材料力学04第四章弯曲内力

1、Mechanics of Materials AB对称轴对称轴纵向对称面纵向对称面梁变形后的轴线与梁变形后的轴线与外力在同一平面内外力在同一平面内梁的轴线梁的轴线RAF1F2RB（。RAAAAAAAAYAAXARHM BAalFYAXARBABFlalFRFlFaRmXFAyBAAx)( , 0 , 00 , 0 MYAXARBABFmmxYAFSCFRBFSCMxYMmlalFYFFACAy , 0)(s , 0FSdxmmFS+dxmmFSFS；mm+（受拉）（受拉）MMmm（受压）（受压）MM0mARBBdEDAabclCFF1F2RA021bFaFlRB0mB0)()(21blFalF

2、lRAlblFalFRA)()(21lbFaFRB21 BdEDAabclCFF1F2RAAECFSERA00S EAyFR,F0, 0cRMmAEEAERFScRMAEAEcFSERAa- cb- cCDl- cBEFSEF1F2 0yF021S FFRFBE0ME0)()()(21McbFcaFclREB+cRMAEAERFS BdEDAabclCFF1F2RAFdBFSFMFRB0, 00, 0S dRMmRFFBFFBFy-+RFBF SdRMBF niiSFF左（右）左（右）1 mkkiniiMaFM左（右）左（右）左（右）左（右）11F2=FACDBbacF1=FRARB kN60

3、FRRBAF2=FACDBbacF1=FRARBkN601SFFCkN.m061.bFMC060601SFRFADkN.m8 .13)(1FacFacRMADC12mkN4SS1RFFAC左左kN.m411RMMAC左左kN4)4(S2SRFFBC右右kN.m651)4()152(2.RMMBC右右B1m2.5m10kN.mAC12RARB xFs(x)Fs 图的坐标系图的坐标系OM 图的坐标系图的坐标系xOM(x)BAFlx)0()()0()(SlxFxxMlxFxF0SFA左左0SFA右右FSxFFlxMAFBlx)0()()0()(SlxFxxMlxFxF2qlRRBAlqRARBABx

4、)0(222)()0(2)(2SlxqxqlxxqxxRxMlxqxqlqxRxFAA )0(2)(SlxqxqlxF2SqlF 2SqlF +ql/2ql/2BlqRAAxRB)0(222)(2lxqxqlxxqxxRxMAlqRAABxRB00,Mx0,Mlx02)(dqxqldxxM2lx 822maxqlMMlx+82qll/2 lqRAABxRB+ql/2ql/2+82qll/282maxqlM2maxSqlFlFABCabRARBlFbRAlFaRB xxlFABCabRARB)2()0()()1()0()(SaxxlFbxMaxlFbxF)4()()()()()3()()()(S

5、lxaxllFaaxFxlFbxMlxalFalblFFlFbxF)1()0()(SaxlFbxF)3()()(SlxalFaxFxxlFABCabRARB+lFblFa)4()()()(lxaxllFaxM)2()0()(axxlFbxMxxlFABCabRARB+lFbaxxlFABCabRARB+lFbalFblFalmRAlmRB)1()0()(SlxlmxFlABCabRARBmxxlABCabRARBm(2)xlmxM)()0(ax (3)()(xllmmxlmxM)(lxalABCabRARBm)1()0()(SlxlmxFlmF S+lmxlABCabRARBm(2)xlmxM

6、)()0(ax (3)()(xllmmxlmxM)(lxa lmaMC左左 0M lmbMC右右+lmalmblABCabRARBm+lm+lmalmbABFlxlxlFRA)( lFxRBxlxlFxRMAC)( 0ddxMC0)2(xllF2lx 2lx xlxlFxRMAC)( FlM41maxxyq(x)Fmxyq(x)FmFs(x)M(x)Fs(x)+dFs(x)M(x)+dM(x)mmnnq(x)C .xmmnn dxFs(x)M(x)Fs(x)+dFs(x)M(x)+dM(x)mmnnq(x)C0d)()(d)()( 0SSS xxqxFxFxFFx )(d)(dSxqxxF02

7、d)d(d )s()( )(d)( 0 xxxqxxFxMxMxMMC)(d)(dSxFxxM)(d)(dSxqxxF)(d)(dSxFxxM)(d)(d22xqxxMxFs(x)OxOM(x)(d)(dSxqxxF)(d)(dSxFxxM)(d)(d22xqxxM xFs(x)OxOM(x)(d)(dSxqxxF)(d)(dSxFxxM)(d)(d22xqxxMOM(x)x)(d)(dSxqxxF)(d)(dSxFxxM)(d)(d22xqxxMFCmC或或q0FmC)(d)(dSxqxxF2121)()(dSxxxxdxxqxF21)()()(1S2SxxdxxqxFxF2112)(SSx

