________________________________________________________________________ PROBLEM (11.36) A 0.5-m-long, 50-mm by 75-mm rectangular column is pinned at both ends. If the stress-strain curve for the material is approximated as shown in Fig.P11.36, what is the buckling load P cr ? SOLUTION A = 50 × 75 = 3.75 × 103 mm 2 r= I A= b 2 3 L r = 500 14.4 = 34.7 (inelastic buckling) Use Eq. (11.12): π 2 Et π 2 Et = = 0.0082 Et σ cr = ( L r ) 2 (34.7) 2 Elastic range: σ cr = 0.0082(20 ×109 ) = 164 MPa Figure shows that E is not valid above 40 MPa. = 50 = 14.4 mm 2 3 (1) Second range: σ cr = 0.0082(20 ×109 ) = 82 MPa Et1 is not valid above 60 MPa. Third range: σ cr = 0.0082(7.5 ×109 ) = 61.5 MPa Et 2 is valid between 60 MPa and 75 MPa. Thus, Pcr = 61.5 ×106 (3.75 ×10−3 ) = 231 kN 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.