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451_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 451_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 05Ch05.qxd 9/25/08 2:29 PM Page 445 445 SECTION 5.8 Shear Stresses in Rectangular Beams Problem 5.8-5 A steel beam of length L 16 in. and crosssectional dimensions b 0.6 in. and h 2 in. (see figure) supports a uniform load of intensity q 240 lb/in., which includes the weight of the beam. Calculate the shear stresses in the beam (at the cross section of maximum shear force) at points located 1/4 in., 1/2 in., 3/4 in., and 1 in. from the top surface of the beam. From these calculations, plot a graph showing the distribution of shear stresses from top to bottom of the beam. q = 240 lb/in. h = 2 in. b = 0.6 in. L = 16 in. Solution 5.8-5 Shear stresses in a simple beam y1 (in.) t (psi) 0 1.00 0 0.25 0.75 1050 0.50 0.50 1800 0.75 0.25 2250 0 2400 Distance from the top surface (in.) V h2 a 2I 4 y2 b 1 1920 lb I bh3 12 Eq. (5-39): t V qL 2 1.00 (N.A.) 0.4 in.4 GRAPH OF SHEAR STRESS t UNITS: POUNDS AND INCHES t 1920 (2)2 c 2(0.4) 4 (t psi; y1 y2 1 (2400)(1 y2) d 1 in.) Problem 5.8-6 A beam of rectangular cross section (width b and height h) supports a uniformly distributed load along its entire length L. The allowable stresses in bending and shear are sallow and tallow, respectively. (a) If the beam is simply supported, what is the span length L0 below which the shear stress governs the allowable load and above which the bending stress governs? (b) If the beam is supported as a cantilever, what is the length L0 below which the shear stress governs the allowable load and above which the bending stress governs? ...
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