2. A prismatic bar AD with length L, area of its cross section A and modulus of
ID: 3146148 • Letter: 2
Question
2. A prismatic bar AD with length L, area of its cross section A and modulus of elasticity E, is subjected to loads 5P, 3P and P acting at points B, C and D respectively. Segments AB, BC and CD have length L / 6, L / 2 and L / 3, respectively. a) Obtain an expression for the strain energy U e the rod, as well as the strain energy density u. b) Calculate the magnitudes described in the previous section for the case where P = 12.5 kN, L = 2.5 m, and A = 8.56 plg2 and the material is aluminum with modulus of elasticity E = 10.4 x 106 psi (resistance I)
L-3 L-2 6 A 1Explanation / Answer
a)
U = 23 P^2 * L/ (12 E A)
derivation , go to following link
http://www.chegg.com/homework-help/mechanics-of-materials-8th-edition-chapter-2.7-problem-1p-solution-9781111577735?trackid=60170be9&strackid=2eda6b79&ii=1
b )
P = 12.5 k , L = 2.5 = 98.4252 inch , A = 8.56 E = 10.4 *10^6
U = 23 * 12.5^2 * 98.4252 10^6) /(12 * 10.4 *10^6 * 8.56)
=331.10506 in-lb {note that i am taking area = 8.56 in ^2 , don't know plg2 is , if not make suitable change)
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