外文翻译--桥梁使用系统可靠性评估 英文版.pdf

BridgeRatingUsingSystemReliabilityAssessment.II:ImprovementstoBridgeRatingPracticesNaiyuWang,M.ASCE1；BruceR.Ellingwood,Dist.M.ASCE2；andAbdul-HamidZureick,M.ASCE3Abstract:Thecurrentbridge-ratingprocessdescribedinAASHTOManualforBridgeEvaluation,FirstEditionpermitsratingstobedeterminedbyallowablestress,loadfactor,orloadandresistancefactormethods.Thesethreeratingmethodsmayleadtodifferentratedcapacitiesandpostinglimitsforthesamebridge,asituationthathasseriousimplicationswithregardtopublicsafetyandtheeconomicwell-beingofcommunitiesthatmaybeaffectedbybridgepostingsorclosures.Thispaperisthesecondoftwopapersthatsummarizearesearchprogramtodevelopimprovementstothebridge-ratingprocessbyusingstructuralreliabilitymethods.Thefirstpaperprovidedbackgroundontheresearchprogramandsummarizedacoordinatedprogramofloadtestingandanalysistosupportthereliabilityassessmentleadingtotherecommendedimprovements.Thissecondpaperpresentsthereliabilitybasisfortherecommendedloadrating,developsmethodsthatcloselycoupletheratingprocesstotheresultsofinsituinspectionandevaluation,andrecommendsspecificimprovementstocurrentbridge-ratingmethodsinaformatthatisconsistentwiththeloadandresistancefactorrating(LRFR)optionintheAASHTOManualforBridgeEvalu-ation.DOI:10.1061/(ASCE)BE.1943-5592.0000171.©2011AmericanSocietyofCivilEngineers.CEDatabasesubjectheadings:Concretebridges；Reinforcedconcrete；Prestressedconcrete；Loadfactors；Reliability；Steel；Ratings.Authorkeywords:Bridges(rating)；Concrete(reinforced)；Concrete(prestressed)；Conditionassessment；Loads(forces)；Reliability；Steel；structuralengineering.IntroductionTheAASHTOManualforBridgeEvaluation(MBE),FirstEdition(AASHTO2008)allowsbridgeratingstobedeterminedthroughthetraditionalallowablestressrating(ASR)orloadfactorrating(LFR)methodsorbythemorerecentloadandresistancefactorrating(LRFR)method,whichisconsistentwiththeAASHTOLRFDBridgeDesignSpecifications(2007).Thesethreeratingmethodsmayleadtodifferentratedcapacitiesandpostedlimitsforthesamebridge(NCHRP2001；Wangetal.2009),asituationthatcannotbejustifiedfromaprofessionalengineeringviewpointandhasimplicationsforthesafetyandeconomicwell-beingofthoseaffectedbybridgepostingsorclosures.Toaddressthisissue,theGeorgiaInstituteofTechnologyhasconductedamultiyearresearchprogramaimedatmakingimprovementstotheprocessbywhichtheconditionofexistingbridgestructuresinGeorgiaareassessed.Theendproductofthisresearchprogramissetofrecommendedguidelinesfortheevaluationofexistingbridges(Ellingwoodetal.2009).Theseguidelinesareestablishedbyaco-ordinatedprogramofloadtestingandadvancedfinite-elementmodeling,whichhavebeenintegratedwithinastructuralreliabilityframeworktodeterminepracticalbridge-ratingmethodsthatareconsistentwiththoseusedtodeveloptheAASHTOLRFDBridgeDesignSpecifications(AASHTO2007).Itisbelievedthatbridgeconstructionandratingpracticesaresimilarenoughinothernon-seismicareastomaketheinferences,conclusions,andrecommen-dationsvalidforlargeregionsinthecentralandeasternUnitedStates(CEUS).TherecentimplementationofLRFDanditscompanionratingmethod,LRFR,bothofwhichhavebeensupportedbystructuralreliabilitymethods,enablebridgedesignandconditionassessmenttobeplacedonamorerationalbasis.Notwithstandingthesead-vances,improvedtechniquesforevaluatingthebridgeinitsinsituconditionwouldminimizethelikelihoodofunnecessaryposting.Forexample,materialstrengthsinsitumaybevastlydifferentfromthestandardizedornominalvaluesassumedindesignandcurrentratingpracticesattributabletostrengthgainofconcreteononehandanddeteriorationattributabletoaggressiveattackfromphysi-calorchemicalmechanismsontheother.Satisfactoryperformanceofawell-maintainedbridgeoveraperiodofyearsofservicepro-videsadditionalinformationnotavailableatthedesignstagethatmightbetakenintoaccountinmakingdecisionsregardingpostingorupgrading.Investigatingbridgesystemreliabilityratherthansolelyrelyingoncomponent-basedratingmethodsmayalsobeofsignificantbenefit.Properconsiderationofthesefactorsislikelytocontributetoamorerealisticcapacityratingofexistingbridges.ThispaperisthesecondoftwocompanionpapersthatprovidethetechnicalbasesforproposedimprovementstothecurrentLRFRpractice.Thefirstpaper(Wangetal.2011)summarizedthecurrentbridge-ratingprocessandpracticesintheUnitedStates,andpresentedtheresultsofacoordinatedbridgetestingandanalysisprogramconductedtosupportrevisionstothecurrentratingpro-cedures.ThispaperdescribesthereliabilityanalysisframeworkthatprovidesthebasisforrecommendedimprovementstotheMBEandrecommendsspecificimprovementstotheMBEthataddresstheprecedingfactors.1SeniorStructuralEngineer,Simpson,Gumpertz,andHeger,Inc.,41SeyonSt.,Waltham,MA02453；formerly,GraduateResearchAssistant,SchoolofCivilandEnvironmentalEngineering,GeorgiaInstituteofTechnology.2Professor,SchoolofCivilandEnvironmentalEngineering,GeorgiaInstituteofTechnology,790AtlanticDr.,Atlanta,GA30332-0355(correspondingauthor).E-mail:ellingwoodgatech.edu3Professor,SchoolofCivilandEnvironmentalEngineering,GeorgiaInstituteofTechnology,790AtlanticDr.,Atlanta,GA30332-0355.Note.ThismanuscriptwassubmittedonMarch19,2010；approvedonAugust2,2010；publishedonlineonOctober14,2011.DiscussionperiodopenuntilApril1,2012；separatediscussionsmustbesubmittedforindi-vidualpapers.ThispaperispartoftheJournalofBridgeEngineering,Vol.16,No.6,November1,2011.©ASCE,ISSN1084-0702/2011/6-863871/$25.00.JOURNALOFBRIDGEENGINEERING©ASCE/NOVEMBER/DECEMBER2011/863Downloaded21Mar2012to180.95.224.53.RedistributionsubjecttoASCElicenseorcopyright.Visithttp:/www.ascelibrary.orgReliabilityBasesforBridgeLoadRatingBridgedesign,ascodifiedintheAASHTO-LRFDspecifications(2007),isestablishedbymodernprinciplesofstructuralreliabilityanalysis.Theprocessbywhichexistingbridgesareratedmustbeconsistentwiththoseprinciples.Uncertaintiesintheperfor-manceofanexistingbridgearisefromvariationsinloads,materialstrengthproperties,dimensions,naturalandartificialhazards,insufficientknowledge,andhumanerrorsindesignandconstruc-tion(Ellingwoodetal.1982；Galambosetal.1982；Nowak1999).Probability-basedlimitstatesdesign/evaluationconceptsprovidearationalandpowerfultheoreticalbasisforhandlingtheseuncertain-tiesinbridgeevaluation.ThelimitstatesforbridgedesignandevaluationcanbedefinedinthegeneralformGðXÞ¼0ð1ÞwhereX¼ðX1；X2；X3；XnÞ=loadandresistancerandomvariables.Onthebasisofbridgeperformanceobjectives,theselimitstatesmayrelatetostrength(forpublicsafety)ortoexcessivedeformation,cracking,wearofthetrafficsurface,orothersourcesoffunctionalimpairment.Astateofunsatisfactoryperformanceisdefined,byconvention,whenGðXÞ<0.Thus,theprobabilityoffailurecanbeestimatedasPf¼P½GðXÞ<0C138¼ZfXðxÞdxð2ÞwherefXðxÞ=jointdensityfunctionofX；and=failuredomaininwhichGðxÞ<0.Inmodernfirst-order(FO)reliabilityanalysis(Melchers1999),Eq.