材料力学专项习题练习-6弯曲内力

40弯曲内力1.长l的梁用绳向上吊起，如图所示。钢绳绑扎处离梁端部的距离为x。梁内由自重引起的最大弯矩|M|max为最小时的x值为：(A)/2l；(B)/6l；(C)(21)/2l；(D)(21)/2l。2.多跨静定梁的两种受载情况如图(a)、(b)所示。下列结论中哪个是正确的？(A)两者的剪力图相同，弯矩图也相同；(B)两者的剪力图相同，弯矩图不同；(C)两者的剪力图不同，弯矩图相同；(D)两者的剪力图不同，弯矩图也不同。3.图示(a)、(b)两根梁，它们的(A)剪力图、弯矩图都相同；(B)剪力图相同，弯矩图不同；(C)剪力图不同，弯矩图相同；(D)剪力图、弯矩图都不同。4.图示梁，当力偶Me的位置改变时，有下列结论：(A)剪力图、弯矩图都改变；(B)剪力图不变，只弯矩图改变；(C)弯矩图不变，只剪力图改变；(D)剪力图、弯矩图都不变。5.图示梁C截面弯矩MC=；为使MC=0，则Me=；为使全梁不出现正弯矩，则Me≥。6.图示梁，已知F、l、a。使梁的最大弯矩为最小时，梁端重量P=。xxllaMe(a)laMe(b)qqa2a(a)qqa2(b)aaaaaFMeaqaaqMel/2BCAl/2al/2al/2PFP417.图示梁受分布力偶作用，其值沿轴线按线性规律分布，则B端支反力为，弯矩图为次曲线，|M|max发生在处。8.图示梁，m(x)为沿梁长每单位长度上的力偶矩值，m(x)、q(x)、FS(x)和M(x)之间的微分关系为：Sd();dFxxd()dMxx。9.外伸梁受载如图，欲使AB中点的弯矩等于零时，需在B端加多大的集中力偶矩（将大小和方向标在图上）。10.简支梁受载如图，欲使A截面弯矩等于零时，则e21e/MM。1-10题答案：1.C2.D3.B4.B5.28e2Mql；42ql；22ql6.alaF247.m0/2；二；l/28.q(x)；FS(x)+m(x)9.10.1/211-60题.作图示梁的剪力图和弯矩图。解：xm=xlABxm0xlm0xdxq(x)m(x)xaaqCABaaqABqa/22Cl/3le1Me2MAq2aqa2qaaaFSxqa/22x3qa/222qa2qa2qa2Mqa2qaq2aqa2qaaaFSxx3qa/222qa2qa2qa2Mqaqaqa242解：解：解：qqa2aaqaqFSxqa/22x5qa/222qa2qa2Mqaqa2qqa2qaaxxFSMqa/22qa/22qa/22qa/42qaqaq2qa3qa22aaxxFSM2qaqa2qa22qa2q2qaqa2aaaxxFSMqaqa/22qaqa/22qa/22qa/22q2aqaqaxxFSMqaqaqa/22qa/22a2aqa2aqqxxFSMqa2qa/22qa/223qa/222qaqa43解：解：解：qa/2a/2xFSxMqa/4qa/2423qa/47qa/242aqa2aqqaxxFSMqa2qa/223qa/22qaqa2qa2aqaqFSMxxqa/62qa/27qa/242qa/2qa/622a2a2q2qa2qFSM3qa4qa2x2qa29qa/42xqa3qa2m2m20kN/mmkN2020kN/mmkN20F/kNSM/mkN2020xx201020203020a4aa2qa4qa2qFSM3qa27qa/22xxqa3qa3qa2qa23qa44解：解：解：aaaqa2qFSM5qa/6qa/6213qa/722xxqa/6qa/625qa/62a0qFSa/Mqa/60qa/30qa/20393xxa/2a/20q0qFSMxxqa/60qa/120qa/60a/12a/1220aq363=0.01620aq0q0qaqa/30aFSMxxqa/60a/3qa/60qa/30qa/309320aq9320aq2m4m8kNmkN162m2kN/m2kN