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1、静力学引言Introduction to Statics,A,静力学 Statics ：,静力学是研究物体的受力分析、力系的等效替换（或简化）、Statics is defined as a subject which study the force analysis, reduction of force system建立各种力系的平衡条件的科学and establish the equilibrium equations of various force system.,A,1、物体的受力分析： Force Analysis分析物体（包括物体系）受哪些力，每个力的作用位置和方向，并画出物体
2、的受力图Analyze the forces acting on the body, and identify the magnitude, direction and active point of the forces draw a Free-body diagram.,2、力系的等效替换（或简化）： Reduction of force system用一个简单力系等效代替一个复杂力系。 A complex force system is replaced by a simple one.,A,3、建立各种力系的平衡条件：Establish the equilibrium equation
3、s of various force system建立各种力系的平衡条件，并应用这些条件解决静力学实际问题 Practical problems is solved by using the established equilibrium equations.,几个基本概念： Fundamental Concepts,刚体：Rigid body在力的作用下，其内部任意两点间的距离始终保持不变的物体. A rigid body is a combination of a large number of particles occupying fixed positions with respec
4、t to each other.,A,力 Force 物体间相互的机械作用，作用效果使物体的机械运动状态发生改变。A force represents the mechanical action of one body on another. The mechanical motion state of the body can be changed by it.力的内效应和力的外效应：The effect of action of the force consists of internal effect and external effect.,力的三要素：大小、方向、作用点。力是矢量Th
5、ree factors of forces are defined as magnitude, direction and point of application. Forces are vectors.,A,力系 Force system一群力可分为：平面汇交（共点）力系；平面平行力系；平面力偶系；平面任意力系；空间汇交（共点）力系；空间平行力系；空间力偶系；空间任意力系。 Force system is defined as a group of forces which act on the same body. Classification of force system Copla
6、nar force system can be classified as coplanar concurrent force system, coplanar parallel force system,coplanar force-couple system and general coplanar force system. Forces in space can be classified as spatial concurrent force system, spatial parallel force system, spatial force-couple system, gen
7、eral spatial force system.,A,平衡Equilibrium 物体相对惯性参考系（如地面）静止或作匀速直线运动。 The body is in equilibrium if it remains at rest or moves with a constant speed in a straight line relative to the inertial reference frame.,A,第一章 静力学公理和物体的受力分析 Chapter 1 Axioms of Statics and Free-body Diagram,1-1 静力学公理Section 1.1
8、 Axioms of Statics,A,公理1 力的平行四边形法则Axiom 1 The parallelogram law,作用在物体上同一点的两个力，可以合成为一个合力 Two forces acting on the same point of a body can be replaced by a resultant force合力的作用点也在该点，合力的大小和方向，由这两个力为边构成的平行四边形的对角线确定，如图所示。 . The resultant force can be obtained by constructing a parallelogram, using the t
9、wo forces as two adjacent sides of the parallelogram. The diagonal that passes through the point of application of two forces represents the magnitude and direction of the resultant force.,A,合力(合力的大小与方向) (矢量的和) Resultant force (the magnitude and direction of the resultant force) (the vector sum),亦可用
10、力三角形求得合力矢Resultant force also can be determined by force triangle rule.,A,公理2 二力平衡条件 Axiom 2 Equilibrium conditions of two forces,作用在刚体上的两个力，使刚体保持平衡的必要和充分条件是：这两个力的大小相等，方向相反，且作用在同一直线上。The sufficient and necessary equilibrium conditions of two forces acting on a rigid body arethat the two forces have
11、the same magnitude and the same line of action but opposite sense.,A,公理3 加减平衡力系原理Axiom 3 The principle of addition and subtraction of equilibrium force system,在已知力系上加上或减去任意的平衡力系，并不改变原力系对刚体的作用。The rigid body will remain unchanged if a equilibrium force system is added or subtracted from the original
12、force system acting on the rigid body.,A,推理1 力的可传性Deduction 1 The principle of transmissibility,作用于刚体上某点的力，可以沿着它的作用线移到刚体内任意一点，并不改变该力对刚体的作用。The conditions of equilibrium or of motion of a rigid body will remain unchanged if a force acting at a given point of the rigid body is replaced by a force of t
13、he same magnitude and same direction, but acting at a different point, provided that the two forces have the same line of action.,A,作用在刚体上的力是滑动矢量，The force is a sliding vector if it acts on a rigid body. 力的三要素为大小、方向和作用线The three factors of a force acting on a rigid body are magnitude, direction and
