土木工程專業(yè)英語 課件 4.1-1 Flexural Behavior of Reinforce Concrete Beam 1

4.1.FlexuralBehaviorofReinforceConcreteBeam

RC受彎構(gòu)件正截面性能

Plainconcretebeamareineffectiveasflexuralmembersbecausethetensilestrengthinbendingisasmallfractionofthecompressivestrength.Asaconsequence,suchbeamsfailonthetensionsideatlowloadslongbeforethestrengthoftheconcreteonthecompressionhasbeenfullyutilized.Reinforcedconcretebeam:steelreinforcingbarsareplacedonthetensionsideasclosetotheextremetensionfiber.Insuchareinforcedconcretebeam,thetensioncausedbythebendingmomentischieflyresistedbysteelreinforcement,whileconcretealoneisusuallycapableofresistingthecorrespondingcompression.ReinforcedconcretebeamunderloadReinforcementPlacementinContinuousBeamsorSlabsSuchjointactionofthetwomaterialsisassured,ifrelativeslipisprevented.Thisisachievedbyusingdeformedbarswiththeirhighbondstrengthatthesteel-concreteinterface,and,ifnecessary,byspecialanchorageoftheendsofthebars.deformedbarsanchorageDeformedbarRibRelativeslipbetweenconcreteandsteelispreventedbyusingdeformedbarswiththeirhighbondstrengthatthesteel-concreteinterfaceThreetypesofreinforcedconcretebeams(a)Singlyreinforcedrectangularbeams單筋梁(b)Doublyreinforcedrectangularbeams雙筋梁(c)SinglyordoublyreinforcedT-beamsT形梁Thereinforcementratioaratioofareasofsteelandconcrete.representtherelativeamountoftensionreinforcementinabeamh0bASReinforcedConcreteBehaviorModerate-reinforcedBehavior適筋

OverreinforcedBehavior

超筋

LightlyReinforcedBehavior少筋ModeratereinforcedBehavior適筋Whentherelativelymoderateamountofreinforcementareemployed,atsomevalueoftheloadthesteelwillreachitsyieldpoint.sefufyoyieldpointcrushingoftheconcreteensuesataloadonlyslightlylargerthanthatwhichcausedthesteeltoyield.ThethreestagesofthebeamsteelyieldConcretecrushtheexternalloadPcausethebottomfiberstoequaltotensilestrengthoftheconcreteThetensilestrengthoftheconcreteexceedsftandcracksdevelop.Concretelosestensilestrengthandsteelstartsworkingeffectivelyandresiststheentiretensileload.ThereinforcementyieldsFailureofthebeamAtthatstress(yieldpoint),thereinforcementyieldssuddenlyandstretchesalargeamountandthetensioncracksintheconcretewidenvisiblyandpropagateupward,withsimultaneoussignificantdeflectionofthebeam.Whenthishappens,thestrainintheremainingcompressionzoneoftheconcreteincreasestosuchadegreethatcrushingoftheconcreteensuesat(跟著發(fā)生)aloadonlyslightlylargerthanthatwhichcausedthesteeltoyield.T=AsfsCecu=0.003CrushingsefufyostretchesalargeamountcrushingoftheconcreteEffectively,therefore,attainmentoftheyieldpointinthesteeldeterminatesthecarryingcapacityofmoderatelyreinforcedbeam.Suchyieldfailureisgradualandisprecededbyvisiblesignofdistress(惡化，損壞),suchasthewideningandlengtheningofcracksandthemarkedincreaseindeflection.Over-reinforcedBehaviorConcretefailsbeforetheyieldofsteelduetothepresenceofahighpercentageofsteelinthesection.*Ontheotherhand,iflargeamountsofreinforcementornormalamountsofsteelofveryhighstrengthareemployed,thecompressivestrengthoftheconcretemaybeexhaustedbeforethesteelstartsyielding.Over-reinforcedBehaviorConcretefailsbycrushingwhenstrainsbecomesolargethattheydisrupttheintegrity[in5te^riti]完整性