8、xxxdxxqFF2112)(SSxxxxdxxqFF)(d)(dSxFxxMbaABdxxFMM)(Sk623.RA kN27 RBBACD2001151265FFRARB231kN6 .23SAARF右右23.61.727+BRBACD2001151265FFRA231kN27SBDRF右右kN0S右右BFkN27SmaxFkN7 . 1SFRFAC右右4.723.11+BACD2001151265FFRARB231mkN11. 3115. 0RMBD0MBmkN72. 4max MmkN72. 42 . 0 RMAC0MABACD2001151265FFRARB2314.723.11+2

9、3.61.727+ RARBEqABCD0.21.612kN806110050RRBA+80kN80kNkN80SAARF右右 kN80SACRFkN80SBDRFkN80S左左BBRFkN0S右右BF),( kN80maxSFRARBEqABCD0.21.6120MAkN.m1620.RMACmkN1620RMBDmkN48)201(212qRMAE +161648单位：单位：kN.mmkN48maxMRARBEqABCD0.21.6123m4mABCDE4m4mRARBF1=2kNq=1kN/mm=10kN.mF2=2kNkN7RAkN5RBkN7S RFAA右右kN34S qRFAC左左

10、kN141S PqRFAC右右kN32S BDRPF3m4mABCDE4m4mRARBF1=2kNq=1kN/mm=10kN.mF2=2kNkN32SBRFFkN22S PFB右右kN7S 右右AFkN3S 左左CFkN1S 右右CFkN3S DF01SFqxRFAx7kN1kN+3kN3kN2kNx=5m0MA204242qRMAC16472mRFMBD左左5 .20maxMMF6472RPMBD右右632PMB0 ME3m4mABCDE4m4mRARBF1=2kNq=1kN/mm=10kN.mF2=2kN201666+20.510.5113F=50kNM=5kN.mAECDKBRARBmA

11、q=20kN/m 10.5113F=50kNM=5kN.mAECDKBRARBmAq=20kN/m81kN31kN29kN+10.5113F=50kNM=5kN.mAECDKBRARBmAq=20kN/m0qxRFBSxm45. 1qRxBx=1.4581kN31kN29kN+B10.5113F=50kNM=5kN.mAECDKRARBmAq=20kN/mmkN5 .96mMAA右右mkN5 .15181MMAE05 . 031MMECmkN31131MMCD96.515.531 B10.5113F=50kNM=5kN.mAECDKRARBmAq=20kN/mmRMBK1mkN345129mR

12、MB45. 2maxmkN5545. 122qmkN5 mMB左左0MB右右96.53115.5x+55345F=50kNM=5kN.mAECDKRARBmAq=20kN/m+abcd18kN2kN14kN3m3m6m+)(dsdxqxFkN18SFB左左kN2S FB右右CABDF=20kN)(ddxqxFSqdxxqFFdcCD6)(SSkN26)2()14(qabcd18kN2kN14kN3m3m6m+q=2kNCABDF=20kN)(d)(dSxFxxMbaABdxxFMM)(SmkN543180abcd18kN2kN14kN3m3m6m+cbSBCxxFMMd)(kN.m 483)2

13、(540Md48dab54c+40kN.mabcd2m2m2m+)(d)(dSxFxxMSS2)(FdxxFMMcbBCkN2024002MSMFBCabcd20kNm)(ddxqxFS0MA左左mkN40右右AM40KN.mabcd2m2m2m+abcd20kNBCAD0SFB左左kN20SFB右右kN20SFB左左0SFB右右FF )()()(),(Sn21S11S21SnnFFFFFFFFFF )()()(),(nn221121FMPMPMFFFMn . xF=ql/3qlxF=ql/3ql2)(2qxFxxMFxqxFxxMF )(2)(2qxxMq2)(2qxFxxMFxFqxlqx

14、+FxxMF)(Fl2)(2qxxMq22ql+-62ql62ql812qlBCF2F3aDEF1AaaaF1291acebdF2e122+acbd215acebdF3aaaa291acebdmkN1312152112229121)()(MCBCF2F3aDEF1Aaaa122+acebd215acebd291215131acebdABCalF1F2ABCM(x)FN(x)FS(x)CxF1xalF1F2ABCFS(x)CBaF1F2FN(x)M(x)x0 FN图图F1|CalF1F2ABFs图图F1+F2+CalF1F2ABF1aF1aF1a+F2l FOR cosFFS sinNFF sinFRM 0sin0N FFFn0cos0S FFFt0sin0 FRMmCFtnC FNFS