A $26$ mm diameter smooth solid shaft is made from a material with yield strength MPa and axial S$-$N curve with the equation ${}_{{?}_{?}}(2)=590*N_f-0\mathrm{.}065.$ The shaft is subjected to in$-$phase bending and torsion. The bending varies from $0$ to $300$ Nm and the torque varies from $-140$ to $300$ Nm $.$

a$)$ Calculate the safety factor against static yielding of the outer surface of the shaft.

b$)$ Can the shaft withstand $10$ million of these combined cycles?

c$)$ What is the minimum allowed diameter of shaft if the shaft should withstand $2\mathrm{.}5$ million cycles?