oftheconcrete.Compressivefailurethroughcrushingoftheconcreteissudden,ofanalmostexplosivenature,andoccurswithoutwarning.sefufyoSteeldosenotyieldcrushingoftheconcreteForthisreason,itisgoodpracticetodimensionbeamsinsuchamannerthatshouldtheybeoverloaded,failurewouldbeinitiatedbyyieldingofthesteelratherthanbycrushingoftheconcrete.LightlyReinforcedBehaviorflexuralstrengthofthecrackedsectionislessthanthemomentthatproducedcrackingofthepreviouslyuncrackedsectionbeamfailsimmediatelyandwithoutwarningofdistressupon緊接著

formationofthefirstflexuralcrack.LightlyReinforcedBehaviorToensureagainstthistypeoffailure,alowerlimitcanbeestablishedforthereinforcementratiobyequatingthecrackingmoment,computedfromthecorrespondingplainconcretebeam,tothestrengthofthecrackedsection.鋼筋混凝土梁的My=素混凝土梁的受彎承載力McrDesignofReinforcedConcreteBeam

StrengthDesignofRectangularbeamwithtensionreinforcementonly(singlyreinforcedbeam)Basicassumptions(1)Sectionsperpendiculartotheaxisofbendingthatareplanebeforebendingremainplaneafterbending.平截面假定Thisassumptionensuresthatthecross-sectionofthememberdoesnotwarp

[wC:p]使翹曲duetotheloadsapplied.Itfurthermeansthatthestrainatanypointonthecross-sectionisdirectlyproportionaltoitsdistancefromtheneutralaxis.strainatanypointonthecross-sectionisdirectlyproportionaltoitsdistancefromtheneutralaxis.Basicassumptions(2)Aperfect[5pE:fikt]bondexistsbetweenthereinforcementandtheconcretesuchthatthestraininthereinforcementisequaltothestrainintheconcreteatthesamelevel.

鋼筋的應(yīng)變和相同位置處混凝土的應(yīng)變相同----假定混凝土與鋼筋之間粘結(jié)可靠(3)Concreteisassumedtofailwhenthecompressivestrainreaches0.0033.Thisisaclearlydefinedlimitingstrainofconcreteinbendingcompressionbeyondwhichtheconcretewillbetakenasreachingthestateofcollapse.Itisveryclearthatthespecifiedlimitingstrainof0.0033doesnotdependonthestrengthofconcrete.

Collapseofconcretelimitingstrainofconcrete(4)Theacceptablestress-straincurveofconcreteisassumedtobeparabolic拋物線的，像拋物線的

混凝土受壓時的應(yīng)力-應(yīng)變關(guān)系

u

0o

cfc

c(5)Thetensilestrengthofconcreteisignored.Concretehassometensilestrength(verysmallbutnotzero).Yet,thistensilestrengthisignoredandthesteelreinforcementisassumedtoresistthetensilestress.

認(rèn)為拉區(qū)混凝土開裂并退出工作However,thetensilestrengthofconcreteistakenintoaccounttocheckthedeflectionandcrackwidthsinthelimitstateofserviceability.(6)Thedesignstressesofthereinforcementarederivedfromtherepresentativestress-straincurves鋼筋的應(yīng)力-應(yīng)變關(guān)系

Themaximumstraininthetensionreinforcementinthesectionatfailureis0.01.Thisassumptionensuresductilefailureinwhichthetensilereinforcementundergoesacertaindegreeofinelasticdeformationbeforeconcretefailsincompression.maximumstraininelasticdeformationrepresentativestress-straincurvesDuringtheloadingtofailureofareinforcedconcretebeam,straindistributionoverthedepthofthebeamisassumedtobelinear.stressdistributionintheconcreteaboveneutralaxisisessentiallyparabolicinshape(idealizedstressdistribution)Equivalentrectangularstressdistribution

