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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

NlN ifNbAo SbfSMfC obSmlNSb lF Teobb-ibAF MASlNov STorCTrobS harapitta iKNI Mouzakis ChKOI Adami ChKJbKPI sintzileou bK4 ABSToACT =qhe=seismic=behavior= of= two=buildingsI= two=storeys= highI= made=of= threeJleaf= masonry= is= numerically=investigatedK=qhe=two=structures=are=identical=in=geometry=and=materialsX=in=one=of=them=timber=ties=are=arranged=at=intervals=along=the=heightK=A=detailed=numerical=finite=element=model=of=each=building=is=developedI=using=shell=elements=and=a=free=meshing=techniqueK=ppecial=care=is=taken=for=the=description=of=timber=ties=and=timber=floorsK=jasonry=is=considered=as=an=equivalent= composite=material=with=non=linear= behaviourX= the=constitutive=model= is=based=on=smeared=crack=approach=and=simulates= the=main=failure= modes= of= masonry= under= tensionI= compression= and= shearK= eysteretic= rules= for= each= type= of=failure=are=describedK=qhe=mechanical=properties=of=the=masonry=are=identified=from=compression=tests=of=single=walletsI=while=non=linear=parameters=are=selected=from=literatureK=qhe=numerical=results=of=the=analysis= of= each= structure= are= verified= with= the= experimental= data= obtained= during= shake= table= tests=conducted=at= the=iaboratory=of=barthquake=bngineering=at=kqrAI= within= the=framework=of=kfhbo=projectK=qhe=comparison=of= numerical=and=experimental=data=demonstrates= that= the=numerical=model=successfully=estimates=the=global=response=of=threeJleaf=masonry=structure=with=and=without=timber=ties=under=seismic=loadsK= heywords: bxplicit dynamic analysisI Constitutive lawI qhreeJleaf masonry NK fNTolarCTflN =fn= the= last= decades= several= efforts= have= been= made= in= experimental= and= numerical= investigation= of=heritage=structuresK=qhis=interest=has=arisen=from=the=need=for=conservation=and=restoration=of=historical=buildingsI=especially=under=earthquake=actionsK=tithin=the=framework=of=kfhbo=projectI=experimental=investigation= on= subJassemblies= and= scaled= models= is= carried= out= at= iaboratory= of= barthquake=bngineering=EibbFI=kational=qechnical=university=of=Athens=EkqrAFK=qheir=response=both=at=asJbuilt=state=and=after=intervention=is=investigatedK=fn=parallelI=the=behaviour=of=the=buildings=is=being=modeled=using=cinite=blement=jethod=EcbjFI=with=the=aim=to=predict= their=pathology=and=the=experimentally=recorded=responseK=cor= the= analysis= of= historical= masonry= structures= and= traditional= buildingsI= very= sophisticated= finite=elements= or= simplified= methods= are= commonly=used= xNI= 4zK= Although=a= large= number= of= monotonic=versions=of=constitutive=models=have=been=proposed=for=masonry=in=the=past=two=decadesI=not=many=of=them=have=been=extended=to=include=cyclic=loadingK=fn=this=paperI=an=efficient=cyclic=material=model= is=presentedK=qhe=obtained=numerical=results=are=compared=with=the=experimental=onesK=======================================================N arK=Civil=bngineerI=kational=qechnical=rniversity=of=AthensI=caculty=of=Civil=bngineeringI=iaboratory=

of=barthquake=bngineeringI=klucia]centralKntuaKgr=O Assistant=mrofessor=I=kational=qechnical=rniversity=of=AthensI=caculty=of=Civil=bngineeringI=iaboratory=

