静力学基本定理Fundamentaltheoremofst

静力学基本定理Fundamentaltheoremofstatics主讲人：申潇概念conception静力学公理是静力学中已被实践反复证实并被认为无需证明的最基本的原理，正确地反映了客观规律，并成为演绎推导整个静力学理论的基础。Theaxiomofstaticsisthemostfundamentalprincipleinstaticsthathasbeenrepeatedlyproveninpracticeandisconsideredunnecessarytoprove.Itcorrectlyreflectsobjectivelawsandservesasthebasisfordeducingtheentiretheoryofstatics.目录CONTENTS1234二力平衡条件Equilibriumconditionsoftwoforces加减平衡力系原理Principleofaddingandsubtractingbalanceforcesystem作用与反作用定理Theoremofactionandreaction力的平行四边形规则Parallelogramruleofforce1二力平衡条件EquilibriumconditionsoftwoforcesONE一、二力平衡条件Equilibriumconditionsoftwoforces公理1二力平衡公理:作用在同一刚体上的两个力，使刚体平衡的必要且充分的条件是，此二力等值、反向、共线。Axiom1:Equilibriumoftwoforces:Thenecessaryandsufficientconditionfortwoforcesactingonthesamerigidbodytobalanceisthatthesetwoforcesareequal,opposite,andcollinear.LocalkeycomponentsPeoplestandingstillAboxthatmovesuniformlyinastraightline一、二力平衡条件Equilibriumconditionsoftwoforces二力构件:只受两个力作用而处于平衡的物体。Twoforcecomponent:anobjectthatisinequilibriumundertheactionofonlytwoforces.一、二力平衡条件Equilibriumconditionsoftwoforces一、二力平衡条件Equilibriumconditionsoftwoforces二力构件的受力特点:不论构件形状如何，其所受力必定通过两点连线。Theforcecharacteristicsofthetwoforcecomponent:regardlessoftheshapeofthecomponent,theforceitissubjectedtomustbeconnectedthroughtwopoints.不是二力构件Notasecondarycomponent一、二力平衡条件Equilibriumconditionsoftwoforces例1:如图所示直杆AD和折杆BC相接触，在力作用下处于静止，若不计自重，分析BC构件的受力。Example1:Asshowninthefigure,thestraightrodADandthefoldedrodBCareincontactandareatrestundertheactionofforce.Iftheselfweightisnotconsidered,analyzetheforceontheBCcomponent.2加减平衡力系公理AxiomforaddingandsubtractingequilibriumforcesystemsTWO公理2加减平衡力系公理:在已知力系上加上或减去任意平衡力系，并不改变原力系对刚体的作用。它是力系替换与简化的等效原理。Axiom2:Addingorsubtractinganyequilibriumforcesystemfromaknownforcesystemdoesnotchangetheeffectoftheoriginalforcesystemonarigidbody.Itistheequivalentprincipleofforcesystemreplacementandsimplification.二、加减平衡力系公理Axiomforaddingandsubtractingequilibriumforcesystems注意:在物体上加减平衡力系，必然引起力对物体内效应的改变，在涉及内力和变形的问题中，公理2不适用。Note:Addingorsubtractingabalancedforcesystemonanobjectwillinevitablycauseachangeintheinternaleffectoftheforceontheobject.Inproblemsinvolvinginternalforcesanddeformations,Axiom2doesnotapply.F1F1’F2F2’加一对平衡力F1和F1’，整体仍旧平衡，却改变了B处内力(杆AD与BC的相互作用力)，也改变了C和A处的作用力。AddingapairofbalancingforcesF1andF1',theoverallbalanceisstillmaintained,butitchangestheinternalforceatB(theinteractionforcebetweenrodADandBC)andalsochangestheforceatCandA.二、加减平衡力系公理Axiomforaddingandsubtractingequilibriumforcesystems推论2力的可传性原理:Inference2:Theprincipleofforcetransferability:作用于刚体上的力，可沿其作用线任意移动而不改变它对刚体的作用效应。Theforceactingonarigidbodycanmovearbitrarilyalongitslineofactionwithoutchangingitseffectontherigidbody.二、机器的组成及特征CompositionandcharacteristicsofthemachineF=F1=F23作用与反作用定理TheoremofactionandreactionTHREE三、作用与反作用定理Theoremofactionandreaction公理3

