_______________________________________________________________________ PROBLEM (*8.49) Redo Prob. 8.48 for the case shown in Fig. P8.49. *SOLUTION 18 MPa y’ σ x’ 14 MPa θ x σ x + σ y = σ x' + σ y' 30 − 20 = −18 + σ ; σ x ' = 28 = or τ x' y' σ = 28 MPa 30 − 20 30 + 20 + cos 2θ + 10sin 2θ 2 2 23 = 25 cos 2θ + 10 sin 2θ = −14 = −25 sin 2θ + 10 cos 2θ Multiply this by − 2.5 : 35 = 62.5 sin 2θ − 25 cos 2θ (1) (2) Add Eqs. (1) and (2), 58 = 72.5 sin 2θ , 2θ = 53.13o or θ = 26.6 o 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.