Problem $2[25$marks$]$

For fatigue analysis, assume that the beam in the previous question $($see Fig. Q$1)$ is a drive shaft that revolves with a speed of $1200$ rpm $.$ Calculate the minimum radius for a steel material of the shaft to get infinite life. Assume appropriate steel material for the automobile applications. Find and provide the appropriate concentration factors for the endurance limit$.$ Use of the Goodman criterion for fatigue calculations. The shaft has a solid $($filled$)$ circular cross section. Describe the procedure and provide meaningful calculations for the lifetime of the rotating machine element.