Calculator · Structural Mechanics
Von Mises Stress Calculator
The von Mises equivalent stress collapses a multiaxial state into the single uniaxial stress that would be equally severe for yielding of a ductile metal. It is the quantity a yield strength should be compared against.
Stress state
Used only for the utilisation and factor of safety below.
σ is tensile positive. τxy acts on the +x face in the +y direction. θ is a counter-clockwise rotation of the axes in physical space.
Results
| Major principal stress σ₁ | 88.31 MPa |
|---|---|
| Minor principal stress σ₂ | -28.31 MPa |
| Von Mises equivalent stress σᵥ | 105.36 MPa |
| Yield strength Sy | 250 MPa |
| Utilisation σᵥ / Sy | 42.143 % |
| Factor of safety n = Sy / σᵥ | 2.3729 |
| Yield verdict | elastic: below the yield strength |
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Technical reference
σᵥ = √( σx² − σx σy + σy² + 3 τxy² ) (plane stress)
σᵥ = √( σ₁² − σ₁ σ₂ + σ₂² ) (in principal form)
n = Sy / σᵥ
- σᵥ
- von Mises equivalent (distortion-energy) stress[Pa]
- Sy
- uniaxial yield strength of the material[Pa]
- n
- factor of safety against yielding[–]
The criterion is a DUCTILE yield criterion, based on distortion energy. It is not a fracture criterion and is inappropriate for brittle materials, where a maximum-normal-stress or Mohr–Coulomb criterion applies instead.
σᵥ is always non-negative and is insensitive to hydrostatic pressure: adding the same normal stress to σx and σy in pure tension changes σᵥ, but a purely hydrostatic 3D state produces none at all.
In pure shear the criterion predicts yielding at τ = Sy/√3 ≈ 0.577 Sy, which is where the shear yield strength of a ductile metal comes from.
Assumptions
- · Plane stress: the out-of-plane face is free, σz = 0.
- · Ductile, isotropic material obeying the distortion-energy (von Mises) yield criterion.
- · Static loading. Fatigue, creep, and stress concentrations are outside this check.