7. In the design of shafts, steps can be used to locate other machine components such as bearings, pulleys, and gears. Consider a shaft with diameters $d$=40 mm and $D$=45 mm and fillet $r$=1.5 mm as shown and made from 1020 CD steel. If the step location is loaded with a constant tensile force $F$=4000 N, an alternating bending moment $M$ of ±1500 N-m, and a torque $T$ alternating between 0 and 750 N-m, determine the factor of safety (a) guarding against first cycle yielding and (b) fatigue based on the Gerber failure criterion. (c) Draw the designer's fatigue diagram. Use a 99% reliability, and a 25 °C operational temperature. (24 Points)
