________________________________________________________________________ PROBLEM (*11.87) A W 410 x 85 steel column ( Table B. 8) of L e =5-m effective length supports an eccentric load of P = 400 kN at a distance e from the center of the section measured along the web (Fig. P11.87). Employ the interaction formula to determine the maximum allowable value of e. Given: ( σall ) b = 140 MPa, E = 210 MPa *SOLUTION A = 2.26 in.2 I z = 316 ×106 mm 4 y 417 mm z P A = 10.8 × 103 mm 2 c = 417 2 = 208.5 mm rz = 171 mm rmin = 40.6 mm Le rmin = 123.2 e W 410x85 Equation (11.25): (σ all )c = π 2E 1.92( Le rmin ) 2 Interaction formula: P A Mc I + ≤1; (σ all )c (σ all )b = π 2 (210 × 109 ) 1.92(123.2) 2 = 71.12 MPa ( P A)ec rz2 P A + ≤1 7.12 × 106 140 × 106 400 × 103 1 e(0.2085) + [ ] ≤1 −3 6 10.8 ×10 (10 ) 71.12 (0.17) 2 (140) e(0.2085) ≤ 0.127 − 0.0141 (140)(0.171) 2 or e≤ Thus, 0.0129(140)(0.171) 2 ≤ 0.253 m 0.2085 e = 253 mm 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.