静力学基本公理和物体的受力分析.ppt

1,Chapter 1 Exordium,工 程 力 学,engineering mechanics,第二章 静力学基本公理和物体的受力分析,2,静力学的基本概念和受力分析 the basic concepts of static and the analysis of all forces which act on the body,21 静力学的基本概念 the concepts of principle of statics,22 静力学公理 the laws of static,23 约束与约束反力 constraint and constraint force,24 物体的受力分析与受力图 the free body diagrams of a single body and system of bodies,3,In this chapter we will introduce the basic Concepts of static and the statements of general static principles. To introduce the Concepts of the constraint forces and discuss how to draw the freebody diagram for a body.,本章目标,Chapter objectives,静力学模型 Static models:,（1） 物体的合理抽象与简化 the reasonable reduction and abstract of the body,（2） 受力的合理抽象与简化 the reasonable reduction and abstract of loadings,（3）接触与连接方式的合理抽象与简化 the reasonable reduction and abstract of contact and joined manners,4,5,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。,力的概念 the concept of force,The force is mechanical actions between one and another body ,it has two effects, one is motion effect ,that it will tend to change the bodys state of motion, the other is deformation effect, that it will tend to change the bodys shape and size.,力的三要素 ： three elements of force,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线段表示力矢量。,Force is a vector, that is represented graphically by an arrow, which is used to define its magnitude, direction, and sense.,The magnitude of the vector is the length of the arrow, the direction is defined by the angle between reference axis and the arrows line of action, and the sense is indicated by the arrowhead.,力的单位 ：units of force,N or KN,6,力系的概念 The concepts of force systems,作用于物体上的一群力,The sum of all loadings acted on the body,平衡力系 equilibrium 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。,A body subjected a force system is equilibrium ,then the force system is called equilibrium force systems,平面力系 force system in a plane.,All forces subjected to the body are the same plane,空间力系 dimensional force system,All forces subjected to the body are different planes,7,平面汇交力系,the current force system in a plane.,所有力的作用线汇交于一点的平面力系,All the forces in a plane act at a point.,平面平行力系,The parallel force system in a plane,所有力的作用线都互相平行,All forces are parallel in a plane .,平面任意力系 Arbitrary force system in a plane,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.,8,It is ideal model of body it can be considered as a combination of a large number of particles in which all the particles remain at a fined distance from one another both before and after applying a load,刚体 Rigid-body,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 any forces .,刚体是物体的理想化模型,平衡equilibrium,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。,A body is in equilibrium provided it is at rest if originally at rest or has a constant velocity if originally in motion.,质点 particle,是指具有一定质量而形状与大小可以忽略不计的物体。 A particle has a mass ,but a size that can be neglected.,9,静力学公理the laws of static,A body is equilibrium due to subjected two forces, the necessary and sufficient conditions is that the two forces has the same magnitude , opposite and collinear.,应用 applying,Construct equilibrium conditions,建立平衡条件的,10,说明：对刚体来说，上面的条件是充要的 Illustrate :the condition mentioned is sufficient and necessary for bodies.,对变形体(或多体中)来说，上面的条件只是必要条件 The condition mentioned is necessary for deformation Body,but not sufficient .,11,二力杆：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。 Only subjected to two forces, they have the same magnitude, opposite direction and collinear.,12,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。,公理2 加减平衡力系原理 Addition and reduction equilibrium force systems law,We can add or reduce equilibrium force systems at a body. The effect of the force system must Be the same as before.,应用 applying,简化力系,Deduct the force systems,13,推论1：力的可传性。 Principle of transmissibility of a force.,因此，对刚体来说，力作用三要素为：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， 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 transmitting.,It states, the elements of a force are magnitude, direction and line of action. the vector of a force is a sliding vector.,A,B,F,F,A,B,B,A,F1,F2,F2=F=-F1,F2,令F=F1=F2,14,公理3 力的平行四边形法则 parallelogram 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 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。