20 points) A cylindrical shaft under torsional load has a lengthwise groove of radius \( b \), as shown in the ketch of the cross section.
(1) Propose a Prandtl stress function that solves the torsional problem.
(2) Determine the ratio of shear stress at \( B \) to shear stress at \( A \).
(3) What stress concentration factor is approached if \( a \gg b \) ?
Figure 1: Cylindrical shaft under torsional load has a lengthwise groove of radius \( b \).