Hwrk_1_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 #1 (due Feb. 4, 2008) 1. Problem (5 points) 1 2 3 4 5 67 1 2 3 4 5 6 7 10 11 8 9 8 8 8 4 4 8 4 10 15 You are asked to determine the internal forces and support reactions for the truss in the figure. To do so, proceed as follows: 1. Set up the equilibrium equations at all free degrees of freedom (dof's). There should be as many equilibrium equations as unknown basic element forces. Write the equations down in the form = ff B PQ , where f P is the applied force vector, f B is the equilibrium matrix for the free dof's and Q is the basic element force vector. 2. Use Mathcad or Matlab to solve for the unknown basic element forces Q by solving the linear system of equations. 3. Use the equilibrium equations at the restrained dof's to determine the support reactions R . 4. Make a clear sketch of the free body of the entire structural model and check global equilibrium.
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Homework 1 CE 121 - Advanced Structural Analysis Filip C. Filippou Homework 1, Problem 1 Numbering of global degrees of freedom 1 2 3 4 5 6 7 1 2 3 4 5 6 7 10 11 8 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Length of inclined elements L 5 4 2 8 2 + := L 5 8.944 = L 6 4 2 8 2 + := L 6 8.944 = L 8 4 2 8 2 + := L 8 8.944 = L 9 4 2 8 2 + := L 9 8.944 = L 10 12 2 12 2 + := L 10 16.971 = L 11 12 2 12 2 + := L 11 16.971 = Page 1
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Homework 1 CE 121 - Advanced Structural Analysis Filip C. Filippou 1. Equilibrium matrix for free dof's Equation for dof 1 B f 11 , 1 := B f 12 , 1 := B f 18 , 8 L 8 := B f 19 , 8 L 9 := Equation for dof 2 B f 28 , 4 L 8 := B f 29 , 4 L 9 := Equation for dof 3 B f 32 , 1 := B f 310 , 12 L 10 := Equation for dof 4 B f 45 , 4 L 5 := B f 48 , 8 L 8 :=
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This note was uploaded on 01/04/2010 for the course CE 121 taught by Professor Filippou during the Fall '09 term at University of California, Berkeley.

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Hwrk_1_Solution - UNIVERSITY OF CALIFORNIA, BERKELEY Spring...

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