工程力學雙語課件ch06-force-analysis-of-structures-and-machines

1、Chapter 6 Force Analysis of Structures and Machines,Wang Ming-lu,2,Specialized Vocabulary,Structures:結構, 構造,構[桁]架 Truss:構架, 桁架, 鋼梁 Joint:接合; 榫; 接點; 聯(lián)軸節(jié); 鉸鏈 Section:截口[面, 線, 點] Frame:框架, 框子; 【機】架, 座身,3,Chapter Ob

2、jectives.,1.Use the method of joints to determine the force in a plane truss.2.Use the method of sections to determine the force in a plane truss.3.Use multiple free-body diagrams to determine the force in a frame or m

3、achine.,4,6.1 Introduction.,5,Structure of truss in engineering 工程中的桁架結構,6.1 Introduction.,6,Structure of truss in engineering 工程中的桁架結構,6.1 Introduction.,7,Structure of truss in engineering

4、 工程中的桁架結構,6.1 Introduction.,8,Structure of truss in engineering 工程中的桁架結構,6.1 Introduction.,9,Structure of truss in engineering 工程中的桁架結構,6.1 Introduction.,10,Truss : a rigid s

5、tructure system composed of straight elements, connected at their ends by pins, without deformation under the action of forces.桁架：由桿組成，用鉸聯(lián)接，受力不變形的系統(tǒng)。,6.2 Simple plane trusses,11,6.2 Sim

6、ple plane trusses,12,The advantage of the truss: light, the capability of the material can exert sufficiently.桁架的優(yōu)點：輕，充分發(fā)揮材料性能。,The characters of the truss:桁架的特點： ①straight members, the weight of themselves can be ne

7、glected, they are all double force equivalent rods; ①直桿，不計自重，均為二力桿；②The straight elements are connected at their ends by joints. ②桿端鉸接；③All external loads on the truss act only at the joints.③外力作用在節(jié)點上。,6.2 Simple p

8、lane trusses,13,The model of truss in mechanics力學中的桁架模型(basic triangle) Triangles ensure stability( 基本三角形)三角形有穩(wěn)定性,6.2 Simple plane trusses,14,The common simplified models for truss in engineering mechanics工程力學中常見的桁架

9、簡化計算模型,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：如圖 P=10kN，求各桿內力？,[Example] [例],Solution: 解： ①study the whole structur

10、e, determine the reaction forces: ①研究整體，求支座反力,17,②Study the joints A, C and D one by one, determine the internal forces of every member.②依次取A、C、D節(jié)點研究，計算各桿內力。,We get: (denote that the r

11、od is compressed),6.4 Method of joints,18,Substituting into,We obtain:,Substituting into we get:,6.4 Method of joints,19,The another equation of the joint D can be used to verify the result of calculation.

12、節(jié)點D的另一個方程可用來校核計算結果,The solution of which is,It equals to , the calculation is accurate. 恰與 相等,計算準確無誤。,6.4 Method of joints,20,6.4.3 Problems.Do the problems 6.1-6.25 by yourself, and then I will tell you the answ

13、ers 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：如圖，h，a，P，求：4，5，6桿的內力。,6.6 Method of sections,22,A',From,6.6 Meth

14、od of sections,23,Instruction:說明 ：Method of Isolation joints: This is convenient when the stresses in all elements of the truss have to be determined.節(jié)點法：用于設計，計算全部桿內力Method of cuts : This is convenient in determ

15、ining the stresses in individual members, notably for verifying results.截面法：用于校核，計算部分桿內力,6.6 Method of sections,24,Before the calculation, assume first all elements to be under tension, if the result is negative it me

16、ans the element concerned is compressed, opposite to the direction assumed. 先把桿都設為拉力,計算結果為負時,說明是壓力,與所設方向相反。,6.6 Method of sections,25,,,,3. The judgments of the internal forces of special elements三、特殊桿件的內力判斷,6.

