中国石油大学工程力学答案合集.pptx
2023/3/19Statics-Problems-1静力学第1章作业/P23-1.1(g)*:第1页/共96页2023/3/19Statics-Problems-2静力学第1章作业/P24-1.2(k):第2页/共96页2023/3/19Statics-Problems-3静力学第1章作业/P27-1.3(c):第3页/共96页2023/3/19Statics-Problems-4静力学第1章作业/P27-1.3(e)*:第4页/共96页2023/3/19Statics-Problems-5静力学第2章作业/P58-2.3*:Solution:由此得到如下方程组：解得：第5页/共96页2023/3/19Statics-Problems-6静力学第2章作业/P60-2.14*:Solution:按定义有:So,expressions(a),(d),(e)are valid.第6页/共96页2023/3/19Statics-Problems-7静力学第2章作业/P61-2.20:Solution:(a)In vector form:第7页/共96页2023/3/19Statics-Problems-8(b)In vector form:第8页/共96页2023/3/19Statics-Problems-9+Solution:静力学第2章作业/P63-2.28*:第9页/共96页2023/3/19Statics-Problems-10+（a)Solution:静力学第2章作业/P63-2.30*:第10页/共96页2023/3/19Statics-Problems-11(b)+第11页/共96页2023/3/19Statics-Problems-12OOriginal forces and couple can be reduced to a force and a couple acting at point O:静力学第2章作业/P64-2.32:Solution:于是得到合力的大小、方向和作用线位置（如图所示）：(或,或)第12页/共96页2023/3/19Statics-Problems-13+Solution:静力学第2章作业/P64-2.34*:第13页/共96页2023/3/19Statics-Problems-14静力学第3章作业/P85-3.2*:Solution:RAyRByFrom the FBD of the beam in Fig:+RBx3kN2m+第14页/共96页2023/3/19Statics-Problems-15静力学第3章作业/P86-3.11:Solution:GPGLStudying person and ladder,draw FBD(a)x=1.5m+RBRAyRAx+第15页/共96页2023/3/19Statics-Problems-16+GPGLRBRAyRAx(b)第16页/共96页2023/3/19Statics-Problems-17静力学第3章作业/P87-3.18:Solution:300N0.5mRDRE(1)Studying entire structureFrom the FBD of entire structure in Fig:+(2)Studying member ABFrom the FBD of member AB in Fig:RBxRByRAxRAy300N0.5m1.6m+第17页/共96页2023/3/19Statics-Problems-18(3)Studying member ACEFrom the FBD of member ACE in Fig:0.8mRERAxRAyAECRCxRCy0.8m0.6m0.6m+第18页/共96页2023/3/19Statics-Problems-19静力学第3章作业/P90-3.28(f)*:Solution:(1)Studying member CDFrom the FBD of member CD in Fig:显然，本题中在约束A、B、C、D处没有水平方向的作用力RCRMRCR2qC3m1m+第19页/共96页2023/3/19Statics-Problems-20(2)Studying member ABCRARCRB2qAC1m2mRARCRB1mFrom the FBD of member CD in Fig:+第20页/共96页2023/3/19Statics-Problems-21静力学第3章作业/P91-3.40:Solution:(1)From the FBD of joint A in Fig:APFABFAD12+第21页/共96页2023/3/19Statics-Problems-22(2)From the FBD of joint B in Fig:BPFBCFBDFAB+第22页/共96页2023/3/19Statics-Problems-23(3)From the FBD of joint D in Fig:DFBD+FDEFADFCD121212第23页/共96页2023/3/19Statics-Problems-24(4)From the FBD of joint C in Fig:CRCFCEFBCFCD12+第24页/共96页2023/3/19Statics-Problems-25静力学第3章作业/P92-3.43*:Solution:(1)From the FBD of joint D in Fig:DPFCDFDH+(1)From the FBD of joint in Fig:HFDHFGFC2323+第25页/共96页2023/3/19Statics-Problems-26Solution:+静力学第4章作业/P111-4.2*:第26页/共96页2023/3/19Statics-Problems-27静力学第4章作业/P113-4.12*:Solution:RAzRAyRByRBxRCxRCzFrom the FBD of bent pipe and cable in Fig:第27页/共96页2023/3/19Statics-Problems-28无解！？