875_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

875_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 11Ch11.qxd 9/27/08 3:39 PM Page 869 869 SECTION 11.4 Columns with Other Support Conditions Solution 11.4-9 Fixed-end column BUCKLING EQUATION deflection in the y direction DIFFERENTIAL EQUATION (EQ.11-3) œœ M El œœ + k2 M0 P k P EI 2 M0 EI B.C. 2 ¿ (0) M0 (1 P M0 P M0 P ‹ C2 0 C1 k cos kx ‹ cos kL k2 C1 sin kx + C2 cos kx + 1 (0) 3 (L) M0 (1 P 00 cos kL) and kL 2p 4p2 4p2 1 CRITICAL LOAD GENERAL SOLUTION B.C. B.C. ‹ C1 2p 2 b L 0 cos kx) P EI 2 L 4p2EI BUCKLED MODE SHAPE L ab 2 kL 2 L b 2 deflection at midpoint a x M0 a1 P d cos p ‹d M0 P kL b 2 M0 (1 P 2M 0 P d a1 2 Problem 11.4-10 An aluminum tube AB of circular cross section has a guided support at the base and is pinned at the top to a horizontal beam supporting a load Q 200 kN (see figure). Determine the required thickness t of the tube if its outside diameter d is 200 mm and the desired factor of safety with respect to Euler buckling is n 3.0. (Assume E 72 GPa.) L2 ; L2 Let d C2 k sin kx 0 Pcr a cos p) d 2 cos 2px b L Q ; 200 kN B 1.0 m 1.0 m 2.0 m d A 200 mm ...
View Full Document

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.

Ask a homework question - tutors are online