Repeat Prob. 6–73 for the Smith-Dolan fatigue failure locus, implementing Eqs. (6–86) and (6–87).
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Eq. (6–86) : \bar{S}_{a}=\frac{r \bar{S}_{u t}+\bar{S}_{e}}{2}\left[-1+\sqrt{1+\frac{4 r \bar{S}_{u t} \bar{S}_{e}}{\left(r \bar{S}_{u t}+\bar{S}_{e}\right)^{2}}}\right]
Eq. (6–87) : \begin{aligned}C_{S a}=& \frac{r \bar{S}_{u t}\left(1+C_{S u t}\right)+\bar{S}_{e}\left(1+C_{S e}\right)}{2 \bar{S}_{a}} \\& \cdot\left\{-1+\sqrt{1+\frac{4 r \bar{S}_{u t} \bar{S}_{e}\left(1+C_{S e}\right)\left(1+C_{S u t}\right)}{\left[r \bar{S}_{u t}\left(1+C_{S u t}\right)+\bar{S}_{e}\left(1+C_{S e}\right)\right]^{2}}}\right\}-1\end{aligned}