第28页/共96页2023/3/19Statics-Problems-29Solution:静力学第4章作业/P113-4.13*:第29页/共96页2023/3/19Statics-Problems-30静力学第4章作业/P114-4.14(b):Solution:S令形心坐标为(xc,yc),按定义有:第30页/共96页2023/3/19Statics-Problems-31静力学第4章作业/P115-4.24:Solution:已知crucible的密度rc=2000kg/m3,外径R=0.28m,内径r=0.2m;iron的密度ri=7200kg/m3OStudying crucible，Drawing FBD in Fig.WiWcGiGcFyFx+第31页/共96页2023/3/19Statics-Problems-32OWiWcGiGcFyFx第32页/共96页2023/3/19Statics-Problems-33Solution:x=0 静力学第4章作业/P116-4.27*:第33页/共96页2023/3/19Statics-Problems-34xyO2xyO1静力学第5章作业/P131-5.2:解：3036lb20lb18in假设系统是静力平衡的先研究圆柱，有P1G1G2N1N2f2f1P1得再研究方块，有得而因，所以系统不能保持静力平衡第34页/共96页2023/3/19Statics-Problems-35Discussion:1.方块会不会先翻倒?3036lb20lb18in2.如果圆柱和方块的接触面不光滑,会怎样?xyO2G2N2f2P1x2x2=?第35页/共96页2023/3/19Statics-Problems-36Solution:总体分析:分析木条:圆盘分析:解之得：NfffCBA.=22.06=达到最大静摩擦力时:解之得：静力学第5章作业/P132-5.10*:第36页/共96页2023/3/19Statics-Problems-379000N/mBCDBCD静力学第5章作业/P132-5.12:解：P假设系统是静力平衡的先研究桩子CBD，有NBNBNAfAfBRxRy再研究杆AB，有P9000N/m1.5m2m3m0.8mABCDABfBAB第37页/共96页2023/3/19Statics-Problems-38只有当fAfAmax或fBfBmax时，杆AB才能移动，由以上计算结果可知，当P6300(N)，杆AB在A点处开始移动第38页/共96页2023/3/19Statics-Problems-39静力学第5章作业/P133-5.18*:Solution:因此:第39页/共96页2023/3/19Statics-Problems-40Solution:木块翻转临界时：滑动时：静力学第5章作业/P133-5.19*:第40页/共96页2023/3/19Statics-Problems-41当P=600 lb时：当P=200 lb时：Solution:静力学第5章作业/P134-5.22*:第41页/共96页2023/3/19MOM-Problems-42第六次作业/P34-1.1(b):SolutionPPPP332211PPPPPPPPPPPPN1N2N3N1=PN2=0N3=PNPP第42页/共96页2023/3/19MOM-Problems-43第六次作业/P34-1.6:SolutionPpd1DPpp6Pb研究活塞杆，有研究右挡盖，有得第43页/共96页2023/3/19MOM-Problems-44第六次作业/P34-1.7*:SolutionPBPsPwBSteelWoodP30AC研究节点B，有研究杆BC，有研究杆AB，有取第44页/共96页2023/3/19MOM-Problems-45第六次作业/P35-1.13*:SolutionBPPCASteelAluminumL1L21m根据题意列出方程组：解得总伸长为第45页/共96页2023/3/19MOM-Problems-46第六次作业/P37-1.14*:SolutionBCA(1)A formula for the downward displacement dC of point CPP(2)The elongation dB of the entire bar第46页/共96页2023/3/19MOM-Problems-47(3)The ratio r of the elongation of the upper half of the bar to the elongation of the lower half of the barThe elongation of the upper half of the barThe elongation of the lower half of the