Question

The column shown is fabricated from two C250 x 30 standard steel shapes (see Appendix B for its cross-sectional properties) that are oriented back-to-back with a gap of 29 mm between the two channels. The column is fixed at its base and free to translate in the y direction at its upper end. Translation in the z direction, however, is restrained at its upper end. A load Pis applied at an offset distance of 430 mm from the channel flanges. Use the AISC equations given in Section 16.5, and assume that L = 4.6 m, 5 = 29 mm, E = 200 GPa, Or =250 MPa, and allow =150 MPa. Using the interaction equation method, determine (a) whether the column is safe for a load of p = 65 kN; report the value of the interaction equation. (b) the magnitude of the largest load P that may be applied to the column. Offset distance e Lateral bracing in z direction C250 x 30 C250 x 30 Cross section.

Answer 1

giren l = 4.6 m, s = 29 mm E = 200 GPa 64 = 280MPa (Gallow) - 150 MPa , offret distance =430 m For c250x30 A = 3790 mm, d=254 mm, In = 32.8x106mmy ra 293 mm a 1.17X108 mm4, ł: 15.4 mm IZ = 2 (33.8X106 ) = 65.6X10* mmf Ty 31.17X00* +(24+ 154)*6770) = 9.1168106 mm 4 туу 9, 116x160 - 34.68 mm 2x3790 • Kzl 2X4, 6X1000 98.924 VE 93 0.7x4, 6x1000 = 92.89 34,68 KAL = 98.924 controls

AISC allowable stress RTVE 2 x 200 x103 -=125.664 since ky llo The column is intermediate 125-664 J - 1.90 allow 2002 250 - la (98.924) ► 1.90 I - 2X 125.6642 ) - 90.809 MPa

o interaction method P = 65 KN Mc (Gallowa (Gallow lb 658103 (2 х3790) frasmiwa ) (430 +233) (59) 65-68106 90.809 150 e 0.094 + 0.467 = 0.561 21 hence hase largest load P 243760) (430+25 (2 X 3790 (430+ 254 ) @547 90.809 65.68100 El 150 p [1.45278 810* + 7.1889 816 6] =) 3) PL 115717.935N - p = 115.719 KN

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