OUT-OF-PiANE FAIiURE MECHANISM OF MASONRY BUIiDING CORNERS
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- Clarence Arnold
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1 Structural Analysis of Historical Constructions Jerzy Jasieńko (ed) 2012 DWE, Wrocław, oland, ISSN , ISBN UT-F-iANE FAIiURE MECHANISM F MASNRY BUIiDING CRNERS Mariateresa duadagnuolo N I Alfonso aonadio I diuseppe caella ABSTRACT fnthelastyearsahighercarefulnessisfocusedonthesafetyofoldtowncentresthreatenedbyseismic events.qheirbuildingsarejoinedbytheuseofmasonryandsimilarstructuralfeaturesialthough differentintypologyandbuildingtechnièues.qhebuildingsusuallyarecharacterizedbyconnected blocksthatmakeupcurtainwallstwoorthreestoreyshighandsometimeshundredmeterslong.qhe extensiveandwide-irregularplanimetricgrowthithedifferentbehaviourofin-planeandout-of-plane loadedwallsitheineffectivenessofwallconnectionandwall-floorconnectionandthepresenceof thrustingstructuresfreèuentlycausecollapsemechanismsinvolvingwallportionsmoreorlesslarge. qheseismicanalysisoftheseportionscanbeperformedusingintuitivecomputingmodelsclosetothe originaldesigncriteriabymeansofkinematicprocedures.qhispaperisaimedatevaluatingthe mechanisminvolvingmasonrybuildingcornersthatcanoccurattheintersectionofwellconnected wallssubjectedtoout-of-planeseismicforces.iinearkinematicanalysesareperformedconsidering thethree-dimensionalfeatureofthemechanism.allthemainresistancecontributionsaretakeninto accountaswellasthekeyparametersareconsideredandvariedwithinawiderangeofpossible values.qheinfluenceofconstraintsprovidedbytheroofisalsostudied. heywords: lld town centresi lutjofjplane responsei hinematic analysis NK INTRDUCTIN mreventionandmitigationofseismicdisasteratlandscapescalereèuirestheseismicriskassessmentof existingbuildingsandprotectedculturalheritage.qerritorialscaleestimatescanhelpindeveloping databasesofbuildingsandarchitectonicgoodsiwhereeachdatasetcontainsinformationonbuilding constructioniactualstateiseismicvulnerabilityandriskiprecautionarymeasurestoberealized.apart fromthelevelofbuildingknowledgeitheevaluationofseismicactionandsafetyindexattheultimate limitstatearemandatoryinordertooutlinecriticalsituationsandassignprioritytofuture interventions. fnthelastfewyearsahigherconsiderationisfocusingontheseismicsafetyandconservationof historiccitycentresthreatenedbyearthèuakesiwheresuchmethodologyisfullyaccomplished.crom astructuralpointofviewibuildingsofseveralhistoricurbancentresiarejoinedbytheuseofmasonry andstructuralfeaturesialthoughdifferentintypologyandbuildingtechnièues.fnfactitheyare markedbyreducednumberofstoreysandjoinedhousingunitsibuiltatthesametimeorindifferent periods. eistoriccentresfreèuentlyhavetownhouseswherehousingunitsmakeupcurtainwallstwoorthree storeyshighandsometimeshundredmeterslong.qheseunitsoutlinethetownstreetsandformclosed builtblocks.fnthesmallurbanagglomerationsof`ampaniaoegioninftalyiconstructivetypologies basedoncourtyardsopenedinwardsandclosedtotheoutsideareinsteadmorewidespread.fngenerali theresidentialbuildingsarefromtwotofourstoreyshighiwithloweradjacentbuildingsthatoutline thecentralarea.jarketservicesarelocatedonthegroundflooriwhereashomesarelocatedatthe upperfloorsandareaccessiblethroughopenstaircasesandloggias.anotherrecurringtypologyisthe N AssistantmrofessorIpecondrniversityofkaplesIp.iorenzoadpeptimumAbbeyIAversaE`bFIftaly mh.a.ipecondrniversityofkaplesip.iorenzoadpeptimumabbeyiaversae`bfiftaly cullmrofessoripecondrniversityofkaplesip.iorenzoadpeptimumabbeyiaversae`bfiftaly 4UN
