(Solved): 11. The rotating solid shaft is simply supported by bearings at points B1 and B2 and it's made of a ...

11. The rotating solid shaft is simply supported by bearings at points B1 and B2 and it's made of a heat-treated steel (yield strength $=450\mathrm{MPa}$ and ultimate strength $=700\mathrm{MPa})$ with a small diameter of $(d=20\mathrm{mm})$, large diameter of $(\mathrm{D}=30$ $\mathrm{mm})$, and fillet radius of $(\mathrm{r}?2\mathrm{mm})$ at its shoulder for bearing support. The shaft is driven by a gear (not shown) which meshes with a spur gear at mid point between B1 and B2. The gear has a $75?\mathrm{mm}$ piteh diameter where the resulting force of $2\mathrm{kN}$ is applied at $20^{?}$ line of action. Follow the steps below to calculate the fatigue safety factor using DEGoodman criterion if the reliability goal for the endurance limit is $95\%$. (70 pts)