Below shaft has two rotating components as shown. Solve for $F_B$ force first. Then resolve the load components into y and z components.

The details of the stepped shaft is shown below. All the dimensions in above and below figures are in mm $.$ Please compare the diameters of portions and lengths in x direction between two figures to match locations.

Perform a fatigue analysis by assuming that the shaft is made of $1050$ CD steel $($Sut $=690$MPa,$Sy=580$MPa. Find the approximate location by using Shear and Moment diagrams. After that check for the stress concentration point to find the lowest fatigue factor of safety. Your goal is to find the smallest fatigue factor of safety and the location of it$.$ Follow the example $7-1$ and $7-2$ in your textbook or

ME $3365$

HOMEWORK $4$

lecture notes. Also, recall that we will use only the DE$-$Goodman criterion for fatigue, not Gerber or ASME elliptic. All diameters are given in this question, which makes things a bit easier than the examples.

You will use stress concentration factors in your calculations. You may assume all fillets are $2$ mm $.$ Use figures $A-15-8$ and $A-15-9$ for Kt values. Use Figures $6-20$ and $6-21$ for q values.