/m4kN/mF/kNSM/mkN4xx128844440qa/2a/2FSMxxqa/40qa/40qa/120245解：解：解：0q0qaaFSMxxqa/20qa/20qa2/602aaaq2qaqaFSMxx9qa/82qa23qa/2qa/2qa/23qa/23qa/22aqaFSMxx7qa/125qa/12211qa/12qa/12121qa/2882aaaqqaqa/22FSMxxqaqa/22qa/2qa/2qa/222aaqqFSMxxqa/2225qa/3225qa/43qa/4qaaaaqaqqa2FSMxxqaqa/223qa/42qa/43qa/4qa/4246解：解：解：2m10kNmkN1m1m1m2kN2kN/m4xxF/kNSM/mkN28477372aaaqqaqa2FSMxxqaqa/423qa/42qa/4qa25qa/4aaaqqqa2FSMxxqaqa/22qa/2qa2qa/82aaaqqqaqa2FSMxxqaqa/223qa/22qa/2qa/23qa/2qa/822m2kN/mmkN2m2m2kN4xxF/kNSM/mkN262144aaaqaaqqa2qa/22FSMqaxxqaqa/45qa/42qa2qa/4247解：解：解：aaaqqqaqa2FSMxxqaqa/223qa/22qa/2qa/22qa3qa/2213qa/823m40kN3m2m50kN/m50kN/mxxF/kNSM/mkN4061.713.388.31.74m46.380a2aaq2qa2qa2FSxMxqa2qa23qa2qa2qa2a2a2aqqa2FSxMxqa/25qa/2qa22qa22qaaaaqqaqa2qaFSMqaqa/22xxqa/2qa2aaaqqqa2FSqaqa/22qa2Mqaxxqa/2248解：aa2aqaqqa2FSqa/82qa2Mxx3qa/2qa/23qa/22qa2qa/222m80kNmkN4m8m2m10kN/m64xF/kNSM/mkNx5822408016080104.2645.8maaaaqqa2FS13qa/722Mqa/65a/6xx5qa/65qa/62qa/62qa/62qa/62a2aqqaqa2FSMxxqa22qa2qa2qaaa/20qFSa/qa/42Mxxqa/60qa/307qa/1200qa/20393mF2m1m1mFS100NmN100Mxx49a/2a/2a/20q0qFSMxxqa/60qa/120qa/60a/12a/1220aq363=0.01620aq20aq/12aaaqqa/22FS5qa/42Mxx7qa/4qa/425qa/45a/43qa/429qa/322aaaqqa2FSqa/22qa/2Mxqa/2xqa/82qa/22aaaq2qa2FSqaqa/82qa/2qa2M3qa/2xxqa2aaaqqFSqa/32qa/2Mxxqa/1822qa/3qa/3qa/62aaaqqaqa2FSqa/42Mqa/2xxqa/23qa/2qa25061.图示结构，作梁ABC的剪力图和弯矩图。解：62.作图示刚架的轴力、剪力和弯矩图。63.作图示刚架的轴力、剪力和弯矩图。解：qaaaaaaqqaqaABCqaaaaqABC3qa/2qa/22qa2FSMqa/223qa/22qa/2xxqa/82qa/23qa/2qa2qaaaqaqaaaqa2qa2qaqaF图NF图SM图qa/22qaqa/22qa/22qa2q2qa22a2aq2qa22a2a2qa2qa2qa2qa2qa2qa2qa22qa22qa2F图NF图SM图qaaaqa2qa2qaqaF图NF图SM图qa/22qaqa/22qa/22qa25164.作图示刚架的轴力、剪力和弯矩图。65.作图示刚架的轴力、剪力和弯矩图。66.作图示刚架的轴力、剪力和弯矩图。