396_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

396_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 05Ch05.qxd 9/24/08 390 4:59 AM Page 390 CHAPTER 5 Stresses in Beams (Basic Topics) Problem 5.4-3 A 4.5 in. outside diameter polyethylene pipe designed to carry chemical wastes is placed in a trench and bent around a quarter-circular 90° bend (see figure). The bent section of the pipe is 46 ft long. Determine the maximum compressive strain âmax in the pipe. Solution 5.4-3 90° Polyethylene pipe Angle equals 90° or p/2 radians, L length of 90° bend L 46 ft d r r r L p/2 4.5 in. 2pr 4 L 552 in. pr 2 radius of curvature 2L p pd 4L âmax y r âmax d/2 2L/p p 4.5 in. a b 4 552 in. Problem 5.4-4 A cantilever beam AB is loaded by a couple M0 at its free end (see figure.) The length of the beam is L 1.5 m and the longitudinal normal strain at the top surface is 0.001. The distance from the top surface of the beam to the neutral surface is 75 mm. Calculate the radius of curvature r, the curvature k, and the vertical deflection d at the end of the beam. 6400 * 10 6 ; d A B M0 L Solution 5.4-4 Deflection: constant curvature for pure bending so gives a circular arc; assume flat deflection curve (small defl.) so BC L NUMERICAL DATA âmax L 2.0 m c 82.5 mm 0.0012 RADIUS OF CURVATURE c r r 68.8 m âmax sin(u) 1 r k 1.455 * 10 u L asin a b r ; u CURVATURE k L r 5 m 1 ; 0.029 radians 1 cos(u) d r (1 L r 4.232 * 10 cos(u)) d 0.029 4 r 29.1 mm 6.875 * 104 mm ; ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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