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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
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:
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
b From Appendix C: sin 2
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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- Fall '11