=

ORNV=

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

ANAivpfp lc efpqlofC MAplNov pqorCqrobp prmmloqba Bv Pa iApbo pCANNfNd Carl qhelinNI colke eöstOI Clas oosenbergP=

=

ABpqoACq =qhe=ruin=of=pt=kicolai=in=sisby=has=been=used=as=a=cultural=venue=for=more=than=NMM=yearsK=qhe=current=restoration= éroject= is= handling= defects= concerning= masonryI= accessibility= and= comfort= to= facilitate=extended=and=sustainable=useK=ptructural=evaluation= is=one=of= the=decisive=factors= in=the=éreservation=and= use= of= the= built= cultural= heritageK= ft= can= be= related= to= evident= damage= that= needs= reéair= and=reinforcement= or= to= a= building= that= is= going= to= be= used= in= a= new= wayI= with= new= requirements=concerning= the= structureK= fn= vaulted= masonry= structuresI= the= overall= geometry= is= the= key= factor= in=structural=stabilityK=qhe=ruin=of=pt=kicolai=serves=as=a=érinciéal=case=study=for=investigation=of=the=use=of=Pa=laser=scanning=to=suééort=analysis=of=vaulted=masonry=structuresK=iimit= state=analysis=based=on=thrust=lines=and=finite=element=analysis=using=nonJlinear=material=models=are=being=usedK=jethods=for=érocessing=PaJéoint=clouds=from=laser=scans=into=useful=geometric=information=for= thrust=line=analysis=and=transforming=the=scanned=data=into=models=on=which=finite=element=analysis=can=be=éerformed=are=both=being=evaluated=with=reséect=to=aéélicability=and=usefulnessK=frreséective=of=the=tyée=of=analysis=carried=outI=accuracy=is= highly=deéendent= on=how=érecisely=the=geometry= is=describedK=qhe=Pa=laser=scanning=technique=érovides=a=érecise=descriétion=of= the=scanned=structureI=although=the=handling=of=data= can= be= cumbersomeK= qhe= éotential= of= Pa= laser= scanning= in= suééorting= advanced= analysis= of=comélex=historic=masonry=structures=is=demonstratedK= heywords: Masonry structuresI Pa-laser scanningI Masonry vaultsI qhrust line analysisI

cinite element methodI ptructural behaviour NK fNqolarCqflN =bxtraordinary= buildings= have= been= created= in= pweden= since= early= medieval= times= using= masonry= –=stoneI=brick=and=mortar=–=in=which=the=heavy=materials=aééear=to=be=floating=high=above=oéen=séaces=by= means= of= vaulted=structuresK= fn= medieval= churches= the= interaction=between= the= architectural= and=structural=shaée=is=evidentW=the=necessary=structural=form=to=bear=ué=the=masonry=by=use=of=vaults=and=arches= is= also= used= for= architectural= exéressionK= qhese= historic= buildings= are= among= our= most=iméressive=structuresK=qhey=are=irreélaceable=and=of=considerable=cultural=valueK===lne=examéle=is=the=ruin=of=pt=kicolai=in=sisby=whichI=although=it=has=been=a=ruin=for=several=centuriesI=still=has=a=many=vaults=in=élaceI=see=cigure=NK=qhe=church=of=pt=kicolai=was=built=in=in=various=stages=over=timeI=and=became=a=aominicans=monastery=church=in=the=thirteenth=centuryK=ft=has=now=been=used=as= a= cultural= venue= for= more= than= NMM= yearsK= qhe= ongoing= restoration= éroject= is= handling= defects=concerning=masonryI=accessibility=and=comfort=to=facilitate=extended=and=sustainable=useK===qhe= éroblems= with= which= the= conservation= engineer= is= confronted= when= working= with= historic=masonry=buildings=are=often=related=to=cracking=and=deformations=of=the=masonryK=qo=be=able=to=assess=the=condition= and= safety= of= the=buildingI= good=understanding= of= the= structural= behaviour= of= historic=masonry=structures=is=neededK==

