When using the Gerber fatigue failure criterion in a stochastic problem, Eqs. (6–80) and (6–81) are useful. They are also computationally complicated. It is helpful to have a computer subroutine or procedure that performs these calculations. When writing an executive program, and it is appropriate to find S_{a} \text { and } C_{S a} , a simple call to the subroutine does this with a minimum of effort. Also, once the subroutine is tested, it is always ready to perform. Write and test such a program.
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Eqs. (6–80) : \bar{S}_{a}=\frac{r^{2} \bar{S}_{u t}^{2}}{2 \bar{S}_{e}}\left[-1+\sqrt{1+\left(\frac{2 \bar{S}_{e}}{r \bar{S}_{u t}}\right)^{2}}\right]
Eqs. (6–81) : C_{S a}=\frac{\left(1+C_{S u t}\right)^{2}}{1+C_{S e}} \frac{\left\{-1+\sqrt{1+\left[\frac{2 \bar{S}_{e}\left(1+C_{S e}\right)}{r \bar{S}_{u t}\left(1+C_{S u t}\right)}\right]^{2}}\right\}}{\left[-1+\sqrt{1+\left(\frac{2 \bar{S}_{e}}{r \bar{S}_{u t}}\right)^{2}}\right]}-1