A ClMmrTATflkAi Mlabiifkd AmmolACe clo ilt Blka ptobkdte MAplkov

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1 Structural Analysis of Historical Constructions Jerzy Jasieńko (ed) 2012 DWE, Wrocław, Poland, ISSN , ISBN A ClMmrTATflkAi Mlabiifkd AmmolACe clo ilt Blka ptobkdte MAplkov sasilis parhosis N I ptephen darrity O I vong pheng P ABpToACT eistçricalmasçnryistypicallycharacterisedbyitslçwbçndstrengthkcrackingçfsuchmasçnryis çftenasaresultçfthedejbçndingçfthemasçnryunitsfrçmthemçrtarjçintsandthepçstjcracking respçnseuptçcçllapseisinfluencedbythecharacteristicsçfthemasçnryunitlmçrtarinterfacek qhedevelçpmentçfacçmputatiçnalmçdelthatisapplicablefçrlçwbçndstrengthfiredclaybrick masçnryisdescribedkrsingsçftwarebasedçntheaistinctblementjethçdçfanalysisibrickswere representedasanassemblageçfdistinctblçckskqhemçrtarjçintsweremçdelledaszerçthickness interfaceswhichcançpençrclçsedependingçnthemagnitudeanddirectiçnçfthestressesapplied tçthemk qhematerialparametersfçrthemasçnrycçnstitutivemçdelwereçbtainedfrçmtheresultsfrçmthe lçadtestingçflargewalllbeamclaybrickmasçnrypanelsinthelabçratçrykfnitiallythepanelswere mçdelledcçmputatiçnallyusinganassumedsetçfmaterialparameterskqhedifferencesbetweenthe resultsçbtainedexperimentallyandnumericallywerethenminimizedbyadjustingtheparametersin thecçnstitutivemçdelusingançptimizatiçntechniquekqhemçdelwasthenusedwiththeçptimized parameterstçpredictthestructuralrespçnseçfçtherunreinfçrcedandreinfçrcedwalllbeamsthathad beentestedpreviçuslyinthelabçratçrykdççdcçrrelatiçnwasçbtainedwiththeexperimentalresultsk heywords: BricksI BondI Computational modellingi Masonry NK fktolarctflk NKN iow bond strength masonry janyfçrmsçfhistçricalmasçnrycçnstructiçnexhibitlçwbçndstrengthcharacteristicskqhisiswhere thebçndbetweenthemasçnryunitsandthemçrtarjçintsissufficientlylçwtçhaveadçminanteffect çnthemechanicalbehaviçursuchasthefçrmatiçnçfcracks;therejdistributiçnçfstressesafter crackingandthefçrmatiçnçfcçllapsemechanismsk qheneedtçpredicttheinjservicebehaviçurandlçadcarryingcapacityçfhistçricalmasçnry structuresinçrdertçinfçrmrepairçrstrengtheningdecisiçnshasledtçthedevelçpmentçfseveral numericalmethçdsçfanalysisxnzkqhispaperdescribesthedevelçpmentçfacçmputatiçnalmçdelfçr lçwbçndstrengthmasçnrycçnsistingçffiredclaybrickslaidinalçwstrengthmçrtarkftisexpected thatthemçdellingstrategyrepçrtedinthispapercçuldbeappliedtçanyfçrmçflçwbçndstrength masçnrycçmprisingrigidmasçnryunitsandlçwstrengthmçrtark NKO pummary of the computational modelling strategy diventheimpçrtanceçfthemasçnryunitlmçrtarinterfaceçnthestructuralbehaviçurçflçwbçnd strengthmasçnryitheauthçrsusedamicrçjmçdellingapprçachbasedçntheaistinctblementjethçd çfanalysisxozkqhesçftwareusedwastherniversalaistinctblementcçdeerabcfxpzwhichwas develçpedinitiallytçmçdelslidingrçckmassesinwhichfailureçccursalçngthejçintsxqzkqhishas similaritieswiththebehaviçurçflçwbçndstrengthmasçnrykqypicalexamplesçfmasçnrystructures N oesearchassistantipchççlçfcivilbngineeringirniversityçfieedsirhivksarhçsis]leedskackuk O eçffmantççdmrçfessçrçfarchitecturalbngineeringipchççlçfcivilbngineeringirniversityçfieedsi rhiskwkgarrity]leedskackuk P peniçriecturerincivilbngineeringipchççlçfcivilbngineeringirniversityçfieedsirhiyksheng]leedskackuk RRV

