1、2022-1-822022-1-832022-1-842022-1-852022-1-862022-1-87 二、根本概念二、根本概念(Basic concepts). .2022-1-88AB對(duì)稱軸對(duì)稱軸縱向?qū)ΨQ面縱向?qū)ΨQ面梁變形后的軸線與梁變形后的軸線與外力在同一平面內(nèi)外力在同一平面內(nèi)梁的軸線梁的軸線FRAF1F2FRB2022-1-892022-1-810FRAAAAA2022-1-8112022-1-812AAAFRAyAFRAxFRyFRxM2022-1-8132022-1-8142022-1-815BAalFFRAyFRAxFRBABF , , () , RRR0000 xAxAB

2、yAyFFFaMFlF laFFl2022-1-816MFRAxFRBABFmmxFSCFFRBFSCM() , , SRR00yAyCAyF laFFFlMMFx2022-1-817FSdxmmFS+dxmmFSFS2022-1-818mm+MMmm受壓受壓MM2022-1-8190AMFRBBdEDAabclCFF1F2FRA021R bFaFlFB0BM0)()(21R blFalFlFAlblFalFFA)()(21R lbFaFFB21R 2022-1-820BdEDAabclCFF1F2FRAAEcFSEFRA00SR EAyFF,F0, 0R cFMMAEEAEFFRS cFMA

3、E R2022-1-821AEcFSEFRAa-cb-cCDl-cBEFSEF1F2 0yF021RS FFFFBE0ME0)()()(21R McbFcaFclFEB+cFMAE RAEFFRS 2022-1-822 計(jì)算計(jì)算F點(diǎn)橫截面處的剪力點(diǎn)橫截面處的剪力FSF 和彎矩和彎矩MF .BdEDAabclCFF1F2FRAFdBFSFMFFRB,SRR0000yFBFFBFFFMMF d-+BFFFRS dFMBFR 2022-1-823FAyFBy 0yFFFFByAy2 0AMaFFaaFBy233FFBy35FFAyFAyFSEME 0yF352FFFSE 0EM233522aFMaF

4、E3FFSE23FaME例題例題 求圖示簡(jiǎn)支梁求圖示簡(jiǎn)支梁E E 截面的內(nèi)力截面的內(nèi)力FAy2022-1-824FByFByFAyFSEMEO3FFBy35FFAyFSEMEO 0yF0BySEFF3FFFBySE 0oMFaaFMByE2323FaME2022-1-825 niiFF左（右）1S 2022-1-826 mkkiniiMaFM左（右）左（右）左（右）左（右）112022-1-827F2=FACDBbacF1=FFRAFRB 解：解：kN60RR FFFBA2022-1-828F2=FACDBbacF1=FFRBkN601SFFCmkN061 .bFMC060601RS FFFA

5、DmkN8 .13)(1R FacFacFMAD2022-1-829C12MkN4RSS1 ACFFF左mkN41R1 ACFMM左kN4)4(RS2S BCFFF右mkN651)4()152(R2 .FMMBC右B1m2.5m10kNmAC12FRAFRB2022-1-830m3m3m2kN61212AmkNq2343455CBmkN 6練習(xí)練習(xí)2022-1-8312022-1-832 以平行于梁軸的橫坐標(biāo)以平行于梁軸的橫坐標(biāo)x表示橫截面的位置表示橫截面的位置,以縱坐標(biāo)表示相以縱坐標(biāo)表示相應(yīng)截面上的剪力和彎矩應(yīng)截面上的剪力和彎矩.這種圖線分別稱為剪力圖和彎矩圖這種圖線分別稱為剪力圖和彎矩圖x

6、FS(x)FS 圖的坐標(biāo)系圖的坐標(biāo)系OM 圖的坐標(biāo)系圖的坐標(biāo)系xOM(x)2022-1-833BAFlx)0()()0()(SlxFxxMlxFxF 0SFA左左FFA 右右SFSxFFlxM2022-1-8342RRqlFFBA lqFRAFRBABx)0(222)()0(2)(2RRSlxqxqlxxqxxFxMlxqxqlqxFxFAA 2022-1-835)0(2)(SlxqxqlxF2SqlF 2SqlF +ql/2ql/2BlqFRAAxFRB2022-1-836)0(222)(2RlxqxqlxxqxxFxMA lqFRAABxFRB00 Mx，0, Mlx( )d0d2M xq

