_______________________________________________________________________ PROBLEM (9.102) At a particular point in a cast aluminum alloy ( σ u = 10 ksi, σ u ' = 26 ksi) structure subjected to plane stress, the stresses have the magnitudes and directions shown in Fig. P9.102. Determine whether failure occurs at the point according to: (a) The maximum principal stress theory. (b) Coulomb-Mohr theory. SOLUTION We have σ y = −25 ksi τ xy = 30 ksi σ x = 0. Thus σ 1,2 = − σy ± ( σy 2 σ 1 = 5.54 ksi 2 ) 2 + τ xy2 = −3 ± (3) 2 + (8) 2 σ 2 = −11.54 ksi (a) Maximum principal stress theory: But σ1 = 1; σu 5.54 < 10 σ2 = 1; σu 11.54 > 10 (b) Coulomb-Mohr Theory: σ1 σ 2 − = 1; σ u σ u' gives (failure occurs) 5.54 −11.54 − =1 10 26 0.554 + 0.443 = 0.998 < 1 (no fracture) Comment: Coulomb-Mohr criteria is more reliable when σ u >> σ u ' , as in this problem. 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.