第4章材料力學

Copyright?2014PearsonEducation,AllRightsReservedSAINT-VENANT’SPRINCIPLEstressandstrainproducedatpointsinabodysufficientlyremovedfromtheregionofloadapplicationwillbethesameasthestressandstrainproducedbyanyappliedloadingsthathavethesamestaticallyequivalentresultant,andareappliedtothebodywithinthesameregionELASTICDEFORMATIONOFANAXIALLYLOADEDMEMBERProvidedthesequantitiesdonotexceedtheproportionallimit,wecanrelatethemusingHooke’sLaw,i.e.σ=E

εConstantLoadandCross-SectionalAreaIfi)thecrosssectionareaisconstant;ii)thematerialrequiredtobeconsideredishomogenousiii)constantloadisappliedForP(x)=P;A(x)=A,andsoaboveequationcanbeconvertedtobeIfthebarissubjectedtoseveraldifferentaxialforcesalongitslength,orthecross-sectionalareaormodulusofelasticitychangesabruptlyfromoneregionofthebartothenext,theaboveequationcanbeappliedtoeachsegmentofthebarwherethesequantitiesremainconstant.SignConventionFORTHECONVENIENCEOFANALYSIS,THESIGNCONVENTIONISDEFINEDAS:theforceanddisplacementtobepositiveiftheycausetensionandelongation,consequently,anegativeforceanddisplacementwillcausecompressionandcontraction,respectivelyPRINCIPLEOFSUPERPOSITIONItcanbeusedtosimplyproblemshavingcomplicatedloadings.Thisisdonebydividingtheloadingintocomponents,thenalgebraicallyaddingtheresults.ItisapplicableprovidedthematerialobeysHooke’sLawandthedeformationissmall.IfP=P1+P2andd≈d1≈d2,thenthedeflectionatlocationxissumoftwocases,δx=δx1+δx2Heredeformationissignificant,andsodisnotequaltod1,d2,andsoprincipleofsuperpositionisnotvalidinthiscase.StaticallyIndeterminateAxiallyLoadedMember(軸向超靜定結構）Astaticallydeterminatestructure(靜定結構）isonewherethereisonlyonedistributionofinternalforcesandreactionswhichsatisfiesequilibrium.Inastaticallydeterminatestructure,internalforcesandreactionscanbedeterminedbyconsideringnothingmorethanequationsofequilibrium.Astaticallyindeterminatestructure（超靜定結構）isonewherethereismorethanonedistributionofinternalforcesand/orreactionswhichsatisfiesequilibrium.BadengineeringdesignGood!TheForceMethodofAnalysisforAxiallyLoadedMembersThermalStressSTRESSCONCENTRATIONThestressconcentrationfactorKisaratioofthemaximumstresstotheaveragestressactingatthesmallestcrosssection;i.e.STRESSCONCENTRATION(cont.)KisindependentofthematerialpropertiesKdependsonlyonthespecimen’sgeometryandthetypeofdiscontinuityINELASTICAXIALDEFORMATIONWhenamaterialisstressedbeyondtheelasticrange,itstartstoyieldandtherebycausespermanentdeformation.Amongvariousinelasticbehavior,thecommoncasesexhibitelastoplasticorelastic-perfectly-plasticbehavior.RESIDUALSTRESSAfteranaxiallyloadedmemberisstressedbeyondyieldstress,itwillcreateresidualstressinthememberwhentheloadsareremoved.Considerthestresshistoryofaprismaticmembermadefromanelastoplasticmaterial.Path