受彎構(gòu)件斜截面承載力計(jì)算教學(xué)課件

Chapter4ShearCapacityofFlexuralMember4.1Introduction4.2Diagonalcracks（斜裂縫）,Shearspanratio（剪跨比）andfailuremodesofinclinedsection（斜截面的破壞形態(tài)）4.3Inclined-sectionshearmechanismofsimplebeam4.4Calculationofshearcapacity4.5Detailingrequirementssatisfyinginclined-sectionalflexuralcapacity(保證斜截面受彎承載力的構(gòu)造措施)4.6Somedetailingrequirementsforbeamsandslabs5.1IntroductionFFaM圖V圖WebreinforcementsStirrupsBent-upbars1.Stressanalysisofflexuralmember12345234123454.2.1Flexural-shearcracksandweb-shearcracksPrincipaltensilestressPrinciplestresstrajectoryFlexural-shearcracksWeb-shearcracks2、Typesofcracks4.2.3Threemainfailuremodesofinclinedsection<1（1）Diagonalcompressionfailure：1.Failuremodesofinclinedsectionofbeamwithoutwebreinforcements(無腹筋梁的斜截面破壞形態(tài))ShearforceishighandbendingmomentissmallWed-shearcrackscutthebeamintodiagonalshortcolumnsTheprincipalcompressivestressexceedsthecompressivestrength.1≤≤3（2）Shearcompressionfailure：Severaldiagonalcracksformbetweentheconcentratedloadandsupport.Oneofthemdevelopsintocriticaldiagonalcracks.Concreteinshear-compressionzonecrushesonthetopofthecriticaldiagonalcracks.（3）Diagonaltensionfailure：>3Thediagonaloccursanddevelopsintocriticalcrack.Thecriticaldiagonalcracksplitbeamintotwo.Theamountofwebreinforcementisappropriate>3andtheamountofreinforcementisinadequateTheamountofwebreinforcementistoomuchShearcompressionDiagonaltensionAvoiditbyshearcapacitydesign2.Failuremodesofinclinedsectionofbeamwithwebreinforcements(有腹筋梁的斜截面破壞形態(tài))AvoiditbystipulatetheminimumamountofshearreinforcementDiagonalcompressionAvoiditbyCheckthesectiondimension4.3Mechanicalmechanismofinclinedsection4.3.1Tied-archstructureTheforcesintheinclinedsection

：(1)TensionforceTinlongitudinalreinforcement

；(2)ShearforeVcandcompressionforceCintheresidualconcrete；(3)InterlockforceofaggregateVa；(4)DowelforceVd。VdTVaVcC4.3.3TrussmodelCDiagonalcompressionstrutVerticaltensionstrutTensionchordCompressionchordVdTVaVcCVsvTheforcesintheinclinedsection

：(1)TensionforceTinlongitudinalreinforcement

；(2)ShearforeVcandcompressionforceCintheresidualconcrete；(3)InterlockforceofaggregateVa；(4)DowelforceVd。(5)TensionforceinstirrupsVsv4.4.2Formulasforshearcapacityininclinedsection1.FundamentalassumptionVdTVaVcCVsvVsbNeglecttheinterlockforce,dowelforce.TheforcesbalancingtheVerticalforce：(1)ShearforeVc

intheresidualconcrete；(2)VerticalcomponentforceofinterlockforceofaggregateVa；(3)DowelforceVd。(4)TensionforceinstirrupsVsv。(5)VerticalcomponentforceoftensionforceVbinbent-upbars2.CalculationformulasforshearcapacityOnlyStirrupStirrupandbent-upbarsIndependentbeamsprominentlysubjectedtoconcentratedloadsOtherbeams3、FormulasforVcsNew2010Code4、CalculationformulaforVsbfyAsbasAnglebent-upbarswithrespecttotheaxisofbeam.Generally45°，60°whenthedepthofsectionismorethan800mm（2）

Theminimumamountofstirrup（Lowerlimit）AreaofstirrupswithinacrosssectionSpacingofstirrups6.ConditionsofselectingstirrupaccordingtominimumstirruprationanddetailingrequirementsFormulasforshearcapacity（1）Independentbeamsprominentlysubjectedtoconcentratedloads（1）Otherbeams1234523412345CalculationformulaforshearcapacityOnlyStirrupStirrupandbent-upbarsIndependentbeamsprominentlysubjectedtoconcentratedloadsOtherbeams4.5DetailingRequirementforFlexuralCapacityofInclinedSection4.5.1Momentcapacitydiagram（正截面受彎承載力圖-材料圖）4.5.2Bent-upoflongitudinalreinforcements(縱向鋼筋的彎起)4.5.3Cutoffoflongitudinalreinforcements(縱向鋼筋的截?cái)?4.5.3Cutoffoflongitudinalreinforcements(縱筋的截?cái)啵?.Theprinciplesforcutoff(截?cái)嗟脑瓌t)：(1)Thenegativebarsresistingthenegativemomentmaybecutoff.(允許抵抗支座負(fù)彎矩的縱筋延長截?cái)?；(2)Thepositivebarsresistingthepositivemomentwithinthespanmaynotbecutoff.(一般不截?cái)嗟挚箍缰姓龔澗氐目v筋)Barsarecutoffatadistancebeyonditstheoreticalcutoffpointorthefully-stressedpoint.(在離開理論斷點(diǎn)或充分利用點(diǎn)以外一定距離截?cái)啵㎝ethod2.Methodofcutoff(截?cái)嗟姆椒?：Itmaynotbecutoffatitstheoreticalcutoffpoint.(不能在理論斷點(diǎn)處截?cái)?ChineseCodeFig.5abcd32132133Fig.1Fig.2Takethebar③asanexampleabcd321Assumingthebar③isbentupatpointa,themomentcapacityMuwilllessthanthemomentM.Fig.3Fig.54.6Detailingrequirementsforbeamsandslabs4.6.1Longitudinalstressedsteelbars4.6.2Bent-upsteelbars4.6.3Stirrupinbeams4.6.4ErectionsteelbarsandotherlongitudinaldetailingsteelbarsAnchorageoflongitudinalsteelbarsinsupports(縱向受力鋼筋在支座中的錨固)1)Simplysupportedbeams2)Continuousbeams4.6.1Longitudinalstressedsteelbars1.Anchorage（2）Spliceoflongitudinalsteelbars(縱向受力鋼筋搭接)（3）Erectionsteelbars(stirrup-supportbars)（4）Longitudinaldetailingsteelbarsalongthedepth