山农双语材力附录.ppt

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1、MechanicsofMaterialsAppendixGeometricpropertiesofplanargraphsAppendixGeometricpropertiesofplanargraphs§I-1StaticMomentandCentroid§I-2MomentofInertiaandRadiusofInertia§I-3ProductofInertia§I-5TransferAxisFormulaandPrincipalInertiaAxis§I-4ParallelAxisFormulaShearingstressonthecrosssectioni

2、ntorsion§I-1StaticMomentandCentroid1、StaticMomentoyzyzAydAAzdAdAThestaticmomentofmicroareaforzaxisydAThestaticmomentofmicroareaforyaxiszdAThestaticmomentofthewholeplanargraphforz,yaxisesPositive,negative,zeroyzodAyz2.FormulaofcentroidcoordinateycThestaticmomentofthesectionforthecentro

3、idalaxisisequaltozero.Ifthestaticmomentofanysectionforanyaxisisequaltozero,theaxispassesthecentroid.3、StaticMomentandCentroidofthecombinedgraphs1010120o80Solution：Dividethesectioninto1，2parts12yxSample1TrytodeterminethepositionofthecentroidC.1010120o8012yxGraph1Graph2So1010120o8012yx§I-

4、2MomentofInertiaandRadiusofInertiaoyzyzdA1、MomentofinertiaandradiusofinertiaAy2dAAz2dAy2dAz2dAThemomentofinertiaofmicroareaforzaxisThemomentofinertiaofmicroareaforyaxisThemomentofinertiaofthewholeplanargraphforz,yaxisesPositiveoyzyzdAThepolarmomentofinertiaofplanargraphforcoordinateor

5、igin:istheradiusofinertiaforyaxis.istheradiusofinertiaforxaxis.Sample2:DetermineoftheplanargraphyzbhzdzcyzdSample3:DetermineoftheplanargraphdDyzSample4:Determineoftheplanargraph3、MomentofinertiaofthecombinedgraphsbhyThinking:oyzyzdAyzWhenoneofthetwocoordinateaxisissymmetryaxis，theproduc

6、tofinertiaoftheplanargraphfortheaxisisequaltozero.§I-3ProductofInertiaPositive,negative,zeroTheproductofinertiaofplanargraphfory,zaxisyczcyczcODetermine:Knowing：Solution：dAC0§I-4ParallelAxisFormula0yczcyczcOdAC0ParallelaxisformulaSample5：DeterminetheMomentofInertiaofthegraphforcentroida

7、xisYc.oyzdAyz§I-5TransferAxisFormulaandPrincipalInertiaAxisoyzAdAyzTrigonometricfunction:Sample6：DeterminethemomentofinertiaandproductofineritaforoftheplanargraphSolution:yzabODiscussion：Whenaisequaltob，theresult?PrincipalInertiaAxis??DeterminethetwoanglesPrincipalInertiaAxis:P