(1.3.1)-ch0-1 Introduction and course re材料力学材料力学

Chapter0IntroductionIntroductionandcoursereviewPrerequisite-StaticsHelloeveryone,withthisvideo,westartthestudyofMechanicsofMaterials,thisvideogivestheintroductionandreviewforthiscourse.ThiscoursecontinuesfromthepreviouscoursetheoreticalmechanicsStatics,Therefore,youareexpectedtohavesolidfoundationinstatics.Ifthisnotthecase,youarestronglyencourgedtoreviewstaticsbeforeyoustartlearningthiscourse.Inthiscourse,itstilldealswithobjectsthatareinstaticequilibrium.Therefore,themostimportantsetofequilibriumequationsinstaticsstillapplyhere.StaticsEquilibriumofforcesonrigidbodiesatrestMechanicsofMaterialsEffectsofforcesondeformablebodiesAppliedforce(F)Reactionforce(R)Dealswithrigidbody(undeformable)Dealswithreal,defromablematerialsStudieshowmaterialsbehaveunderloadingDistributionofinternalforces*Staticsdiscussesthe*equilibriumofrigidbodieswhileatrest.*Instatics,objectsareassumedtoberigidbodies,*whichmeansanychangeinshapeandsizeisneglected.Butitcannotbeture.Becauseifthatisthecase,wecanbuildupbuildingsthatcanwithstandasmuchloadaswewant.Butrealobjectsdodeform.Thatiswhatthiscoursestudies.*Mechanicsofmaterialsdiffersfromstatics,**insteaditdealswiththerealobjectsthatdeformsunderappliedforces.Theintensityofdeformationandthedistributionofinternalforcesaretheprimaryinterestsinmechancisofmaterials.Wecanusethisknowledgetodesignstructuresthatarebotheconomicandstrongenough.PPPPScenario1:P=10kNWillthesecondbarfailunderthesameP=10kN?Nowlet’slookatsomesenariosandconsidersomequestions.Senarioone,*hereisonesolidrodwithaforcePappliedatitsendsalongthelongitudinalaxisoftherod,*iftherodbreakswhen*Preaches10KN.Itlookslikethis10KNisacriticalvalue,foritmarksthefailurepointofthematerial.*Nowimagineanotherrodwiththesamematerial,samelength,samedensity,butsignificantlythicker.Andsame10KNappliedonit,willitbreak?Theanswerisno.Sincethesecondrodisthicker,itisexpectedtobestrongerandcanbearalargerload.Thistellsusthatthemagnitudeofloadisnotthecriticalparametertodeterminehowthematerialbehaves.Scenario2:Willthecastironbarsbehavethesame?PTensionCompressionPPSenariotwo,twocircularbarsmadewiththesamematerialcastiron,sameshapeandsamesize,*oneisintension,pulledbyforcePatitsends.Pisincreasedgraduallytillthebarfails.Asshown,*thisbarbreaksintotwopartsthroughacrosssection.Imaginetheotheroneisincompression,compressedbysameforceP,whichisalsoincreasedgradually.*QuestionisWilltheybehavethesameatfailure?TheansweragainisNO.Infact,thefailureofthesecondbarfailsinaspiralfracturepattern.Thisindicatescastironbehavesdifferentlyundertensionorcompression.Asweallknow,castironhasalowertensilestrenth.Therefore,castironiseasilytofailfollowingthedirctionalongwhichitstensilestrengthisexceeded.Differentfailuremodesindicatesdifferentinternaltensileforcedistributioninsidethem.Thistellsusthatevenweapplythesameloadonthesamemember,thematerialbehavesdifferentlydepending‘how’theloadisapplied.Scenario3:MMWillthestickfailattheendswheretheloadingsapplied?Senariothree,achopstickisbendedatthetwoends.Willthestickfailattheendswheretheloadingsapplied?TheansweragainisNO.Fromourexpeience,thechopstickfailsatsomepointnearthemiddleofit.Thistellsusthatthefailureofamemberisnotdirectlyrelatedtoexternalloadingsbuttointernalforcesinsidethemember.Whyaretheinternalreactionsinanobjectimportant?Sowhyaretheinternaleffectsofforcesinanobjectimportant?Toanswerthisquestion,weneedtozoombackandseewhatengineersdoingeneral.Engineersaretypicallyrequiredtodesignandmakeavarityofstucturesthataresubjectedtoloading,suchas*bridges,*airplanes,*buildings,*automibles,*tunnels,*pipelines,machinesandmanyotherload-carringstructures.Internalforcesarethemostimportantfactorthatengineersneedtoconsiderwhencompletingthestructuraldesignofloadcarryingmembers.Themagnitudeandsenseofinternalforcesaffectmembershape,material,anddimensions.Designcriteria-Strength-Stiffness-StabilityRegardingtheseapplications,asafeandsuccesfuldesignshouldadressthreemaincriteria.Thatisstrength,stiffnessandstability.Strength

Isthestucturestrongenoughtocarrytheappliedloadswithoutbreaking?CristobalHerrera/EPA-EFE/REX/ShutterstockDesignersneedtoensuretheloading-carryingcomponentsofstucturesarestrongenoughtocarrypredictedloadsforintendeduseduringtheirlifespan.Thepropertiesofstructures,suchasmaterialused,cross-sectionshapeandsizeshouldbeconsideredastheyallaffectthestengthofstrctures.Therefore,componentsshouldbestrongenoughtowithstandthemaximumexpectedloadwithoutfailure,andcouldperformnormallyduringtheirservicelife.StiffnessIsthereexcessivedeformationinthestuctureunderloadingsothatitcannolongercontinuetopepformitsfuction?TacomaNarrowsBridgeTacomaNarrowsBridgeThesecondcriterionisstiffness.Itreflectstheresistanceofstructuresagainstdeformationunderloading.Itispossbilethatthecomponentiscapableofcarryingloadbutthedeformationistoohighthatmakesthestructureisunusable.Forexample,lookingatthevideoandpicture,showingTacomaNarrowsBridge,asuspensionbridgethatisshakingduetowind.Allcomponentscanwithstandloadwithoutbreaking,buteasy-to-deformpreventsitfromservicing.Stability