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OK ClNSTfTrTfsb Mlabi =qhe=uniaxial=total=strain=smeared=crack=model=used=to=simulate=the=nonlinear=behavior= of=masonry=in=this= study= is= recently= described= in= xRzK= ft= is= based= on= smeared= crack= approach= in= conjunction= with=explicit=dynamic=procedureK=qhe=material=system=is=assumed=to=be=identical=to=the=global=xJy=systemI=with= the= bed= joints= along= the= xJaxis= and= the= head= joints= along= the= yJaxisK= fn= this= modelI= the= three=fundamental= inJplane= failure= modes= of= unreinforced= masonry= are= consideredW= cracking= normal= and=parallel=to=bed=jointsI=crushing=normal=and=parallel=to=bed=joints=and=shear=under=compressive=vertical=stressK =qhree=separate =total =strain=based=criteria =are =used=for =failure=initiationK =Cracking=and=crushing=are=controlled=through=normal=strainsI=while=shear=strain=controls=failure=in=shearK=qhe=equivalent=strain=xSz= and= fracture= energy= concepts= xTz= are= also= adoptedK= qhe= latter= is= used= in= order= to= overcome= the=problem=of=meshJdependent=resultsK=qhe=monotonic=shearI=tensile=and=compressive=behavior=of=model=is=shown=in=cigure=NK=fn=tensionI=the=material= is= initially= linear= elastic= and= when= the= maximum= strain= reaches= the= tensile= strainI= cracks=initiateK= After= crackingI= the= tensile= stress=decays= exponentially= EmodeJf= fractureF=as= shown=in=cigure=NaK=fn=compressionI=the=material=exhibits=a=linear=elastic=behaviorI=followed=by=a=strain=hardening=and=a=strain=softening=behaviorK==

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OKNK Calibration of three-leaf masonry qhe=complete=definition=of=the=constitutive=model=requires=NU=parameters=that=account=for=the=different=tensile =and =compressive =strength =parallel =and =normal =to =the =bed =jointsK =fn =the =case =of =threeJleaf =masonry=which=is=examined=in=this=studyI=the=compressiveLtensile=strengths=normal=and=parallel=to=the=bed=joints=are=assumed=to=be=equalI=since=rubble=masonry=tends=to=behave=as=a=homogenous=material=xUzK=ConsequentlyI=the=number=of=required=parameters=is=reduced=to=NP=namelyW=jodulus=of=blasticityI=moisson’s= ratioI= tensile= strengthI= modeJf= fracture= energyI= compressive= strengthI= compressive= strainI=crack= closing= strengthI= unloading= parameters= in= tension= and= compressionI= shear= strengthI= modeJff=fracture=energyI=residual=shear=strength=and=unloading=parameter=in=shearK=qhe=elastic=properties=of=the=masonry=Ejodulus=of=blasticity=and=moisson’s=ratioF=were=based=on=the=experimental=dataK=eoweverI=the= selection= of= postJelastic= and= unloading= parameters= is= a= rather= complex= taskI= since= no= relevant=experimental=data=are=usually=availableK=ConsequentlyI=sensible=assumptions=were=madeI=on=the=basis=of=the=literature=xRI=VJNNzK=ft=is=noted=that=the=value=of= the=phear=jodulus=d=is=obtained=assuming=the=relationship=with=the=jodulus=of=blasticity=d=Z=MK4MbI=as=suggested=by=bCS=xNOzK=qhe=masonry=density=is=measures=NKVMjgrLmPK=fn=qable=NI=the=material=parameters=used=in=the=analysis=are=presentedK=

==

Table N=jechanical=characteristics=of=masonry==

mroperties= salue=jodulus=of=blasticity= MKRM=dma=moisson’s=ratio= MKO=qensile=strength= MKRM=jma=jodeJf=fracture=energy== MKMMMRLMKMMMR=jkm–N=

meak=compressive=strength= JNKRM=jma=meak=compressive=strain= JMKMMOR=rnloading=from=tension=to=compression=parameter= MKUR=Crack=closing=strength= JMKRM=jma=rnloading=from=compression=to=tension=parameter= MKUR=phear=strength= MKNM=jma=jodeJff=fracture=energy= MKMMMN=jkm–N=

