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Sophia Ross
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1 Structural Analysis of Historical Constructions Jerzy Jasieńko (ed) 2012 DWE, Wrocław, Poland, ISSN , ISBN pbfpmfc CAmACfqv lc qebdefoiakafka qltbo fk MlabkAI fqaiv aiqommasoangelo N Iiancellottaoenato O Icocaccicrancesco P Ioomarocederica Q ABpqoACq qhispaperpresentsasimplifiedvulnerabilityassessmentmethçdfçrmasçnrytçwerstakingintç accçuntthesçiljstructureinteractiçnandmasçnrylimitanalysismethçd.amçdeltçdeterminethe planeçffracturethatdefinesthekinematicblçcksçfançverturningmechanismisprçpçsedibasedçn simpleequilibriumcçnditiçnsandisappliedtçthedhirlandinaqçwerinjçdena. AccçrdingtçtheftaliancçdesItçwersareclassifiedasamacrçelementcharacterizedbypeculiar cçllapsemechanisms.cçrtçwersaslightvariatiçninmechanismgeçmetryimpliesrelevantvariatiçns incçllapsemultipliervaluesxthisismainlyduetçtheimpçrtanceçfmassandheightinthese structures.eenceacçrrectdefinitiçnçfmechanismgeçmetryisveryimpçrtant. qheassessmentisbasedçnainsituinvestigatiçndefiningadetailedsçilprçfileandtherelevant mechanicalparametersiaimedatmçdellingthesçiljstructureinteractiçnduringbçthstaticlçngjtermlife andduringexpectedseismicevents.marameterswereusedtçrunafrequencyanalysisetçdetermine seismicdemandfiinwhichdifferentstiffnessvaluesfçrsçilrestraintwereusedicçrrespçndingtç differenthypçthesisabçutsçilbehaviçur. iimitanalysismethçdwasthenappliedtçidentifythecçllapsemechanismsgeçmetryiunderthe assumptiçnthatmasçnryisançjtensiçnmaterialihenceatthelimitçfçverturningiapartçfthe masçnrywillremainattachedtçthebaseandastressjfreediagçnalsurfaceçffracturewillfçrm. qheseanalysesallçwedfçrcçmparingçfthelimitlçadsrelatedtçthecçllapseçfthefractured masçnrywiththçserelatedtçtheçverturningçfthetçwerasawhçleithehçrizçntalrçtatiçnaxis beinglçcatedattheinterfacefçundatiçnjsubsçiliestablishingahierarchyçfmechanisms. heywordsw MedievaltowersICollaésemechanismsIpeismicassessment N. fkqolarcqflk N.N. fntroduction qhedhirlandinatçweristheancientbelltçwerçfthe`athedralçfjçdenaibçthfçrmpartçfthe rkbp`lsiteçfmiazzadrande.qhedhirlandinatçwerisasquarebasedesidewnm.umfstructurei UTmhighXthestructurehasahçllçwcrçsssectiçnIthickerçnthecçrnerbecauseçfthepresenceçf fçurmasçnrypillarsasshçwninfigurenxintheinnerpartiançpenstairrunsalçngthetçwerfrçmthe basetçthehigherpartwherethebelfryandthespirerççfcçmpletethestructure. qhetçwerischaracterizedbyatallandslenderspirebuiltçnitstçpandpreciçuslydecçrated EghirlandinaFIdefiningitsslenderarchitecturalappearance. qhemasçnrydiaphragmsbuiltinthetçwerarewthevaultçnthefirstflççritheflççrçftheqçrresani cellandthevaultabçvethebelfryethedeckinsteadisatimberstructuref.atgrçundlevelitwç masçnryarchescçnnectthetçwerwiththeadàacentcathedral. N cullmrçfessçrirniversityçfbçlçgnaiangelç.ditçmmasç]unibç.it O cullmrçfessçrimçlitecnicçdiqçrinçirenatç.lancellçtta]pçlitç.it P AssistantmrçfessçrIrniversitybJcampusIfrancescç.fçcacci]uniecampus.it Q mhairniversityfrasçfseniceifederica]rçmarç.it NQTQ

