# What really is so special about principal stresses or stress invariants?

At any point inside a structural element under deformation, we can always find three planes such that when we define a coordinate system with basis vectors lying on those planes, the shear stresses at that point are zero and the stress tensor is diagonal.

The principal stresses are the eigenvalues of the stress tensor, and are invariant of the rotation of the coordinate system.

This last feature on bold is recited everywhere.But my question is, so what? Why is it so useful to find these stresses whose components don't change with rotation of the coordinate system? And why would I even want to rotate my coordinate system?

• I wouldn't have stated three planes but rather four dimensions. I say this because any stresses are operational in time and are dimensional vectors Jun 8, 2019 at 12:46