Finding the max shear stress at a point on a plate (with a hole)

[bill nye scienceguy!]

i need to find max shear stress at a point on a plate (with a hole) under tension. i found using experimental data the principle strains at the point but i need to find the max shear stress using this data to compare it with a result found analytically.

any suggestions?

 

[FredGarvin]

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:

$$\tau_{max}=\sqrt{\left[ \frac{\sigma_x-\sigma_y}{2}\right]^2 + \tau_{xy}^2}$$