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Unformatted text preview: Problem 3 (a) Derive the complementary strain energy for a linearly elastic Timoshenko beam. (b) Consider a cantilever beam with a vertical point load applied at its free end. Use the minimum complementary energy theorem (or equivalently, Castigliano’s Second Theorem) to find the deflection of the tip of the beam. How does this compare to the same quantity for an EulerBernoulli beam? Problem 4 Starting from the general expression for the complementary strain energy of a linear elastic body, W * = i B 1 2 σ ij e ij dV, show that for a Kirchhoff plate this takes the form W * = i Ω 1 2 [ M 2 x2 νM x M y + M 2 y + 2(1 + ν ) M 2 xy ] dS. Hint: make use of the generalized plane stress constitutive equations and the definitions of the Moment resultants as given in the handout on plates. 1...
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This note was uploaded on 03/06/2008 for the course MAE 261A taught by Professor Klug during the Fall '04 term at UCLA.
 Fall '04
 Klug
 Strain

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