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858_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 858_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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852 CHAPTER 11 Columns Solution 11.3-4 C OLUMN CD ( STEEL ) Square cross section: Factor of safety: I b 4 12 I 2.00 * 10 6 mm 4 n 2.0 b 70 mm E 200 GPa L 2.4 m d L 2 d 1.2 m Beam ACB ; M allow P allow d M allow 1143 kN # m © M A 0 M Pd P allow P cr n P allow 952.3 kN P cr p 2 EI (0.6 L ) 2 P cr 1905 kN Solution 11.3-3 Column with pinned supports steel column (a) B UCKLING ABOUT STRONG AXIS P cr p 2 EI 1 L 2 650 k ; I 1 248 in. 4 I 2 53.4 in. 4 A 13.3 in. 2 L 28 ft 336 in. E 30 * 10 6 psi W 10 * 45 (b) B UCKLING ABOUT WEAK AXIS NOTE: Solution is satisfactory if s PL Ú 49 ksi s cr P cr A 650 k 13.3 in. 2 49 ksi P cr p 2 EI 2 L 2 140 k ; Problem 11.3-4 A horizontal beam AB is pin-supported at end A and carries a load Q at end B , as shown in the figure. The beam is supported at C by a pinned-end column of length L ; the column is restrained laterally at from the base at D . Assume the column can only buckle in the plane of the frame. The column is a solid steel bar of square cross section having length side dimensions . Let dimensions . Based upon the critical load of the column, determine the allowable
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