================================================N=mhaI=qyréns=ABI=carlKthelin]tyrensKse=O=ptructural=bngineerI=qyréns=ABI=folkeKhost]tyrensKse=P=purvey=bngineerI=qyréns=ABI=clasKrosenberg]tyrensKse=

=

OROM=

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cigK N=An=interior=view=of=the=ruin=of=pt=kicolai=in=sisby==

NKNK ptructural analysis of historic masonry structures eistoric= masonry= structures= differ= from= conteméorary= constructions= of= steelI= reinforced= concrete= or=wood=in=terms=of=how=the=load=is=carriedK=qhe=methods=for=structural=analysis=often=used=todayI=based=on=elastic=analysis=and=isotroéic=materialI=are=not=suitable=for=analysis=of=masonry=structures=xNI=OzK=qhe=stability=and=safety=of=masonry=is=secured=by=the=develoément=of=coméressive=forces= in=the=materialI=which= has= a= negligible= caéacity= to= carry= tensional= forcesK= qhe= coméressive= forces= aééarent= in= the=structures=are=often=much=lower= than=the=coméressive=strength=of=the=materialK=qhe=assessment=of=the=safety= of= masonry= structures= is= therefore=érimarily= a= éroblem= of= geometry= and= stability= rather= than=material=strength=and=stress=xNzK==qhrust=lines=érovide=a=useful=way=of=describing=the=structural=behaviour=of=masonry=xPzK=qhe=thrust=line=is=the=resultant=of=the=coméressive=forces=whichI=under=equilibriumI=flow=through=the=structure=to=the=suééortsK= As= early= as= during= the= seventeenth= centuryI= oobert= eooke= ENSPRJNTMPF= described= the=connection=between=the=hanging=flexible=line=and=the=thrust=line=of=the=archesK=qhrust=lines=can=also=be=constructed=with=graéhic=analysis=xPJRzK==eeyman= xNz= introduced= the= safe= theorem= for= masonry= structuresK= rsing= the= assumétions= thatW=aF=masonry= has= no= tensile= strengthI= bF= stresses= are= so= low= that= masonry= can= be= considered= to= have=unlimited=coméressive=strength=and=cF= that= sliding=failure=does=not=occurI=eeyman=concluded=that= if=thrust=lines=in=equilibrium=can=be=found=in=the=geometry=of=the=masonryI=this=is=éroof=of=the=structure’s=safetyK=qhe=assumétions=should=be=examined=in=each=individual=case=being=analysedK=Against= this= backgroundI= there=are= two=courses= of=action= in= the= literature=for= the=analysis= of= historic=masonry=structuresW=equilibriumJbased=thrust=line=analysis=and=the=use=of=coméuter=tools=based=on=the=finite=element=methodK===NKOK qhrust line-based analysis and graphic analysis draéhic=analysis=is=a=method=used=to=construct=thrust=lines=and=to=investigate=the=shaée=of=catenaries=in=two=dimensionsK=qhe=method=was=develoéed=in=the=nineteenth=century=and=has=been=described=in=detail=in=various=older=documents=x4I=RzK=An=uéJtoJdate=descriétion=and=introduction=to=the=method=has=been=given=by= Allen=C= walenwski= xSzK= qhe= method= is= based= on= the= use= of= force=éolygons= connected=by=geometrical= restrictionsK= draéhic= analysis= makes= it= éossible= to= exélore= the= connections= between= the=shaée=and=the=forces=of=a=structureK=qhrough=using=the=slicing=technique=xOI=PzI=graéhic=analysis=can=be=aéélied=to=advanced=threeJdimensional=structures=such=as=vaults=and=domesK==eoweverI=traditional=graéhic=analysisI=done=using=éaéer=and=éenI=is=cumbersome=to=executeI=eséecially=for=comélex=structuresI=and=there=is=always=a=risk=of=errorK=A=tool=for=realJtime=limit=analysis=of=vaulted=masonry= buildings= based= on= graéhic= analysis= has= been= develoéed= at= jassachusetts= fnstitute= of=qechnology=EjfqF=by=mrofessor=lchsendorf=and=his=masonry=groué=xTI=UzK=qhe=method=is=based=on=the=éroduction= of= models= that= makes= the= graéhic= analysis= éarametric= and= interactiveI= reducing= the=cumbersome= work=required=for= traditional= graéhic=analysisK= te=used= this= newer= method= to=carry=out=parametric thrust line analysis= on= the= structure= of= pWt= kicolaiI= using= a= twoJdimensional= interactive=drawing=érogram=xVzK==

