工程力学双语课件ch06-Force-Analysis-of-Structures-and-Machines

1、Chapter 6 Force Analysis of Structures and Machines,Wang Ming-lu,2,Specialized Vocabulary,Structures:结构, 构造,构桁架 Truss:构架, 桁架, 钢梁 Joint:接合; 榫; 接点; 联轴节; 铰链 Section:截口面, 线, 点 Frame:框架, 框子; 【机】架, 座身,3,Chapter Objectives.,1.Use the method of joints to determine the force in a plane truss. 2.Use the metho

2、d of sections to determine the force in a plane truss. 3.Use multiple free-body diagrams to determine the force in a frame or machine.,4,6.1 Introduction.,5,Structure of truss in engineering 工程中的桁架结构,6.1 Introduction.,6,Structure of truss in engineering 工程中的桁架结构,6.1 Introduction.,7,Structure of trus

3、s in engineering 工程中的桁架结构,6.1 Introduction.,8,Structure of truss in engineering 工程中的桁架结构,6.1 Introduction.,9,Structure of truss in engineering 工程中的桁架结构,6.1 Introduction.,10,Truss : a rigid structure system composed of straight elements, connected at their ends by pins, without deformation under the

4、action of forces. 桁架：由杆组成，用铰联接，受力不变形的系统。,6.2 Simple plane trusses,11,6.2 Simple plane trusses,12,The advantage of the truss: light, the capability of the material can exert sufficiently. 桁架的优点：轻，充分发挥材料性能。,The characters of the truss: 桁架的特点： straight members, the weight of themselves can be neglected

5、, they are all double force equivalent rods; 直杆，不计自重，均为二力杆； The straight elements are connected at their ends by joints. 杆端铰接； All external loads on the truss act only at the joints. 外力作用在节点上。,6.2 Simple plane trusses,13,The model of truss in mechanics力学中的桁架模型 (basic triangle) Triangles ensure stabi

6、lity ( 基本三角形)三角形有稳定性,6.2 Simple plane trusses,14,The common simplified models for truss in engineering mechanics 工程力学中常见的桁架简化计算模型,6.2 Simple plane trusses,15,6.2 Simple plane trusses,16,6.4 Method of joints,P=10kN, determine the internal forces on every elements. 已知：如图 P=10kN，求各杆内力？,Example 例,Soluti

7、on: 解： study the whole structure, determine the reaction forces: 研究整体，求支座反力,17,Study the joints A, C and D one by one, determine the internal forces of every member. 依次取A、C、D节点研究，计算各杆内力。,We get: (denote that the rod is compressed),6.4 Method of joints,18,Substituting into,We obtain:,Substituting int

8、o we get:,6.4 Method of joints,19,The another equation of the joint D can be used to verify the result of calculation. 节点D的另一个方程可用来校核计算结果,The solution of which is,It equals to , the calculation is accurate. 恰与 相等,计算准确无误。,6.4 Method of joints,20,6.4.3 Problems. Do the problems 6.1-6.25 by yourself, a

9、nd then I will tell you the answers of them.,6.4 Method of joints,21,Example h, a and P are given, determine the internal forces on the element 4, 5 and 6. 例 已知：如图，h，a，P，求：4，5，6杆的内力。,6.6 Method of sections,22,A,From,6.6 Method of sections,23,Instruction: 说明 ： Method of Isolation joints: This is conv

10、enient when the stresses in all elements of the truss have to be determined. 节点法：用于设计，计算全部杆内力 Method of cuts : This is convenient in determining the stresses in individual members, notably for verifying results. 截面法：用于校核，计算部分杆内力,6.6 Method of sections,24,Before the calculation, assume first all elem

11、ents to be under tension, if the result is negative it means the element concerned is compressed, opposite to the direction assumed. 先把杆都设为拉力,计算结果为负时,说明是压力,与所设方向相反。,6.6 Method of sections,25,3. The judgments of the internal forces of special elements 三、特殊杆件的内力判断,6.6 Method of sections,26,6.6 Method

12、of sections,27,6.6 Method of sections,28,Again,6.6 Method of sections,29,6.6.3 Problems. Do the problems 6.27-6.34 by yourself, and then I will tell you the answers of them.,6.6 Method of sections,30,Example 例,Equilibrium of a body system 物体系统的平衡问题,Body system (BS): A system composed of several rigi

13、d bodies connected together by constraints. 物体系统（物系）：由若干个物体通过约束所组成的系统。,6.7 Frames and machines,31,External forces: forces which act on the body system from outside. 外力：外界物体作用于系统上的力叫外力。 Internal forces: forces among the bodies of the body system. 内力：系统内部各物体之间的相互作用力叫内力。,6.7 Frames and machines,32,The

