Von Mises Stress Calculator
Plane stress with σx = 100 MPa and τxy = 50 MPa has a von Mises equivalent stress of 132.288 MPa, against a Tresca value of 141.4 MPa.
132.28756555323 MPa
Full answer, then cut to fewer decimals (not rounded):
- 132.28756555323 MPa
- 132.2875655532 MPa
- 132.287565553 MPa
- 132.28756555 MPa
- 132.2875655 MPa
- 132.287565 MPa
- 132.28756 MPa
- 132.2875 MPa
- 132.287 MPa
- 132.28 MPa
- 132.2 MPa
- Principal stresses σ₁, σ₂, σ₃
- 120.711, 0, -20.7107 MPa
- Tresca equivalent σ₁ − σ₃
- 141.4213562 MPa
- Maximum shear stress (σ₁ − σ₃)/2
- 70.71067812 MPa
- Factor of safety (von Mises)
- 1.889822365
- Factor of safety (Tresca)
- 1.767766953
- Factor of safety (maximum normal stress)
- 2.071067812
Step-by-step solution
- σ₁,₂ = (σx + σy)/2 ± √(((σx − σy)/2)² + τxy²) → 120.711, 0 MPa (σ₃ = 0)
- σ_v = √(½[(σ₁ − σ₂)² + (σ₂ − σ₃)² + (σ₃ − σ₁)²]) = 132.2875656 MPa
- Tresca: σ₁ − σ₃ = 141.4213562 MPa
Von Mises Stress Formula
σ_v = √(½[(σ₁ − σ₂)² + (σ₂ − σ₃)² + (σ₃ − σ₁)²])
plane stress: σ_v = √(σx² − σxσy + σy² + 3τxy²); Tresca σ₁ − σ₃
Worked Example
A plane stress state of σx = 100 MPa and τxy = 50 MPa:
- σ₁,₂ = (σx + σy)/2 ± √(((σx − σy)/2)² + τxy²) → 120.711, 0 MPa (σ₃ = 0)
- σ_v = √(½[(σ₁ − σ₂)² + (σ₂ − σ₃)² + (σ₃ − σ₁)²]) = 132.2875656 MPa
- Tresca: σ₁ − σ₃ = 141.4213562 MPa
Tresca equivalent σ₁ − σ₃: 141.4213562 MPa · Maximum shear stress (σ₁ − σ₃)/2: 70.71067812 MPa · Factor of safety (von Mises): 1.889822365 · Factor of safety (Tresca): 1.767766953 · Factor of safety (maximum normal stress): 2.071067812
GATE tip
In pure shear τ, von Mises gives σ_v = √3 τ, so the shear yield strength is S_y/√3 = 0.577 S_y; Tresca gives 0.5 S_y.
More Structures Calculators
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Thin-Walled Torsion Calculator
q = T / (2A), τ = q/t, J = 4A²t / ∮ds
open section J = Σ bt³/3, τ_max = Tt/J; twist θ = TL/(GJ)
Example: A closed aluminium tube enclosing 20,000 mm² with 2 mm walls and 600 mm perimeter under 1 kN·m: Shear stress τ = 12.5 MPa.
Frequently asked questions
Von Mises or Tresca?
Both predict yield in ductile metals; Tresca is slightly more conservative (up to 15 % lower allowable stress in pure shear). Brittle materials use the maximum normal stress theory.
Why include σ₃ = 0 in plane stress?
The out-of-plane principal stress is zero but still counts: if σ₁ and σ₂ have the same sign, the largest shear acts out of plane, (σ₁ − 0)/2.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Von Mises Stress Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/von-mises-stress-calculator/
IEEE
Scientific Converters, "Von Mises Stress Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/von-mises-stress-calculator/