ofrmeioeliimpbbefpp - universidade do minho · ort= = cigt piç=str=distributiç=an=resultan=çce =...

ORP=

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

TofrMmeAi AoCe CliiAmpb MbCeANfpMp =Alessandra=dubanaNI=fvan=ai=dianantonioO===ABpToACT

=qhe= evaluatiçn= çf= seismic= respçnse= çf= existing= masçnry= buildings= has= tç= be= faced= with= different=analytical=apprçachesI=as=in=absence=çf=rigid=diaphragm=flççrs=it=is=nçt=pçssible=tç=cçnsider=a=building=glçbal=behaviçurW=structure=respçnse=displacements= and=acceleratiçns= may=be=greatly=mçdified=frçm=the= inJplane= structural= wall= valuesK= fn= particular= in= churches= çnly= the= rççf= can= eventually= play= the=diaphragm=rçleI=but= it= is= nçt= çften=structurally=çrganized=fçr= itK=qhe=cinematic=behaviçur=analysis=çf=macrçJelementsI=which=are=structure=pçrtiçns=split=frçm=the=çthers=due=tç=the=cracks=develçped=during=the=earthèuakeI=can=be=a=valid=apprçachK==qhe=present=paper=fçcuses=çn=the=cçllapse=mechanisms=çf=church=triumphal=archesI=which=divide=the=nave=frçm=the=chancel=and=are=çften=painted=with=frescçes=in=ancient=churchesK=A=study=çn=the=rçle=çf=the= different= geçmetrical= and= mechanical= characteristics= invçlved= has= been= faced= by= means= çf=a=prçperly= designed= numerical= prçcedureK= qhe= analysesI= based= çn= the= cinematic= behaviçurI= were=cçnducted= with= bçth= a= linear= and= a= nçn= linear= apprçachK= qhe= results= çbtained= agree= with= the=çbservatiçns= çf= earthèuake= damages= and= shçw= the= different= impçrtance= çf= the= investigated=parametersK= fn=particular= a=significant= influence=çn= the=cçllapse=lçad=factçrs=and=çn=the=pçsitiçn=çf=the= plastic= hinges= is= linked= with= the= ratiçs= çf= the= geçmetrical= characteristics= çf= the= different= parts=cçnstituting=the=archesK==heywords:= jasonry=archI=Collapse=mechanisms===N. fNTolarCTflN =jasçnry= buildings= can= have= different= respçnses= tç= seismic= actiçnsI= depending= çn= their= structural=systemsK= ff= they= can= rely= çn= a= bçx= structure= behaviçurI= with= hçrizçntal= diaphragmsI= seismic= inertia=fçrces= are= channeled= vertical= dçwnwards= by= the= inJplane= shear= wallsK= ft= is= sç= pçssible= tç= cçnsider=a=glçbal=building=behaviçurI=which=can=be=evaluated=by=means=çf=linear=çr=nçn=linear=analysesK=But=the=bçx=effect=dçes=nçt=generally=regard=buildings=like=churchesI=which=are=vulnerable=tç=different=cçllapse=mechanismsK=qhe=damage=survey=campaigns=çn=churches=strçke=by=the=mçst=intensive=earthèuakes=in=ftaly= during= the= last= 4M= years= EiKeK= criuli= NVTSI= rmbria= jarche= NVVTI= içmbardia= Benacç= OMM4I=i’Aèuila= OMNMF= demçnstrated= that= damages= and= cracks= are= always= lçcalized= in= the= same= structural=elementsK=qhe=cçllapse=happens=when=parts=çf=structuresI=called=macrçJelementsI=which=are=nçt= mçre=cçnnected=with=the=çthers=due=tç=cracksI=lççse=their=eèuilibrium=cçnditiçnK==qhe=different=damage=typçlçgies=cause=peculiar=cçllapse=mechanisms=K=qhe=cinematic=analysisI=based=çn=limit=eèuilibrium=theçremsI=is=cçnsidered=nçwadays=çne=çf=the=mçst=cçrrect=apprçach=tç=study=the=seismic=effects=çn=these=buildings=xNzI=xOzI=xPzI=x4zK=fn=the=present=wçrk=the=seismic=mechanism=çf=the=triumphal=arch=was=analyzedK=fn=`hristian=churchesI=since =the =fsth= centuryI= the=triumphal= arch=has= been=dividing=the=principal= nave= frçm=the=presbyteryI=emphatically=framing=the=space=where=the=altar=is=situatedK=qhe=masçnry=structure=çver=the=arch=is=çften=painted=with=antièue=frescçs=and=it=is=sç=particularly=preciçusK==qhe=seismic=behaviçr= çf= the= triumphal=arch=macrçJelements= is= cçdified=amçng=the=pçssible=cçllapse=mechanisms=çf=cultural=heritage=buildings=xRzI=the=cçllapse=dependence=çn=the=different=geçmetric=and=mechanical=characteristics=is=generally=based=çn=çbservatiçns=çf=the=damaged=structuresK=fn=the=present=================================================N=Assçciate=mrçfessçrI=rniversity=çf=rdineI=aepartment=çf=`ivil=bngineering=and=ArchitectureI=

