________________________________________________________________________ PROBLEM (11.29) A fixed-ended long column of rectangular cross section 1 in.by 3 in. is made of aluminum alloy. Determine the minimum length L c that the column may have and the corresponding critical load P cr . Given: E = 10 x 10 6 psi, σp = 18 ksi SOLUTION 1 (3)(1)3 = 0.25 in.4 , A = 1× 3 = 3 in.2 12 rmin = 0.25 3 = 286.68 × 10−3 in. Equation (11.10): I min = Le π 2E 10 ×106 =π = 74.048 ( )C = 18 × 103 r σ pl or Le = 21.376 in. , LC = Le = 42.752 in. 0.5 Thus, Pcr = or π 2 EI L2e = π 2 (10 ×106 )(0.25) (21.376) 2 = 54 kips Pcr = σ p A = 18(3) = 54 kips 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.