工程力学-3 shear force and bending moment

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1、第三章剪力和弯矩Chapter3ShearForcesandBendingMoments6/13/20211KylinsoftqIntroductionBAPBeam:thestructuralmembertoresistforcesactingtransversetoitsaxisSimplebeamSimplysupportedbeam6/13/20212KylinsoftBAP2P1Beamwithanoverhang6/13/20213KylinsoftPABCantileverbeam6/13/20214Kylinso

2、ftPlaneBendinghavingsymmetriccrosssectionsLoadsactinthesymmetricplanethebendingdeflectionsoccurinthisplane6/13/20215KylinsoftSectionsofcommonlyusedbeams6/13/20216KylinsoftPlanebendingand3Dbending6/13/20217Kylinsoft6/13/20218KylinsoftConcentratedLoadPDistributedLoadqC

3、oupleMTypeofLoads6/13/20219KylinsoftSimpleBeamBeamwithanOverhangCantileverBeamFAxFAyFByFAxFAyFByFAxFAyMAReactionsinvarioustypesofsupportsHowtofindthereactions?6/13/202110KylinsoftAxPShearForcesandBendingMomentsMMethodofsectionBMSY=0P-V=0V=PoSMo=0M-Px=0M=PxSignConvent

4、ionMVVMMVVMVVVVMMMMVABmnxPV6/13/202111KylinsoftBendingMomentandShearForceRAFindtheBendingMomentandShearForceoncrosssectionofI-IReactionsRA,RBP2PaxIIABlaSMB=0RAl-P(l-a)-2Pa=0SY=0RA+RB-3P=0RBPaxRAVMVMRB2PSM0=0SY=0RA-P-V=0RAx-P(x-a)-M=06/13/202112KylinsoftShear-Forceand

5、Bending-MomentDiagramsRARBxARAM(x)V(x)ConcentratedLoadsReactionsSY=0RA-V(x)=0(0

6、)(0

7、a2a3b6/13/202116KylinsoftRARBM(x)V(x)DistributedLoadsBAlxSY=0RA-V(x)-qx=0SM=0(0

8、2m2mBAqxmCDRBRAVM+8.5kN6kN3.5kN+6kNm6.04kNm4kNm7kNm4.83mV(x)=-qxM(x)=-qx2/2V(x)=RA-qx=14.5-3xM(x)=RA(x-2)-qx2/2=14.5(x-2)-1.5x2x=4.