_______________________________________________________________________ PROBLEM (8.79) A point in a structure is subjected to state of stress with σx = 15 ksi σy τ xz = 10 ksi acting as shown on a three-dimensional element in Fig. P8.79. Calculate two values of σy for which the maximum shear stress equals 13 ksi. SOLUTION τ (ksi) τ=13 σavg =7.5 R O 1 2 1 = (15 + 0) = 7.5 ksi 2 σ −σ z 2 2 R= ( x ) + τ xz 2 σ avg = (σ x + σ z ) C σ1 σ (ksi) 15 − 0 2 ) + 10 2 = ( 2 = 12.5 ksi τ=−13 We have σ 1,3 = σ avg ± R σ 1 = 7.5 + 12.5 = 20 ksi σ 3 = 7.5 − 12.5 = −5 ksi Assume: σ max = σ 1 = 20 ksi Then σ y = σ min = σ 1 − 2τ max = 20 − 2(13) = −6 ksi Assume : σ min = σ 3 = −5 ksi Then σ y = σ max = σ min + 2τ max = −5 + 2(13) = 21 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.