Calculate Von Mises stress from 2D plane stress, 3D principal stresses, or full stress components, with optional yield-strength check.

Von Mises Stress Calculator

Calculate equivalent stress directly from a known 2D or 3D stress state.

2D Plane Stress
3D Principal Stresses
3D Stress Components
Use σx, σy, and τxy to calculate equivalent stress for plane stress.
Formula: σv = √(σx² – σxσy + σy² + 3τxy²)
Use principal stresses σ1, σ2, and σ3 to calculate equivalent stress.
Formula: σv = √(((σ1 – σ2)² + (σ2 – σ3)² + (σ3 – σ1)²) / 2)
Use full 3D stress components to calculate equivalent stress.
Formula: σv = √(0.5[(σx – σy)² + (σy – σz)² + (σz – σx)² + 6(τxy² + τyz² + τzx²)])

Optional Yield Check

Result

Von Mises Stress Formula

The following equation is used to calculate the von mises stress acting on an object. 

V = √(σx^2 - (σx * σy) + σy^2 + (3 *txy^2))
  • Where V is the Von Mises Stress
  • σx is the normal stress x component
  • σy is the normal Stress y component
  • τxy is the Shear Stress

Von Mises Stress Definitoin

A von Mises stress is a measure of the total overall stress acting on material included normal stress in the x and y direction as well as the shear stress.

Von Mises Stress Example

How to calculate Von Mises stress?

  1. First, calculate the normal stresses.

    Calculate the normal stress in the x and y planes.

  2. Next, determine the shear stress.

    Determine the total shear stress.

  3. Finally, calculate Von Mises stress.

    Calculate the Von Mises stress using the formula above.

FAQ

What is von Mises stress?

Von Mises stress is used to determine if a ductile metal will yield when subjected to complex loading conditions. These complex loading conditions include x and y components of stress along with shear stress.

How is von mises stress calculted?

Von Mises stress is calculated using the 3 components of stress, x, y, and shear, and the formula above.

When was Von Mises stress discovered?

Von mises stress was first proposed in 1904 by Huber and later popularized by von Mises.