Hwrk_7_Solution

Hwrk_7_Solution - CE 121 - Advanced Structural Analysis...

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CE 121 - Advanced Structural Analysis Homework 7 Filip C. Filippou Problem 1 Set up the compatibility relations between element deformation and free global degree-of- freedom displacements in the form ff = VAU . Show that the compatibility matrix f A is equal to the transpose of the equilibrium matrix f B from the last homework set. 4 4 3 3 a b c d e 1 2 3 4 Assume now that elements b and c are delivered longer than shown in the above figure: element b by 0.1 and element c by 0.2 units of length. Elements a and e are delivered with the required length. What should be the length of member d so as to avoid stresses due to restraint? Suppose that you were given all element lengths and corresponding deformation values from the start. Show that they are compatible by using the relation T x 0 = BV (good for hand calculations). Page 1
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CE 121 - Advanced Structural Analysis Homework 7 Filip C. Filippou 4 4 3 3 a b c d e 1 2 3 4 Geometric information L a 5 := L b 5 := L c 4 2 6 2 + := L d 3 := L e L c := Page 2
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CE 121 - Advanced Structural Analysis Homework 7 Filip C. Filippou The structure has four free independent dofs. These are shown in the following figure 4 4 3 3 1 2 3 4 We impose a unit value at each free dof in turn and write down the change in distance between nodes. The resulting matrix is known as structure compatibility matrix A f . Page 3
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CE 121 - Advanced Structural Analysis Homework 7 Filip C. Filippou The compatibility matrix becomes column corresponds to degree of freedom 2 (unit global dof displacement) row corresponds to change of length between nodes 1 and 3 row corresponds to change of length between nodes 2 and 3 A f 4 L a 4 L b 0 0 0 3 L a 3 L b 0 1 0 0 0 4 L c 0 4 L e 0 0 6 L c 1 6 L e
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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_7_Solution - CE 121 - Advanced Structural Analysis...

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