结构力学课程作业-超静定梁影响线(详解)

结构力学课程作业-超静定梁影响线(详解) ——连续梁的影响线、最不利荷载布置 及内力包络图 班级 学号 姓名 华中科技大学土木工程与力学学院 二0一三年十月 结构力学课程作业 一、 题目 KEI=C 0123 x lll123 序号 L L L X 123 25 15 12 12 X=0.25L 3二、 要求 1、用力法计算求得支点弯矩、的影响线; MM12 2、用挠度法计算求得支点弯矩、的影响线; MM21 3、求第二跨内截面K的弯矩，剪力影响线及支座1反力影响线; 4、在求影响线的基础上，进行均布移动荷载的最不利布置; 5、连续梁承受均布活荷载及恒载时，绘出弯矩、剪力包络图。 pKNm,18qKNm,12 三、 计算 由此可以求得 ()ll，()lll，23122,,,,=,,,,,11122122363EIEIEI lm,15lm,12lm,12xlm,,，,0.250.251231233已知 当 0 ,,,,Xl，即 0,1时11 2,,，，ds1l1MMl,,，,，1,,,P1，，P11,EIEI23l1 dsMM,,0P1,P2,EIl1 得力法方程: 2()llll，1221,,,MXMX()()(1)(1)0，，,，,1121366EIEIEI ()ll，l232MXMX()()0，,112163EIEI 解之得 75MX()(1)(1),,,，,,,1117 75MX()(1)(1),,，,,,2168 大致弯矩图如下: 由图可求出: 3()()MXMX，8251121,,,MX()(1)(1),,,,，K14272 MXMX()(),1252111FX()(1)(1),,,，,,,QK1l2722 MXMXMX()()(),205112111FX()=(1)(1)+,,，，,，R11,,,,,ll27212 当 0 ,,,,Xl，即 0,1时22 2,,，，lds12,,，,，MMl1,,,1P，，12P,EIEI23l2 1，,，，lds12,,，,，MMl1,,,2P，，22P,EIEI23l2 得力法方程: 2()llll，1222,,,MXMX()()(1)(2)0，，,,,1222366EIEIEI 2()ll，ll2322MXMX()()(1)(1)0，，,，,,,,1222636EIEIEI 解之得 12,,,,,,, MX()(1)(75)1217 6,,,，,,,MX()(1)(511)2217 大致弯矩图如下: 由图可求出: 当 0,,,,X3,0.25即 0,时2 3()()MXMX，(1)(57141),,,,,1222MX()99,，,，,, K2434 MXMX()(),(1)(921),,,,,2212FX(),,,,,,QK2l342 MXMXMX()()(),(1)(101145),,122212,,,FX()(1)(1),,，，,,，,R12,, ll17012 大致弯矩图如下: 由图可求出: 当 3,,,,X12,1即 0.25,时2 3()()MXMX，(1)(57141),,,,,1222MX()3(1)3(1),，,,，,,, K2434 MXMX()(),(1)(921),,,,,2212FX()(1)(1),，,,，,,,QK2l342 MXMXMX()()(),(1)(101145),,122212,,,FX()(1)(1),,，，,,，,R12,,ll17012 当 0 ,,,,Xl，即 0,1时33 ds,,,0MM1P1P, EIl3 2,,l，，ds13,,，,，MMl1,,,2P，，23P,EIEI23l3 得力法方程 ()lll，122MXMX()()0，,132336EIEI 2()lll，l2332,,,MXMX()()(1)(2)0，，,,,1323636EIEIEI 解之得 12,,,,,,MX()(1)(2)1317 54,,,,MX()(1)(2),,,2317 大致弯矩图如下: 由图可知: 当 0,,,,X12，即 01,时3 3()()MXMX，91323MX()(1)(2),,,,,,,,K3434 MXMX()(),11 2313FX()(1)(2),,,,,,,,QK3l342 MXMXMX()()(),63132313FX()(1)(2),,，,,,,R13,,,ll17012 下面用挠度法计算M1(X),M2(X) 2l1yX()(1)(1),,，,,,116EI 2l2yX()(1)(75),,,,,,1224EI 2l3yX()(1)(2),,,,13,,,24EI ll8.512,,,,，,，，,,2(20.25) 111111,,,66EIEIEI yX()7511MX()(1)(1),,,,,，11,,,1711, yX()1212MX()(1)(75),,,,,,12,,,1711,yX()1212MX(),,,,,,,,(1)(2)1317,11 同理求得 yX()7521,,,,，,,,MX()(1)(1)2168,22 yX()622 ,,,,,，MX()(1)(511),,,2217,22 yX()5422,,,,,,MX()(1)(2)23,,,1722, 与力法求得值相同 画出M1，M2 影响线 根据力法中求得的、、MXFXFX()()() KQKR1 集中力位 QR1,总长度/m Mk(X) Fk(X) F(X) 置 0 0 0.0000 0.0000 0.0000 1.5 0.1 -0.3003 0.0455 0.1746 3 0.2 -0.5824 0.0882 0.3447 4.5 0.3 -0.8280 0.1255 0.5058 6 0.4 -1.0191 0.1544 0.6532 7.5 第一跨 0.5 -1.1374 0.1723 0.7826 9 0.6 -1.1647 0.1765 0.8894 10.5 0.7 -1.0828 0.1641 0.9691 12 0.8 -0.8735 0.1324 1.0171 13.5 0.9 -0.5187 0.0786 1.0289 15 1 0.0000 0.0000 1.0000 16.2 0.1 0.5419 -0.0817 0.9458 17.4 0.2 1.1901 -0.1774 0.8678 18 0.25 1.5510 -0.2293 0.8214 18 0.25 1.5510 0.7707 0.8214 18.6 0.3 1.3347 0.7167 0.7710 19.8 0.4 0.9656 0.6042 0.6607 第二跨 21 0.5 0.6728 0.4890 0.5419 22.2 0.6 0.4461 0.3746 0.4198 23.4 0.7 0.2756 0.2648 0.2994 24.6 0.8 0.1511 0.1633 0.1859 25.8 0.9 0.0626 0.0738 0.0844 27 1 0.0000 0.0000 0.0000 28.2 0.1 -0.0453 -0.0553 -0.0634 29.4 0.2 -0.0762 -0.0932 -0.1067 第三跨 30.6 0.3 -0.0945 -0.1155 -0.1323 31.8 0.4 -0.1016 -0.1242 -0.1423 33 0.5 -0.0993 -0.1213 -0.1390 34.2 0.6 -0.0889 -0.1087 -0.1245 35.4 0.7 -0.0723 -0.0883 -0.1012 36.6 0.8 -0.0508 -0.0621 -0.0712 37.8 0.9 -0.0262 -0.0320 -0.0367 39 1 0.0000 0.0000 0.0000 求出Mk的影响线 求出FQk的影响线 求出FR1的影响线 我们知道，求某一截面的Mmax,Mmin，FQmax，FQmin，要先求出这一截面的M恒，F恒，这种情况下全梁布满荷载q，如下图所示 然后根据此截面的弯矩、剪力影响线布置荷载，若其M影响线为 Mmax的荷载布置 Mmin的荷载布置 FQmax的荷载布置 FQmin的荷载布置 则M恒=q*(S1+S2+S3+S4) Mmax=M恒+P*(S2+S4) Mmin=M恒+P*(S1+S3) FQ同理求出 (S表示曲线与横轴所包围的面积,上为“+”，下为“—”，也就是对应包络图函数对坐标轴的积分) 显然仅仅单跨满载组合无法计算出绝对的Mmax、Mmin、FQmax、FQmin，现在考虑每跨仅有部分布置荷载的情况～～～ 现在求某一点(K点)的弯矩、剪力影响线的函数表达式 一、集中力在第一跨时 75MX()(1)(1),,,，,,,1117 75MX()(1)(1),,，,,,2168 当 K点在第一跨时，设，则Xl,,K1当 0,,时，,, 75()()+(1-)(1)(1)15(1-)MXMXl,,,,，，,,,,,,,,,K111117 ()5MX11()(1)(1)FX,,,,,，,QK1,,,,,17l1 1当 ,,时，,, 75()()+(1)(1)(1)+15(1)MXMXl,,,,,，,K1111,,,,,,,,,17 ()5MX11,,,,,，，,()(1)FX,，,,,(1)(1)(1)QK1,17l1 当 K点在第二跨时，设，则Xl,,K2 75()(1)()()(54)(1)(1)MXMXMX,,，,,,，,,,,,,K1112168 ()()125MXMX,2111()(1)(1)FX,,,，,,,QK1272l2 当 K点在第三跨时，设Xl,, ，则K3 75()(1)()(1)(1)(1)MXMX,,,,,，,,,,,K12168 ()25MX21()(1)(1)FX,,,,,，,,,QK1272l3 二、集中力在第二跨时 12,,,,,,,MX()(1)(75)1217 6,,,，,,,MX()(1)(511)2217 当 K点在第一跨时，设，则Xl,,K1 12()()(1)(75)MXMX,,,,,,,,,, K21217 ()4MX12()(1)(75)FX,,,,,,,,QK285l1 当 