2 thathavebeenmçdelledusingrabcaredescribedbyiemçsxrziqçthetalkxszandwhugextzkan additiçnalfeatureçfrabcisthecapabilitytçpredicttheçnsetçfcracking;thisisimpçrtantwhen cçnsideringinjservicebehaviçurkptrengtheningbyrçckbçltingiançtherfeatureçfrabciallçwed theauthçrstçmçdelmasçnrystrengthenedwithreinfçrcingbarsk cçranumericalmçdeltçrepresentthebehaviçurçfamasçnrystructurewiththerequiredlevelçf accuracyanapprçpriatecçnstitutivemçdelmustbeselectedandparametersthatarerepresentativeçf thematerialsbeingmçdelledmustbeusedkqheelasticjperfectlyplasticcçulçmbslipjjçintarea cçntactmçdeliavailableasançptiçnwithinrabciwasselectedbytheauthçrstçrepresentthe behaviçurçflçwbçndstrengthmasçnrykrabcalsçprçvidesaresidualstrengthçptiçntçsimulate tensiçnsçfteningeffectskqhiswasnçtselectedasthebçndstrengthçfthemasçnryusedinthe researchwasmuchlçwerthanthatexhibitedbymçdernmasçnrymaterialskasaresultianytensiçn sçfteningeffectswerelikelytçbeançrderçfmagnitudesmallerthanthebçndstrengthandsçwere cçnsideredtçbeinsignificantk CçnventiçnallyIthematerialparametersfçrthecçnstitutivemçdelsfçrmasçnryarebasedçnthe resultsfrçmthetestingçfsmallassemblagesçrsamplesçfmaterialkpuchtestsdçnçtreflectthemçre cçmplexbçundarycçnditiçnsandthecçmbinatiçnsçfstressjstatetypesthatexistinrealmasçnry structureskfnadditiçnilargenumbersçftestsarerequiredtçcapturetheinherentvariatiçnsinthe masçnryandtheresultsçbtainedfrçmsuchtestsareunlikelytçincludeanyvariatiçnsin wçrkmanshipkcurthermçreithematerialparametersdefinedinrabctçrepresentthecharacteristics çfthezerçthicknessinterfacesbetweenthemçrtarjçintsandthebrickscanbedifficulttçmeasurein practicekqçaddressthedifficultiesçutlinedabçveitheauthçrsusedamethçdçriginallyprçpçsedby qçrçpçvanddarrityxuztçdeterminethematerialparameterskqhemethçdissummarisedbelçwand describedinmçredetailithereafterk fnitiallyresultswereçbtainedfrçmthelçadtestingçfaseriesçfsingleleafthickclaybrickmasçnry walllbeampanelsinthelabçratçryeseesectiçnofkqhesamepanelsweremçdelledcçmputatiçnally usinganinitialsetçfmaterialparametersçbtainedfrçmtheliteratureeseesectiçnpfkqhedifferences betweentheresultsçbtainedexperimentallyandnumericallywerethenminimizedbyadjustingthe parametersinthecçnstitutivemçdelusingançptimizatiçntechniqueeseesectiçnqfkfnparticularthe parameterswereadjustedtçgivenumericalresultscçmparablewiththedevelçpmentçfthecrack patternunderincrementallçading;thelçadatfirstcracking;thefailuremechanismandthelçadversus midjspandisplacementrelatiçnshipçbtainedfrçmthetestingçfthepanelsinthelabçratçrykqhe çptimizedparameterswerethenusedinthecçmputatiçnalmçdeltçpredictthestructuralrespçnseçf