alessandraKgubana]uniudKit=O=bngineerI=rniversity=çf=rdineI=aepartment=çf=`ivil=bngineering=and=Architecture=

OR4=

paper= the= results= çf= an= investigatiçn= çn= the= rçle= çf= different= parameters= is= presentedI= based= çn= the=results=çf=linear=and=nçn=linear=cinematic=analyses=run=by=a=dedicated=sçftwareK==O. TofrMmeAi AoCe CliiAmpb MbCeANfpMp =iimit=analysis=applied=tç=nç=tensiçn=materials=as=masçnry=is=based=çn=sçme=hypçtheses=by=hççharian=xSz=and=eeyman=xTzIxUzK=fn=particular=with=reference=tç=masçnry=arch=cçllapse=these=hypçtheses=areW=- nç= tensiçn= materialW= it= cçrrespçnds= tç= the= actual= behaviçur= if= the= arch= is= made= çf= vçuissçirs=

assembled=with=lçw=strength=mçrtarI=the=blçcks=may=have=a=tensiçn=resistance=but=this=is=absent=in=the=àçints=

- infinite= cçmpressiçn= strengthW= it= can= be= cçnsidered= reliable= fçr= the= evaluatiçn= çf= the= cçllapse=mechanismI=but=afterwards=it=is=necessary=tç=verify=that=a=lçcal=cçmpressiçn=crush=çf=the=material=dçes=nçt=happen=fçr=lçwer=lçad=values=

- nç= slipW= it= is= eèuivalent= tç=pçstulate= that= the= shear= cçmpçnent= çf= the= fçrce= transmitted= by= twç=adàacent=vçuissçirs=never=çverlçads=the=frictiçn=resistance=in=the=àçintK=

fn= reality= the= masçnry=cçmpressiçn= strength=has= finite= values=and= the=cçllapse=jçmentJAxial= içad=interactiçn=diagram=can=be=described=by=a=parabçlic=line=EcigK=NF=with=the=fçllçwing=eèuatiçnW===

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==

cig. N fnteractiçn=diagram=fçr=masçnry=sectiçn==

qhe= arch= cçllapses= when= the= lçads= prçvide= a= sufficient= number= çf= hinges= tç= turn= it= intç=a=mechanismK=qhe=hinges=are=alternatively=fçrmed=alçng=the=arch=intradçs=and=extradçsK=qhe=minimum=hinge= number= depends= çn= the= geçmetrical= arch= cçnfiguratiçn= and= çn= the= lçad= pçsitiçnsK= cçr=a=symmetric=archI= symmetrically= lçadedI= five=hinges=are=neededI=with=çne=in= the=keystçneI= while=fçr=a=asymmetric=cçnfiguratiçnI=çr=asymmetric=lçadI=fçur=hinges=are=sufficient=EcigK=OFK==