Willtherebeanysuddenfailureorbucklinginstructuralcomponentsbeforereachingtheirmaximumstrength？Thelastimportantcriteriaisstability.Instabilityreferstoasuddenfailureorbucklinginstructuralcomponentsbeforereachingtheirmaximumstrength.Theactualfailure,astypicallyshowninthe

pictures,isfrequentlyencounteredinengineeringstructuresofslendermembers

subjecttocompression,suchascrane,columnandlandinggear.Inordertodesigncomponentsbasedonstrength,stiffnessandstabilitycriteria,engineersneedtoknowhowmuchforcesineachcomponents,andhowabodybehaveswhenaforceapplied,whichisprimarilydiscusssedintheMechanicsofMaterials.MehcanicsofMaterials

-Afundamentalsubject-Dealswithreal,

defromablematerials-Studieshowmaterialsbehave

underloading-Distribution

of

internalforces

and

deformationisofprimaryinterest-Variousmethodsofcalculatingthestressesandstrains

instructuralmembers,suchasbars,shafts,beamsandcolumns.Mechanicsofmatrialscananswersuchquestions,howthestressesdistributeinstuctures?Ifitdeforms,howmuchisthedeformation?Willitbreak?Howcanitbemadestronger?Inotherwords,mechanicsofmetarialsstudieshowadeformablebodybehaveswhenaforceisappliedtoit.Andhowmuchforceitcanwithstandwithoutbreaking?externalloadingsinternalreactionsdeformationmaterialfailureWhatdowelearn?stressHopefully,youcanunderstanditisinternalreactionsrespondingtoexternalloadingsonanobject,thatcausestressdistributionandmaterialdeformation,evenmaterialfailureintheobject.Thisunderstandingisimportanttostudythiscourse.InternalreactionsMzTxNxVyVzMybNx-axialforceTx-torqueVy,Vz-shearforceMy,Mz-bendingmomentσ-normalstressτ-shearstress

N

T

VM

Forinternalreactions,fromtheStatics,weknowthattherecanbeamaximumofsixindependantinternalreactioncomponents,*threeinternalforcesand*threecouplemoments.These

sixinternalforcescanbeclassifiedintofourcategories,axialforceFX,transverseshearforcesFYandFZ,torsinalmomentMX,bendingmomentMYandMZ.Andtheseinternalforcescausedifferentstresses,eithernormalstressorshearstress.Normalforceandbendingmomentcausenormalstresses,whileshearforceandtorsionalmomentcauseshearstresses.DeformationsTensionCompressionShearTorsionBendingActually,theclassificationoftheinternalforcesandcouplemomentsisbasedonthedeformations(physicaleffects)theycauseonabody.Therefore,thesefourcategoriesofinternalforcescorrespondtofourtypesofdeformations,axialtensionandcompression,shear,torsionandbending,respectively.

Chapter1-Tension,Compression,andShearMehcanicsofMaterials

Chapter1-Tension,Compression,andShearChapter2-AxiallyLoadedMembersChapter1-Tension,Compression,andShearChapter2-AxiallyLoadedMembersChapter3-TorsionChapter1-Tension,Compression,andShearChapter2-AxiallyLoadedMembersChapter3-TorsionChapter4-ShearForcesandBendingMomentsChapter5-StressesinBeams(BasicTopics)Chapter6-StressesinBeams(AdvancedTopics)Chapter1-Tension,Compression,andShearChapter2-AxiallyLoadedMembersChapter3-TorsionChapter4-ShearForcesandBendingMomentsChapter5-StressesinBeams(BasicTopics)Chapter6-StressesinBeams(AdvancedTopics)Chapter7-AnalysisofStressandStrainChapter1-Tension,Compression,andShearChapter2-AxiallyLoadedMembersChapter3-TorsionChapter4-ShearForcesandBendingMomentsChapter5-StressesinBeams(BasicTopics)Chapter6-StressesinBeams(AdvancedTopics)Chapter7-AnalysisofStressandStrainChapter8-ApplicationsofPlaneStress

(PressureVessels,Beams,andCombinedLoadings)Chapter1-Tension,Compression,andShearChapter2-AxiallyLoadedMembersChapter3-TorsionChapter4-ShearForcesandBendingMomentsChapter5-StressesinBeams(BasicTopics)Chapter6-StressesinBeams(AdvancedTopics)Chapter7-AnalysisofStressandStrainChapter8-ApplicationsofPlaneStress

(PressureVessels,Beams,andCombinedLoadings)Chapter9-DeflectionsofBeamsChapter1-Tension,Compression,andShearChapter2-AxiallyLoadedMembersChapter3-TorsionChapter4-ShearForcesandBendingMomentsChapter5-StressesinBeams(BasicTopics)Chapter6-StressesinBeams(AdvancedTopics)Chapter7-AnalysisofStressandStrainChapter8-ApplicationsofPlaneStress

(PressureVessels,Beams,andCombinedLoadings)Chapter9-DeflectionsofBeamsChapter10-StaticallyIndeterminateBeamsChapter1-Tension,Compression,andShearChapter2-AxiallyLoadedMembersChapter3-TorsionChapter4-ShearForcesandBendingMomentsChapter5-StressesinBeams(BasicTopics)Chapter6-StressesinBeams(AdvancedTopics)Chap