The AA $2024($E $=76$ GPa, v $=0\mathrm{.}34)$ torsion shaft $($modeled in Figure $2)$ is composed of $2$ pieces ofcircular hollow tube welded together, and is subjected to a $300$ Nm external torque. The first piece $($AB$)$ has outside and inside diameters of $30$ mm and $20$ mm$,$ respectively. The wall thickness ofthe second piece $($BC$)$ is $2\mathrm{.}5$ mm$,$ and the outside diameter is $25$ mm$.$ A fillet of radius r $=5$ mm iscreated at the junction of the two tubes.$($a$)$ With reference to Figure $3,$ calculate the Safety Factor of the shaft if the maximum allowable shear stress is $235$ MPa. $($Note: The chart in Figure $3$ is for solid shafts. The chart for hollow sections is more complex, and it is outside the scope of this course.$)($b$)$ Calculate the total twist angle.