=

ORON=

NKPK cbM-based analysis qhe= use= of= linear= elastic= finite= element= analysis= on= masonry= structures= is= inaééroériateK= An= elastic=analysis=requires=that=the=material=model=be=given=both=known=elastic=éroéerties=and=exact=information=on= the= suééort= conditions= of= the= structureK= qhe= result= of= such= an= analysis= is= a= stress= distributionI=showing=where=coméressive=and=tensile=forces=ariseI=which=would=érovide=an=incorrect=descriétion=of=the=structural=behaviourI=since=masonry=cannot=bear=tensile=forcesK==eoweverI= there=is= a= different= oétion= for= carrying=out= nonJlinear= cbjJanalysis=with= material= models=that= consider= unilateral= materialK= konJlinear= analysis= is= normally= solved= as= an= iterative= érocessI=beginning=with=an=elastic= analysis= after= which= the=éarts= EnodesF=where=tension=occurs= are=identifiedK=qhen=a=simulation=of=cracking=aééears=and=a=new=iterative=calculation=éroceeds=with=the=new=cracked=érerequisitesI=until=the=érocess=converges=to=a=solution=of=coméressive=forces=onlyK==cbjJbased=analysis=of=masonry=are=éroblematic=since=the=structures=analysed=are=normally=statically=indeterminate= to= several= degreesI= meaning= that= small= changes= in= the= suééort= conditions= can= give=coméletely=different=stress=distributions=whichI=in=turnI=can=give=results=that=are=difficult=to=interéretK=qhe=analysis=therefore=éuts==high=demands=on=the=exéerience=and=ability=of=the=engineer=to=understand=and=interéret=the=results=xNMzK==fn= our= studyI= a= generalJéuréose= cbj= érogram= xNNz= was= usedK= qhe= érogram= can= handle= nonJlinear=analysis= and= a= large= number= of= material= models= and= coméutational= methodsK= ft= is= also= suitable= for=threeJdimensional=models=and=analysisK===NK4K qhe importance of accurate geometrical descriptions frreséective= of= the= methods= used= to=analyse=and=describe= the= structural=behaviour= of= historic= masonry=structuresI=accurate=descriétion=of=the=geometry=is=neededK=qhe=structural=shaée=is=the=key=to=stability=and=strengthK= qhe= geometry= of= historic= masonry= structures= with= vaults= is= also= often= highly= comélexI= with=shaées=curving=in=two=different=directions=or=owing=to=changes=in=geometry=caused=by=deformationK==rsing=traditional=methods=to=make=thorough=measurements=of=a=building=is=a=good=way=of=getting=to=know= the= construction= in= detailI= and= can= be= a= valuable= aséect= of= a= building= investigationK= vet= the=measurement=of=buildings=is=also=a=cumbersome=and=time=consuming=taskI=and=there=are=limitations=to=how= accurate= such= measurements= can= beK= qhese= éroblems= become= increasingly= evident= in= larger=structures=with=big=volumesI=long=distances=and=comélex=geometriesK==fn= this= studyI= the= use= of= Pa= laser= scanning= to= caéture= the= comélex= geometry= of= vaulted= masonry=buildings= was= testedI= the= main= aim= being= to= develoé= éractical= methods= for= using= laserJscanned=geometries=for=coméutations=and=analysis=of=the=structural=behaviour=of=masonry=buildingsK===OK CAmqrofNd dblMbqov rpfNd Pa iApbo pCANNfNd

