________________________________________________________________________ PROBLEM (12.30) An element is subjected to equal tension and compression: pure shear (Fig. P12.30). Compute the strain-energy densities for the states of stress shown in the figure. Then, equating the results found, verify that G = E/2(1 + ν ). σ 2 = −σ 1 SOLUTION Refer to P12.30, Equation (12.17) gives σ2 1 U0 = (σ 12 + σ 22 − 2νσ 1σ 2 ) = 1 (1 +ν ) 2E E τ max = σ 1 U0 = 2 τ max 2G = σ 12 2G σ1 (1) (2) Equating σ 12 from Eqs. (1) and (2), and simplifying the result: G = E 2(1 + ν ) Q.E.D. 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.