Ashaft of diameter 2.2-in has a groove where the diameter reduces to 2.0-in. the radius of the fillet at the groove is 0.1-in. the shaft carries a bending moment which varies between 5500 b. in to 11 kip. in. using modified-goodman and soderberg criteria find safety factor at the bottom-most point in the groove for a life of 250,000 cycles if the shaft is made of steel of ultimate strength 120 ksi and yield strength 85 ksi. also find the langer yield safety factor as part of the first cycle yield check. ignore transverse shear stress. a. max and min bending stresses without considering the effect of stress concentration. b. midrange stress and stress amplitude. c. static stress concentration factors d. fatigue strength at 250,000 cycles, e. safety factors using modified goodman and soderberg criteria. f. first cycle yield safety check.