==========================================EaF=================================================================EbF=

cig. O pymmetric=and=asymmetric=arch=mechanisms=

ORR=

qhe= asymmetric= mechanisms= develçp= under= hçrizçntal= and= seismic= fçrcesK= qhe= fçur= hinges= can= be=placed=çnly= in= the=arch=çr= in=çne=çr= bçth= the=abutmentsI= in= this= case=the=whçle= arch=çverturning= is=pçssibleK= eçrizçntal= cracks= in= the= abutments= and= radial= cracks= in= the= arch=are= typical= marks= çf= this=mechanism=startK=phear= mechanisms= are= instead= similar= tç= what= happens= in= masçnry= walls= with= çpeningsW= diagçnal=cracks=are=presentI=beginning=in=the=abutment=and=extending=up=tç=the=archK=pliding=mechanisms=are=mçre=rareI=as=frictiçn=between=the=vçuissçirs=is=generally=an=effective=cçntrastK==P. NrMbofCAi ANAiYpbp lc CfNbMATfC MbCeANfpMp =qhe=turning=intç=a=mechanism=çf=a=triumphal=arch=depends=çn=the=material=mechanical=characteristics=and= geçmetric= arch= dimensiçnsK= A= prçperly= designed= sçftware= was= develçped= tç= evaluate= these=dependences=by=means=çf=parametric=analyses=xVzK===P.N. iinear Cinematic Analysis qhe= sçftware= autçmatically= creates= a= mçdel= çf= the= structure= çn= the= basis= çf= the= geçmetric= and=mechanical= dataK= ft= is= pçssible= tç= evaluate= the= hçrizçntal= lçad= factçr= fçr= a= fçur= hinge= mechanismK=Afterwards=a =check=çn=the=çther =pçssible =mechanisms=is =madeK =qhe=arch=geçmetry=is =defined=by=the=fçllçwing=parameters=EcigK=PFW=

- intradçs=radius=o=- abutment=height=habutment==- abutment=length=labutment==- abutment=depth=s=- keystçne=height=hkeystçne==- eave=inclinatiçn=a =çr=alternatively=eave=height=

jçreçver=the=fçllçwing=data=have=tç=be=definedW=- specific=gravity=lçad=- cçmpressiçn=strength=- shear=strength=- frictiçn=cçefficientK=

=

cig. P deçmetrical=arch=data =qhe= arch= is= then= subdivided= intç= fictitiçus= vçuissçirsK= qhe= abutment= çnes= are= rectangular= with=hçrizçntal=àçintsI=while=the=arch=çnes=are=radially=placedK=qhe=vçuissçir=shape=and=the=àçint=pçsitiçns=are=cçmpatible=with=the=fçur=hinge=cçllapse=mechanismK=All=the=vçuissçirs=are=autçmatically=numbered=and=their=cççrdinatesI=gravity=centres=and=weights=are=calculatedK==qhe=cinematic=analysis= is=based=çn=the=mrinciple=çf=sirtual=tçrk=and=it= is=necessary=tç=chççse=and=tç=investigate=different=pçsitiçns= çf= the= fçur=hingesK= qhe=gravity= centre=virtual=displacements=çf= all= the=vçuissçirs=have=tç=be=calculatedK=qhe=referring=parameter=chçsen=is= the=rçtatiçn=qN=arçund=the=hinge=a=çf=the=macrçJelement=delimitated=by=hinges=a=and=b=EcigK=4FK=fn=functiçn=çf=the=infinitesimal=rçtatiçn=qN=the=variatiçn=çf=the=all=significant=pçint=pçsitiçns=are=evaluatedK=As=it=is=well=knçwnI=the=prçcedure=starts=frçm=a=pçssible=hinge=distributiçnI=as=in=cigK=RI=by=applying=the=vertical=fçrces=mi=at=the=vçuissçirs=gravity=centresI =a =vertical =fçrce=çn=the=key=stçne=tç=simulateI =if =necessaryI =the=lçad=cçming=frçm=the=ridge=beam=and=the=hçrizçntal=fçrcesI=made=prçpçrtiçnal=tç=lçads=tçwards=the=lçad=factçr=aMK==

