Problem $3(3$ points, fatigue loading, fluctuating load, ME $3670$ review$)$: Same figure and values from Problem $2,$ but if the force is now a fluctuating

force with $F_{\text{m}\text{i}\text{n}}=20kN$ and $F_{\text{m}\text{a}\text{x}}=50KN,$

Obtain the modified endurance limit $S_2$ after accounting for all modification factors. Use $k_a$ value from Problem $(2).$

Using suitable formulae, obtain ${}_{\text{m}\text{a}\text{x}}$ and ${}_{\text{m}\text{i}\text{n}}.$ Then, calculate mean stress ${}_m$ and amplitude stress ${}_a$

Determine whether shaft will fail based on the Langer and the Goodman equation. Sketch and mark the Goodman and Langer lines.

Comment on shaft life