2 one-family housing block with front and rear courtyardsi external staircase leaning against the constructionandterraceorpitchroofidependingontheterritoriallocation. qheextensiveandunevenplanimetricgrowthithedifferentbehaviourunder earthèuakes ofin-plane andout-of-planeloadedwallsithefreèuentinefficacyofconnectionsbetweenwallsandbetweenwalls andfloorithepresenceofthrustingstructuresifreèuentlycausecollapsemechanisminvolvingvarious masonryportions. iocal and simplified numerical models allow analyzing these masonry partsi sometimes using intuitivecomputingschemesclosetotheoriginaldesigncriteria.puchmodelsareprevalentlyusedfor checking the mechanism activation in walls loaded orthogonally to their own planei since their behaviourisnotsignificantlyinfluencedbytheoverallbuildingresponse. qhe presence of common geometric and constructive features permits the analysis of out-of-plane collapsemechanismtobesuitableinawiderangeofapplicationsisuchasthevulnerabilityanalysisof entireoldtowncentresformedbytheagglomerationofdifferentheightsandrooftypebuildings. qhis paperi which is included in a research program dealing with the seismic safety of historic city centres and urban agglomerationsi focuses on the failure mechanism of building cornersi that can involve well-connected masonry walls under orthogonal forces Ecigure NF. qhe activation of such amechanismneedsthemasonrycontinuityoftwoorthogonal walls tobebroken. poi inorder toget reliableresultsiitisnecessarytotakeintoaccountatleastthemasonryunitsslidingat mortarjoints andthentheexistingfriction.qheintroductionofthefrictionstrengthcausesdifficultiesinkinematic analysesandconseèuentlyreèuires further approximations. qhereforei initiallya concise description of the main characteristics concerning the mechanism studied in the paper is provided and the dependenceonthefrictionstrengthandtheroleoftheroofconstraintxnzarepresented.pubseèuentlyi the proposed model is described in detail and the out-of-plane response is analysed through linear kinematic procedures in order to evaluate the seismic safety. qhe analysed schemes feature typical cornersofmasonrybuildingsofhistoriccentressupportingroofswithorwithouthorizontalconstraint. fnfluenceandroleoffrictionalforcesontheout-of-planeseismicresponseareassessedbycomparing theseismicloadmultiplierobtainedwithandwithoutfriction. K CiiASE MECHANISM INViVING BUIiDING CRNERS qhemethodicalobservationofseismicdamageonmasonrybuildingsallowedtheidentificationofthe most recurrent collapse mechanisms in each building type Ei.g. palacei churchi etc.f. qhe collapse partialorcomplete is mainlyduetotheeèuilibriumlossofconstructionpartscharacterizedbyan independent behaviour with respect the overall building response. qhe mechanisms that can be activated are generally schematized in the well-known wall overturning and vertical or horizontal bending. eoweveri earthèuakes freèuently produce damage and collapse involving more complex mechanismsiandtheir activationdepends ongeometricfeaturesandlateralandupper constraintsof the concerned masonry portioni as well as on windows location and thrusting elements action. fn buildingsofurbanagglomerationsianindependentbehaviourisgenerallyexhibitbyhousingunitsxzi andthemechanismsthatcanbeactivateddependontheirlocationinsidetheagglomerationandonthe buildingtypexi4z. FigK N `ollapseofbuildingcornerini AèuilaandmaganicaEMMVAbruzzobarthèuakeF 4U