2 NQTR hn ho hp ht -zf x EMIMF i x y i Section 0 inok4m pectionnizmkmmm Section 1 ienmktm iiskumm ipnksmm ie ie ii ii ip ip x y pectionmiz-rksrm z Section 2 ienmktm iitktmm ie ie ii ii x y pectionoizpukmmm x y ie ie ii ii Section 3 iepkumm iioktmm pectionpizrnkpmm x y ie ie ii ii Section 4 ieokvom iiokmtm pection4izsmkmmm x y ie Section 5 ienkuvm iinkm4m ie ii ii pectionrizsvkrmm ka zf-rksrm hnpum hornkpm hpsmkmm htuskum cig. Ndeçmetricalmçdelçfthetçwer qhetçwer sverticalityhasbeencçrrectedseveraltimesduringdifferentphasesçfcçnstructiçnxitisin factpçssibletççbserveialçngthefaçadesisegmentsçfvariableleaningassignsçfcçrrectiçnsfçr settlementprçblems.qhetçwertçdaypresentsavisibleleaningiinparticularçnthepjtcçrnerwhere themasçnryarchescçnnectthetçwertçthecathedral. qhecçnstructiçnçfatçwerisaneventçfgreatstructuraleffçrtianditsleaninginfacthidessçme prçblemsrelatedtçtheinteractiçnwiththefçundatiçnsçilithataresçmetimesnçtsçevidentatfirst glance.ft simpçrtanttçrememberthatduringthefirststageçfcçnstructiçnthetçwercçuldnçthave beensçfarfrçmabearingcapacitycçllapseiduetçalackçfsçilstrengthiandcçuldhavesafely survivedthankstçsçmedelayçrinterruptiçninthebuildingprçcess.qherefçreiitisçfparamçunt interesttçgetafulldescriptiçnçfthetçwer shistçryandtçhighlightthecçnstructiçnstagesandrest periçdsthatallçwedthefçundatiçnsçiltçimprçveitsstrengthiduringthecçnsçlidatiçnprçcessunder cçnstantexternallçadiandthatallçwedthetçwertçbesuccessfullyfinished.qhearchaeçlçgical surveyxnzidentifiesfçurdifferentcçnstructiçnphasesçfthetçweriacçmpletechrçnçlçgyiincluding alltheeventsdeterminingstructuraleffectsefiresiearthquakes...fcanbefçundinxoz. AtthesametimeIbyinvestigatingthetçwer sreactiçnifperturbedbyanyexternalactiçnthispaper dealswiththestabilityçfequilibriumithedangerçfaleaninginstabilityasrelatedtçthelackçf stiffnessçfthesçil.jçvingfrçmtheseargumentsitheçbàectiveçfthispaperistçprçvideapictureçf thesubsçilcçnditiçnsenamelysçilprçfileigrçundwatercçnditiçnsandrelevantmechanical parametersfthathaveamaàçrrçleindefiningtheseismicbehaviçuriincludingsçiljstructure interactiçniandtçpresentthemçstrelevantpçtentialcçllapsemechanismsarisingfrçmexpected seismicactiçns. O. dblqbcekfcai ApmbCqp O.N. poil profile pincenvumthetçwncçuncilçfjçdenahasprçmçtedstudiesandinvestigatiçnsrelatedtçthe subsidenceçfthejçdenaalluvialplainxpjtz.fnadditiçntçthesestudiesiitisrelevanttççutlinethat thejçdenaalluvialplainischaracterizedbyauniqueabundanceçfarchaeçlçgicalsitesiandthatthe relatedinterestinthisprçmçtedresearchçnthenuaternarysedimentatiçnçfthejçdenaplainxujnmz. cinallyiinçrdertçdefineadetailedsçilprçfileandtherelevantmechanicalparametersaimedat investigatingthebehaviçurçfthetçwerinrelatiçntçsubsçilcçnditiçnsiarathercçmprehensivesite investigatiçnwasplannedfçrpeptemberommtandaecemberommuasdescribedbyxnnz. ByreferringtçcigureOIthesçilprçfiledçwntçtheinvestigateddepthçfUMmiscçmpçsedçfafirst hçrizçnçfmediumtçhighplasticityinçrganicclaysiwithanabundanceçflaminaeçfsandsandpeati çnlymillimetresthick.qheupperpçrtiçnçfthishçrizçnecigureofiwhçsethicknessrangesfrçmrtç

3 TmetersIisknçwnasjçdenarnitandislinkedtçtheflççdingeventsEçfpçstJoçmanageFprçduced byminçrstreamseq.cçssaj`ercaf. qhesubsequentunderlayinghçrizçnsirangingindepthfrçmootçrqmirepresenttheresultçf acçmpletetransgressivejregressivecyclewthefinejgrainedsedimentsibelçngingtçthehçrizçnknçwn askiviançrnitiweredepçsitedduringthepenultimateinterglacialcycleiandthesuperimpçsed cçarsejgrainedmaterialsibelçngingtçthesignçlarnitiarelinkedtçtranspçrtactivitiesçfthe pecchiaoiver. AsecçndhçrizçnçfcçarseJgrainedmaterialsisencçunteredatdepthsrangingfrçmRQtçSPmIand thereafterafinejgrainedmaterialshçrizçnisfçunddçwntçadepthçftumihereagaincharacterized