Mohr's Circle Calculator

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This free Mohr's Circle tool calculates 2D stress states and principle stresses for a material given normal and shear stress. 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) = `