壓區(qū)混凝土等效矩形應(yīng)力圖形

Thecompressivezoneismodeledwithaequivalentstressblock.Itisassumedthatatfailurethetensionreinforcementhasyieldedandthatthemaximumcompressivestrainis0.0033.Theintensityoftheequivalentuniformcompressivestressanditsdepthareeasilycalculatedfromthetwoconditionsthat(1)thetotalcompressionforceC,and(2)itslocation,i.e.,distancefromthetopfiber,mustbethesameintheequivalentrectangularasintheidealizedstressdistribution.idealizedstressdistributionequivalentrectangularxnxnSameamountandlocationoftotalcompressionforceC原則：C的大小和作用點位置不變idealizedstressdistributionequivalentrectangularstressdistributionEquivalentrectangularstressdistribution

壓區(qū)混凝土等效矩形應(yīng)力圖形極限受彎承載力moment/

ultimatestrength

Theequivalentrectangularstressdistributioncanbeusedforderivingtheultimatestrengthdesignequationsofbeams.Thebasicdesignequationsforthemomentcapacityofasinglyreinforcedrectangularbeamcanbeestablishedbyconsideringtheequilibriumofforcesandmomentsbh0h0-x/2h0UltimatestrengthdesignequationsofbeamsForbeamsreinforcedwithmoderateamountofsteel

ss=fyxbh0bh0h0-x/2h0EquilibriumofforcesandmomentsmomentcapacityBalancedStrainConditionatbalancedfailure,thesteelstrainisexactlyequaltotheyieldstrainwhenthestrainintheconcretesimultaneouslyreachesthecrushingstrainofRelativeconcretecompressionzonedepth相對受壓區(qū)高度ReinforcementRatio

x

revealsthearearatioandstrengthratiobetweenreinforcementandconcreteStrengthratioArearatioBalancedrelativeconcretecompressionzonedepth界限受壓區(qū)高度)5.01(20max,bbcubhfMxxa-=Momentcapacity

atbalancedfailuretherelativeconcretecompressionzonedepthisonlyrelatedtothematerialproperties.

Balancedreinforcementratio

適筋梁的最大配筋率（平衡配筋梁的配筋率）rmax=uniquer

valuetogetsimultaneousec=0.003&es=eyfy0.0015Theconcretecrushesandthesteelyieldssimultaneously.Whichtypeoffailureisthemostdesirable?Themoderate-reinforcedbeamisthemostdesirable.fs=fyes>>eyYouwantductilitysystemdeflectsandstillcarriesload.moderate-reinforcedbeam適筋梁的判別條件

Toensureanmoderate-reinforcedbeamwithductileandyieldingofthetensionreinforcement,DesigncodeGB50010-2002limitstheamountofreinforcementorrelativeconcretecompressionzonedepthinordertopreventnonductilebehavior:

balancedreinforcementratio同時不應(yīng)小于0.2%

；對于現(xiàn)澆板和基礎(chǔ)底板沿每個方向受拉鋼筋的最小配筋率不應(yīng)小于0.15%。最小配筋率規(guī)定了少筋和適筋的界限Minimumreinforcementratio

適筋梁的最小配筋率

Topreventlightlyreinforcedbehaviorρ≥ρminor

As≥As，min=ρminbh。Aminimumreinforcementratioisrequiredtoensurethattheflexuralstrengthofthereinforcedsectionisgreaterthanthatoftheuncrackedconcretesectionotherwisesuddenfailureoccurswhenthetensilestrengthofconcreteisexceededandthefirstflexuralcrackforms.TheminimumallowablereinforcementratiogivenbyGB50010-2002isRectangularBeamswithTensionandCompressionReinforcement雙筋矩形截面受彎構(gòu)件Doublyreinforcedbeam-reinforcementinthecompressionzoneandtensionzonebeamcrosssectionislimitedbecauseofarchitectureorotherconsiderationsothattheconcretecannotdevelopthecompressionforcerequiredtoresistthegivenbendingmoment