_______________________________________________________________________ PROBLEM (8.13) At a critical point A in the loaded member in Fig. P8.13, the stresses on the inclined plane are σ = 28 MPa and τ = 10 MPa, and the normal stress on the y plane is zero. Calculate the normal and shear stresses on the x plane through the point. Show the results on a properly oriented element. SOLUTION σ x’ τ θ = 120o θ 30o x y’ σ = 28 = σx + 0 σx −0 2 + 2 cos 240o + τ xy sin 240o σ x = 112 + 3.464τ xy σx −0 o (1) τ = −10 = − sin 240 + τ xy cos 240o 2 σ x = −23.094 + 1.155τ xy Solving (1) and (2): σ x = −90.6 MPa (2) τ xy = −58.5 MPa y 58.5 MPa A 90.6 MPa 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.