Von Mises Stress Calculator

von Mises Stress in Plane Stress

von Mises stress combines normal and shear components into one scalar value used to compare a 2D stress state against a material yield strength. It is widely used for ductile metals where yielding depends on the overall distortion energy, not a single stress component alone.

Plane Stress Formula

$$\sigma_{\mathrm{vm}} = \sqrt{\sigma_x^2 - \sigma_x \sigma_y + \sigma_y^2 + 3\tau_{xy}^2}$$

Enter normal stresses $\sigma_x$, $\sigma_y$ and shear stress $\tau_{xy}$ on the same reference plane. If $\sigma_{\mathrm{vm}}$ exceeds the yield strength, the material is predicted to yield under the von Mises (distortion energy) criterion.

Design Use

Compare von Mises stress to yield strength with an appropriate factor of safety. For combined loading in sheets, shells, and thin-walled pressure vessels, plane stress is often a good approximation.

Frequently Asked Questions

What is von Mises stress?

von Mises stress is an equivalent scalar stress derived from the stress tensor. For ductile materials it predicts yielding when it reaches the uniaxial yield strength.

When is plane stress valid?

Plane stress applies when stress in one direction is negligible, such as thin plates with negligible through-thickness normal stress.

What units should I use?

Use consistent stress units such as MPa or psi for all three inputs. The output uses the same unit system.

How does this relate to Mohr's circle?

Mohr's circle visualizes the same 2D stress state and can also report von Mises stress from the same σx, σy, and τxy inputs.

Does von Mises apply to brittle materials?

Not reliably. Brittle failure is often governed by maximum principal stress or fracture mechanics rather than von Mises yielding.

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Von Mises Stress Calculator

von Mises Stress in Plane Stress

Plane Stress Formula

Design Use

Frequently Asked Questions

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