215_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

215_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.7.qxd 9/25/08 11:42 AM Page 209 209 SECTION 2.7 Strain Energy (c) STRAIN ENERGY U1 IS NOT EQUAL TO Pd 1 P1(2 s) P1s 2 2 (This quantity is greater than U1.) For d U1 2s: Pd 2 Pd area under a straight line from O to B, which 2 is larger than U1. Pd Thus, is not equal to the strain energy because 2 the force-displacement relation is not linear. 2(k1 + k2)s2 area under line OAB. Problem 2.7-12 A bungee cord that behaves linearly elastically has an unstressed length L0 760 mm and a stiffness k 140 N/m.The cord is attached to two pegs, distance b 380 mm apart, and pulled at its midpoint by a force P 80 N (see figure). A b B (a) How much strain energy U is stored in the cord? (b) What is the displacement C of the point where the load is applied? (c) Compare the strain energy U with the quantity P C/2. (Note: The elongation of the cord is not small compared to its original length.) C P Solution 2.7-12 Bungee cord subjected to a load P. DIMENSIONS BEFORE THE LOAD P IS APPLIED 1 2L2 0 2 From triangle ACD: d b2 329.09 mm DIMENSIONS AFTER THE LOAD P IS APPLIED L0 b 760 mm L0 2 380 mm 380 mm Let x k 140 N/m Let L1 distance CD stretched length of bungee cord (1) ...
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