________________________________________________________________________ PROBLEM (11.33) A 6-ft-long column of 4-in. by 2-in. rectangular cross section fits between a rigid ceiling and a rigid floor. Calculate the change in temperature that - will cause the column to buckle. Given: E = 30 x 10 6 psi, α = 6.7 x 10 -6 /°F, σy = 34 ksi Assumption: The ends are taken to be rounded . SOLUTION Assume that σ y = σ cr . So L π 2 (30 ×106 ) ( )c = = 93.3 , I min = 4(2)3 12 = 2.667 in.4 34 × 103 r A = 2 × 4 = 8 in.2 , r = I min A = 0.578 in. and L r = 6 ×12 0.578 = 124.6 Thus, σ = α E (ΔT ) = π 2E (L r) Substituting the given data: ΔT = , 2 π2 −6 6.7 ×10 (124.6) 2 ΔT = π2 α ( L r )2 = 94.9o F Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.