________________________________________________________________________ PROBLEM (7.157) A curved bar with a rectangular cross section is subjected to the bending moment as shown in Fig. P7.157. Calculate: (a) The stresses σ i and σ o of the inside and outside fibers, respectively, using the curved beam formula. (b) Resolve item (a) using the flexure formula. Given: M = 1.2 kN ⋅ m, b = 25 mm, h = 50 mm, ri = 60 mm SOLUTION ro = ri + h = 60 + 50 = 110 mm A = bh = (50)(25) = 1, 250 mm 2 We have h 50 R= = = 82.4898 ro 110 ln ln 60 ri 1 r = (ri + rθ ) = 85 mm 2 e = r − R = 2.5102 mm (a) Using Eq.(7.67): 1200(82.4898 − 60) σi = − = −143.3 MPa 1250(10−6 )(0.06)(85 − 82.4898) σo = − 1200(82.4898 − 110) = 98.6 MPa 1250(10−6 )(0.11)(85 − 82.4898) (b) σ o = −σ i = Mc 1.2 × 103 (0.025) = = 66.7 MPa 1 I 3 (0.025)(0.06) 12 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.