**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 comple-mentary 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 Euler-Bernoulli 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 x-2 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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- Fall '04
- Klug
- Energy, Kinetic Energy, Potential Energy, Strain, strain energy, Castigliano, complementary strain energy