________________________________________________________________________ PROBLEM (12.6) The stepped bar seen in Fig. P12.6 consists of a square cross section with sides a and a circular cross section of diameter d. The bar is subjected to a tensile force P. Determine the ratio of d/a so that the strain energy in both parts is the same. SOLUTION Axial strain energy P2 L = UC = 2 AE Use Eq. (12. 2), circular Part: P2 L 2P2 L = πd2 π d 2E 2( )E 4 Square Part: US = P 2 L P 2 ( L 2) P 2 L = = 2 2 AE 2a 2 E 4a E Requirement:: UC = U S ; 2P2 L P2 L = π d 2 E 4a 2 E d 8 = π a 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.