byadiffusepresenceçflaminaeçfsand. O.O. fnvestigation on seismic parameters peismicactiçnstçbecçnsideredataspecificsiteareusuallydescribedintermsçfpeakgrçund acceleratiçna g IbeingassçciatedtçarigidsçilfçrmatiçnandtçfreeJfieldcçnditiçnsIandtçtheelastic respçnsespectrump e EqF.qhereisalsçcçnsiderableevidenceIbçththeçreticalandexperimentalIthat earthquakewavesareaffectedbysçilcçnditiçnandtçpçgraphyisçthatseismicwavesmaybe mçdifiedebçthinamplitudeandfrequencycçntentfastheypassfrçmtherigidbasementtçthesçil surface.qhisphençmençniknçwnassçilamplificatiçnirequiresspecificsitestudiesiçrmaybebased çnlumpedparameters.lneçftheseparametersistheshearwavesvelçcitys spm Icharacterizingthe upperpmmthickhçrizçn. cçrthisreasçnthegeçtechnicalactivitywascçmplementedwiththeexecutiçnçfcrçssjhçletests EfigurePF.fnthisrespectIitmustberememberedthatshallçwseismicexplçratiçntestsçfsçils representanimpçrtantclassçffieldtestsbecauseçftheirnçnjinvasivecharacter.qhisallçwsfçr preservatiçnçftheinitialstructureçfsçildepçsitsaswellastheinfluenceçfalldiagenetic phençmenacçntributingtçastiffermechanicalrespçnse.qherefçreithecrçssjhçletestrepresentsçne çfthemçstreliablemethçdsçfdeterminingtheshearmçdulusatsmallstrainamplitude.basedçnthe resultsreferredtçincigurepiarelevantshearwavevelçcitys sipm equaltçnvomlswasdeducedi allçwingthesubsçiltçbeclassifiedintçclass`iaccçrdingtçxnoinpz. cig. OaetailsçfsçilprçfileandfçundatiçnçfdhirlandinaqçwerxNNz NQTS

4 cig. P`rçssJhçletests O.P. poil-structure interaction peismicanalysisisstrçnglydependentçnthesçilrespçnseiandinçrdertçmçdelitwerelyçnthesçj calledmacrçjelementapprçachxnqjomz.qhisapprçachisaimedatrepresentingsçilrespçnseinterms çfgeneralizedfçrcesandrelateddisplacementcçmpçnentsii.e.afçrmulatiçnsuitablefçrsçilj structureinteractiçnimçvingfrçmadvancedhardeningplasticityiinçrdertçaccçuntfçrthe irreversibleandnçnjlinearsçilbehaviçur.asacçnsequenceçfsuchnçnjlinearityiinthepresent analysistwçassumptiçnsregardingtherçtatiçnalstiffnesswereused. EaFjçvingfrçmtheshearwavevelçcityequaltçv s NORmLsIasmallJstrainshearmçdulushasbeen deducedw d M Zrv O s ZNUMM NOR O ZOUjma ENF qhisvaluereferstçfreefieldcçnditiçnsisçthatithasbeencçrrectedinçrdertçaccçuntfçrthestress levelinducedbythetçwered M ZQQjmaF.cinallyItakingintçaccçuntthestrainlevelItheçperatiçnal valuewasestimatedtçbeequaltçd eél ZT.OSjmaIthecçrrespçndingrçtatiçnalstiffnessbeing P db h P.S NTNR.VS d t m N-u NOQRTUU a EOF whereobzno.qmmisthefçundatiçnwidthandnisthemçissçnratiç. qhisvaluewasfurtherincreasedinçrdertçaccçuntfçrthefçundatiçndepthedlbzr.srls.ozm.vnx dlaznfxonzitherelatedcçefficientbeingw M.O ïì d é d æ a ö b ùïü f a ín + N.OS ên + ç úý P.NV EPF ïî b êë b è d ø l úû ïþ wherew ObandOlarethefçundatiçnsidesX aisthefçundingdepthx NQTT

5 aisthefractiçnçfathatcçntributestçthecçnstraintehereassumedequaltçaf. ByusingthiscçefficientacçrrectedstiffnesswasçbtainedequaltçW P P.Sdb S h a P.NV P.VT NM t m N-u EQF thatibecauseçfthecçnsideredstrainleveliisapprçpriatefçrstrçngseismicmçtiçn. EbFfnadditiçnIanupperbçundvaluewasestimatedbyusingtheelasticshearmçdulusImçvingfrçm theassumptiçnthatsçilbehaviçurcçuldstillbedçminatedbyanelasticrespçnseduetçcreep hardeningw P P.Sdb S h a P.NV OQ NM t m N-u ERF qhisvalueisapprçpriatefçrlçwintensityseismicevents. P. pbfpmfc abmaka P.N. katural frequencies of the tower oeferringtçfigureqinwhichthetçweriscçnsideredtçbemadeçfelasticmaterialandsçiljstructure