3 cailuremechanismsinvolvingbuildingcornersshowtherigidrotationofamasonryprism with respecttoahingelocatedatitsbase shapedbydiagonalfracturesurfacesinthewallsconcurrentin thebuildingcorner.puchmechanismsarefreèuentinbuildingswherethrustsactatthetopofthe cornerispeciallyduetothehiproofstrutsload.qhegeometryoftheprismaticportiondependsonthe masonryèualityofthewallsconnectedatthecorneriwhichinfluencesthefracturesurfaceanglein boththewallsiaswellasonthepossiblewindowslocationclosetothebuildingcorner.qheprism overturningoccursalongthedirectiondefinedbythethrustingandoverturningforcesiwithrotation aroundtheabovementionedhinge.qhereforeithephenomenoncaninvolvedifferentgeometriesof prismaticmasonryportionsattheupperstoryibutinabsenceofefficientconnectionsatthefloorlevel canalsospreadtofloorsbelow. fntheout-of-planewallresponseithemassesassociatedtofloorgravitationalloadscanparticipateor nottothefailuremechanismsisincetheirinvolvementdependsonthebuildingstructuregeometryand constraints.tithreferencetothesimplecondition`nofcigureiiftheroofcantranslateithemass duetotheroofloadisinvolvedintheoverturningmechanismofpiersbelowandthisisusually consideredincludingahorizontalforcelsinthekinematicmodelebeingsthetotaldeadandlive loadduetotheroofandlthehorizontalloadmultiplierf.fnsuchaconditione`nftheupperpointsof piershavethesamedisplacementoftherooftilltheslidingforceattheinterfacewall-roofissmaller thanthefrictionstrength.qhereforeislidingbetweenwallandroofoccursonlyiftheslidingforceis largerthanthefrictionalresistance.creèuentlyitisassumedthatthefrictionstrengthbetweenroofand masonrywallisverylargeandsuchtoexcluderelativedisplacementsuntilthecollapse.lnthe contraruiiftheroofiskeptfromhorizontaltranslationbyrearconstraintsiasillustratedincigure condition`ithewalloverturningmechanismcanbeonlyactivatedifthefrictionstrengthatthe interfacebetweentheuppersideofwallandtheroofisexceeded.qhereforeiinthiscaseismandatory toconsiderthefrictionissuetoanalysepossiblefailuremechanismsievenifbyanapproximate approach.fnfactidisregardpossiblemechanismscouldleadtooverestimatethewallseismiccapacityi whereasneglectthefrictionalresistancecouldimplyunjustifiedunderestimations.asamatteroffacti theroofcouldnotbesubjectedtohorizontaldisplacementifitiswell-restrainedtomasonrywallsthat areorthogonaltotheexaminedoneandhavelargestiffnessxorigenerallyiifthewallunder investigationbelongstoalargebuildingandtheroofabovesuchwallissomehowkeptfrom translating.fnthesituation`ntheassumptionofperfectpier-rooflinkduringthewholeevolutionof themechanismessentiallycorrespondstoaninfinitefrictionbetweenthemasonrypierandtheupper roof.fnthesituation`iinsteadithefaithfulresponseofthemasonrywallbelowneedsthesliding betweenpierandrooftobeconsideredinpresenceoffriction. FigK `onstraintduetotheroof cinallyimanyout-of-planemechanismsiincludingthatconcernedireèuirecracksspreadinginthe involvedmasonrywallsiandthisimpliesthatfrictionamongmasonryunitsatmortarjointsshouldbe takenintoaccount. fnthispaperithecollapsemechanisminvolvingbuildingcornersialreadystudiediisreviewed consideringitsafeatureandtakingintoaccountthemajorresistantcontributionsianalysingmasonry wallswithdifferentgeometryandconstraintasdescribedinthefollowing. 4U
4 K GEMETRY AND CNSTRAINTS F THE ANAiYZED BUIiDING CRNER qhebehaviourofthebuildingcorneroutlinedbythewallsreportedasaandbincigureisanalysed. BothwallsareassumedtobewithoutopeningsandmadebycoursedashlarmasonryIsofailuredueto crumblinganddisaggregationisprevented.qoobtainresultsrepresentativeofawideandrecurring rangeofsituationsiwallsfrom.mto4.mhigheefareconsiderediwhereasthethicknesst A andt B is assumedeèualtom.smm.qhelengthsi A andi B thatoutlinethegeometryoftheprisminvolvedinthe out-of-planemechanismarebothassumedtobedefinedbyafractureangleofm respecttothe horizontalplane. qheanalysedprismishyphotizedtobelocatedattheupperstoryofbuildingsiandtwotypologiesare consideredfortheroofithatistimberpitchecase`nfandtimberlacunarecase`froof.fnthecase `NItheroofloadingisassumedtobetransmittedtotheprismonlythroughtheforces A ErepresentativeofthepitchloadonthewallAFandtheforcec m Erepresentativeoftheloadduetothe hip-rafterf.fnthecase`itheloadingduetotheroofisconsideredthroughtwoforcess A ands B I representativeofloadsactingalongthelengthi A andi B ofthewalls. 