PROBLEM (9.1) A cylinder with external diameter D and internal diameter d is subjected to an axial compressive load P and a torque T (Fig. P9.1). Calculate the maximum principal stress and the maximum shearing stress. Show the results on a properly oriented element. Given: D = 6 in., d = 4 in., P = 20 π kips, T = 15 π kip ⋅ in. SOLUTION State of stress on an element at the cylinder’s surface is σx = σx = Tc τ xy = J P A τ =− −20π ×103 = −4 ksi π (32 − 22 ) 15π × 103 (3) π 2 = −1.385 ksi (3 − 2 ) 4 4 Equation (9.1): 4 4 2 2 σ 1 = 0.433 ksi σ 2 = −4.433 ksi τ max = 2.433 ksi Equation (9.3): 2(−1.385) tan 2θ p = , 2θ p = 34.7o −4 Equation (4.4a) gives 1 1 σ x ' = (−4) + (−4) cos 34.7o − 1.385sin 34.7o 2 2 = −4.433 ksi Thus θ p " = 17.35o σ 1,2 = − ± (− ) 2 + (−1.385) 2 = −2.433 2.433 ksi 4.433 ksi 17.35o x 0.433 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.