《第2章 静力学基本公理和物体的受力分析.ppt》由会员分享，可在线阅读，更多相关《第2章 静力学基本公理和物体的受力分析.ppt（42页珍藏版）》请在taowenge.com淘文阁网|工程机械CAD图纸|机械工程制图|CAD装配图下载|SolidWorks_CaTia_CAD_UG_PROE_设计图分享下载上搜索。
1、1静力学的基本概念和受力分析静力学的基本概念和受力分析thebasicconceptsofstaticandtheanalysisofallforceswhichactonthebody21静力学的基本概念静力学的基本概念theconceptsofprincipleofstatics22静力学公理静力学公理thelawsofstatic 23约束与约束反力约束与约束反力constraintandconstraintforce24物体的受力分析与受力图物体的受力分析与受力图thefreebodydiagramsofasinglebodyandsystemofbodies2Inthischapte
2、rwewillintroducethebasicConceptsofstaticandthestatementsofgeneralstaticprinciples.TointroducetheConceptsoftheconstraintforcesanddiscusshowtodrawthefreebodydiagramforabody.本章目标本章目标Chapterobjectives 静力学模型静力学模型Staticmodels:（1）物体的合理抽象与简化物体的合理抽象与简化thereasonablereductionandabstractofthebody（2）受力的合理抽象与简化受力
3、的合理抽象与简化thereasonablereductionandabstractofloadings（3）接触与连接方式的合理抽象与简化）接触与连接方式的合理抽象与简化thereasonablereductionandabstractofcontactandjoinedmanners3 34 4力是物体间相互的机械作用，它具有两种效应；一是使物体的运动状态发生力是物体间相互的机械作用，它具有两种效应；一是使物体的运动状态发生改变，二是使物体产生变形。前者称为力的外效应。后者称为力的内效应。改变，二是使物体产生变形。前者称为力的外效应。后者称为力的内效应。力的概念力的概念theconcepto
4、fforceTheforceismechanicalactionsbetweenoneandanotherbody,ithastwoeffects,oneismotioneffect,thatitwilltendtochangethebodysstateofmotion,theotherisdeformationeffect,thatitwilltendtochangethebodysshapeandsize.力的三要素力的三要素：threeelementsofforce力是一个矢量，具有大小方向和作用点三个要素，常用一个带箭头力是一个矢量，具有大小方向和作用点三个要素，常用一个带箭头的有方向
5、线段表示力矢量。的有方向线段表示力矢量。Force is a vector,that is represented graphically by an arrow,which Force is a vector,that is represented graphically by an arrow,which is used to define its magnitude,direction,and sense.is used to define its magnitude,direction,and sense.Themagnitudeofthevectoristhelengthofthea
6、rrow,thedirectionisdefinedbytheanglebetweenreferenceaxisandthearrowslineofaction,andthesenseisindicatedbythearrowhead.力的单位力的单位：unitsofforce NorKN5 5力系的概念力系的概念The concepts of force systems The concepts of force systems 作用于物体上的一群力作用于物体上的一群力 Thesumofallloadingsactedonthebody平衡力系平衡力系equilibrium force sy
7、stemsequilibrium force systems 物体在力系作用下处于平衡，我们称这个力系为平衡力系。物体在力系作用下处于平衡，我们称这个力系为平衡力系。Abodysubjectedaforcesystemisequilibrium,thentheforcesystemiscalledequilibrium force systemsequilibrium force systems 平面力系平面力系forcesysteminaplane.Allforcessubjectedtothebodyarethesameplane 空间力系空间力系dimensionalforcesyste
8、mAllforcessubjectedtothebodyaredifferentplanes6 6平面汇交力系平面汇交力系 thecurrentforcesysteminaplane.所有力的作用线汇交于一点的平面力系所有力的作用线汇交于一点的平面力系Alltheforcesinaplaneactatapoint.平面平行力系平面平行力系 The parallel force system in a plane The parallel force system in a plane 所有力的作用线都互相平行所有力的作用线都互相平行 All forces are parallel in a p
9、lane.All forces are parallel in a plane.平面任意力系平面任意力系 Arbitrary force system in a planeArbitrary force system in a plane 所有力的作用线任意分布在一个平面内所有力的作用线任意分布在一个平面内All the forces distributed arbitrary in a plane.All the forces distributed arbitrary in a plane.7Itisidealmodelofbodyitcanbeconsideredasacombinati
10、onofalargenumberofparticlesinwhichalltheparticlesremainatafineddistancefromoneanotherbothbeforeandafterapplyingaload刚体刚体 Rigid-bodyRigid-body就是在力的作用下，大小和形状都不变的物体。就是在力的作用下，大小和形状都不变的物体。there is no deformation whenever a body subjected to there is no deformation whenever a body subjected to any forces.