14、the line of its action.,推理2 三力平衡汇交定理Deduction 2 Principle of equilibrium of a three- force body,A,平衡时 必与 共线则三力必汇交O 点，且共面,作用于刚体上三个相互平衡的力，若其中两个力的作用线汇交于一点，则此三力必在同一平面内，且第三个力的作用线通过汇交点。 A rigid body is subjected to forces acting at only three points. It will be shown that if the body is in equilibrium and
15、 two of them are concurrent, the lines of action of the three forces must be concurrent.,A,公理4 作用和反作用定律Axiom 4 Law of action and reaction,作用力和反作用力总是同时存在，同时消失，等值、反向、共线，作用在相互作用的两个物体上The forces of action and reaction must have the same magnitude and the same line of action but opposite sense.The forces
16、 of action and reaction act on various rigid body.,在画物体受力图时要注意此公理的应用,A,公理5 刚化原理Axiom 5 Rigidified principle,变形体在某一力系作用下处于平衡，如将此变形体刚化为刚体，其平衡状态保持不变A deformable body is in equilibrium acted by a force system.The equilibrium state of the deformable body will remain unchanged if it is rigidified to a rig
17、id body.,柔性体（受拉力平衡）,刚化为刚体（仍平衡）,Deformable body (in equilibrium),Be rigidified ( in equilibrium),A,反之不一定成立，因对刚体平衡的充分必要条件，对变形体是必要的但非充分的,刚体（受压平衡）,柔性体（受压不能平衡）,Rigid body (in equilibrium),Deformable body (instability),A,1-2 约束和约束力Section 1.2 Constraints and Reactions of Constraints,约束：对非自由体的位移起限制作用的物体.,C
18、onstraint The body limits the position of the non-free body,约束力：约束对非自由体的作用力,Constraint reaction The action of the constraint to the non-free body,A,大小待定,方向与该约束所能阻碍的位移方向相反,作用点接触处,Magnitude Undetermined,Direction The direction of the constraint reaction is opposite to the direction of which the constr
19、aint can prevent the motion of the rigid body.,Point of action The contact point,约束力Constraint reaction,A,工程中常见的约束,Constraint,1、具有光滑接触面（线、点）的约束（光滑接触约束）,1) Frictionless Surface,A,Constraint Reaction The direction of the force is along the normal line of the contact surface and points to the non-free
20、body. is usually used to represent the constraint reaction.,光滑支承接触对非自由体的约束力，作用在接触处；方向沿接触处的公法线并指向受力物体，故称为法向约束力，用 表示,A,2 、由柔软的绳索、胶带或链条等构成的约束,2) Flexible Cable,柔索只能受拉力，又称张力.用 表示,The flexible cable only can provide tension force to the non-free body. We usually use to represent the tension force.,A,柔索对物
21、体的约束力沿着柔索背向被约束物体,胶带对轮的约束力沿轮缘的切线方向，为拉力,3 、光滑铰链约束（径向轴承、圆柱铰链、固定铰链支座等）,3) Smooth cylindrical hinge,（1） 径向轴承（向心轴承）,(1) Radial Bearing,A,约束特点： 轴在轴承孔内，轴为非自由体、轴承孔为约束,This kind of constraint can prevent the body from moving awaythe radial direction but not the axial direction and rotating aroundthe axial lin
22、e of bearing.,约束力： 当不计摩擦时，轴与孔在接触为光滑接触约束法向约束力 约束力作用在接触处，沿径向指向轴心 Constraint Reaction The direction could not be determined immediately, 当外界载荷不同时，接触点会变，则约束力的大小与方向均有改变,We usually use two orthogonal component forces to represent the constraint reaction.,可用两个通过轴心的正交分力 表示,A,（2）光滑圆柱铰链,(2) Smooth cylinder pi
23、n,约束特点：由两个各穿孔的构件及圆柱销钉组成，如剪刀,The characteristics of the constraint reaction is the same to the radial bearing.,A,A,约束力：,光滑圆柱铰链：亦为孔与轴的配合问题，与轴承一样，可用两个正交分力表示,其中有作用力和反作用的关系,一般不必分析销钉受力，如要分析时，必须把销钉单独取出,A,（3） 固定铰链支座,(3) Coplanar supports (pin supports),约束特点： 由上面构件1或2 之一与地面或机架固定而成,The characteristics of the
24、constraint reaction is the same to the smooth cylindrical hinge.,A,约束力：与圆柱铰链相同,以上三种约束（径向轴承、光滑圆柱铰链、固定铰链支座）其约束特性相同，均为轴与孔的配合问题，都可称为光滑圆柱铰链,4、其它类型约束,4) The other constraint,（1）滚动支座,(1) Coplanar supports (roller),A,约束特点： 在上述固定铰支座与光滑固定平面之间装有光滑辊轴而成,约束力：,构件受到垂直于光滑面的约束力,This kind of constraint can be regarded
25、 as a smooth roller installed between a coplanar supports (pin supports) and the smooth surface.,Constraint Reaction The direction of the force is along the normal line of the contact surface and points to the non-free body.,A,(2) 球铰链,(2) Ball and Socket joint,约束特点：通过球与球壳将构件连接，构件可以绕球心任意转动，但构件与球心不能有任
26、何移动,Constraint reaction The vector of force is from the contact point to the center of the ball.,A,可用三个正交分力表示 We usually use three orthogonal component forces to represent the constraint reaction.,约束力：当忽略摩擦时，球与球座亦是光滑约束问题,约束力通过接触点，并指向球心，是一个不能预先确定的空间力。,（3）止推轴承,(3) Axial thrust bearing supports,A,约束力：比
