`sigma_x = `

`sigma_y = `

`tau_(xy) = `

`sigma_1 = `

`sigma_2 = `

`theta_p = `

`theta = `

`sigma_x' = `

`sigma_y' = `

`tau_(xy)' = `

`sigma_(avg) = `

`tau_(max)' = `

`theta_(tau_(max))' = `

`sigma_(avg) = (sigma_x + sigma_y) / 2 = (sigma_1 + sigma_2) /2 = `

`R = tau_(max) = (sigma_1 - sigma_2) / 2 = sqrt((sigma_x - sigma_(avg))^2 + tau_(xy)^2) = `

`sigma_(1) = sigma_(avg) + R = `

`sigma_(2) = sigma_(avg) - R = `

`theta_(p) = tan^(-1)(tau_(xy)/(sigma_x - sigma_(avg))) / 2 = `

`theta_(tau_(max)) = theta_p - pi/4 = `

`sigma_x' = sigma_(avg) + (sigma_x - sigma_y)/2 * cos(2*theta) + tauxy * sin(2*theta) = `

`sigma_y' = sigma_(avg) - (sigma_x - sigma_y)/2 * cos(2*theta) - tauxy * sin(2*theta) = `

`tau_(xy)' = -(sigma_x-sigma_y) * sin(2*theta)/2 + tau_(xy)*cos(2*theta) = `

`sigma_x = sigma_(avg) + R + cos(2*theta_p) = `

`sigma_y = sigma_(avg) - R + cos(2*theta_p) = `

`tau_(xy) = R + sin(2*theta_p) = `