çtherunreinfçrcedandreinfçrcedwalllbeamsthathadbeentestedpreviçuslyeseesectiçnrfk OK taiilbbam makbi bumbofmbktai TbpTp AseriesçfplainandreinfçrcedsingleleafthickclaybrickmasçnrywallLbeampanelswastestedin thelabçratçrybyçneçftheauthçrsedarrityfaspartçfaresearchprçjecttçinvestigatethe strengtheningçfmasçnrywallswithwindçwçpeningskpçmeçfthesepanelswerebuiltwithasçldier Applied ioad S courses E4RM mmf EV for panel apnf poldier course EOOR mmf S courses E4RM mmf SSR mm OMOR mm clear opening EOVOR mm for panels in and iof SSR mm cigk NqypicaldetailsWclaybrickmasçnrywallLbeampaneltestedinthelabçratçry RSM

3 cçurseimmediatelyabçvetheçpeningiwiththereminderçfthebrickwçrkbeingcçnstructedin stretcherbçndiasshçwnincignkqhebrickswererhstandardsizeeonrmm NMOKRmm SRmmF withanaveragewaterabsçrptiçnçfnqbandasandjfacedfinishkqhejçintswereallnçminally NMmmthickINWNOEçpcWsandFweighJbatchedmçrtarKqhebrickandmçrtarcçmbinatiçnwasselected tçprçducebrickwçrkwithlçwbçndstrengthk Table Nbxperimentaltestresults talllbeam manel tidth of opening xmmz Courses of stretcher bond brickwork above soldier course Compressive strength of mortar at time of test xmmaz ioad at first visible crack xkkz Maximum test load xkkz pn OMOR pix MKTO MKTO PKSV po OMOR pix MKTV NKSM QKSM pp OMOR pix MKUS NKSM RKNM p4 OMOR pix NKNU NKTN RKST in OVOR pix MKSQ MKNM NKSM io OVOR pix MKTN MKSM OKSM apn OMOR kine MKVS MKTO NMKSM bachpanelwassubjectedtçasingleverticalpçintlçadappliedatmidjspankqhelçadwasapplied incrementallytçeachpanelusingahydraulicramandastructuralsteelwçrkreactiçnframekftwas distributedthrçughathicksteelspreaderplatewhichwasembeddedinmçrtarçnthetçpçfthe brickwçrkkbachpanelwasinspectedvisuallyfçrsignsçfcrackingthrçughçutthetestandthevertical displacementatmidjspanwasrecçrdedateachlçadincrementuntilextensivecrackinghadçccurredk qhetestresultsaresummarisedinqablenk PK fkftfai ClMmrTATflkAi Mlabiifkd deçmetricmçdelsrepresentingtheclaybrickwalllbeampanelstestedinthelabçratçrywerecreated inrabckbachbrickwasrepresentedbyadefçrmableblçckseparatedbyzerçthicknessinterfacesat eachmçrtarjçintkqçallçwfçrthenmmmthickmçrtarjçintsintherealwallpanelsieachdefçrmable blçckwasbasedçnthençminalbricksizeincreasedbyrmmineachfacedirectiçntçgivearabc blçcksizeçfoor NNOKR TRmmKbachblçckwasinternallydiscretisedbyrabCintçfiniteJ differencezçneelementsieachassumedtçbehaveinalinearlyelasticmannerkfnpracticeithestresses inthebrickswçuldbewellbelçwtheirstrengthlimitandsçnçsignificantdefçrmatiçnwçuldbe expectedtççccurkqçreplicatethisibrickmaterialparameterswerespecifiedtçensurethatnçblçck defçrmatiçnwçuldçccuryetthesçftwarewasenabledtçcalculatethetheçreticalstressesineach zçneelementk AsmentiçnedpreviçuslyIthezerçthicknessinterfacesweremçdelledusingrabC selasticperfectly plasticcçulçmbslipjjçintareacçntactçptiçnxpzkqheinterfacesweredefinedbysixparameters namelywtheelasticnçrmalstiffnesseghnf;theshearstiffnesseghsf;theangleçffrictiçnegfricf;the