土木工程专业毕业设计英文翻译.docx

土木工程专业毕业设计英文翻译.docx

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土木工程专业毕业设计英文翻译

CriticalReviewofDeflectionFormulasforFRP-RCMembers

CarlosMota1;SandeeAlminar2;andDagmarSvecova3

1ResearchAssistant,Dept.ofCivilEngineering,Univ.ofManitoba,

WinnipegMB,CanadaR3T5V6.

2ResearchAssistant,Dept.ofCivilEngineering,Univ.ofManitoba,

WinnipegMB,CanadaR3T5V6.

3AssociateProfessor,Dept.ofCivilEngineering,Univ.ofManitoba,

WinnipegMB,CanadaR3T5V6_（correspondingauthor）.

Abstract:

Thedesignoffiber-reinforcedpolymerreinforcedconcrete_FRP-RC_istypicallygovernedbyserviceabilitylimitstaterequirementsratherthanultimatelimitstaterequirementsasconventionalreinforcedconcreteis.Thus,amethodisneededthatcanpredicttheexpectedserviceloaddeflectionsoffiber-reinforcedpolymer_FRP_reinforcedmemberswithareasonablyhighdegreeofaccuracy.Ninemethodsofdeflectioncalculation,includingmethodsusedinACI440.1R-03,andaproposednewformulainthenextissueofthisdesignguide,CSAS806-02andISISM03-01,arecomparedtotheexperimentaldeflectionof197beamsandslabstestedbyother

investigators.ThesemembersarereinforcedwitharamidFRP,glassFRP,orcarbonFRPbars,havedifferentreinforcementratios,geometricandmaterialproperties.Allmembersweretestedundermonotonicallyappliedloadinfourpointbendingconfiguration.TheobjectiveoftheanalysisinthispaperistodetermineamethodofdeflectioncalculationforFRPRCmembers,whichisthemostsuitableforserviceabilitycriteria.TheanalysisrevealedthatboththemodulusofelasticityofFRPandtherelativereinforcementratioplayanimportantroleintheaccuracyoftheformulas.

CEDatabasesubjectheadings:

Concrete,reinforced;Fiber-reinforcedpolymers;Deflection;Curvature;Codes;Serviceability;Statistics.

Introduction

Fiber-reinforcedpolymer_FRP_reinforcingbarsarecurrentlyavailableasasubstituteforsteelreinforcementinconcretestructuresthatmaybevulnerabletoattackbyaggressivecorrosiveagents.Inadditiontosuperiordurability,FRPreinforcingbarshaveamuchhigherstrengththanconventionalmildsteel.However,themodulusofelasticityofFRPistypicallymuchlowerthanthatofsteel.ThisleadstoasubstantialdecreaseinthestiffnessofFRPreinforcedbeamsaftercracking.Sincedeflectionsareinverselyproportionaltotheflexuralstiffnessofthebeam,evensomeFRPover-reinforcedbeamsaresusceptibletounacceptablelevelsofdeflectionunderserviceconditions.Hence,thedesignofFRPreinforcedconcrete_（FRP-RC）istypicallygovernedbyserviceabilityrequirementsandamethodisneededthatcancalculatetheexpectedserviceloaddeflectionsofFRPreinforcedmemberswithareasonabledegreeofaccuracy.

Theobjectiveofthispaperistopointouttheinconsistenciesinexistingdeflectionformulas.Onlyinstantaneousdeflectionswillbediscussedinthispaper.

EffectiveMomentofInertiaApproach

ACI318_（ACI1999）andCSAA23.3-94_（CSA1998）recommendtheuseoftheeffectivemomentofinertia,Ie,tocalculatethedeflectionofcrackedsteelreinforcedconcretemembers.Theprocedureentailsthecalculationofauniformmomentofinertiathroughoutthebeamlength,anduseofdeflectionequationsderivedfromlinearelasticanalysis.Theeffectivemomentofinertia,Ie,isbasedonsemiempiricalconsiderations,anddespitesomedoubtaboutitsapplicabilitytoconventionalreinforcedconcretememberssubjectedtocomplexloadingandboundaryconditions,ithasyieldedsatisfactoryresultsinmostpracticalapplicationsovertheyears.InNorthAmericancodes,deflectioncalculationofflexuralmembersaremainlybasedonequationsderivedfromlinearelasticanalysis,usingtheeffectivemomentofinertia,Ie,givenbyBranson’sformula_（1965）

（1）

=crackingmoment;

=momentofinertiaofthegrosssection;

=momentofinertiaofthecrackedsectiontransformedtoconcrete;and

=effectivemomentofinertia.

ResearchbyBenmokraneetal._（1996）suggestedthatinordertoimprovetheperformanceoftheoriginalequation,Eq.

（1）willneedtobefurthermodified.Constantstomodifytheequationweredevelopedthroughacomprehensiveexperimentalprogram.TheeffectivemomentofinertiawasdefinedaccordingtoEq.

（2）ifthereinforcementwasFRP

（2）

FurtherresearchhasbeendoneinordertodefineaneffectivemomentofinertiaequationwhichissimilartothatofEq.

