We can use the formula $w = \frac{\sigma_y \cdot d}{\sigma_a}$, where $\sigma_y$ is the yield stress, $d$ is the depth, and $\sigma_a$ is the applied stress. Substituting the given values, we get:
\[w = \frac{\sigma_y \cdot d}{\sigma_a} = 1.1667 \, \text{inches}\]
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