barSo第47页/共96页2023/3/19MOM-Problems-48第六次作业/P37-1.21:SolutionE1E2eebbPPP1P1P2P2(1)静力平衡方程：研究右挡板，有(2)变形协调方程：PeP1P2O(3)求解方程组：第48页/共96页2023/3/19MOM-Problems-49P第六次作业/P37-1.23*:SolutionPB1A2CD(1)Equation of equilibrium BACD(2)Equation of compatibility(3)Force-displacement relations 得补充方程第49页/共96页2023/3/19MOM-Problems-50解得有第50页/共96页2023/3/19MOM-Problems-51第六次作业/P37-1.24*:Solution 变形过程中3根杆的长度始终满足下面的关系：而3根杆的长度变化满足下面的关系：(1)静力平衡方程：研究节点A，有132P3030APAP1P3P2(2)变形协调方程：第51页/共96页2023/3/19MOM-Problems-52(3)求解方程组：第52页/共96页2023/3/19MOM-Problems-54RBRA第六次作业/P37-1.26:SolutionA1A2(1)Equation of equilibrium(2)Equation of compatibility A1A2RBA1A2A1A2RB(3)Force-displacement relations 得补充方程第54页/共96页2023/3/19MOM-Problems-55解得第55页/共96页2023/3/19MOM-Problems-56T2T1材料力学第2章作业/P58-2.1(b):Solutionm3mmm3mT2mm第56页/共96页2023/3/19MOM-Problems-57材料力学第2章作业/P59-2.11:Solution123ABC400500N1N2N3(1)123ABCm1m2m3对于AB段，由强度条件得 由刚度条件得 第57页/共96页2023/3/19MOM-Problems-58取由强度条件得 由刚度条件得 对于BC段，取(2)取(3)齿轮1安放在齿轮2、3中间。123ABC400500N1N2N3123ABCm1m2m3第58页/共96页2023/3/19MOM-Problems-59材料力学第2章作业/P59-2.14:Solution方法一（传统法）：L/4L/4L/2AB3T0T01.解除某些约束，施加相应约束反力，使之成为静定基；2.扭矩与变形协调方程：得TB=5T0/43.外扭矩3T0和T0作用处的转角分别为：3T03T0T0TBT0TB=第59页/共96页2023/3/19MOM-Problems-61材料力学第3章作业/P72-3.1(c):BqaqACaaqa21122Solutionqaqqa2V1M1对于1-1截面，有qaqqa2V2M2对于2-2截面，有第61页/共96页2023/3/19MOM-Problems-62补充：内力图BqaqACaaqa2V-第62页/共96页2023/3/19MOM-Problems-63(1)Shear-Force and Bending-Moment Equations 材料力学第3章作业/P73-3.2(a):Solution2PBACaaPa2PBACPaVM2PBACPaVM第63页/共96页2023/3/19MOM-Problems-64(2)Shear-Force and Bending-Moment Diagrams 2PBACaaPaV-(3)Maximum Shear Forces and Bending Moments第64页/共96页2023/3/19MOM-Problems-65材料力学第3章作业/P73-3.3(b)*:qABCL/2L/2SolutionxVMVMxxM控制截面法？V第65页/共96页2023/3/19MOM-Problems-66Solution材料力学第4章作业/P90-4.6*:PPACDB2m2m2mNo20a1.求约束反力2.求弯矩作出弯矩图RARB3.求许用载荷M由强度条件得危险截面在C或D，有查表得第66页/共96页2023/3/19MOM-Problems-67材料力学第4章作业/P91-4.8:SolutionA T-beam made of cast iron in pure bending.Knowing the ratio of tensile allowable stress to compressive allowable stress is st/sc=1/4.Determine the reasonable width b of the flange.bzC3060400MM第67页/共96页2023/3/19MOM-Problems-68材料力学第4章作业/P91-4.13:Solution1.求剪力和弯矩作出剪力图和弯矩图V2.根据胶合面强度条件求P1mPAB505050100G整个截面都是危险截面，考虑剪应力互等定理，有M第68页/共96页2023/3/19MOM-Problems-69V1mPAB505050100GM3.根据截面剪应力强度条件求P整个截面都是危险截面，有4.根据截面正应力强度条件求PA截面是危险截面，有5.综上所述，取第69页/共96页2023/3/19MOM-Problems-70q0LBAyx材料力学第5章作业/P110-5.3(c)*:Solution1.求约束反力RARB2.求弯矩方程OARAV Mx第70页/共96页2023/3/19MOM-Problems-713.