A rotating shaft is $2\mathrm{.}50"$ in diameter. It is made of steel with a yield strength of $210$ kpsi and an ultimate tensile strength of $250$ kpsi $.$ It has a ground surface finish, is subjected to bending and torsion and will be operating at a temperature of $100$ deg F$.$ Below which cyclic stress amplitude will the shaft survive for a theoretical infinite number of cycles with $\mathrm{.}90$ reliability? $(10$ points total$)$