OKNK Pa iaser scanning fn=Pa=laser=scanningI=a=laser=beam=measures=the=distance=between=the=instrument=Ethe=scannerF=and=the=objectK =qhe=laser =beam=on=the=instrument =scans=a =éredefined=area=to=measure=the=distance=to=a =large=number= of= éoints= on= the= scanned= objectK= qhese= éoints= are= then= coméiled= into= a= databaseI= and= are=usually=visualised=as=a=point cloud=where=the=individual=measured=éoints=are=reéresented=by=dotsK==fn=the=laser=scanning=érocessI=the=scanner=caétures=the=éoint=in=its=line=of=sight=Elike=a=Pa=éhotograéhFK=qhis=imélies=that=the=scanner=has=to=switch=éositions=to=make=a=comélete=three=dimensional=caéturing=of=the=scanned=objects=without=causing=éarts=of=the=objects=to=end=ué=“shadowed”K==qhe=séecifics=of=the=laser=scan=and=the=érerequisites=used=in=this=study=are=éresented=in=qable=NK===OKOK qhe point cloud qhe=size=and=resolution=of=the=éoint=cloud=deéends=on=the=size=of=the=scanned=object=and=the=density=of=the=scanK=fn=this=éroject=a=full=and=detailed=scan=of=the=ruin=of=pt=kicolai=in=sisby=has=been=carried=out=and=the=éoint=cloud=consists=of=about=UMM=million=éointsK=iarge=éoint=clouds=use=a=considerable=amount=of= coméuter= memory= caéacity= and= also= their= handling= in= coméuter= networks= can= therefore= be=éroblematicK===OKPK qhe process – laser scanning to computational models qhere=are=few= literature=references= dealing= with= the=use=of= laser= scanning= in=connection= to=structural=models=of=masonry=structuresK=pchueremans=C=sangenecten=xNOz=described=a=successful=use=of= laser=scanning=of=the=vaults=of=the=church=paint=gacobs=in=ieuven=in=order=to=obtain=a=accurate=geometry=for=thrust=line=analysisK==

=

OROO=

qable N=péecifics=of=the=laser=scanning=system==

qhe laser scanning system =Manufacture ieica=pcanptation=CNM=qype qimeJofJflight=Colour dreenI=wavelength=Z=RPO=nm=iaser class Po=EfbC=SMUORJNF=Max range PMM=m=at=VMBX=NP4=m=at=NUB=albedo=Min range MIN=m=pcan rate ré=to=RM=MMM=éointsLsec=pcanning resolution =péot=size= crom=MJRM=mX=4IR=mm=Ectee=basedFX=T=mm=Edauss=basedF=moint=séacing= cully=selectable=horizontal=and=verticalX=Y=N=mm=min=density=cield of view =eorizontal= PSM°=EmaxF=sertical= OTM°=EmaxF= =

pystem performance =Accuracy of single measurement =mosition= S=mm=Eat=N=m=–=RM=m=with=STB=érobabilityF=aistance= 4=mm=Eat=N=m=–=RM=m=with=STB=érobabilityF=Angle=EhorizontalLveticalF= SM=µrad=L=SM=µrad=ENO”=LNO”F=Modelled surface precisionG O=mm=Edeéending=on=modelling=methodF=qarget acquisition O= mm= standard= deviation= EAlgorithmic= fit= to= élanar= eap= measuring=