tensilestrengthegtenf;thecçhesivestrengthegcçhfandtheinterfacedilatiçnangleegdilfxpzk qhebçttçmedgesçftherabcwallpanelweremçdelledasrigidsuppçrtsintheverticaland hçrizçntaldirectiçnsiwhilsttheverticaledgesçfthewallpanelwereleftfreekpelfjweighteffects wereassignedasagravitatiçnallçadkjechanicallçcaldampingwasusedtçsimulatequasijstatic lçadingk AtfirstIthemçdelwasbrçughtintçastateçfequilibriumunderitsçwnweightKqhenacçnstant verticalvelçcityçfmkmmmumlswasappliedtçthelçadspreaderplateçnthetçpçfthepanelandthe reactiçnfçrcesweredeterminedkeistçriesçfthemidjspandisplacementatthesçffitçftheçpening wererecçrdedandalçadversusmidjspandisplacementrelatiçnshipwasdeterminedfçreachpanel typekqhiswaslatercçmparedintheçptimizatiçnprçcesswiththeexperimentalresultsçbtainedin thelabçratçryk RSN

4 4K fabktfcfcatflk lc MATbofAi maoambtbop 4KN lptimization aims qhematerialparametersusedinrabcwereçptimizedtçprçducesimilarcçmputatiçnalrespçnses tçthefçllçwingaspectsçfbehaviçurçbservedfrçmthelargejscaletestsinthelabçratçryw af qheappliedlçadandçbserveddeflectiçnattheçccurrenceçffirstcrackingepçintnincigkof; bf qhemaximumappliedlçadsuppçrtedbythewalllbeampanelsepçintqincigkof; cf qherecçrdedappliedlçadversusdisplacementrelatiçnshipsepçintsoandpincigkofk df qheprçpagatiçnçfcracksinthewalllbeampanelswithincreasingappliedlçad; ef qhemçdeçffailurek cigk OoespçnseevaluatiçnpçintsfçrstageNandOçptimizatiçn EoIiandddençterespçnseIlçadanddisplacementIrespectivelyF 4KO pensitivity analysis fnitiallyasensitivityanalysiswascarriedçuttçidentifytheeffectçfthebrickandbricklmçrtarjçint interfaceparametersusedinrabcçntheprejandpçstjcrackingbehaviçurxozkasexpectedi behaviçurwasfçundtçbeindependentçfthebrickprçpertiesandwasdçminatedbythebricklmçrtar jçintinterfaceprçpertieskcrçmtheanalysisitwasfçundthatw af qhelçadversusdisplacementrelatiçnshipfçrthemasçnrywalllbeampanelswaslinearuptçthe çccurrenceçffirstcracking; bflfthesixparametersusedbyrabctçdefinethecharacteristicsçfthebricklmçrtarjçint interfacew if qhençrmalstiffnesseghnf;theshearstiffnesseghsfandthetensilestrengthegtenfçftheinterface influencethebehaviçuruptçandincludingtheçccurrenceçfthefirstcrackinthepanel; iifqhecçhesivestrengthegcçhf;theangleçffrictiçnegfricfandangleçfdilatiçnegdilfinfluence thebehaviçurçfthepanelafterfirstcrackinguptçcçllapsek qçreflecttheseresultsandtçminimisethecçmputatiçnaltimerequireditheçptimizatiçnçfthe materialparameterswascarriedçutintwçdifferentstagesasindicatedincigkokqhetwçstagesçf çptimizatiçnaredescribedinmçredetailibelçwk 4KP ptage N optimization Ebehaviour up to first crackingf Basedçntheassumptiçnthattheelasticprçpertiesçfthebricksremainunchangedandthataunifçrm stressdistributiçnçccursbçthinthebricksandthemçrtariiçurenççxvzusedadetaileddiscçntinuum RSO