(2)isoftenapproximatedbyPf¼ðC0Þð3ÞwhereðÞ=standardnormaldistributionfunction；and=reliabilityindex.Forwell-behavedlimitstates,Eq.(3)usuallyisanexcellentapproximationtoEq.(2),andandPfcanbeusedinterchangeablyasreliabilitymeasures(Ellingwood2000).WhenthefailuresurfaceinEq.(1)iscomplexorwhenthereliabilityofastructuralsystem,inwhichthestructuralbehaviorismodeledthroughfinite-elementanalysis,isofinterest,Eq.(2)canbeevalu-atedefficientlybyMonteCarlo(MC)simulation.TheAASHTOLRFDBridgeDesignSpecifications(2007)areestablishedonFOreliabilityanalysis,appliedtoindividualgirders(Nowak1999；KimandNowak1997；TabshandNowak1991).Withthesupportingprobabilisticmodelingofresistanceandloadterms(Nowak1993；BartlettandMcGregor1996；MosesandVerma1987),anexaminationofexistingbridgedesignpracticesledtoatargetreliabilityindex,equalto3.5basedona75-yearserviceperiod(Nowak1999,Moses2001).Consistentwithsuchreliability-basedperformanceobjective,theAASHTO-LRFDspec-ificationsstipulatethatinthedesignofnewbridges1:25Dþ1:5DAþ1:75ðLþIÞ<Rnð4ÞwhereD=deadloadexcludingweightofthewearingsurface；DA=weightofthewearingsurface(asphalt)；(LþI)representsliveloadincludingimpact；Rn=designstrength,inwhichRn=nominalresistance；and=resistancefactorwhichdependsontheparticu-larlimitstateofinterest.Thisequationisfamiliartomostdesigners.Whenthereliabilityofanexistingbridgeisconsidered,allow-anceshouldbemadeforthespecificknowledgeregardingitsstruc-turaldetailsandpastperformance.Fieldinspectiondata,loadtesting,materialtests,ortrafficsurveys,ifavailable,canbeutilizedtomodifytheprobabilitydistributionsdescribingthestructuralbehaviorandresponseinEq.(2).Themetricforacceptableperfor-manceisobtainedbymodifyingEq.(2)toreflecttheadditionalinformationgatheredPf¼P½GðXÞ<0jHC138<PTð5ÞwhereHrepresentswhatislearnedfromprevioussuccessfulperformance,in-serviceinspection,andsupportinginsitutesting,ifany.Thetargetprobability,PT,shoulddependontheeconomicsofrehabilitation/repair,consequencesoffutureoutages,andthebridgeratingsought.IntheAASHTO-LRFRmethod(2007),thetargetfordesignlevelcheckingbyusingHL-93loadmodel(atinventorylevel)is3.5,whichiscomparabletothereliabilityfornewbridges,whereasthetargetforHL-93operatinglevelandforlegal,andpermitloadsisreducedto2.5owingtothereducedloadmodelandreducedexposureperiod(5years)(Moses2001).ThepresenceofHinEq.(5)isaconceptualdeparturefromEqs.