02-06ChapGere.0015

02-06ChapGere.0015 - W W W 5 Weight Properties of elastic...

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Problem 2.8-14 A rigid bar AB having mass M 5 1.0 kg and length L 5 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 5 30 mm 2 , length b 5 0.25 m, and modulus of elasticity E 5 2.1 GPa. If the bar is raised to its maximum height and then released, what is the maximum stress in the cord? Problem 2.8-13 A weight W rests on top of a wall and is attached to one end of a very flexible cord having cross-sectional area A and modulus of elasticity E (see figure). The other end of the cord is attached securely to the wall. The weight is then pushed off the wall and falls freely the full length of the cord. (a) Derive a formula for the impact factor. (b) Evaluate the impact factor if the weight, when hanging statically, elongates the band by 2.5% of its original length. Solution 2.8-13 Weight falling off a wall 158 CHAPTER 2 Axially Loaded Members
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Unformatted text preview: W W W 5 Weight Properties of elastic cord: E 5 modulus of elasticity A 5 cross-sectional area L 5 original length d max 5 elongation of elastic cord P.E. 5 potential energy of weight before fall (with respect to lowest position) P.E. 5 W ( L 1 d max ) Let U 5 strain energy of cord at lowest position U 5 EA d max 2 2 L C ONSERVATION OF ENERGY S OLVE QUADRATIC EQUATION FOR d max : S TATIC ELONGATION I MPACT FACTOR N UMERICAL VALUES d st 5 (2.5%)( L ) 5 0.025 L Impact factor 5 1 1 [1 1 2(40)] 1 / 2 5 10 d st 5 WL EA Ê W EA 5 0.025 Ê EA W 5 40 d max d st 5 1 1 B 1 1 2 EA W R 1 / 2 d st 5 WL EA d max 5 WL EA 1 B¢ WL EA ≤ 2 1 2 L ¢ WL EA ≤R 1 / 2 or d max 2 2 2 WL EA d max 2 2 WL 2 EA 5 P . E . 5 U Ê W ( L 1 d max ) 5 EA d max 2 2 L A B C W b L A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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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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