QUESTION 3 (30 pts) At a machined shaft shoulder, the small diameter d is 25 mm , the large diameter \( D \) is 27.5 mm and the fillet radius is 1.25 mm . At the given location, the bending moment is 200.0 Nm and the steady torsion moment is 150.0 Nm . The midrange value of axial normal stress is 50 MPa and amplitude is 15 MPa . The heat-ireated steei shaft has an uitimate tensie strength of \( S_{u t}=1200 \mathrm{iviPa} \) and a vieid strength of \( S_{r}=920 \mathrm{MPa} \). The reliability goal is 0.99 . The operation temperature is room temperature at average. Determine the fatigue factor of safety of the design using Soderberg and modified Goodman criteria. Check static yield for modified Goodman.