_______________________________________________________________________ PROBLEM (8.14) At a particular point in a loaded machine part (use Fig. P8.9), the stresses are as follows: σx = 6 ksi, σy = -4 ksi , and τ xy = 0. Determine the normal and shear stresses on the plane whose normals are at angles of -30o and 120o with the x axis. Sketch the results on a properly oriented elements. SOLUTION y’ x At θ = −30 : o o 30 x’ 4.33 ksi 3.5 ksi 6−4 6+4 cos(−60o ) + 0 = 1 + 2.5 = 3.5 ksi + 2 2 6+4 sin(−60o ) + 0 = 4.33 ksi =− 2 σ x' = τ x' y' 1.5 ksi x’ 4.33 ksi At θ = 120o : 120o y’ x 6−4 6+4 cos 240o = −1.5 ksi + 2 2 6+4 sin 240o = 4.33 ksi =− 2 σ x' = τ x' y' 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.