11、any forces.刚体是物体的理想化模型刚体是物体的理想化模型平衡平衡equilibriumequilibrium是指物体相对于惯性参考系保持静止或作匀速直线运动的状态。是指物体相对于惯性参考系保持静止或作匀速直线运动的状态。Abodyisinequilibriumprovideditisatrestiforiginallyatrestorhasaconstantvelocityiforiginallyinmotion.质点质点质点质点 particleparticleparticleparticle是指具有一定质量而形状与大小可以忽略不计的物体。是指具有一定质量而形状与大小可以忽略不计的
12、物体。A particle has a mass,but a size that can be neglected.A particle has a mass,but a size that can be neglected.8 静力学公理静力学公理静力学公理静力学公理the laws of staticthe laws of staticthe laws of staticthe laws of static 公理公理1 1 二力平衡公理二力平衡公理 The two force equilibrium law The two force equilibrium law 作用于刚体上的两个力，
13、使刚体平衡的必要与充分条件是：作用于刚体上的两个力，使刚体平衡的必要与充分条件是：这两个力这两个力大小相等大小相等|F1|=|F2|方向相反方向相反F1=F2 作用线共线，作用线共线，作用于同一个物体上。作用于同一个物体上。刚体F1F2 A body is equilibrium due to subjected two forces,thenecessaryandsufficientconditionsisthatthetwoforceshasthesamemagnitude,oppositeandcollinear.应用应用applyingapplying Constructequilib
14、riumconditions建立平衡条件的建立平衡条件的9说明说明：对刚体来说，上面的条件是充要的对刚体来说，上面的条件是充要的Illustrate:the condition mentioned is sufficient Illustrate:the condition mentioned is sufficient and necessary for bodies.and necessary for bodies.对变形体对变形体(或多体中或多体中)来说，上面的条件只是必要条件来说，上面的条件只是必要条件The condition mentioned is necessary for d
15、eformation The condition mentioned is necessary for deformation Body,but not sufficientBody,but not sufficient.1010二力杆二力杆：members subjected to two forces.members subjected to two forces.二力杆只在两个力作用下平衡的刚体叫二力杆。只在两个力作用下平衡的刚体叫二力杆。Only subjected to two forces,they have the same Only subjected to two force
16、s,they have the same magnitude,opposite direction and collinearmagnitude,opposite direction and collinear.11 在已知力系上加上或减去任意一个平衡力系，并不在已知力系上加上或减去任意一个平衡力系，并不改变原力系对刚体的作用。改变原力系对刚体的作用。公理公理2 2 加减平衡力系原理加减平衡力系原理Addition and reduction equilibrium force Addition and reduction equilibrium force systems lawsystem
17、s law We can add or reduce equilibrium force systemsWe can add or reduce equilibrium force systemsat a body.The effect of the force system mustat a body.The effect of the force system mustBe the same as beforeBe the same as before.应用应用applyingapplying 简化力系简化力系Deduct the force systemsDeduct the force
18、 systems12推论推论1：力的可传性。：力的可传性。Principleoftransmissibilityofaforce.因此，对刚体来说，力作用三要素为：因此，对刚体来说，力作用三要素为：大小，方向，作用线大小，方向，作用线作用于刚体上的力可沿其作用线移到同一刚体内的任一点，作用于刚体上的力可沿其作用线移到同一刚体内的任一点，而不改变该力对刚体的效应。而不改变该力对刚体的效应。the force can transmit along with its action line,the effect of the force must be the same as before tran
19、smitting.It states,the elements of a force are magnitude,direction and line of action.the vector of a force is a sliding vector.ABFFABBAF1F2F2=F=-F1F2令F=F1=F213公理公理3 3 力的平行四边形法则力的平行四边形法则parallelogram lawparallelogram law 作用于物体上同一点的两个力可合成一个合力，此合力也作用于该点，合力作用于物体上同一点的两个力可合成一个合力，此合力也作用于该点，合力的大小和方向由以原两力矢为
20、邻边所构成的平行四边形的对角线来表示。的大小和方向由以原两力矢为邻边所构成的平行四边形的对角线来表示。Makeasketchshowingthevectoradditionusingtheparallelogramlaw.Two“component”forcesaddaccordingtotheparallelogramlaw.Yieldingaresultantforcethatformsthediagonaloftheparallelogram AF1F2RAF1F2R1414If a forceis to be resolvedcomponents along two axes dire
