材料力学第四章 弯曲内力

1、2022-3-1122022-3-1132022-3-1142022-3-1152022-3-1162022-3-117 2022-3-118AB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FRAF1F2FRB2022-3-119。FAAAA2022-3-1110AAAFRAyAFRAxFFM2022-3-1111 2022-3-11122022-3-1113 BAalFFFFRBABF , , () , RRR0000 xAxAByAyFFFaMFlF laFFl2022-3-1114MFRAxFABFmmxRAyFSCFF

2、RBFSCM() , , SRR00yAyCAyF laFFFlMMFx2022-3-1115FSdxmmFS+dxmmFSFS2022-3-1116；mm+MMmm（受压）（受压）MM2022-3-11170AMFRBBdEDAabclCFF1F2FRA021R bFaFlFB0BM0)()(21R blFalFlFAlblFalFFA)()(21R lbFaFFB21R 2022-3-1118 BdEDAabclCFF1F2FRAAEcFSEFRA00SR EAyFF,F0, 0R cFMMAEEAEFFRS cFMAE R2022-3-1119AEcFSEFRAa-cb-cCDl-cBE

3、FSEF1F2 0yF021RS FFFFBE0ME0)()()(21R McbFcaFclFEB+cFMAE RAEFFRS 2022-3-1120 BdEDAabclCFF1F2FRAFdBFSFMFFRB,SRR0000yFBFFBFFFMMFd-+BFFFRS dFMBFR 2022-3-1121 niiFF左（右）1S 2022-3-1122 mkkiniiMaFM左（右）左（右）左（右）左（右）112022-3-1123F2=FACDBbacF1=FFF kN60RR FFFBA2022-3-1124F2=FACDBbacF1=FFRBkN601SFFCmkN061 .bFMC06

4、0601RS FFFADmkN8 .13)(1R FacFacFMAD2022-3-1125C12MkN4RSS1 ACFFF左mkN41R1 ACFMM左kN4)4(RS2S BCFFF右mkN651)4()152(R2 .FMMBC右B1m2.5m10kNmAC12FF2022-3-1126 2022-3-1127 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)2022-3-1128BAFlx)0()()0()(SlxFxxMlxFxF 0SFA左左FFA 右右SFSxFFlxM2022-3-11292RRqlFFBA lqFFABx)0(222)()0(2)

5、(2RRSlxqxqlxxqxxFxMlxqxqlqxFxFAA 2022-3-1130)0(2)(SlxqxqlxF2SqlF 2SqlF +ql/2ql/2BlqFAxF2022-3-1131)0(222)(2RlxqxqlxxqxxFxMA lqFABxF00 Mx，0, Mlx( )d0d2M xqlqxx2lx 822maxqlMMlx+82qll/22022-3-1132 lqFABxF+ql/2ql/2+82qll/282maxqlM2maxSqlF2022-3-1133lFABCabFFlFbFA RlFaFB R2022-3-1134 xxlFABCabFRAFRB)2()0

6、()()1()0()(SaxxlFbxMaxlFbxF )4()()()()()3()()()(SlxaxllFaaxFxlFbxMlxalFalblFFlFbxF 2022-3-1135)1()0()(SaxlFbxF)3()()(SlxalFaxF xxlFABCabFRAFRB+lFblFa)4()()()(lxaxllFaxM )2()0()(axxlFbxM+lFba2022-3-1136xxlFABCabFRAFRB+lFbalFblFa2022-3-1137R AMFlR BMFl( )() ( )S01MFxxlllABCabFRAFRBM+Ml2022-3-1138xxlAB

7、CabFRAFRBM( ) MM xxl)0(ax ( )()MMM xx Mlxll)(lxa CMaMl左左 0M CMbMl右右+MalMbl2022-3-1139lABCabFRAFRBM+/M l+MalMbl2022-3-11402022-3-1141ABFlxlxlFFA)(R lFxFB RxlxlFxFMAC)(R 0ddxMC0)2(xllF2lx 2022-3-11422lx xlxlFxFMAC)(R FlM41max2022-3-1143xyq(x)FM2022-3-1144xyq(x)FMFS(x)M(x)FS(x)+dFS(x)M(x)+dM(x)mmnnq(x)

8、C .nxmmn dx2022-3-114502d)d(d )()( )(d)( 0 S xxxqxxFxMxMxMMCFS(x)M(x)FS(x)+dFS(x)M(x)+dM(x)mmnnq(x)C0d)()(d)()( 0SSS xxqxFxFxFFx )(d)(dSxqxxF)(d)(dSxFxxM2022-3-1146)(d)(dSxqxxF)(d)(dSxFxxM)(d)(d22xqxxM2022-3-1147xFS(x)OxOM(x)(d)(dSxqxxF)(d)(dSxFxxM)(d)(d22xqxxM2022-3-1148xFS(x)OxOM(x)(d)(dSxqxxF)(d)

9、(dSxFxxM)(d)(d22xqxxMOM(x)x2022-3-1149)(d)(dSxqxxF)(d)(dSxFxxM)(d)(d22xqxxM2022-3-1150FCMC或或q0FMC2022-3-1151)(d)(dSxqxxF ( )( )2211SddxxxxFxq xx()()( )21S2S1dxxFxFxq xx()()( )21S2S1dxxFxFxq xx2022-3-1152)(d)(dSxFxxM( )()()21S21dxxFxxM xM x()()( )21S2S1dxxFxFxq xx)()(2S1SxFxF2022-3-1153k623R.FA kN27R

