材料力学(英文版)chap4

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1、M.VableMechanicsofMaterials:Chapter4AxialMembers•Memberswithlengthsignificantlygreaterthanthelargestcross-sec-tionaldimensionandwithloadsappliedalongthelongitudinalaxis.CablesofMackinawbridgeHydrauliccylindersinadumptruck(a)(b)Learningobjectivesare:•Under

2、standthetheory,itslimitations,anditsapplicationsfordesignandanalysisofaxialmembers.•Developthedisciplinetodrawfreebodydiagramsandapproximatedeformedshapesinthedesignandanalysisofstructures.Printedfrom:http://www.me.mtu.edu/~mavable/MoM2nd.htm4-1M.VableMec

3、hanicsofMaterials:Chapter4TheoryTheoryObjective•toobtainaformulafortherelativedisplacements(u2-u1)intermsoftheinternalaxialforceN.•toobtainaformulafortheaxialstressσxxintermsoftheinternalaxialforceN.u1u2yxF2zx1x2Printedfrom:http://www.me.mtu.edu/~mavable/

4、MoM2nd.htm4-2M.VableMechanicsofMaterials:Chapter4Kinematicsoriginalgriddeformedgrid(a)(b)(c)yxAssumption1Planesectionsremainplaneandparallel.uu=()x•Thedisplacementuisconsideredpositiveinthepositivex-direction.du()xAssumption2Strainsaresmall.ε=xxdxMaterial

5、ModelAssumption3Materialisisotropic.Assumption4Materialislinearlyelastic.Assumption5Therearenoinelasticstrains.duFromHooke’sLaw:σ=Eε,weobtainσ=ExxxxxxdxInternalAxialForceyyN=∫σdAxxzdNxxxdAyAONxOduduxN==∫EdA∫EAddxdxyAA•Forpureaxialproblemstheinternalmome

6、nts(bending)MyandMzmustbezero.•Forhomogenousmaterialsallexternalandinternalaxialforcesmustpassthroughthecentroidsofthecross-sectionandallcentroidsmustlieonastraightline.Printedfrom:http://www.me.mtu.edu/~mavable/MoM2nd.htm4-3M.VableMechanicsofMaterials:Ch

7、apter4AxialFormulasAssumption6Materialishomogenousacrossthecross-section.dududuNN==E∫dAEAor=-------dxdxdxEAAdu⎛⎞NNσ==EE-------orσ=----xxdx⎝⎠EAxxA•ThequantityEAiscalledtheAxialrigidity.Assumption7Materialishomogenousbetweenx1andx2.Assumption8Thebarisnottap

8、eredbetweenx1andx2.Assumption9Theexternal(henceinternal)axialforcedoesnotchangewithxbetweenx1andx2.N()x–x21u–u=--------------------------21EATwooptionsfordetermininginternalaxialforceN•Nisalwaysdrawnintensionattheim