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1、DefmationAnalysisofPrestressedContinuousSteelConcreteCompositeBeamsJianguoNie1MuxuanTao2C.S.Cai3ShaojingLi4Abstract:Defmationcalculationofprestressedcontinuoussteelconcretecompositebeamsaccountingftheslipeffectbetweenthe
2、steelconcreteinterfaceunderserviceloadsisanalyzed.Asimplifiedanalyticalmodelispresented.Basedonthismodelfmulasfpredictingthecrackingregionofconcreteslabneartheinterisupptstheincreaseoftheprestressingtendonfcearederived.A
3、tablefcalculatingthespandeflectionoftwospanprestressedcontinuouscompositebeamsisalsoproposed.Itisfoundthattheinternalfceoftheprestressingtendonunderserviceloadscanbeaccuratelycalculatedusingtheproposedfmulas.Byigningthei
4、ncreaseofthetendonfcethecalculateddeflectionareoverestimatedconsideringtheincreaseofthetendonfcecansignificantlyimprovetheaccuracyofanalyticalpredictions.Asthecalculatedvaluesshowgoodagreementwiththetestresultsthepropose
5、dfmulascanbereliablyappliedtothedefmationanalysisofprestressedcontinuouscompositebeams.Finallybasedonthefmulasfcalculatingthedefmationoftwospanprestressedcontinuouscompositebeamsageneralmethodfdefmationanalysisofprestres
6、sedcontinuouscompositebeamsisproposed.DOI:10.1061?E?ST.1943541X.0000067CEDatabasesubjectheadings:PrestressedconcreteCompositebeamsDefmationDeflectionCrackingConcreteslabsContinuousbeams.IntroductionContinuoussteelconcret
7、ecompositebeamsarewidelyusedinbuildingsbridgesfhigherspandepthratioslessdeflectionetc.whichresultsinsuperieconomicalperfmancecomparedwithsimplysupptedcompositebeams.Fcontinuouscompositebeamsnegativebendingnearinterisuppt
8、swillresultinearlycrackingofconcreteslabreductionofstiffness.Whenbeamsaredesignedfspanlengthsloadsgreaterthanusualtherequirementofserviceabilitylimitstateduetounacceptabledeflectioncrackwidthwouldrequireusingprestressing
9、technique.Comparedwithconventionalsteelconcretecompositebeamsprestressedsteelconcretecompositebeamshaveafewmajadvantages:?1?extendingtheelasticrangeofstructuralbehavi?2?increasingtheultimateloadingcapacity?3?decreasingth
10、edefmationunderserviceloads?4?beingfavableincrackwidthcontrol?5?fullyusingthematerialsthusreducingthestructuralheightoveralldeadload?6?improvingthefatiguefracturebehavi.SinceSzilard?1959?suggestedamethodfthedesignanalysi
11、sofprestressedsteelconcretecompositebeamsconsideringtheeffectsofconcreteshrinkagecreepmanyresearchershavedevelopedmethodsfanalyzingthebehaviofsimplysupptedprestressedcompositebeams?Hoadley1963Klaiberetal.1982Dunkeretal.1
12、986Saadatmanesh1986Saadatmaneshetal.1989abcAlbrechtetal.1995Nieetal.2007?.Howevercontinuousprestressedcompositebeamshavenotbeenresearcheduntilthelate1980s?TroitskyRabbani1987Troitsky1990Dall’AstaDezi1998Ayyubetal.1990199
13、2abDall’AstaZona2005?.Asaresultprestressedcontinuouscompositebeamshavenotwidelybeenusedpartlyduetothelackofdesignthey.Infactthebehaviofprestressedcontinuouscompositebeamsdependsontheinteractionbetweenfourmaincomponents:t
14、hereinfcedconcreteslabthesteelprofileofbeamstheshearconnectionstheprestressingtendonswhichmakesprestressedcontinuouscompositebeamsmecomplexthanconventionalones.Dall’AstaZona?2005?proposedanonlinearfiniteelementmodelsimul
15、atingthebehaviofprestressedcontinuouscompositebeamsaccurately.Thisnumericalapproachisaverypowerfulresearchtoolfanalyzingtheexternallyprestressedstructuresbutitperhapsistoocomplicatedfaroutinedesignpractice.Asprestressing
16、techniqueisaneffectivewaytoreducedefmationcrackwidthunderserviceloadsparticularattentionhastobepaidtothedefmationcalculationofprestressingcontinuouscompositebeams.Themainobjectiveofthisresearchistodevelopcalculationmetho
17、dsfthedefmationofprestressingcontinuouscompositebeamsbasedonthereducedstiffness1ProfessDept.ofCivilEngineeringKeyLabatyofStructuralEngineeringVibrationofChinaEducationMinistryTsinghuaUniv.Beijing100084China.2Ph.D.CidateD
18、ept.ofCivilEngineeringKeyLabatyofStructuralEngineeringVibrationofChinaEducationMinistryTsinghuaUniv.Beijing100084China?crespondingauth?.Email:ghua.3AssociateProfessDept.ofCivilEnvironmentalEngineeringLouisianaStateUniv.B
