A state of plane stress in an aircraft skin panel is defined by $\sigma_x = 120\text{ MPa}$, $\sigma_y = 40\text{ MPa}$, and $\tau_{xy} = 30\text{ MPa}$. What is the maximum in-plane shear stress $\tau_{\max}$ in MPa?

Answer Key:

50

### Solution: $\tau_{\max} = \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2} = \sqrt{\left(\frac{120 - 40}{2}\right)^2 + 30^2} = \sqrt{40^2 + 30^2} = \sqrt{1600 + 900} = 50\text{ MPa}$. Correct: 50.

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