（1）,andconvergestothecrackedmomentofinertiaquickerthanthecubicequation.Manyresearchers_（Benmokraneetal.1996;BrownandBartholomew1996;ToutanjiandSaafi2000）arguethatthebasicformoftheeffectivemomentofinertiaequationshouldremainasclosetotheoriginalBranson’sequationaspossible,becauseitiseasytouseanddesignersarefamiliarwithit.Themodifiedequationispresentedinthefollowingequation:

（3）

AfurtherinvestigationoftheeffectivemomentofinertiawasperformedbyToutanjiandSaafi_（2000）.ItwasfoundthattheorderoftheequationdependsonboththemodulusofelasticityoftheFRP,aswellasthereinforcementratio.Basedontheirresearch,ToutanjiandSaafi_（2000）haverecommendedthatthefollowingequationsbeusedtocalculatethedeflectionofFRP

reinforcedconcretemembers:

（4）

Where

If

Otherwise（5）

m=3

where

=reinforcementratio;

=modulusofelasticityofFRPreinforcement;and

=modulusofelasticityofsteelreinforcement.

TheISISDesignManualM03-01_（RizkallaandMufti2001）hassuggestedtheuseofaneffectivemomentofinertiawhichisquitedifferentinformcomparedtothepreviousequations.Itsuggestsusingthemodifiedeffectivemomentofinertiaequationdefinedbythefollowingequationtobeadoptedforfutureuse:

（6）

where

=uncrackedmomentofinertiaofthesectiontransformedtoconcrete.

Eq._（6）isderivedfromequationsgivenbytheCEB-FIPMC-90_（CEB-FIP1990）.Ghalietal._（2001）haveverifiedthatIecalculatedbyEq.（6）givesgoodagreementwithexperimentaldeflectionofnumerousbeamsreinforcedwithdifferenttypesofFRPmaterials.

AccordingtoACI440.1R-03_（ACI2003）,themomentofinertiaequationforFRP-RCisdependentonthemodulusofelasticityoftheFRPandthefollowingexpressionforIeisproposedtocalculatethedeflectionofFRPreinforcedbeams:

（7）

where

（8）

whereβ=reductioncoefficient;α=bonddependentcoefficient_（untilmoredatabecomeavailable,α=0.5）;and

=modulusofelasticityoftheFRPreinforcement.

UponfindingthattheACI440.1R-03_（ACI2003）equationoftenunderpredictedtheserviceloaddeflectionofFRPreinforcedconcretemembers,severalattemptshavebeenmadeinordertomodifyEq.（7）.Forinstance,Yostetal._（2003）claimedthattheaccuracyofEq.（7）primarilyreliedonthereinforcementratioofthemember.Itwasconcludedthattheformulacouldbeofthesameform,butthatthebonddependentcoefficient,α,hadtobemodified.Amodificationfactor,α,wasproposedinthefollowingform:

（9）

where

=balancedreinforcementratio.

TheACI440Committee_（ACI2004）hasalsoproposedrevisionstothedesignequationinACI440.1R-03_（ACI2003）.ThemomentofinertiaequationhasretainedthesamefamiliarformasthatofEq.（7）intheserevisions.However,theformofthereductioncoefficient,,tobeusedinplaceofEq.（8）wasmodified.Thenewreductioncoefficienthaschangedthekeyvariableintheequationfromthemodulusofelasticitytotherelativereinforcementratioasshowninthefollowingequation:

（10）

Moment–CurvatureApproach

Themoment–curvatureapproachfordeflectioncalculationisbasedonthefirstprinciplesofstructuralanalysis.Whenamoment–curvaturediagramisknown,thevirtualworkmethodcanbeusedtocalculatethedeflectionofstructuralmembersunderanyloadas

（11）

whereL=simplysupportedlengthofthesection;M/EI=curvatureofthesection;andm=bendingmomentduetoaunitloadappliedatthepointwherethedeflectionistobecalculated.

Amoment–curvatureapproachwastakenbyFazaandGangaRao_（1992）,whodefinedthemidspandeflectionforfourpointbendingthroughtheintegrationofanassumedmomentcurvaturediagram.FazaandGangaRao_（1992）madetheassumptionthatforfour-pointbending,thememberwouldbefullycrackedbetweentheloadpointsandpartiallycrackedeverywhereelse.Adeflectionequationcouldthusbederivedbyassumingthatthemomentofinertiabetweentheloadpointswasthecrackedmomentofinertia,andthemomentofinertiaelsewherewastheeffectivemomentofinertiadefinedbyEq.

（1）.ThroughtheintegrationofthemomentcurvaturediagramproposedbyFazaandGangaRao_（1992）,thedeflectionforfour-pointloadingisdefinedaccordingtothefollowingequation:

（12）

whereɑ=shearspan.

Eq.（12）haslimitedusebecauseitisnotclearwhatassumptionsfortheapplicationoftheeffectivemomentofinertiashouldbeusedforotherloadcases.However,itworkedquiteaccuratelyforpredictingthedeflectionofthebeamstestedbyFazaandGangaRao_（1992）.

TheCSAS806-02_（CSA2002）suggeststhatthemoment–curvaturemethodofcalculatingdeflectioniswellsuitedforFRPreinforcedmembersbecausethemoment–curvaturediagramcanbeapproximatedbytwolinearregions:

onebeforetheconcretecracks,andthesecondoneaftertheconcretecracks_（Razaqpuretal.2000）.Therefore,thereisnoneedforcalculatingcurvatureatdifferentsectionsalongthelengthofthebeamasforsteelreinforcedconcrete.Thereareonlythreepairsofmomentswithcorrespondingcurvaturethatdefinetheentiremoment–curvaturediagram:

atcracking,immediatelyaftercracking,andatultimate.Withthisinmind,simpleformulaswerederivedfordeflectioncalcula