917_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

917_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 11.9 Aluminum Columns 911 Solution 11.9-35 Wood column(square cross section) (a) M AXIMUM LENGTH L max FOR b d 3.5 in. From Eq. (11-92): From Eq. (11-95): Trial and error: From Eq. (11-94): (21.23)(3.5 in.) 74.3 in. ; L max 21.23 d L d A K cE E f F c 21.23 f 1.1094 C P 0.72562 1 + f 1.6 A c 1 + f 1.6 d 2 f 0.8 C P P F c b 2 0.72562 K cE 0.3 P 8.0 k F c 900 psi E 1,500,000 psi c 0.8 (b) M INIMUM DIMENSION b min FOR L 10 ft Trial and error. Given load: 8000 lb P P F c C P b 2 C P 1 + f 1.6 A c 1 + f 1.6 d 2 f 0.8 L d L b f K cE E F c ( L / d ) 2 Trial (mm) (kN) 180 22.22 0.69429 0.55547 189.0 182 21.98 0.70980 0.56394 196.1 183 21.86 0.71762 0.56814 199.8 184 21.74 0.72549 0.57231 203.5 b min 184 mm ; P C P f L d L b b (b) M INIMUM DIMENSION b min FOR L 4.0 m Trial and error: Given load: P 200 kN P F c C P b 2 C P 1 + f 1.6 A c 1 + f 1.6 d 2 f 0.8 L d L b f K cE E F c ( L / d ) 2 Problem 11.9-35 A square wood column with side dimensions
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Unformatted text preview: b (see figure) is constructed of a structural grade of spruce for which F c ± 900 psi and E ± 1,500,000 psi. An axial force P ± 8.0 k acts on the column. (a) If the dimension b ± 3.5 in., what is the maximum allowable length L max of the column? (b) If the length L ± 10 ft, what is the minimum required dimension b min ? Trial (in.) (lb) 4.00 30.00 0.55556 0.47145 6789 4.20 28.57 0.61250 0.50775 8061 4.19 28.64 0.60959 0.50596 7994 ‹ b min ± 4.20 in. ; P C P f L d ± L b b 11Ch11.qxd 9/27/08 2:27 PM Page 911...
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