________________________________________________________________________ PROBLEM (11.11) Two equal round bars are supported in line with one another and are separated by a small gap (Fig. P11.11). Determine the temperature rise necessary to cause them to: (a) Just touch. (b) Buckle elastically. Given: a = 12 x 10 -6 /°C, L = 1 m, d = 25 mm, δ = 1.2 mm SOLUTION (a) α L(ΔT ) = δ ΔT = , δ 2α L 2 Substituting the given data: 1.2 × 10−3 ΔT = = 50o C −6 2(12 × 10 )1 (b) A = π (0.025) 2 = 490.9 ×10−6 m 2 I = 4 We have α L(ΔT ) − π 64 (0.025) 4 = 19.17 ×10−9 m 4 PL δ = AE 2 Thus, ΔT = δ π 2I + 2α L 4 Aα L2 or π 2 (19.17 × 10−9 ) = 50 + 8 = 58o C 4(490.9 ×10−6 )(12 × 10−6 )(1) 2 Justification of the formula used: r = I A = d 4 = 6.25 mm L r = 1000 6.25 = 160 O.K. ΔT = 50 + 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.