材料力學-自考 05 - 第14章 梁的彎曲內(nèi)力 - 習題解答 - 白若陽

第14章梁的彎曲內(nèi)力習題解答14-1試用截面法計算圖示各梁指定截面1-1、2-2、3-3上的剪力和彎矩。333ABC1122aa(a)qABCDaaaFFa112233(c)33(b)CABMe=450Nm1m0.5m112211aaaDBC2233qqa/4(d)AqACB1qACB1習題14-1(a)圖aa12233各截面的剪力和彎矩為，，2FSqa2FSqaAC1Baa3312習題14-1(a)解答圖剪力圖剪力圖和彎矩圖，如圖所示223qa2/2M1ACB3312aa習題14-1(a)解答圖彎矩圖qa2/22211C2211CBMe=450Nm習題14-1(b)圖A0.5m1m33由平衡方程求得約束力（↑），（↓）各截面的剪力和彎矩為450N30.5m450N30.5m1mFS習題14-1(b)解答圖剪力圖21C21BA3，，剪力圖和彎矩圖，如圖所示BBC31221450N·m3M0.5m1m習題14-1(b)解答圖彎矩圖A33321DFaA21B習題14-1(c)圖aaaFC題14-1(c)解：由平衡方程求得約束力，（↑）CC3321DA21BFaaa習題14-1(c)解答圖剪力圖FS各截面的剪力和彎矩為，，321Fa321FaDA321BaaaC習題14-1(c)解答圖彎矩圖M剪力圖和彎矩圖，如圖所示3213D3213DA21Bqa/4Caaa習題14-1(d)圖q由平衡方程求得約束力（↓），（↑）CDCD3321A21Baaa習題14-1(d)解答圖剪力圖FSqa3qa/4qa/4，，C321C321D3A21BMqa2/4aaa習題14-1(d)解答圖彎矩圖qa2/22a/3剪力圖和彎矩圖，如圖所示xyFABxyFABl/2(d)Fl/4l/2FAB(b)2l/3l/3xyABql(a)xyABl(c)MexyCC(b)(d)題14-2(a)解：剪力方程為彎矩方程為qAqABl習題14-2(a)圖yxFFSABl習題14-2(a)解答圖剪力圖qlMMABlql2/2習題14-2(a)解答圖彎矩圖FACB習題FACB習題14-2(b)圖l/2l/2Fl/4yxAC段的剪力方程和彎矩方程分別為FACBFACBl/2l/2習題14-2(b)解答圖剪力圖FSCB段的剪力方程和彎矩方程分別為Fl/4AFl/4ACBl/2l/2習題14-2(b)解答圖彎矩圖MFl/4剪力圖和彎矩圖，如圖所示MeAByMeAByxl習題14-2(c)圖由平衡方程求得約束力（↓），（↑）MMe/lABl習題14-2(c)解答圖剪力圖剪力方程和彎矩方程分別為ABMeABMel習題14-2(c)解答圖彎矩圖剪力圖和彎矩圖，如圖所示題14-2(d)解：BABAFC習題14-2(d)圖2l/3l/3yx（↑），（↑）AC段的剪力方程和彎矩方程分別為BACFBACF/32l/3l/3習題14-2(d)解答圖剪力圖FS2F/3CB段的剪力方程和彎矩方程分別為BAC2BAC2Fl/92l/3l/3M習題14-2(d)解答圖彎矩圖剪力圖和彎矩圖，如圖所示14-3試建立圖示各梁的剪力方程和彎矩方程，并繪制剪力圖和彎矩圖。AAABql/2(a)xyl/2ql2CqB(b)l/2l/2xyCxyqABl/2(c)qll/2ABl/2(d)Fl/2xyl/2CFC(c)(b)ACBl/2ACBl/2l/2yql2x習題14-3(a)圖q1.求約束力：（↑），（順時針）2.剪力方程和彎矩方程：ACBACBl/2l/2習題14-3(a)圖剪力圖ql/2FSACBlACBl/2l/25ql2/8M習題14-3(a)圖彎矩圖7ql2/8ql2/83.剪力圖和彎矩圖：如圖所示題14-3(b)解：ACByACByqlqxl/2l/2習題14-3(b)圖（↑），（逆時針）2.剪力方程和彎矩方程：ACBACBl/2l/2ql/2FS習題14-3(b)圖剪力圖qlACBACB7ql2/8Ml/2l/2習題14-3(b)圖彎矩圖ql2/2CB段：3.剪力圖和彎矩圖：如圖所示AC3ql/8FSAC3ql/8FSBl/2l/2習題14-3(c)解答圖剪力圖ql/83l/8ACByqxl/2l/2習題14-3(c)圖ql2/16CAMB3l/8l/2l/2習題14-3(c)解答圖彎矩圖9ql2/1281.求約束力：（↑），（↑）2.剪力方程和彎矩方程：AC段：CB段：3.剪力圖和彎矩圖：如圖所示ACyFBACyFBxl/2l/2習題14-3(d)圖Fl/21.求約束力：（↓），（↑）2.剪力方程和彎矩方程：AB段：AFCBAFCBFS2Fl/2l/2習題14-3(d)解答圖剪力圖BC段：Fl/2AFl/2ACBMl/2l/2習題14-3(d)解答圖彎矩圖Fl/23.剪力圖和彎矩圖：如圖所示14-4試利用剪力、彎矩與載荷集度之間的微分關系繪制圖示各梁的剪力圖和彎矩圖。AAqBl/2ql2/2Cl/2(d)FBAl/3l/3(a)l/3FCDABl/2(b)Fll/2CFqABqll/2l/2(c)C題14-4(a)解：DDABFCl/3l/3l/3習題14-4(a)圖FFA=FFB=FFSFFMFl/3FFFS3FFlMFl/2FACBFll/2l/2習題14-4(b)圖FB=4FFA=3F題14-4(b)解：題14-4(c)解：AACBqlql/2l/2習題14-4(c)圖FA=0MA=0ql/2FSql/2ql2/8M題14-4(d)解：qlql/2FSACqBl/2l/2習題14-4(d)圖MA=ql2/4FA=0qql2/2ql2/8Mql2/43ql2/814-5試利用剪力、彎矩與載荷集度之間的微分關系繪制圖示各梁的剪力圖和彎矩圖。aaaFFaFaABC(a)aaABCqqaqa2(b)AqqaBC2a(c)aaABMeMeCa(d)aaDE2Me(d)(b)習題14-5(a)解答習題14-5(a)解答圖ABCaFaFA=FaFFaMA=0FFSMFaFa題14-5(b)解：習題習題14-5(b)解答圖ADCBEMeMe2MeaaaaFE=Me/2aFA=Me/2aFSMe/2aMMe/2Me/2Me/22Me3Me/2題14-5(c)解：習題習