19、atonRougeLA70803presentlyAdjunctProfessSchoolofCivilEngineeringArchitectureChangshaUniv.ofScienceTechnologyChangshaChina.4FmerlyGraduateStudentDept.ofCivilEngineeringKeyLaboratyofStructuralEngineeringVibrationofChinaEduc
20、ationMinistryTsinghuaUniv.Beijing100084China.Note.ThismanuwassubmittedonAugust102008approvedonApril202009publishedonlineonOctober152009.DiscussionperiodopenuntilApril12010separatediscussionsmustbesubmittedfindividualpape
21、rs.ThispaperispartoftheJournalofStructuralEngineeringVol.135No.11November12009.?EISSN073394452009111377–1389$25.00.JOURNALOFSTRUCTURALENGINEERING?ENOVEMBER20091377Downloaded19Feb2012to218.197.119.130.Redistributionsubjec
22、ttoElicensecopyright.Visit:www.elibrary.gPredictionofCrackingRegionofConcreteSlabInthispartthelengthofcrackingregionofconcreteslaboverinterisupptswillbetheeticallyanalyzedbasedonthecalculationmodelshowninFig.4?a?.Afterth
23、einitialfceT0isprestressedastructuralanalysisgivesthesaggingmomentattheinterisupptasMT0=T0e0232m?1?m?T0?L?1?Accdinglytheinitialcompressivestressatthetopofconcreteslabattheinterisupptiscalculatedas?pc=MT0WT0A=T0e02W3m?1?m
24、?T0?L2WT0A?2?whereW=sectionmodulusoftransfmedcompositesectionatthetopofconcreteflangeA=crosssectionalareaoftransfmedsection.ThemomentneededtoeliminatethecompressivestressattheinterisupptisobtainedasM0=?pcW=12T0e032m?1?m?
25、T0?LT0AW?3?Theprestressingdegreeisdefinedas?=M0Mk?4?whereMk=momentattheinterisupptduetoserviceloadPk?excludingprestressingeffect?.IntroducingEq.?3?intoEq.?4?givesMk=T0e02?3m?1?m?T0?L2?T0WA??5?Itisfoundinexperimentsthatth
26、emomentredistributioncoefficient?aattheinterisupptcanreachabout15%underserviceloadconditions.Therefe15%isusedtocalculatethemomentattheinterisupptunderserviceloadsapproximatelyasMk=0.85Mek=5140m?1?m?PkL?6?whereMek=momentd
27、uetoPkigningthemomentredistribution.TherelationshipbetweentheserviceloadtheinitialprestressingfcecanbederivedusingEqs.?5??6?asPk=40T051m?1?m??L?e02WA?2017T0???7?Undertheapplicationofexternalfceprestressingfcethedistribut
28、ionofmomentalongthebeamisshownasFigs.4?bc?respectively.ThetensionstressatthetopofconcreteattheboundaryofthecrackingregionequalstozerowhichleadstoMT?x=nL?MP?x=nL?W?TA=0?8?whereT=tendonfceunderserviceloadconditions.Compare
29、dwiththeinitialprestressingfcetheincreaseoftendonfceisrelativelysmallTcanbetakenproximatelyasT0MT?x?=momentdistributionalongthebeamduetotheprestressingfceMP?x?=momentdistributionalongthebeamduetotheserviceload.Theyarecal
30、culatedasMT?x?=32Te0Lx?12Te0??32m232m1?T?x?32m?1?m?T?L?0?x?nL??9?MP?x?=?5140m2?5140m?1?Pkx5140m?1?m?PkL?0?x?nL??10?IntroducingEqs.?7??9??10?intoEq.?8?leadstotheexpressionofnasafunctionof?n=A???1?B??CA?11?whereABCcanbecal
31、culatedasA=12WAe032?1?m?m?Le0B=32??32m321m?m?Le0C=51m2?51m?4051m2?51mFromEq.?11?wecanseethatthemainfactsinfluencingtherangeofconcretecrackingregionincludetheprestressingdegree?theparameterW?Ae0?theparameterm?Le0theloadin
32、gpositionm.TheireffectsonnareplottedinFigs.5–7.FromFigs.5–7wecanseethatthelengthofconcretecrackingregionfallsmemequicklyastheprestressingdegreerises.Whentheprestressingdegreeistakenas1thelengthofconcretecrackingregionisz
33、eroreferredtoasfullyprestressedcompositebeams.Similarlyazerooftheprestressingdegreeresultsinthelengthofconcretecrackingregionbeingas1Cwhichdependsonlyontheloadingpositionmcrespondstoconventionalcompositebeams.Fig.5indica
34、teshownvarieswithintheusualrangeofparameterW?Ae0?whentheotherparametersarefixed.ItisFig.4.Theeticalanalysisofthelengthofcrackingregionofconcreteslab:?a?calculationmodeloftwospanprestressedcontinuouscompositebeams?b?momen
35、tdistributionduetoprestressingtendonfce?c?momentdistributionduetoexternalloadsJOURNALOFSTRUCTURALENGINEERING?ENOVEMBER20091379Downloaded19Feb2012to218.197.119.130.RedistributionsubjecttoElicensecopyright.Visit:www.elibra
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