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,
