A shaft ABC consisting of two solid circular segments is subjected to torques $T_1$ and $T_2$ acting in opposite directions, as shown in the figure. The larger segment of the shaft has diameter $d_1=55mm.$ and length $L_1=760mm.$; the smaller segment has diameter $d_2=44$ mm $.$ and length $L_2=500mm.$ Shear modulus of the shaft material, $G=76$GPa, and the torques are $T_1=2260N.m.$ and $T_2=900N.m.$ Draw the Torque diagram. Calculate;

$($a$)$ the maximum shear stress max in the shaft,

$($b$)$ the angle of twist C $($in degrees$)$ at end C