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857_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

857_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Critical Loads of Columns with Pinned Supports The problems for Section 11.3 are to be solved using the assumptions of ideal, slender, prismatic, linearly elastic columns (Euler buckling). Buckling occurs in the plane of the figure unless stated otherwise. Problem 11.3-1 Calculate the critical load P cr for a steel column (see figure) having length and under the following conditions: (a) The column buckles by bending about it’s strong axis (axis 1-1), and (b) the column buckles by bending about its weak axis (axis 2-2). In both cases, assume that the column has pinned ends. E 30 * 10 6 psi L 24 ft W 8 * 35 SECTION 11.3 Critical Loads of Columns with Pinned Supports 851 Solution 11.3-1 Column with pinned supports steel column (a) B UCKLING ABOUT STRONG AXIS P cr p 2 EI 1 L 2 453 k ; I 1 127 in. 4 I 2 42.6 in. 4 A 10.3 in. 2 L 24 ft
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Unformatted text preview: (b) B UCKLING ABOUT WEAK AXIS NOTE : Solution is satisfactory if s PL Ú 44 ksi ‹ s cr ± P cr A ± 453 k 10.3 in. 2 ± 44 ksi P cr ± p 2 EI 2 L 2 ± 152 k ; 1 C 1 2 2 Problem 11.3.1-3.3 Problem 11.3-2 Solve the preceding problem for a W 250 ² 89 steel column having length L ± 10 m. Let E ± 200 GPa Solution 11.3-2 B UCKLING ABOUT STRONG AXIS ; 2803 kN P cr1 ± P cr1 ± p 2 EI 1 L 2 I 2 ± 48.3 * 10 6 mm 4 A ± 11400 mm 2 I 1 ± 142 * 10 6 mm 4 E ± 200 GPa L ± 10.0 m W 250 * 89 B UCKLING ABOUT WEAK AXIS Note: Solution is satisfactory if s PL Ú 246 MPa s cr ± P cr1 A s cr ± 246 MPa P cr 2 ± p 2 EI 2 L 2 P cr 2 ± 953 kN ; Problem 11.3-3 Solve Problem 11.3-1 for a steel column having length . L ± 28 ft W 10 * 45 11Ch11.qxd 9/27/08 2:21 PM Page 851...
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