Engineering Basic Mechanics I Statics 工程基础力学Ⅰ 静力学 课件 Chapter 6 Fundamental Concepts of Bar Deformation

StaticsStaticsofdeformablebodyChapter6

FundamentalConceptsofBarDeformation6.1Tasks6.2Simplificationofengineeringmembers6.3Internalforceandstress6.4Displacementandstrain6.5BasicformsofbardeformationContents6.1Tasksstructuralmember：Thepartsofengineeringstructures(variousmachines,instruments,andbuildingstructures,etc.)arecollectivelyreferredtoasmembers.Somebasicrequirementsmetbythemembers：1.sufficientstrengthItisrequiredthatthemembersarenotfracturedorpermanentlydeformed(plasticdeformation)whensubjectedtoload.Theabilityofthemembertoresistdamage.Forexample:craneslingsarenotallowedtobreak,etc2.sufficientrigidityTheelasticdeformationofthememberundertheexternalloadcannotexceedtheallowedvalue.Theabilityofamembertoresistelasticdeformationunderload.Forexample:lathespindle,housefloor,etc.3.adequatestabilityItisrequiredthatthebalanceofthememberisstableunderworkingconditions.Theabilityofthemembertomaintainitsoriginalformofbalance.Forexample:jackingrods,pillarsinmines,etc.Theabilityofthemembertomeettherequirementsofstrength,stiffnessandstabilityiscalledtheload-bearingcapacityofthemember.Bystudyingthestrength,stiffnessandstabilityofmembers,andthemechanicalpropertiesofmaterials,thebasictheoryandcalculationmethodsareprovidedfortheselectionofappropriatematerials,thedeterminationofreasonablecross-sectionalshapesanddimensionsofmembersunderthepremiseofensuringsafety,reliabilityandeconomicsavings.Maintasks：Ⅰ.Basicformsofmembers1.Bar

abarisamemberwhoselengthismuchgreaterthanitstransversedimensions(heightandwidth).bar6.2Simplificationofengineeringmembersbody2.block

Memberswithequivalentdimensionsinthelength,widthandheightdirectionsarecalledblocks.Ⅰ.Basicformsofmembersplateshell3.plate(shell)

Aplate(shell)isamemberwhosethicknessismuchsmallerthanthedimensionsofothertwodirections.Ifthemiddlesurfaceisflat,thememberiscalledaplate.Ifthemiddlesurfaceiscurved,itiscalledashell.Ⅰ.BasicformsofmembersTheassumptionofcontinuity：thememberiscontinuouslyandvoid-freethroughoutitsgeometricvolume.(Physicalquantitiescanbeexpressedasacontinuousfunctionofcoordinates)Theassumptionofhomogeneity:themechanicalpropertiesareidenticalatallpointsinthemember.(anysmallsegmentoftheobjectcanberemovedforanalysisandtheconclusionsobtainedcanbeappliedtothewholeobject)Theassumptionofisotropic：materialshavethesamemechanicalpropertiesalonganydirection.Ⅱ.BasicassumptionsDeformationofdeformablebodyunderloadcanoccurintwodifferentnatureofdeformation：

1.elasticdeformation

2.plasticdeformationElasticrange：Undertheactionofexternalload,theexternalforcerangewithonlyelasticdeformationandnoplasticdeformation(negligible)istheelasticrange.

Smalldeformation：Thedeformationofthememberisextremelysmallcomparedtoitsoriginaldimensions.Ⅲ.Smalldeformationconstraints1.Internalforce——Interactionforcesbetweenapartofamemberanditsadjacentparts

Additionalinternalforce

InternalforcesaredistributedoverthecrosssectionInternalforceispaired2.Sectionmethod：Themethodforshowinganddeterminingtheinternalforcesisthesectionmethod.Thecross-sectionalmethodisbasedontheprinciplethat"anobjectinequilibriumshouldalsohaveallitspartsinequilibrium".6.3InternalforceandstressTheprocessoffindingtheinternalforcebythesectionmethodcanbesummarizedasfollows：(1)CuttingImaginecuttingthememberalongthatsectionanddividingitintotwosegments.(2)Substituteforce

Selectanyonesegmentofthememberandtheotherisremoved.Theactionoftheremovedsegmentontheselectedsegmentisreplacedbythecorrespondinginternalforces.(3)EquilibriumSolvetheinternalforceproblemsusingequilibriumequations3.stressConceptTheinternalforcesatapointiscalledthestressatthatpoint.Lettheinternalforceactingonasmallareabe,thentheaveragesetoftheinternalforceonis（isaveragestress）ThickrodThinrodquestionCADPDCADPDCtsPWhenPointC（infinitelysmall）AlimitvalueWecallPthetotalstressatpointC.Theexpressionis：Theunitofstressis[force]/[length]2(N/m2)

,whichis.Pisavector，Fortheconvenienceandneedofthestudy,wealwaysdecomposeitintotwocomponentsperpendiculartothesectionandparalleltothesection.Theformeriscalledthenormalstressandisdenotedbyσ.Thelatteriscalledshearstressandisdenotedbyτ.CtsPThedifferencebetween"stress"and"pressure"Although"stress"hasthesamedimensionas"pressure",thephysicalmeaningofthetwoisdifferent.Differentdefinitions:

Stress-internalforcePressure-externalforceDifferentmodesofaction:

Stress-decomposable,existsatanypointinsidetheobjectunderloadPressure-actingonthesurfaceoftheobjectanddrapedoverthesurfaceofaction,oftenuniformlyorlinearlydistributedlinedisplacementangulardisplacement{FqAuv1.