902_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

902_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Problem 11.9-11 Determine the maximum permissible length L max for a steel pipe column that is fixed at the base and free at the top and must support an axial load P ± 40 k (see figure). The column has outside diameter d ± 4.0 in. wall thickness t ± 0.226 in., E ± 29,000 ksi, and . s Y ± 42 ksi 896 CHAPTER 11 Columns Solution 11.9-11 Steel pipe column Fixed-free column Use AISC formulas. L c ± 116.7 r K ± 78.03 in. ± 6.502 ft Eq. (11-76): a KL r b c ± A 2 p 2 E s Y ± 116.7 E ± 29,000 ksi s Y ± 42 ksi r ± A I A ± 1.3367 a KL r b max ± 200 I ± p 64 ( d 2 4 ² d 1 4 ) ± 4.7877 in. 4 A ± p 4 ( d 2 2 ² d 1 2 ) ± 2.6795 in. d 2 ± 4.0 in. t ± 0.226 in. d 1 ± 3.548 in. ( K ± 2). P ± 40 k 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). L 7 L c L 6 L c P allow ± P L (ft) 5.20 5.25 5.90 KL/r 93.86 94.26 93.90 n 1 (Eq. 11-79) 1.903 1.904 1.903 n 2 (Eq. 11-80) - - - (Eq. 11-81) s allow / s Y 0.3575 0.3541 0.3555 (Eq. 11-82) s
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Unformatted text preview: allow / s Y---s allow (ksi) 15.02 14.87 14.93 P allow A s allow 40.2 k 39.8 k 40.0 k Solution 11.9-10 Steel pipe column Fixed-free column ( ). Use AISC formulas. E 200 GPa s Y 250 MPa r A I A 47.09 mm a KL r b max 200 I p 64 ( d 2 4 d 1 4 ) 6.4851 * 10 6 mm 4 A p 4 ( d 2 2 d 1 2 ) 2924.8 mm 2 d 2 140 mm t 7.0 mm d 1 126 mm K 2 L c 125.7 r K 2959 mm 2.959 m Eq. (11-76): a KL r b c A 2 p 2 E s Y 125.7 L 2.6 m 2.8 m 3.0 m 3.2 m KL/r 110.4 118.9 127.4 135.9 n 1 (Eq. 11-79) 1.911 1.916--n 2 (Eq. 11-80)--1.917 1.917 (Eq. 11-81) s allow / s Y 0.3212 0.2882--(Eq. 11-82) s allow / s Y--0.2537 0.2230 s allow (MPa) 80.29 72.06 63.43 55.75 P allow A s allow 235 kN 211 kN 186 kN 163 kN For P 40 k, L max 5.23 ft ; 11Ch11.qxd 9/27/08 2:27 PM Page 896...
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