interactiçnismçdelledasanequivalentelasticspringwithrçtatiçnalstiffnessh a it sclearthatthe elasticprçpertiesçfthesystememasçnryvçungmçdulusandspringstiffnessh a FIdeterminingits naturalfrequenciesimçdifytheseismicactiçnintermsçfspectralacceleratiçn. AccçrdingtçlimitanalysisIdescribedinthefçllçwingparagraphsIthetçwerwillbeassumedtçbe arigidelementfixedçnelasticrestraintxneverthelessitçassessthereliabilityçftherigidity assumptiçninaturalfrequencieswerefirstdeterminedfçrdifferentvaluesçfmasçnryvçungmçdulus andelasticsçilrestraint. katuralfrequenciesçfthetçwerweredeterminedbycbjanalysisçnanelasticmçdelmadeçfbeam elementsebasedçngeçmetryasdescribedinfigurenf. deçtechnicalanalysisgivestwçdifferentstiffnessvaluesfçrtheelasticspringicçrrespçndingtç differentassumptiçnsçnsçilbehaviçurxasimpleparametricanalysiswasperfçrmedtçevaluatethe effectçfthetwçstiffnessvaluesçnseismicactiçnwhilealsçcçnsideringtheinfluenceçfthemasçnry vçungmçdulus.qhisparameterwasvariedirangingbetweenommmjmaandqmmmjmaxthetçwer s naturalfrequencieswerethencalculatedfçrfivedifferentstiffnessvaluesebetweenm.rnm U kkmand O.RNM U kkmfçfthespringrepresentingthesçilrestraintxooz. qheresultsçftheanalysisareshçwninfigurerfçrfmçde. E:MasonryYoungmodulus:Emin E Emax h a:soilrestraintstiffness:h amin ha h amax EEmin hahamin qqee minih aminfq max pdpdeqmaxfpdmin EEmax hahamax qqee maxih amaxfq min pdpdeqminfpdmax E ppectralaccelerationipdeqf ACCEiEoAqflk pmecqorm h a pdmaxpdeqminf pdminpdeqmaxf qmin qmax meriodiq cig. 4bxpectedspectralacceleratiçndependingçn elasticprçpertiesçfthesystem cig. Rkaturalfrequenciesçffmçdedependingçn elasticprçpertiesçfthesystem oesultscçrrespçndingtçtherigidbehaviçurassumptiçnçfmasçnryareinsteadcalculatedasw B 7 ESF NQTU

6 f t beingthemassmçmentçfinertiaabçutahçrizçntalaxisthrçughthecentrçidçfthebasecrçss sectiçnandhthesçiljstructurerestraintstiffness. eencethecçrrespçndingperiçdandfrequenciesresultinw q MImax ZPIQPTsXf MImin ZMIOVezfçrh min q MImin ZN.PVUsXf MImax ZMITNezfçrh max qhesevaluesaresimilartçthçseçbtainedwhencçnsideringthedefçrmatiçnçfthetçweriespecially inthecaseçfthelçwervalueçfh a P.O. ppectral acceleration qheinfluenceçfvçungmçdulusvaluesdependsçnthevalueassumedfçrsçilstiffnessibeing negligibleinthecaseçflçwervaluesçfhandmçreprçnçuncedinthecaseçfhighersçilstiffness. ppectralacceleratiçnvaluesçbtainedfçrhypçthesisafandbfeseepreviçusparagraphfassuming arigidbehaviçurçfthemasçnrytçweriareillustratedçnthedesignspectrumxnozinfigures. ppectralaccelerationegf MKS MKR MK4 MKP MKO MKN elasticip eeqfisoilc designip deqfiqokmisoilc q MImin p deq MIminFMKMVRg q MImax p deq MImaxFMKMORg M MKR NKM NKR OKM OKR PKM PKR 4KM meriodqesf cig. SppectralacceleratiçnscçrrespçndingtçassumptiçnsaFandbFçnsçilJstructureinteractiçn 4. pbfpmfc CAmACfqv peismiccapacityçfthetçwerwascalculatedaccçrdingtçftaliancçdeprescriptiçnxnozfçllçwingthe cçllapsemechanismsapprçach.jechanismsinvçlvingan çpening çfthestructurealçngthe existingverticalcrackswerençtincludedbecauseinçrdertçguaranteeaunitarybehaviçurçfthe tçwerapreventiveinterventiçnwithtiejrçdshçldingtçgetherçppçsitewallswasmade. qhecçllapsemechanismsareidentifiedbythegeçmetryçftheçverturningblçckandbythepçsitiçn çfhinges.eenceiinthisanalysisthefçllçwingcçnditiçnseasinaplaneprçblemfwerecçnsideredw çverturningblçckdefinedbyadiagçnalfracturesurfacei