________________________________________________________________________ PROBLEM (*11.35) A 60-in. long, 2 in.-diameter round column is fixed at its base and pinned at its top. Calculate the axial buckling load P cr , if the stress-strain diagram for the material is approximated as depicted in Fig. P11.35. *SOLUTION A= πd2 4 I= πd4 64 r= Le = 0.7 L = 0.7(60) = 42 in. I d 2 = = = 0.5 in. A 4 4 (see Fig. 11.3c), Le 42 = = 84 r 0.5 Equation (11.12): π 2 Et π 2 Et = = 141.7(10−6 ) Et (1) σ cr = 2 2 ( Le r ) (84) From stress-strain diagram, we have 15 ×103 (45 − 15)103 Et = E = = 15 × 106 psi Et = = 5 × 106 psi 0.001 0.007 − 0.001 Equation (1) gives σ cr = 141.7(10−6 )(15 ×106 ) = 2.13 ksi < 15 ksi (O.K.) σ cr = 141.7(10−6 )(5 × 106 ) = 0.709 ksi < 15 ksi (not valid) Thus Pcr = σ cr A = 2.13[π (1) 2 ] = 6.69 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.