________________________________________________________________________ PROBLEM (11.17) A round steel column of length L is fixed at its base and pinned at its top end supports a maximum permissible load P (Fig. P11.17). Calculate the diameter d of the member based on a safety factor of n s with respect to buckling. Given: L = 50 in., P = 4.5 kips, E = 30 x 10 6 psi. n s = 3, σy = 55 ksi SOLUTION Pcr = ns P = 3(4.5) = 13.5 kN , I= π d4 A= πd 2 r= Le = 0.7 L = 0.7(50) = 35 in. d 4 64 4 Equation (11.5) gives 64 Pcr L2e 64(13.5 × 103 )(35) 2 d4 = , = π 3E π 3 (30 × 106 ) Hence Le 35 = = 135.5 r 1.033 4 Equation (11.10): ( d = 1.033 in. Le 30 × 103 E )c = π =π = 73.4 < 135.5 r σy 55 Euler formula applies, Hence d = 1.033 in. 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.