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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
ppect
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MAMAGN LIMITATION
Artistic Asset Conservation
Building Conservation
RNSTORABLN MAMAGN LOSS PRNVNNTIONNNAR INTNGRITY
SIGNIFICANT BUT RNSTORABLN MAMAGN
CAPACITY CURVN
NNAR COLLAPSN
ppectral aisplacement
RNMUCNM MNMANM
PNRFORMANCN POINT
rse and euman iife
IMMNMIATN OCCUPANCY LIFN SAFNTY
Building Conservation mis
Artistic Asset Conservation mis
rse and euman iife mis
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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==
=
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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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