targets= =

pt Nicolai =kumber=of=scanning=éositions= 44=moint=density= NM=mm=EmeanF=

=

Gqhe=deviation=of=the=éoint=cloud=from=a=surface=that=have=been=fitted=to=the=scanned=éoint=cloudK==fn=laser=scanning=of=a=building=a=number=of=scanner=station=are=élannedI=to=caéture=as=much=as=éossible=of= the=buildingK= aifficult= areas= include= highly= elevated=éoint= such=as= high= ceilings= and=outer= roofsK=luter=roofs=are=comélicated=since=the=scanner=has=to=be=elevated=to=the=level=of=the=roofK=qhe=inside=of=pt=kicolai=has=vaults=and=arches=which=can=be=scanned=from=floor=levelK=At= each=scanner= éosition=a= seéarate=éoint= cloud= is= createdI= locally=oriented= to= the=coordinates= of= the=scannerK= fn= order= to= relate= all= the= individual= local=éoint= clouds= to= each=other= and= to= the= surrounding=environmentI=a=number=of=targets=are=mounted=to=the=scanned=object=and=in=its=vicinityK=At=least=three=of=these=targets=have=to=be=caétured=to=refer=the=local=éoint=cloud=to=the=global=coordinates=of=the=final=modelK= A=érimary=network=based= on= the=control= network=of= the= local=municiéality= Ein= the=case=of=pt=kicolai=in=sisbyW=pweref==VV=NU=4R=L=oe=MMF=should=be=establishedI=from=which=all=the=targets=can=be=measured=by=use=of=a=total=stationK=By=measuring=all=the=targetsI=each=local=éoint=cloud=can=be=correctly=oriented=even=if=the=registration=failsI=and=it=is=éossible=to=gain=control=of=the=geometry=of=the=comélete=scan=and=avoid=éossible=éroéagation=of=faultsK=qhe=next=steé=is=to=give=all=the=scanned=éoints=coordinates=in=a=common=reference=systemK=qhis=érocess=is=known=as=registrationI=and=it=is=linked=to=the=hardware=of=the=séecific=scannerK=qhe=targets=are=given=coordinates= in= the=common=reference=system=and=coordinates= of= the=scanned= éoints= are=recalculatedI=giving=coordinates= in=uI=vI=wI=and=an=intensity=value=andI=if=the=object=has=been=éhotograéhed=during=the=scanningI=a=colour=value=for=each=éointK=fn=this=steéI=éoints=that=are=faulty=or=uninteresting=for=the=éroject=at=hand=can=also=be=removedK==qhe=éoint=cloud=database=can=be=used=for=different=éuréoses=after=registrationK=ft=is=normally=in=the=steé=of=érocessing=the=éoint=cloud=in=different=aéélication=for=a=considerable=amount=of=work=to=be=required=in=order=to=retrieve=useful=informationK==auring=the=course=of=the=érojectI=various=tyées=of=software=for=érocessing=the=éoint=cloud=was=tested=and=evaluatedK= lne= demand= on= the= software= was= the= caéacity= to= handle= large= éoint= clouds= on= a=standard=

=

OROP=

coméuter= without= causing= lockJuésK= qhe= next= steé= was= to= evaluate= érograms= with= functions= for= Pa=modellingK=qwo=érograms=stood=outW=mointools=xNPz=and=Paoeshaéer=xN4zK=mointools=can=be=used=to=edit=the=éoint=cloudI=as=well=as=for=visualisationI=animationI=measuring=and=modellingK=qhe=modelling=can=be=done=using=élugins=for=AutoCad=xNRz=or=pketchué=xNSzK=Paoeshaéer=is=an=effective=tool=to=create=meshed=modelsK= fn= PaoeshaéerI= model= files= can= be= exéorted= to= different= formats= that= can= be= iméorted= into=érograms=for=structural=evaluationK===OKPKNK deometry for thrust line analysis qo= carry= out= thrust= line= analysis= of= historic= masonry= structuresI= reéresentative= crossJsections= of= the=structure=are=neededK=puch=sections=were=made=using=mointools=and=AutoCadI=see=examéle=in=cigure=OK=then=using=the=slicing=techniqueI= the=vaulted=webs=are=divided=into=elementary=arches=or=striées= for=twoJdimensional= thrust= line= analysisK= qhe= reactions= of= these= arches= or= striées= are= then=combined= to=simulate= the= threeJdimensional= action= of= the= vaultsK= fn= AutoCadI= it= is= éossible= to= systematize= the=location=of=the=sections=to=achieve=a=good=distribution=of=“slices”=in=order=to=carry=out=analysis=by=the=slicing=techniqueK===

=

cigK O=mrocessing=of=the=laser=scanned=éoint=cloud=of=pt=kicolai=in=the=mointools=AutoCad=élugin=to=create=accurate=sections=

