Principal Stresses in Two and Three Dimensions
The principal stresses are the components of the stress tensor when the basis is changed in such a way that the shear stress components become zero. To find the principal stresses in two dimensions, we have to find the angle at which . This angle is given by
Plugging into the transformation equations for stress we get,
Where are the shear tractions usually zero in a body?
The principal stresses in three dimensions are a bit more tedious to calculate. They are given by,
The quantities are the stress invariants.