10、 BFBACD2001151265FFFF231kN6 .23RS AAFF右2022-3-115423.61.727+BFRBACD2001151265FFFRA231kN27RS BDFF右kN0S右右BFkN27SmaxFkN7 . 1RS FFFAC右2022-3-11554.723.11+BACD2001151265FFFRAFRB231mkN11. 3115. 0R BDFM0MBmkN72. 4max MmkN72. 42 . 0R ACFM0MA2022-3-1156BACD2001151265FFFRAFRB2314.723.11+23.61.727+2022-3-1157

11、FEqABCD0.21.612kN806 . 11005 . 0RR BAFF2022-3-1158+80kN80kNkN80RS AAFF右 kN80RS ACFFkN80RS BDFFkN80RS左 BBFFkN0S右右BF kN80maxS FFEqABCD0.21.6122022-3-11593m4mABCDE4m4mFRAFRBF1=2kNq=1kN/mM=10kNmF2=2kNkN7R AFkN5R BFkN7RS AAFF右kN34RS qFFAC左kN141RS FqFFAC右kN3R2S BDFFF2022-3-11603m4mABCDE4m4mFRAFRBF1=2kNq=1

12、kN/mM=10kNmF2=2kNkN3R2S BFFFkN22S FFB右kN7S 右右AFkN3S 左左CFkN1S 右右CFkN3S DF01RS FqxFFAx7kN1kN+3kN3kN2kNx=5m2022-3-11610MA 2R7164DBMFMF左左5 .20maxMMF647R2 BDFFM右632 FMB0 ME201666+20.53m4mABCDE4m4mFRAFRBF1=2kNq=1kN/mM=10kNmF2=2kN204242R qFMAC2022-3-11623m4mABCDE4m4mFRAFRBF1=2kNq=1kN/mM=10kNmF2=2kN7kN1kN+3

13、kN3kN2kNx=5m201666+20.52022-3-116310.5113F=50kNM=5kNmAECDKBFRAFRBMAq=20kN/m2022-3-1164 81kN31kN29kN+10.5113F=50kNM=5kNmAECDKBFRAFRBMAq=20kN/m2022-3-11650RS qxFFBxm45. 1R qFxBx=1.4581kN31kN29kN+10.5113F=50kNM=5kNmAECDKBFRAFRBMAq=20kN/m2022-3-1166kN mAAMM右右9 96 6. .5 5mkN5 .15181MMAE05 . 031MMECmkN311

14、31MMCD96.515.53110.5113F=50kNM=5kNmAECDKBFRAFRBMAq=20kN/m2022-3-1167 R1KBFMMmkN345129.maxR2 45BMFMmkN5545.122q5kN mBMM左左0MB右右96.53115.5x+5534510.5113F=50kNM=5kNmAECDKBFRAFRBMAq=20kN/m2022-3-1168+10.5113F=50kNM=5kNmAECDKBFRAFRBMAq=20kN/m2022-3-1169abcd18kN2kN14kN3m3m6m+( )SddFq xxkN18SFB左左kN2S FB右右CA

15、BDF=20kN2022-3-1170( )SddFq xx( )SSd6dDCcq xxqFFkN/m26)2()14( qabcd18kN2kN14kN3m3m6m+q=2kNCABDF=20kN2022-3-1171)(d)(dSxFxxM( )SdbBAaMMFxxmkN543180abcd18kN2kN14kN3m3m6m+cbSBCxxFMMd)() 542348 kN m0Md48dab54c+2022-3-117240kNmabcd2m2m2m+)(d)(dSxFxxM( )SSd2cCBbFxxFMMS0 4020kN22CBMMFabcd20kN2022-3-1173Me)

16、(ddxqxFS0MA左左mkN40右右AM40KNmabcd2m2m2m+abcd20kNBCAD0SFB左左kN20SFB右右kN20SFB左左0SFB右右FF2022-3-1174 )()()(),(Sn21S11S21SnnFFFFFFFFFF (,)()()()121122nnnM F FFM FM FMF2022-3-1175xF=ql/3ql2022-3-1176xF=ql/3ql2)(2qxFxxMxqxFxxMF )(2)(2qxxMq2)(2qxFxxM2022-3-1177Fxqxlqx+FxxMF)(Fl2)(2qxxMq22ql+-62ql62ql812ql2022-

17、3-1178BCF2F3aDEF1AaaaF1291acebdF2e122+acbd215acebdF3aaaa2022-3-1179291acebdmkN1312152112229121)()(MCBCF2F3aDEF1Aaaa122+acebd215acebd291215131acebd2022-3-1180ABC2022-3-11812022-3-1182alF1F2ABCM(x)FN(x)FS(x)CxF1x2022-3-1183alF1F2ABCFS(x)CBaF1F2FN(x)M(x)x2022-3-11840 FN图图F1|CalF1F2ABFS图图F1+F2+2022-3-1185CalF1F2ABF1aF1aF1a+F2l 2022-3-11862022-3-1187FOR ScosFF NsinFF sinMFR 0sin0N FFFn0cos0S FFFt0