机制材料力学试卷A答案

厦门理工学院机械工程系12008机制材料力学试卷A一、（20）5.83Theworkingstressesforthemanufacturedwoodbeamare10MPainbendingand1.0MPainshear.Determinethelargestallowablevalueoftheloadintensityw0.Solution5(a)DesignforshearThemaximumshearforceis厦门理工学院机械工程系20max7wVthefirstmomentofthecross-sectionalareaabovetheneutralaxisis332)(108828.02)252300(2522530025200mQ3themomentofinertiaofthecross-sectionalabovetheneutralaxisis4333)(102221.01225017512300200mI360330maxmax1019.1112025.0102221.0108828.07wwbIQV--------P163)/(8985.0)/(5.8980mkNmNw4(b)DesignforbendingThenormalstress0max75.7wM6030maxmax10105234102221.075.723.023.0wwIM)/(91.1)/(19100mkNmNw4Sothelargestallowablevalueoftheloadintensity)/(8985.0)/(5.8980mkNmNw1二、（20）TheoverhangingbeamABCcarriestheuniformlydistributedloadbetweenitssupportsandtheconcentratedloadPatendC.DeterminethedisplacementofthebeamattheC,bysuperposition.5厦门理工学院机械工程系3Accordingtodeflectionformulasforbeams,weknowEIwEIwLBw24a2433，bEIwbEIwLBw24a24335EIbwEIPbEIMLBM3a3a32，EIbwbEIPbbEIMLBM3a3a335EIwbEIPbCP33434EIwbEIbwEIbwCPCMCwC33a24a4331三、（20）8.27Thecrosssectionsofthemembersofthepin-jointedstructureare200-mmsquare.FindthemaximumcompressivestressinmemberBDE.15SolutionThemaximumcompressivestressinmemberBDE厦门理工学院机械工程系4)(95.682.02.010001.582.02.010009062maxMPaC5四、（20）8.110Determinethesmallestallowablediameteroftheshaftthatcarriesthethreepulleys.Theworkingstressesareσw=18ksiandτw=8ksi.NeglecttheweightsofthePulleysandtheshaftaswellasthestressduetothetransverseshearforce.SolutionAccordingthesupport,weknowthereisthelargestbendingmomentoccursatC,thelargesttorqueoccursinsegmentBC.Showinthefigure.01012006030810100440BYF，FBY=938.33(lb)0701200603081040440DYF，FDY=1511.67(lb)C点弯矩和扭矩：.).(9.26493067.1511401200inlbMCZ，.).(18000100018inlbMCx).(01.1819422inlbMMMCxCZCD点弯矩和扭矩：.).(12000101200inlbMDZ，.).(18000100018inlbMDx).(08.2163322inlbMMMDxDZD厦门理工学院机械工程系5B点弯矩和扭矩：.).(1760040440inlbMBZ，.).(540015360inlbMBx).(78.1840922inlbMMMBxBZB7AtDsection,wehave).(08.2163322inlbMMMDxDZD.).(12000101200inlbMDZ，.).(18000100018inlbMDxTherefore,thestressatthebottomofthesectionare3333maxmax.)(.).(10123232indinlbdMSM43333.)().(10181616indinlbdTJrTBCBC4DrawtheMohr’scircleAccordingtoMohr’scircle,wehave32233max1018]181212[1016Wdd=2.119(in.)W22max)2(2WBCTMMd][1622maxmax3maxW22max)2(4Settleit,weget)(108.).(1016)1812(33322maxksidinlbd=2.397(in.)五、（20）厦门理工学院机械工程系6Forthetrussshowninthefigure(a),thecrosssectionofbarCDisshowinFig.(b),usingAISCcolumnspecificationswithE=200GPaandσyp=250MPa.,determinethemaximumsafevalueofP.Assumethatcross-bracingpreventsthejointsfromdeflectingperpendiculartotheplaneofthetruss.SolutionDeterminetheforceFcx0)523038(3038520PPFMCXA）（，PPFCX615.352188Determinethemomentofinertiaofthecross-sectionalareaaboutthez-axis284441)(1075.6)(1075.61230mmmI厦门理工学院机械工程系7)(10122.5)(10122.51228484442mmmIthemomentofinertia)(10628.14821zmIIIArea)(1016.1028.003.02422mA，Theslendernessratioofa1600mmx2400mmrectangleTheleastradiusofgyrationwithz-axis)(644.038.052.022mlCD)(0118.0)(1016.1)(10628.12448mmmAIrzz258.540118.0644.0mmCzC4CXCXCDF38.0644.038.038.052.0FP22Theslendernessratio7.12525010002002222ypCEC4FortheslendernessratiozCyCCC,islessthanCC,sothattheconcretecolumnisofintermediatelength.Theseequationsyieldthefactorofsafety82.112686.5412686.54335883353333CzCCzCzCCCCN4andtheworkingstress)(12482.12012626.541212222MPaNCCypCzCzw4Thelargestallowableaxialloadthusbecomes)(384.14)(143841016.11012446CDkNNAPzwaccordingtoCXCXCDF38.0644.038.038.052.0FP22，PPFCX615.352188SoweobtainaxialloadP)(348.2644.038.0615.31615.31kNPFPCDCX2