7-3 The rotating 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 150mm pitch diameter. The force F from the drive gear acts at a pressure angle of 20°. The shaft transmits a torque to point A of TA = 340 N*m. The shaft is machined from steel with Sy = 420 MPa and Sut = 560 MPa. Using a safety factor of 2.5determine the minimum allowable diameter of the 250mm section of the shaft based on a) a static yield analysis using the distortion energy theory and b) a fatigue-failure analysis using Goodman. Assume sharp fillet radii at the bearing shoulders for estimating stress concentration factors.

Fig: 1

Fig: 2