229_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

229_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.8-2.12.qxd 9/25/08 11:44 AM Page 223 223 SECTION 2.8 Impact Loading Problem 2.8-14 A rigid bar AB having mass M 1.0 kg and length L 0.5 m is hinged at end A and supported at end B by a nylon cord BC (see figure). The cord has cross-sectional area A 30 mm2, length b 0.25 m, and modulus of elasticity E 2.1 GPa. If the bar is raised to its maximum height and then released, what is the maximum stress in the cord? C b A B W L Solution 2.8-14 Falling bar AB GEOMETRY OF BAR AB AND CORD BC CD CB b AD AB L RIGID BAR: W Mg (1.0 kg)(9.81 m/s2) h height of center of gravity of raised bar AD 9.81 N L max 0.5 m elongation of cord From triangle ABC:sin u NYLON CORD: A b 0.25 m E cos u 30 mm2 2.1 GPa Find maximum stress From line AD: sin 2 u max in cord BC. 2b + L bL2 2b2 + L2 2h 2h AD L b From Appendix C: sin 2 ‹ 2h L and h 2a b 2 b2 + L2 2 2b2 + L2 L 2b + L 2 sin ba cos L 2 (Eq. 1) 2 b 2bL 2 b + L2 ...
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