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Von Mises stress

The von Mises stress combines several stress components into one equivalent stress that can be compared directly with the yield strength. The criterion states that the material yields when the equivalent stress reaches ReR_e, and it is used mostly for ductile materials.

σv=σ2+3τ2\sigma_v = \sqrt{\sigma^2 + 3\tau^2}von Mises, uniaxial stress with shear

Symbols

σv\sigma_vvon Mises stressPa
σ\sigmanormal stressPa
τ\taushear stressPa

Example

σ=100\sigma = 100 MPa, τ=40\tau = 40 MPa:

σv=1002+3⋅402≈131\sigma_v = \sqrt{100^2+3\cdot40^2} \approx 131 MPa.

Always compare σv\sigma_v with the yield strength ReR_e, not the ultimate strength RmR_m, for ductile materials.
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