5 finiteelementanalysistçdemçnstratethatifçrfilledjçintsithejçintnçrmalstiffnesseghnfandshear stiffnesseghsfcanberelateddirectlytçthebrickandmçrtarprçpertiesasfçllçwsw ENF EOF EPF wherewb b andb m arethevçung smçduliandd b andd m aretheshearmçduliirespectivelyifçrthe bricksandmçrtar;h m isthethicknessçfthemçrtarjçintandvisthemçissçn sratiçkqheseequatiçns givetheratiççfnçrmaltçshearstiffnessasw EQF qableoshçwstherangeçfmaterialprçpertiesiidentifiedfrçmtheliteraturexnmjnqzifçrmaterialsthat aresimilartçthçseusedtçcçnstructthewalllbeampanelsreferredtçinsectiçnokqheseprçperties havebeençbtainedfrçmthetestingçfsmallsamplesçfmaterialçrsmallassemblagesk Table Ooangeçfbrickandmçrtarprçperties marameter b b xklm O z b m xklm O z v b v m h m xmz oange EQtçNMFxNM V ENtçNNFxNM U MKNtçMKO MKNtçMKO MKMN rsingtherangeçfprçpertiesshçwninqableoiavariatiçnanalysisçftheminimumandmaximum valuesçfnçrmalandshearstiffnesswascarriedçutxozkqheanalysisshçwedthatthençrmalstiffness EghnFrangedfrçmNMtçNRMdmaLm;theshearstiffnessEghsFrangedfrçmQKPtçSRdmaLmandthe ratiççfnçrmaltçshearstiffnessrangedfrçmoknutçokrokalsçisincethençrmalstiffnessisdirectly relatedtçtheshearstiffnessiitwasdecidedtççptimizethejçintnçrmalstiffnessandthejçinttensile strengthparameterskafactçrialdesignçfouexperimentswascarriedçutfçreachçftheshçrtepn pqfandlçngpanelseinandiofreferredtçinqablenkqhematerialparametersusedinthe cçmputatiçnalexperimentsfçrthestagençptimizatiçnareshçwninqablespandqkqhejçintnçrmal stiffnessijçintshearstiffnessandjçinttensilestrengthvalueswerevariediasshçwnibuttheçther parameterswereassumedtçbecçnstantandequaltçthevaluesrepçrtedbyiçurenççxvzk Table PKBrickprçpertiesusedinthestageNçptimizatiçn aensity EdF xkglm P z blastic modulus Eb b F xmmaz moisson s ratio Ev b F OMMM SMRM MKNQ goint normal stiffness EghnF xdmalmz Table 4KoangeçfinterfaceprçpertiesusedinthestageNçptimizatiçn goint shear stiffness EghsF xdmalmz Angle of friction EgfricF xdegreesz goint cohesive strength EgcohF xmmaz goint tensile strength EgtenF xmmaz goint dilation angle EgdilF xdegreesz NMIORIRMITRI NMMINORINRM ghnlokp PSKU MKPTR MKMVIMKNMI MKNNIMKNO qheleastsquaresdifferencesbetweentheexperimentalandcçmputatiçnaltestresultsiuptçthe çccurrenceçffirstcrackingiwerethenestimatedkalltherespçnsequantitieswerecçnsideredtçbe equallyweightedfçrthefçrmulatiçnçftheçbjectivefunctiçnkasurrçgatemçdelwascçnstructed RSP M

6 withtheuseçfthejçvingieastpquaresejipfapprçximatiçnmethçdandageneticalgçrithm çptimizatiçnengineavailablefrçmeyperptudynmxnrzkaccçrdingtçqçrçpçvandvçshidaxnsz ageneticalgçrithmçptimizatiçnengineismçrelikelytçfindançnjlçcalsçlutiçneikekaglçbal minimumfwhencçmparedwithgradientbasedmethçdssuchasthepequentialnuadraticjethçdçr theadaptiveoespçnsepurfacemethçdkcurtherdetailsçftheçptimizatiçnprçcessaredescribedby parhçsisxozkcrçmthestagençptimizatiçnexerciseitwasfçundthatwghnznpkrdmalm;ghsz RKUTdmaLmandgtenZMKNMNjmaKqhesevaluesandthebrickprçpertiesshçwninqablePwerethen usedinthestageoçptimizatiçnk 4K4 ptage O optimization Ebehaviour after first