çverturningblçckdefinedbyahçrizçntalfracturesurfacei rçtatiçnalhingeattheedgeçfcrçsssectiçneassumptiçnçfinfinitivecçmpressivestrengthçfthe materialfi rçtatiçnalhingeatacalculateddistancefrçmthesectiçnedgeeassumptiçnçffinitecçmpressive strengthçfthematerialf. oesultswerethencçmparedandareliabilityassessmentwasperfçrmed.qhesimplifiedgeçmetrical mçdelcçnsideredisshçwninfigureniwherethemaindiscçntinuitiesçfthecrçsssectiçnare includedxwindçwsandçpeningsareignçredandahçllçwbasecrçssjsectiçnisassumed.qhe fçundatiçnareaisassumedtçbeafullsquaredsectiçnçfno.qmmwidth.fnfactibesidesacçllapse mechanismfçrançverturningatbaselevelemeaningatthelevelçfthegrçundiatheightzzmmin figurenofiacçnservativeevaluatiçnfçrtheçverturningatfçundatiçnlevelemeaningatfçundatiçn sçillevelizzjrmfwasalsçperfçrmeditakingintçaccçuntthesçilprçperties. thencçnsideringshçrtjtermperturbatiçnseearthquakesçrwindeffectsfifailuremechanismsare explçredwithreferencetçundrainedsçilcçnditiçns.cçrthisreasçnithebearingcapacityhasbeen evaluatedintermsçftçtalstressandassumedaswq lim M.TNQjmaxNNz. jasçnrycçmpressivestrengthicçnsideringtheresultsçfsçnictestandtheheterçgeneityçfcalculated velçcitiesiisassumedaspjma. ieaningçfthetçwerendegreefhasbeentakenintçaccçuntcçnsideringtheeffectivepçsitiçnçfthe centreçfmass. NQTV

4.N. lverturning block geometry fnthecaseçfatçwerstructureitheçverturningçftheupperpartçnthebaseusuallyrepresentsthe weakestmechanism.

$Asimplifiedgeçmetrywithastraighthçrizçntalfracturesurfaceisincçnsistentwiththeevidenceçf realcçllapsemechanismsiwhichhaveçccurredduringpastearthquakesefiguretf.$

7 4.N. lverturning block geometry fnthecaseçfatçwerstructureitheçverturningçftheupperpartçnthebaseusuallyrepresentsthe weakestmechanism. qhemçstunfavçurablehingepçsitiçncanbeeasilydeterminedxinsteadtheidentificatiçnçfthe çverturningblçckgeçmetryisamçrecçmplextask. Asimplifiedgeçmetrywithastraighthçrizçntalfracturesurfaceisincçnsistentwiththeevidenceçf realcçllapsemechanismsiwhichhaveçccurredduringpastearthquakesefiguretf. qhepresenceçfadiagçnalfracturesurfaceisàustifiedbythefactthatmasçnryisaunilateralmaterial abletçresisthighcçmpressivestressesbutwithfeebletensilestrength.asacçnsequenceatthelimit çfçverturningiapartçfthemasçnrywillremainattachedtçthebaseandastressjfreediagçnal surfaceçffracturewillfçrmxntz. eenceiamethçdabletçincludethisprçpertyieveninasimplifiedassessmentisuchasthecçllapse mechanismsanalysisiprçvesveryimpçrtant. fnthepresentpaperthefracturelineisidentifiedbythepçsitiçnçftheneutralaxesçfthecrçss sectiçns.accçrdingtçsimpleelastictheçryiwhenthelineçfthrustfallsçutsidethesectiçnkern astressjfreezçnewilldevelçpefigureuf. cig. T Belltçwerçfpanjartinç oesiutta ErdineFdamagedbycriuliearthquakeinNVTS cig. Umçsitiçnçflineçfthrustrespecttçsectiçnkernand fracturedevelçping fnthecaseçfrectangularcrçsssectiçnsthedepthiçftheneutralaxisandthedepthrçfthethrust linesatisfytherelatiçnrblp.fngeneralthelimitdistancevaluermustbecalculatedinfunctiçnçf Bfçreachtçwercrçsssectiçn. AnexampleçfthisprçcedureisgiveninxOPzwherethemethçdisappliedtçtheanalysisçf buttresses. `çnsideringamasçnrytçwerandsimplifyingtheprçblemintçaplaneprçblemiwithreferencetç figurenniadifferentialequatiçnissearchedwhçsesçlutiçnisthecurveçffracturezzelfizbeing averticalreferenceaxiswiththeçriginatthebase. Atçwerçfheighth t IiscçnsideredXçnthetçwerthedeadlçadandahçrizçntallçadwithdistributiçn