02-05ChapGere.0004

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Unformatted text preview: A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark SECTION 2.7 Strain Energy 137 Strain Energy When solving the problems for Section 2.7, assume that the material behaves linearly elastically. 5P Problem 2.7-1 A prismatic bar AD of length L, cross-sectional area A, and modulus of elasticity E is subjected to loads 5P, 3P, and P acting at points B, C, and D, respectively (see figure). Segments AB, BC, and CD have lengths L /6, L /2, and L /3, respectively. A 3P B P C L — 6 L — 2 D L — 3 (a) Obtain a formula for the strain energy U of the bar. (b) Calculate the strain energy if P 6 k, L 52 in., A 2.76 in.2, and the material is aluminum with E 10.4 106 psi. Solution 2.7-1 Bar with three loads 5P A B L — 6 P 52 in. E 10.4 A P C L — 2 6k L 3P 2.76 in.2 (a) STRAIN ENERGY OF THE BAR (EQ. 2-40) U 106 psi 3P NBC 2P NCD LENGTHS LAB L 6 N2Li i a 2E A 1 L B (3P ) 2 ¢ ≤ 2EA 6 i i P2L 23 ¢≤ 2EA 6 INTERNAL AXIAL FORCES NAB D L — 3 P ( 2P ) 2 ¢ 23P2L 12EA L ≤ 2 (b) SUBSTITUTE NUMERICAL VALUES: LBC L 2 LCD L 3 U 23(6 k ) 2 (52 in.) 12(10.4 106 psi)(2.76 in.2 ) 125 in.-lb (P)2 ¢ L ≤R 3 ...
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Tech.

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