求挠曲线方程：代入边界条件：得：最大挠度：两端转角：中间挠度：取合理解第71页/共96页2023/3/19MOM-Problems-72材料力学第5章作业/P111-5.8:SolutionThe cantilever beam shown in the figure has moments of inertia I1 and I2 in parts AC and CB,respectively.(a)Using the method of superposition,determine the deflection dB at the free end due to the load P.(b)Determine the ratio r of the deflection dB to the deflection d1 at the free end of the prismatic cantilever beam with moment of inertia I1 carrying the same load.BAL/2L/2C(a)BCA第72页/共96页2023/3/19MOM-Problems-73BAL/2L/2CBACBCBCA第73页/共96页2023/3/19MOM-Problems-74BAL/2L/2C(b)BAL第74页/共96页2023/3/19MOM-Problems-75BAL/2L/2CDiscussionUse energy method第75页/共96页2023/3/19MOM-Problems-76材料力学第5章作业/P111-5.9:SolutionBAqL/2L/2BAq1.解除某些约束，施加相应约束反力，使之成为静定基；2.变形协调方程：RB=BAqBARBfBufBd查表得第76页/共96页2023/3/19MOM-Problems-773.求其它约束反力：BAqRBRAMAL/2L/2第77页/共96页2023/3/19MOM-Problems-78材料力学第5章作业/P112-5.13*:SolutionThe bars 1 and 2 have the same tensile rigidity EA.(1)If the beam AB is considered as rigid,determine the internal forces in the two bars.(2)If the beam AB is considered as deformable with bending rigidity EI,determine the internal forces in the two bars.(1)the beam AB is considered as rigidPAB21CPBAC(a)Equation of equilibrium(b)Equation of compatibility 第78页/共96页2023/3/19MOM-Problems-79(1)the beam AB is considered as rigidPAB21CPBAC(a)Equation of equilibrium(b)Equation of compatibility(c)Force-displacement relations 得补充方程解得第79页/共96页2023/3/19MOM-Problems-80(2)the beam AB is considered as deformablePAB21CPBAC(a)Equation of equilibrium(b)Equation of compatibility(c)Force-displacement relations 得补充方程解得第80页/共96页2023/3/19MOM-Problems-811.危险点位于圆轴固定端横截面的最上处和最下处（A点和B点）材料力学第6章作业/P135-6.1(d):mPLdTMSolution:忽略横力弯曲剪力的影响2.用单元体表示危险点的应力状态V3.用应力圆表示危险点的应力状态(,)(-,)(0,-,-)B点点A点点ABA点：或B点：或第81页/共96页2023/3/19MOM-Problems-82材料力学第6章作业/P135-6.3(d):402040如右图所示单元体，画出对应的应力圆Solutions st tt tmaxmax(-40,-40)(-20,40)1.主应力和主方向s s3 3s s1 111.2371.232.如图所示在单元体上画出主平面方向52.023.最大剪应力第82页/共96页2023/3/19MOM-Problems-83材料力学第6章作业/P135-6.4(b)*:30305020如右图所示单元体，画出对应的应力圆Solutions st ts s1 1s s2 2t tmaxmax(30,-20)(50,20)60(52.32,-18.66)a a=30第83页/共96页2023/3/19MOM-Problems-84材料力学第6章作业/P136-6.7*:Solution30如右下图所示，在A点取单元体并进行应力状态分析a a=120A test of thin walled tube is shown in the figure.If the loads are a concentrated force P=20kN and a torque T=600Nm.The diameter of the tube is d=50mm,thickness is d=2mm.(1)Determine the normal and shear stresses on the inclined section at point A.