Gere & Goodno — Torsion: Problem 3.12-1

3.12-1 A stepped shaft consisting of solid circular segments having diameters \( D_1 = 50 \text{ mm} \) and \( D_2 = 60 \text{ mm} \) (see figure) is subjected to torques \( T \). The radius of the fillet is \( R = 2.5 \text{ mm} \). If the allowable shear stress at the stress concentration is \( 110 \text{ MPa} \), what is the maximum permissible torque \( T_{\max} \)?