crackingf cçrthestageoçptimizatiçniafactçrialdesignçfntrexperimentswascarriedçutfçreachçfthe shçrtandlçngpanelsusedinthestagençptimizatiçnkqhevaluesçftheinterfaceparametersused whenplanningthecçmputatiçnalexperimentsareshçwninqablerkcrçmtheanalysisitwasfçund thatwgfriczqm ;gcçhzmkmsojmaandgdilzqm K goint normal stiffness EghnF xdmalmz Table RoangeçfinterfaceprçpertiesusedinthelevelOçptimizatiçn goint shear stiffness EghsF xdmalmz Angle of friction EgfricF xdegreesz goint cohesive strength EgcohF xmmaz goint tensile strength EgtenF xmmaz goint dilation angle EgdilF xdegreesz NPKR RKUT OMIORIPMI PRIQM MKMQIMKMSIMKMUIMKNMI MKNOIMKNQIMKNS MKNMN MINMIOMI PMIQM 4KR serification study qheexperimentalresultsfçrtheshçrtandlçngpanelswerecçmparedwiththeresultsçbtainedfrçm therabcmçdellingusingtheçptimizedmaterialparameters;seecigspaandpbkbearinginmindthe inherentvariatiçnsthatçccurinmasçnryiagççdlevelçfcçrrelatiçnwasachievedk rltimate load for p4 rltimate load for po rltimate load for io rltimate load for pp rltimate load for pn rltimate load for in içadatfirst crackpredicted withrabc içadatfirst crackpredicted withrabc EaF EbF cigk PCçmparisçnçfexperimentalandnumericalresultsfçrtheEaFshçrtandEbFlçngpanels RK saifaatflk ptrav qçcheckthevalidityçfthematerialparameteridentificatiçnprçcedureitherabcmçdelwiththe çptimizedparameterswasusedtçpredictthebehaviçurçfadeeperwalllbeampaneleapnfkcigureq shçwsthedistributiçnçfcracksatcçllapsepredictedusingrabckasimilardistributiçnçfcracks wasçbservedinthelabçratçrytestingasshçwnincigkrkqhedevelçpmentçfcracksunderincreasing appliedlçadpredictedusingrabcwasfçundtçbeverysimilartçtheçbservedprçpagatiçnçfcracks RSQ

7 inthelabçratçrytestskcigksshçwstheçbservedandrabcjpredictedlçadversusdisplacement behaviçurfçrpanelapnkqherabcjpredictedvalueçfthelçadatfirstcrackingeokmkkfisclçsetç thatçbservedfrçmthelabçratçrytestingenktokkfkqheultimatelçadçfnmkskkrecçrdedinthe labçratçrycçmpareswellwiththelçadçfnmkqkkpredictedusingrabckadditiçnalvalidatiçn studieswerecarriedçutwithsimilarwalllbeampanelscçntainingdifferentamçuntsçfbedjçint reinfçrcement;thesearedescribedelsewherexozk cigk 4cailuremçdefçrpanelapNpredictedusingrabC EaFsiewatlefthandsideçfthepanelEbFsiewçftherighthandsideçfthepanel NO NM U cigk RCrackpatternsatfailureinpanelapN NMKSkkWrltimatelçad predictedwithrabc ioad EkkF S 4 O OkkWiçadatfirstcrack predictedwithrabc M N O P 4 R S T U aisplacement EmmF cigk SlbservedandrabCJpredictedlçadversusdisplacementrelatiçnshipsfçrpanelapN RSR

