Problem $2.$

The shaft shown in the figure is machined from AISI $1030$ CD steel. The shaft rotates at $900$ rpm and is supported in rolling bearings at position I and $2.$ The applied forces are $F=2500dbf$ bending. The axial $P$ is repetitive with a maximum of$,P_{\text{m}\text{a}\text{x}}=900lbs.$ A variable torque with value of $T_{\text{o}\text{u}\text{x}}=550dbf-in$ and $T_{\text{m}\text{i}\text{n}}=-200lbf-in.$ The surfaces are machined, the shaft will be working at $400F$ and reliability of $\mathrm{.}999.$ The value of $d=1\mathrm{.}25$inch. Determine the factor of safety for fatigue based on infinite life using the modified Goodman criterion. If infinite life is not predicted, estimate the number of cycles to failure, always check for yielding. Using the Goodman graphical method determine the fatigue factor de safety. $($Goodman diagram$)$