oesidual=shear=strength= MKMR=jma=rnloading=shear=parameter= MKVM=

PK SeAhfNd TABib TbSTS =A=series=of=experiments=have=been=performed=in=the=framework=of=kfhbo=project=with=the=purpose=to=investigate=the=dynamic=behaviour=of=historical=masonry=structures=under=seismic=excitationsK= fn=this=studyI=plain=and=timberJlaced=threeJleaf=masonry=models=have=been=chosen=for=numerical=analysisK=qhe=numerical= results= are=compared= to= those=obtained=by= the= experimental= investigation= of= two= modelsK=qhe=tests=have=been=performed=at=ibbLkqrA=using=the=shaking=table=facilityK==qhe=specimens=were=a=NWO=scaleI=OJstorey=threeJleaf=masonry=models=with=timber=floors=Ecigure=4aJ4cFK=jasonry= walls= consisted= of= three= Eapproximately= equal= in= thicknessF= leavesK= qhe= total= thickness= of=walls=was=equal=to=ORM=mmK=qhe=mean=compressive=strength=of=the=limestone=is=approximately=equal=to=

=

NRVP=

NMM=jpaK=qhe=mortar=was=a=limeJpozzolan=one=with=a=mixed=aggregate=matrix=composed=of=siliceous=river=sand=and=limestone=gravelsK=qhe=compressive=strength=of=mortar=was=equal=to=4KSM=jma=Eat=the=age=VM=daysFK=qhe=inner=part=of=the=walls=consists=of=small=stones=and=mortar= in=a=proportion=of=OLNK=qhe=floors=consist=of=timber=beams=ESM=×=NMM=mmF=placed=every=P4M=mm=and=supported=by=masonry=through= a= collector= beamK= A=timber= pavementI= made=of= NMM=×= NM= mmO= timber= planks= was= provided=Enailed=on=the=timber=beamsFK =qimber=lintels =are =provided=at =the=top=of =all =openingsK =fn=the=timber=–laced=specimenI= timber=ties=were=positioned=aFW=at=floor=levels=and=bF=at= top=and=bottom=of=openingsK=qhe= timber= laces= consist= of= two= longitudinal= timber= elements= running= along= the= perimeter= of= the=building= Ecigure= 4dF= connected= among= them= through= transverse= timber= elements= every= MKRM=m=approximatelyK=qhe=cross=section=of=all=timber=elements=were=4M=×=4M=mmOK=qhe=timber=elements=were=made=of=coniferous=wood=Estrength=class=COOFK=auring=testingI=additional=masses=were=placed=on=the=two=floorsI=namelyI=4KR=jgr=and=P=jgr= on= the=floor =of =the =Nst= and =Ond= level= respectivelyK= qhusI= the= total= mass= of= each= specimen= was= approximatly=OO=jgrK=qhe=instrumentation=setJup=was=organised=to=measure=acceleration=and=absolute=displacement=at=various=critical=positions=of=each=specimenK==qhe= specimens= were= subjected= to= stepJwise= increasing= base= motion= in= both= horizontal= directions=EuJlongitudinal= directionI= vJtransversal= directionFI= using=halamata= recordsK= Before= the= execution= of=shaking=table=testsI=the=dynamic=properties=of=each=specimen=Einitial=frequency=and=relating=dampingF=were=measured=through=a=sine=logarithmic=sweep=signal=of=low=amplitudeK==

== ===== == == aF= bF= cF= dF=

FigK 4=aF=qypical=planI=bF=plain=masonry=buildingI=cF=timberJlaced=masonry=buildingI=dF=inJthickness=layout==of=longitudinal=and=transverse=timber=elements==