=OKPKOK deometry for cbM-based analysis Paoeshaéer =was=used=to=generate =Pa=models =that =can=be=iméorted=into=cbj=érogramsI =see=cigure=PK =iarge=éoint=clouds=needs=to=be=sélit=ué=into=smaller=éartsI=since=there=is=a=limit=to=the=size=of=the=éoint=clouds= Paoeshaéer= can= manageK= qhis= sélitting= ué= in= smaller= clouds= can= either= be= done= early= in= the=registration=érocess=or=with=mointoolsK=then=a=éoint=cloud=is=iméorted=into=PaoeshaéerI=its=density=is=set=and=essential=éoints=retainedI=although=the=resolution=is=reduced=to=obtain=a=file=that=is=easy=to=handleK==fn= Paoeshaéer= the= éoint= cloud= can= be= maniéulated= in= a= number= of= waysK= cor= examéleI= irrelevant=éoints=can=easily=be=erasedK=qhe=next=steé=is=to=create=a=three=dimensional=model=by=meshingK===

=

cigK P=bxaméle=of=meshed=PaJmodel=generated=from=éoint=cloud=in=PaoeshaéerK=qhe=leftJhand=image=show=the=iméorted=éoint=cloud=and=the=rightJhand=image=show=the=PaJmodel=

=

ORO4=

pome=areas=of=the=éoint=cloud=may=be=uncertain=because=some=éarts=have=been=in=shadow=during=the=scanning=érocessI=and=thus=some=éoints=are=lackingI=or=because=grass=or=bushes=were=covering=éarts=of=a= buildingK= fn= the= case= of= pt= kicolai= there= is= grass= growing= on= the= toé= of= the= ruinI= see= cigure= 4K=mroblems=like=these=can=have=a=major=iméact=on=the=amount=of=work=neededI=since=the=mesh=may=have=to=be=adjusted=manually=in=the=érogramK==

=

=

cigK 4=qhe=image=to=the=left=show=a=éart=of=the=laser=scanned=éoint=cloud=of=pt=kicolaiK =qhe=éoint=cloud=shows=uncertainties =where =grass =is =growing =on =the =toé =of =the =ruinK =qhe =image =to =the =right =shows =difficulties =in =generating=Pa=models=by=Paoeshaéer=when=there=are=unclear=éoint=cloudsK=qhe=Pa=model=needs=to=be=manually=== adjusted=

=PK ANAivpfp lc pq NfCliAf =qhe=church=ruin=of=pt=kicolai=has= three=naves=with=six=vaulted=bays= in=each=nave=and=ten=éillarsI= see=the=drawings=in=cigure=RK=qo=the=eastI=the=ruin=ends=in=a=fiveJsided=choirK=cigure=R=éresents=the=notation=used=for=the=vaultsI=arches=and=éillars=as=well=as=the=éarts=of=the=ruin=where=the=vaults=have=collaésedK=sault=jOI=jRI=jS=and=jT=are=missing=todayK=fn=élace=of=jO=there=is=a=wooden=roof=and=in=élace=of=jR=a=new=roof=of=wood=and=steel=has=been=mountedK===

=

cigK R=iayout=of=the=ruin=of=pt=kicolaiK=qhe=uééer=drawing=show=the=notations=used=to=denote=the=vaultsI=arches=and=éillarsK=fn=the=lower=drawing=the=red=markings=show=vaults=that=are=missing=today=

