材料力學雙語教學學習資料

1、第七章 應力和應變分析 強度理論Chapter Seven Stress and Strain Analysis Strength Theories§71 應力狀態(tài)概述§71 Concepts of the State of Stress1一點的應力狀態(tài)：過一點有無數(shù)的截面，這一點的各個截面上應力情況的集合，稱為這點的應力狀態(tài)。The state of stress at a point: There are countless sections through a point. The gathering of stresses in all sections is ca

2、lled the state of stress at this point. 2單元體：構件內的點的代表物，是包圍被研究點的無限小的幾何體，常用的是正六面體。Element: Delegate of a point in the member. It is an infinitesimal geometric body enveloping the studied point. In common use it is a correctitude cubic body. * 3主單元體：各側面上剪應力均為零的單元體。Principal element :The element in whic

3、h the shearing stresses in side planes are all zero.* 4主平面：剪應力為零的截面。Principal Planes:The planes on which the shearing stresses are zero.* 5主應力：主平面上的正應力。Principal stresses: Normal stresses acting on the principle planes.6主應力排列規(guī)定；按代數(shù)值大小Convention of the order for three principal stresses: In magnitude

4、 of the algebraic value.7三向應力狀態(tài)：三個主應力都不為零的應力狀態(tài)。State of the triaxial stress（three dimensional state of stress）:State of stress that all the three principal stresses are not equal to zero.二向應力狀態(tài)：一個主應力為零的應力狀態(tài)。state of the biaxial stress（plane state of stress）:state of stress that one principal stress

5、is equal to zero. 單向應力狀態(tài)：一個主應力不為零的應力狀態(tài)state of the uniaxial stress（unidirectional state of stress）:state of stress that one principal stress is not equal to zero.§72 二向應力狀態(tài)分析解析法§72 Analysis of the State of Plane Stress Analytical Method1.任意斜截面上的應力：stresses acting in arbitrary inclined plan

6、e2.正負規(guī)定：sa 截面外法線同向為正； 繞研究對象順時針轉為正； 逆時針為正。 Sign Stipulate ：sa is positive if its direction is the same with one of the external normal line of the section； is positive if it make the element rotate clockwise； A counterclockwise angle is considered to be positive. §73 二向應力狀態(tài)分析圖解法§73 Analysis

7、 of the State of Plane Stress Graphical Method1.應力圓 ：stress circle 2.單元體與應力圓的對應關系：Corresponding relation between the element and stress circle(1)a面上的應力(s a，t a) « 應力圓上一點(s a，t a)(2)a面的法線 « 應力圓的半徑(3)兩面夾角a « 兩半徑夾角2a ；且轉向一致。(1) stress(s a，t a) in a plane « a point (s a，t a) on the s

8、tress circumference(2) normal line of a plane « radius of the stress circle(3) angle a between two sections « angle 2a between two radiuses；And the direction of rotation is the same.§710 強度理論概述§710 Concepts of Strength Theories * 1材料的破壞形式： 屈服 斷裂 ： Types of failure of materials： y

9、ield rupture 2強度理論：是關于“構件發(fā)生強度失效起因”的假說。theories of strength：some assumptions about the cause of the strength failure of materials .§711 四種常用強度理論§711 Four Common Used Strength Theories1.最大拉應力（第一強度）理論:認為構件的斷裂是由最大拉應力引起的。當最大拉應力達到單向拉伸的強度極限時，構件就斷了。Theory of the maximum tensile stress（the first st

10、rength theory）:This theory considers the main cause of rupture to be the maximum tensile stress. The member will rupture as the maximum tensile stress reaches the strength limit in axial tension.2. 最大伸長線應變（第二強度）理論： 認為構件的斷裂是由最大伸長線應變引起的。當最大伸長線應變達到單向拉伸試驗下的極限應變時，構件就斷了Theory of the maximum tensile strain

11、（the second strength theory）:This theory considers the main cause of rupture to be the maximum tensile strain. The member will rupture as the maximum tensile strain reaches the limit strain in axial tension 3.最大剪應力（第三強度）理論：認為構件的屈服是由最大剪應力引起的。當最大剪應力達到單向拉伸試驗的極限剪應力時，構件就破壞了。Theory of the maximum shearing

12、 stress（the third strength theory）:This theory considers the main cause of rupture to be the maximum shearing stress. The member will rupture as the maximum shearing stress reaches the limit shearing stress in axial tension. 4畸變能密度（第四強度）理論：認為構件的屈服是由形狀改變比能引起的。當形狀改變比能達到單向拉伸試驗屈服時的形狀改變比能時，構件就破壞了。Theory