K点在第二跨时，设，Xl,,K2 0当时,,,, 126()(1)()()+(1)(1)(1)(75)(1)(511)MXMXMXl,,，,,,,,,,,，,,,,,,,,,,,,K2122221717 +12(1),,, ()()(1)(921)MXMX,,,2212,,,()FX,,,,QK2,,34l2 当时,,,,1 126MXMXMXl()(1)()()+(1)(1)(1)(75)(1)(511),,，,,,,,,,,，,,,,,,,,,,,,K2122221717 ，,12(1),, MXMX()(),(1)(921),,2212,,,FX()(1)(1),，,,，,QK2,,l342 当 K点在第三跨时，设，则Xl,,K3 6()(1)()(1)(1)(511)MXMX,,,,,,，,,,,,K22217 ()1MX22()(1)(511)FX,,,,，,,,QK234l3 三、集中力在第三跨时 12,,,,,,MX()(1)(2)1317 54,,,,MX()(1)(2),,,2317 当 K点在第一跨时，设，则Xl,,K1 12()()(1)(2)MXMX,,,,,,,,,K31317 ()4MX13()(1)(2)FX,,,,,,,QK3 85l1 当 K点在第二跨时，设，Xl,,K2 0当时,,,, 1254()(1)()()(1)(1)(2)(1)(2)MXMXMX,,，,,,,,,,,,,,,,,,,,K313231717 ()()MXMX,112313()(1)(2)FX,,,,,QK3,,,34l2 当 K点在第三跨时，设，则Xl,,K3 当 0,,时，,, 54()(1)()+(1-)(1)(1)(2)12(1-)MXMXl,,,,,,,，,,,,,,,,,K323317 ()MX923()(1)(2)FX,,,,,,,QK3,,,,,34l3 1当 ,,时，,, 54()(1)()+(1)(1)(1)(2)12(1)MXMXl,,,,,,,,，,K1233,,,,,,,,, 17 ()X9M32，,,,,，,,,,,,(1)(1)(2)(1)()FX,,QK1l343 现在对这些函数进行积分 当点在第一跨时K ,7515322MXd()(2)(1),,,,,,,,，,1K,0682 51,222FXd()(2),,,,,,,,1QK,0682 17515222MXd()(1)(1),,,，,1K,,,,,,682, 151222FXd()(1)(1),,,，,1QK,,,,682, 19MXd()=,K2,0,,17 13FXd(),,QK2,0,85 13MXd(),3K,017,, 11FX()d,,3QK,085 当点在第二跨时K 175MXd()=(54),,,1K,0272 1125FXd(),,1QK,01088 ,621252554322MXd()(7)6(1),,,，,，，,2K,,,,,,,,017422 12191,4322FXd()(10),,，,2QK,,,,,,03442213621252554322MXd()(6)(7)6(1),,，，,，,，，,2K,,,,,,,,,3417422, 11121914322F(Xd)(10)(1),,,,,,,,，，,QK2,,136344221633,,MXd(),,3K,034 111FXd(),,3QK,,0136 当点在第三跨时K 175MXd()=(1),,,K1,0272 125FXd(),,,QK1,01088121MXd()(1),,,K2,,,034 17FXd(),QK2,,0136 ,5414322MXd()(1)()6(1),,,,，，,K2,0,,,,,,,174 911,4322FXd()(),,，,QK2,0,,,,,3442 15411，，4322MXd()(1)(,,,,,，)6(1)，,,,K2,,,1744,,,,,，，, 19111，，4322FXd()()(1),,,，，,,,,,,QK2,,,,34442，， 根据计算所需，计算下列积分 K点在第一跨时 , , 1 1 1 1 1 MXd(),FXd(),MXd(),FXd(),MXd(),MXd(),FXd(),1 11233K1QK1KQKKKQK,,,,,,,00,,000 FXd(),,2QK,0 0.0 0.0000 0.0000 0.0000 0.4265 0.0000 -0.0353 0.0000 0.0118 0.1 0.0653 -0.0065 0.4994 0.3329 -0.0529 -0.0353 0.0176 0.0118 0.2 0.2227 -0.0258 0.7567 0.2522 -0.1059 -0.0353 0.0353 0.0118 0.3 0.4156 -0.0576 0.8285 0.1841 -0.1588 -0.0353 0.0529 0.0118 0.4 0.5901 -0.1016 0.7687 0.1281 -0.2118 -0.0353 0.0706 0.0118 0.5 