Hwrk_10_Solution - UNIVERSITY OF CALIFORNIA, BERKELEY...

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Unformatted text preview: UNIVERSITY OF CALIFORNIA, BERKELEY Spring Semester 2008 Dept. of Civil and Environmental Engineering Instructor: Filip C. Filippou CE 121 – Advanced Structural Analysis Homework Set #10 (due April 11, 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 all elements. The axial stiffness of elements a and b is EA=10,000 units, the axial stiffness of element c is EA=20,000 units. The coefficient of −5 thermal expansion is α = 2 ⋅10 per unit of temperature change. Select the basic force in element b as redundant. For each load case separately 1. Set up the particular and the homogeneous solution of the equilibrium equations. 2. Determine the gap in element b due to the particular and the homogeneous solution. 3. Determine the value of the redundant basic force. 4. Determine the basic forces in all elements. 5. Determine the translations at the free dofs. 6. What happens to the answers in (4) and (5) if the axial stiffness of all elements is doubled. 30 a 50 b c 6 8 8 1 For the thermal expansion problem the basic forces are proportional to the axial stiffness and thus double when the axial stiffness is doubled. The deformations remain the same, since the mechanical strain does not change when the forces are doubled and the stiffness is doubled, while the non-mechanical strain is not affected. The global dof displacements remain the same since they depend on the deformations. ...
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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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