9 - Strain energy expressions for a beam

9 - Strain energy expressions for a beam - Work and Energy...

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1 Work and Energy Principles – Strain energy and complementary strain energy (Beam) To calculate the strain energy, we use the same expressions for e z from before, substitute them into: Remember, 2 1 2 T z z z V U E E dV e e e     2 2 2 2 2 2 2 2 2 1 2 o o o o o o VV dw d v d u dw d v d u U E y x dV E T y x dV dz dz dz dz dz dz  22 2 2 2 2 2 2 2 2 2 2 2 2 2 0 1 2 2 2 2 o o o o o o o o o A L o o o A A A dw d v d u dw d v dw d u d v d u U E y x y x xy dAdz dz dz dz dz dz dz dz dz dz dw d v d u E TdA y TdA x TdA dz dz dz dz     T T T yx A A A P E TdA M E TxdA M E TydA 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 o o o o o o o A A A
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This note was uploaded on 05/19/2010 for the course MAE 472 taught by Professor Peters during the Spring '08 term at N.C. State.

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9 - Strain energy expressions for a beam - Work and Energy...

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