抗力的可靠度模型和統(tǒng)計(jì)分析Chapter4:ProbabilityModels&StatisticalAnalysisofLoads4.2ProbabilityModelsofLoads4.4RepresentativeValuesofLoads4.1LoadsandActionsContents4.5CombinationofLoadEffects4.3StatisticalAnalysisofLoads4.1LoadsandActionsChapter4

ProbabilityModelsandStatisticalAnalysisofLoads4.1LoadsandActions…1Anactionis:Anassemblyofconcentratedordistributedmechanicalforcesactingonastructure(directactions),orThecauseofdeformationsimposedonthestructureorconstrainedinit(indirectactions)4.1.1DefinitionsofLoadsandActionsActionDirectAction—LoadIndirectAction4.1LoadsandActions…24.1.2TypesofActions1.ClassificationaccordingtothevariationoftheirmagnitudewithtimePermanentaction,whichislikelytoactcontinuouslythroughoutagivenreferenceperiodandforwhichvariationsinmagnitudewithtimearesmallcomparedwiththemeanvalue.4.1LoadsandActions…34.1.2TypesofActions1.ClassificationaccordingtothevariationoftheirmagnitudewithtimeVariableaction,forwhichthevariationinmagnitudewithtimeisneithernegligibleinrelationtothemeanvaluenormonotonic.Accidentalaction,whichisunlikelytooccurwithasignificantvalueonagivenstructureoveragivenreferenceperiod.Impact,Explosion,RareEarthquake,Tornado,Fire,SevereCorrosion,Flood,etc.4.1LoadsandActions…42.ClassificationaccordingtotheirvariationwithspaceFixedaction,whichhasafixeddistributiononastructure;Freeaction,whichmayhaveanarbitraryspatialdistributionoverthestructurewithingivenlimits.3.ClassificationaccordingtothestructuralresponseStaticaction,i.e.notcausingsignificantaccelerationofthestructuralorstructuralelements;Dynamicaction,i.e.causingsignificantaccelerationofthestructuralorstructuralelements.4.1.2TypesofActions4.1LoadsandActions…5LoadCodefortheDesignofBuildingStructures(GB50009-2001)4.1.3DesignCodesforLoadsandActions4.1LoadsandActions…6MinimumDesignLoadsforBuildingsandOtherStructures(ASCE7-05)4.1.3DesignCodesforLoadsandActions4.1LoadsandActions…7BS_EN_1991-1-1_Eurocode_1:GravityLoadsBS_EN_1991-1-2_Eurocode_1:FireActionsBS_EN_1991-1-3_Eurocode_1:SnowloadsBS_EN_1991-1-4_Eurocode_1:WindActionsBS_EN_1991-1-5_Eurocode_1:ThermalActionsBS_EN_1991-1-6_Eurocode_1:ActionsduringExecutionBS_EN_1991-1-7_Eurocode_1:AccidentalActions4.1.3DesignCodesforLoadsandActions4.1LoadsandActions…8ProbabilityModelCode(JCSS,2001):PartII4.1.3DesignCodesforLoadsandActions4.1LoadsandActions…94.1.3DesignCodesforLoadsandActionsProbabilityModelCode(JCSS,2001):PartII4.2ProbabilisticModelsofLoadsChapter4

ProbabilityModelsandStatisticalAnalysisofLoads4.2ProbabilityModelsofLoads…14.2.1StochasticProcessModelofLoadsActually,loadsarerandomvariablesvaryingwithtimeinthedesignreferenceperiodi.e.loadsarerandomprocess.4.2ProbabilityModelsofLoads…24.2.1StochasticProcessModelofLoadsActually,loadsarerandomvariablesvaryingwithtimeinthedesignreferenceperiodi.e.loadsarerandomprocess.excitationintensityOccurrenceTime4.2ProbabilityModelsofLoads…34.2.2StationaryBinomialRandomProcess(FBCModel)AssumptionsofStationaryBinomialRandomProcessIngeneral,loadsaretreatedasstationarybinomialrandomprocess.(1)Thedesignreferenceperiodisdividedintorequalintervals(2)Ineachinterval,theprobabilityoftheloadQoccurringisp,whiletheprobabilityofnotoccurringis.(3)Ineachinterval,whentheloadQoccurs,itsmagnitudeisanon-negativerandomvariable,anditsprobabilitydistributionsduringdifferentintervalsareidentical.LettheprobabilitydistributionoftheloadQinintervalbedenotedbyThefunctioniscalledanarbitrarypoint-in-time

