2016工程力学-材料力学（高教版）教案：第七章 应力状态与应变状态分析 .docVIP

第七章 应力状态与应变状态分析 Mechanics of MaterialsCHAPTER 7 ANALYSIS OF THE STATE OFSTRESS AND STRAIN§ 7–4 PRINCEPAL STRESSES AND THEIR TRAJECTORIES OFTHE BEAM § 7–5ANALYSIS OF TRIAXIAL STRESSED STATE—METHODOF STRESS CIRCLE§ 7–6 ANALYSIS OF STRAIN IN A PLANE§ 7–7 RELATION BETWEEN STRESS AND STRAIN UNDERCOMPLEX STRESSED STATE—（ GENERALIZED HOOKE’S LAW ）§ 7–8 STRAIN -ENERGY DENSITY UNDER COMPLEXSTRESSED STATE§ 7–1 CONCEPTS OF THE STATE OF STRESS§ 7–2 ANALYSIS OF THE STATE OF PLANE STRESS —ANALYTICAL METHOD§ 7–3 ANALYSIS OF THE STATE OF PLANESTRESS — GRAPHYCAL METHOD第七章 应力状态与应变状态分析§ 7–1 应力状态的概念§ 7–2 平面应力状态分析 ——解析法§ 7–3 平面应力状态分析 ——图解法§ 7–4 梁的主应力及其主应力迹线§ 7–5 三向应力状态研究 ——应力圆法§ 7–6 平面内的应变分析§ 7–7 复杂应力状态下的应力 -- 应变关系——（ 广义虎克定律 ）§ 7–8 复杂应力状态下的变形比能§ 7–１ CONCEPTS OF THE STAFE OF STRISS1,Forward1),Investigation on the tensile,compressive and torsional test of cast ironand low-carbon steelMLow-carbonsteelCast ironPP Cast iron intension PCast iron incompression2),How will the member rupture incombined deformations？MP§ 7–１ 应力状态的概念一、引言1、铸铁与低碳钢的拉、压、扭试验现象是怎样产生的？M低碳钢铸铁 PP 铸铁拉伸P铸铁压缩2、组合变形杆将怎样破坏？MP4,Expression of stresses in general case3,Element,?Element— Delegate of a point in the member,It is a infinitesimalgeometric body enveloping the studied point,In common use it is a correctitude cubicbody,?Properties of an element—a,Stresses are distributeduniformly in the sections；b,The stresses in two planes that areparallel to each other are equal,2,State of stress at a point,There are countless sections through a point,The gathering of stresses in allsections is called the state of stress at this point,xyzs xszs ytxy四、普遍状态下的应力表示三、单元体, ?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。?单元体的性质 ——a、平行面上，应力均布；b、平行面上，应力相等。二、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（ State of Stress at a Given Point）。xyzs xszs ytxyxyzs xszs ytxy5,Theorem of conjugate shearing stress,Shearing stresses on perpendicular planes are equal in