7、lqxx2lx 822maxqlMMlx+82qll/22022-1-837lqFRAABxFRB+ql/2ql/2+82qll/282maxqlM2maxSqlF2022-1-838lFABCabFRAFRBlFbFA RlFaFB R2022-1-839 AC段段xxlFABCabFRAFRB)2()0()()1()0()(SaxxlFbxMaxlFbxF )4()()()()()3()()()(SlxaxllFaaxFxlFbxMlxalFalblFFlFbxF 2022-1-840)1()0()(SaxlFbxF)3()()(SlxalFaxF xxlFABCabFRAFRB+lFbl

8、Fa)4()()()(lxaxllFaxM )2()0()(axxlFbxM+lFba2022-1-841xxlFABCabFRAFRB+lFbalFblFa2022-1-842R AMFlR BMFl( )() ( )S01MFxxlllABCabFRAFRBM+Ml2022-1-843xxlABCabFRAFRBM( ) MM xxl)0(ax ( )()MMM xx Mlxll)(lxa x = a ,CMaMl左左 x = 0 ,0M x = a, CMbMl右右+MalMbl2022-1-844lABCabFRAFRBM+/M l+MalMbl2022-1-8452022-1-846

9、ABFlxlxlFFA)(R lFxFB RxlxlFxFMAC)(R 0ddxMC0)2(xllF2lx 2022-1-8472lx xlxlFxFMAC)(R FlM41max2022-1-848xyq(x)FM2022-1-849xyq(x)FMFS(x)M(x)FS(x)+dFS(x)M(x)+dM(x)mmnnq(x)Cnxmmn dx2022-1-85002d)d(d )()( )(d)( 0 S xxxqxxFxMxMxMMCFS(x)M(x)FS(x)+dFS(x)M(x)+dM(x)mmnnq(x)C0d)()(d)()( 0SSSyxxqxFxFxFF)(d)(dSxqxx

10、F)(d)(dSxFxxM2022-1-851)(d)(dSxqxxF)(d)(dSxFxxM)(d)(d22xqxxM2022-1-852xFS(x)OxOM(x)(d)(dSxqxxF)(d)(dSxFxxM)(d)(d22xqxxMOM(x)x2022-1-853xxlFABCabFRAFRB+lFbalFblFa2022-1-854xFS(x)OxOM(x)(d)(dSxqxxF)(d)(dSxFxxM)(d)(d22xqxxM2022-1-855lqFRAABxFRB+ql/2ql/2+82qll/22022-1-856)(d)(dSxqxxF)(d)(dSxFxxM)(d)(d22

11、xqxxM2022-1-857lABCabFRAFRBM+/M l+MalMbl2022-1-858FCMC或或q0FMC2022-1-859)(d)(dSxqxxF ( )( )2211SddxxxxFxq xx()()( )21S2S1dxxFxFxq xx2022-1-860)(d)(dSxFxxM( )()()21S21dxxFxxM xM x()()( )21S2S1dxxFxFxq xx)()(2S1SxFxF2022-1-861lABCabFRAFRBM+/M l+MalMbl2022-1-862k623R.FA kN27R BFBACD2001151265FFFRAFRB231

12、kN6 .23RS AAFF右2022-1-86323.61.727+BFRBACD2001151265FFFRA231kN27RS BDFF右kN0S右右BFkN27SmaxFkN7 . 1RS FFFAC右2022-1-8644.723.11+BACD2001151265FFFRAFRB231mkN11. 3115. 0R BDFM0MBmkN72. 4max MmkN72. 42 . 0R ACFM0MA2022-1-865BACD2001151265FFFRAFRB2314.723.11+23.61.727+2022-1-866FRBEqABCD0.21.6122022-1-867)(

13、d)(dd)(dS22xqxxFxxM2022-1-8683m4mABCDE4m4mFRAFRBF1=2kNq=1kN/mM=10kNmF2=2kNkN7R AFkN5R BFkN7RS AAFF右kN34RS qFFAC左kN141RS FqFFAC右kN3R2S BDFFF2022-1-8693m4mABCDE4m4mFRAFRBF1=2kNq=1kN/mM=10kNmF2=2kNkN3R2S BFFFkN22S FFB右kN7S 右右AFkN3S 左左CFkN1S 右右CFkN3S DF01RS FqxFFAx7kN1kN+3kN3kN2kNx=5m2022-1-8700MA 2R716