=Both =models =were =subjected =to =the =halamata =uJ =and =vJ =recordX =a =sequence =of =tests =was =carried =out =with= stepwise= increasing= acceleration= of= the= input= motionK= qhe= unreinforced= masonry= model= was=subjected=to= tests=up= to=VMB= of= the=original= halamata= earthquakeI= whereas= tests=up= to=NOMB= of= the=original=records=were=imposed=to=the=timberJlaced=modelK=qhe=plain=masonry=model=is=characterized=by=pronounced=vulnerability=of= longitudinal=walls= to=outJofJplane=bendingK=qhusI=almost= vertical=cracks=appear=to=all=four=corners=of=the=building=EcigK=RaFK=joreoverI=shear=cracks=appeared=in=the=corners=of=several=openingsK=qhe=crack=pattern=of=the=timberJlaced=model=isI=in=generalI=similar=to=that=of=the=plain=masonry =modelK =eoweverI =the =presence =of =timber =ties =has =prevented =the =opening =of =cracks =in =the =corners=of=openingsI=has=postponed=the=occurrence=and=has= limited=the=opening=and=the=length=of=the=cracks=due=to=the=outJofJplane=bending=of=the=perimeter=wallsK=fn=cigure=Ra=and=RbI=the=damage=pattern=at=the=end=of=tests=is=shown=for=unreinforced=and=timberJlaced=masonry=building=respectivelyK=

=

= == aF= bF=

FigK R=qypical=damages=recorded=at=the=long=and=short=wall=at=the=end=of=testingW=aF=plain=masonry=building=EVMB=halamata=earthquakeFI=bF=timberJlaced=masonry=building=ENOMB=halamata=earthquakeF=

=

NRV4=

After=the=first=series=of=testsI=both=models=were=strengthened=and=retestedK=A=detailed=description=of=the=experimental=campaign=can=be=found=in=xNPI=N4zK==

=4K NrMbofCAi ANAivSfS =qhe=constitutive=modelI=described=in=pection=OI=is=implemented=in=the=generalJpurpose=finiteJelement=code= Abaqus= bxplicit= xNRzI= using= the= sumat= user= subroutineK= qhe= explicit= procedure= requires= no=iterations=and=no=tangent=stiffness=matrix=and=is=based=on=an=explicit=central=difference=integration=rule=together=with=the=use=of=a=diagonal=lumpedJmass=matrixK=qhe=integration=through=time=is=performed=by=using=many=small= incrementsK=A=detailed=discussion=of=the=explicit=dynamic=procedure=in=Abaqus= is=given= in= xNPzK= fn= this= studyI= in= all= analysesI= both= physical= and= geometrical= nonlinearities= are=consideredK=

=4KNK Finite elements of models qhe=numerical=model=of=the=two=buildings=is=shown=in=cigure=SK=cor=the=simulation=of=wallsI=four=node=shell= elements= with= reduced= integration=scheme= were= usedI= whereas= for= modeling=of= timber= beamsI=collector= beams= and= planks= three= dimensional= beam= elements= were= selectedK= qhe= size= of= finite=elements=was=approximately=equal=to=MKNUmK=ft=should=be=noted=that=the=non=linear=material=modeling=refers=to=the=composite=material=and=not=to=the=individual=components=of=masonry=EunitsI=mortarFK=qhe=behavior= of= the= connection= between= floors= and= the= walls= is= not= knownK= cor= the= purpose= of= these=analysesI= full= wallJtimber= beams= connections= were= assumed= for= the= identification= of= the= natural=frequencies= of= each= model= as= well= as= for= dynamic= analysisK= qhe= timber= parts= of= each= structure=were=modeled=as=elasticI=since=no=visisble=damage=was=observed=during=testingK=qhe=modulus=of=blasticity=of=timber=was=taken=equal=to=NMdmaX=its=shear=modulus=was=taken=eqaul=to=MKSPM=dmaK=qhese=values=are=typical= for= coniferous= wood= of= strength= class= COOK=qhe=building= models= were=assumed= fixed= to= the=baseX=the=translation=degrees=of=freedom=in=the=base=were=restrainedK=qhe=additional=masses=were=taken=into=account=by=increasing=the=density=of=planks=on=which=masses=were=fixedK=

