879_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

879_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 11Ch11.qxd 9/27/08 3:39 PM Page 873 873 SECTION 11.5 Columns with Eccentric Axial Loads Solution 11.5-3 Column with eccentric loads Column has pinned ends. Use EQ. (11-49): e a tan M Pe 1b kL sin kx + cos kx 2 From Eq. (11-45): ‹M Pe a tan FOR P M Pe 0.3 Pcr: M Pe P 1.162 a sin 1.721 x x b + cos 1.721 L L (NOTE: kL and kx are in radians) ; p 10.3 A Pcr p From Eq. (11-52): kL 1.7207 x x b a sin 1.7207 b + cos 1.7207 2 L L or P kL sin kx + cos kx b 2 a tan BENDING-MOMENT DIAGRAM FOR P 0.3 Pcr 1.7207 Problem 11.5-4 Plot the load-deflection diagram for a pinned-end column with eccentric axial loads (see figure) if the eccentricity e of the load is 5 mm and the column has length L 3.6 m, moment of inertia I 9.0 * 106 mm4, and modulus of elasticity E 210 GPa. Note: Plot the axial load as ordinate and the deflection at the midpoint as abscissa. Solution 11.5-4 Column with eccentric loads Column has pinned ends. pP b 2 A Pcr SOLVE EQ. (2) FOR P: Use Eq. (11-54) for the deflection at the midpoint (maximum deflection): d e c sec a 1d P (1) DATA e I 5.0 mm L 6 3.6 m E 210 GPa 4 9.0 * 10 mm CRITICAL LOAD Pcr p2EI (5.0) [sec (0.041404 1P) L2 1439.3 kN MAXIMUM DEFLECTION (FROM EQ. 1) d Units: P kN d Angles are in radians. mm 1] (2) 583.3 c arccos a 2 5.0 bd 5.0 + d LOAD-DEFLECTION DIAGRAM ; ; ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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