= related= to= the= rse and euman iife= or =to =the =Building ConservationI=some=additional= refinements= may=be= introducedK= As= matter=of= factI= criteria= introduced= in=§4KNI= seem=consistent=in=terms=of=structural=éerformance=exéected=EBuilding Conservation=targetFI=but=could=be=not=always= suitable= in= terms= of= “life= safety”K= fn= factI= as= regard= the= rse and euman iife= éerformance=targetsI= the= occurrence= of= a= heavy= damage= in= a= quite= small= éortion= of= the= asset= could= éroduce= not=coméatible=consequences=for=the=i-th=mi=examinedK=aue=to=this=issueI=it=seems=reasonable=to=introduce=some=more=cautionary=checks=at=macroelement=scale=in=case=of=miP=associated=to=the=rse=and=euman=iife=target=EeKgK=by=adoéting=more=restrictive=values=for=bjIiFK=fn= order= to= establish= a= more= aware= correlationI= the= érobabilistic= distribution= of= ais= is= introducedK=aamage= levels= reéresent=discrete=damage=conditionsW= from=a=érobabilistic=éoint= of=view=it= is=usually=assumed= that= these= thresholds= correséond= to= the= conditional= érobability= of= RMB= of= being= in= or=exceeding=the=correséonding=damage=levelK=ft=means=that=in=correséondence=with=the=disélacement=daii=there=is=a=“small”=érobability=of=having=damage=levels=higher= than=iJthI=with=consequences=that=could=be=incoméatible=with=the=fulfilment=of=the=examined=miW=as=a=consequenceI=in=generalI=to=assume=mis=as= strictly= coincident= with= the= correséonding= damage= levels= could= be= not= always= on= the= safe= sideK=A=refinement= of= the= definition= of= mis= on= the= caéacity= curve= could= be= obtained= by= introducing=a=érobabilistic=aééroach= through=fragility=curves= and=by=checking= the=fulfilment=of= some=acceétance=criteria =Efor =examéleI =defined =in =terms =of =admissible= éercentage= of= collaésed= buildings= or= injured=

Î

ÎÎ

ÎÎÎ Î Î

ÎÎ

ÎÎ Î Î

Î Î

0

0,2

0,4

0,6

0,8

1

0 0,5 1 1,5 2 2,5 3

0

0,2

0,4

0,6

0,8

1

0 0,5 1

aiP

ai4

aiPai4

aiR

db,5

db xBzdb xBz

sLs

u

sLs

u

aiR

db,4 db,5db,4db,3db,3

bb,3 su

bb,4 su bb,3 su

=

OVOO=

éeoéleFK= qhis= refinement= has= to= be= defined= for= each= séecific= examined= structure= and= cannot= be=quantified=in=general=termsW=in=factI=the=distribution=histogram=of=damage=levels=deéends=on=the=relative=éosition=of=each=damage=level=on=the=overall=caéacity=curve=Efunction=of=the=ductility=of=the=structureF=and=on=the=uncertainties=Eeéistemic=and=randomF=which=are=éresent=in=the=assessmentK=cigure=S=clarifies=this= issueW= the=érobability=of= having=ai= 4=and=R= deéends=by= the= relative= difference= on= the= caéacity=curve=of==daiP=and=daiQI=as=well=as=on=the=sloée=of=the=fragility=curvesK==

=

cigK S Correlation=between=mis=and=ais=through=a=érobabilistic=aééroach=based=on=fragility=curves=

=RK cfNAi obMAohp =tithin =the =éerformance =based =assessmentI =in =the =éaéer =a =érocedure =to =correlate =damage =and =éerformance= levels= based= on= a= multicriteria= aééroach= is= éroéosedK= fn= éarticularI= it= is= addressed= to=combine=all=the=different=scales=Esingle=structural=elementI=macroelement=and=globalF=that=may=concur=to=define=the=whole=reséonse=of=comélex=assetsI=such=as=the=case=of=masonry=historical=constructionsK=Although =the =limit =values =to =be =adoéted =as =reference =may =be =refined =on =the =basis =of =éarametric =numerical= analyses= and= the= suééort= of= exéerimental= caméaigns= Ein= éarticular= at= element= scaleFI= the=érocedure=seems=caéable=to=caéture=the=wide=variety=and=comélexity=of=these=structuresK===AChNltibadbMbNTp =qhe= results= have= been= achieved= in= the= éroject= mbombqrAqb= EwwwKéeréetuateKeuFI= funded= by= the=buroéean= Commission= in= the= peventh= cramework= mrogramme= EcmTLOMMTJOMNPFI= under= grant=agreement=n°=O44OOVK= obcbobNCbp xNz creeman=pKAKI= kicoletti= gKmK= C=qyrell= gKsK= ENVTRFK= “bvaluation=of= existing=building=for= seismic=

riskJ=A=case=study=of=muget=pound=kaval=phyéyard”I= BrementonI=tashingtonI= mrocK of the rKpK kational Conference on barthquake bngineersI=bbofI=NNPJNOOI=BerkeleyK=

xOz cajfar= mK= EOMMMFK= “A= non= linear= analysis= method= for= éerformanceJbased= seismic= design”I=barthquake ppectraI NSWPI=RTPJRVNK=

xPz drunthal= dK= ENVVUFK”buroéean= jacroseismic= pcale”I= Centre= buroééen= de= déodynamiqueet= de=péismologieI=iuxembourgK=solK=NRK=

x4z iagomarsino=pKI=Abbas=kKI=Calderini=CKI=Cattari=pKI=oossi=jKI=dinanniCorradini=oKI=jarghella=dKI=jattolin=cKI=miovanello=sK=EOMNNFK=“Classification=of=cultural=heritage=assets=and=seismic=damage=variables= for= the= identification= of= éerformance= levels”I= mrocK of ptructural repairs and jaintenance of eeritage Architecture conferenceI=SVTJTMU=I=tfq=mressI=fppk=NT4PJPRMVK=

xRz ApCbLpbf= 4NLMS= EOMMSFK= “peismic= oehabilitation= of= bxisting= Buildings”K= American= pociety= of=Civil=bngineersI=rpAK=

xSz burocode=U=–=mart=P=EOMMRFK=“aesign=of=structures=for=earthquake=resistanceK=mart=PW=Assessment=and=retrofitting=of=buildings”K=bks=NVVUJPI=CbkW=BrusselsI=OMMRK=

xTz Beyer= hK= EOMNOFK= “meak= and= residual= strengths= of= brick= masonry= séandrels”I= bngineering ptructuresI=4NI=RPPJR4TK=

xUz ftalian=Code=for=ptructural=aesign=EOMMUFK=aKjK=N4LNLOMMUI=lfficial=Bulletin=noK=OV=4LOLOMMUK=

ais defined on basis of multicriteriaapproach

aiN aiO ai3 ai4

cragilitycurves

0

0,5

1

50%=of probability ofbeing or=exceeding aiP

ML1

ML2

ML3

ML4

d

mrobabilitydistribution of ais

M

MIN

MIO

MI3

MI4

MIR

M N O 3 4 Raamagelevel

ff the=acceptance criterion isn’t=satisfied I=the=mi=limit threshold may moved back=with respect the=corresponding ai

Corresponding to ppp=aiP

s

d dai4dai3daiOdaiN

miP