作用与反作用定理:两物体间相互作用的力，总是大小相等、方向相反，且沿同一直线，分别作用在这两个物体上。Axiom3ActionandReactionTheorem:Theforcesthatinteractbetweentwoobjectsarealwaysequalinmagnitude,oppositeindirection,andactingoneachotheralongthesamestraightline.FT与G是一对平衡力FTandGareapairofequilibriumforcesFT’与FT是一对作用力与反作用力FT'andFTareapairofforcesandreactions三、作用与反作用定理Theoremofactionandreaction作用力与反作用力跟平衡力有什么相同点和不同点呢?Whatarethesimilaritiesanddifferencesbetweenforcesandreactionsandequilibriumforces?相同:两力大小相同，方向相反，作用在同一直线上。Same:Twoforceswiththesamemagnitudeandoppositedirectionsactonthesamestraightline.不同:Different:作用力与反作用力（异物）灯拉绳的力绳拉灯的力灯的重力作用力与反作用力（异物）平衡力（同物）Equilibriumforce(equivalenttomatter)Forcesandreactions(foreignobjects)TheforceofthelamppullropeTheforceofaropepullinglampTheGravityofaLamp三、作用与反作用定理Theoremofactionandreaction问题2:绳子被剪断，会怎样呢?Question2:Whathappensiftheropeiscut?可见作用力和反作用力具有同时性，同时产生、同时消失。Itcanbeseenthattheforcesandreactionshavesimultaneity,producinganddisappearingsimultaneously.:三、作用与反作用定理Theoremofactionandreaction作用力与反作用力的特点：Characteristicsofforcesandreactions:大小相等，方向相反，作用在一条直线上;Equalinsize,oppositeindirection,actingonastraightline;作用点在不同的物体上;Thepointofactionisondifferentobjects;性质相同;同生同灭。

Samenature;.Bornanddiedtogether例2:如图所示直杆AD和折杆BC相接触，在力作用下处于静止，若不计自重，分析AD构件的受力。Example2:Asshowninthefigure,thestraightrodADandthefoldedrodBCareincontactandareatrestundertheactionofforce.Iftheselfweightisnotconsidered,analyzetheforceontheADcomponent.三、课程内容ContentFFB’FA4力的平行四边形规则ParallelogramruleofforceFOUR一、二力平衡条件Equilibriumconditionsoftwoforces公理4力的平行四边形规则:作用于物体上的两个力，其合力也作用在该点上，合力的大小和方向则由以这两个力为边所构成的平行四边行的对角线来表示，而该两个力称为合力的分力。Axiom4:Theparallelogramruleforforces:Whentwoforcesactonanobject,theircombinedforcealsoactsonthatpoint.Themagnitudeanddirectionofthecombinedforcearerepresentedbythediagonallinesoftheparallelogramformedbythesetwoforcesasedges,andthesetwoforcesarecalledthecomponentforcesofthecombinedforce.矢量式:FR=F1+F2Vectorformula:FR=F1+F2一、二力平衡条件EquilibriumconditionsoftwoforcesF1F2FRF1力的相加FR=F1+F2F2F1FRF1FR’力的相减FR’=F2-F1ThesumofforcesFR=F1+F2SubtractionofforcesFR'=F2-F1力三角形——力的相加与相减ForceTriangle-AdditionandSubtractionofForcesF1、F2可以合成为一个合力FR。合力的作用点也在该点，合力的大小和方向用两分力为邻边所构成的平行四边形的对角线表示。F1andF2canbecombinedintoacombinedforceFR.Thepointofactionoftheresultantforceisalsoatthispoint,andthemagnitudeanddirectionoftheresultantforcearerepresentedbythediagonalofaparallelogramformedbytwoadjacentsidesoftheforce.三、课程内容Content推论2Inference2:

力平衡汇交定理:作用于刚体上的三个力相互平衡时，若其中两个力的作用线相交于一点，则此三力必在同一平面内，且第三个力的作用线必通过汇交点。Theoremofforceequilibriumintersection:Whenthreeforcesactingonarigidbodyareinequilibriumwitheachother,ifthelinesofactionoftwoofthemintersectatapoint,thenthesethreeforcesmustbeinthesameplane,andthelinesofactionofthethirdforcemustpassthroughtheintersectionpoint.三、课程内容Content该定理说明三个不平行力平衡的必要条件，容易推广到更一般的情形:刚体受n个力作用而平衡，若其中n-1个力交于同一点，则第n个力的作用线必过此点。Thistheoremexplainsthenecessaryconditionsforthebalanceofthreenonparallelforcesandcanbeeasilygeneralizedtoamo