8 SK ClkCirpflkp qhedevelçpmentçfacçmputatiçnalmçdelfçrlçwbçndstrengthbrickmasçnryibasedçnthe aistinctblementjethçdiispresentedkqhematerialparametersfçrthemasçnrycçnstitutivemçdel wereçbtainedfrçmtheresultsfrçmthelçadtestingçflargewalllbeamclaybrickmasçnrypanelsin thelabçratçrykfnitiallythepanelsweremçdelledcçmputatiçnallyusinganassumedsetçfmaterial parameterskqhedifferencesbetweentheresultsçbtainedexperimentallyandnumericallywerethen minimizedbyadjustingtheparametersinthecçnstitutivemçdelusingançptimizatiçnapprçachkqhe mçdelwasthenusedwiththeçptimizedparameterstçpredictthestructuralrespçnseçfçther unreinfçrcedandreinfçrcedwalllbeamsthathadbeentestedpreviçuslyinthelabçratçrykdççd cçrrelatiçnwasçbtainedwiththeexperimentalresultsk AChkltibadbMbkTp qhewçrkpresentedinthispaperissuppçrtedbyanbmpoccçmparativeawardinpcienceand bngineeringecapblcaklmtloofandberschejoçltitdkmarticularthanksareduetçjessrsdkbdscer andckpmithçfberschejoçltitdfçrtheirsuppçrtkqhanksarealsçduetçmrçfkskskqçrçpçvand arkgkbvesçfthecacultyçfbngineeringattherniversityçfieedsifçrtheirassistancewiththe çptimizatiçnwçrkk obcbobkcbp xnz oçcamkicerverajkidariupdkiandmelaikeomnmfptructuralanalysisçfmasçnryhistçrical cçnstructiçnskclassicalandadvancedapprçacheskarchives of Computational Methods in bngineeringntepfwovvjpork xoz parhçsisskomnnkcçmputatiçnalmçdellingçflçwbçndstrengthmasçnrykmhathesisi rniversityçfieedsiieedsirhk xpz fqapcaeommqfrabc rniversal aistinct blement Code ManualK Theory and BackgroundK ftascacçnsultingdrçupijinneapçlisirpak xqz CundallmKAKandeartmKENVTNFAcçmputermçdelfçrsimulatingprçgressivelargescale mçvementsinblçckyrçcksystemskfnwmrock of the pymposium of the fnternational pociety of oock MechanicsIkancyIcranceK xrz iemçsgkskeommtfkaiscreteelementmçdellingçfmasçnrystructureskfnternational gournal of Architectural eeritagenwvmjonpk xsz qçthakokilrbanwkandbagihkeommvfaiscreteelementanalysisçfamasçnryarchkmechanics oesearch Communications PSEQFWQSVJQUMK xtz whugevkeommofjicrçjmçdellingçfmasçnryshearpanelswithdistinctelementapprçachk Advances in Mechanics of ptructures and MaterialsNWNPNJNPSK xuz qçrçpçvskskanddarritypktkenvvufjaterialparameteridentificatiçnfçrmasçnrycçnstitutive mçdelskfnwmrock U th Canadian Masonry pymposiumgasperialbertaicanadairrnjrsok xvz içurenççmkbkenvvsfcçmputatiçnalstrategiesfçrmasçnrystructuresimhathesisiaelft rniversityçfqechnçlçgyiaelftiqheketherlandsk xnmz eendryaktkenvvufptructural masonrykmalgravejacmillaniiçndçnirhk xnnz oçtsgkdkenvvnfkumericalsimulatiçnçfcrackinginmasçnrykebolkipseofwqvjspk xnoz oçtsgkdkenvvtfptructural masonry: An experimental/numerical basis for practical design rulesk BalkemamublishersIqheketherlandsK xnpz parangapanidkisenkataramaokbkskandgagadishhkpkeommrfbrickjmçrtarbçndandmasçnry cçmpressivestrengthk gournal of Materials in bngineering NTEOFWOOVJOPT xnqz sandermluijmokenvvpfphearbehaviçurçfbedjçintskfnwmrock S th korth American Masonry ConferenceIarexelrniversityImhiladelphiaIrpAINORJNPSK xnrz AltairbngineeringEOMNMFrser s ManualI aesign of experimentsi lptimization and ptochastic studieskalterbngineeringfnckirpak xnsz qçrçpçvskskandvçshidackeommrfapplicatiçnçfadvancedçptimizatiçntechniquestç parameteranddamageidentificatiçnprçblemskfnwjrçzwkandptavrçulakisdkbkeedfmarameter fdentification of Materials and ptructureskcfpjkiftalyinttjospk RSS