Stress_strain_intro

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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:LoadStressxUniaxialStressCaseLink2:StressStrainFFxLLDD/2Poisson’sRatio(greek“nu”):Anaxialst

5、resswillproducebothaxialandlateralstrain!AxialStrainLateralStrainBiaxialStressCaseLink1:LoadStressEg.ApressureVesselBiaxialStressCaseLoadisfrompressureX(hoopdirection)y(axialdirection)BiaxialStressCaseLink2:StressStrainσxCorrespondingstrainsStress

6、esBiaxialStressCaseLink2:StressStrainσxσyεxεyRearranged,wecanuseourstrainstofigureoutstressesUniaxialStressCaseLink1:LoadStressisanaxialstressattheupper/lowersurface.Ex.CATILEVERSUBJECTEDTOBENDINGSTRESSCantileverstrain….UnderuniaxialstressBiaxials

7、train(transversestrainduetoPoisson’seffect)Link2:StressStrainElasticPropertiesofSolidsWehavebeenassumingthattheobjectsdonotchangetheirshapeswhenexternalforcesareexertingonit.Itthisrealistic?No.Inreality,theobjectsgetdeformedasexternalforcesactonit,t

8、houghtheinternalforcesresistthedeformationasittakesplace.DeformationofsolidscanbeunderstoodintermsofStressandStrainStress:Aquantityproportionaltotheforcecausingdeformation.Strain:MeasureofdegreeofdeformationItisempiricallyknownthatforsmallstre