_______________________________________________________________________ PROBLEM (8.130) Using a 60° rosette, we find the following strains at a critical point on the surface of a loaded beam shown in Fig. P8.130: ε a = -200 μ , ε b = -350 μ , εc = -500 μ Determine: (a) The maximum in-plane shear strains and the accompanying normal strains. (b) The true maximum shear strain. Use ν = 0.3. Sketch the results found in part (a) on a properly oriented distorted element. SOLUTION Using Eq. (8.45): 1 3 ε x = −200 μ γ xy = ε y = [2(−850) + 200] = −500 μ 2 (−350 + 500) = 173 μ 3 (a) γ max = 2 ( 300 2 173 2 ) +( ) = 346 μ 2 2 1 2 ε ' = − (200 + 500) = −350 μ 1 2 θ s = tan −1[− 300 ] = −30o 173 ε 2 = −350 + 173 = −177 μ , ε 3 = −350 − 173 = −523 μ Check: γ x ' y ' = −( −200 + 500) sin( −60 o ) + 173 cos( −60 o ) = 346 μ = γ max Thus, θ s ' = 30o 350 μ x 30o 346 μ x’ 350 μ 0.3 (−700) = 300 μ 0.7 (γ max ) a = 300 + 523 = 823 μ (b) ε z = ε1 = − 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.