1、Mechanics of Materials 9-1 概述概述9-2 杆件变形能的计算杆件变形能的计算9-3 互等定理互等定理9-4 单位荷载法单位荷载法 莫尔定理莫尔定理9-5 卡氏定理卡氏定理9-6 计算莫尔积分的图乘法计算莫尔积分的图乘法 EAlFEAlFlFlFWV2221212N2N niiiiiAElFV12N2 lxEAxxFV02N)(2)d(222122EE 或或p2p2epeee222121GIlTGIlMGIlMMMWV lxxGIxTVd)(2)(p2 niiiiiIGlTV1p22EIlMMWV2212 xxEIxMVld)(2)(2 xxEIxMxxGIxTxxEA
2、xFVllld)(2)(d)(2)(d)(2)(2p22N 123FV21 F3BCF2AF1)(233221123322112FFCCFFCFFCFCFC F3ABCF1F2123 iF3ABCF1F2123)(21332211FFFV i 1 2F1F2F1F2 1 2F3 3 4F422112121FF 44332121FF F1F2 1 2F3 3 4F42 1 FF2211 FFFFFFV221144332211121212121 F1F2 1 2 3 4F4F3FFFFFFV443344332211221212121 21VV FFFF44332211 4 3 FF3311 31
3、F1F2A A lxEIxMVd2)(2 lxEIxMVd2)(2AwVVV 11AF1F2=1F0AF1F2wA)()(xMxM lxEIxMxMVd2)()(2212VV lAxEIxMxMwVVd2)()(12 llllAxEIxMxMxEIxMxEIxMxEIxMxMwVVd)()(d2)(d2)(d2)()(1222 lAxEIxMxMwd)()(lxEIxMxMd)()(lxEIxMxMd)()(niiiiEAlFF1NN lllxEIxMxMxGIxTxTxEAxFxFd)()(d)()(d)()(pNN 2 1 3F1F2F3 332211212121FFFWV,321 2 1
4、 3F1F2F3iiF21 iiFFF2211 iiiiFFFFV221121iiF21 iiFFFV2211iiiiFFFF 2211iiFV iiFV iiFV iiFV xFxFEAxFEAxxFFFViiiid)()(2)d(NN2N xFxTGIxTGIxxTFFViiiid)()(2)d(pp2 xFxMEIxMEIxxMFFViiiid)()(2)d(2 ijnjjjiiFFEAlFFV N1NiiFV 2)d(2)d(2)d(2p22N llliEIxxMGIxxTEAxxFFxFxMEIxMxFxTGIxTxFxFEAxFiiid)()(d)()(d)()(pNN xxMxM
5、EIl)d()(1 xEAFFldNN xGITTldp xxMxMl)d()(ldxxCxCMMxxMxMl)d()(EIMxEIxMxMCl d)()(xxMxl)d(tg CCMx tgxCCM(x)xx)(xMlBxAxM )(xxMxBxxMAxxM)BxA(xxMxMllll)d()d()d(d)()(000 lxxM0)d(xxMl 0)d(M(x)xlx)(xMxCC lxxxM0)d(ClxxxM 0)d(CCClllMxBAxBAxxMxBxxMAxxMxM )()d()d(d)()(00CxBA M(x)xlx)(xMxcCEIMxxMxMEICl d)()(1balhC
6、Clh顶点顶点3bl 3al 2hl 85l83llh 32lh顶点顶点clh顶点顶点c3hl 1 nhllnn2)1(2 nl0ie WW 1 2 3 4AlBF4F1F2F3RARBiiiBAiiiFRRFW 4141e00dxMM+dMd2 d2 F4F1F2F3RAAlRBBdxFSMFS+dFSM+dM2d)d(2d MMMdxdxd2 d2 d2 d2 2d)d(2dSSSFFF F4F1F2F3RAAlRBBdxdxFSMFS+dFSM+dMFMddS 2d)d(2d MMM2d)d(2dSSSFFF 0)dd(dddSiei FMWWW)dd(dSiFMW lSlii)dd(dFMWW0)dd(lS41 FMFiii lNS41)dddd(TFFMFiii