4K MDEi USED IN THE KINEMATIC ANAiYSIS qhemechanismisstudiedbymeansofaamodeleciguresand4fiwheretheapplicationpointsof forcesandloadsarelocatedatdifferentheight.ftisassumedthattheprismoverturningoccursaround ahorizontalrotationaxisthroughpointo N IrotatedoftheangleaEassumedeèualto4R Frespecttothe axisofwalla.qherotationdirectiondefinedbytheselectedangleof4r canbeconsideredcloseto theoneduetothethrustofroofrip-raftersinmanysituationsieventhoughitwouldbesuitableto considertheanglethatminimizesthehorizontalloadmultiplierl. AsitisshownincigureIthefollowingforcesareconsideredtoactWthemasonryblockself-weight m A andm B Ithedeadandtheliveloadss A ands B duetotheroofithecorrespondinghorizontalforces lm A Ilm B Ils A andls B Itheforcec m Kqheforcesm A andm B Easwelllm A andlm B Fareappliedatthe centreofgravityofeachblockitheloadss A ands B Easwellls A andls B Fareappliedatthemidthicknessofthewalls.qheforcec m isappliedattheinsideupperedgeofthebuildingcorner.besidesi thefrictionforcesc A andc B atthewallandwall-roofinterfaceandthefrictionforcesc g ateach mortarjointsalongthefracturesurfacesarealsoconsideredasdescribedinthefollowing. RB F R R RA FigK Analyzedbuildingcorner qheanalysesarecarriedoutassumingtheresultantsoftheloadss A ands B eèualtoapercentageofthe entireprismself-weightiandspecificallytovarybetweennmbandrmboftheself-weightm A andm B. qhefrictionforcesareoutlinedbythesimpleiconservativeandapproximatedmodelproposedby `oulombxrziwhereapredeterminedvalueisassignedtothefrictioncoefficientm.arangeofvalues betweenm.andm.4hasbeenselectedbecausetheyarewidelyusedintheliteratureforcontact 4U4
5 surfacesasthosehereinconcerned.curthermoreithefrictioncoefficientisassumedtobeconstant alongallthecontactsurfaceisotheresistantforceisonlydependentonthenormalforcesactingonthe interfaceandnotontheirdistribution.qhisassumptionalsoagreeswiththehypothesisthattheoverall frictionalresistancedoesnotdependonthecontactsurfacedimensionbutonlyontheresultantofthe actingnormalforces.qheassumptionofsuchasimplifiedmodelanyhowhasbeenconsidered adeèuatefortakingintoaccounttheslidingresistanceamongblocksandbetweenmasonrywalland roof.curthermoreithedilatancyisassumedeèualtozero.denerallyiifthedilatancyofblocksiszeroi itisdifficulttoassesstheloadfactorsincethenormalforcetransmittedbetweenblockscanbe indeterminate.konethelessisupposingthatthenormalforcesaresomehowevaluateditheloadfactor maybeeasilycomputed.fnfactitheassessmentofthefrictioncoefficientthroughaverysimplified approachcanbeadeèuatetotakeintoaccounttheslidingamongsomekeycontactsurfacesinthe kinematicanalysisofout-of-planefailuremechanisms. la lva B A lb lvb FigK 4eorizontalandverticalsectionsoftheamodel qhehorizontalloadmultiplierl o thatcausestheactivationofthemechanismisobtainedapplyingthe sirtualtorkmrinciplexszibyeèuatingthetotalworkdonebytheexternalforcestothatdonebythe internalforceselinearkinematicanalysisf.byassigningavirtualrotationytothemasonryprismiitis possibletodeterminethevirtualdisplacementsedinhorizontaldirectionandhinverticaldirectionfof anypointonthebasisoftheprismgeometry. qhesirtualtorkmrincipleleadstothefollowingexpressionofthehorizontalloadmultiplierl o W ma d A + mb d B + sa dsa + sb dsb - cm + ca dsa + cb dsb + å cg ii d g Ii lo ENF ma h A + mb hb + sa hsa + sb hsb + cm hcm wheres B Ic A andc B areeèualtozerointhecase`niwhilec m iseèualtozerointhecase`. qhevirtualdisplacementsappearinginbènenfiestimatedatthezheightwheretherelatedforcesact andwritteninconciseformiareprovidedbyw inhorizontaldirectionw x A y B d A d B d sa d sb EF inverticaldirectionw h A h h B h h sa h h sb h EF qhecoordinatesoftheapplicationpointsaibio A ando B oftheactingforcesicomputedwithrespect tohingeonareeèualtow 4UR x sa y sb