prçpçrtiçnaltçthemassareapplied.qhehçrizçntallçadiscçnsideredhighençughtçprçducethe crçsssectiçnpartializatiçnbetweenzzmandzh fé.qhefçllçwingassumptiçnsaremadew nullmasçnrytensilestrengthençjtensiçnmaterialfi elasticbehaviçurçfmasçnryincçmpressiçni çnlythemasçnryincçmpressiçnisinvçlvedinthecçllapsemechanismi crçssjsectiçniscçnstantwherethefracturedevelçps. eenceithefracturewillfçrmineachcrçssjsectiçnwhenthelineçfthrustreachestheedgeçfthe sectiçnkern. qhedistanceçfsectiçnkernfrçmtheexternaledgeiincaseçfsquaredcrçssjsectiçnçfsidei e IisW ( ) B ETF fncaseçfhçllçwsquaredcrçssjsectiçnsthefunctiçnmustbepreliminarilycalculatedasw ( ) ( ) ( ) EUF ( ) NQUM

8 wherew ( ) B ( ) ( ) relfbeingtheradiusçfgyratiçnçftheuncrackedsectiçnii g ElFisthedistanceçfthesectiçncentrçidtç thecçmpressededgexaelfandgelfarerespectivelytheareaçfthecçmpressedpartçfthecrçsssectiçn anditsmçmentçfinertiaibeingi i andi e definedinfigurenn. aistancefrçmtheedgeinçrmalizedwithrespecttçtheuncrackedlengthçfthesectiçnisw i(q)b Z(q) EVF Q j -q AnexamplesisshçwninfigureVfçrtwçdifferentvaluesçfratiçi e Li i delf M.PR ie M.P iizm.rie thdt M.OR M.O M.NR M iizm.uie cig. 9saluesçfequatiçndElFfçrdifferentvalues çfratiçi e Li i l ie hfé z l iejl ehde z l dt de t m dz r e cig. NM blementarysliceçfthetçwerinthefractured zçne qheequatiçnçfthefractureisdeterminedbasedçntheequilibriumcçnditiçnsçfanelementaryslice çfthetçwerinthefracturedzçneefigurenmf.ftisidentifiedbythedifferentialequatiçnxoqz (, ( )) ( ( )) ( ) ( ) ( ) (, ) theretelizelfft M Eh fé FHt c ElIzElFFistheweightçfthetçwerabçvetheabscissazIg m isthemasçnry density. ENMF cig. NN deçmetricalmçdelçfthetçwer NQUN cig. NO cractureplçtunderassumptiçnçfinfinite masçnrycçmpressivestrength

9 eenceeelizfcanbedefinedasw (, ( ))B (, ( )) ` (, ( )) ( ) ( )b ENNF (, ( )) therei dt ElIzElFFandz dt ElIzElFFarethecççrdinatesçftheçverturningblçckcentrçid. qhefracturelineisthesçlutiçnçfdifferentialequatiçnenvfwithbçundarycçnditiçnzemfh fé I.qhis equatiçnwassçlvedviaanumericallabsolverthatusestheoungejhuttamethçdinthefçurthçrder incrementapprçximatiçniçbtainingafamilyçffracturecurveszelfvaryingwithparameterh fé.fn afirstsçlutiçnstepithealgçrithmperfçrmsadçjlççpçntheh fé parameteruntilthefracturecurve reachestheexternaledgeçfthesectiçnthatcçrrespçndstçanassumptiçnçfinfinitemasçnry cçmpressivestrengthefigurenof.fnasecçndstepthecurveçffracturehasbeendeterminedby impçsingtheattainmentçftheultimateresistingmçmentatthebasesectiçncçnsideringafinitevalue çfmasçnrycçmpressivestrengthiwhichdefinesthefinalh fé intheiterativescheme. eavingçncedeterminedtheh fé andthecçrrespçndingfracturelineithecçllapsemultiplierlcanbe çbtainedastheratiçbetweenthehçrizçntalfçrceandthedeadlçadçftheçverturningpart. 4.O. Cracked tower overturning qhefracturelineisdefinedbyequatiçnenmfanditwasevaluatedincasesçfw rçtatiçnatbaselevelandmasçnryinfinitecçmpressivestrengthi rçtatiçnatbaselevelandmasçnryfinitecçmpressivestrengthi rçtatiçnatsçilfçundatiçnlevelandsçilfinitecçmpressivestrength. QKOKNK Baselevel fnthefirstcaseithefracturelinedefinedbyenmfiinterceptstheedgeçfthebasecrçsssectiçnxthe cçrrespçndinghçrizçntallçadcçllapsemultiplieriswlzm.nqp. fnthesecçndcaseithemasçnrycçmpressivestrengthisassumedf m ZPjmaIthehçrizçntallçad cçllapsemultiplierislzm.not QKOKOK coundationlevel bvaluatingtheçverturningatfçundatiçnlevelejrmfrçmthebaselevelfthebearingcapacityçfsçil mustbetakenintçaccçunticçnsideringthatattheçverturninglimitcçnditiçnthençrmalstressçn fçundatiçnlevelisunifçrmandequaltçthestrengthçfthesçiljfçundatiçnsystem. z h t hp ho lmn ElgNIzgNF lmn ElgNIzgNF lmn hn mn mn m N EMIMF l -zf ElNIzNF El NIz NF q lim q lm u g y d mn l mn xn ie cig. NPdeçmetricalmçdelfçrlimitanalysisWçverturningmechanismatfçundatiçnlevel NQUO

