The rotating solid steel shaft is simply supported by bearings at points B and C and is driven by a gear (not shown) which meshes with the spur gear at D, which has a 6-in pitch diameter. The force F from the drive gear acts at a pressure angle of 20o. The shaft transmits a torque to point A of TA = 3000 lbf • in. The shaft is machined from steel with Sy = 60 kpsi and Sut = 80 kpsi. Using a factor of safety of 2.5, determine the minimum allowable diameter of the 10 in section of the shaft based on
(a) a static yield analysis using the distortion energy theory and
(b) a fatigue-failure analysis. Assume sharp fillet radii at the bearing shoulders for estimating stress concentration factors