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Dec6-07, 10:54 AM
Sci Advisor
FredGarvin's Avatar
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

[tex]\tau_{max} = \frac{\sigma_1-\sigma_2}{2}[/tex]

This also assumes that you follow the standard practice of numbering the highest principal stress as [tex]\sigma_1[/tex].

You can double check it by running the calculation with the regular stress components:

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