10 bquilibriumbetweentheselfjweightçfthetçwerandsçilreactiçnresultantgivesthewidthçfthe cçmpressedareaefigurenpfw B B >-< t tçt ZURRQSkkbeingthetçwerweightIi e ZNO.Qmthesideçfthesquaredfçundatiçnareaand q lim ZM.TNQjmathesçilstrength. qhefracturelineinterceptingtheedgeçfthecçmpressiçnpartatfçundatiçnlevelwascalculatedand thecçrrespçndingcçllapsemultiplierresultslzm.moo 4.P. rncracked tower overturning fnçrdertçevaluatetheinfluenceçfcçnsideringaninclinedfracturelineithepreviçusanalyseswere alsçperfçrmedcçnsideringahçrizçntallineçffractureatbçthbaselevelefçrmasçnryinfinitelfinite cçmpressivestrengthfandfçundatiçnlevel. qheseresultsintermsçflandthçsepresentedinthepreviçusparagrapharecçmparedinfigurenq uncracked fractured ENOF acceleration [g] h amax lmknvs amkn4rg lmknrp amknnpg lmkmpu lmkn4p lmknot lmkmoo amkmoug amknmsg amkmv4g amkmnsg iesei iesei iesei 0 cig. N4`çllapsemultiplierandacceleratiçnvalues cig. NR`çmparisçnbetweenseismicdemandand seismiccapacityfçrdifferentcçnfiguratiçnsçfglçbal çverturning 4.4. peismic assesment AccçrdingtçxNOztçahçrizçntallçadmultiplieracçrrespçndingspectralacceleratiçnactivatingthe mechanismcanbeassçciatedwseismiccapacityfçrtheuncrackedandfracturedtçwerwasthan cçmparedtçtheseismicdemandidefinedinparagraphp.oefiguresf.fnfigurenrthecçllapse multiplierscalculatedandthecçrrespçndingacceleratiçnsarecçmparedfçrdifferentmechanisms. lverturningatfçundatiçnlevelisthemechanismwiththelçwestcçllapsemultiplieriduetçthesmall dimensiçnsçffçundatiçnareaandtheslightincreaseçftheglçbalcentrçidheightxinthiscasealmçst thewhçlefçundatiçnareaisneededtçrespectthecçnditiçnçnsçilbearingcapacityihencethelineçf fractureseparatesàustasmallpartçfthemasçnryxneverthelessarelevantinfluenceçnmultiplier valuescanbeçbserved. cçrtheçthercasesiwherethecçnditiçnçnmaterialsstrengthdeterminesafracturethatprçpagates higherinthetçweritheeffectçfcçnsideringtheinclinedlineçffracturereducestheresistanceçfthe tçwertççverturningbypsbeneglectingmasçnrycçmpressivestrengthfandbyombecçnsidering masçnrycçmpressivestrengthfiindicatingthatfçrasafesimplifiedassessmentthesecçnditiçnsmust beevaluated. R. ClkCirpflkp qhispaperwasaimedatpresentingasimplifiedbuteffectivevulnerabilityassessmentfçrmasçnry tçwers.qwçmaàçraspectswerecçnsideredwtheinfluenceçfsçiljstructureinteractiçnandthe influenceçfthemasçnrytçwerasançjtensiçnmaterial. fnparticularitheinfluenceçfsçilnçnjlinearbehaviçurwastakenintçaccçuntibyselectinganupper andalçwervalueçfsçilstiffnessirepresentativeçfsmallstrainandlargestrainrespçnseiapprçpriate fçrlçwandhighintensityseismicevents. qheçbtainedresultssuppçrtthecçnclusiçnthatthestructurejsçilinteractiçnstrçnglyaffectsthe seismicdemandidependingçnthesçilstiffnessiaswellasçnthesystemcapacityirelatedtçsçil strength. NQUP BApE BApE clrkaaqflk h amin

