For a state of plane stress (sigma_x, sigma_y, tau_ xy ), the maximum in-plane shear stress is:

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Mechanical Engineering QUESTION #2510

Question 1

For a state of plane stress \((\sigma_x, \sigma_y, \tau_{xy})\), the maximum in-plane shear stress is:

\(\tau_{max} = \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2}\)✔️
\(\tau_{max} = \frac{\sigma_x + \sigma_y}{2}\)
\(\tau_{max} = \sigma_x - \sigma_y\)
\(\tau_{max} = \tau_{xy}\)

Correct Answer Explanation

The maximum in-plane shear stress equals the radius of Mohr's circle: \(\tau_{max}=\sqrt{\left(\frac{\sigma_x-\sigma_y}{2}\right)^2+\tau_{xy}^2}\).