450_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

450_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 05Ch05.qxd 9/25/08 444 2:29 PM Page 444 CHAPTER 5 Stresses in Beams (Basic Topics) Solution 5.8-3 L b 8 ft 4 in. t allow h 6 in. 200 psi A g 35 q g A weight of beam per unit distance q 5.833 qL M + L 2 V b#h lb 3V 2A tmax ft3 2 AL t 3 max M 1b ft 2 AL t 3 allow Mmax Maximum load Mmax qL 3M a+ b 2A L 2 Mmax ; 25.4 k-ft Problem 5.8-4 A cantilever beam of length L 2 m supports a load P 8.0 kN (see figure). The beam is made of wood with cross-sectional dimensions 120 mm * 200 mm. Calculate the shear stresses due to the load P at points located 25 mm, 75 mm, and 100 mm from the top surface of the beam. from these results, plot a graph showing the distribution of shear stresses from top to bottom of the beam. qL2 2 qL2 2 P = 8.0 kN 200 mm L=2m 120 mm Solution 5.8-4 Shear stresses in a cantilever beam Distance from the top surface (mm) y1 (mm) t (MPa) 0 Vh a 2I 4 V P 8.0 kN I h 200 mm (y1 t (200)2 4 2(80 * 106) t 50 * 10 6 mm) c 6 (10,000 50 0.375 375 25 0.469 469 0 0.500 500 GRAPH OF SHEAR STRESS t 4 80 * 10 mm 8,000 219 100 (N.A.) 8,000 N bh3 12 0.219 75 y2 b 1 75 50 Eq. (5-39): t 100 25 2 y2 d 1 (t y2) (y1 1 N/mm2 mm; t MPa) MPa) 0 t (kPa) 0 ...
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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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