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Chapter4SystemReliabilityAnalysisofStructuresChapter4:SystemReliabilityAnalysisofStructures4.2ReliabilityofSimpleSystems4.3ReliabilityBoundsforStructuralSystems4.1ElementsandSystemsContents4.1ElementsandSystemsChapter4

SystemReliabilityAnalysisofStructures4.1ElementsandSystems…1Therearetwoextremetypesofstructuralelementsthatarecommonlyconsideredinsystemreliabilityanalyses.Theseextremetypesarebrittlemembersandductilemembers.Amemberisclassifiedasbrittleifthememberbecomescompletelyineffectiveafteritfails.Amemberisclassifiedasductileifthememberisabletomaintainitsload-carryingcapacityafteritfails.LoadDisplacementDisplacementLoadBrittlememberDuctilemember4.1ElementsandSystems…2Inconductingsystemreliabilityanalysisofstructures,itisconvenienttodistinguishbrittleandductilemembersbyusingdifferentsymbols.LoadDisplacementDisplacementLoadBrittlememberDuctilemember4.2ReliabilityofSimpleSystemsChapter4

SystemReliabilityAnalysisofStructures4.2ReliabilityofSimpleSystems…14.2.1ReliabilityofSeriesSystems

Consideraseriessystemwithnelements.Letrepresenttheevent“safetyoftheithelement”,representtheevent“failureoftheithelement”.SandFrepresenttheevents“safety”and“failure”ofthesystemrespectively.Assumethatallfailureeventsareallstatisticallyindependent,wehaveTheprobabilityoffailureofthesystemislargerthanthatofeitherelement.4.2ReliabilityofSimpleSystems…24.2.2ReliabilityofParallelSystemsConsideraparallelsystemwithnperfectductileelements.Assumethatallfailureeventsareallstatisticallyindependent.

Theprobabilityoffailureofthesystemissmallerthantheprobabilityoffailureofeithercomponent.4.2ReliabilityofSimpleSystems…34.2.2ReliabilityofParallelSystems…Thesystemstrengthisthesumofallthestrengthsoftheelements,Consideraspecialsystemthathasnparallel,uncorrelated,identicallydistributedelements.Thecoefficientofvariationforasystemofnparallel,uncorrelated,identicallydistributedelementsissmallerthanthecoefficientofvariationofeachelement.4.2ReliabilityofSimpleSystems…44.2.3ReliabilityofHybridorCombinedSystems

parallelseriessystemseriesparallelsystemExample4.1~4.44.2ReliabilityofSimpleSystems…5Pleaserefertothetextbook“ReliabilityofStructures”byProfessorA.S.Nowak.P.257,Example9.1P.258,Example9.2P.261,Example9.3P.253,Example9.44.3ReliabilityBoundsforStructuralSystemsChapter4

SystemReliabilityAnalysisofStructures4.3ReliabilityBoundsforStructuralSystems…14.3.1SeriesSystemswithPositiveCorrelationForaseriessystemwithpositivecorrelationbetweenpairsofelements,thatis,,theprobabilityoffailuremustsatisfyThelowerboundistheprobabilityoffailurewhenallelementsarefullycorrelated,thatis,.Inthiscase,themostunsafeelementdeterminesthereliabilityofthesystem.Theupperboundistheprobabilityoffailurewhenallelementsarestatisticallyindependent,oruncorrelated,thatis,.Inthiscase,thesystemsurvivesonlyifalltheelementssurvive.4.3ReliabilityBoundsforStructuralSystems…24.3.2ParallelSystemswithPositiveCorrelationForaparallelsystemwithnductileelements,theboundsontheprobabilityoffailurefortheparallelsystemwithpositivecorrelationareasfollows:Theupperboundistheprobabilityoffailurewhenallelementsareperfectlycorrelated,thatis,.Inthiscase,thesafestelementdeterminesthereliabilityofthesystem.Thelowerboundistheprobabilityoffailurewhenallelementsarestatisticallyindependent,.Inthiscase,thesystemfailsonlyifalltheelementsfail.Example4.5~4.6Pleaserefertothetextbook“ReliabilityofStructures”byProfessorA.S.Nowak.P.268,Example9.5P.269,Example9.64.3ReliabilityBoundsforStructuralSystems…3Homework44.1Solvethep

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