材料力学双语教学学习资料.doc

第七章 应力和应变分析 强度理论Chapter Seven Stress and Strain Analysis Strength Theories71 应力状态概述71 Concepts of the State of Stress1一点的应力状态：过一点有无数的截面，这一点的各个截面上应力情况的集合，称为这点的应力状态。The state of stress at a point: There are countless sections through a point. The gathering of stresses in all sections is called the state of stress at this point. 2单元体：构件内的点的代表物，是包围被研究点的无限小的几何体，常用的是正六面体。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主单元体：各侧面上剪应力均为零的单元体。Principal element :The element in which the shearing stresses in side planes are all zero.* 4主平面：剪应力为零的截面。Principal Planes:The planes on which the shearing stresses are zero.* 5主应力：主平面上的正应力。Principal stresses: Normal stresses acting on the principle planes.6主应力排列规定；按代数值大小Convention of the order for three principal stresses: In magnitude of the algebraic value.7三向应力状态：三个主应力都不为零的应力状态。State of the triaxial stress（three dimensional state of stress）:State of stress that all the three principal stresses are not equal to zero.二向应力状态：一个主应力为零的应力状态。state of the biaxial stress（plane state of stress）:state of stress that one principal stress is equal to zero. 单向应力状态：一个主应力不为零的应力状态state of the uniaxial stress（unidirectional state of stress）:state of stress that one principal stress is not equal to zero.72 二向应力状态分析解析法72 Analysis of the State of Plane Stress Analytical Method1.任意斜截面上的应力：stresses acting in arbitrary inclined plane2.正负规定：sa 截面外法线同向为正； 绕研究对象顺时针转为正； 逆时针为正。 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 二向应力状态分析图解法73 Analysis of the State of Plane Stress Graphical Method1.应力圆 ：stress circle 2.单元体与应力圆的对应关系：Corresponding relation between the element and stress circle(1)a面上的应力(s a，t a) 应力圆上一点(s a，t a)(2)a面的法线 应力圆的半径(3)两面夹角a 两半径夹角2a ；且转向一致。(1) stress(s a，t a) in a plane a point (s a，t a) on the stress 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 强度理论概述710 Concepts of Strength Theories * 1材料的破坏形式： 屈服 断裂 ： Types of failure of materials： yield rupture 2强度理论：是关于“构件发生强度失效起因”的假说。theories of strength：some assumptions about the cause of the strength failure of materials .711 四种常用强度理论711 Four Common Used Strength Theories1.最大拉应力（第一强度）理论:认为构件的断裂是由最大拉应力引起的。当最大拉应力达到单向拉伸的强度极限时，构件就断了。Theory of the maximum tensile stress（the first strength 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. 最大伸长线应变（第二强度）理论： 认为构件的断裂是由最大伸长线应变引起的。当最大伸长线应变达到单向拉伸试验下的极限应变时，构件就断了Theory of the maximum tensile strain（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.最大剪应力（第三强度）理论：认为构件的屈服是由最大剪应力引起的。当最大剪应力达到单向拉伸试验的极限剪应力时，构件就破坏了。Theory of the maximum shearing 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畸变能密度（第四强度）理论：认为构件的屈服是由形状改变比能引起的。当形状改变比能达到单向拉伸试验屈服时的形状改变比能时，构件就破坏了。Theory 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.相当应力：equivalent stress6.断裂准则：criterion of rupture 屈服准则: criterion of yield第八章 组合变形Chapter Eight Composite Deformation81 组合变形和叠加原理81 Composite Deformation and Superposition Principle1.叠加原理的步骤：The steps for principle of superposition外力分析：外力向形心简化并沿形心主惯性轴分解Analysis of external forces：External forces are reduced along the centroid of section and resolved along principal axes of inertia. 内力分析：求每个外力分量对应的内力方程和内力图，确定危险面。Analysis of internal forces：Determine the internal force equation and its diagram corresponding to each external force component and the critical section.应力分析：画危险面应力分布图，叠加，建立危险点的强度条件。Analysis of stresses：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 压杆稳定Chapter Nine Stabilization of Compressive Columns 91 压杆稳定性的概念91 Concepts of Stability ofCompressed Columns* 1.失稳：loss of stability 2.稳定与不稳定平衡: stable and instable equilibrium * 3.临界压力： critical pressure 92 两端铰支细长压杆的临界压力92 Critical Pressure of The Slender Compressed Column With Two Hinged Ends1.欧拉公式: Eulers formula2.理想压杆：材料绝对理想；轴线绝对直；压力绝对沿轴线作用。Ideal compressive column: the material is absolutely ideal；the axis is absolutely straight；the compressive force is absolutely along the axis of the column.93 其它支座条件下细长压杆的临界压力93Critical Pressure of The Slender Compressed Column With Other End Conditions1. m长度系数（约束系数）：length coefficient（or constraint coefficient）2. 两端铰支: two hinged ends3. 一端固定另一端自由: one fixed end and one free end4. 两端固定: two fixed ends5. 一端固定另端铰支: one fixed end and one hinged end94 欧拉公式的适用范围 经验公式 94 Application Range of Eulers Formula Empirical Formula 1.临界应力: 压杆处于临界状态时横截面上的平均应力。Critical stress : average stress in the cross section of the compressive column in the critical state. * 2.柔度（或长细比）：flexibility (or slenderness ratio) 大柔度杆的临界应力由欧拉公式来求;小柔度杆的临界应力就是它的屈服极限; 中柔度杆的临界应力由经验公式来求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 the middle flexibility column may be determined by the empirical formula. 95 压杆的稳定校核 95 Stability Check of Compressed Column 1.稳定安全因数：safety coefficient of stability2.稳定条件：stability condition 96 提高压杆稳定性的措施 96 Method to Improve Stability of Compressed Column 1.选择合理的截面形状: choose reasonable section of the column:2.改变压杆的约束条件:change constraint condition of the column3.合理选择材料: choose reasonable material.第十章 动载荷Chapter Ten Dynamic Load101 概述101 Introduction1.静载荷：static loadsThe loads dont change with time (or change very stably and slowly) and acceleration of each member is zero or may be neglected 2.动载荷：dynamic loadsThe loads change sharply with time and the velocity of the member changes obviously92动静法的应用 92 Application of The Method ofKinetic Statics1.惯性力：inertia force2.动荷系数：dynamic load coefficient3.达朗伯原理：处于不平衡状态的物体，存在惯性力，惯性力的方向与加速度方向相反，惯性力的数值等于加速度与质量的乘积。只要在物体上加上惯性力，就可以把动力学问题在形式上作为静力学问题来处理，这就是动静法。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 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 shown in the figur