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Hwrk_12_Solution

Hwrk_12_Solution - UNIVERSITY OF CALIFORNIA BERKELEY Spring...

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1 UNIVERSITY OF CALIFORNIA, BERKELEY Dept. of Civil and Environmental Engineering Spring Semester 2008 Instructor: Filip C. Filippou CE 121 – Advanced Structural Analysis Homework Set #12 (due April 25, 2008) 1. Problem (10 points) The truss structure in the figure is subjected to two load cases: (a) a horizontal force of 50 units with a concurrent vertical force of 30 units as shown, and (b) a thermal loading consisting of a temperature change of 100 degrees that affects only element c. The coefficient of thermal expansion is 5 2 10 α = per unit of temperature change. The truss elements have the following properties: elements a and b has axial section stiffness EA=10,000 units, while elements c and d have axial section stiffness EA=20,000 units. Use the displacement method of analysis for each load case separately to determine 1. The displacements (translations) at the free dofs of the structural model 2. The basic forces in all truss elements 3. The support reactions; use the support reactions to check global equilibrium. What happens to the basic forces of the truss elements if the section stiffness EA is doubled for all elements? What happens to the global dof displacements in this case? 50 30 a b c 8 8 6 d
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CE121 - Advanced Structural Analysis Homework 12 Filip C. Filippou Problem 1 50 30 a b c 8 8 6 d Element properties EA a 10000 := EA b EA a := EA c 20000 := EA d EA c := L a 8 := L c 6 := L b 10 := L d 10 := Compatibility relations: V 1 U 1 = V 2 0.8 U 1 0.6 U 2 + = thus, A f 1 0.8 0 0.8 0 0.6 1 0.6 := A f T 1 0 0.8 0.6 0 1 0.8 0.6 = V 3 U 2 = V 4 0.8 U 1 0.6 U 2 + = and the equilibrium equations are P 1 Q
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