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OVN4 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 Cattari N I pergio iagomarsino O ABpToACT ti thin 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 merfor mance 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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OVN4=

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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cigK O Correséondence=between=éerformance=and=damage=levels==As=regard=the=first=issueI=in=mbombqrAqb=éroject=a=classification=based=on=“mechanical”=criteria=has=been= éroéosed= x4zI= starting= from= the= identification= of= the= most= relevant= macroelements= in= historic=buildings=and=of=the=correséonding=damage=tyéesK=peven=architectonic=asset=classes=are=identifiedI=as=followsW= A= –= assets= subjected= to= érevailing= inJélane= damage= EeKgK= éalacesI= castlesIKKKF;= B= – =assets =subjected=to=érevailing=outJofJélane=damage=EeKgK=churchesI=mosquesI…F;=C –=slender=assets=that=can=be= reéresented= by= a= monoJdimensional= masonry= element= EeKgK= towersI= minaretsI…F;= a –=arched=structures= subject= to= inJélane= damage= EeKgK= triuméhal= archesI= aqueductsI= cloistersIKKKF;= b –=massive=structures= in= which= local= failure= of= masonry= érevails= EeKgK= fortressesI= city= wallsIKKF;= c –=blocky=structures= subjected= to=overturning=and=sliding= EeKgK= columnsI= archaeological= ruinsF;=d –=aggregated=

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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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OVNU=

I =

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