The thin$-$walled box section beam ABCD shown in Figure is attached at each end to supports that allow rotation of the ends of the beam in the longitudinal vertical plane of symmetry but prevent rotation of the ends in vertical planes perpendicular to the longitudinal axis of the beam. The beam is subjected to a uniform torque loading of $20$N$-$m$/$mm over the portion BC of its span. Calculate a$)$ the maximum shear stress in the cross$-$section of the beam and b$)$ the distribution of angle of twist along its length, G$=70,000$N$/$mm$2.$