_______________________________________________________________________ PROBLEM (9.26) A hollow shaft with outer diameter D and inner diameter d is acted upon by an axial tensile load P, a torque T, and a bending moment M, as portrayed in Fig. P9.26. Use Mohr’s circle to determine the principal stresses and the plane on which they act. Given: D = 50 mm, d = 30 mm, P = 40 kN, T = 500 N ⋅ m, M = 200 N ⋅ m SOLUTION M M T P P T A A = π ( 25 2 − 152 ) = 1256.6 mm 2 σx = A τ= P Mc + A I J= π (254 − 154 ) = 534 × 103 mm 4 2 I = J 2 = 267 × 10 3 mm 4 Tc J 500(25 × 10−3 ) = −23.4 MPa τ =− 534 × 10−9 40 × 103 200(25 × 10−3 ) + = 31.83 + 18.73 = 50.56 MPa σx = 1256.6 × 10−6 267 ×10−9 τ (MPa) (50.56, 23.4) 2θp’ σ2 σ1 C R σ (MPa) R = (25.28) 2 + (23.4) 2 = 34.45 MPa σ ' = 25.28 MPa σ' tan 2θ p ' = 23.4 , θ p ' = 21.4o 25.28 σ 1 = 25.28 + 34.45 = 59.73 MPa σ 2 = 25.28 − 34.45 = −9.17 MPa 21.4 ο 59.73 MPa A 9.17 MPa 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.