m-虎克定律-强度理论311.ppt
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1、3. 广义虎克定律,Generalized Hookes law,考虑 Poisson 效应,3.1 定律及其应用,Generalized Hookes law and its applications,1) 广义虎克定律 ( Generalized Hookes law for the general state of stress,正应力与正应变之间的关系,切应力与切应变之间的关系,在小变形情况下,切应力不影响正应变,正应力不影响切应变,2) Generalized Hookes law for the two-dimensional stress state,For the plane
2、state of stress , its strain state is three-dimensional,平面应力状态的虎克定律,3) 平面应力状态斜方位的广义虎克定律 ( Generalized Hookes law for the plane stress state along the slope direction,例 图示简支梁横截面为高度是 h、宽度是 b 的矩形,已知材料的弹性模量E,泊松比 。欲在轴线 K 点处测出该点的最大拉应变,应变片应沿什么方向粘贴?应变片的理论读数是多少,由于 K 点处于中性层上,因此该点处横截面上只有切应力而无正应力,故该点处于纯剪状态,K 点所
3、在横截面剪力,切应力,该点主应力沿 45 方向,应变片应沿这一方向粘贴,主应力,主方向应变,Example : A bar was acted by an axial force P shown follows , known E and v of the material , determine the tension of line AB,Solve,Where is wrong ,Solve,Suppose C is an abtrary point on the line AB , its state of stress can be shown in the follows figu
4、re,Acoording to the formula of , we can get,Example : A bar was acted by an axial force P shown follows , known E and v of the material , determine the tension of line AB,Acoorging to the generalized Hooks law , follows result can be attained,Because C is an abtrary point on the line AB , so the nor
5、mal strain along the line AB is uniform . Acoorging to the difinition of normal strain we can get,The tension of line AB is,Example : Point K was on the surface of a shaft shown in follows figure , known E , v and , determine the external moment m . The diameter of the shaft is d,Solve,The stat of s
6、tress at point K is pure shearing,Acoording to the formula of , we can get,Acoorging to the generalized Hooks law , follows result can be attained,例 对如图均匀变形的板,求: 厚度的改变量; 板面积的改变量; 体积的改变量,板中各方向上的应变,厚度的改变量,板面积的改变量,体积的改变量,4. 强度理论,Strength Criteria,4.1 强 度 理 论 的 概 念,Concept of strength criteria,假设点A是结构中最
7、危险的点,材料力学中通常只考虑杆件结构,点A可能处于简单应力状态也可能处于复杂应力状态,那么该点安全或是不安全?又怎样判别其强度,Question,Simple stress state,Complex stress state,简单应力状态,复杂应力状态,For the simple state of stress,Strength criteria,Why we can determine the point is in safety or not by the strength criteria shown before ,The most important thing is that
8、 there is only one stress on the surface of element ! The strength of point A is decided just only by one stress parameter or , and its limit value can be easily determined by tension test . So for the simple state of stress we can get the strength criteria of materials at one point very easy,对简单应力状
9、态来说 , 其单元体的微分面上只有一个应力 , 也即该点的强度控制参数只有唯一的一个 , 所以可以很容易根据实验建立起其强度准则来,For the complex stress state,When,Perhaps point A is not in safety,How to determine the safety of the point ,对处于复杂应力状态的点来说 , 不能应用前述简单应力状态的强度条件判别其安全性,called equivalent stress,How to determine the function ,称为等效应力,Because there are thre
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- 定律 强度 理论 311
