_______________________________________________________________________ PROBLEM (*8.124) A steel shaft of radius r is loaded by a torque T, as shown in Fig. P8.124. A strain gage is placed at point A measures the strain is the value of the torque T ? Given: r = 2 in., G = 11.5 x 106 psi , εφ εφ at an angle of = 500 μ, φ τ xy = Tc J J= φ to the axis of the shaft. What = 25o *SOLUTION y π 2 c3 γ xy = x τ Mohr’s circle for strain: 1 ε avg = (ε x + ε y ) = 0 2 γ 2 1 R = γ xy 2 1 2 ε φ = ε avg + R sin 2θ = γ xy sin 2θ This gives T= τ xy 2G sin 2φ = r=c G σ x = σ y = 0 ε x = ε y = 0 θ = φ = 25o A = τ xy Tc sin 2φ 2GJ x A’ x’ 2φ R O ε y 2GJ ε φ c sin 2φ Substitute the given data: π (11.5 ×106 )(2)3 (500 × 10−6 ) T= = 94.3 kip ⋅ in. (2) sin 50o 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.