Von Mises Stress Calculator

Find the von Mises equivalent stress from two principal stresses.

Von Mises stress (MPa) 105.83

Formula: σ_v = √(σ₁² − σ₁σ₂ + σ₂²)

Step-by-step with your numbers:
1. Values used:
2. Principal stress σ₁ = 120 MPa
3. Principal stress σ₂ = 40 MPa
4.
5. Von Mises stress = 105.83MPa
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Von Mises stress predicts yielding of ductile materials under combined loading.

The math behind it

For plane stress, σ_v = √(σ₁² − σ₁σ₂ + σ₂²). Yielding starts when σ_v reaches the yield strength.

Worked example

σ₁ 120, σ₂ 40 MPa → σ_v ≈ 105.8 MPa.

FAQ

Why not just use the largest stress?

Ductile failure depends on distortion energy, captured by the von Mises criterion.