受力分析和受力圖BasiccForceanalysisandforcediagramonceptsofstatics主講人：申瀟123目錄CONTENTS約束和約束力受力分析和受力圖例題解析ConstraintsandBindingForcesForceanalysisandforcediagramExampleanalysis1約束和約束力ConstraintsandBindingForcesONE一、約束和約束力ConstraintsandBindingForces1.基本概念Basicconcepts●自由體:在空間能向一切方向自由運動的物體。Freebody:anobjectthatcanmovefreelyinalldirectionsinspace.●非自由體:不可能產生某方向的位移的物體。Nonfreebody:anobjectthatcannotproducedisplacementinacertaindirection.●約束:由周圍物體所構成的、限制非自由體位移的條件。Constraints:Conditionsformedbysurroundingobjectsthatrestrictthedisplacementofnonfreebodies.●約束力:約束施加于被約束物體上的力。Constraint:Constrainstheforceappliedtotheconstrainedobject.●主動力:約束力以外的力。Activeforce:aforcebeyondtheconstraintforce.一、約束和約束力ConstraintsandBindingForces約束constraint約束力FtBindingforceFt被約束物體一一非自由體Constrainedobject-nonfreebody主動力PActiveforceP工程中常見的約束Commonconstraintsinengineering柔體約束Softbodyconstraints繩子、鏈條、皮帶等并不是理想化的柔索，但可簡化成這種約束。Ropes,chains,belts,etc.arenotidealizedflexiblecables,butcanbesimplifiedintosuchconstraints.一、約束和約束力Coupleofforces柔繩約束實例Exampleofflexibleropeconstraint皮帶約束實例Beltconstraintinstance一、約束和約束力Coupleofforces一、約束和約束力ConstraintsandBindingForces理想剛性約束:當物體變形可以忽略時，約束與被約束體之間的接觸可假設為剛性。Idealrigidconstraint:Whenthedeformationofanobjectcanbeignored,thecontactbetweentheconstraintandtheconstrainedbodycanbeassumedtoberigid.一、約束和約束力ConstraintsandBindingForces(2)光滑面約束Smoothsurfaceconstraint當物體與固定約束或活動約束間的接觸表面非常光滑，摩擦可以忽略不計時，就可簡化為光滑面約束。Whenthecontactsurfacebetweenanobjectandafixedoractiveconstraintisverysmooth,frictioncanbeignoredandsimplifiedasasmoothsurfaceconstraint.阻礙物體沿兩接觸面法線n方向往約束內部的運動，不能阻礙沿切線τ方向的運動。Obstaclethemovementofanobjecttowardstheinterioroftheconstraintalongthenormalndirectionofthetwocontactsurfaces,butnotalongthetangentlineτMovementindirection.(2)光滑面約束Smoothsurfaceconstraint光滑面約束力一一法向力(FN)Smoothsurfaceconstraintforce-normalforce(FN)一、約束和約束力Coupleofforces光滑接觸面約束Smoothcontactsurfaceconstraint法線normal切線tangentFNFNFN法線normal法線normal切線tangent切線tangent一、約束和約束力Coupleofforces切線tangentPFN一、約束和約束力ConstraintsandBindingForces(3)光滑鉸鏈約束Smoothhingeconstraint用光滑銷釘和圓孔組成的局部結構，稱為光滑圓柱鉸鏈。Alocalstructurecomposedofsmoothpinsandcircularholesiscalledasmoothcylindricalhinge.(3)光滑鉸鏈約束Smoothhingeconstraint一、約束和約束力ConstraintsandBindingForcesa.固定鉸鏈支座:Pinsupport：Figure1Physicalimage圖1實物圖Figure3Stressdiagram圖3受力圖Figure2Structuraldiagram圖2結構簡圖(3)光滑鉸鏈約束Smoothhingeconstraint一、約束和約束力ConstraintsandBindingForcesb.活動鉸鏈支座：Movablehingesupport:Figure1Physicalimage圖1實物圖Figure3Stressdiagram圖2受力圖(3)光滑鉸鏈約束Smoothhingeconstraint一、約束和約束力ConstraintsandBindingForcesc.光滑球鉸鏈:Smoothballhinge:Figure1Physicalimage圖1實物圖Figure3Stressdiagram圖3受力圖Figure2Structuraldiagram圖2結構簡圖(4)固定端約束Fixedendconstraint一、約束和約束力ConstraintsandBindingForces2受力分析和受力圖ForceanalysisandforcediagramTWO二、受力分析和受力圖Forceanalysisandforcediagram畫受力圖的方法與步驟:Methodandstepsfordrawingforcediagrams:取分離體(研究對象)Taketheseparatedbody(researchobject)畫出研究對象所受的全部主動力(使物體產生運動或運動趨勢力)。Drawalltheactiveforcesactingontheresearchobject(causingtheobjecttomoveormovetowardsforce).在存在約束的地方，按約束類型逐一畫出約束反力(研究對象與周圍物體的連接關系)Drawconstraintreactionsonebyoneaccordingtothetypeofconstraintinthepresenceofconstraints(studyingtheconnectionrelationshipbetweentheresearchobjectandsurroundingobjects)3例題解析ExampleanalysisTHREE例1:用力F拉動碾子以軋平路面，重為P的碾子受到一石塊的阻礙，如圖所示。試畫出碾子的受力圖。Example1:PulltherollerwithforceFtoflattentheroadsurface,andtherollerweighingPisobstructedbyastoneblock,asshowninthefigure.Trytodrawtheforcediagramoftheroller.三、例題解析Exampleanalysis解:畫出簡圖Drawadiagram畫出主動力Drawtheinitiative畫出約束力DrawconstraintsSolution:例2:等腰三角形構架ABC的頂點A、B都用鉸鏈連接，底邊AC固定，而AB邊的中點D作用有平行于固定邊AC的力F，如圖所示。不計各桿自重，試畫出桿AB和BC的受力圖。三、例題解析Exampleanalysis解:

Solution:(1)桿BC(二力構件)的受力圖TheforcediagramofrodBC(twoforcecomponent)(2)桿AB的受力圖TheforcediagramofrodABFBFCFB’FAXFAyFA例3:如圖所示力F作用在AB的中點，F與AB梁的夾角為30°，已知力F=2kN，AB=400mm，畫出AB的受力圖并求A、B端的約束力。Example3:Asshowninthefigure,theforceFactsonthemidpointofAB,andtheanglebetweenFandtheABbeamis30°.GiventheforceF=2kNandAB=400mm,drawtheforcediagramofABandcalculatetheconstraintforcesatendsAandB.三、例題解析Exampleanalysis固定鉸鏈支座Pinsupport活動鉸鏈支座Movablehingesupport三、例題解析Exampleanalysis解:Solution:進行受力分析，并作受力圖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自測題——判斷題Selftestquestions-TrueorFalse如圖所示力F作用在AB的中點，F與AB梁的夾角為45°，已知力F=2kN，AB=400mm，畫出AB的受力圖并求A、B端的約束力。Asshowninthefigure,thef