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Chaper7Torsionalstrengthofmembers,7.1Introduction7.2Experimentaboutpuretorsionmember7.3Torsionalcapacityofmembersunderpuretorsion7.4Torsionalcapacityofmemberundercombinedflexure,shearandtorsion7.7Detailingrequirements,7.1Introduction,Twotypesoftorsion,Equilibriumtorsion(平衡扭矩)：staticallydeterminatetorsion;primarytorsion,Itisdeterminedbasedonstaticequilibrium,andnotrelatedtothetorsionalstiffness.,Compatibilitytorsion(协调扭矩)：staticallyindeterminatetorsion;secondarytorsion,Itcannotbedeterminedbasedonstaticequilibriumalone,andrelatedtothetorsionalstiffnessanddeformationofmembers.,7.2Experimentofpuretorsion,1.Mechanicalanalysisofpuretorsionbeforecrack,Whentheprinciplestressesexceedthetensilestrength,cracksformatthemiddlepointoflongersideandextenddiagonallyalong45linetotheneighboringfaces.Finally,cracksarespiralwhenconcreteinonesidecrushes.,Spiralcracks,2.Torsionalreinforcements,2.Failuremodesoftorsionalmemberswithtorsionalreinforments,Failuremodesarecloserelatedtotheratioofreinforcements.,Under-reinforcedmember,scarce-reinforcedmember,Over-reinforcedmember,Over-reinforcedmember,Calculationoftorsionalstrength,Minimumamountoftorsionalreinforcements,Partiallyover-reinforcedmember,Checktheminimumdimensionofsection,7.3Torsionalresistanceofmemberunderpuretorsion,1、CrackingtorqueTcr,Principlestress,Ifconcreteisidealplasticmaterial,membercrackswhenprinciplestressesatallpointsofsectionexceedtensilestrength,2、Torsionalcapacityofmemberwithtorsionalreinforcements,(1)Mechanicalmodel-spacetrussanalogy,Longitudinalbars-tensionchordsStirrups-tensionwebmembersconcrete-compressiondiagonals,(2)Torsionalstrengthofrectangularmemberunderpuretorsion,Tmemberand-shapedmemberunderpuretorsion,Thesectionisdividedintoseveralrectangularsection.,1、Experimentandfailuremodes,7.4Torsionalcapacityofmemberundercombinedflexure,shearandtorsion,Flexureisdominant.,Concreteatthebottomcracks,thenextendingtotheneighboringsides.Finally,concreteatthetopcrushes.,Torsionisdominant,atthesametimetheamountofreinforcementsatthetopislittle.,Concreteinthelongersidecracks,thenextendingtotheneighboringside.Finally,concreteatthebottomcrushes.,Torsionandsheararedominant,Concreteinthelongersidecracks,thenextendingtotheneighboringsidetop.Finally,concreteintheoppositesidecrushes.,2、Torsionalcapacityofmemberundercombinedflexure,shearandtorsion,Becauseoftorsion,theshearstrengthofmemberwilllowerthanthatofpureshear.(1.5-t),(1)Correlativerelationshipofshearandtorsion,t-Reductioncoefficientoftorsionalstrength,Becauseofshear,thetorsionstrengthofmemberwilllowerthanthatofpuretorsion.,Calculationformulasoftorsionandshear,Formulasofpuretorsionandshear,3、Designmethodsofmemberundercombinedflexure,shearandtorsion,Totalstirrups,7.7Detailingrequirements,1、Minimumratiooftorsionallongitudinalreinforcements,2、Minimumratioofshearandtorsionalstirrups,3、Minimumdimensionofsection,4、Shearandtorsionreinforcementscanbearrangedaccordingtodetailingrequirementswhenthefollowingconditionsaresatisfied.,5、Shearortorsioncannotbeconsideredwhenthefollowingconditionsaresatisfied.,Shearcannotbeconsidered(V0),Torsioncannotbeconsidered(T0),DesignProcedure,1、Checktheminimumdimensionofsection；2、Checkifshearandtorsionreinforcementscanbearrangedaccordingtodetailingrequirements；3、Checkwhethershearortorsioncanbeneglected.4、Computetheflexuralstrengthtodeterminetheflexuralreinforcements.5、Computetorsionstrengthtodeterminethetorsionalstirrupsandlongitudinalbars.6、Computetheshearstrengthtodeterminetheshearstirrups.7、Addtheamountofthesametypeofreinforcementsandselectreinforcements8、Sketchthesection,弯型破坏,2、满足下列条件可按构造配置剪扭钢筋：,3、出现下列情况时，可不考虑剪力或扭矩的作用,(1)当,(2)当,可不考虑剪力，即V0,可不考虑扭矩，即T0,1、截面尺寸验算,二者中的较大值,4、最小配筋率,Whenisfrom0.333to3，alltorsionalreinforcementscanyieldatultimatetorsionmoment.ChineseCode:=0.6-1.7,-Ratioofstrengthoflongitudinalbarstostirrups,例题,雨篷剖面见图7-16。雨篷板上承受均布荷载（已包括板的自身重力）q=3.6kN/m2（设计值），在雨篷自由端沿板宽方向每米承受活荷载p=1.4kN/m（设计值）。雨篷梁截面240mmX240mm，计算跨度2.5m，采用C30混凝土，箍筋采用HPB300，纵向钢筋采用HRB400，环境类别为二类a。经计算知，雨篷梁玩具设计值M=14kN.m，剪力设计值V=30kN。确定雨篷梁的配筋数量。,例题图,1、计算简图及内力,2、几何参数,例题图,3、验算截面尺寸,4、是否可按构造配置剪扭钢筋,5、验算是否可忽略剪力或者扭矩,构造要求,6、受弯纵筋计算,7、受剪计算,计算公式,8、受扭计算,计算公式,9、受剪扭钢筋最小配筋率验算,构造要求,10、配筋,
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