– A circular shaft of radius c

– A circular shaft of radius c is subjected to torsion, and the material has an elastic, powerhardening curve for shear stress versus shear strain. In particular, τ = Gγ for (τ ≤ τo), and τ = H4γ n4 for (τ ≥ τo). Show that the torque T is related to γc, the strain at r = c, by

where (a) applies for (γc ≤ γo), and (b) applies for (γc ≥ γo), with γo = τo/G being the yield strain. Does the postyield solution (b) reduce to the elastic case for incipient yielding at the beam edge? Does it reduce to Eq. 13.46 for large strains?