A rotating shaft has power transferred into a gear at B by a bevel gear, resulting in a steady radial force F1=100lb, and a steady axial force F2=20lb plus an applied torque of T1=200lb-ft as shown in the figure. The power is removed by a spur gear at C, resulting in a torque T2(which must equal T1) and with a steady radial force F3=200lb that is in the same plane as F1 and the shaft axis.

The shaft diameter between A and B is 1.00 inch with a 1/8 inch shoulder at B and the diameter increasing to 1.25 inches between B and C, and another 1/8 inch shoulder at C with the diameter decreasing to 1.00 inch between C and D. Ignore any shoulders at A and D to retain the bearings in position. The fillet radius is 1/16 inch at both B and C.

The shaft is supported at A and D by a roller bearing and a tapered roller bearing(thrust bearing) respectively. For now, all you need to be concerned with is that the bearings provide the reaction forces necessary to balance the gear forces. Neither bearing resists a torque. The bearing at A provides only a radial reaction force, and the bearing at D provides both a radial and a axial reaction force.

a) What are the possible failure modes for the shaft that must be considered to determine if the shaft is safe?

b) Where are the critical points on the shaft were failure would likely occur first for each failure mode identified in (a)?

c) What are the factors of safety for failure by each of the failure modes?