Notice that in the example of Chapter 7.1, the shear stress increased in magnitude while the normal stresses decreased. The opposite can occur as well; you can rotate the element in such a way to reduce the shear stress and “contribute” it to the normal stresses.

What if we wanted to “contribute” *all* shear stress to the normal stresses? The result will be maximum normal stresses, or what we call *principal stresses*.

Similarly we can rotate the element in such a way to get the maximum shear stress or τ_{max in-plane}.
In this case we get average stresses for the normal stress instead (you’ll see why in Mohr’s Circle).

Here are the formulas for you to get principal σ and τ_{max in-plane}:

Notice that in the example of Chapter 7.1, the shear stress increased in magnitude while the normal stresses decreased. The opposite can occur as well; you can rotate the element in such a way to reduce the shear stress and “contribute” it to the normal stresses.

What if we wanted to “contribute” *all* shear stress to the normal stresses? The result will be maximum normal stresses, or what we call *principal stresses*.

Similarly we can rotate the element in such a way to get the maximum shear stress or τ_{max in-plane}.
In this case we get average stresses for the normal stress instead (you’ll see why in Mohr’s Circle).

Here are the formulas for you to get principal σ and τ_{max in-plane}: