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 max in the pipe. Solution 5.4-3 Polyethylene pipe 286 CHAPTER 5 Stresses in Beams (Basic Topics) 90 ° Angle equals 90º or /2 radians, r radius of curvature e max d 4 L 4 ¢ 4.5 in. 552 in. 6400 10 6 r L 2 2 L e max y r d 2 2 L r 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 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.
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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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