6 i A ta tb æ ib ö xa tb + y A - xb - yb -çta + E4F è ø i A æ ib ö xsa tb + ysa - t A x sb tb ysb -çt A + ERF è ø cinallyithesafetyindexf p iscomputedasratioofcapacitytodemandintermsofacceleration accordingtotheprocedurereportedinxsz. RK RESUiTS bxtensiveparametricanalyseswerecarriedoutinordertoestimatethedependenceoftheload multiplierl o andthesafetyindexf p ontheparametersinvolvedinthestudiedmechanism. cigurershowstheinfluenceofthefrictionstrengthontheloadmultiplierl o iftheroofiswellrestrainedandthemasonryprismundergoesoverturning.qhefigureconcerns.mmeterhighwalls underasiteaccelerationpageèualtom.mgiandcontainsthevaluesofl o astheratiooftheroofload sess A Hs B Ftotheprismself-weightmEmm A Hm B Fvaries.keglectingthefrictioncontributionIl o assumeslowvaluesandslightlydependsonloadings.ffthefrictionatthemasonrylroofsurfaceonly isconsiderederedlinefil o assumeshighervaluesandrisesinproportiontosxwhenthefrictionatthe mortarjointsisalsotakenintoaccountebluelinefithetrendofl o isèualitativelyunchangedialthough slightlyhigher.qheinfluenceofthewallheighteandthesiteaccelerationpagisshowninciguresi wherethesafetyindexf p isplottedversustheratioslm.qheresultsshowaratherevident proportionalityoff p withrespecttoslmitosomeextentlargerforthehigherwalls.eoweveriinall cases independentlyonpag f p islargerthanunityiandthereforethemechanismdoesnotappear feasibleiftheroofiswell-restrainedeasithappensintimberlacunarceilingwithperimeterbeamsf. ioadmultiplierl o 2I0 NIR NI0 tell-restrainedroof(c2f withoutfrictionstrength withfrictionstrength withwalllrooffrictiononly e.0m pag0.0g pafetyindexfs RI00 4I00 I00 2I00 pag0.2rg pag0.0g pag0.rg tell-restrainedroof(c2f 0IR NI00 e4.2m em 0I0 0 N R0 S0 oatioofloadstoprismself-weightmx%] 0I S0 oatioofloadstoprismself-weightmx%] FigK Rfnfluenceoffrictionstrength FigK S fnfluenceofprismheightand seismicinput oesultsobtainedforrestrainede`fandnot-restrainede`nfroofarecomparedinciguret.qhefigure stillconcernsmasonrywallswithemunderasiteaccelerationpagofm.mgiasincigureriwith s s A Hs B andm m A Hm B inthecase`andss A Imm A andtheforceduetothehip-rafterc m Rkk inthecase`n.mlotsundoubtedlyshowthenoteworthyroleoftheroofconstraintwindependentlyof frictionil o isnotablysmallerinpresenceofnot-restrainedroofeaspitchrooffiwithvalueseèualto halfofthosecomputedforwell-restrainedrooffors NMBmandnotablylessthanhalfiftheratio slmincreases.puchresultsalsoprovethattheloadmultiplierisnotinfluencedbytheroofloadingif theroofisnot-restrainedebecauseincreasingsithecorrespondingoverturningforcel o s proportionallyincreasesf.fncondition`theloadmultiplierl o ishigherbecauseofthefrictional resistanceatthewall-roofsurfaceandbecausetheoverturningforcel o sbecomeseèualtozerowhen themechanismactivates.cinallyiresultsofciguretshowhowthefrictionatthejointfracture surfaces inadditiontotheoneatthewalllroofsurface slightlyincreasesthevaluesofcollapseload multiplieriindependentlyoftheroofconstraint. 4US
7 ioadmultiplierl o NI00 0I80 0IS0 0I40 0I20 withfrictionstrength withwalllrooffrictiononly tell-restrainedroof(c2f em pag0.0g kot-restrainedroof(cnf 0I00 0 N R0 S0 oatioofloads i toprismself-weightm i x%] pafetyindexfs 2I00 NI7R NIR0 NI2R NI00 0I7R 0IR0 0I2R kot-restrainedroof(cnf-e.0m-cprkk pag0.2rg pag0.0g pag0.rg withfrictionstrength withoutfrictionstregth 0I S0 oatioofloads A toprismself-weightm A x%] FigK Tfnfluenceofroofconstraint FigK U fnfluenceoffrictionand seismicinput saluesofthesafetyindexf p areprovidedincigureuforthesamecase`nofciguret.joreoveri curvesatseveralsiteaccelerationspagareplottedinpresenceorabsenceoffrictionithusshowingthat thelatterincreasesf p toalargerextentifpagdecreases.f p