山东建筑大学2009—度弹性力学考试试题及答案

1、山东建筑大学试卷答案 共 3 页 第 1 页班级 姓名 学号 装订线 2009 至 2010 学年第 一 学期 课程名称 弹性力学 （本）试卷专业： 土木工程 ； 考试形式：开卷 考试时间 120 分钟题号1234总分分数1. Determine the stress boundary conditions for the column shown in the figure, where M is the bending moment on the unit width. (25 points).Solution: (1) left face: (2) right face: （3）uppe

2、r face： ( 5 points for each boundary equation) 2. Determine whether , where is a positive constant, is a possible stress function. If it is, derive formulas for the corresponding stress components, and draw the surface forces on the boundaries of the rectangular plate shown in the figure. Body force

3、s are zero. (25 points) Solution：(a) Substitution into equation , the left side is This show is a possible stress funtion. (9 points) (b)The corresponding stress components are (8 points)(c)Surface forces on the boundaries are(8 points)装订线山东建筑大学试卷 共 3 页 第 2 页 3. A cantilever, with length l and depth

4、 h as well as unit width, is subjected to the concentrated load p at left face as shown in the figure. Neglecting body forces, find the stress components. (25 points)Hint:Take as stress function.(5 points)Solution1.Show that the stress function satisfies the compatibility equation.2. The correspondi

5、ng stress components are (5 points)3.The stress boundary conditions on the upper and lower faces are On the left boundary, we haveWe get(5 points)(5 points)(5 points)Finally4. A circular ring has a unit thickness perpendicular to its plane. Its inner boundary (r=a) is fixed. Its outer boundary (r=b)

6、 is subjected to a uniform shearing stress directed in the clockwise sense as shown in the figure. Taking as stress function , where is the angular coordinate and C is an arbitrary constant, find the stress components and displacement components in the circular ring. (25 points)Solution(5 points)1.

7、Show that the stress function satisfies the compatibility equation.(5 points)2. The corresponding stress components are3. The boundary conditions are(5 points)then4. The stresses are5. From physical equation, we haveFrom geometrical equation, we getBy integration, then(5 points)山东建筑大学试卷 共 3 页 第 3 页Using boundary condition at r=a, that is ThenSo Substitution into the third of geometr