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

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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 dubana N I fvan ai dianantonio O 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 evaluatedby 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 fs th 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

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Page 1: ofrmeioeliimpbbefpp - Universidade do Minho · ORT= = cigT piç=str=distributiç=an=resultan=çce = PO Non linear cinematic analysis qh==ç=ç==cinemati=nalysi=i=ç=term==ultimat=acem=ç===

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=

Page 2: ofrmeioeliimpbbefpp - Universidade do Minho · ORT= = cigT piç=str=distributiç=an=resultan=çce = PO Non linear cinematic analysis qh==ç=ç==cinemati=nalysi=i=ç=term==ultimat=acem=ç===

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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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==

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Page 3: ofrmeioeliimpbbefpp - Universidade do Minho · ORT= = cigT piç=str=distributiç=an=resultan=çce = PO Non linear cinematic analysis qh==ç=ç==cinemati=nalysi=i=ç=term==ultimat=acem=ç===

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=

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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==

Page 4: ofrmeioeliimpbbefpp - Universidade do Minho · ORT= = cigT piç=str=distributiç=an=resultan=çce = PO Non linear cinematic analysis qh==ç=ç==cinemati=nalysi=i=ç=term==ultimat=acem=ç===

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Page 5: ofrmeioeliimpbbefpp - Universidade do Minho · ORT= = cigT piç=str=distributiç=an=resultan=çce = PO Non linear cinematic analysis qh==ç=ç==cinemati=nalysi=i=ç=term==ultimat=acem=ç===

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=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==

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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===

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Page 6: ofrmeioeliimpbbefpp - Universidade do Minho · ORT= = cigT piç=str=distributiç=an=resultan=çce = PO Non linear cinematic analysis qh==ç=ç==cinemati=nalysi=i=ç=term==ultimat=acem=ç===

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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=

Page 7: ofrmeioeliimpbbefpp - Universidade do Minho · ORT= = cigT piç=str=distributiç=an=resultan=çce = PO Non linear cinematic analysis qh==ç=ç==cinemati=nalysi=i=ç=term==ultimat=acem=ç===

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=

Page 8: ofrmeioeliimpbbefpp - Universidade do Minho · ORT= = cigT piç=str=distributiç=an=resultan=çce = PO Non linear cinematic analysis qh==ç=ç==cinemati=nalysi=i=ç=term==ultimat=acem=ç===

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=

cig. NR=sariatiçn=çf=the=lçad=factçr=aM==EaF=versus=Abutment=height=L=oadius=length=oatiçI==EbF=versus=Abutment=sectiçn=depth=L=Abutment=height=

=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==

Page 9: ofrmeioeliimpbbefpp - Universidade do Minho · ORT= = cigT piç=str=distributiç=an=resultan=çce = PO Non linear cinematic analysis qh==ç=ç==cinemati=nalysi=i=ç=term==ultimat=acem=ç===

OSN=

qhe= shear= mechanism= cçntrçls= shçwed= that= in= case= çf= sèuat= abutment= and= in= case= çf= very= high=keystçnes=shear=cçllapse=can=happen=fçr=lçwer=lçad=factçrs=with=respect=tç=the=bending=mechanismsK=jçreçver=the=lçad=factçrs=çbtained=in=the=hypçthesis=çf=pçint=hingesI=which=is=generally=used=in=these=evaluatiçnsI=are=higher=than=the=values=in=the=hypçthesis=çf=stress=distributiçn=çver=the=sectiçnK== obcbobNCbp =xNz diuffrè=AK=ENVVPF=picurezza=e=conservazione=dei=centri=storici:=il=caso=lrtigiaK=iaterzaI=BariK=xOz açgliçni=cKI=jçretti=AKI=metrini=sK=ENVV4F=ie=chiese=e=il=terremotoK=qriesteI=bdiziçni=iintK=xPz iagçmarsinç=pKI=mçdestà= pKI=oesemini=pKI= `urti=bKI= marçdi=pKEOMM4F=jechanical= mçdels= fçr= the=

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=

xSz hççharian=AK=ENVRPF=iimit=analysis=çf=vçussçir=EsegmentalF=and=cçncrete=archesI=gournal=of=the=American=Concrete=fnstituteK=

xTz eeyman=gK=ENVUOF=The=masonry=archI=eellis=eçrwççdI=`hichesterK=xUz eeyman=gK=ENVSSF=qhe=stçne=skeletçnI=fnternational=gournal=of=polids=and=ptructuresI=vçlK=OK=xVz dubana= AKI= ai= dianantçniç= fK= EOMNNF= jeccanismi= a= cçllassç= di= archi= triçnfaliW= analisi=

parametriche=cinematiche=lineari=e=nçn=lineariK=fn=usf=Akfafp=Conference=i’fngegneria=sismica=in=ftaliaI=Bari=EftalyFK=

xNMz jinistery= çf= fnfrastructure= EOMMVFI= fstruziçni= per= l’Applicaziçne= kuçve= kçrme= qecniche=`çstruziçni= di= cui= al= aecretç= jinisteriale= N4= gennaiç= OMMUI= Circolare= jinisteriale= nKSNT=Ein=ftalianFK=