Prob. $1(25$ pts$)$

A nonrotating, machined steel rod has a square section with $40$mm$\backslash$times $40$mmM$\_($min$)=0,$M$\_($max$)=2560$N$-$m

A$)$ Determine its corrected endurance limit$,$S$\_($e$)$ with $99\mathrm{.}9\%$ reliability if it is used in an environment that has a temperature at $500\backslash$deg C$.$ The material has an ultimate tensile strength of $680$ MPa $.$

$($B$)$ Build the S$-$N equation, S$=$aN$^($b$).$

$($C$)$ Find the factor of safety against a fatigue failure using the Goodman criterion.

How many cycles of life can be expected?