Hwrk_14_Solution

Hwrk_14_Solution - UNIVERSITY OF CALIFORNIA, BERKELEY...

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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 #14 (due May 9, 2008) 1. Problem (2 points) For the structure in the figure, which is the same as the second problem of the last homework, set up the initial force vector 0 P for two separate load cases: (a) uniformly distributed element load of 5 units in element c, as shown in the figure (b) thermal curvature 3 0 210 κ =⋅ in the girder, i.e. in elements b and c. For this question assume that the flexural stiffness of the girder is 50,000 g EI = units. 4 4 6 1 3 2 4 EI EA EI w=5 EI a b c c g g
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CE121 - Advanced Structural Analysis Homework 14 Filip C. Filippou Problem 1 4 4 6 1 3 2 4 EI EA EI EI a b c c g g note that EI a EI g = EI b EI g = EI c EI g = w5 := L c 4 := Restrain all global dofs and determine restraint moments and dependent forces. 4 4 6 w=5 2 8 c wL 8 c wL 2 c wL 2 c wL equilibrium tranverse forces restraint moments and corresponding transverse forces P 0 0 0 wL c 2 c 8 + c 2 8 := P 0 0 0 12.5 10 = note that these are the forces on the right hand side of the equilibrium equations according to PK U P 0 + = to solve for the free dof displacements we move them first to the left hand side and then solve PP 0 KU = Page 14-1
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CE121 - Advanced Structural Analysis Homework 14 Filip C. Filippou for thermal heating of elements b and c we have EI 50000 := 4 4 6 0 1.5 EI κ 0 1.5 c
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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 Berkeley.

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Hwrk_14_Solution - UNIVERSITY OF CALIFORNIA, BERKELEY...

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