Assignment $4-$ Fatigue Failure:

A solid round bar with a diameter of $50$ mm has a groove cut to a diameter of $45$ mm with a radius of $2\mathrm{.}5$ mm $.$ The bar is not rotating. At a service temperature of $240C$ and with a reliability of $99\mathrm{.}99\%,$ the bar is loaded with a repeated bending load that causes the bending moment at the groove to fluctuate between $0$ and $2825$ Nm $.$ The bar is hot$-$rolled AISI $1095,$ but the groove has been machined providing the stress concentration. With miscellaneous effect factor $K_f=1,$ determine the factor of safety for fatigue based on infinite life according to the modified Goodman line.