$3.$ The machine shaft shown in Fig. $2$ is made of $1095$ HR steel, and is supported by roller bearings at A and B$.$ The shaft is subjected to constant bending forces of F$1=15$ kN and F$2=5$ kN$,$ as well as a constant torque Tx $=1\mathrm{.}5$ kN$-$m along the entire length of the shaft section with the $45$ mm diameter. Determine the critical location on the shaft, calculate the mean and cyclic stresses at this location, and finally determine the fatigue factor of safety using the Soderberg criteria. All fillets $1\mathrm{.}5$ mmR$.$