Engineering Basic Mechanics I Statics 工程基础力学Ⅰ 静力学 课件 Chapter 4 Space Force System

StaticsStaticsofrigidChapter4SpaceForceSystemMaincontents4.1Concurrentforcesysteminspace4.2Systemofcouplesinspace4.3Themomentofaforceaboutapointoranaxis4.4Reductionofaforcesysteminspace4.5Equilibriumequationsofgeneralforcesysteminspace1.Howtorepresentaforceinspace(1)directprojection(2)directprojectionAforcecanbedescribedas4.1Concurrentforcesysteminspace2.Thecompositionandequilibriumofaconcurrentforcesysteminspace(1)CompositionTheresultantforceofconcurrentforcesysteminspaceisequaltovectorsumofthecomponents.

4.1ConcurrentforcesysteminspaceThelawofprojectionoftheresultantforce:Theprojectionoftheresultantforceofaforcesysteminspaceontoanaxisisequaltothealgebraicsumoftheprojectionsofthecomponentforcesontothesameaxis.(2)EquilibriumTheanalyticalmethodforequilibriumequations:4.1ConcurrentforcesysteminspaceThenecessaryandsufficientconditionofequilibriumisthattheresultantforceiszero:1.Coupleinspace(1)Couplemomentvector(2)Coupleinspaceisafreevector4.2Systemofcouplesinspace(3)Thenecessaryandsufficientconditionoftheequivalenceoftwospacecouplesisthatthecouplemomentvectorsofthetwocouplesareequal.2.Compositionandequilibriumofasystemofcouplesinspace(1)CompositionTheresultantmomentofcoupleisthesumofthemomentsofthecomponentcouples.Theprojectionsare

4.2Systemofcouplesinspace(2)Equilibrium1.Themomentofaforceaboutapoint(1)Definition:aforce

acting

ontheApoint,themomentofaforceaboutOpointinspaceisisvector4.3Themomentofaforceaboutapointoranaxis(2)analysisformula4.3Themomentofaforceaboutapointoranaxis(1)Definition:themomentofaspaceforceaboutanaxisisascalar,whichisequaltothemomentoftheprojectionofthisforceonaplaneperpendiculartothisaxisabouttheintersectingpointofthisplaneandthisaxis.4.3Themomentofaforceaboutapointoranaxis2.Themomentofaforceaboutaaxis4.3Themomentofaforceaboutapointoranaxis(2)Analysisformula4.3Themomentofaforceaboutapointoranaxis3.TherelationshipbetweenthemomentoftheforceaboutapointandthemomentoftheforceaboutanaxisthroughthepointTheorem:theprojectionofthevectorofthemomentofaforceaboutapointonanaxisthroughthispointisequaltothemomentoftheforceabouttheaxis.

ThehandleABCEisintheplaneAxy,FactingontheD

pointlocatesinaplanenormaltoyaxis,and

theangleis

α.If

CD=b,rodBCparallelsto

xaxis,rod

CEparallelstoyaxis,thelenghtofABandBCare

l,respectively.DeterminethemomentofFaboutx，yandzaxis,respectively.4.3ThemomentofaforceaboutapointoranaxisExample4-1AsweknownTheprojectionofforce

F

alongeverycoordinateaxis：thecoordinateofpointD:thenSolution：

1.

Theoremoftranslationofaforce

4.4ReductionofaforcesysteminspaceAforceactingonarigidbodycanbemovedparalleltoanyspecifiedpointintherigidbody,butacouplemustbeaddedatthesametime,andthemomentvectorofthecoupleisequaltothemomentvectoroftheoriginalforceaboutthespecifiedpoint.PrinciplevectorPrinciplemoment4.4Reductionofaforcesysteminspace

2.

Reduction

Aspacegeneralforcesystemcanbereducedtoaforceandcouple.Theforceactsonthesimplifiedcenter,

theforcevectorisequaltotheprincipalvectoroftheforcesystem;

themomentvectorofthecoupleisequaltotheprincipalmomentoftheforcesystemaboutthesimplifiedcenter.4.4Reductionofaforcesysteminspace

3.

Analysisformulaofprinciplevectorandprinciplemoment

theforcesystemisinequilibrium.theforcesystemisequivalenttoacouple.4.4Reductionofaforcesysteminspace

4.

Discussionofreductionresults

theforcesystemisequivalenttoaresultantforce.theforcesystemcanbefurtherreduced.4.4ReductionofaforcesysteminspaceForcewrench4.4ReductionofaforcesysteminspaceThenecessaryandsufficientconditionsforequilibriumofaforcesysteminspaceareAnalysisformula4.5EquilibriumequationsofgeneralforcesysteminspaceThegravityGofthecaris8kN,acingontheEpoint,F1=10kN，actingontheCpoint.Determineconstraintsforcesfromthegroundactingonthewheelsofthecar.4.5Equilibriumequationsofgeneral