21、ctedformthetailoftheforce,thenstartattheheadoftheforceandconstruct lines parallel to the axes,thereby forming theparallelogram.The sides of the parallelogram represent thecomponents.Labelalltheknowandunknownforcemagnitudesandtheanglesonthesketchandidentifythetwounknowns.Redraw a half portion of the
22、parallelogram to illustrate thetriangularhead-to-tailassertionofthecomponents.Themagnitudeoftheresultantforcecanbedeterminedfromthelawofcosines,anditsdirectionisdeterminedfromthelawofsignsThemagnitudeoftwoforcecomponentsaredeterminedfromthelawofsigns 三角形法则三角形法则TrigonometryTrigonometry15力平衡汇交定理F3F1F2
23、O问:平衡吗?若不平衡,加一个什么样的力使之平衡?F1616刚体受三力作用而平衡，若其中两力作用线汇交于一点，则另一力的作用线必汇刚体受三力作用而平衡，若其中两力作用线汇交于一点，则另一力的作用线必汇交于同一点，且三力的作用线共面。（必共面，在特殊情况下，力在无穷远处汇交于同一点，且三力的作用线共面。（必共面，在特殊情况下，力在无穷远处汇交交平行力系。）平行力系。）推论推论2：三力平衡汇交定理三力平衡汇交定理Thecommentlawaboutthreeforceequilibriumwhenabodyisequilibriumsubjectedtotheactionofthreeforces
24、.Iftwoforcescurrentatapoint,thenthethirdforcemustbeactedatthepointandthethreeforcesmustbeinthesameplane应用应用Applying 画画受力图受力图Todrawthefree-bodydiagramF3F1F2ABCO17公理公理4 4 作用力和反作用力定律作用力和反作用力定律 action and reaction lawaction and reaction law等值、反向、共线、异体、且同时存在。等值、反向、共线、异体、且同时存在。例例 吊灯Themutualforcesofaction
25、andreactionbetweentwobodiesareequal,oppositeandcollinear.18Itisnecessarytostudytheconceptsofstaticandthelawsofstatic,theyarethebasistoresolveengineeringproblemsonmechanics.Thestaticinvolvesthreecontents.Law4anddeduction2areusedindrawingfree-bodydiagrams.1drawthefreebodydiagramsofbodys2reductionofafo
26、rcesystem.3toconstructequilibriumconditionsandtheapplyingofequilibriumequationsSummarizeLaw1areimportantbasisofequilibriumconditionsLaw2andlaw3areusedinreductionofforcesystemsDeduction1is main properties of a force.19约束与约束反力约束与约束反力约束与约束反力约束与约束反力constraint and constraintconstraint and constraintconst
27、raint and constraintconstraint and constraintforceforceforceforce 一、概念一、概念conceptsconcepts自由体：位移不受限制的物体叫自由体。自由体：位移不受限制的物体叫自由体。FreeFree body body TheThe bodies are only bodies are only subjected subjectedtoto active active forces forces 主动力主动力activeactive forces forces 产生运动或运动趋势的力。产生运动或运动趋势的力。They cr
28、eate the body motion or tend to set the body motionThey create the body motion or tend to set the body motion 非自由体非自由体Constraint body20对非自由体的某些位移预先施加的限制条件对非自由体的某些位移预先施加的限制条件称为约束。称为约束。（这里，约束是名词，而不是动词的约束。）（这里，约束是名词，而不是动词的约束。）约束反力：约束给被约束物体的力叫约束反力。约束反力：约束给被约束物体的力叫约束反力。thebodiesthatresistedthemotionofthe
29、referredbodyconstraintforces:theytendtopreventmotion threeelementsofconstraintforcesthemagnitudeisdeterminedbytheequationsofequilibrium.thedirectionisoppositefromactivemotionortendencyofactivemotion.thesenseisthepointorplaneofsupported约束约束constraint21约束反力特点：约束反力特点：thepropertiesofconstraintforcesGGN1