valuesalsoconfirmthatiftheroofisnot keptfromtranslatingithemechanismisnotactivableonlyinsomespecificcasesef p isfreèuently lowerthanunityf.qheinfluenceoftheforcec m duetothehip-rafterisevaluatedincigurevwherethe multiplierl o isplottedversustheratios A Lm A formasonryprism.mand4.meterhigh.qheforcec m israngedfromrtonrkk.qhefigureshowsthatincreasinginc m causesreversalinthetrendofl o withrespecttotheratios A Lm A El o increaseswiths A L m A ifc m islargerfimostlyinlowerwalls. cinallyicigurenmshowsthesafetyindexf p asthefrictioncoefficientmvarieswithinthecustomary rangem. M.4M.qhefigureconcernsaprism4.mhighunderpagM.Rgandc m Rkk.As expectedi f p increaseswiththefrictioncoefficientmwithapercentageconfirminghowunsuitable assessmentofmcanleadtowrongsafetyestimates.qhefigurealsoshowshowtheincreaseinmcan thoroughlychangetheseismicsafetyagainstthebuildingcorneroverturningisincef p canbecome greaterthanunity. SK CNCiUSIVE REMARKS qheout-of-planebehaviourofseveralmasonrybuildingcornershasbeenanalysedinthepaper.qhe performedanalyseshaveenabledtohighlightsomekeyissuesregardingtheexpectedout-of-plane ioadmultiplierl o 0IR0 0I40 0I0 0I20 0IN0 e4.2m-pag0.0g kot-restrainedroof(cnf cprkk cpnrkk em-pag0.0g cprkk cpnrkk 0I S0 oatioofloads A towallself-weightm A x%] 4UT pafetyindexfs NIR0 NI2R NI00 0I7R kot-restrainedroof(cnf m 0.4 m0. m 0.2 e4.2m pag0.rg c m Rkk 0IR0 0 N R0 S0 oatioofloads A towallself-weightm A x%] FigK Vfnfluenceofhip-rafterforce FigK NM fnfluenceoffrictioncoefficient failuremechanismiandispecificallyitheroofconstraintithefrictionattheinterfacebetweenwalland roofandamongmasonryunitsitheloadingduetoroofandhip-rafters.oesultsoflinearkinematic analyseshaveshownthatanincorrectassessmentoftheaboveinputdatacanleadtonoteworthy erroneousevaluationofthefailureseismicloadmultiplieriandthenoftheseismicsafety.qheroof
8 constraintnotablyinfluencesthelikelyfailuremechanismofthebuildingcornerwiftheroofiswellrestrainedeasitcanhappenintimberlacunarceilingwithperimeterbeamsfthemechanismdoesnot appearfeasibleiwhereasiftheroofisnotkeptfromtranslatingeasithappensinpitchroofsfiashareof itsmassisinvolvedintheoverturningmechanismthatisnotactivableinsomespecificcasesonly. crictiondoesasignificantroleonthesafetyindeximostlyiftheroofloadingislargerwiftheloaddue totheroofeèualsrmboftheself-weightofthemasonryprismbelowinvolvedinthemechanismithe failureloadmultiplierdoubles.crictionattherooflwallsurfaceseemstohavealargerroleonout-ofplanecollapseofbuildingcornersthanfrictionatthemortarjointsamongblocksalongthecracking surfacesneededforthemechanismactivation.qheforceduetohip-rafterscanhalveorreduceto athirdtheseismicloadmultiplierifvarieswithincustomaryrangeofvalues. REFERENCES xnz duadagnuoloj.icaellad.emuf.qhefrictioninout-of-planefailuremechanismsofmasonry wallsifnw mrock 14th fnternational Brick and Block Masonry Conference EfBMaCFI pydneyi AustraliaIcebruaryNT-M. xz diuffrèa.envvf.picurezza e conservazione dei centri storici in zona sismica fl caso di lrtigiai iaterzaibarieinftalianf. xz AvorioA.IBorriA.IaejariaA.EMMF.pismarmbrojarchigianodelsettembreNVVT esuccessiviapellanowcomportamentodiunaschieradiedificiconsolidatiifnwfngegneria pismicaiannoufuik.einftalianf. x4z driffithij.`.ijagenesid.ijelisid.imicchiii.emmf.bvaluationofout-of-planestabilityof unreinforcedmasonrywallssubjectedtoseismicexcitationifnwgk of Earthquake EngineeringI TEpmNFIpp.N4N-NSV. xrz aruckeria.`.envr4f.`oulombfrictioniplasticityiandlimitloadsifnwgk of Applied Mechanics ApMEINENFIpp.TN-T4. xsz jinisterodellefnfrastruttureedeiqrasportiikormeqecnicheperle`ostruzioni kq`lmmui EMMUF.aKMK 14KM1KMMUI pupplk lrdk nk M della dkrk nk V del 4KKMMUEinftalianF. 4UU
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