,Make a sketch showing the vector addition using the parallelogram law. Two “component” forces add according to the parallelogram law. Yielding a resultant force that forms the diagonal of the parallelogram,A,F1,F2,R,A,F1,F2,R,15,If a force is to be resolved components along two axes directed form the tail of the force,then start at the head of the force and construct lines parallel to the axes, thereby forming the parallelogram. The sides of the parallelogram represent the components. Label all the know and unknown force magnitudes and the angles on the sketch and identify the two unknowns.,Redraw a half portion of the parallelogram to illustrate the triangular head-to-tail assertion of the components. The magnitude of the resultant force can be determined from the law of cosines, and its direction is determined from the law of signs,The magnitude of two force components are determined from the law of signs,三角形法则 Trigonometry,16,力平衡汇交定理,F3,F1,F2,O,问:平衡吗?,若不平衡,加一个什么样的力使之平衡?,F,17,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，力在无穷远处汇交平行力系。）,推论2：三力平衡汇交定理 The comment law about three force equilibrium,when a body is equilibrium subjected to the action of three forces. If two forces current at a point, then the third force must be acted at the point and the three forces must be in the same plane,应用 Applying,画受力图,To draw the free-body diagram,F3,F1,F2,A,B,C,O,18,公理4 作用力和反作用力定律 action and reaction law,等值、反向、共线、异体、且同时存在。,例 吊灯,The mutual forces of action and reaction between two bodies are equal, opposite and collinear.,19,It is necessary to study the concepts of static and the laws of static, they are the basis to resolve engineering problems on mechanics. The static involves three contents.,Law4 and deduction2 are used in drawing free-body diagrams.,1 draw the free body diagrams of bodys,2 reduction of a force system.,3 to construct equilibrium conditions and the applying of equilibrium equations,Summarize,Law 1 are important basis of equilibrium conditions,Law 2 and law 3 are used in reduction of force systems,Deduction1is main properties of a force .,20,约束与约束反力 constraint and constraint force,一、概念concepts,自由体：位移不受限制的物体叫自由体。 Free body The bodies are only subjected to active forces,主动力 active forces,产生运动或运动趋势的力。 They create the body motion or tend to set the body motion,非自由体 Constraint body,21,对非自由体的某些位移预先施加的限制条件 称为约束。 （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。,the bodies that resisted the motion of the referred body,constraint forces:they tend to prevent motion,three elements of constraint forces,the magnitude is determined by the equations of equilibrium. the direction is opposite from active motion or tendency of active motion. the sense is the point or plane of supported,约束 constraint,22,约束反力特点： the properties of constraint forces,G,大小常常是未知的； the magnitude is unknown,方向总是与约束限制的物体的位移方向相反； the direction is opposite from active motion or tendency of active motion,作用点在物体与约束相接触的那一点. the sense is the point or plane of supported,23,绳索类只能受拉，所以它们的约束反力是作用在接触点，方向沿绳索背离物体。,二、约束类型和确定约束反力方向的方法： types of constraint and method to determine the constraint force,1.由柔软的绳索、链条或皮带构成的约束,flexible cable,the reaction is a tension force which acts away from the member,24,约束反力作用在接触点处，方向沿公法线，指向受力物体,2.光滑接触面的约束 (光滑指摩擦不计) Smooth surface constraint,the reaction is a force whish acts perpendicular to surface at the point of contact.,25,齿轮啮合力,26,3.光滑圆柱铰链约束 smooth pin or hinge,圆柱铰链 column pin,27,A,A,28,固定铰支座 fixed pin,29,固定铰支座 Fixed pin,30,滑槽与销钉 （双面约束）,31,二 力 杆 members subjected two forces,32,活动铰支座（辊轴支座） roller support,N的实际方向也可以向下,33,活动铰支座（辊轴支座） roller support,34,恐龙骨骼的铰链连接 the pin contact of dinosaur skeleton,35,一、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受力分析。 作用在物体上的力有：一类是:主动力,如重力,风力,气体压力等。二类是：被动力，即约束反力。,物体的受力分析和受力图 the free body diagram of a single body and system of bodies,We 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 diagram ,This diagram is simply sketch which shows the body “free ”from its surroundings with all the forces that act on it.,36,举例说明如何绘制受力图 illustrate how to draw the free bo