11 obcbobkcbp xnz aieghi`.eommvfcçntiestudiperlastçriadelladhirlandinaiiniaqorredhirlandinakrn érogettoéerlaconservazioneisçl.niqujssipçssellaed.einitalianf. xoz iabatea.eommvfflcçntributçdell archeçlçgiaallaletturadiunmçnumentçiinia qorre dhirlandinakrnérogettoéerlaconservazioneisçl.nissjtuipçssellaedeinitalianf. xpz oussçm.envurfi abbassamentçdelsuçlçnellazçnadijçdenaenvrmjnvuof.qecnicapanitariai uufffiovpjpeinitalianf. xqz `ancellia.envusfaspettigeçtecnicidellasubsidenza.ambientewmrçteziçneeoisanamentç.attio CorsodiAggiornamentoéertecnicidiigieneambientale.jçdena.bd.mitagçraIBçlçgnaEinitalianF. xrz `ancellia.imellegrinij.envuqfmrçblemigeçlçgiciegeçtecnicicçnnessialterritçriçdellacittà dijçdenakattio CongrKkazKAppKfKoKCKCl.IcerraraIRPJSQEinitalianF. xsz mellegrinij.iwavattia.envumfflsistemaacquiferçsçtterraneçfraifiumibnzaimanarçemçw alimentaziçnedellefaldeescambitrafaldeicçrrelaziçniidrçchimiche.nuadkfstkoickpulle AcqueI`koIRNIOMRJONTEinitalianF. xtz oighim.s.envumfoilevamentigeçtecnicinelsçttçsuçlçdelmalazzçkaziçnaledijçdena.atti ufsconvkkazkdeotecnicaicirenzeiniortjosseinitalianf. xuz `remaschij.idasperid.envuvfi alluviçnealtçmediçevaledijutinaejçdenafinrappçrtç allevariaziçniambientaliçlçceniche.memkpockdeolkft.iqointvjnvmeinitalianf. xvz cazzinim.idasperid.envvsfflsçttçsuçlçdellacittàdijçdena.accad.kaz.pci.iett.artidi jçdenaijiscellaneadeçlçgicainriqnjrqeinitalianf. xnmziuglip.ijarchettiaçrip.icçntanaa.imaninic.eommqf`çmpçsiziçnedeisedimentisabbiçsi nellapianuramçdenese.flnuaternariçiftaliangournalofnuaternarypciencesintiptvjpuv EinitalianF. xnnziancellçttao.eommvfaspettigeçtecnicinellacçnservaziçnedellaqçrredhirlandina.fniaqorre dhirlandinakrnérogettoéerlaconservazione.sçl.nipagg.ntujnvqipçssellaed.einitalianf. xnozajnqgennaiçommu.kormeqecnicheéerlecostruzioni.`ircçlareofebbraiçommvin.snt. fstruziçniperldapplicaziçnedellekuçvençrmetecnicheperlecçstruziçnidicuialdecretç ministerialenqgennaiçommukeinitalianf xnpzrkfbknvvujnwommriburçcçdeuiaesignçfstructuresfçrearthquakeresistance martnw deneralrulesiseismicactiçnsandrulesfçrbuildings. xnqzaesideria.isiggiani`.envvqfpçmeremarksçnthestabilityçftçwers.pyméklnaeveloéments indeotechnicalbngineeringibangkçk. xnrzeamblyb.`.envurfpçilbucklingandtheleaninginstabilityçftallstructures.qheptructural bngineerispipittjur. xnszjarchij.ibutterfieldo.idçttardid.iiancellçttao.eomnnfptabilityandstrengthanalysis çfleaningtçwers.déotechniqueisninoinmsvjnmtv. xntzeeymang.envvofieaningtçwers.meccanicaiotinrpjnrv. xnuziancellçttao.envvpfqhestabilityçfarigidcçlumnwithnçnlinearrestraint.déotechniqueippi OIPPNJPPO. xnvzjarchij.eommufptabilityandstrengthanalysisçfleaningtçwers.mhathesisirniversitàdi marma. xomzkçvao.ijçntrasiçi.envvrfrn analisidistabilitàdelcampaniledimisa.oivistaftalianadi deotecnicaioiupjvpeinitalianf. xonzdazetasd.envvnfcçundatiçnvibratiçns.`h.nrincoundationbngineeringeandbooki san kçstrandoeinhçldik.v. xoozaiqçmmasça.iiancellçttao.icçcaccic.ioçmarçc.eomnmfrnçstudiçsullastabilitàdella qçrredhirlandina.fniaqorredhirlandinakptoriaerestauro.sçl.oipagg.omqjontipçssella ed.einitalianf. xopzlchsendçrfg.a.ieernandçg.f.ieuertap.eommqf`çllapseçfmasçnrybuttresses.gournalof architecturalengineeringivçl.nmin.p. xoqzoçmarçc.ieomnnfastudyçnseismicbehaviçurçfmasçnrytçwers.dhirlandinatçwerin jçdena.mh.athesisirniversityçfqrentç. NQUQ

MECHANICAi BEHAVIOUR OF MASONRY PANEiS UNDER IN-PiANE ioads

Structural Analysis of Historical Constructions Jerzy Jasieńko (ed) 2012 DWE, Wrocław, Poland, ISSN 0860-2395, ISBN 978-83-7125-216-7 MECHANICAi BEHAVIOUR OF MASONRY PANEiS UNDER IN-PiANE ioads Barsotti