(2)Determine the magnitude and orientation of the principal stresses at point A.(Draw stress element.)第84页/共96页2023/3/19MOM-Problems-85(2)s st t(61.21,-70.63)(0,70.63)s s3 3s s1 166.5733.29(1)第85页/共96页2023/3/19MOM-Problems-86材料力学第6章作业/P136-6.11:SolutionxxyyWhen a train pass through a steel bridge,the strains tested by instrument are ex=0.0004,ey=-0.00012 at point A.Find the normal stresses in directions x and y at point A.(E=200GPa,m=0.3)第86页/共96页2023/3/19MOM-Problems-87材料力学第6章作业/P137-6.17*:Solution薄壁上任意一点都是危险点，在薄壁上任一点A取单元体并进行应力状态分析AA thin-walled tube shown in the figure is made of cast iron.Knowing its outside diameter is D=200mm,thickness of the wall is t=15mm,the inner pressure is p=4MPa,the compressive force is P=200kN.The allowable tensile and compressive stresses of cast iron are st=30MPa and sc=120MPa,respectively.Exam the strength of the thin-walled tube.第87页/共96页2023/3/19MOM-Problems-88由上可知由第一强度理论可知强度满足由第二强度理论可知强度满足由莫尔强度理论可知强度满足第88页/共96页2023/3/19MOM-Problems-89材料力学第6章作业/P137-6.18:Solution1.求A点所在横截面的内力PV M2.在点A处取单元体并进行应力状态分析AA cantilever beam of rectangular cross section is subjected to a concentrated load P=120kN,acting at the free end.The beam has width b=100mm,and height h=200mm.Point A is located at distance c=0.5m from the free end and distance d=50mm from the bottom of the beam.Calculate the principal stresses and the maximum shear stress tmax at point A,and the equivalent stresses of third and fourth strength condition.第89页/共96页2023/3/19MOM-Problems-903.点A处主应力A4.点A处等效应力第90页/共96页2023/3/19MOM-Problems-91材料力学第7章作业/P145-7.2:Solution1.求约束反力2.求-横截面的内力RVMN3.-横截面性质RA construct is shown in the figure.Find the maximum normal stress on section I-I and the stress at point A.第91页/共96页2023/3/19MOM-Problems-924.应力RVMN（压应力，在横截面上端）（拉应力，在横截面下端）第92页/共96页2023/3/19MOM-Problems-93材料力学第7章作业/P146-7.10:Solution1.简化模型，作内力图P0.18P0.18PTMV0.18P0.2P0.5P0.5P2.由内力图可见，中间横截面为危险截面，忽略横力弯曲剪力的影响，在危险截面处为弯扭组合变形In figure there is a manual winch.The diameter of the steel shaft is d=30mm and the allowable stress is s=80MPa.Find the maximum load for the winch,according to the third strength condition.第93页/共96页2023/3/19MOM-Problems-94Pyxzyx材料力学第7章作业/P146-7.12*:Solution如右下图所示，力P在a、b点所在横截面中心处产生的内力作用为一主失和一主矩：OabzF Fx xF Fy yF Fz zM Mz zM Mx xM My y第94页/共96页2023/3/19MOM-Problems-95yxOabzF Fx xF Fy yF Fz zM Mz zM Mx xM My ya点：a、b点的应力状态如右下图所示aaaxyb点：bbbxy第95页/共96页感谢您的观看！第96页/共96页
