Principal stresses
Given the stress components s_{x}, s_{y}, and t_{xy}, this calculator computes the principal stresses s_{1}, s_{2}, the principal angle q_{p}, the maximum shear stress t_{max} and its angle q_{s}. It also draws an approximate Mohr's circle for the given stress state.
The Mohr's circle associated with the above stress state is similar to the following figure. However, the exact location of the center s_{Avg}, the radius of the Mohr's circle R, and the principal angle q_{p} may be different from what are shown in the figure.


Equations behind the Calculator 


The formulas used in this calculator are,

Principal Stress
Need to find the principal stresses and their directions for a given input
stress state? These calculators do the math for you for the case of Plane
Stress and Plane
Strain.
http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/calc_principal_stress.cfm


Introduced by Otto Mohr in 1882, Mohr's Circle illustrates principal stresses and stress transformations via a graphical format,
The two principal stresses are shown in red, and the maximum shear stress is shown in orange. Recall that the normal stesses equal the principal stresses when the stress element is aligned with the principal directions, and the shear stress equals the maximum shear stress when the stress element is rotated 45° away from the principal directions. As the stress element is rotated away from the principal (or maximum shear) directions, the normal and shear stress components will always lie on Mohr's Circle. Mohr's Circle was the leading tool used to visualize relationships between normal and shear stresses, and to estimate the maximum stresses, before handheld calculators became popular. Even today, Mohr's Circle is still widely used by engineers all over the world. 

The average stress, s_{avg}, and a "radius" R (which is just equal to the maximum shear stress),