14、characteristics of the equilibrium of a body system: 物系平衡的特点： The body system is static 物系静止 Every body in the body system is also in equilibrium. 物系中每个单体也是平衡的。,6.7 Frames and machines,33,for every body there are 3 equilibrium equations, so the whole system of the bodies has 3n equations. (n is numb

15、er of bodies in the body system) 每个单体可列3个平衡方程，整个系统可列3n个方程 （设物系中有n个物体）,6.7 Frames and machines,34,Example Let OA horizontal (OA=R, AB= l) and the pressure force to be P. 例 已知：OA=R, AB= l , 当OA水平时，冲压力为P时， Determine: M, the reaction forces of point O, the internal forces of the rod AB,the side pressure

16、 acting on the lead rail. 求：M=？O点的约束反力？AB杆内力？冲头给导轨的侧压力？,Solution: Study the point B 解：研究B,6.7 Frames and machines,35,6.7 Frames and machines,36,Then study the wheel: 再研究轮,6.7 Frames and machines,37,the sign of minus means the direction of the forces is opposite to the direction indicated in the diag

17、ram 负号表示力的方向与图中所设方向相反,6.7 Frames and machines,38,6. The steps and skills of solving problems: 六、解题步骤与技巧 STEPS解题步骤 Select a body to study; 选研究对象 Draw the force diagram (force analysis); 画受力图（受力分析） Select the coordinates, a center, and write down equilibrium equations; 选坐标、取矩点、列平衡方程。 Solve the equatio

18、ns, determine the unknown quantities. 解方程求出未知数,6.7 Frames and machines,39,Example 1 All elements are connected with each other by joints, the bottom B is inserted into the earth ,P=1000N, AE=BE=CE=DE=1m, the weight of the elements are negligible. Determine the internal forces of the member AC and th

19、e reaction forces of the point B. 例1 已知各杆均铰接，B端插入地内，P=1000N，AE=BE=CE=DE=1m，杆重不计。 求AC 杆内力？B点的反力？,6.7 Frames and machines,40,Solving them, we obtain: 解方程得,6.7 Frames and machines,41,6.7 Frames and machines,42,6.7 Frames and machines,43,Example 2Let P=100N,AC=1.6m,BC=0.9m,CD=EC=1.2m,AD=2m AB is horizon

20、tal, ED is vertical, BD is perpendicular to the incline. Determine and the reaction force of the constraints. 例2 已知:P=100N. AC=1.6m,BC=0.9m,CD=EC=1.2m,AD=2m 且AB水平, ED铅垂,BD垂直于斜面； 求 ?和支座反力？,Solution: 解： Study the whole rigid structure; 研究整体 Draw the force diagram; 画受力图,6.7 Frames and machines,44,Selec

21、t a coordinate system, write down the equations 选坐标列方程,6.7 Frames and machines,45,6.7 Frames and machines,46,6.7 Frames and machines,47,6.7 Frames and machines,48,6.7 Frames and machines,49,6.7 Frames and machines,50,6.7 Frames and machines,51,A ladder placed on the smooth horizontal surface is in e

22、quilibrium, F=60kN, l=3m, =45o,compute the reaction forces on pin C and surface,solution,Firstly, draw the FBDs of the whole and each part, find out the number of unknowns.,6.7 Frames and machines,Sample problem 5,52,From the FBDs above, we can make the procedure of solving the problem, that is: FA,

23、 FBFcx,Fcyverify,6.7 Frames and machines,53,6.7 Frames and machines,54,6.7 Frames and machines,55,Verify:,If the following equations are satisfied, then your results are correct.,6.7 Frames and machines,56,Sample problem 6,The structure shown in the figure left, AB=BC=1 m, EK=KD, P=1732 kN, Q=1000 k

24、N, neglect all the gravity forces, compute the reaction forces and force in lever DC,6.7 Frames and machines,57,solution Draw the FBDs, find out the path of solution:,FBD of the whole,Coplanar common force system 3 equations 5 unknowns can not determine all the unknowns,6.7 Frames and machines,58,FB

25、D of DE and CD,Coplanar common force system 3 equations 3 unknowns resolvable,Here the lever DC is a lever subjected two forces.,6.7 Frames and machines,59,FBD of DE and CD,Coplanar common force system 3 equations 4 unknowns can not determine all the unknowns,From the FBDs above, we can find out the path of solution as following:,6.7 Frames and machines,60,Path of solution,Fex , Fey , FD,FAx , FAy , MA,FBD of the w