probabilitydistributionoftheloadQ.(4)Themagnitudesoftheloadduringdifferentintervalsareindependentrandomvariables,andtheyarealsoindependentoftheeventthattheloadoccursintheseintervals.FeaturesofStationaryBinomialRandomProcess(1)Theparametersofthestationarybinomialrandomprocessare:Theparametersandaredeterminedbystatisticalsurveysorexperientialjudgments.ThedistributiontypeofshouldbevalidatedbyK-Stest.4.2ProbabilityModelsofLoads…44.2ProbabilityModelsofLoads…5(2)Thesamplefunctionofcanberepresentedbyarectanglewavefunctionwithequalintervals.4.2ProbabilityModelsofLoads…64.2.2RandomVariableModelofLoads1.PrincipleofTransformationRandomProcessLoadModelRandomVariableLoadModelTheloadQisrepresentedbythemaximumvalueoftherandomprocessloadduringthedesignreferenceperiod.Obviously,thevalueisarandomvariable.representsthemeantimesofoccurringinthedesignreferenceperiodT.2.TheProbabilitydistributionof4.2ProbabilityModelsofLoads…74.2.2RandomVariableModelofLoads2.TheProbabilitydistributionofCase14.2ProbabilityModelsofLoads…84.2.2RandomVariableModelofLoads2.TheProbabilitydistributionofCase24.2ProbabilityModelsofLoads…93.beingnormaldistribution4.2ProbabilityModelsofLoads…104.beingExtremeⅠdistribution4.3StatisticalAnalysisofLoadsChapter4

ProbabilityModelsandStatisticalAnalysisofLoads4.3StatisticalAnalysisofLoads…14.3.1StatisticalAnalysisofPermanentLoad4.3StatisticalAnalysisofLoads…24.3.2StatisticalAnalysisofVariantLoads1.SustainedLiveLoad4.3StatisticalAnalysisofLoads…32.TransientLiveLoad4.3StatisticalAnalysisofLoads…44.3.3StatisticalAnalysisofEnvironmentalLoads1.WindLoadDon’tconsiderwinddirectionConsiderwinddirection4.3StatisticalAnalysisofLoads…52.SnowLoad4.4RepresentativeValuesofLoadsChapter4

ProbabilityModelsandStatisticalAnalysisofLoads4.4RepresentativeValuesofLoads…14.4.1RepresentativeValuev.s.DesignValueofaLoadTherepresentativevalueofaloadisavalueusedfortheverificationofalimitstate.1.RepresentativeValueofaLoadRepresentativevaluesgenerallyconsistofcharacteristicvalues,frequentvalues,quasi-permanentvalues,combinationvalues.2.DesignValueofaLoadDesignvalueofaloadisavalueobtainedbymultiplyingtherepresentativevaluebythepartialfactor.4.4RepresentativeValuesofLoads…24.4.2CharacteristicValueThecharacteristicvalueofaloadisthemaximumvalueoftheloadthatactsonthestructureduringthedesignreferenceperiod.1.DefinitionItistheprincipalrepresentativevaluewhendesigningstructures.Theotherrepresentativevaluesareobtainedbyconversionofthecharacteristicvalue.Itischoseneitheronastatisticalbasis,sothatitcanbeconsideredtohaveaspecialprobabilityofnotbeingexceededtowardsunfavorablevaluesduringthedesignreferenceperiod;oronacquiredexperience;oronphysicalconstraints.Itisusedinbothultimatelimitstateverificationandserviceabilitylimitstateverification4.4RepresentativeValuesofLoads…3(1)Determinedbythereturnperiodofaload2.Methodswhere,iscalled(mean)returnperiod.where,iscalledyearlyexceedanceprobability.4.4RepresentativeValuesofLoads…4(2)Determinedbythepercentileof2.Methods…where,istheprobabilityofnotbeingexceededduringthereferenceperiod,itisalsocalled“guaranteeprobability”.4.4RepresentativeValuesofLoads…5Example4.1Pleaserefertothetextbook“Structural

