11-04 Chap Gere - SECTION 11.9 Design Formulas for Columns...

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SECTION 11.9 Design Formulas for Columns 711 Problem 11.9-9 Determine the allowable axial load P allow for a steel pipe column that is fixed at the base and free at the top (see figure) for each of the following lengths: L 5 6 ft, 9 ft, 12 ft, and 15 ft. The column has outside diameter d 5 6.625 in. and wall thickness t 5 0.280 in. (Assume E 5 29,000 ksi and s Y 5 36 ksi.) Solution 11.9-9 Steel pipe column P L A A Section A - A t d Probs. 11.9-9 through 11.9-12 Fixed-free column ( K 5 2). Use AISC formulas. d 2 5 6.625 in. t 5 0.280 in. d 1 5 6.065 in. E 5 29,000 ksi s Y 5 36 ksi r 5 B I A 5 2.2455 ¢ KL r max 5 200 I 5 p 64 ( d 4 2 2 d 4 1 ) 5 28.142 in. 4 A 5 p 4 ( d 2 2 2 d 2 1 ) 5 5.5814 in. 2 Eq.(11-76): L c 55 141.6 in. 5 11.8 ft 126.1 r K ¢ KL r c 5 B 2 p 2 E s Y 5 126.1 L 6 ft 9 ft 12 ft 15 ft KL / r 64.13 96.19 128.3 160.3 n 1 (Eq. 11-79) 1.841 1.897 n 2 (Eq. 11-80) 1.917 1.917 s allow / s Y (Eq. 11-81) 0.4730 0.3737 s allow / s Y (Eq. 11-82) 0.2519 0.1614 s allow (ksi) 17.03 13.45 9.078 5.810 P allow 5 A s allow 95.0 k 75.1 k 50.7 k 32.4 k Problem 11.9-10 Determine the allowable axial load P allow for a steel pipe column that is fixed at the base and free at the top (see figure) for each of the following lengths: L 5 2.6 m, 2.8 m, 3.0 m, and 3.2 m. The column has outside diameter d 5 140 mm and wall thickness t 5 7 mm. (Assume E 5 200 GPa and s Y 5 250 MPa.) Solution 11.9-10 Steel pipe column Fixed-free column ( K 5 2). Use AISC formulas. d 2 5 140 mm t 5 7.0 mm d 1 5 126 mm E 5 200 GPa s Y 5 250 MPa r 5 B I A 5 47.09 mm ¢ KL r max 5 200 I 5 p 64 ( d 4 2 2 d 4 1 ) 5 6.4851 3 10 6 mm 4 A 5 p 4 ( d 2 2 2 d 2 1 ) 5 2924.8 mm 2 Eq. (11-76): L c 2959 mm 5 2.959 m 125.7 r K ¢ KL r c 5 B 2 p 2 E s Y 5 125.7 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 s allow / s Y (Eq. 11-81) 0.3212 0.2882 s allow / s Y (Eq. 11-82) 0.2537 0.2230 s allow (MPa) 80.29 72.06 63.43 55.75 P allow 5 A s allow 235 kN 211 kN 186 kN 163 kN
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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 5 40 k (see figure). The column has outside diameter d 5 4.0 in., wall thickness t 5 0.226 in., E 5 29,000 ksi, and s Y 5 42 ksi. Solution 11.9-11 Steel pipe column 712 CHAPTER 11 Columns Fixed-free column ( K 5 2). P 5 40 k Use AISC formulas. d 2 5 4.0 in. t 5 0.226 in. d 1 5 3.548 in. E 5 29,000 ksi s Y 5 42 ksi Eq. (11-76): L c 5 116.7 r K 5 78.03 in. 5 6.502 ft ¢ KL r c 5 B 2 p 2 E s Y 5 116.7 r 5 B I A 5 1.3367 ¢ KL r max 5 200 I 5 p 64 ( d 4 2 2 d 4 1 ) 5 4.7877 in. 4 A 5 p 4 ( d 2 2 2 d 2 1 ) 5 2.6795 in. 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 P allow 5 P . Note: If L , L c , use Eqs. (11-79) and (11-81). If L . L c , use Eqs. (11-80) and (11-82). For P 5 40 k, L max 5 5.23 ft L (ft) 5.20 5.25 5.23 KL / r 93.86 94.26 93.90 n 1 (Eq. 11-79) 1.903 1.904 1.903 n 2 (Eq. 11-80) s allow / s Y (Eq. 11-81) 0.3575 0.3541 0.3555 s allow / s Y (Eq. 11-82) s allow (ksi) 15.02 14.87 14.93 P allow 5 A s allow 40.2 k 39.8 k 40.0 k Problem 11.9-12 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 5 500 kN (see figure). The column has outside diameter d 5 200 mm, wall thickness t 5 10 mm, E 5 200 GPa, and s Y 5 250 MPa.
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11-04 Chap Gere - SECTION 11.9 Design Formulas for Columns...

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