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cig. 4 Arch=macrçJelement=cinematic=chain==

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cig. R lne=çf=the=pçssible=fçur=hinge=pçsitiçn==

qhe=lçad=factçr=aM=is=evaluated=by=applying=the=mrinciple=çf=sirtual=tçrk=and=eèuating=the=sum=çf=the=internal=and=external=wçrkK==

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=where=mi===the=vertical=fçrces=applied=çn=the=vçuissçirsI=n=the=number=çf=all=the=gravity=lçadsI=mj===the=gravity=lçads=transmitted=by=çther=parts=çf=the=structure=tç=the=archI=m==the=number=çf=the=gravity=lçads=transmitted= by= çther= parts= çf= the= structure= tç= the= archI= ch== the= external= fçrcesI= o= = =the =number =çf =external=fçrcesI=δxIi===hçrizçntal=virtual=displacement=çf=mi=Iδx= Ij===hçrizçntal=virtual=displacement=çf=mjI=δy= Ii===vertical=virtual=displacement=çf=miI=δh===virtual=displacement=çf=chI=ifi===eventual=internal=wçrk=taken=eèual=tç=zerç=in=the=hypçthesis=çf=rigid=macrçJelementsK=qhe=evaluatiçn=çf=aM=is=autçmatically=repeated=fçr=all=the=pçssible=hinge=pçsitiçnsI=the=lçwest=value=çf=the=lçad=factçr=is=chçsen=tç=identify=the=cçllapse=mechanismK==Afterwards= by= eèuilibrium= eèuatiçns= at= the= cçnstraints= and= at= the= hinges= it= is= pçssible= tç= draw= the=thrust=line=EcigK=SFK=qhe=pçssibility=çf=a=shear=cçllapse=is=checkedI=as=it=cçuld=happen=fçr=a=lçwer=value=çf=the=lçad=factçrK==fn=all= the=plastic= apprçaches= hinges=are= cçnsidered=as= a= pçint= at= the=sectiçn=edgeI= this= hypçthesis= is=cçmpatible= with=masçnry= infinite= cçmpressiçn= strengthI= but= in=reality=high= stress= can=develçpI= even=greater=than=the=material=resistanceK=fn=the=present=mçdel=it=is=sç=pçssible=tç=have=the=hinge=pçint=inside=the=sectiçn=and=nçt=çn=the=edgeI=taking=intç=accçunt=the=stress=distributiçn=EcigK=TFK=qhe=distance=çf=the=virtual=hinge=pçint=frçm=the=sectiçn=edge=sensibly=depends=çn=the=value=çf=the=axial=stress=and=sç=it=has=tç=be=calculated=in=cçrrespçndence=çf=each=àçintK==

=

cig. S=Arch=thrust=line=at=the=cçllapse=

ORT=

=cig. T pectiçn=stress=distributiçn=and=resultant=fçrce

=P.O. Non linear cinematic analysis qhe=aim=çf=nçn= linear= cinematic= analysis= is= tç=determine= the=ultimate=displacement=çf= the= structure=befçre=the=cçllapseK=ft=is=necessary=tç=evaluate=the=lçad=factçr=a=fçr=each=varied=cçnfiguratiçnI=defined=by=displacement=dk=çf=a=target=pçintK=qhe=ultimate=displacement=dkM=cçrrespçnds=tç=the=nullifying=çf=the=lçad=factçr=aK=fn=the=present=wçrk=an=analyticalJnumerical=prçcedure=was=usedI=fçllçwing=an=iterative=pathI=where=the=initial= step= cçrrespçnds= tç= the= start=up=çf= the= cçllapse=mechanismK= At= a= general= step= k= the= structure=geçmetry=is=varied=and=the=lçad=factçr=is=revaluated=again=çn=the=new=cçnfiguratiçnK==qhe=prçcedure=can=be=fçllçwed=bçth=in=the=hypçthesis=çf=infinite=and=finite=cçmpressiçn=strengthK=qwç=different= target=displacements=are=chçsenI=which=are=the=thçse=çf=the=central=intradçs=keystçne=m=and=çf=the=gravity=centre=çf=the=structure=d=EcigK=UFK==

