Equivalent stress
MPa
Von Mises intensity to compare with the allowable value.
Mechanics · Stress and deformation
Von Mises equivalent stress
Add axial normal stress and bending normal stress algebraically at the checked fibre, then combine that sum with shear stress.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
03
MetricResults
Utilization
%
Ratio σᵥ/σallow expressed as a percentage.
Safety factor
—
Simplified ratio σallow/σᵥ.
Combined normal stress
MPa
Algebraic sum of normal stresses σa + σb at the same point.
View calculation detailsFormulas, conversions, numerical substitution and resultsOpen ↓
Calculation note
Full calculation details
Isotropic ductile material. Static loading and a stress state representative of the checked point. No fatigue, buckling, stress concentration or additional code interaction. Allowable stress must be selected for the material, temperature, process and applicable design rule.
01Formulas and symbols
Formulas used
σ
σ = σa + σbCombined normal stress at the checked fibreσᵥ
σᵥ = √(σ² + 3τ²)Von Mises for one normal stress and shearσᵥ
σᵥ = √{[(σ₁−σ₂)²+(σ₂−σ₃)²+(σ₃−σ₁)²]/2}General form using principal stressesη ; S
η = σᵥ/σadm ; S = σadm/σᵥSimplified utilization and safety02Assumptions and limits
Scope of validity
- Isotropic ductile material.
- Static loading and a stress state representative of the checked point.
- No fatigue, buckling, stress concentration or additional code interaction.
- Allowable stress must be selected for the material, temperature, process and applicable design rule.
03Validation example
Reference numerical case
- σa = 80 MPa, σb = 40 MPa, τ = 30 MPa and σallow = 250 MPa.
- σ = 120 MPa.
- σᵥ = √(120² + 3×30²) = 130.77 MPa.
- Utilization = 52.31% and safety factor = 1.912.
04Frequently asked questions
Questions about the calculation
Can axial and bending stress be added directly?
Yes at the same point and in the same normal direction, while respecting signs. The checked fibre may be in tension or compression.
Is Von Mises suitable for brittle materials?
The criterion is mainly used for ductile materials. Brittle materials generally require a different criterion.
Is the displayed factor code-compliant?
No. It is the direct ratio between the entered allowable stress and calculated equivalent stress.
05References
Technical references
- Budynas & Nisbett, Shigley’s Mechanical Engineering Design, distortion-energy criterion.
- Gere & Goodno, Mechanics of Materials, stress states and principal stresses.
- BIPM, The International System of Units (SI), 9th edition.