Final answer:
This is a mechanical engineering problem that requires calculating the necessary shaft diameter to withstand specified torsional and bending moments, applying material property criteria and a surface finish factor.
Step-by-step explanation:
The student is dealing with a problem in the field of mechanical engineering, specifically in the area related to the strength of materials, combining torsional and bending moments on a shaft. Given the alternating torsional moments (from -250 N-m to +500 N-m) and bending moments (from +100 N-m to +200 N-m), along with the material properties of steel (tensile strength and yield stress), and a surface finish factor, the student is asked to calculate the required diameter of the shaft that would ensure it withstands the given moments without failure. The calculation should involve considering the combined loading effects and safety factors.