受力分析和受力图BasiccForceanalysisan

受力分析和受力图BasiccForceanalysisandforcediagramonceptsofstatics主讲人：申潇123目录CONTENTS约束和约束力受力分析和受力图例题解析ConstraintsandBindingForcesForceanalysisandforcediagramExampleanalysis1约束和约束力ConstraintsandBindingForcesONE一、约束和约束力ConstraintsandBindingForces1.基本概念Basicconcepts●自由体:在空间能向一切方向自由运动的物体。Freebody:anobjectthatcanmovefreelyinalldirectionsinspace.●非自由体:不可能产生某方向的位移的物体。Nonfreebody:anobjectthatcannotproducedisplacementinacertaindirection.●约束:由周围物体所构成的、限制非自由体位移的条件。Constraints:Conditionsformedbysurroundingobjectsthatrestrictthedisplacementofnonfreebodies.●约束力:约束施加于被约束物体上的力。Constraint:Constrainstheforceappliedtotheconstrainedobject.●主动力:约束力以外的力。Activeforce:aforcebeyondtheconstraintforce.一、约束和约束力ConstraintsandBindingForces约束constraint约束力FtBindingforceFt被约束物体一一非自由体Constrainedobject-nonfreebody主动力PActiveforceP工程中常见的约束Commonconstraintsinengineering柔体约束Softbodyconstraints绳子、链条、皮带等并不是理想化的柔索，但可简化成这种约束。Ropes,chains,belts,etc.arenotidealizedflexiblecables,butcanbesimplifiedintosuchconstraints.一、约束和约束力Coupleofforces柔绳约束实例Exampleofflexibleropeconstraint皮带约束实例Beltconstraintinstance一、约束和约束力Coupleofforces一、约束和约束力ConstraintsandBindingForces理想刚性约束:当物体变形可以忽略时，约束与被约束体之间的接触可假设为刚性。Idealrigidconstraint:Whenthedeformationofanobjectcanbeignored,thecontactbetweentheconstraintandtheconstrainedbodycanbeassumedtoberigid.一、约束和约束力ConstraintsandBindingForces(2)光滑面约束Smoothsurfaceconstraint当物体与固定约束或活动约束间的接触表面非常光滑，摩擦可以忽略不计时，就可简化为光滑面约束。Whenthecontactsurfacebetweenanobjectandafixedoractiveconstraintisverysmooth,frictioncanbeignoredandsimplifiedasasmoothsurfaceconstraint.阻碍物体沿两接触面法线n方向往约束内部的运动，不能阻碍沿切线τ方向的运动。Obstaclethemovementofanobjecttowardstheinterioroftheconstraintalongthenormalndirectionofthetwocontactsurfaces,butnotalongthetangentlineτMovementindirection.(2)光滑面约束Smoothsurfaceconstraint光滑面约束力一一法向力(FN)Smoothsurfaceconstraintforce-normalforce(FN)一、约束和约束力Coupleofforces光滑接触面约束Smoothcontactsurfaceconstraint法线normal切线tangentFNFNFN法线normal法线normal切线tangent切线tangent一、约束和约束力Coupleofforces切线tangentPFN一、约束和约束力ConstraintsandBindingForces(3)光滑铰链约束Smoothhingeconstraint用光滑销钉和圆孔组成的局部结构，称为光滑圆柱铰链。Alocalstructurecomposedofsmoothpinsandcircularholesiscalledasmoothcylindricalhinge.(3)光滑铰链约束Smoothhingeconstraint一、约束和约束力ConstraintsandBindingForcesa.固定铰链支座:Pinsupport：Figure1Physicalimage图1实物图Figure3Stressdiagram图3受力图Figure2Structuraldiagram图2结构简图(3)光滑铰链约束Smoothhingeconstraint一、约束和约束力ConstraintsandBindingForcesb.活动铰链支座：Movablehingesupport:Figure1Physicalimage图1实物图Figure3Stressdiagram图2受力图(3)光滑铰链约束Smoothhingeconstraint一、约束和约束力ConstraintsandBindingForcesc.光滑球铰链:Smoothballhinge:Figure1Physicalimage图1实物图Figure3Stressdiagram图3受力图Figure2Structuraldiagram图2结构简图(4)固定端约束Fixedendconstraint一、约束和约束力ConstraintsandBindingForces2受力分析和受力图ForceanalysisandforcediagramTWO二、受力分析和受力图Forceanalysisandforcediagram画受力图的方法与步骤:Methodandstepsfordrawingforcediagrams:取分离体(研究对象)Taketheseparatedbody(researchobject)画出研究对象所受的全部主动力(使物体产生运动或运动趋势力)。Drawalltheactiveforcesactingontheresearchobject(causingtheobjecttomoveormovetowardsforce).在存在约束的地方，按约束类型逐一画出约束反力(研究对象与周围物体的连接关系)Drawconstraintreactionsonebyoneaccordingtothetypeofconstraintinthepresenceofconstraints(studyingtheconnectionrelationshipbetweentheresearchobjectandsurroundingobjects)3例题解析ExampleanalysisTHREE例1:用力F拉动碾子以轧平路面，重为P的碾子受到一石块的阻碍，如图所示。试画出碾子的受力图。Example1:PulltherollerwithforceFtoflattentheroadsurface,andtherollerweighingPisobstructedbyastoneblock,asshowninthefigure.Trytodrawtheforcediagramoftheroller.三、例题解析Exampleanalysis解:画出简图Drawadiagram画出主动力Drawtheinitiative画出约束力DrawconstraintsSolution:例2:等腰三角形构架ABC的顶点A、B都用铰链连接，底边AC固定，而AB边的中点D作用有平行于固定边AC的力F，如图所示。不计各杆自重，试画出杆AB和BC的受力图。三、例题解析Exampleanalysis解:

Solution:(1)杆BC(二力构件)的受力图TheforcediagramofrodBC(twoforcecomponent)(2)杆AB的受力图TheforcediagramofrodABFBFCFB’FAXFAyFA例3:如图所示力F作用在AB的中点，F与AB梁的夹角为30°，已知力F=2kN，AB=400mm，画出AB的受力图并求A、B端的约束力。Example3:Asshowninthefigure,theforceFactsonthemidpointofAB,andtheanglebetweenFandtheABbeamis30°.GiventheforceF=2kNandAB=400mm,drawtheforcediagramofABandcalculatetheconstraintforcesatendsAandB.三、例题解析Exampleanalysis固定铰链支座Pinsupport活动铰链支座Movablehingesupport三、例题解析Exampleanalysis解:Solution:进行受力分析，并作受力图ConductforceanalysisandcreateforcediagramsFAyFAxFBx方向受力平衡:ΣFx=0:FAx-Fcos30°=0FAx=1.732KNForcebalanceinthex-direction:ΣFx=0:FAx-Fcos30°=0FAx=1.732KNy方向受力平衡:ΣFy=0:FAy-Fsin30°+FB=0Forcebalanceiny-direction:ΣFy=0:FAy-Fsin30°+FB=0力矩平衡:ΣMA(F)=0:FBx0.4-Fsin30°x02=0Torquebalance:

ΣMA(F)=0:FBx0.4-Fsin30°x02=0dFB=0.5KNFay=0.5KN1自测题——判断题Selftestquestions-TrueorFalse如图所示力F作用在AB的中点，F与AB梁的夹角为45°，已知力F=2kN，AB=400mm，画出AB的受力图并求A、B端的约束力。Asshowninthefigure,thef