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ID:38439617
大小:2.27 MB
页数:43页
时间:2019-06-12
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1、Strain(应变)andStress(应力)MeasurementsXueChenyangWhatisStrain?Defn:Elongationperunitlengthofamembersubjecttoanappliedforce.Strain(ε)isnondimensionalε=ΔL/LCanbepositiveornegativeDirectionmustbedefinedLoadLΔLWhatisStress?Defn:Internalforcesperunitarea.Thes
2、einternalforcesmaintaininequilibriumtheappliedexternalforces.LoadUnitofstress(σ):PaorpsiInternalstressLoadStressmaybethoughtofasadescriptionofforceconcentrationStressonaplane(traction),s=F/A1N/m2=1Pawhataboutunitsofstress?100MPa=1kbarThelinkfromLoadto
3、StrainForce;Torque;Pressure;Vibrations….CausestressStresscausesstrainWecan’tmeasurethis!Wecanmeasurethis!Isthereapredictablerelationshipbetweenstressandstrain?Stressandstrainareconnectedinelasticregion.Whereεx=straininxdirectionσx=stressinxdirectionE=
4、Young’sModulusThelinkbetweenStressandStrainεσFFBBFBBWhereA=areaofcrosssectionEx.AtrussUniaxialstateofstressLoadisfromexternalforceUniaxialStressCaseLink1:LoadStressxUniaxialStressCaseLink2:StressStrainFFxLLDD/2Poisson’sRatio(greek“nu”):Anaxialst
5、resswillproducebothaxialandlateralstrain!AxialStrainLateralStrainBiaxialStressCaseLink1:LoadStressEg.ApressureVesselBiaxialStressCaseLoadisfrompressureX(hoopdirection)y(axialdirection)BiaxialStressCaseLink2:StressStrainσxCorrespondingstrainsStress
6、esBiaxialStressCaseLink2:StressStrainσxσyεxεyRearranged,wecanuseourstrainstofigureoutstressesUniaxialStressCaseLink1:LoadStressisanaxialstressattheupper/lowersurface.Ex.CATILEVERSUBJECTEDTOBENDINGSTRESSCantileverstrain….UnderuniaxialstressBiaxials
7、train(transversestrainduetoPoisson’seffect)Link2:StressStrainElasticPropertiesofSolidsWehavebeenassumingthattheobjectsdonotchangetheirshapeswhenexternalforcesareexertingonit.Itthisrealistic?No.Inreality,theobjectsgetdeformedasexternalforcesactonit,t
8、houghtheinternalforcesresistthedeformationasittakesplace.DeformationofsolidscanbeunderstoodintermsofStressandStrainStress:Aquantityproportionaltotheforcecausingdeformation.Strain:MeasureofdegreeofdeformationItisempiricallyknownthatforsmallstre
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