ConsiderationofuncertaintiesinseismicanalysisofcoupledbuildingpipingsystemsOriginalResearchArticle

Inthispaper,wepresentananalyticalstudyforincorporatingtheeffectofuncertaintiesinmodalpropertiesofuncoupledprimaryandsecondarysystemsintheseismicanalysisofnon-classicallydampedcoupledsystemssuchasbuildingpipingbyresponsespectrummethod.MonteCarlosimulationisusedtoillustratethatthesecondarysystemdesignresponsewhendefinedatanon-exceedenceprobabilityof0.84overtheindividualresponsesobtainedfrommultipleresponsespectrumanalysesbyconsideringuncertaintiesinmodalparametersisexcessivelyhigherthanthedesignresponsespecifiedatthesamenon-exceedenceprobabilityovertheresponsesobtainedfrommultipletimehistoryanalyses.Thisissobecausetheearthquakeinputinaresponsespectrummethodischaracterizedbyadesignspectrumwhichbyitselfisspecifiedatanon-exceedenceprobabilityof0.84overthemultipletimehistorieswithnormalizedpeakgroundacceleration.Accurateevaluationofdesignresponseatanon-exceedenceprobabilityof0.84intheresponsespectrummethodrequiresthattheindividualmodalresponsesbedefinedatappropriateprobabilitylevelsthatmaybedifferentthantheconventionallyusednon-exceedenceprobabilityvalueof0.84.Therequiredprobabilityvaluesareevaluatedbyusingfirstorderreliabilitymethod.Itisshownthatthemodalresponses,whendefinedatanon-exceedenceprobabilityof0.84,wouldgiverelativelyaccuratevaluesofdesignresponseonlyiftheindividualmodesareperfectlycorrelatedorasinglemodecontributestotheparticularresponsequantityofinterest.Forallothercases,thedesignresponsewouldbeexcessivelyhigh.Theaccurateprobabilityvaluesneededtospecifyeachmodalresponseevaluatedusingthefirstorderreliabilitymethodcannotbeincorporateddirectlyinaresponsespectrumanalysisduetocomputationalinefficiency.Twosimplifiedmethods,basedontotalprobabilitytheorem,aredevelopedinthispapertoovercomethislimitation.Itisshownthatthesemethodsgivedesignresponsevaluesthatareveryclosetothetruevaluesobtainedfrommultipletimehistoryanalyses.