第七章 应力状态与应变状态分析.pptVIP

§7–１ CONCEPTS OF THE STAFE OF STRISS §7–１ 应力状态的概念 用纵截面将容器截开，取长为L的一部分为研究对象，受力如图c所示 2、环向应力：(hoop stress) 3、求内压（以应力应变关系求之） ?t ?m 外表面 y p s t s t D q dq z 图c O §7－8 STRAIN-ENERGY DENSITY OF COMPLEX STRESSED STATE ?2 ?3 ? 1 Fig. a Fig. c ?3 -?m ? 1 -?m ?2 -?m ?m Fig. b ?m ?m §7－8 复杂应力状态下的变形比能 ?2 ?3 ? 1 图 a 图 c ?3 -?m ? 1 -?m ?2 -?m ?m 图 b ?m ?m Where ux is called the strain-energy density corresponding to the distortion. Fig. c ?3 -?m ? 1 -?m ?2 -?m Strain energy of the element shown in Fig.c is 称为形状改变比能或歪形能。 图 c ?3 -?m ? 1 -?m ?2 -?m Example 9 Prove the relations between three elastic constants by the energy method. ?Specific strain energy of the element in pure shear is： ? Expression of the specific strain energy of the element in pure shear by principal stresses is： txy A ?1 ?3 [例9] 用能量法证明三个弹性常数间的关系。 ?纯剪单元体的比能为： ?纯剪单元体比能的主应力表示为： txy A ?1 ?3 Chapter 7 Exercises As shown in the figure, a certain point is in biaxial stress. Try to determine when the two principal stresses are both tensile stresses. Solution: 第七章 练习题 一、某点应力状态为图示二向应力状态。试求该点的两个主应力均为拉应力时 的取值范围。 解: 2. The stress state of an element is shown in the figure. Knowing E andμof the material. Try to determine the maximum shearing strain of this element. Solution: 二、图示单元体的应力状态,已知材料的E和μ, 试求该单元体的最大剪应变 。 解: 3. The stresses on sections ac and bc at a certain point of a force-acting member are shown in the figure. Try to determine the magnitude and the directions of the stresses on section ab by the stress circle and plot them on an element. 三、受力构件某点处两截面ac和bc上的应力如图所示,试利用应力圆确定ab面上应力的大小和方向，并画在单元体上。 D D3 E E3 ? x y O a b c d a A O B 2)、Plot the strain circle according to strain( )of a