Asolid round bar with diameter of 2 in has a groove cut to a diameter of 1.8 in, with a radius of 0.1 in. the bar is not rotating. the bar is loaded with a repeated bending load that causes the bending moment at the groove to fluctuate between 0 and 25 000 lbf in. the bar is hot-rolled aisi 1095, but the groove has been machined. determine the factor of safety for fatigue based on infinite life using the modified goodman criterion, and the factor of safety for yielding.