$7-(10$ pts$)$ A $42$ mm diameter steel shaft with a $19$ mm transverse hole is subjected to a sinusoidal combined stresses of $=+-150$MPa and a steady torsion of $=110$MPa. The ultimate strength of the material is $S_{ut}=1000$ MPa $.$ Use $K_{fm}=1\mathrm{.}0($stress concentration factor applied to the mean stress$).$ Assume machined surface finish and $50\%$ reliability. If the safety factor is less than $1\mathrm{.}0,$ find the number of cycles to failure $($infinite life $={10}^6$ cycles$).$ Use von Mises stress and modified Goodman Diagram.