(1.3.2)-ch0-2 Statics材料力学材料力学

Chapter0Introduction

MechanicsofMaterialsStaticsreviewWelcometomechanicsofmaterials.Inthelastvideo,ageneralintroductionforthiscoursewasgiven,thisvideoisgoingtoreviewstatics.StaticanalysisMostproblemsinmechanicsofmaterialsrequireastaticanalysisasthefirststep.ThestaticanalysisisintroducedintheprerequisitecourseonStatics.Staticsstudiestheequilibriumofrigidbodiesacteduponbyavarietyofdifferentforces.

Todoastaticanalysis,itneedstodrawfree-bodydiagramoftheentirebody,orofcomponentsofthebody,andthenapplytheequationsofequilibriumtofindunknownexternalreactionforces.Therefore,allforcesactingonthebodyandcausingitsdeformationareknown.Onceallexternalandinternalforcesofinteresthavebeenfound,youcanproceedwiththeevaluationofstresses,strains,anddeformationsofbars,shafts,beams,andcolumnsasdescribedinsubsequentchapters.Inthissection,thebasicstaticequilibriumequationsarereviewedandthenappliedtothesolutionofexample

structures(bothtwoandthree-dimensional).EquilibriumequationsVectorformScalarform2D3DRigidordeformablebodyinequilibriumEquilibriumequationsdescribethestateofabodyinequilibrium.TheresultantforceRandmomentMofallforcesandmomentsonthebodyinequilibriumarebothzero.Theresultingequilibriumequationscanbeexpressedinvectorformorscalarform.Itisoftenmoreconvenienttowritetheequilibriumequationsinscalarformeitherintwodimensionsorthreedimensions.Bytheway,thesumofthe

momentsmaybetakenaboutanyarbitrarypoint.Notethatequilibriumequationscanbeusedbothforevaluatingrigidbodiesordeformablebodies,Whichmeansthatdeformationsduetoloadingsareirrelevantinstaticforceanalysis.AppliedForcesconcentratedloadconcentratedmomentdistributedloaddistributedmomentFq0Fq2Fq1Externalloadsappliedtoabodyorstructuremaybeeitherconcentratedloadsormoments,ordistributedloadsormoments.Distributedforcesmayactalongornormaltoamember.Distributedforcesmayhaveconstantintensity,oralinear(orother)variationwithsomepeakintensity.

Andanydistributedloadingcanbereplacedbya

staticallyequivalentforceatthecenterofgravityofthedistributedloading.SuppportsModelingreaction

forcesandsupportconditionsin2Dstaticanalysisgiveninthetable.ThesehavebeencoveredinStatics.-Cornerstoneofallworkinthiscourse-AllforcesmustbedisplayedonFBDs

-Determinethe

unknown

external

reactionforcesFree

BodyDiagramseperateFBDsconnectionforceoverallFBD

FCEDXDYBXBYAfree-bodydiagramisanessentialpartofastaticanalysisDrawingfreebodydiagramsisthecornerstoneofallworkinthiscourse.Allforcesactingonthebodymustbedisplayedonthefree-bodydiagramifacorrectequilibriumsolutionistobeobtained.Thisincludesappliedforcesandmoments,reactionforcesandmoments,andanyconnectionforcesbetweenindividualcomponents.overallFBD

ExampleFCEDXDYBXBYConsidertheframeshownbelow,drawtheFBDfortheentirestructure,andFBDsforindividualcomponents.Fortheoverallfreebodydiagram,asmemberCEisatwo-forcemembersinceforcesareappliedatonlytwolocations,CandE.Hence,theloadingonCEatpinCalignedwithlineCE,denotedbyFCE.Ontheotherhand,membersABandADareNOTtwoforcememberssinceforcesareappliedatmorethantwolocationsoneachmember.Therefore,thereactionsatPinsBandDarewrittenintermsofgeneralxandycomponents,denotedbyBX,BY,DXandDY.seperateFBDstwoforcememberHerearethefreebodydiagramsoftheindividualmembersoftheframe.AsmemberCEisatwo-forcemember,theloadingonCEatpinCandconnectionjointEareequal,oppositeandalignedwithlineCE,bothdenotedbyFCE.ByNewtons3rdlaw,theforceonmemberADatEisequalandoppositeoftheforceonCEatE,alsodenotedbyFCE,

asshowninthefreebodydiagrams.Ontheotherhand,membersABandADareNOTtwoforcemembers,therefore,thereactionsatA,BandDareallwrittenintermsofgeneralxandycomponents.Pleasetrythefollowingexercisesyourself.Ifyoufindyourskillsonstaticsarerusty,pleasereviewthispart.Pleasedrawtheforcediagramsforallcomponentsforthestructure.[Exercise1]Asshowninthefigure,RC=100mm,RD=50mm,Px=466N,Py=352NandPz=1400N.Whenthesystemisineq