============= ================================================EaF========================================================================EbF===========

cig. U=fnitial=cçnfiguratiçn=EaF=and=changed=cçnfiguratiçn=after=sçme=steps=fçr=nçn=linear=cinematic=analysis=EbF==At =each=step=çf =the=prçcedure=the=twç=target =displacements =are =alsç=evaluated=again=and=it =is =pçssible =tç =draw=the=dependence=çf=the=lçad=factçr=versus=displacementI=resulting=in=the=capacity=curve=çf=the=structureK==P.P. salidation of the numerical procedure qhe=prçpçsed= numerical=prçcedure=was= tested=and=validated=by=studying= the=seismic=respçnse=çf= the=small= panta= iucia= `hurch= in= senzçne= EftalyFI= partially= destrçyed=by=NVTS= criuli= earthèuakeK= fn= the=fçllçwing=cigK= V= twç=pictures= shçw=the=church=befçre=and=after= the=earthèuakeK=qhanks= tç=a= damage=survey=campaign=several=images=and=crack=pattern=drawings=are=dispçsable=xOzK=fn=cigK=NM=the=results=çbtained=by=the=numerical=prçcedure=are=cçmpared=with=the=crack=patternK===

==================================================EaF=========================================================================EbF=

cig. V panta=iucia=`hurch=befçre=EaF=and=after=EbF=NVTS=criuli=earthèuake=

ORU=

fn= the= abutment= çn= the= left= there= is= an= almçst= hçrizçntal= crack= near= the= basisI= identified= by= the=numerical=prçcedureK=At=the=arch=left=spring=there=is=a=very=dense=crack=pattern=where=a=cçmpressiçn=cçllapse= çf= masçnry= tççk= placeK= qhe=presence= çf= the= small= windçw= in= the=upper= part= çf= the= façade=determines=a=shear=cçllapseI=which=is=signaled=by=the=sçftware=as=the=shear=cçntrçl=is=nçt=verifiedK==

===============================================EaF=====================================================EbF==

cig. NM A=picture=çf=the=arch=cçllapse=EaF=and=the=drawing=çf=the=thrust=line=çver=the=crack=pattern=EbF =jçreçver=nçn=linear=cinematic=analyses=were=perfçrmed=fçllçwing=the=prçcedure=suggested=by=ftalian=`çde= xNMzK= fn=cigK= NN= the= cçmparisçn=between= the= capacity= curve= and= the= demand= curve= fçr= a= 4TR=return=periçd=earthèuake=çn=a=sçft=sçil=is=plçttedK=qhe=nçminal=cçde=capacity=dsG=results=less=than=the=demand=and=sç=the=arch=dçes=nçt=suppçrt=the=seismic=strçkeK==

=cig. NN=Analysis=results=çf=panta=iucia=triumphal=arch=fçr=a=4TR=years=return=periçd=earthèuake==

=4. mAoAMbTofC ANAiYpbp =marametric= analyses= were=perfçrmed= in=çrder= tç=study= the=respçnse=variatiçn=çf= the= triumphal=arches=with= regard= tç= significant= parameters= as= geçmetry= and= masçnry= mechanical= characteristicsK= qhe=geçmetrical=parameters=taken=intç=cçnsideratiçn=are=EcigK=PFW=

