A 300-mm-long, solid, straight shaft is supported in self-aligning bearings at each end. A gear is attached at the middle of the shaft with a 10-mm square steel key in a slot. The geometric stress. concentration factor in the key slot is 2.5 and its comer radius is 0.5 mm. The gear drives a fluctuating load which creates a bending moment that varies from +10 N-m to +100 N-m and a torque that varies from 35 N-m to +170 N-m cach cycle. The material chosen is cold-drawn 4140 steel, hardened and tempered to Rockwell C45 (Sut = 1250 MPa). 

Design the shaft for infinite life and determine the diameter needed for a safety factor of 1.5.