中英用碳纤维板cfr修复剪切不足的矩形简支梁

山东建筑大学毕业设计外文文献及译文PAGE67-英文原文：RehabilitationofrectangularsimplysupportedRCbeamswithsheardeficienciesusingCFRPcompositesAhmedKhalifaa,*,AntonioNannibaDepartmentofStructuralEngineering,UniversityofAlexandria,Alexandria21544,EgyptbDepartmentofCivilEngineering,UniversityofMissouriatRolla,Rolla,MO65409,USAReceived28April1999;receivedinrevisedform30October2001;accepted10January2002AbstractThepresentstudyexaminestheshearperformanceandmodesoffailureofrectangularsimplysupportedreinforcedconcrete(RC)beamsdesignedwithsheardeficiencies.Thesememberswerestrengthenedwithexternallybondedcarbonfiberreinforcedpolymer(CFRP)sheetsandevaluatedinthelaboratory.Theexperimentalprogramconsistedoftwelvefull-scaleRCbeamstestedtofailinshear.Thevariablesinvestigatedwithinthisprogramincludedsteelstirrups,andtheshearspan-to-effectivedepthratio,aswellasamountanddistributionofCFRP.TheexperimentalresultsindicatedthatthecontributionofexternallybondedCFRPtotheshearcapacitywassignificant.Theshearcapacitywasalsoshowntobedependentuponthevariablesinvestigated.Testresultswereusedtovalidateasheardesignapproach,whichshowedconservativeandacceptablepredictions.eq\o\ac(○,C)2002ElsevierScienceLtd.Allrightsreserved.Keywords:Rehabilitation;Shear;Carbonfiberreinforcedpolymer1.IntroductionFiberreinforcedpolymer(FRP)compositesystems,composedoffibersembeddedinapolymericmatrix,canbeusedforshearstrengtheningofreinforcedcon-crete(RC)members[1–7].ManyexistingRCbeamsaredeficientandinneedofstrengthening.TheshearfailureofanRCbeamisclearlydifferentfromitsflexuralfailure.Inshear,thebeamfailssuddenlywithoutsufficientwarninganddiagonalshearcracksareconsid-erablywiderthantheflexuralcracks[8].Theobjectivesofthisprogramwereto:1.InvestigateperformanceandmodeoffailureofsimplysupportedrectangularRCbeamswithsheardeficien-ciesafterstrengtheningwithexternallybondedCFRPsheets.2.Addressthefactorsthatinfluenceshearcapacityofstrengthenedbeamssuchas:steelstirrups,shearspan-to-effectivedepthratio(a/dratio),andamountanddistributionofCFRP.3.Increasetheexperimentaldatabaseonshearstrength-eningwithexternallybondedFRPreinforcement.4.Validatethedesignapproachpreviouslyproposedbytheauthors[9].Fortheseobjectives,12full-scale,RCbeamsdesignedtofailinshearwerestrengthenedwithdifferentCFRPschemes.Thesemembersweretestedassimplebeamsusingafour-pointloadingconfigurationwithtwodifferenta/dratios.2.Experimentalprogram2.1.TestspecimensandmaterialsTwelvefull-scalebeamspecimenswithatotalspanof3050mm.andarectangularcross-sectionof150-mm-wideand305-mm-deepweretested.ThespecimensweregroupedintotwomainseriesdesignatedSWandSOdependingonthepresenceofsteelstirrupsintheshearspanofinterest.SeriesSWconsistedoffourspecimens.ThedetailsanddimensionsofthespecimensdesignatedseriesSWareillustratedinFig.1a.Inthisseries,four32-mmsteelbarswereusedaslongitudinalreinforcementwithtwoattopandtwoatbottomfaceofthecross-sectiontoinduceashearfailure.Thespecimenswerereinforcedwith10-mmsteelstirrupsthroughouttheirentirespan.Thestirrupsspacingintheshearspanofinterest,righthalf,wasselectedtoallowfailureinthatspan.SeriesSOconsistedofeightbeamspecimens,whichhadthesamecross-sectiondimensionandlongitudinalsteelreinforcementasforseriesSW.NostirrupswereprovidedinthetesthalfspanasillustratedinFig.1b.Eachmainseries