# Principal stresses

From Wikiversity

## Principal Stresses in Two and Three Dimensions[edit]

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,

where,

The quantities are the **stress invariants**.