Mohr's Circle

2D Plane Stress Calculations

Welcome to the Mohr's Circle Plane Stress Calculator. Enter an initial stress state below to calculate Principal Stress, Rotated Stress and Max Shear Stress.

Instructions

  1. Choose the Plane Stress or Principal Stress tab.
  2. Enter Stresses and Rotations (results are updated automatically).
  3. Scroll down to see Stress Blocks, Equations and Results.

Mohr's Circle
Initial Stress
`sigma_x = `
`sigma_y = `
`tau_(xy) = `
Principal Stress
`sigma_1 = `
`sigma_2 = `
`theta_p = `

Rotated Stress
`theta = `
`sigma_x' = `
`sigma_y' = `
`tau_(xy)' = `
Max Shear Stress
`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) = `