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The von Mises stress combines a plane stress state into a scalar measure based on distortion energy.
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Formula
σv, σx, σy and τxy in Pa
| Symbol | Meaning | Unit |
|---|---|---|
| Von Mises equivalent stress | Pa | |
| σx, σy | Normal stresses along the plane axes | Pa |
| In-plane shear stress | Pa |
\sigma_\mathrm{v}=\sqrt{\sigma_x^2-\sigma_x\sigma_y+\sigma_y^2+3\tau_{xy}^2}This is the plane-stress form of the von Mises criterion for isotropic ductile materials. It combines stress components using distortion energy; purely hydrostatic stress contributes no von Mises stress. Yield onset is assessed by comparison with a measured yield strength in a material model. This is not a normative safety design and does not directly apply to brittle or anisotropic materials.
This is the plane-stress form of the von Mises criterion for isotropic ductile materials. It combines stress components using distortion energy; purely hydrostatic stress contributes no von Mises stress. Yield onset is assessed by comparison with a measured yield strength in a material model. This is not a normative safety design and does not directly apply to brittle or anisotropic materials.
The von Mises stress combines a plane stress state into a scalar measure based on distortion energy.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Von Mises equivalent stress in plane stress” and check its unit and magnitude.
With σx=100 MPa, σy=0 and τxy=20 MPa, σv=√(1002+3·202)≈105.8 MPa.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: σv, σx, σy and τxy in Pa.
Formula cluster
The von Mises stress combines a plane stress state into a scalar measure based on distortion energy.
With σx=100 MPa, σy=0 and τxy=20 MPa, σv=√(1002+3·202)≈105.8 MPa.
Compare multiaxial elastic stress states for ductile isotropic materials.
Here is how to work through a typical Von Mises equivalent stress in plane stress (σv = √(σx² − σxσy + σy² + 3τxy²)) task step by step:
Task
Work through the numerical example for “Von Mises equivalent stress in plane stress” and check its unit and magnitude.
Solution path
With σx=100 MPa, σy=0 and τxy=20 MPa, σv=√(1002+3·202)≈105.8 MPa.
It combines several stress components into one scalar associated with yielding of isotropic ductile material in the von Mises model. It does not replace individual components for every other question. In particular, it is not a force direction or automatically an allowable stress. This plane-stress expression is for isotropic ductile materials under an appropriate elastic/yield model. Use consistent stress units and sign conventions. Von Mises stress is an equivalent scalar, not a normal stress acting on a plane, and the criterion does not itself provide a safety factor.
The term 3τxy2 raises equivalent stress because shear contributes to distortion energy. Under pure shear, σv=√3|τxy|. Squaring makes the sign of τxy irrelevant to this scalar, while the product σxσy means the signs of normal stresses still matter. This plane-stress expression is for isotropic ductile materials under an appropriate elastic/yield model. Use consistent stress units and sign conventions. Von Mises stress is an equivalent scalar, not a normal stress acting on a plane, and the criterion does not itself provide a safety factor.
The classical criterion primarily suits isotropic ductile materials whose yielding is approximately governed by distortion energy. Brittle materials, strong anisotropy, pressure-dependent yielding and damage require other criteria or material models. Even a correct σv does not replace a code-based safety assessment of a real component. This plane-stress expression is for isotropic ductile materials under an appropriate elastic/yield model. Use consistent stress units and sign conventions. Von Mises stress is an equivalent scalar, not a normal stress acting on a plane, and the criterion does not itself provide a safety factor.
Write the quantity and unit from the variable list next to every value: σv, σx, σy and τxy in Pa. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example With σx=100 MPa, σy=0 and τxy=20 MPa, σv=√(1002+3·202)≈105.8 MPa. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. This plane-stress expression is for isotropic ductile materials under an appropriate elastic/yield model. Use consistent stress units and sign conventions. Von Mises stress is an equivalent scalar, not a normal stress acting on a plane, and the criterion does not itself provide a safety factor.
The background states this starting condition: This is the plane-stress form of the von Mises criterion for isotropic ductile materials. It combines stress components. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. This plane-stress expression is for isotropic ductile materials under an appropriate elastic/yield model. Use consistent stress units and sign conventions. Von Mises stress is an equivalent scalar, not a normal stress acting on a plane, and the criterion does not itself provide a safety factor.
Quanta exam set
Curated exam set for "Von Mises equivalent stress in plane stress":
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Which formula describes Von Mises equivalent stress in plane stress?
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How do you rearrange Von Mises equivalent stress in plane stress for Base equation for the target quantity?
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Which common mistake happens with Von Mises equivalent stress in plane stress?
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Create a curated FSRS exam set for σv = √(σx² − σxσy + σy² + 3τxy²): formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.
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