结构力学第5章习题及参考答案5-9——5-11

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1、基本结构BACD4i5-9试用位移法计算图示结构，并作弯矩图。EI为常数。4m2m4m10kN20kN/m(a)BACDE图及系数k11、k21的求解BACD3i4i2i3i4ik11Ck21Δ1=1k11k21图及系数k12、k22的求解k126i/4mCk22BACDΔ2=1k22k12MP图(kNm)及自由项F1P、F2P的求解BACDE3020CF2PF1P30F1PF2P24060920180460M图(kNm)解(b)3m3m3m60kNABCDE3mBD基本结构Δ20.5ii=EI/3ii图及系数k11、k21的

2、求解1.5i2i4i4i2ik114i4i1.5ik21Δ1=1k11k21图及系数k12、k22的求解k12k22k12Δ2=1k22图(kNm)及自由项F1P、F2P的求解F2P67.5F1P67.5F2PF1P270108027054054017100M图()解5-10试用位移法计算图示结构，并作弯矩图（提示：结构对称）。(a)10kN/mKNKNkN/m6m6mABCDEFGEI=常数6m6m6m习题5-10(a)解将荷载分解成对称和反对称两组，分别求解。(a-1)对称荷载组5kN/mKNKNkN/m5kN/mKNKN

3、kN/mABCDEFGEI=常数对称结构5kN/mKNKNkN/m半结构基本结构4i4i2i图及系数k11的求解4ik114i2iΔ1=1k11M图(kNm)图(kNm)及自由项F1P的求解90F1P1590151552.53.7518.7537.590F1P(a-2)反对称荷载组5kN/mKNKNkN/mABCDEFGEI=常数反对称荷载5kN/mKNKNkN/mC半结构5kN/mKNKNkN/mABDD基本结构图及系数k11的求解4i4i2i2i3i4ik114i3iΔ1=1k11MP图（kNm）及自由项F1P的求解F1P

4、1522.522.51515M图(kNm)3903003060450F1PD76515308851770306048603090765153043519801980将对称和反对称的弯矩图叠加，得总弯矩图。M图(kNm)20kN6m6m40kNABCDEEIEIEI2EIEIF习题5-10(b)图6m6mABCDEIEIEI半结构10kNACEIEI1/4结构ACEIEI基本结构图及系数k11、k21的求解AC6i4i2iC6i4ik11k21Δ1=1k11k21图及系数k12、k22的求解Cik12k22Ai图及自由项F1P、

5、F2P的求解AF1PF2P10k12Δ2=1k22F1PF2PM图（kNm）180180240240480240180180180360180M图（kNm）解5-11作图示刚架的内力图基本结构ii1®¥ABCFDEiii（a）qii1®¥ABCFDEiii3qlllll图及系数k11、k21的求解3iDABCFE4i2i2iB4i3ik11F6i/lk21Δ1=1k11k21图及系数k12、k22的求解Bk126i/lDABCF6i/l6i/l6i/lF12i/l2k2212i/l23i/l2k12Δ2=1k223i/lMP图

6、及自由项F1P、F2P的求解DABCFEql2/8BF1Pql2/8FF2P3qlF1PF2P3qlM图()DAFE39582020195829解FQ图()DAFE-145429-59116FN图()DAFE-1459-29-58AEDi2i基本体系i=EI/4ii5-11(b)HGAEDG1.5EI3EIEIEI半结构3EI4m4mEIEI46.5kNm46.5kNmDFE1.5EI1.5EIEIEIEIBCA6m6mAE图及系数k11、k21的求解4i2i2ik114i2ik212iAE图及系数k12、k22的求解4i2i

7、k122ik224i2i3i4i4i3iΔ1=1k11k21k12Δ2=1k22AM图(kNm)9020864MP图（kNm）及自由项F1P、F2P的求解AD626293F1P62F2P6293F1PF2P解2M图(kNm)42090864862090AAFQ图(kNm)-76.5109.51-1-115.570.5-76.5109.5-115.570.5AFN图(kNm)-90-2252