Physics

Von Mises Stress Calculator

Find the von Mises equivalent stress from two principal stresses.

Calculated Output

Von Mises stress (MPa) 105.83

Formula: σ_v = √(σ₁² − σ₁σ₂ + σ₂²)

Step-by-Step Breakdown

1. Values used:

2. Principal stress σ₁ = 120 MPa

3. Principal stress σ₂ = 40 MPa

5. Von Mises stress = 105.83MPa

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The math behind it

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

σ₁ 120, σ₂ 40 MPa → σ_v ≈ 105.8 MPa.

Why not just use the largest stress?

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