(i.e.seriesSWandSO)wassubdividedintotwosubgroupsaccordingtoshearspan-to-effectivedepthratio.Thiswasselectedtobea/d=3and4,resultinginthefollowingfoursubgroups:SW3;SW4;SO3;andSO4.ThemechanicalpropertiesofthematerialsusedformanufacturingthetestspecimensarelistedinTable1.FabricationofthespecimensincludingsurfacepreparationandCFRPinstallationisdescribedelsewhere[10].Table12.2.StrengtheningschemesOnespecimenfromeachseries(SW3-1,SW4-1,SO3-1andSO4-1)wasleftwithoutstrengtheningasacontrolspecimen,whereaseightbeamspecimenswerestrengthenedwithexternallybondedCFRPsheetsfollowingthreedifferentschemesasillustratedinFig.2.InseriesSW3,specimenSW3-2wasstrengthenedwithtwoCFRPplieshavingperpendicularfiberdirections(90°/0°).ThefirstplywasattachedintheformofcontinuousU-wrapwiththefiberdirectionorientedperpendiculartothelongitudinalaxisofthespecimen(90°).Thesecondplywasbondedonthetwosidesofthespecimenwiththefiberdirectionparalleltothebeamaxis（0°）.Thisply[i.e.0°ply]wasselectedtoinvestigatetheimpactofadditionalhorizontalrestraintonshearstrength.InseriesSW4,specimenSW4-2wasstrengthenedwithtwoCFRPplieshavingperpendicularfiberdirection(90°/0°)asforspecimenSW3-2.FourbeamspecimenswerestrengthenedinseriesSO3.SpecimenSO3-2wasstrengthenedwithone-plyCFRPstripsintheformofU-wrapwith90°-fiberorientation.Thestripwidthwas50mmwithcenter-to-centerspacingof125mm.SpecimenSO3-3wasstrengthenedinamannersimilartothatofspecimenSO3-2,butwithstripwidthequalto75mm.SpecimenSO3-4wasstrengthenedwithone-plycontinuousU-wrap(90°).SpecimenSO3-5wasstrengthenedwithtwoCFRPplies(90°/0°)similartospecimensSW3-2andSW4-2.InseriesSO4,twobeamspecimenswerestrengthened.SpecimenSO4-2wasstrengthenedwithone-plyCFRPstripsintheformofU-wrapsimilartospecimenSO3-2.SpecimenSO4-3wasstrengthenedwithone-plycontinuousU-wrap(90°)similartoSO3-4.Fig.1.Configurationandreinforcementdetailsforbeamspecimens.Fig.2.SchematicrepresentationofCFRPstrengtheningschemes.2.3.Testset-upandinstrumentationAllspecimensweretestedassimplespanbeamssubjectedtoafour-pointloadasillustratedinFig.3.Auniversaltestingmachinewith1800KNcapacitywasusedinordertoapplyaconcentratedloadonasteeldistributionbeamusedtogeneratethetwoconcentratedloads.Theloadwasappliedprogressivelyincycles,usuallyonecyclebeforecrackingfollowedbythreecycleswiththelastoneuptoultimate.Theappliedloadvs.deflectioncurvesshowninthispaperaretheenvelopesoftheseloadcycles.Fourlinearvariabledifferentialtransformers(LVDTs)wereusedforeachtesttomonitorverticaldisplacementsatvariouslocationsasshowninFig.3.TwoLVDTswerelocatedatmid-spanoneachsideofthespecimen.Theothertwowerelocatedatthespecimensupportstorecordsupportsettlement.Fig.3.Schematicrepresentationoftestset-upforspecimen(a)SW3-1,and(b)SW3-2.ForeachspecimenofseriesSW,sixstraingaugeswereattachedtothreestirrupstomonitorthestirrupstrainduringloadingasillustratedinFig.1a.ThreestraingaugeswereattacheddirectlytotheFRPsheetonthesidesofeachstrengthenedbeamtomonitorstrainvariationintheFRP.Thestraingaugeswereorientedintheverticaldirectionandlocatedatthesectionmid-heightwithdistancesof175,300and425mm,respectively,fromthesupportforseriesSW3andSO3.ForbeamspecimensofseriesSW4andSO4,thestraingaugeswerelocatedatdistanceof375,500and625mm,respectively,fromthesupport.3.ResultsanddiscussionInthefollowingdiscussion,referenceisalwaysmadetoweakshearspanorspanofinterest.3.1.SeriesSW3ShearcracksinthecontrolspecimenSW3-1wereobservedclosetothemiddleoftheshearspanwhentheloadreachedapproximately90kN.Astheloadincreased,additionalshearcracksformedthroughout,wideningandpropagatinguptofinalfailureataloadof253kN(seeFig.4a).InspecimenSW3-2strengthenedwithCFRP(90°/0°),nocrackswerevisibleonthesidesorbottomofthetestspecimenduetotheFRPwrapping.However，alongitudinalsplittingcrackinitiatedonthetopsurfaceofthebeamatahighloadofapproximately320kN.Fig.4.FailuremodesofseriesSW3specimens.Thecrackinitiatedatthelocationofappliedloadandextendedtowardsthesupport.Thespecimenfailedbyconcretesplitting(seeFig.4b)attotalloadof354kN.Thiswasanincreaseof40%inultimatecapacitycomparedtothecontrolspecimenSW3-1.Thesplittingfailurewasduetotherelativelyhighlongitudinalcompressivestressdevelopedattopofthespecimen,whichcreatedatransversetension,ledtothesplittingfailure.Inaddition,therelativelylargeamountoflongitudinalsteelreinforcementcombinedwithover-strengtheningforshearbyCFRPwrapprobablycausedthismodeoffailure.Theloadvs.mid-spandeflectioncurvesforspecimensSW3-1andSW3-2areillustratedinFig.5,toshowtheadditionalcapacitygainedbyCFRP.Fig.5.Appliedloadvs.mid-spandeflectionforseriesSW3specimens.ThemaximumCFRPverticalstrainmeasuredatfailureinspecimenSW3-2wasapproximately0.0023mm/mm,whichcorrespondedto14%ofthereportedCFRPultimatestrain.Thisvalueisnotanabsolutebecauseitgreatlydependsonthelocationofthestraingaugeswithrespecttoacrack.However,therecordedstrainindicatesthatifthesplittingdidnotoccur,theshearcapacitycouldhavereachedhigherload.ComparisonbetweenmeasuredlocalstirrupstrainsinspecimensSW3-1andSW3-2areshowninFig.6.Thestirrups1,2and3werelocatedatdistanceof175,300and425mmfromthesupport,respectively.Theresultsshowedthatthestirrups2and3didnotyieldatultimateforbothspecimens.Thestrains(andtheforces)inthestirrupsofspecimenSW3-2were,ingeneral,smallerthanthoseofspecimenSW3-1atthesamelevelofloadingduetotheeffectofCFRP.Fig.6.Appliedloadvs.straininthestirrupsforspecimensSW3-1andSW3-2.3.2.SeriesSW4InspecimenSW4-1,thefirstdiagonalcrackwasformedinthememberatatotalappliedloadof75kN.Astheloadincreased,additionalshearcracksappearedthroughouttheshearspan.Failureofthebeamoccurredwhenthetotalappliedloadreached200kN.Thiswasadecreaseof20%inshearcapacitycomparedtothespecimenSW3-1witha/dratio=3.Fig.7.Appliedloadvs.mid-spandeflectionforseriesSW4specimens.InspecimenSW4-2,thefailurewascontrolledbyconcretesplittingsimilartotestspecimenSW3-2.Thetotalappliedloadatultimatewas361kNwithan80%increaseinshearcapacitycomparedtothecontrolspecimenSW4-1.Inaddition,themeasuredstrainsinthestirrupsforspecimenSW4-2werelessthanthoseofspecimenSW4-1.Theappliedloadvs.mid-spandeflectioncurvesforbeamsSW4-1andSW4-2areillustratedinFig.7.ItmaybenotedthatspecimenSW4-2resultedingreaterdeflectionwhencomparedtospecimenSW4-1.WhencomparingthetestresultsofseriesSW3specimenstothatofseriesSW4,theultimatefailureloadofspecimenSW3-2andSW4-2wasalmostthesame.However,theenhancedcapacityofspecimenSW3-2(a/d=3)duetotheadditionoftheCFRPreinforcementwas101kN,whilespecimenSW4-2(a/d=4)was161kN.ThisindicatesthatthecontributionofexternalCFRPreinforcementmaybeinfluencedbytheaydratioandappearstodecreasewithadecreasinga/dratio.Further,forbothstrengthenedspecimens(SW3-2andSW4-2),CFRPsheetsdidnotfractureordebondfromtheconcretesurfaceatultimateandthisindicatesthatCFRPcouldprovideadditionalstrengthifthebeamsdidnotfailedbysplitting.3.3.SeriesSO3Fig.8illustratesthefailuremodesforseriesSO3specimens.Fig.9detailstheappliedloadvs.mid-spandeflectionforthespecimens.ThefailuremodeofcontrolspecimenSO3-1wasshearcompression.Failureofthespecimenoccurredatatotalappliedloadof154kN.Thisloadwasadecreaseofshearcapacityby54.5kNcomparedtothespecimenSW3-1duetotheabsentofthesteelstirrups.Inaddition,thecrackpatterninspecimenSW3-1wasdifferentfromofspecimenSO3-1.InspecimenSW3-1,thepresenceofstirrupsprovidedabetterdistributionofdiagonalcracksthroughouttheshearspan.InspecimenSO3-2,strengthenedwith50-mmCFRPstripsspacedat125mm,thefirstdiagonalshearcrackwasobservedatanappliedloadof100kN.ThecrackpropagatedastheloadincreasedinasimilarmannertothatofspecimenSO3-1.SuddenfailureoccurredduetodebondingoftheCFRPstripsoverthediagonalshearcrack,withspalledconcreteattachedtotheCFRPstrips.Thetotalultimateloadwas262kNwitha70%increaseinshearcapacityoverthecontrolspecimenSO3-1.ThemaximumlocalCFRPverticalstrainmeasuredatfailureinspecimenSO3-2was0.0047mm/mm(i.e.28%oftheultimatestrain),whichindicatedthattheCFRPdidnotreachitsultimate.SpecimenSO3-3,strengthenedwith75-mmCFRPstripsfailedasaresultofCFRPdebondingatatotalappliedloadof266kN.NosignificantincreaseinshearcapacitywasnotedcomparedtospecimenSO3-2.Themaximum-recordedverticalCFRPstrainatfailurewas0.0052mmymm(i.e.31%oftheultimatestrain).SpecimenSO3-4,whichwasstrengthenedwithacontinuousCFRPU-wrap(908),failedasaresultofCFRPdebondingatanappliedloadof289kN.ResultsshowthatspecimenSO3-4exhibitedincreaseinshearcapacityof87,10and8.5%overspecimensSO3-1,SO3-2andSO3-3,respectively.Appliedloadvs.verticalCFRPstrainforspecimenSO3-4isillustratedinFig.10inwhichstraingaugessg1,sg2andsg3werelocatedatmid-heightwithdistancesof175,300and425mmfromthesupport,respectively.Fig.10showsthattheCFRPstrainwaszeropriortodiagonalcrackformation,thenincreasedslowlyuntilthespecimenreachedaloadintheneighborhoodoftheultimatestrengthofthecontrolspecimen.Atthispoint,theCFRPstrainincreasedsignificantlyuntilfailure.ThemaximumlocalCFRPverticalstrainmeasuredatfailurewasapproxi-mately0.0045mm/mm.WhencomparingtheresultsofbeamsSO3-4andSO3-2,theCFRPamountusedtostrengthenspecimenSO3-4was250%ofthatusedforspecimenSO3-2.Onlya10%increaseinshearcapacitywasachievedfortheadditionalamountofCFRPused.ThismeansthatifanendanchortocontrolFRPdebondingisnotused,thereisanoptimumFRPquantity,beyondwhichthestrengtheningeffectisquestionable.Apreviousstudy[11]showedthatbyusinganendanchorsystem,thefailuremodeofFRPdebondingcouldbeavoided.Reportedfindingsareconsistentwiththoseofotherresearch[7],whichwasbasedonareviewoftheexperimentalresultsavailableintheliterature,andindicatedthatthecontributionofFRPtotheshearcapacityincreasesalmostlinearly,withFRPaxialrigidityexpressedby(istheFRPareafractionandistheFRPelasticmodulus)uptoapproximately0.4GPa.Beyondthisvalue,theeffectivenessofFRPceasestobepositive.InspecimenSO3-5,theuseofahorizontalplyoverthecontinuousU-wrap(i.e.90°/0°)resultedinaconcretesplittingfailureratherthanaCFRPdebondingfailure.Thefailureoccurredattotalappliedloadof339kNwitha120%increaseintheshearcapacitycomparedtothecontrolspecimenSO3-1.Thestrengtheningwithtwoperpendicularplies(i.e.90°/0°)resultedina17%increaseinshearcapacitycomparedtothespecimenwithonlyoneCFRPplyin90°orientation(i.e.specimenSO3-4).ThemaximumlocalCFRPverticalstrainmeasuredatfailurewas0.0043mm/mm.BycomparingthetestresultsofspecimensSW3-2andSO3-5,havingthesamea/dratioandstrengtheningschemesbutwithdifferentsteelshearreinforcement,theshearstrength(i.e.177and169.5kNforspecimensSW3-2andSO3-5,respectively),andtheductilityarealmostidentical.OnemayconcludethatthecontributionofCFRPbenefitsthebeamcapacitytoagreaterdegreeforbeamswithoutsteelshearreinforcementthanforbeamswithadequateshearreinforcement.Fig.8.FailuremodesofseriesSO3specimens.Fig.9.Appliedloadvs.mid-spandeflectionforseriesSO3specimens.Fig.10.MeasuredverticalCFRPstrainforspecimenSO3-4.3.4.SeriesSO4SeriesSO4exhibitedthelargestincreaseinshearcapacitycomparedtotheotherseriesinvestigatedwiththisresearchstudy.Theexperimentalresultsintermsofappliedloadvsmid-spandeflectionforthisseriesisillustratedinFig.11.ThecontrolspecimenSO4-1failedasaresultofshearcompressionatatotalappliedloadof130kN.SpecimenSO4-2,strengthenedwithCFRPstrips,thefailurewascontrolledbyCFRPdebondingatatotalloadof255kNwith96%increaseinshearcapacityoverthecontrolspecimenSO4-1.ThemaximumlocalCFRPverticalstrainmeasuredatfailurewas0.0062mmymm.WhencomparingthetestresultsofspecimenSO4-2tothatofspecimenSO3-2,theenhancedshearcapacityofspecimenSO4-2(a/d=4)duetoadditionofCFRPstripswas62.5kN,whilespecimenSO3-2(a/d=3)resultedinaddedshearcapacityof54kN.Asexpected,thecontributionofCFRPreinforcementtoresisttheshearappearedtodecreasewithdecreasinga/dratio.SpecimenSO4-3,strengthenedwithcontinuousU-wrap,failedasaresultofconcretesplittingatanappliedloadof310kNwitha138%increaseinshearcapacitycomparedtothatofspecimenSO4-1.ThemaximumlocalCFRPverticalstrainmeasuredatfailurewas0.0037mm/mm.4.DesignapproachThedesignapproachforcomputingtheshearcapacityofRCbeamsstrengthenedwithexternallybondedCFRPreinforcement,expressedinACIdesigncode[12]format,wasproposedandpublishedin1998[13].ThedesignmodeldescribedtwopossiblefailuremechanismsofCFRPreinforcementnamely:CFRPfracture;andCFRPdebonding.Furthermore,twolimitsonthecontributionofCFRPshearwereproposed.Thefirstlimitwassettocontroltheshearcrackwidthandlossofaggregateinterlock,andthesecondwastoprecludewebcrushing.Also,theconcretestrengthandCFRPwrap-pingschemeswereincorporatedasdesignparameters.Inrecentstudy[9,10],modificationswereproposedtothe1998designapproachtoincluderesultsofanewstudyonbondmechanismbetweenCFRPsheetsandconcretesurface[14].Inaddition,themodelwasextendedtoprovidethesheardesignequationsinEurocodeaswellasACIformat.Comparingwithalltestresultsavailableintheliteraturetodate,76tests,thedesignapproachshowedacceptableandconservativeestimates[10,13].Inthissection,thesummaryofthedesignapproachispresented.Thecomparisonbetweenexperimentalresultsandthecalculatedfactoredshearstrengthdemonstratestheabilityofthedesignapproachtopredicttheshearcapacityofthestrengthenedbeams.demonstratestheabilityofthedesignapproachtopredicttheshearcapacityofthestrengthenedbeams.Fig.11.Appliedloadvs.mid-spandeflectionforseriesSO4specimens.Fig.12.DimensionsusedtodefinetheareaofFRP(a)verticalorientedFRPstrips,and(b)inclinedstrips.4.1