Mohr's circle is a tool for analyzing element stress. The drawing below shows mohr's circle and some of the relavent points of interest.
Given a state of stress, ( σ x , σ y , τ x y ) {\displaystyle (\sigma_x,\sigma_y,\tau_{xy})} , we can calculate the principle stresses,
σ 1 = 1 2 ( σ x + σ y ) + 1 2 ( σ x − σ y ) 2 + 4 τ x y 2 {\displaystyle \sigma_1=\frac{1}{2}\left(\sigma_x+\sigma_y\right)+\frac{1}{2}\sqrt{\left(\sigma_x-\sigma_y\right)^2+4\tau_{xy}^2}}
σ 2 = 1 2 ( σ x + σ y ) − 1 2 ( σ x − σ y ) 2 + 4 τ x y 2 {\displaystyle \sigma_2=\frac{1}{2}\left(\sigma_x+\sigma_y\right)-\frac{1}{2}\sqrt{\left(\sigma_x-\sigma_y\right)^2+4\tau_{xy}^2}}
, we can calculate the principle stresses,