14、4DBMFMF左左5 .20maxMMF647R2 BDFFM右632 FMB0 ME201666+20.53m4mABCDE4m4mFRAFRBF1=2kNq=1kN/mM=10kNmF2=2kN204242R qFMAC2022-1-8713m4mABCDE4m4mFRAFRBF1=2kNq=1kN/mM=10kNmF2=2kN7kN1kN+3kN3kN2kNx=5m201666+20.52022-1-87210.5113F=50kNM=5kNmAECDKBFRAFRBMAq=20kN/m2022-1-87381kN31kN29kN+10.5113F=50kNM=5kNmAECDKBFRA

15、FRBMAq=20kN/m2022-1-8740RS qxFFBxm45. 1R qFxBx=1.4581kN31kN29kN+10.5113F=50kNM=5kNmAECDKBFRAFRBMAq=20kN/m2022-1-875kN mAAMM右右9 96 6. .5 5mkN5 .15181MMAE05 . 031MMECmkN31131MMCD96.515.53110.5113F=50kNM=5kNmAECDKBFRAFRBMAq=20kN/m2022-1-876 R1KBFMMmkN345129.maxR2 45BMFMmkN5545.122q5kN mBMM左左0MB右右96.531

16、15.5x+5534510.5113F=50kNM=5kNmAECDKBFRAFRBMAq=20kN/m2022-1-877+10.5113F=50kNM=5kNmAECDKBFRAFRBMAq=20kN/m2022-1-878abcd18kN2kN14kN3m3m6m+( )SddFq xxkN18SFB左左kN2S FB右右CABDF=20kN2022-1-879( )SddFq xx( )SSd6dDCcq xxqFFkN/m26)2()14( qabcd18kN2kN14kN3m3m6m+q=2kNCABDF=20kN2022-1-880)(d)(dSxFxxM( )SdbBAaMMF

17、xxmkN543180abcd18kN2kN14kN3m3m6m+cbSBCxxFMMd)() 542348 kN m0Md48dab54c+2022-1-88140kNmabcd2m2m2m+)(d)(dSxFxxM( )SSd2cCBbFxxFMMS0 4020kN22CBMMFabcd20kN2022-1-882Me)(ddxqxFS0MA左左mkN40右右AM40KNmabcd2m2m2m+abcd20kNBCAD0SFB左左kN20SFB右右kN20SFB左左0SFB右右FF2022-1-883)()()(),(Sn21S11S21SnnFFFFFFFFFF (,)()()()121

18、122nnnM F FFM FM FMF2022-1-884xF=ql/3ql2022-1-885xF=ql/3ql2)(2qxFxxMxqxFxxMF )(2)(2qxxMq2)(2qxFxxM2022-1-886Fxqxlqx+FxxMF)(Fl2)(2qxxMq22ql+-62ql62ql812ql2022-1-887BCF2F3aDEF1AaaaF1291acebdF2e122+acbd215acebdF3aaaa2022-1-888291acebdmkN1312152112229121)()(MCBCF2F3aDEF1Aaaa122+acebd215acebd291215131ace

19、bd2022-1-889ABC2022-1-8902022-1-8912022-1-892alF1F2ABCM(x)FN(x)FS(x)CxF1x2022-1-893alF1F2ABCFS(x)CBaF1F2FN(x)M(x)x2022-1-894FN圖圖F1|CalF1F2ABFS圖圖F1+F2+2022-1-895CalF1F2ABF1aF1aF1a+F2l2022-1-896Bql22qlyq 例題19 知平面剛架上的均布載荷集度q,長(zhǎng)度l。B試：畫出剛架的內(nèi)力圖。試：畫出剛架的內(nèi)力圖。ql22ql解：解：1 1、確定約束力、確定約束力22ql2 2、寫出各段的內(nèi)力方程、寫出各段的內(nèi)力方程FN(y)FS(y)M(y)豎桿豎桿ABAB：A A點(diǎn)向上為點(diǎn)向上為y y lyqyqlyFqlqyyFFSSx000 lyqlyFqlyFFNNy02/02/0 l