m-虎克定律-强度理论m-克定律-强度理论m-虎克定律-强度理论m-虎克定律-强度理论.ppt

* 3. 广义虎克定律 Generalized Hooke’s law (1) 广义虎克定律 ( Generalized Hooke’s 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 Hooke’s law for the two-dimensional stress state For the plane 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 Hooke’s law for the plane stress state along the slope direction ) x y 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 . P A B Solve : b h Cross section Where is wrong ? P A B Solve : b h Cross section Suppose C is an abtrary point on the line AB , its state of stress can be shown in the follows figure . Acoording to the formula of , we can get : C x y Simple tension 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 Hook’s law , follows result can be attained . Because C is an abtrary point on the line AB , so the normal strain along the line AB is uniform . Acoorging to the difinition of normal strain we can get : The tension of line AB is : h = 600 b = 800 ?y = 40 ?x = 80 例 对如图均匀变形的板，求： ① 厚度的改变量； ② 板面积的改变量； ③ 体积的改变量。 板中各方向上的应变 h = 600 b = 800 ?y = 40 ?x = 80 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 Suppose point A is the most dangerous point in a structure , ordinarily bars were considered in Mechanics of Materials . For this point of the materials , its stress state perhaps is simple or complex stress state . Is it in safety or not ? How to determine its strength ? Question : A The