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Chaper7Torsionalstrengthofmembers7.1Introduction7.2Experimentaboutpuretorsionmember7.3Torsionalcapacityofmembersunderpuretorsion7.4Torsionalcapacityofmemberundercombinedflexure,shearandtorsion7.7Detailingrequirements7.1IntroductionTwotypesoftorsionEquilibriumtorsion(平衡扭矩)：staticallydeterminatetorsion;primarytorsionItisdeterminedbasedonstaticequilibrium,andnotrelatedtothetorsionalstiffness.Compatibilitytorsion(协调扭矩)：staticallyindeterminatetorsion;secondarytorsionItcannotbedeterminedbasedonstaticequilibriumalone,andrelatedtothetorsionalstiffnessanddeformationofmembers.7.2Experimentofpuretorsion1.MechanicalanalysisofpuretorsionbeforecrackWhentheprinciplestressesexceedthetensilestrength,cracksformatthemiddlepointoflongersideandextenddiagonallyalong45°linetotheneighboringfaces.Finally,cracksarespiralwhenconcreteinonesidecrushes.maxSpiralcracks2.TorsionalreinforcementsStirrupsLongitudinalbars2.FailuremodesoftorsionalmemberswithtorsionalreinformentsFailuremodesarecloserelatedtotheratioofreinforcements.scarce-reinforcedmemberTensionfailureUnder-reinforcedmemberBendingfailureUnder-reinforcedmember,scarce-reinforcedmember,Over-reinforcedmember,Over-reinforcedmemberWhenmemberisadequatelyreinforced,thereinforcementsyieldbeforeconcretecrushes.CalculationoftorsionalstrengthWhentorsionalreinforcementsareinadequate,membersfailassoonascracksform.MinimumamountoftorsionalreinforcementsPartiallyover-reinforcedmemberOver-reinforcedmemberCompressionfailureWhentwotypesoftorsionalreinforcementsareexcessive,thereinforcementsdonotyieldbeforeconcretecrushes.Whenonetypeoftorsionalreinforcementsisexcessive,theexcessivereinforcementsdonotyieldbeforeconcretecrushes.ChecktheminimumdimensionofsectionControltheratiooflongitudinalbarstostirrups（）7.3Torsionalresistanceofmemberunderpuretorsion1、CrackingtorqueTcrmax45°F1F2F3F4tttcrWfbhbfT)3(6.2ttcrWfT7.0tPrinciplestressIfconcreteisidealplasticmaterial,membercrackswhenprinciplestressesatallpointsofsectionexceedtensilestrength2、Torsionalcapacityofmemberwithtorsionalreinforcements(1)Mechanicalmodel-spacetrussanalogyLongitudinalbars-tensionchordsStirrups-tensionwebmembersconcrete-compressiondiagonals(2)TorsionalstrengthofrectangularmemberunderpuretorsioncorstyvttscuAsAfWfTTT12.135.0yvycorststffuAsA1TmemberandⅠ-shapedmemberunderpuretorsionThesectionisdividedintoseveralrectangularsection.TWWTWebttww.TWWTflangeecompressivttff.''TWWTflangeTensilettff.)3(62bhbWw)(2'2''bbhWfftf)(22bbhWfftftftftwtWWWW'1、ExperimentandfailuremodesFlexure-typedfailureTorsion-typedfailureTorsionandshear-typedfailure7.4Torsionalcapacityofmemberundercombinedflexure,shearandtorsionFlexureisdominant.Concreteatthebottomcracks,thenextendingtotheneighboringsides.Finally,concreteatthetopcrushes.Torsionisdominant,atthesametimetheamountofreinforcementsatthetopislittle.Concreteinthelongersidecracks,thenextendingtotheneighboringside.Finally,concreteatthebottomcrushes.TorsionandsheararedominantConcreteinthelongersidecracks,thenextendingtotheneighboringsidetop.Finally,concreteintheoppositesidecrushes.2、Torsionalcapacityofmemberundercombinedflexure,shearandtorsionTVBecauseoftorsion,theshearstrengthofmemberwilllowerthanthatofpureshear.(1.5-t)(1)Correlativerelationshipofshearandtorsiont-Reductioncoefficientoftorsi...