Von Mises Stress Calculator

What is von Mises stress?

Stress in a machine part or structural member is rarely uniaxial: tension, compression and shear act together at the same point. The yield strength of a material, however, comes from a uniaxial tensile test. The von Mises equivalent stress reduces a multiaxial stress state to a single number that can be compared with that test. When it reaches the yield strength, a ductile material begins to yield.

For plane stress the formula is σ_vM = √(σx² − σx × σy + σy² + 3 × τxy²). With the three principal stresses known, use σ_vM = √(½ × [(σ1 − σ2)² + (σ2 − σ3)² + (σ3 − σ1)²]).

The Tresca criterion

The Tresca (maximum shear stress) criterion is simpler: the equivalent stress is the difference between the largest and the smallest principal stress. It is always equal to or larger than the von Mises value, so it is the more conservative of the two. Tests on ductile metals agree better with von Mises. The calculator reports both side by side.

Safety factor

The safety factor against yield is n = S_y / σ_vM. A value of 1 means the material is at the yield point. What value is adequate depends on load uncertainty, the consequence of failure and the standard you work to.

Example

At a point σx = 60, σy = 40 and τxy = −15 MPa, and the yield strength is 100 MPa. Then σ_vM = √(60² − 60 × 40 + 40² + 3 × 15²) = √3475 = 58.95 MPa and n = 1.70. The principal stresses are 68.03 and 31.97 MPa. Because the third principal stress is zero, the Tresca equivalent stress is 68.03 MPa and its safety factor is 1.47.

Limits

These criteria predict only the onset of yielding in ductile materials under static load. Fatigue may govern under repeated loading and buckling in slender members under compression. Brittle materials such as cast iron, concrete and glass need different criteria. The stresses you enter should already include stress concentration at notches and holes.