(2)and(3),whichprovidethebasisforLRFD.Forexample,trafficdemandsonbridgeslocatedindifferentplacesinthehigh-waysystemmaybedifferent.Totakethissituationintoaccount,LRFRintroducesasetoflive-loadfactorsforthelegalloadrating,whichdependontheinsitutrafficdescribedbytheaveragedailytrucktraffic(ADTT).Furthermore,thecomponentnominalresis-tanceinLRFRisfactoredbyasystemfactorsandamemberconditionfactorcinadditiontothebasicresistancefactorforaparticularcomponentlimitstate.Thesystemfactordependsontheperceivedredundancylevelofagivenbridgeinitsrating,whereastheconditionfactoristoaccountforthebridgessite-specificdeteriorationcondition,andpurportstoincludetheaddi-tionaluncertaintybecauseofanydeteriorationthatmaybepresent.ThebasisfortheLRFRtabulatedvaluesforcwillbefurtherexaminedlaterinthispaper.TheLRFRoptionintheAASHTOMBEextendsthelimitstatedesignphilosophytothebridgeevaluationprocessinanattempttoachieveauniformtargetlevelofsafetyforexistinghighwaybridgesystems.However,theuncertaintymodelsofloadandresistanceembeddedintheLRFRratingformatrepresenttypicalvaluesforalargepopulationofbridgesinvolvingdifferentmaterials,con-structionpractices,andsite-specifictrafficconditions.AlthoughtheLRFRlive-loadmodelhasbeenmodifiedforsomeofthespe-cificcasesasdiscussedpreviously,thebridgeresistancemodelshouldalsobe“customized”foranindividualbridgebyincorpo-ratingavailablesite-specificknowledgetoreflectthefactthateachbridgeisuniqueinitsas-builtcondition.Aratingprocedurethatdoesnotincorporateinsitudataproperlymayresultininaccurateratings(andconsequentunnecessaryrehabilitationorpostingcosts)forotherwisewell-maintainedbridges,asindicatedbymanyloadtests(NowakandTharmabala1988；BakhtandJaeger1990；Mosesetal.1994；FuandTang1995；Faberetal.2000；Barker2001；Bhattacharyaetal.2005).Improvementsinpracticalguidancewouldpermitthebridgeengineertoincludemoresite-specificknowledgeinthebridge-ratingprocesstoachieverealisticevalu-ationsofthebridgeperformance.Thisguidancemusthaveastruc-turalreliabilitybasis.ImprovementsinBridgeRatingbyUsingReliability-BasedMethodsInthissection,thebridgeratingsinlightofthereliability-basedupdatingofin-servicestrengthdescribedintheprevioussectionareexamined.Thepossibilitiesofincorporatingavailablesite-specificdataobtainedfrommaterialtests,loadtests,advanced864/JOURNALOFBRIDGEENGINEERING©ASCE/NOVEMBER/DECEMBER2011Downloaded21Mar2012to180.95.224.53.RedistributionsubjecttoASCElicenseorcopyright.Visithttp:/www.ascelibrary.orgstructuralanalysis,andsuccessfulserviceperformancetomakefur-therrecommendationsforimprovingratinganalysisareexplored.IncorporationofInSituMaterialTestingThecompanionpapersummarizedtheloadtestofBridgeID129-0045,areinforcedconcreteT-beambridgethatwasdesignedaccordingtotheAASHTO1953designspecificationforH-15loadingandwasconstructedin1957.Thespecified28-daycom-pressionstrengthoftheconcretewas17.2MPa(2,500psi),whereastheyieldstrengthofthereinforcementwas276MPa(40ksi).Thescheduleddemolitionofthisbridgeprovidedanop-portunitytosecuredrilledcorestodeterminethestatisticalproper-tiesoftheinsitustrengthofthe51-yearoldconcreteinthebridge.Four-inchdiameterdrilledcoresweretakenfromtheslabofthebridgebeforeitsdemolition.Sevencoresweretakenfromtheslabatsevendifferentlocationsalongboththelengthandwidthofthebridge.Coresalsoweretakenfromthreeofthegirdersthatwereingoodconditionafterdemolition；thesewerecutinto203mm(8-in.)lengthsandthejaggedendsweresmoothedandcapped,resultinginatotalof14girdertestcylinders.Testsofthese102×203mm(4×8in.)cylindersconformedtoASTMStandardC42(ASTM1995)andtheresultsarepresentedinTable1.Ananalysisofthesedataindicatednostatisticallysignificantdifferenceintheconcretecompressionstrengthinthegirdersandslab,andthedatawerethereforecombinedforfurtheranalysis.Themean(average)com-pressionstrengthoftheconcreteis33MPa(4,820psi)andthecoefficientofvariation(COV)is12%,whichisrepresentativeofgood-qualityconcrete(BartlettandMacGregor1996).Themeanstrengthis1.93timesthespecifiedcompressionstrengthofthecon-crete.Thisincreaseincompressionstrengthoveraperiodofmorethan50yearsistypicaloftheincreasesfoundforgood-qualitycon-cretebyotherinvestigators(WashaandWendt1975).Iftheseresultsaretypicalofwell-maintainedolderconcretebridges,theinsituconcretestrengthislikelytobesubstantiallygreaterthanthe28-daystrengththatiscustomarilyspecifiedforbridgedesignorconditionevaluation.Accordingly,thebridgeen-gineershouldbeprovidedincentivesintheratingcriteriatorateabridgebyusingthebestpossibleinformationfrominsitumaterialstrengthtestingwheneverfeasible(Ellingwoodetal.2009).Itiscustomarytobasethespecifiedcompressionstrengthofconcreteonthe10thpercentileofanormaldistributionofcylinderstrengths(Standard318-05；ACI2005).Asuitableestimateforthis10thper-centilebasedonasmallsampleofdataisprovidedbyfc¼C22Xð1C0kVÞð6ÞwhereC22X=samplemean；V=samplecoefficientofvariation；andk¼p%lowerconfidenceintervalonthe10thpercentilecompres-sionstrength.Byusingthe21testsfromBridgeID129-0045withp%¼75%asanexample,k=1.520(Montgomery1996)andfccanbeexpressedasfc¼ð11:520×0:12Þ×4；820¼3；941psi(27.17MPa),avaluethatis58%higherthanthe17.2MPa(2,500psi)thatotherwisewouldbeusedintheratingcalculations.IntheFEmodelingofthisbridgethatprecededthesestrengthtests,theconcretecompressionstrengthwassetat17.2MPa(2,500psi),whichwastheonlyinformationavailablebeforethematerialtest.Todeterminetheimpactofusingtheactualconcretestrengthinanolderbridgeontheratingprocess,thefinite-elementmodelwasrevisedtoaccountfortheincreasedconcretecompres-sionstrength(andthecorrespondingincreaseinstiffness)intotheanalysisofthebridge.Onlyamodestenhancementintheestimatedbridgecapacityinflexurewasobtained,buta34%increasewasachievedintheshearcapacityratingsforthegirdersbyusingtheresultsofTable1.BridgeSystemReliabilityAssessmentontheBasisofStaticPush-DownAnalysisAlthoughcomponent-baseddesignofanewbridgeprovidesad-equatesafetyatreasonablecost,component-basedevaluationofanexistingbridgeforratingpurposesmaybeoverlyconservativeandresultinunnecessaryrepairorpostingcosts.Itispreferabletoperformloadratingregardingbridgepostingorroadclosurethroughasystem-levelanalysis.Aproperlyconductedproofloadtestcanbeaneffectivewaytolearnthebridgesstructuralperfor-manceasasystemandtoupdatethebridgeloadcapacityassess-mentinsituationsinwhichtheanalyticalapproachproduceslowratings,orstructuralanalysisisdifficulttoperformbecauseofdeteriorationorlackofdocumentation(SarafandNowak1998).However,aproofloadtestrepresentsasignificantinvestmentincapital,time,andpersonnel,andthetrade-offbetweentheinforma-tiongainandtheriskofdamagingthebridgeduringthetestmustbeconsidered.ProoftestsarerarelyconductedbythestateDOTs(Wangetal.2009)forratingpurposes.Oneofthekeyconclusionsfromthecompanionpaper(Wangetal.2011),inwhichbridgeresponsemeasurementsobtainedfromtheloadtestsofthefourbridgeswerecomparedwiththeresultsoffinite-elementanalysesofthosebridgeswithABAQUS(2006),wasthatthefinite-elementmodelingprocedurewassufficientforconductingvirtualloadtestsofsimilarbridges.Thesevirtualloadtestscanprovidethebasisfordevelopingrecommendationsforimprovingguidelinesforbridgeratingsbyusingstructuralreli-abilityprinciples.Asnotedintheintroductorysection,suchguide-linesrequirethebridgetobemodeledasastructuralsystemtoproperlyidentifytheperformancelimitstatesonwhichsuchguide-linesaretobebased.Toidentifysuchperformancelimitstatesandtogainarealisticappraisaloftheconservatisminherentincurrentbridgedesignandconditionratingprocedures,aseriesofstaticpush-downanalysesofthefourbridgeswasperformed.Theseanalysesareaimedatdeterminingtheactualstructuralbehavioroftypicalbridgeswhenloadedwellbeyondtheirdesignlimit；asasidelight,theyprovideadditionalinformationtosupportrationalevaluationofpermitloadapplications(section6A.4.5intheManualofBridgeEvaluation).Inapush-downanalysis,tworatingvehiclesareplacedside-by-sideonthebridgeinapositionthatmaximizestheresponsequan-tityofinterestintheevaluation(e.g.,maximummoment,shear,anddeflection).Theloadsarethenscaledupwardstaticallyandtheper-formanceofthebridgesystemismonitored.Thedeadweightofthebridgestructureisincludedintheanalysis.Theresponseisinitiallyelastic.Asthestaticloadincreases,however,elementsofthebridgestructurebegintoyield,crack,orbuckle,andthegeneralizedload-deflectionbehaviorbecomesnonlinear.Ifthebridgestructureisredundantandthestructuralelementbehaviorsareductile,substan-tialloadredistributionmayoccur.Atsomepoint,however,asmallincrementinstaticloadleadstoalargeincrementindisplacement.Atthatpoint,thebridgehasreacheditspracticalload-carryinglimit,andisatastateofincipientcollapse.Table1.CompressionTestsof4×8in:CoresDrilledfromRCConcreteBridge(ID129-0045)SourceNumberAverage(psi)Standarddeviation(psi)CoefficientofvariationGirder144,8806030.12Slab74,6985730.12Overall214,8205860.12Note:1psi¼6:9Pa.JOURNALOFBRIDGEENGINEERING©ASCE/NOVEMBER/DECEMBER2011/865Downloaded21Mar2012to180.95.224.53.RedistributionsubjecttoASCElicenseorcopyright.Visithttp:/www.ascelibrary.orgThestaticpush-downanalysisisillustratedinFig.1fortheRCT-beambridge(ID129-0045).TheFEmodelingwasperformedwithABAQUS(2006),withrandommaterialpropertiesdeterminedbytheirrespectivemeanvalues.Thepointofinitialyieldingoccursatapproximately4.31timestheHS20-44designloadconfigura-tion,atadeflectionofapproximately36mm(1.4in.),whichisequaltoapproximately1=345timesthespan.Theultimatelive-loadcapacityofthebridgeisapproximately4.8timestheappliedHS20-44loads.FromFig.1,this52-year-oldbridgeshowsacon-siderabledegreeofductilityinbehavior.ThelevelofloadimposedbythefourfullyloadedtrucksduringtheloadtestdescribedinthecompanionpaperisalsoshowninFig.1；thetestload(inmaximumgirdermoment)wasapproximately1.3timesthetwoside-by-sideHS20-44loads.Thecapacityofthisbridgesystemissubstantiallyinexcessofwhatagirder-basedcalculationwouldindicate.Similarpush-downanalyseswereperformedontheotherbridgesdescribedinthecompanionpaper,yieldingtheresultssummarizedinTable2.Theelasticrangesofallfourbridgesareinexcessof4timesthedesignloadlevel,indicatingthelevelofconservatismassociatedwithtraditionaldesignandratingprocedures.AspartoftheefforttodeveloptheAASHTOLRFDBridgeDesignSpecifications,extensivedatabasesweredevelopedtodescribethestrengthofindividualbridgegirdersandvehicleliveloadsprobabilistically(Nowak1999；Moses2001).