549_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 549_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 6.9 Shear Centers of Thin-Walled Open Sections 543 Moment of inertia: I ± 109.295 in. 4 I ± 1 12 ( bh 3 2 ² bh 3 1 + t w h 3 1 ) Maximum shear stress in the web: t max ± 3446 psi ; t max ± V 8 It w ( bh 2 2 ² bh 2 1 + t w h 2 1 ) Problem 6.8-4 Solve the preceding problem for a W 200 ³ 41.7 shape with the following data: b ± 166 mm, h ± 205 mm, t w ± 7.24 mm, t f ± 11.8 mm, and V ± 38 kN. Solution 6.8-4 b ± 166 mm h ± 205 mm t w ± 7.24 mm t f ± 11.8 mm V ± 38 kN (a) C ALCULATIONS BASED ON CENTERLINE DIMENSIONS Moment of inertia: Maximum shear stress in the web: t max ± 27.04 MPa ; t max ± a bt f t w + h 4 b Vh 2 I z I z ± 46.357 * 10 6 mm 4 I z ± t w h 3 12 + bt f h 2 2 (b) C ALCULATIONS BASED ON MORE EXACT ANALYSIS h 2 ± h ´ t f h 2 ± 216.8 mm h 1 ± h ² t f h 1 ± 193.2 mm Moment of inertia: Maximum shear stress in the web: t max ± 27.02 MPa ; t max ± V 8 It w ( bh 2 2 ² bh 2 1 + t w h 2 1 ) I ± 45.556 * 10 6 mm 4 I ± 1 12 ( bh 3 2 ² bh 3 1 + t w h 3 1 ) Shear Centers of Thin-Walled Open Sections
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Unformatted text preview: When locating the shear centers in the problems for Section 6.9, assume that the cross sections are thin-walled and use centerline dimensions for all calculations and derivations. Problem 6.9-1 Calculate the distance e from the centerline of the web of a C 15 ³ 40 channel section to the shear center S (see figure). ( Note : For purposes of analysis, consider the flanges to be rectangles with thickness t f equal to the average flange thickness given in Table E-3a in Appendix E.) Probs. 6.9-1 and 6.9-2 z y C S e 06Ch06.qxd 9/24/08 5:59 AM Page 543...
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