05-01ChapGere.0002

05-01ChapGere.0002 - k and the vertical deflection d at the...

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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 e max in the pipe. Solution 5.4-3 Polyethylene pipe 286 CHAPTER 5 Stresses in Beams (Basic Topics) 90 ° Angle equals 90º or p /2 radians, r 5 r 5 radius of curvature e max 5 p d 4 L 5 p 4 ¢ 4.5 in. 552 in. 5 6400 3 10 2 6 r 5 L p / 2 5 2 L p Ê e max 5 y r 5 d / 2 2 L / p r 5 radius r d L Problem 5.4-4 A cantilever beam AB is loaded by a couple M 0 at its free end (see figure). The length of the beam is L 5 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
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Unformatted text preview: k , and the vertical deflection d at the end of the beam. Solution 5.4-4 Cantilever beam A B M d L L 5 length of beam L 5 1.5 m « max 5 0.001 k 5 1 r 5 0.01333 m 2 1 ∴ r 5 y e max 5 75 mm 0.001 5 75 m y 5 75 mm Ê e max 5 y r A C B M d L r r u ′ L 5 length of 90º bend L 5 46 ft 5 552 in. d 5 4.5 in. L 5 2 p r 4 5 p r 2 Assume that the deflection curve is nearly flat. Then the distance BC is the same as the length L of the beam. u 5 arcsin 0.02 5 0.02 rad d 5 r (1 2 cos u ) 5 (75 m)(1 2 cos (0.02 rad)) 5 15.0 mm N OTE : which confirms that the deflection curve is nearly flat. L d 5 100, ∴ sin u 5 L r 5 1.5 m 75 m 5 0.02 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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