0.6962 -0.1572 0.6273 0.0836 -0.2647 -0.0353 0.0882 0.0118 0.6 0.6893 -0.2234 0.4489 0.0499 -0.3176 -0.0353 0.1059 0.0118 0.7 0.5313 -0.2994 0.2717 0.0259 -0.3706 -0.0353 0.1235 0.0118 0.8 0.1920 -0.3840 0.1256 0.0105 -0.4235 -0.0353 0.1412 0.0118 0.9 -0.3493 -0.4759 0.0317 0.0023 -0.4765 -0.0353 0.1588 0.0118 1.0 -1.1029 -0.5735 0.0000 0.0000 -0.5294 -0.0353 0.1765 0.0118 K点在第二跨时 , MXd(),1,1 K2,0FXd(),MXd(),FXd(),11132QKQK2K 1 ,,,0,, MXd(),FXd(),MXd(),FXd(),,13K2KQK ,1,,QK,00,0 0.0 - 1.1029 0.1149 0.0000 0.0000 -0.5294 0.5074 0.1765 -0.0809 0.1 - 0.9651 0.1149 0.0333 -0.0040 -0.0315 0.4113 0.0794 -0.0809 0.2 - 0.8272 0.1149 0.1220 -0.0168 0.2909 0.3242 -0.0176 -0.0809 0.3 - 0.6893 0.1149 0.2435 -0.0398 0.4606 0.2471 -0.1147 -0.0809 0.4 - 0.5515 0.1149 0.3691 -0.0737 0.5062 0.1810 -0.2118 -0.0809 0.5 - 0.4136 0.1149 0.4660 -0.1190 0.4605 0.1264 -0.3088 -0.0809 0.6 - 0.2757 0.1149 0.4998 -0.1759 0.3578 0.0832 -0.4059 -0.0809 0.7 - 0.1379 0.1149 0.4368 -0.2440 0.2320 0.0513 -0.5029 -0.0809 0.8 0.0000 0.1149 0.2458 -0.3226 0.1142 0.0300 -0.6000 -0.0809 0.9 0.1379 0.1149 -0.0994 -0.4109 0.0306 0.0182 -0.6971 -0.0809 1.0 0.2757 0.1149 -0.6176 -0.5074 0.0000 0.0147 -0.7941 -0.0809 K点在第三跨时 1FXd(),111,,1 QK31 ,, MXd(),MXd(),FXd(),MXd(),FXd(),MXd(),FXd(),,1223KKQKK3QK3K,1,,,,,QK,00000,0 0 0.2757 -0.0230 -0.6176 0.0515 0.0000 0.0000 -0.7941 0.5662 0.1 0.2482 -0.0230 -0.5559 0.0515 0.0282 -0.0026 -0.2029 0.4688 0.2 0.2206 -0.0230 -0.4941 0.0515 0.1097 -0.0114 0.2150 0.3776 0.3 0.1930 -0.0230 -0.4324 0.0515 0.2334 -0.0278 0.4707 0.2940 0.4 0.1654 -0.0230 -0.3706 0.0515 0.3808 -0.0529 0.5827 0.2191 0.5 0.1379 -0.0230 -0.3088 0.0515 0.5267 -0.0878 0.5763 0.1540 0.6 0.1103 -0.0230 -0.2471 0.0515 0.6399 -0.1333 0.4825 0.0995 0.7 0.0827 -0.0230 -0.1853 0.0515 0.6847 -0.1902 0.3370 0.0564 0.8 0.0551 -0.0230 -0.1235 0.0515 0.6216 -0.2590 0.1795 0.0252 0.9 0.0276 -0.0230 -0.0618 0.0515 0.4082 -0.3401 0.0524 0.0063 1 0.0000 -0.0230 0.0000 0.0515 0.0000 -0.4338 0.0000 0.0000 111MqMXdMXdMXd=(()()()),,,，，KKK123恒,,,000 111 FqFXdFXdFXd,，，(()()()),,,QKQKQK123QK恒,,,000 根据影响线方程， 当K点在第一跨:集中力在第一跨的时候，画出Mk的影响线，集中力在其他跨的时候不出现零点(影响线与坐标轴横轴相交)(结点除外);FQ影响线图不出现零点(结点除外)。 