prob_03_11_11

prob_03_11_11 - Problem 3.11-11 Given A bar of length L T...

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Problem 3.11-11 Given: A bar of length L T carries linearly varying axial load. Consider FE models having one, two, and three elements. Find: a) Consistant Nodal Loads b) Solve for displacements and compute element stresses. Solution: a) r e 0 L x N T q d = qN 1 q 1 N 2 q 2 + = r e 0 L x Lx L x L L x L d q 1 q 2 = 0 L x () 2 L 2 L 2 x L 2 x x 2 L 2 d q 1 q 2 = L 6 2 1 1 2 q 1 q 2 = where: 0 L x 2 L 2 d L 3 0 L x L 2 x d L 6 0 L x x 2 L 2 d L 3 1 2 cL T 2 /3 cL T 2 /6 For one element, L = L T q 1 cL T = q 2 0 = r e1 L T 6 2 1 1 2 T 0 = c L T 2 6 2 1 = 1 2 5cL 2 /6 cL 2 /6 3 4cL 2 /6 2cL 2 /6 For two elements, L = L T /2 q 1 T = q 2 T 2 = q 3 0 = r e1 L T 2 6 2 1 1 2 T T 2 = c L T 2 24 5 4 = c L 2 6 5 4 = r e2 L T 2 6 2 1 1 2 T 2 0 = c L T 2 12 1 1 2 = c L 2 6 2 1 = R 2 6 5 6 1 =

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1 2 8cL 2 /6 cL 2 /6 4 7cL 2 /6 5cL 2 /6 3 4cL 2 /6 2cL 2 /6 For three elements, L = L T /3 q 1 cL T = q 2 2c L T 3 = q 3 T
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prob_03_11_11 - Problem 3.11-11 Given A bar of length L T...

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