Reliability”byProfessorOu&Duan.TurntoPage15,lookattheexample1.3carefully!4.4RepresentativeValuesofLoads…64.4.3FrequentValueThefrequentvalueofaloadisthefrequentoccurringloadthatactsonthestructureduringthedesignreferenceperiod.1.DefinitionItistherepresentativevalueofvariableloadswhencheckingtheserviceabilitylimitstatebythefrequent(shortterm)loadeffectcombinationrule.2.Method4.4RepresentativeValuesofLoads…74.4.3FrequentValueMethod1:4.4RepresentativeValuesofLoads…84.4.3FrequentValueMethod2:4.4RepresentativeValuesofLoads…94.4.4Quasi-permanentValueThequasi-permanentvalueofaloadistheoftenoccurringloadthatactsonthestructureduringthedesignreferenceperiod.1.DefinitionItistherepresentativevalueofvariableloadswhencheckingtheserviceabilitylimitstatebythecombinationrulesofquasi-permanentvaluecombinationandfrequentvaluecombination.2.Method4.4RepresentativeValuesofLoads…104.4.5CombinationValue4.4RepresentativeValuesofLoads…114.4.5CombinationValueWhentwoormoreloadsactonthestructureduringthedesignreferenceperiod,themaximumvaluesoftheseloadscannotoccursimultaneously,thentherepresentativevaluesofloadscanbetakenasitscombinationvalues.1.DefinitionItischosensothattheprobabilitythattheloadeffectvaluescausedbythecombinationwillbeexceededisapproximatelythesameaswhenasingleloadisconsidered.2.Method4.5CombinationofLoadEffectsChapter4

ProbabilityModelsandStatisticalAnalysisofLoads4.5CombinationofLoadEffects…14.5.1BasicConceptsThetotalloadQisasumofindividualloadcomponentssuchasdeadload,liveload,windload,snowload,seismicactions,etc.Theyallvarywithtime.Whenonlyonekindofthetime-dependentloadsactsonthestructure,itsmaximumvalueduringthereferenceperiodisthenusedinstructuraldesign.Whentwoormoretime-dependentloadsactonthestructure,theirmaximumvaluesduringthereferenceperiodcannotoccursimultaneously.Therefore,theloadeffectcombinationproblemshouldbeconsidered.4.5CombinationofLoadEffects…2Itisgenerallyassumedthattheloadeffectislinearlyrelatedtotheload:where,iscalledloadeffectcoefficient.Therefore,theloadcombinationproblemisconsistentwiththeloadeffectcombinationproblem.Theessentialpointoftheloadcombinationproblemistofindtheprobabilitycharacteristicsofthemaximumvalueofthetotalloadeffects:4.5CombinationofLoadEffects…34.5.2Turkstra’sRuleforLoadEffectCombinationIfaloadtakeitsmaximumloadeffectduringthedesignreferenceperiod,thentheother(n-1)loadstaketheirtransientvalues.4.5CombinationofLoadEffects…4Example4.2Pleaserefertothetextbook“ReliabilityofStructures”byProfessorA.S.Nowak.TurntoPage170,lookattheexample6.3carefully!4.5CombinationofLoadEffects…54.5.3FBCRuleforLoadEffectCombinationForanarbitraryload,itsmaximumloadeffectduringthedesignreferenceperiodiscombinedwithotherloadeffects.Foreachload,thedesignreferenceperiodTisdividedintoequalintervals.allloadsarereorderedfromsmalltolargeaccordingtothevaluesof,andletthetakeintegervalue.4.5CombinationofLoadEffects…64.5.3FBCRuleforLoadEffectCombination4.5CombinationofLoadEffects…74.5.3FBCRuleforLoadEffectCombination4.5CombinationofLoadEffects…84.5.4JCSS’sRuleforLoadEffectCombinationForanarbitraryload,itsmaximumloadeffectduringthedesignreferenceperiodiscombinedwithotherloadeffects.Foreachload,thedesignreferenceperiodTisdividedintoequalintervals.allloadsarereorderedfromsmalltolargeaccordingtothevaluesof,andletthetakeintegervalue.Fortheloadwhosenumbersofintervalsislargerthan,thelocalmaximumvalueduringt