将第一跨分成十个点0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9 当时=0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9, ,1max+q(()())FFFXFXd,，,13QKQKQKQK恒,,10 1,min+q(()())FFFXFXd,，,12QKQKQKQK恒,,00 当时=0,0.1,0.2,0.3,0.4,0.5,0.6,0.7, ,11maxM,，MqMXdMXdMXd+(()()+()),,,113恒,,,00, 1MMqMXdmin+(),,2恒,0 由图可知，当，时，存在零点=0.80.9, =当0.8时, 当0,,,0.38()0时，MX1=0.8K,, ,,,MX()0当0.38时，1=0.8K,,,0.38MXd()0.0198,,1=0.8K,0,,0.38,,MXdMXdM()(),,()0.2118Xd,,1=0.81=0.8KKK1=0.8,,,,0.3800,,,,11,MMPMXdMXdMXdmax+(()()())9.0392,，，,,,,=0.8=0.81=0.81=0.83=0.8KKK恒,,,,,,,,0.380,0.381MMPMXdMXdmin+(()())7.556854,，,,=0.8=0.81=0.82=0.8,,KK恒,,,,,,00 =0.9当时, ,,0.8()MX当0时，,010.9K,,, 当0.8,,,,,时，MX()0K10.9,, 同理求得 MMmax=3.5701,min23.11196,,,=0.9=0.9,, 当K点在第二跨时:集中力在第二跨的时候出现零点，画出Mk的影响线，集中力在其他跨的时 候不出现零点(结点除外);FQ影响线图不出现零点(结点除外)。 将第二跨分成十个点0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9 11max+q(()())FFFXFXd,，,QKQKQKQK12恒,,0, 1,min+q(()())FFFXFXd,，,QKQKQKQK23恒,,00 当，时=0.2,0.3,0.4,0.5,0.6,0.70.8, 11,max+(())=+(()+()MMqMXdMqMXdMXd,,))222恒恒,,,,,00,11min+(()+()))MMqMXdMXd,,,13恒,,00 =当0时, 1max(())MMqMXd,，3恒,,0 11,min+(()()+()))MMqMXdMXdMXd,，122恒,,,,,,00, =0.10.9由图可知，当，时，存在零点, =当0.1时, 0.33()0,,,MX当时，1=0.1K,,, 1()0当0.33,,,时，MX1=0.1K,,1()MXd,,,0.92632=0.1K,0.33,,11()()()0.06611,,,MXdMXdMXd,,,KKK12=0.12=0.1,,,,,0.330.33=0.1,, 0.331,max+(()()())7.3884,，，,,MMPMXdMXdMXd,,,=0.1=0.12=0.12=0.13=0.1KKK恒,,,,,,,,00,11min+(()(),，MMPMXdMXd,)29.7359,,=0.1=0.11=0.12=KK0.1恒,,,,,,,00.33 =0.9当时, ,,,0.72()0MX当0时，,10.9K,, 当0.72,,,时，MX()010.9K,,,, 同理求得 MMmax=3.461872,min22.77058,,,=0.9=0.9,, 当K点在第三跨:集中力在第三跨的时候，画出Mk的影响线，集中力在其他跨的时候不出现零 点(结点除外);FQ影响线图不出现零点(结点除外)。 将第三跨分成十个点0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9当时,=0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9 1,max+q(()())FFFXFXd,，,23QKQKQKQK恒,,01 1,min+q(()())FFFXFXd,，,13QKQKQKQK恒,,00 当时=0, 1max+()MMqMXd,1恒,,0 ,11min+((MMqMX,)()+())dMXdMXd,,,，恒223,,,00, =0.3,0.4,0.5,0.6,0.7,0.8,0.9当时, 11,MMqMXdMXdMXdmax+(()()+()),，,,,331恒,,,00,1MMqMXdmin+(),2恒,,0 由图可知，当，时，存在零点,=0.10.2 当=0.1时, 当0,,,0.24()0时，MX,K1=0.1, 当0.24,,,时，MX()0,,K1=0.1, 1MXd()0.24064,,K1=0.1,,,0.24 