_______________________________________________________________________ PROBLEM (8.16) At a point in a loaded steel bracket the stresses are σ x = 50 MPa, σ y = -15 MPa, τ xy = -30 MPa , as shown in Fig. P8.16. Determine the stresses acting on an element oriented at an angle θ = 40o from the x axis. Sketch the result on a properly oriented element. and SOLUTION 1 1 2 2 1 1 = (50 − 15) + (50 + 15) cos80o − 30sin 80o = −6.45 MPa 2 2 σ x ' = (σ x + σ y ) + (σ x − σ y ) cos 2θ + τ xy sin 2θ 1 2 1 = − (50 + 15) sin 80o − 30 cos80o = −37.2 MPa 2 τ x ' y ' = − (σ x − σ y ) sin 2θ + τ xy cos 2θ Hence, σ y ' = σ x + σ y − σ x ' = 50 − 15 + 6.45 = 41.4 MPa 41.6 MPa y’ 29.8 MPa 6.4 MPa x’ θ = 40o x 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.