Von Mises Stress Calculator
Combine a 2D plane-stress state — normal stresses σx and σy plus shear τxy — into a single von Mises equivalent stress you can check straight against a material's yield strength. Optionally supply the yield strength to get a safety factor and a pass/fail yield status.
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How to use this calculator
- Enter the normal stresses σx and σy in MPa (tension positive, compression negative).
- Optionally add the in-plane shear stress τxy in MPa; leave it blank for a state with no shear.
- Optionally enter the material yield strength to compute the safety factor and see whether the point yields.
How it works
The von Mises stress for plane stress is σ_vm = √(σx² − σx·σy + σy² + 3·τxy²). It represents the distortion energy in the material as one equivalent uniaxial stress. Under the von Mises (distortion-energy) criterion, a ductile metal is predicted to yield when σ_vm reaches its yield strength, so the safety factor against yielding is simply yield strength divided by σ_vm.
Worked example
Worked example. For σx = 100, σy = 50 and τxy = 30 MPa: σ_vm = √(100² − 100·50 + 50² + 3·30²) = √(10,000 − 5,000 + 2,500 + 2,700) = √10,200 = 100.995 MPa. With a 250 MPa yield strength the safety factor is 250 / 100.995 = 2.4754, so the point is Safe.
Common mistakes
- Applying the 2D form to a genuinely triaxial stress state — use the full 3D von Mises expression when a third stress component matters.
- Using von Mises for brittle materials like cast iron or concrete, which fail by a different mechanism; use a maximum-principal-stress or Mohr–Coulomb criterion instead.
- Dropping the sign on compressive stresses — σx and σy are signed, and the σx·σy cross term changes the result if a sign is wrong.
Frequently asked questions
What does a safety factor below 1 mean?
It means the von Mises stress exceeds the yield strength, so the material is predicted to yield at that point. The status reads 'Yields'. Redesign to reduce the stresses or use a stronger material until the factor comfortably exceeds 1 with your required margin.
Why 3 times the shear term?
The factor of 3 on τxy² falls out of the distortion-energy derivation of the von Mises criterion. It makes a pure shear stress τ reach yield when √3·τ equals the yield strength, matching the observed shear yield strength of ductile metals being about 0.577 of the tensile yield.
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Tip: Enter any known values to calculate the remaining results.
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