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HW10sol

# HW10sol - CE121 Advanced Structural Analysis Homework 10...

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CE121 - Advanced Structural Analysis Homework 1 0 Filip C. Filippou Problem 1 100 20 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. 20 20 40 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 1 0 -1

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CE121 - Advanced Structural Analysis Homework 1 0 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 L 2 3 c EI L dof 1 dof 2 dof 3 K 11 4EI L a 4 EI L b + := K 21 6EI L b 2 := K 31 2EI L b := K 12 6EI L b 2 := K 22 12EI L b 3 3EI L c 3 + := K 32 6EI L b 2 3EI L c 2 + := K 13 2 EI L b := K 23 6EI L b 2 3EI L c 2 + := K 33 4EI L b 3EI L c + := thus, the stiffness matrix is K K 11 K 21 K 31 K 12 K 22 K 32 K 13 K 23 K 33 := K 90 4.5 30 4.5 0.56 2.25 30 2.25 105
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HW10sol - CE121 Advanced Structural Analysis Homework 10...

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