_______________________________________________________________________ PROBLEM (*8.135) The strain readings at a point on the free surface of a steel bracket subjected to plane stress (see Fig. 8.134) are ε a = 400 μ ε b = 350 μ for θa = 0o, θb = 45°, and θc εc = 800 μ = 135°. Calculate: (a) The maximum in-plane shearing strains. (b) The true maximum shear strain (ν = 1/3). Show the results found in part (a) on properly oriented distorted element. *SOLUTION Equations (8.43): ε x = 400 μ 350 = ε x (0.5) + ε y (0.5) + γ xy (0.5) (1) 800 = ε x (0.5) + ε y (0.5) + γ xy ( −0.5) (2) γ xy = −450 μ Subtract Eq. (2) from Eq. (1): Equation (1) yields 350 = 200 + 0.5ε y − 225 , ε y = 750 μ (a) γ 2 (μ) ε' (400, 225) ε'= x ε3 O ε2 2θ p " 10 R = 1752 + 2252 = 285 μ ε1 C R 400 + 750 = 575 μ 2 ε(μ) y 1 225 = 26.1o 2 175 = 2r = 570 μ , θ s " = 18.9o θ p " = tan −1 γ max ε 1 = 575 + 285 = 860 μ ε 2 = 575 − 285 = 290 μ Continued on next slide 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. 13 (400 + 750) = −575 μ 1−1 3 (γ max ) a = 860 + 575 = 1435 μ (b) ε 3 = ε z = − 575 μ 570 μ 18.9o 575 μ x 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.