0.2411MXdMXdMXd,,,()()()0.2118KKK1=0.11=0.11=0.1,,,,,,0.24,,,,,1,0.24dMXdMXd，，,()())0.1354,,,MMPMXmax+((),=0.1=0.11=0.1KKK3=0.13=0.1恒,,,,,00,,,, 11MMPMXdMXdmin+(()())20.1269,，,,,,=0.1=0.12=0.13=0.1KK恒,,,,,,00.24 当时=0.2, 当0时，,,,0.78()0MX10.2K,,, 当0.78时，,,,MX()0K10.2,,,, 同理求得 MMmax=10.4164,min,,8.3148=0.2=0.2,, 根据以上公式求出 M恒，Mmax，Mmin，F恒，Fmax，Fmin 总长度 M恒 Mmax Mmin F恒 Fmax Fmin 0 0 0.0000 0.0000 0.0000 4.8353 12.7235 4.2000 1.5 0.1 6.3529 16.8353 5.4000 3.6353 9.8399 2.8837 3 0.2 10.9059 29.1706 9.0000 2.4353 7.1873 1.3362 4.5 0.3 13.6588 37.0059 10.8000 1.2353 4.7610 -0.4375 6 0.4 14.6118 40.3412 10.8000 0.0353 2.5532 -2.4296 7.5 0.5 13.7647 39.1765 9.0000 -1.1647 0.5526 -4.6290 9 0.6 11.1176 33.5118 5.4000 -2.3647 -1.2551 -7.0214 10.5 0.7 6.6706 23.3471 0.0000 -3.5647 -2.8872 -9.5893 12 0.8 0.4235 9.0292 -7.5569 -4.7647 -4.3645 -12.3120 13.5 0.9 -7.6235 -3.5701 -23.1120 -5.9647 -5.7107 -15.1658 15 1 -17.4706 -14.2941 -46.8529 -7.1647 -6.9529 -18.1235 15 0 -17.4706 -14.2941 -46.8529 6.4963 17.6967 5.0404 16.2 0.1 -10.6068 -7.3884 -29.7359 5.2963 14.7679 3.7692 17.4 0.2 -5.1829 2.2500 -20.3903 4.0963 11.9993 2.3378 18.6 0.3 -1.1991 11.4750 -15.6719 2.8963 9.4127 0.7244 19.8 0.4 1.3447 17.1000 -12.3935 1.6963 7.0232 -1.0861 21 0.5 2.4485 19.1250 -10.5551 0.4963 4.8392 -3.1020 22.2 0.6 2.1124 17.5500 -10.1568 -0.7037 2.8624 -5.3252 23.4 0.7 0.3362 12.3750 -11.1984 -1.9037 1.0879 -7.7508 24.6 0.8 -2.8800 3.6000 -13.6800 -3.1037 -0.4959 -10.3670 25.8 0.9 -7.5362 -3.4619 -22.7706 -4.3037 -1.9072 -13.1557 27 1 -13.6324 -8.6691 -39.0441 -5.5037 -3.1710 -16.0919 27 0 -13.6324 -8.6691 -39.0441 7.1360 18.2537 6.7224 28.2 0.1 -5.7891 0.1354 -20.1269 5.9360 15.3007 5.4754 29.4 0.2 0.6141 10.4164 -8.3148 4.7360 12.4593 4.1168 30.6 0.3 5.5774 21.7257 -2.2050 3.5360 9.7539 2.6223 31.8 0.4 9.1006 29.4221 2.4300 2.3360 7.2058 0.9703 33 0.5 11.1838 33.5184 5.6250 1.1360 4.8336 -0.8575 34.2 0.6 11.8271 34.0147 7.3800 -0.0640 2.6532 -2.8771 35.4 0.7 11.0303 30.9110 7.6950 -1.2640 0.6773 -5.1012 36.6 0.8 8.7935 24.2074 6.5700 -2.4640 -1.0841 -7.5398 37.8 1.9 5.1168 13.9037 4.0050 -3.6640 -2.6238 -10.2001 39 1 0.0000 0.0000 0.0000 -4.8640 -3.9375 -13.0864 根据以上表格内容画出弯矩、剪力包络图