_______________________________________________________________________ PROBLEM (8.23) At a point in a loaded structure, the stresses are as shown in Fig. P8.23. Determine the allowable value of σ if the normal and shearing stresses acting simultaneously in the inclined plane are limited to 5 and 3 ksi, respectively . SOLUTION We have θ = 15o and τ xy = 0 σ x' = 5 = σ − 2.5 σ + 2.5 cos 30o + 2 2 10 = σ − 2.5 + 0.866σ + 2.165 , σ = 5.54 ksi σ + 2.5 sin 30o , σ = 9.5 ksi τ x ' y ' = −3 = − 2 Thus, σ all = 5.54 ksi 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.