=4KOK bigenvalue and time history analysis An=eigenvalue=analysis=using=the=elastic=properties=of= materials=was= first=performed=for= each=modelK=qhe= results= of= this= analysis= are= used= for= comparison= with= the= experimental= values= of= natural=frequenciesK=joreoverI=this=procedure=is=nessecary=to=check=the=stiffness=and=the=mass=of=the=numerical=model =in =the =elastic =stateK =cor =the =plain =specimenI =the =resonance =frequency =in =transversal =and =longitudinal= directions=was=calculated=to=be=4KUT=ez=and=SKRU=ez=respectivelyK=qhose=values=are=quit=close=to=4KOM=ez=and=SKOO=ezI=values=derived=from=sineJ=transversal=and=longitudinal=sweep=testsK=cor=the= timberJlaced=specimenI= the=values= of= frequncies=derived= from=eigenvalue=analysis=were=SKST=ez=and= UKRU= ez= along= v= and= u= directionK= Also= in= this= caseI= the= numerical= values= of= frequencies= are=approximatly=equal=to=the=experimental=ones=ESKTO=ez=and=UKNU=ez=respectivelyFK=fn=cigure=T=the=mode=shapes=corresponding=to=the=calculated=fundamental=frequencies=along=the=two=main=axes=are=presented=for=both=examined=modelsK=

=

== == == =aF= bF=

FigK S=deometry=and=numerical=model=aF=unreinforced=masonry=buildingI=bF=timberJlaced=masonry=building====

pubsequentlyI= a= time=history=analysis= was=performed=using= the=explicit= dynamic= techniqueK=cor= each=building=modelI=a=constant=damping=ratio=of=4B=and=NMB=for= the=first=mode=along=u=and=v=direction=respectively=was=usedKqhese=values=were=determined=during=the=experimental=procedure=through=sineJsweep=testsK=lnly=mass=proportional=oayleigh=damping=was=usedK==

=

NRVR=

ft=is=well=known=that=masonry=buildings=present=nonlinear=behaviour=under=acceleration=with=very=low=amplitudeI=or=even=under=self=weight=and=static=loadsI=due=to=the=low=tensile=strength=of=masonryK=qhus=the=adopted=procedure=for=the=comparison=between=experimental=and=numerical=response=is=to=apply=to=the= base= of= each= modelI= the= acceleration= time= histories= Ewith= increasing= amplitudeF= imposed= to= the=models=during=the=experimental=testingX=both=material=and=geometrical=nonlinearities=were=taken=into=acountK= As= nonlinear= dynamic= analyses= are= time= consumingI= at= presentI= only= one= numerical= test= is=examined= for= each= model= buildingK= qo= check= the= accurancy= of= the= numerical= simulationI= for= each=modelI =the =test =at =which =the =first =damages =were =recorded =was =selectedK =qhusI =for =the =plain =masonry =buildingI=the=qest=ko=S=Ebase=motion=scaled=to=SMB=of=kalamata=rekord=–=cigK=UF=was=simulatedK=cor=the=timberJlaced=modelI=the=qest=ko=NM=Ebase=motion=scaled=to=NOMB=of=halamata=rekord=–=cigK=VF=was=simulatedK=qo=further= reduce= the=computing=timeI= in=both=casesI=only= the=first=NMsec=of= the=recorded=signals=were=imposedK==

= = = == fyZ4KUTez= fxZSKRUez= fxZSKSTez= fxZUKRUez=

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FigK NO=qimberJlaced=specimenW=comparison=between=experimental=and=numerical=results=at=points=APu=and=ATv===

cigures=NP=and=N4=illustrate=the=damage=pattern=Eshear=and=tensile=damage=indexF=obtained=in=numerical=simulations=for=plain=and=timberJlaced=masonry=buildings=respectivelyK=qhe=figures=refer=to=the=end=of=the=load=history=and=show=the=accumulated=failure=during=the=analysisK=Compressive=failures=were=not=detectedK=As= it= can=be=observedI= for=both=specimensI= the=damage=pattern=derived=on= the=basis=of=the=nonlinear=material=model=is=consistent=with=the=experimental=one=Esee=cigK=RFK=

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