Hwrk_13_Solution

# Hwrk_13_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 #13 (due May 2, 2008) 1. Problem (7 points) The two span continuous beam in the figure is subjected to a concentrated force of 100 units at midspan of the right span, as shown. The flexural section stiffness of all members is EI = 300,000. It is obvious from the absence of axial forces, that axial deformations are irrelevant for the solution. 1. Use the displacement method to solve for the basic element forces. 2. Draw the bending moment diagram. 3. Determine the support reactions and check global equilibrium. 4. Draw the deformed shape under the given loading. 100 20 20 1 2 3 4 40 5. Use the displacement method of analysis to solve for the case of a uniform distributed load of 5 units of force per unit of length acting over the right span of the beam. 40 40 5

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CE121 - Advanced Structural Analysis Homework 13 Filip C. Filippou Problem 1 100 20 1 2 3 4 40 L a 40 := L b 20 := L c 20 := EI 300000 := There are 3 free dofs, and 5 basic forces, as shown in the following figure. 1 2 3 Q 1 Q 2 Q 3 Q 4 Q 5 the equilibrium equations are P 1 Q 2 Q 3 + = P 2 Q 3 Q 4 + 20 Q 5 20 + = P 3 Q 4 Q 5 + = Page 13-1
CE121 - Advanced Structural Analysis Homework 13 Filip C. Filippou for the displacement method of analysis we need to set up the stiffness matrix at the free dofs 4 b EI L 2 b EI L 4 b EI L 2 b EI L 3 c EI L 4 a EI L 2 a EI L 2 6 b EI L 2 6 b EI L 2 6 b EI L 2 6 b EI L 2 3 c EI L 2 3 c EI L 3 12 b EI L 3 12 b EI L 2 6 b EI L 2 6 b EI

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Hwrk_13_Solution - UNIVERSITY OF CALIFORNIA BERKELEY Spring...

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