Zeng et$.$ al$.(2002)$ produced a nice data set for cyclic loading of S$240$MC steel. I have generated the corresponding SN curve for the data set and approximated the low cycle $($blue$),$ high cycle $($red$),$ and endurance $($yellow$)$ portions with linear approximations $($please note, the data does not appear to have an endurance limit$,$ but for the sake of this problem we will approximate one$).$

Using the SN$-$curve, and assuming a piece of S$240$MC steel is cyclically loaded as shown below, determine the factor of safety using the a$)$ Soderberg, b$)$ Goodman, and c$)$ Gerber criterions.

$lon$

$$

$$

$$

$5$

$5$

$s$

iog$($iv$)$