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211_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 211_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 205 205 SECTION 2.7 Strain Energy Solution 2.7-8 Rigid bar supported by springs (c) FORCES IN THE SPRINGS F1 F3 3W F2 10 3kd kd W 10 3k k2 1.5k k3 k W ; ; 600 N k U 5kd2 kd2 Eq. (2-38b) 2 (a) STRAIN ENERGY U OF ALL SPRINGS 2a 2 3kd 1.5kd kd b + 2a b+ 2 2 2 W 10k 8.0 mm F1 3W 10 180 N F2 3W 20 90 N F3 W 10 2 5kd2 ; Work done by the weight W equals Wd 2 Strain energy of the springs equals 5k 5kd2 and d W 10k 2 ; NOTE: W Problem 2.7-9 A slightly tapered bar AB of rectangular cross section and length L is acted upon by a force P (see figure). The width of the bar varies uniformly from b2 at end A to b1 at end B. The thickness t is constant. (a) Determine the strain energy U of the bar. (b) Determine the elongation of the bar by equating the strain energy to the work done by the force P. 60 N 2F1 7500 N/mm W2 20k ; 2.4 J d (b) DISPLACEMENT Wd 2 W2 b 10k 2.4 N # m For a spring: U 2 7.5 N/mm 5k a downward displacement of rigid bar ... 3W 20 (d) NUMERICAL VALUES k1 U 1.5kd ; ; ; ; 2F2 F3 A 600 N (Check) B b2 L b1 P ...
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