Mohr's Circle can be used to find the directions of the principal axes. To show this, first suppose that the normal and shear stresses, s_{x}, s_{y}, and t_{xy}, are obtained at a given point O in the body. They are expressed relative to the coordinates XY, as shown in the stress element at right below.
The Mohr's Circle for this general stress state is shown at left above. Note that it's centered at s_{avg} and has a radius R, and that the two points {s_{x}, t_{xy}} and {s_{y}, t_{xy}} lie on opposites sides of the circle. The line connecting s_{x} and s_{y} will be defined as L_{xy}.
The angle between the current axes (X and Y) and the principal axes is defined as q_{p}, and is equal to one half the angle between the line L_{xy} and the saxis as shown in the schematic below,
A set of six Mohr's Circles representing most stress state possibilities are presented on the examples page.
Also, principal directions can be computed by the principal stress calculator.
