Mohr's Circle can be used to find the directions of the principal axes. To show this, first suppose that the normal and shear strains, ex, ey, and exy, are obtained at a given point O in the body. They are expressed relative to the coordinates XY, as shown in the strain element at right below.
The Mohr's Circle for this general strain state is shown at left above. Note that it's centered at eAvg and has a radius R, and that the two points (ex, exy) and (ey, -exy) lie on opposites sides of the circle. The line connecting ex and ey will be defined as Lxy.
The angle between the current axes (X and Y) and the principal axes is defined as qp, and is equal to one half the angle between the line Lxy and the e-axis as shown in the schematic below,
A set of six Mohr's Circles representing most strain state possibilities are presented on the examples page.
Also, principal directions can be computed by the principal strain calculator.