Engineering Basic Mechanics I Statics 工程基础力学Ⅰ 静力学 课件 Chapter 2 Coplanar Concurrent Force System

StaticsStaticsofrigidChapter2

CoplanarConcurrentForceSystemandCoupleSystemMaincontents2.1Reductionofcoplanarconcurrentforcesystem2.2Equilibriumofcoplanarconcurrentforcesystem2.3ConplanarcouplesystemWhatiscoplanarconcurrentforcesystem?Aforcesystemisconcurrentiftheactionlinesofallforcesintersectatacommonpoint.F1F2F3F4Conclusion:Aconcurrentcoplanarforcesystemcanbereducedtoasimpleresultantforce.Theactionlineoftheresultantforcepassessthroughtheintersectingpointoftheoriginalforcesystem.Theresultantforcevectorcanbeobtainedbyvectorsummationoftheconcurrentforces.2.1ReductionofcoplanarconcurrentforcesystemThemagnitudeoftheresultantforceprojectiontoanaxisequalsthealgebraicsumofallthecomponentforcesprojectiontothesameaxis.Equilibriummeansthattheresultantforceshouldbezero.Twoequilibriumconditions:Theseequationscanbeusedtodetermineunknownreactionforces.2.2EquilibriumofcoplanarconcurrentforcesystemDetermineforcesofthebarsABandBC,G=20kN,ThegravityofthebarsAB,BCandpulleyarenegligible.30°BGAC30°

a

Example2-1(1)DrawtheforceanalysisofpinB(2)Equilibriumequation

yFBCFFABGx30°30°BSolution:TheminussignforFABindicatesthatFABpointsleft.●Acoupleisdefinedastwoparallelforcesthathavethesamemagnitudeandoppositedirections,andareseparatedbyaperpendiculardistance(noncollinear).

1.DefinitionofCouple

●Theplaneinwhichtheforcesofacoupleactiscalledtheplaneofthecouple.

●Theperpendiculardistancebetweentheactionlinesoftheforceiscalledthearmofthecouple.

●Themomentproducedbyacoupleiscalledacouplemoment.2.3Planarcouple2.Thevalueofacouplemoment

●Momentofacoupleaboutapointisavalueofscalar.Symbol:Counterclockwise“+”Clockwise“-”

●Thevalueofacouplemomentcanbedeterminedby2.3Planarcouple

●Acouplehasnoresultantforce,sonoforcecanbeequivalenttoacouple;

3.CharacteristicsofCouple

●Themomentofacoupleisthesameaboutanypointintheplaneofcouple.2.3Planarcouple

4.EquivalentCouples●Twocouplesthathavethesamemomentaresaidtobeequivalent.●Thefollowingthreeoperationsonacouplewillnotchangeitsmoment:(1)ChangingthemagnitudeofeachforceFandtheperpendiculardistancedwhilekeepingtheproductFdconstant.(2)Movingthecoupletoaparallelpositioninitsplane.(3)Theeffectofacoupleonarigidbodyiscompletelydeterminedbythemagnitudeand

senseofrotationofthemomentofthecouple.2.3PlanarcoupleFromthecharacteristicsofcouples,wecanobtainthemomentofresultantcoupleequalsthescalarsumofallthecomponentcouples,thatis

5.ResultantCouple

Fortheequilibriumcondition:

2.3PlanarcoupleDeterminethereactiveforceatApointandBpoint.TheweightofthebeamABandbar