=

OROR=

qhe=vaults=of=pt=kicolai=have=a=high=rise=Edomical=shaéeFI=meaning=that=the=keystones=of=the=vaults=are=in=a=much=higher=éosition=than=the=keystones=of=the=transverse=and=wall=archesK=qhe=main=nave=vaults=are=higher=than=the=side=navesK==qhe=ruin=has=been=restored=several=times=over= the=centuriesI=and=both=the=various=reinforcements=and=the=collaésed=éarts=are=evidence=of=érior=structural=éroblemsK=qhe=causes=of=collaése=are=not= knownI=but=we=can=assume=that=a=number=of=factors=contributed=to=the=develoémentK=qhe=main=issueI=as=always=in=ruinsI=is=the=lack=of=an=outer=érotective=roofK=qodayI=the=toé=of=the=ruin=is=érotected=with=a=covering=made=of=roofing=felt=covered=with=turfI=but=it=érobably=stood=for=several=centuries=without=érotectionI=leading=to=erosion=and=growth=of=vegetationK=mart=of=the=ruin=has=also=been=used=as=a=quarryI=causing=the=buttresses=of=the=choir=to=lose=their=stabilizing=functionK==lur=analyses= of= the=vaulted=structure=have=been=concentrated=on= the=éart= around=the=oéening=where=vault=jR=and=jS=used=to=standK=qhe=missing=vaults=cause=an=imbalance=in=the=structureK=ft=is=also=this=éart =of =the =structure =that =was =éreviously =reinforced =with =several =tieJrodsK =fn =the =élace =of =vault =jRI =a=new=roof=structure=of=wood=and=steel=has=been=erectedK==qhe= area= around= éillar= CS= was= analysed= using= both= éarametric= thrustJline= analysis= and= cbjJbased=analysisK=qhe=loads=borne=by=éillar=CS=consist=of=the=vertical=load=from=the=dead=weight=of=the=masonry=and= the=horizontal= load= from= vaults= pR= and=pS= and= the= transverse= arch=aSCSK= qhe=horizontal= thrust=from=the=wall=arches=CRCS=and=CSCT=balance=each=otherK=millar=CS=was=the=only=éillar=around=vault=jR=that=had=no=tieJrod=until=recentlyK==

=4K obpriqp

4KNK marametric thrust-line analysis fn=cigure=S=a=éarametric= thrust= line=analysis=based=on= the=slicing= technique=of=vault=pR= is=éresentedK=qhe=results= indicate=the=range=of= the=level=of=éossible=horizontal= thrust=generated=by=the=vaultK=pince=éillar=CS=is=standing=free=towards=the=main=nave=it=is=likely=that=the=thrust=lines=of=vault=pR=and=pS=as=well=as=transverse=arch=aSCS=will=take=a=éassive=éosition=giving=the=least=éossible=horizontal=thrustK==fn=cigure=SI=a=éarametric=thrust=line=analysis=of=éillar=CS=is=shownK=qhe=result=indicates=that=the=thrust=line=can=be=contained=within=éillar=CS=but= it= is= clearly=outside=the=middle=third=of= the=éillar= and=the=margin=to=the=edge=of=the=éillar=is=smallK=qhis=imélies=that=there=is=a=risk=of=cracking=on=the=oééosite=side=of=the=éillarK=qhe=safety=of=the=structure=can=be=exéressed=as=a=geometrical=factor=of=safety=xNzK=qhe=geometrical=factor=of=safety=for=éillar=CSI=under=these=circumstances=is=NIOTK=qhe=value=has=to=be=above=N=for=the=structure=to=be=stableK=eeyman=xNz=writes=that=a=value=of=about=O=for=arches=and=bridges=for=worst=case=scenarios=seems=to=be=safe=and=éracticalK===

=

cigK S=marametric=thrust=line=analysis=based=on=the=slicing=method=of=vault=pRI=transverse=arch=aSCS==and=éillar=CS=

=4KOK Non-linear cbM-based analysis qhe=result=of=the=nonJlinear=cbj=analysis=of=éillar=CS=is=éresented=in=cigure=T=as=crack=éroéagation=and=coméression=Eminimal=érinciéal=stressesFK=qhe=location=of=cracks=is=in=accord=with=theory=and=it=is=élausible= that= there=are= cracks= at= those= locations= in= the= ruinI= although= they=are=not= visible= from= the=groundK=qhe=coméressive=flow=indicates=the=élacement=of=the=thrust=line=and=correséonds=to=the=results=of=the=éarametric=thrustJline=analysisK===

=

OROS=

=

cigK T=konJlinear=cbj=analysis=of=éillar=CS=in=pt=kicolaiK=qhe=image=to=the=left=show=location=of=cracks=and=the=image=to=the=right=show=the=flow=of=coméressive=forces=in=the=centre=of=éillar=CS=

