548_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

548_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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542 CHAPTER 6 Stresses in Beams (Advanced Topics) Solution 6.8-2 S IMPLE BEAM : L ± 3.5 m C ROSS SECTION : h ± 267 mm b ± 148 mm t f ± 13 mm t w ± 7.62 mm I z ± 80.667 * 10 6 mm 4 I z ± t w h 3 12 + bt f h 2 2 V ± | R ² qd | V ± 56.3 kN R ± qL 2 R ± 78.8 kN d ± 0.5 m q ± 45 kN/m (a) M AXIMUM SHEAR STRESS (b) S HEAR STRESS AT POINT B t B ± a b/2 ( t 1 ) t B ± 4.65 MPa ; t 1 ± bhV 4 I z t 1 ± 999.1 psi a ± 50 mm b /2 ± 74.0 mm t max ± 29.7 MPa ; t max ± a bt f t w + h 4 b Vh 2 I z Problem 6.8-3 A beam of wide-flange shape, W 8 ³ 28, has the cross section shown in the figure. The dimensions are b ± 6.54 in., h ± 8.06 in., t w ± 0.285 in., and t f ± 0.465 in. The loads on the beam produce a shear force V ± 7.5 k at the cross section under consideration. (a) Using centerline dimensions, calculate the maximum shear stress t max in the web of the beam. (b) Using the more exact analysis of Section 5.10 in Chapter 5, calculate
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Unformatted text preview: the maximum shear stress in the web of the beam and compare it with the stress obtained in part a. Probs. 6.8-3 and 6.8-4 b h z y C t f t f t w Solution 6.8-3 b 6.54 in. h 8.06 in. t w 0.285 in. t f 0.465 in. V 7.5 k (a) C ALCULATIONS BASED ON CENTERLINE DIMENSIONS Moment of inertia: I z 111.216 in. 4 I z t w h 3 12 + bt f h 2 2 Maximum shear stress in the web: (b) C ALCULATIONS BASED ON MORE EXACT ANALYSIS h 2 h t f h 2 8.5 in. h 1 h t f h 1 7.6 in. t max 3448 psi ; t max a bt f t w + h 4 b Vh 2 I z 06Ch06.qxd 9/24/08 5:59 AM Page 542...
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