27、径向轴承多一个轴向的约束力，亦有三个正交分力 ,Constraint reaction We usually use three orthogonal component forces to represent the constraint reaction.,约束特点： 止推轴承比径向轴承多一个轴向的位移限制,The constraint reaction of axis is added to the axial thrust bearing supports by comparing with the radial bearing.,A,（2）柔索约束张力,球铰链空间三正交分力,止推轴承
28、空间三正交分力,（4）滚动支座 光滑面,（3）光滑铰链,（1）光滑面约束法向约束力,1. Frictionless Surface - normal force,2. Flexible Cable - tension force,3. Smooth cylindrical hinge -,4. Coplanar supports (roller) - normal force,Ball and Socket joint -,Axial thrust bearing supports -,three orthogonal component forces,three orthogonal com
29、ponent forces,A,1-3 物体的受力分析和受力图,Section 1.3 Free-Body Diagram,在受力图上应画出所有力，主动力和约束力（被动力）,The free-body diagram (FBD) of a body is a sketch of the body showing all active forces and constraint reactions acting on it.,A,3、按约束性质画出所有约束（被动）力,2、画出所有主动力,2) Draw all the active forces,3) Draw all the constrain
30、t reaction,画受力图步骤：,Steps of drawing FBD,The part of study is chosen and separated from the body system,1、取所要研究物体为研究对象（隔离体），画出其简图,A,例1-1,碾子重为 ，拉力为 ， 、 处光滑接触，画出碾子的受力图,SAMPLE PROBLEM 1.1,A wheel of weight P is placed on a smooth corner. A force of F is applied on the wheel. Draw the free-body diagram o
31、f the wheel.,A,画出简图Choose the wheel as a free body.,Draw the active forces on the wheel.,Draw the constraint reactions on the wheel.,解：SOLUTION,画出主动力,画出约束力,A,例1-2,屋架受均布风力 （N/m）， 屋架重为 ，画出屋架的受力图,The weight of the roof is P. The distributed load of q (N/m) is applied on the roof. Draw the free-body dia
32、gram of the roof.,SAMPLE PROBLEM 1.2,A,解：SOLUTION取屋架, 画出简图,画出主动力,画出约束力,Choose the roof as a free body.,Draw the active forces of the roof.,Draw the constraint reactions on the roof.,A,例1-3,水平均质梁AB重为P1 ，电动机重为P2 ，不计杆CD的自重，画出杆CD 和梁AB的受力图,The homogeneous beam AB of weight P1 is supported by a bar CD of
33、negligible mass. A electromotor of weight P2 is placed on the beam AB. Draw the free-body diagram of bar CD and beam AB.,SAMPLE PROBLEM 1.3,A,解：取CD 杆，其为二力构件，简称二力杆，其受力图如图(b),Choose the bar CD as a free body.Bar CD is a two-force member, and the free-body diagram is shown as the figure.,SOLUTION,取 梁，其
34、受力图如图 (c),Choose the beam AB as a free body, and the free-body diagram is shown as the figure.,A,若这样画，梁 的受力图又如何改动?,杆的受力图能否画为图（d）所示？,A,例1-4,不计三铰拱桥的自重与摩擦，画出左、右拱 的受力图与系统整体受力图,The three-hinged arch is shown as figure. A force of F is applied on the left side of the arch. If the weight and the friction o
35、f the three-hinged arch are neglected, draw the free-body diagram of the left side of the arch, right side of the arch and the body system.,SAMPLE PROBLEM 1.4,A,解：右拱 为二力构件，其受力图如图（b）所示,The right side of the arch CB is a two-force member, and the free-body diagram is shown as follows.,SOLUTION,取左拱 ,其受
36、力图如图（c）所示,The free-body diagram of the left side of the arch is shown as figure.,A,系统整体受力图如图（d）所示The free-body diagram of the body system is shown as figure.,另解Another solution,考虑到左拱 三个力作用下平衡，也可按三力平衡汇交定理画出左拱 的受力图，如图（e）所示,The free-body diagram of left side of the arch is shown.,A,此时整体受力图如图（f）所示,The f
37、ree-body diagram of the body system is shown.,A,讨论：Discussion若左、右两拱都考虑自重，If the weights of the two arches are considered,如何画出各受力图？,how to draw the free-body diagram.,如图,（g）,（h）,（i）,A,例1-5,不计自重的梯子放在光滑水平地面上，The ladder of negligible mass is placed on the smooth surface.画出梯子、梯子左右两部分与整个系统受力图图(a),Draw the
38、 free-body diagram of the left side of the ladder, the right side of the ladder and the body system.,SAMPLE PROBLEM 1.5,A,解：绳子受力图如图（b）所示,The free-body diagram of the cable is drawn.,SOLUTION,梯子左边部分受力图如图（c）所示,The free-body diagram of the left side of the ladder is shown.,A,梯子右边部分受力图如图（d）所示,The free-body diagram of the right side of the ladder is shown.,整体受力图如图（e）所示,The free-body diagram of the body system is shown.,A,问题 Question 左右两部分梯子在A处，绳子对左右两部分梯子均有力作用，为什么在整体受力图没有画出？,The forces at point A and the tension forces of the cable do not appear in the free-body diagram of the body system. Why?,A,
