材料力学(英文版)chap2

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1、M.VableMechanicsofMaterials:Chapter2Strain•Relatingstrainstodisplacementsisaproblemingeometry.KinematicsLearningobjectives•Understandtheconceptofstrain.•Understandtheuseofapproximatedeformedshapeforcalculatingstrainsfromdisplacements.Printedfrom:http://www.me.mtu.edu/~mavable/MoM2nd

2、.htm2-1M.VableMechanicsofMaterials:Chapter2PreliminaryDefinitions•Thetotalmovementofapointwithrespecttoafixedreferencecoordi-natesiscalleddisplacement.•Therelativemovementofapointwithrespecttoanotherpointonthebodyiscalleddeformation.•Lagrangianstrainiscomputedfromdeformationbyusingt

3、heoriginalundeformedgeometryasthereferencegeometry.•Eulerianstrainiscomputedfromdeformationbyusingthefinaldeformedgeometryasthereferencegeometry.Printedfrom:http://www.me.mtu.edu/~mavable/MoM2nd.htm2-2M.VableMechanicsofMaterials:Chapter2AverageNormalStrainL–Lfoδε==------------------

4、-----ABavLLABooLoLf•Elongations(Lf>Lo)resultinpositivenormalstrains.Contractions(Lf

5、oint.•in/in,orcm/cm,orm/m•percentage.0.5%isequaltoastrainof0.005•prefix:μ=10-6.1000μin/inisequaltoastrain0.001in/inPrintedfrom:http://www.me.mtu.edu/~mavable/MoM2nd.htm2-3M.VableMechanicsofMaterials:Chapter2C2.1DuetotheapplicationoftheforcesinFig.C2.1,thedisplace-mentoftherigidplate

6、sinthexdirectionwereobservedasgivenbelow.DeterminetheaxialstrainsinrodsinsectionsAB,BC,andCD.u=–1.8mmu=0.7mmu=3.7mmBCDxF1F2F3ABCDF3FF211.5m2.5m2mFig.C2.1Printedfrom:http://www.me.mtu.edu/~mavable/MoM2nd.htm2-4M.VableMechanicsofMaterials:Chapter2Averageshearstrain.UndeformedgridDefor

7、medgrid(a)(b)WoodenBarwithMaskingTapeAWoodenBarwithMaskingTapeAA1γBπ/2CαBCWoodenBarwithMaskingTapeWoodenBarwithMaskingTapeπγ=---–αav2•Decreasesintheangle(α<π/2)resultinpositiveshearstrain.Increaseintheangle(α>π/2)resultinnegativeshearstrainUnitsofaverageshearstrain•Todifferentiateav

8、eragestrainfromstra