东南大学材料力学试卷2

Page1of9材料力学考试卷课程名称考试学期得分适用专业80学时考试形式闭卷考试时间长度120分钟1.(20′)Blankfillingandchoiceproblems【填空和选择题】(1).(4′)Thestress-straincurvefromatensiontestisshownbelow.【下图所示为一拉伸应力应变曲线】Determinethefollowingquantities:【试决定下列各量的值】(a)Proportionallimit【比例极限】().(b)Modulusofelasticity【弹性模量】().(c)Ultimatestrength【强度极限】().(d)Determinetheplasticstrainatthestresslevelof450MPa【对应于450MPa的塑性应变】().(2).(2′)IfthejointissubjectedtoanaxialforceofP,determinetheaverageshearstressdevelopedineachofthefourboltswithdiameterd【试求如图所示螺栓接头中，每个螺栓(直径为d)所受的平均切应力】().Also,determinethemaximumnormalstressactingonthecross-sectionoftheplate【并确定木板横截面上的最大正应力】().自觉遵守考场纪律如考试作弊此答卷无效密封线学号姓名Page2of9(3).(2′)AssociatethebeambelowwithALLappropriateconditionsnecessaryforsolvingthebeamdeflectionw(x).【悬臂梁如图所示，选出积分法求解挠曲线时的所有适用条件】()1122112212121212:00:20:20:0:'00:'20:'20:'0:22:22:'2'2:'2'2awxbwxLcwxLdwxLewxfwxLgwxLhwxLiwxLwxLjwxLwxLkwxLwxLlwxLwxL(4).(2′)Determinethelocationofthemaximumtransverseshearstressforacircularcross-sectionbeamundertransverseloading【在横力弯曲的情况下,圆截面梁横截面上最大弯曲切应力发生在何处】().Howmuchistheratioofthisstressoverthecross-sectionalaverage?【最大弯曲切应力是截面平均切应力的多少倍】()(5).(2′)AssociatethetwostresscubeswiththeappropriateMohr’scircleshownbelow.Cube1();Cube2().【为下列两个单元体选择相应的莫尔应力圆】Page3of9(6).(3′)Thestateofstressatapointisshownontheelement.Determinetheprincipalstressesandprincipaldirections.Showdirectlytheresultsontheoriginalelement.【已知一点的应力状态如图所示，试求其主应力大小和主方向，并在原图中作图标示】(7).(3′)Identifythemembersinthetwo-barstructuresthatyouwouldcheckforbuckling.Structure1();Structure2();Structure3();【试分别确定下列三个两杆结构中需要进行稳定性分析的杆件】(8).(2′)Forthelinearlyelasticbeamsubjectedtotheloadsshown,identifythephysicalinterpretationofthefollowingpartialderivativesbasedonthesecondtheoremofCastigliano,withUdenotingtheelasticstrainenergy.【对于图示线弹性梁，试根据卡氏第二定理确定下列偏导数的意义，其中U表示梁内应变能】:UP()；:UM().Page4of92.(10′)Drawtheshearandmomentdiagrams.Determinetheabsolutemaximumbendingnormalstressinthetubularshaft(NOTthin-walled)ifdi=160mmanddo=200mm.【试作图示梁的剪力图和弯矩图，并求当空心圆杆（非薄壁）内外直径分别为di=160mm和do=200mm时所承受的最大弯曲正应力】Page5of93.(12′)Thesteelshafthasadiameterof60mmandisfixedatitsendsAandB.Ifitissubjectedtothetoquesshown,determinethemaximumshearstressdevelopedintheshaft.【已知图示钢轴直径为60mm，A和B两端固定，承受如图所示的两个集中扭矩，试求轴内承受的最大切应力】Page6of94.(15′)Ifthetemperatureofthe75-mm-diameterpostCDisincreasedby600C,determinetheforcedevelopedinthepost.ThepostandthebeamaremadeofmaterialhavingamodulusofelasticityE=200GPaandthecoefficientofthermalexpansionα=12(10-6)0C-1m-1.ThemomentofinertiaofthebeamisI=255106mm4.【图示结构中柱CD直径为75mm，试求当柱内温度上升600C时该柱所承受的轴力。设梁和柱的的弹性模量E=200GPa，柱的热膨胀系数α=12(10-6)0C-1m-1，且梁的惯性矩为I=255106mm4】Page7of95.(15′)IftheresultantinternalmomentactingonthecrosssectionofthealuminumstruthasamagnitudeofM=520Nmandisdirectedasshown,determinethebendingnormalstressatpointAandB.Alsodeterminetheequationoftheneutralaxis.【已知一铝杆某截面上的内力弯矩为M=520Nm，作用方向如图所示，试求该截面上A和B两点所受的弯曲正应力，并确定截面中性轴方程。】Page8of96.(14′)Determinethemaximumallowableintensityqofthedistributedloadthatcanbeappliedonthebeamwithoutcausingthecompressivemembersofthesupportingtrusstobuckle.Themembersofthetrussaremadefromsteelrodsandhavea60-mmdiameter.Useafactorofsafetyagainstbucklingof2.E=200GPaandσP=250MPa.【试求使得图示结构中支撑桁架内的压杆不发生失稳所允许的最大均布荷载集度q。桁架构件均由直径为60mm的钢杆组成，其弹性模量E=200GPa，比例极限σP=250MPa，失稳安全系数为2】Page9of97.(14′)Thecompositealuminumbarismadefromtwosegmentshavingdiametersof5mmand10mm,respectively.Determinethemaximumaxialstressdevelopedinthebarifthe5kgcollarisdroppedfromaheightofh=100mm.E=70GPa,p=410MPa.【如图所示，试求当质量为5kg的套环从h=100mm的高度自由下落时在圆形截面铝棒内所产生的最大轴向应力。设E=70GPa,p=410MPa.】