Q$2.$ Three solid shafts $AB,BC$ and $CD$ of the same diameter are connected and fixed at end A under loadings shown in Figure $2.$ Given the allowable shear stress $60$ MPa and shear modulus $50$ GPa, $($a$)$ determine the minimum diameter for the shafts; $($b$)$ with this diameter, determine the twist angle of end $D,$ and state whether clockwise or counter$-$clockwise in the view from $D$ towards $A.[10$ marks$]$

Figure $2$