13、of the distortional energy density (the fourth strength theory）:This theory considers the main cause of yield to be the distortional strain energy. The member will rupture as the distortional strain energy reaches the distortional strain energy of yield in axial tension 5.相當應力：equivalent stress6.斷裂準

14、則：criterion of rupture 屈服準則: criterion of yield第八章 組合變形Chapter Eight Composite Deformation§81 組合變形和疊加原理§81 Composite Deformation and Superposition Principle1.疊加原理的步驟：The steps for principle of superposition外力分析：外力向形心簡化并沿形心主慣性軸分解Analysis of external forces：External forces are reduced along

15、the centroid of section and resolved along principal axes of inertia. 內力分析：求每個外力分量對應的內力方程和內力圖，確定危險面。Analysis of internal forces：Determine the internal force equation and its diagram corresponding to each external force component and the critical section.應力分析：畫危險面應力分布圖，疊加，建立危險點的強度條件。Analysis of stres

16、ses：Plot the distribution diagram of the stress in the critical section，do the superposition of the stresses and establish the strength condition of the critical point. 第九章 壓桿穩(wěn)定Chapter Nine Stabilization of Compressive Columns §91 壓桿穩(wěn)定性的概念§91 Concepts of Stability ofCompressed Columns* 1.失

17、穩(wěn)：loss of stability 2.穩(wěn)定與不穩(wěn)定平衡: stable and instable equilibrium * 3.臨界壓力： critical pressure §92 兩端鉸支細長壓桿的臨界壓力§92 Critical Pressure of The Slender Compressed Column With Two Hinged Ends1.歐拉公式: Eulers formula2.理想壓桿：材料絕對理想；軸線絕對直；壓力絕對沿軸線作用。Ideal compressive column: the material is absolutely i

18、deal；the axis is absolutely straight；the compressive force is absolutely along the axis of the column.§93 其它支座條件下細長壓桿的臨界壓力§93Critical Pressure of The Slender Compressed Column With Other End Conditions1. m長度系數(shù)（約束系數(shù)）：length coefficient（or constraint coefficient）2. 兩端鉸支: two hinged ends3. 一端

19、固定另一端自由: one fixed end and one free end4. 兩端固定: two fixed ends5. 一端固定另端鉸支: one fixed end and one hinged end§94 歐拉公式的適用范圍 經驗公式 §94 Application Range of Eulers Formula Empirical Formula 1.臨界應力: 壓桿處于臨界狀態(tài)時橫截面上的平均應力。Critical stress : average stress in the cross section of the compressive column

20、 in the critical state. * 2.柔度（或長細比）：flexibility (or slenderness ratio) 大柔度桿的臨界應力由歐拉公式來求;小柔度桿的臨界應力就是它的屈服極限; 中柔度桿的臨界應力由經驗公式來求The critical stress of the large flexibility column is calculated by Eulers formula.The critical stress of small flexibility column is its yield limit.The critical stress of th

21、e middle flexibility column may be determined by the empirical formula. §95 壓桿的穩(wěn)定校核 §95 Stability Check of Compressed Column 1.穩(wěn)定安全因數(shù)：safety coefficient of stability2.穩(wěn)定條件：stability condition §96 提高壓桿穩(wěn)定性的措施 §96 Method to Improve Stability of Compressed Column 1.選擇合理的截面形狀: choose

22、reasonable section of the column:2.改變壓桿的約束條件:change constraint condition of the column3.合理選擇材料: choose reasonable material.第十章 動載荷Chapter Ten Dynamic Load§101 概述§101 Introduction1.靜載荷：static loadsThe loads dont change with time (or change very stably and slowly) and acceleration of each me

23、mber is zero or may be neglected 2.動載荷：dynamic loadsThe loads change sharply with time and the velocity of the member changes obviously§92動靜法的應用 §92 Application of The Method ofKinetic Statics1.慣性力：inertia force2.動荷系數(shù)：dynamic load coefficient3.達朗伯原理：處于不平衡狀態(tài)的物體，存在慣性力，慣性力的方向與加速度方向相反，慣性力的數(shù)值等于

24、加速度與質量的乘積。只要在物體上加上慣性力，就可以把動力學問題在形式上作為靜力學問題來處理，這就是動靜法。DAlemberts principle: There is inertial force on the body in unequilibrium. The direction of the inertial force is opposite to the acceleration of the body and the magnitude of the inertial force is the product of the mass and the acceleration of

25、the body. After the inertial force is applied on the body the dynamic problem may be dealt with the static problem in form, which is called the method of kinetic statics. Exercise 1: The state of stress at a point as shown . (unit:Mpa) ,try to determine the three principal stresses.(either by analytical method or by graphical method). And compute the equivalent stress of the fourth strength theory.Exercise 2: A circular rod made of cast iron is subjected to the loads T=7kNm, P=50kN as sho