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 Sci Advisor P: 5,095 Are you considering this plane stress? If you are, you'll have two principal stresses. Think about Mohr's Circle for a second...The principal stresses lie in a plane with no shear stresses (they lie on the horizontal axis). So if you rotate around 90° in Mohr's circle, you'll get to the point of max shear (the highest point on the vertical axis). Geometrically speaking that is the same as saying $$\tau_{max} = \frac{\sigma_1-\sigma_2}{2}$$ This also assumes that you follow the standard practice of numbering the highest principal stress as $$\sigma_1$$. You can double check it by running the calculation with the regular stress components: $$\tau_{max}=\sqrt{\left[ \frac{\sigma_x-\sigma_y}{2}\right]^2 + \tau_{xy}^2}$$