.Summaryofthesheardesignapproach—ACIformatIntraditionalsheardesign(includingtheACICode),thenominalshearstrengthofanRCsectionisthesumofthenominalshearstrengthsofconcreteandsteelshearreinforcement.ForbeamsstrengthenedwithexternallybondedFRPreinforcement,theshearstrengthmaybecomputedbytheadditionofathirdtermtoaccountoftheFRPcontribution.Thisisexpressedasfollows:Thedesignshearstrength,,isobtainedbymultiplyingthenominalshearstrengthbyastrengthreductionfactorforshear,.Itwassuggestedthatthereductionfactor=0.85giveninACI[12]bemain-tainedfortheconcreteandsteelterms.However,amorestringentstrengthreductionfactorof0.7fortheCFRPcontributionwassuggestedw10x.Thisisduetotherelativenoveltyofthisrepairtechnique.Thus,thedesignshearstrengthisexpressedasfollows.4.2.ContributionofCFRPreinforcementtotheshearcapacityTheexpressionusedtocomputeshearcontributionofCFRPreinforcementisgiveninEq.(3).ThisequationissimilartothatforshearcontributionofsteelstirrupsandconsistentwiththeACIformat.TheareaofCFRPshearreinforcement,,isthetotalthicknessofthesheet(usuallyorsheetsonbothsidesofthebeam)timesthewidthoftheCFRPstrip.ThedimensionsusedtodefinetheareaofCFRPinadditiontothespacingandtheeffectivedepthofCFRP,，areshowninFig.12.Notethatforcontinuousverticalshearreinforcement,thespacingofthestrip,,andthewidthofthestrip,,areequal.InEq.(3),aneffectiveaverageCFRPstress,smallerthanitsultimatestrength,,wasusedtoreplacetheyieldstressofsteel.Attheultimatelimitstateforthememberinshear,itisnotpossibletoattainthefullstrengthoftheFRP[7,13].FailureisgovernedbyeitherfractureoftheFRPsheetataveragestresslevelswellbelowFRPultimatecapacityduetostressconcentrations,debondingoftheFRPsheetfromtheconcretesurface,orasignificantdecreaseinthepost-crackingconcreteshearstrengthfromalossofaggregateinterlock.Thus,theeffectiveaverageCFRPstressiscomputedbyapplyingareductioncoefficient,R,totheCFRPultimatestrengthasexpressedinEq.(4).Thereductioncoefficientdependsonthepossiblefailuremodes(eitherCFRPfractureorCFRPdebonding).Ineithercase,anupperlimitforthereductioncoefficientisestablishedinordertocontrolshearcrackwidthandlossofaggregateinterlock.4.3.ReductioncoefficientbasedonCFRPsheetfracturefailureTheproposedreductioncoefficientwascalibratedonallavailabletestresultstodate,22testswithfailurecontrolledbyCFRPfracture[10，13].Thereductioncoefficientwasestablishedasafunctionof(whereistheareafractionofCFRP)andexpressedinEq.(5)for0.7GPa.4.4.ReductioncoefficientbasedonCFRPdebondingfailureTheshearcapacitygovernedbyCFRPdebondingfromtheconcretesurfacewaspresented[9,10]asafunctionofCFRPaxialrigidity,concretestrength,effectivedepthofCFRPreinforcement,andbondedsurfaceconfigurations.Indeterminingthereductioncoefficientforbond,theeffectivebondlength,,hastobedeterminedfirst.Basedonanalyticalandexperimentaldatafrombondtests,Miller[14]showedthattheeffectivebondlengthslightlyincreasesasCFRPaxialrigidity,,increases.However,hesuggestedaconstantconservativevalueforequalto75mm.Thevaluemaybemodifiedwhenmorebondtestsdatabecomesavailable.Afterashearcrackdevelops,onlythatportionofthewidthofCFRPextendingpastthecrackbytheeffectivebondedlengthisassumedtobecapableofcarryingshear.[13]Theeffectivewidth,,basedontheshearcrackangleof45°,andthewrappingschemeisexpressedinEqs.