30、N2大小常常是未知的大小常常是未知的；themagnitudeisunknown方向总是与约束限制的物体的位移方向相反；方向总是与约束限制的物体的位移方向相反；thedirectionisoppositefromactivemotionortendencyofactivemotion作用点在物体与约束相接触的那一点作用点在物体与约束相接触的那一点.thesenseisthepointorplaneofsupported2222绳索类绳索类只能受拉只能受拉，所以它们的约束反力是，所以它们的约束反力是作用在接触点作用在接触点，方向沿绳索，方向沿绳索背离背离物体。物体。二、约束类型和确定约束反力方向
31、的方法：二、约束类型和确定约束反力方向的方法：typesofconstraintandmethodtodeterminetheconstraintforce1.由柔软的绳索、链条或皮带构成的约束由柔软的绳索、链条或皮带构成的约束PPTS1S1S2S2 flexiblecablethereactionisatensionforcewhichactsawayfromthemember2323约束反力作用在作用在接触点接触点处处，方向沿沿公法线公法线，指向，指向受力物体受力物体2.光滑接触面的约束光滑接触面的约束(光滑指摩擦不计光滑指摩擦不计)SmoothsurfaceconstraintPNNPN
32、ANBthereactionisaforcewhishactsperpendiculartosurfaceatthepointofcontact.24齿轮啮合力齿轮啮合力齿轮啮合力齿轮啮合力F FRRF FRR 253.光滑圆柱铰链约束光滑圆柱铰链约束smoothpinorhinge圆柱铰链圆柱铰链columnpin26AAXAYAA27固定铰支座固定铰支座fixedpin28固定铰支座固定铰支座Fixedpin29滑槽与销钉滑槽与销钉滑槽与销钉滑槽与销钉（双面约束）（双面约束）（双面约束）（双面约束）3030二二二二 力力力力 杆杆杆杆 memberssubjectedtwoforcesme
33、mberssubjectedtwoforces3131活动铰支座（辊轴支座）活动铰支座（辊轴支座）rollersupportN的实际方向也的实际方向也可以向下可以向下32活动铰支座（辊轴支座）活动铰支座（辊轴支座）rollersupport33恐龙骨骼的铰链连接恐龙骨骼的铰链连接恐龙骨骼的铰链连接恐龙骨骼的铰链连接 the pin contact of dinosaur skeletonthe pin contact of dinosaur skeleton3434一、受力分析一、受力分析 解决力学问题时，首先要选定需要进行研究的物体，即选择研究对象；然后根解决力学问题时，首先要选定需要进行研
34、究的物体，即选择研究对象；然后根据已知条件，约束类型并结合基本概念和公理分析它的受力情况，这个过程称为物据已知条件，约束类型并结合基本概念和公理分析它的受力情况，这个过程称为物体的体的受力分析受力分析。作用在物体上的力有：一类是作用在物体上的力有：一类是:主动力主动力,如重力如重力,风力风力,气体气体压力等。二类是：被压力等。二类是：被动力，即约束反力。动力，即约束反力。物体的受力分析和受力图物体的受力分析和受力图物体的受力分析和受力图物体的受力分析和受力图the free body diagram of a single body and system of bodiesthe free b
35、ody diagram of a single body and system of bodiesthe free body diagram of a single body and system of bodiesthe free body diagram of a single body and system of bodiesWe must account for all the known and unknown forces which ant on the body The best way to do this is to draw the bodys free body dia
36、gram,This diagram is simply sketch which shows the body“free”from its surroundings with all the forces that act on it.35举例说明如何绘制受力图举例说明如何绘制受力图 illustrate how to draw the free body diagram by using illustrate how to draw the free body diagram by using examplesexamples画图中每个物体的受力图画图中每个物体的受力图Todrawthefr
37、eebodydiagramofeachbody solutionCanyoudeterminethereactionatpointA?OWNENDABDNDTABXAYARANDTB36例例2画出下列各构件的受力图画出下列各构件的受力图To draw the free body diagram of each member ABNANBDEQNDNEDNDBNBC3737例例3画出下列各构件的受力图Todrawthefreebodydiagramofeachmember WTHDSDCSCBXBYBTBTHCSCB XBY,BAXAYAABCDHSDTBTHXAYA3838 受力分析与受力图受
38、力分析与受力图 例例 题题 4 4试画出各构件的受力图。试画出各构件的受力图。To draw the free-body diagram of each element.To draw the free-body diagram of each element.解：解：解：解：structure整体受力整体受力：draw the free-body diagram ABCDEIKWHFTFKFAXFAY39 受力分析与受力图受力分析与受力图 2 2、CB杆受力：杆受力：CB杆为二力杆杆为二力杆 rod BC is member subjected to two forcesrod BC is
39、member subjected to two forces3、CID杆受力杆受力:draw the free-body diagram of rod CIDCBFCBFBC4 4、AB杆受力：杆受力：draw free-body diagram of rod AB draw free-body diagram of rod AB CDIFCBFIXFIYFDXFDYAIKBFAXFAYFIXFIYFKFBC40 受力分析与受力图受力分析与受力图 如果以如果以CD杆和轮杆和轮D组成的系统作为研究对象组成的系统作为研究对象，请画出其受力图。，请画出其受力图。ifweconsiderthesystemofrodCDandwheelD,drawthefree-bodydiagram.讨论：讨论：讨论：讨论：Discuss41414242