A shaft rotating at $60re\frac{v}{m}in$ is subjected to a fully reversed bending normal stress with varying amplitude. The material is steel with a tensile strength of $145$ ksi $.$ The shaft has a diameter of $25$ mm and a hot$-$rolled surface finish. A reliability of $50\%$ is assumed and there are no hightemperature effects. The duty cycle calls for:

$10\%$ of the time spent at ${}_{M1}=20$ksi

$40\%$ of the time spent at $m2=40$ksi

$20\%$ of the time spent at ${}_{M3}=60$ksi

Remainder of the time spent at ${}_{M4}=80$ksi

$($a$)$ Use Miner's rule to estimate the total number of load cycles to failure.

$($b$)$ How long in hours can we expect the shaft to last before fatigue failure occurs?

Answers

$($a$)$ N $($cycles$)$

$($b$)$ Life $($hours$)$