2aqaqa2aqa2aqaqa2aqaqaqa3qa/22qaqaqaqaqaqa/223qa/22qa2F图NF图SM图2aqaaF图NF图SM图2aqa/4qaqaqaaqa/4qaqa/4qaqa/4qaqaqa/22qa/22qa/4aqa2qa2aaqF图NF图SM图2aqa/4qaqaqaaqa/4qaqa/4qaqa/4qaqaqa/22qa/22qa/42aqaqa2aqaqaqa3qa/22qaqaqaqaqaqa/223qa/22qa2F图NF图SM图52解：67.作图示刚架的轴力、剪力和弯矩图。解：aqa2qa2aaqqa5qa/45qa/45qa/4qa5qa/4qa5qa/4qa/425qa/42qa2qa/42F图NF图SM图aq2aqaaaq3qa/2qa/2qaqa/23qa/23qa/2qa/2qa22qa2F图NF图SM图2aqaaqaqaqa7qa/82aq3qa/2qa/2qaqa/23qa/23qa/2qa/2qa22qa2F图NF图SM图2aqaaqaqaqa7qa/825368.作图示刚架的轴力、剪力和弯矩图。解：69-70.梁的剪力图如图所示，作弯矩图及载荷图。已知梁上没有作用集中力偶。解：qa2qaaaqqa3qa/22qa2qaaaqqaqaqaqaqa/223qa/22qa23qa/22F图NF图SM图FSx3qa/2qa/2qa/23qa/22aaaq2qaqaMx9qa/82qa23qa/23qa/223qa/22aaaFSx3qa/2qa/2qa/23qa/22aaaq2qaqa3qa/23qa/2Mx9qa/82qa23qa/225471-72.梁的剪力图如图所示，作弯矩图及载荷图。已知梁上B截面作用一集中力偶。解：73-74.已知梁的弯矩图如图所示，作梁的载荷图和剪力图。解：a3aABCFS2qaxqaa3aM2qa23qa/22qa/22xq7qa/22ABC2qaqa2a2aFS3qaxqa3qaABC2a2a2q2qa2q3qa3qaM4qa2x2qa29qa/42ABCxMaa二次抛物线顶点3qa/22qa2qaqaaaqFSxqaqa二次抛物线直线直线aax3qa/222qa2qa2qa2Mqa2aaq2aqa2qaaaFSxqaqa5575-76.已知梁的弯矩图如图所示，作梁的载荷图和剪力图。解：77.处于xy平面内的开口圆环，半径为R，A端固定，C端受Fx=F、Fz=F（垂直纸面向里）力作用，则B截面的扭矩T=；弯矩Mx=，Mz=。(z轴垂直纸面向里)答：FR；FR；-FR。78.一结构由直杆AB和曲杆BC在B点刚结而成，支承和受载如图所示。作结构的剪力图和弯矩图。对于曲杆段要求先写出剪力方程和弯矩方程，然后作图。解：BC段剪力方程和弯矩方程分别为S()sin;()(1cos)22FFaFMaaqa/22x5qa/222qa2qa2Ma顶点拐点顶点qqa2aaFSxqaqaqqaaaaMqa/22qa/22x二次抛物线光滑aaaqaqa/22qFSqaqaxR=aFBaaAOCF图SFa/2M图F/2F42xFROByAxFz5679.写出图示曲杆的内力方程，并作内力图（轴力、剪力、弯矩图）。解：N(1cos)cosFqR；S(1cos)sinFqR；22(1cos)2qRM。80.图示梁上，作用有集度为q=q(x)的分布载荷及m=m(x)的分布力偶。试建立力偶矩集度m(x)、分布载荷集度q(x)、剪力FS(x)和弯矩M(x)间的微分关系。解：微段dx的平衡方程为SSS0,()()d[()d()]0yFFxqxxFxFx(a)Sd0,()d()()d()d()()d02CxMMxMxqxxFxxMxmxx(b)由式(a)得Sd()()dFxqxx由式(b)并略去二阶微量，得Sd()()()dMxFxmxxRBqAORBAOq45212qRqRqR/22F图N