(TheHL-93live-loadmodelisanoutgrowthofthispreviousresearch.)Thatresearchfocusedonthecapacityofindividualbridgegirders；sys-temeffectswereincludedindirectlyandapproximatelythroughnewgirderdistributionfactorsthatweredevelopedinthecourseoftheproject.Thecapacityofabridgestructuralsystemislikelytobedifferentfromthecapacitypredictedfromananalysisofindi-vidualgirders.Todeterminetheadditionallevelofconservatism(ifany)thatarisesfromsystembehavior,afinite-element-basedsystemreliabilityanalysisofallfourstudybridgeswasconducted.Thissystemreliabilityanalysisprovidesadditionalperspectiveonthe(unknown)levelofconservatismfurnishedbythecurrentgenerationofreliability-basedconditionevaluationandratingpro-ceduresembodiedintheAASHTOManualforBridgeEvaluation,andhasimplicationsfortheuseofsuchmethodsinpermitratingsforextremevehicleloads.ToacceleratetheFE-basedreliabilityanalysis,efficientFEmodelsofthesamplebridgesweredevelopedwiththeopen-sourceplatform,OpenSeesVersion2.2.2.ThemoredetailedABAQUSmodels,whichhadbeenvalidatedfromtheload-testresults,wereemployedtoconfirmthebridgestructuralbehaviorpredictedbytheOpenSeesmodelsasthesystemwasloadedbeyonditsdesignlimit.ByusingtheRCT-beambridgeagainasanexample,Fig.1illus-tratestheconsistencyachievedbetweentheABAQUS(2006)andtheOpenSeesmodelsthroughacompletepush-downanalysis,inwhichthebridgeisloadedwellintotheinelasticrange.Followingthisvalidation,thesystemperformanceofthesamplebridgeswascharacterizedstatisticallybypropagatingtheuncertaintiesinmaterialstrengths,stiffnesses,andgeometrythroughtheOpenSeesanalysisbyusingaLatinHypercubeSamplingtechnique(ImamandConover1980)toachieveefficientcoverageofthesamplespacewitharelativelyfewFEanalyses.TherandomvariablesinvolvedintheseFEanalysestocapturebridgestructuralperfor-mancearedescribedwithstatisticsdefinedintheLRFDdatabasesmentionedpreviously.Thelimitstateofperformancewasassumedasthepointatwhichthebridgesystemexitstheelasticrange,asidentifiedfromitsload-deflectioncurve(seeFig.1).Theflexuralcapacitiessodeterminedfromthissystemreliabil-ityanalysiswererank-orderedandplottedonlognormalprobabilitypaper,asillustratedinFig.2forthestraightapproachRCbridge(ID129-0045).Thelognormaldistributionprovidesagoodfittothesedata.Themeanandcoefficientofvariationinthesystemcapacityofthisbridge(atfirstyield)are4.31timestheappliedFig.1.Push-downanalysisofRCT-beambridgeID129-0045(1in¼25:4mm)Table2.AnalysisofBridgeCapacityDeterminedasthePointofFirstYieldBridgeIDCountyTypeDesignloadLoadfactorondesignloadLoadfactoronHS-20129-0045-0GordonRC；Tstraight；notpostedH-157.464.31015-0108-0BartowRC；Tskewed；postedHS-156.004.50223-0034-0PauldingPrestressed；straight；notpostedHS-205.945.94085-0018-0DawsonSteelgirder；straight；postedH-159.935.37Fig.2.LognormalfitofthebridgesystemresistanceoftheRCBridge(ID129-0045)866/JOURNALOFBRIDGEENGINEERING©ASCE/NOVEMBER/DECEMBER2011Downloaded21Mar2012to180.95.224.53.RedistributionsubjecttoASCElicenseorcopyright.Visithttp:/www.ascelibrary.org