- the=radius=çf=the=arch=o=- the=height=çf=the=abutments=habutment==- the=length=çf=the=abutment=basis=sectiçn=l=abutment=- the=depth=çf=the=abutment=basis=sectiçn=s=- the=keystçne=height=h=keystone=- inclinatiçn=çf=the=upper=part=çf=the=arch=a=K=

jçreçver=sçme=ratiçs=amçng=these=geçmetrical=parameters=have=been=cçnsideredI=which=were=already=repçrted=as=significant=xOzW=

- the=ratiç=between=the=abutment=height=and=the=arch=radius=habutment==L=o=- the=ratiç=between=the=length=çf=the=abutment=basis=sectiçn=and=the=arch=radius=l=abutment=L=o=- the=ratiç=between=the=keystçne=height=and=the=arch=radius=h=keystoneL=o=- the=ratiç=between=the=length=çf=abutment=basis=sectiçn=and=the=abutment=height=l=abutment=L=h=abutmentK=

Alsç=different=mechanical=characteristicsI=in=accçrdance=with=xNMzI=have=been=taken=intç=cçnsideratiçnK=cçr=each=parameter=a=range=çf=values=has=been=chçsenI=cçnsidering=the=panta=iucia=`hurch=values=the=mean=çf=the=rangeK=All=the=ranges=and=the=reference=values=are=repçrted=in=qable=NK=

ORV=

pçme=çf= the=çbtained=results= are=graphically=described=with= reference= tç= twç=different= mçdelsW=case=A=refers= tç= the= limit= pçsitiçn= çf= the= hinge= at= the= sectiçn= bçrderI= while= case= B= refers= tç= a= stress=distributiçn= çn= the= sectiçn= and= an= inside= hinge=pçsitiçnK fn= cigK= NO= cigK= NOthe=variatiçn=çf= the= lçad=factçr=aM=versus=the=arch=radius=is=plçttedK=qhe=results=shçw=a=difference=çf=PPB=in=case=A=and=4PB=in=case=BI=at= the=grçwing=çf=the=radiusK=qhe=lçad=factçr= is=always=greater=çf=cçurse=in=the=hypçthesis= çf=pçint= hingeK= fn=cigK= NP= the=different= pçsitiçns= çf= the=hinges= at= the= grçwing=çf= the= radius= length= are=drawnK=fn=case=A=there=is=always=an=çverturn=çf=bçth=the=abutmentsI=while=in=case=BI=when=the=radius=length=grçws=frçm=PKTR=m=tç=4=mI=the=hinge=at=the=basis=rises=up=at=the=springK=qhe=shear=cçllapse=never=takes=placeK=fn=cigK=N4=the=relatiçnship=between=the=lçad=factçr=aM=and=the=abutment=height=is=plçttedK=As=expected=the= lçad= factçr= diminishes= at= the= height= grçwingK= qhe= parametric= analyses= perfçrmed= shçw= that= fçr=a=MKP=m=sectiçn=depth=shear=mechanisms=take=place=befçre=bending=hingesK==qhe=inclinatiçn=çf=the=eave=shçws=tç=be=nçt=sç=impçrtant=çn=the=lçad=factçr=valuesK=fnstead=the=mçst=significative=parameters=are=sçme=geçmetric=ratiçs=amçng=the=arch=dimensiçnsI=such=as= the= ratiç=between= the= abutment= height= and= the=radius= length= and= the= ratiç=between= the= abutment=sectiçn=depth=and=abutment=heightK==

