905_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

905_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 11.9 Design Formulas for Columns 899 Problem 11.9-15 A W 8 ± 28 steel wide-flange column with pinned ends carries an axial load P . What is the maximum permissible length L max of the column if (a) P ² 50 k, and (b) P ² 100 k? (Assume E ² 29,000 ksi and .) s Y ² 36 ksi Solution 11.9-15 Steel wide-flange column Pinned ends ( K ² 1). Buckling about axis 2-2 (see Table E-1a). Use AISC formulas. For each load P , select trial values of the length L and calculate the corresponding values of P allow (see table). Interpolate between the trial values to obtain the value of L that produces . Note: If , use Eqs. (11-79) and (11-81). If , use Eqs. (11-80) and (11-82). (a) P ² 50 k L 7 L c L 6 L c P allow ² P L c ² 126.1 r ² 204.3 in. ² 17.0 ft Eq.(11-76): a L r b c ² A 2 p 2 E s Y ² 126.1 E ² 29,000 ksi s Y ² 36 ksi a L r b max ² 200 W 8 * 28
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Unformatted text preview: A 8.25 in. 2 r 2 1.62 in. L (ft) 14.3 14.4 14.5 L/r 105.9 106.7 107.4 n 1 (Eq. 11-79) 1.908 1.908 1.909 n 2 (Eq. 11-80)---(Eq. 11-81) s allow / s Y 0.3393 0.3366 0.3338 (Eq. 11-82) s allow / s Y---s allow (ksi) 12.21 12.12 12.02 P allow A s allow 100.8 k 100.0 k 99.2 k L (ft) 21.0 21.5 21.2 L/r 155.6 159.3 157.0 n 1 (Eq. 11-79)---n 2 (Eq. 11-80) 1.917 1.917 1.917 (Eq. 11-81) s allow / s Y---(Eq. 11-82) s allow / s Y 0.1714 0.1635 0.1682 s allow (ksi) 6.171 5.888 6.056 P allow A s allow 50.9 k 48.6 k 50.0 k (b) P 100 k For P 50 k, L max 21.2 ft ; For P 100 k, L max 14.4 ft ; Probs. 11.9-15 and 11.9-16 11Ch11.qxd 9/27/08 2:27 PM Page 899...
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