(60 pts) A hot-rolled steel shaft with a shoulder fillet is subjected to an axial load P which varies from 1000 N to 10,000 N. The shaft operates at 100 C. The dimensions of the shaft are D = 30 mm, d = 20 mm and r = 2 mm. The yield strength of the material is 355 MPa. Find the safety factor for infinite life if ut = 420 MPa and the reliability is 99.99%.