Table N=marameter=values==

marameter= oeference=salue= salue=oange==

o= OKOS=m= NKRJ4=m=

eabutment= PKUR=m= OKMJSKM=m=

labutment= NKVS=m= OKMJ4KR=m=

ekeystone= OKRT=m= NKRJ4KM=m=

s= MKSR=m= MKPJNKM=m=

rpper=inclination= OP=°= M°J4M=°=

eabutment=Lo= NKTM= MKRJOKR=

labutment=Lo= MKUT= MKRJOKM=

ekeystone=Lo= NKN4= MKTRJOKMM=

labutment=Leabutment= MKRN= MKPJNKN=

dravity=load=on=the=roof= NMMM=kLmO= MJOMMM=kLmO=

jedium=compression=strength=fcm= OKS=jma= NJU=jma=

=

0.0

0.1

0.2

0.3

0.4

0.R

0.6

0.7

0.8

0 0.R 1 1.R 2 2.R 3 3.R 4 4.R RArch radius (m)

alfa

0 Case A Case B

=cig. NO=salues=çf=aM=cçefficient=versus=arch=radius=

OSM=

== = Case A Case B=

cig. NP sariatiçn=çf=hinge=pçsitiçns=at=the=grçwing=çf=the=radius=length =

0.0

0.1

0.2

0.3

0.4

0.R

0.6

0.7

0.8

0 1 2 3 4 R 6 7Abutment height (m)

alfa

0

Case A Case B

cig. N4=salues=çf=aM=cçefficient=versus=abutment=height==

As=shçwn=in=cigK=NRaI=at=the=grçwing=çf=the=ratiç=abutment=height=çver=radius=length=frçm=MKR=tç=PI=the=lçad=factçr=variatiçn=is=eèual=tç=O4PB=in=`ase=A=and=OTVB=in=case=BI=whileI=as=shçwn=in=cigK=NRbI=the=lçad=factçr=variatiçn=is=eèual=tç=O4PB=in=`ase=A=and=PUNB=in=`ase=BI=when=the=ratiç=abutment=sectiçn=depth=versus=abutment=height=grçws=frçm=MKP=tç=NKNK==fn=all=the=situatiçn=faced=the=lçad=factçr=is=lçwer=in=`ase=BI=where=the=mechanical=strength=çf=masçnry=is=taken=intç=cçnsideratiçnK=

0.0

0.1

0.2

0.3

0.4

0.R

0.6

0.7

0.8

0 0.R 1 1.R 2 2.R 3 3.R 4Abutment height / oadius length

alfa

0 Case A Case B

==

0.0

0.1

0.2

0.3

0.4

0.R

0.6

0.7

0.8

0 0.R 1 1.RAbutment section depth / Abutment height

alfa

0

Case A Case B

===========================================EaF================================================================================EbF=

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=R. ClNCirpflNp qhe=lçad=factçr=values=in=case=çf=fçur=hinge=arch=cçllapse=mechanisms=were=investigated=in=the=present=paper= by= using= a= dedicated= sçftwareK= qhe= parametric= analyses= perfçrmed= cçnfirmed= several=çbservatiçns= made= çn= the= basis= çf= crack= patterns= çn= triumphal= arches= subàected= tç= earthèuakesK= fn=particular=the=mçst=significative=parameters=are=sçme=building=ratiçs=amçng=parts=çf=the=arch=structureI=which=can=determine=an=impçrtant=variatiçn=çf=the=lçad=factçrs=and=the=hinge=pçsitiçnsK==

OSN=

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seismic= vulnerability= assessment= çf= churchesK= fnW= mrocK= of= fs= fnternational= Conference= on=ptructural=Analysis=of=eistoric=Construction=pAeCI=madçva=EftalyFI=AKAK=BalkemaI=içndçnK=

x4z diuriani= bKI= jarini= AK= EOMMUF= bxperiences= frçm= the= kçrthern= ftaly= OMM4= earthèuakeW=sulnerability= assessment= and= strnthening= çf= histçric= churchesK= fnW= mrocK= of= pixth= fnternational=Conference= on= ptructural= Analysis= of= eistoric= Construction= pAeCI= Bath= ErhFI= `o`= mressL=BalkemaI=ieidenK=

xRz jinistry=çf=`ultural=eeritage=and=Activities=EOMNMFI=duidelines=fçr=the=evaluatiçn=çf=the=seismic=risk=çf=cultural=heritage=Ein=ftalianFK=

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