=RK ClNCirpflNp =Assessment=and=understanding=of=structural=behaviour=are=decisive=factors= in=conservation=of=historic=buildingsK=qhe=aim=of=the=éresent=study=was=to=investigate=the=use=of=Pa=laser=scanning=in=suééorting=structural=evaluation=of=historic=masonry=structuresK==rsing= Pa= laser= scanningI= it= is= éossible= to= obtain= a= very= accurate= descriétion= of= the= geometry= of=comélex= masonry= structures= by= effective= meansK= Although= the= érocess= from= the= laser= scan= to=a=functional= coméutational= model= in= some= cases= requires= extensive= workI= this= study= shows= that= the=method= is= aéélicable= and= coméetitive= in= éractical= engineering= commissionsK= fn= coméarison= with=traditional=measuring=methodsI=Pa=laser=scanning=can=be=assumed=to=be=both=efficient=in=terms=of=time=and=a=great=deal=more=accurateI=éroviding=conditions=for=higher=quality=analysisK==qhe= éoint= cloud= generated= by= the= Pa= laser= scan= can= be= used= for= several= different= aéélicationsI=including=documentationI=creating=drawingsI=virtual=modelsI=virtual=acousticsI=etcK==qo=minimize=the=work= load= later= in=the=érocessI=close=communication=between=the=individuals=doing=the= scanning= and= the= individuals= érocessing= the= éoint= cloud= to= functional= coméutational= models= is=neededK= ft= is= essential= to= avoid= the= occurrence= of= shadows= leading= to= missing= éoints= and= other=discreéancies=in=order=to=avoid=a=greatly=increased=work=load=later=in=the=érocessK===qhe=accurate=descriétion=of=the=geometry=and=the=data=format=érovide=oééortunities=to=carry=out=both=éarametric=thrustJline=analysis=and=cbjJbased=analysis=of=historic=masonry=structuresK===AChNltibadbMbNqp =qhis=study=is=a=éart=of=the=éroject=fncreased rse of ouins qhrough pecured Masonry and Comfortable Climate= which= is= being= funded= by= the= hh= foundation= in= pweden= together= with= several= coméanies=éarticiéating=in=the=érojectK=qhe=pven=qyrén=qrust=at=qyréns=AB=has=funded=a=major=éart=of=the=study=éresented=in=this=éaéerK== obcbobNCbp xNz eeyman=gK=ENVVRF=qhe ptone pkeleton: ptructural bngineering of Masonry ptructuresK=CambridgeI=

Cambridge=rniversity=mressK= xOz Block= mK= EOMMVF= qhrust ketwork Analysis: bxploring qhree-dimensional bquilibriumK= aissK=

jassachusetts=fnstitute=of=qechnologyI=CambridgeI=jAK= xPz euerta=pK= EOMMUF=qhe=Analysis= of=jasonry= ArchitectureW= A=eistorical=AééroachK= Architectural

pcience oeview=solK=RNK4W=OVTJPOUK= x4z rngewitter=CKdK= ENVMNF=iehrbuch der gotischen konstruktionen: fs Auflage neu bearbaitet von

hK MohrmannK E4th=edFK=ieiézigI=ChrK=eermK=qauchnitzK=

=

OROT=

xRz tolfe=tKpK=ENVONF=draphical Analysis: A handbook on graphic staticK=kew=vorkI=jcdrawJeill=Book=ComéanyK

xSz Allen= bKI= walewski= tK= EOMNMF= corm and corces: designing efficientI expressive structuresK=eobokenI=tiley

xTz Block=mK= EOMMRF=bquilibrium pystems: ptudies in masonry structuresK=jp= thesisK= jassachusetts=fnstitute=of=qechnologyI=CambrigdeI=jAK=

xUz Block= mKI= Ciblac= qKI= lchsendorf= gKAK= EOMMTF= oealJtime= limit= analysis= of= vaulted= masonry=buildingsK=Computers and ptructures=U4=EOVJPMFI=NU4NJNUROK=

xVz CABof ff mlus EOMNOF=xComéuter=érogramz=CabrilogK=httéWLLwwwKcabriKcom=xOMNOJMOJOMzK= xNMz hurrer=hKbK=EOMMUF=qhe eistory of the qheory of ptructures: form arch analysis to computational

mechanicsK=BerlinI=brnst=C=pohnK xNNz BrigadeH=EOMNOF=xComéuter=érogramz=pcanscot=qechnologyI=httéWLLwwwKscanscotKcomLéroductsL=

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