17、6 Method of sections,26,,,,,6.6 Method 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

18、 Method of sections,30,[Example][例],Equilibrium of a body system物體系統(tǒng)的平衡問題,Body system (BS): A system composed of several rigid bodies connected together by constraints.物體系統(tǒng)（物系）：由若干個物體通過約束所組成的系統(tǒng)。,6.7 Frames and machi

19、nes,31,External forces: forces which act on the body system from outside.外力：外界物體作用于系統(tǒng)上的力叫外力。Internal forces: forces among the bodies of the body system.內力：系統(tǒng)內部各物體之間的相互作用力叫內力。,6.7 Frames and machines,32,The characteris

20、tics of the equilibrium of a body system:物系平衡的特點： ①The body system is static ①物系靜止 ②Every body in the body system is also in equilibrium. ②物系中每個單體也是平衡的。,6.7 Frames and machines,33,for every body there are 3 equil

21、ibrium equations, so the whole system of the bodies has 3n equations. (n is number of bodies in the body system)每個單體可列3個平衡方程，整個系統(tǒng)可列3n個方程 （設物系中有n個物體）,6.7 Frames and machines,34,[Example] Let OA horizontal (OA=R,

22、AB= l) and the pressure force to be P. [例] 已知：OA=R, AB= l , 當OA水平時，沖壓力為P時， Determine: ①M, ②the reaction forces of point O, ③the internal forces of the rod AB,④the side pressure acting on the lead rail.求：①M=？②O點的約束反力

23、？③AB桿內力？④沖頭給導軌的側壓力？,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:再研究輪,6.7 Frames and machines,37,[the sign of minus means the direction of the forces is op

24、posite to the direction indicated in the diagram][負號表示力的方向與圖中所設方向相反],6.7 Frames and machines,38,①,②,③,④,6. The steps and skills of solving problems:六、解題步驟與技巧 STEPS解題步驟 Select a body to study; 選研究對象

25、Draw the force diagram (force analysis); 畫受力圖（受力分析） Select the coordinates, a center, and write down equilibrium equations; 選坐標、取矩點、列平衡方程。 Solve the equations, determine the unknown quantities. 解方程求出未

26、知數(shù),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

27、internal forces of the member AC and the reaction forces of the point B. [例1] 已知各桿均鉸接，B端插入地內，P=1000N，AE=BE=CE=DE=1m，桿重不計。 求AC 桿內力？B點的反力？,6.7 Frames and machines,40,,,Solving them, we obtain: 解方程得,6.7 Frames and mac

28、hines,41,6.7 Frames and machines,42,6.7 Frames and machines,43,[Example 2]Let P=100N,AC=1.6m,BC=0.9m,CD=EC=1.2m,AD=2m AB is horizontal, ED is vertical, BD is perpendicular to the incline. Determine

29、 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鉛垂,BD垂直于斜面； 求 ?和支座反力？,Solution:解： Study the whole rigid structure; 研究整體

30、Draw the force diagram; 畫受力圖,6.7 Frames and machines,44,Select a coordinate system, write down the equations 選坐標列方程,6.7 Frames and machines,45,6.7 Frames and machines,46,6.7 Frames and machines,47,6.7 Frame

31、s 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 equilibrium, F=60kN, l=3m, α=45o,compute the reaction forces on p

32、in 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 pr

33、oblem, that is: FA, FB?Fcx,Fcy?verify,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 mac

34、hines,56,Sample problem 6,The structure shown in the figure left, AB=BC=1 m, EK=KD, P=1732 kN, Q=1000 kN, neglect all the gravity forces, compute the reaction forces and force in lever DC,6.7 Frames and machines,57,[solu

35、tion] Draw the FBDs, find out the path of solution:,[FBD of the whole],Coplanar common force system3 equations5 unknownscan not determine all the unknowns,6.7 Frames and machines,58,[FBD of DE and CD],Coplanar commo

36、n force system3 equations3 unknownsresolvable,Here the lever DC is a lever subjected two forces.,6.7 Frames and machines,59,[FBD of DE and CD],Coplanar common force system3 equations4 unknownscan not determine

37、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 whole,Verify,6.7 Frames and machines,6

38、1,6.7 Frames and machines,62,Verify--omitted,6.7 Frames and machines,63,Sample problem 7,A structure shown as the figure left, l=2R, BD=2l, compute the external reaction forces at pin A and B.,6.7 Frames and machines,64,

39、[solution] Draw the FBDs, find out the path of solution:,[FBD of the whole],Coplanar common force system3 equations4 unknowns,6.7 Frames and machines,65,[FBD of the BC-Wheel ],Coplanar common force system3 equations

40、4 unknowns,If FBx has been known, then3 equations, 3 unknown.,6.7 Frames and machines,66,[FBD of the ACB ],Coplanar common force system3 equations4 unknowns,If FAx has been known, then3 equations, 3 unknown.,6.7