(6a)and(6b);ifthesheetintheformofaU-wrap(6a)ifthesheetisbondedonlytothesidesofthebeam.(6b)Thefinalexpressionforthereductioncoefficient,R,forthemodeoffailurecontrolledbyCFRPdebondingisexpressedinEq.(8)Eq.(7)isapplicableforCFRPaxialrigidity,,rangingfrom20to90mm-GPa(kN/mm).Researchintoquantifyingthebondcharacteristicsforaxialrigiditiesabove90mm·GPaisbeingconductedattheUniversityofMissouri,Rolla(UMR).4.5.UpperlimitofthereductioncoefficientInordertocontroltheshearcrackwidthandlossofaggregateinterlock,anupperlimitofreductioncoefficient,R,wassuggestedandcalibratedwithalloftheavailabletestresults[10]tobeequaltowhereistheultimatetensileCFRPstrain.ThislimitissuchthattheaverageeffectivestraininCFRPmaterialsatultimatecannotbegreaterthan0.006mm/mm(withoutthestrengtheningreductionfactor,).4.6.ControllingreductioncoefficientThefinalcontrollingreductioncoefficientfortheCFRPsystemistakenasthelowestvaluedeterminedfromthetwopossiblemodesoffailureandtheupperlimit.Notethatifthesheetiswrappedentirelyaroundthebeamoraneffectiveendanchorisused,thefailuremodeofCFRPdebondingisnottobeconsidered.ThereductioncoefficientisonlycontrolledbyFRPfractureandtheupperlimit.4.7.CFRPspacingrequirementsSimilartosteelshearreinforcement,andconsistentwithACIprovisionforthestirrupsspacing[12],thespacingofFRPstripsshouldnotbesowideastoallowtheformationofadiagonalcrackwithoutinterceptingastrip.Forthisreason,ifstripsareused,theyshouldnotbespacedbymorethanthemaximumgiveninEq.(8).4.8.LiimitonttotallsheearrreinfforceementtACI3188M-955[122]aand111.5..6.8setaliimitontthettotallsheearsstrenngththattmayybeprovvideddbymoreethaanonnetyypeoofshhearreinnforccemennttoopreecluddethheweebcrrushiing.FRPsheaarreeinfoorcemmentshouuldbbeinncluddediinthhisllimitt.AmodiificaationntoACI318MM-95Secttion8wasssugggesttedaasfoollowws:4.9.ShhearcapaacityyofaCFFRPsstrenngtheenedsecttion—EurrocoddefoormattTheprooposeeddeesignnequuatioonwEEq.((3)xforcompputinngthhecoontriibutiionoofexxternnallyybonndedCFRPPreiinforrcemeentmmaybbereewrittteninEEuroccode(EC2219992)[[15]formmataasEqq.(110).Inthissequuatioon,ttheppartiialssafettyfaactorrforrCFRRPmaateriials,,,waassuuggesstedequaaltoo1.33[100].4.10.CCompaarisoonbeetweeenthheteestrresulltsaandccalcuulateedvaaluessThetesstsuummarryanndthhecoomparrisonnbettweenntheetesstreesulttsanndthhecaalcullateddsheearsstrenngth,,usiingttheddesiggnappproaach((ACIformmat),,areedettaileedinnTabbles2annd3,,resspecttivelly.FForCCFRPstreengthheneddbeaams,themeassureddconntribbutioonoffconncrette,VVc,andsteeelsttirruups,Vs,(wheenprresennt)wwereconssiderredeequalltothesheaarstrrengtthoffannon-sstrenngtheenedbeamm.ThhenoominaalshhearstreengthhproovideedbyyconncretteanndstteelstirrrupsswasscommputeedussingEquaationns(111-5))andd(111-15))inACI--3188-95[12]].InnEquuatioon(111-5)),thhevaaluessofVuaandMMuweerettakennatthepoinntoffappplicaationnoftheloadd.Thhecoomparrisonninddicattestthatthedesiignaapprooachgiveescoonserrvatiiverresulltsffortthesstrenngtheenedbeammsassilllus-ttrateedinnFigg.133.5.ConcclusiionsandfurttherrecoommenndatiionAnexpeerimeentallinvvestiigatiionwwascconduucteddtostuddythheshhearbehaaviorranddtheemoddesooffaailurreoffsimmplysuppporteedreectanngulaarseectioonRCCbeaamswwithsheaardeeficiienciies,streengthheneddwitthCFFRPssheetts.TThepparammeterrsinnvesttigattediinthhispprogrramww