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547_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

547_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 6.8 Shear Stresses in Wide-Flange Beams 541 Shear Stresses in Wide-Flange Beams When solving the problems for Section 6.8, assume the cross sections are thin-walled. Use centerline dimensions for all calculations and derivations, unless otherwise specified Problem 6.8-1 A simple beam of W 10 30 wide-flange cross section supports a uniform load of intensity q 3.0 k/ft on a span of length L 12 ft (see figure). The dimensions of the cross section are h 10.5 in., b 5.81 in., t f 0.510 in., and t w 0.300 in. (a) Calculate the maximum shear stress t max on cross section A–A located at distance d 2.5 ft from the end of the beam. (b) Calculate the shear stress t at point B on the cross section. Point B is located at a distance a 1.5 in. from the edge of the lower flange.
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Unformatted text preview: S IMPLE BEAM : L ² 12 ft C ROSS SECTION : h ² 10.5 in. b ² 5.81 in. t f ² 0.510 in. t w ² 0.30 in. I z ² t w h 3 12 + bt f h 2 2 I z ² 192.28 in. 4 V ² | R ³ qd | V ² 10.5 k R ² qL 2 R ² 18.0 k d ² 2.5 ft q ² 3.0 k/ft (a) M AXIMUM SHEAR STRESS (b) S HEAR STRESS AT POINT B t B ² a b 2 ( t 1 ) t B ² 430 psi ; t 1 ² bhV 4 I z t 1 ² 832.8 psi a ² 1.5 in. b 2 ² 2.9 in. t max ² 3584 psi ; t max ² a bt f t w + h 4 b Vh 2 I z A A L q d a z y C B t f t w h 2 — b 2 — b 2 — h 2 — Problem 6.8-2 Solve the preceding problem for a W 250 ± 44.8 wide-flange shape with the following data: L ² 3.5 m, q ² 45 kN/m, h ² 267 mm, b ² 148 mm, t f ² 13 mm, t w ² 7.62 mm, d ² 0.5 m, and a ² 50 mm. 06Ch06.qxd 9/24/08 5:59 AM Page 541...
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