Von Mises Stress Calculator
Calculate equivalent stress from multiple stress components for material yield analysis
Calculate Von Mises Stress
2D General Stress Components
Von Mises Stress Results
Configuration: 2D - General
Formula used: σᵥ = √(σₓ² - σₓσᵧ + σᵧ² + 3τₓᵧ²)
Example Calculation
2D Plane Stress Example
Problem: A steel plate under biaxial loading
σₓ = 100 MPa (tension)
σᵧ = 50 MPa (tension)
τₓᵧ = 25 MPa (shear)
Calculation
σᵥ = √(σₓ² - σₓσᵧ + σᵧ² + 3τₓᵧ²)
σᵥ = √(100² - 100×50 + 50² + 3×25²)
σᵥ = √(10000 - 5000 + 2500 + 1875)
σᵥ = 96.82 MPa
Stress Types
Normal Stress
Perpendicular to surface
Tension (+) or compression (-)
Shear Stress
Parallel to surface
Causes deformation
Principal Stress
Maximum/minimum normal stresses
No shear on these planes
Von Mises Tips
Used for ductile materials under complex loading
Compare result with material yield strength
If σᵥ > Sᵧ, material will likely yield
Accounts for both normal and shear stresses
Understanding Von Mises Stress
What is Von Mises Stress?
Von Mises stress is an equivalent stress that combines multiple stress components into a single value. It represents the uniaxial tensile stress that would create the same distortion energy as the actual combination of applied stresses.
Why is it Important?
- •Predicts material yielding under complex loading
- •Simplifies stress analysis to single value
- •Enables comparison with material properties
- •Essential for engineering design safety
Applications
Structural Engineering
Bridge design, building frames, pressure vessels
Mechanical Design
Machine components, automotive parts, aircraft structures
Materials Science
Material testing, failure analysis, safety factors
Note: Von Mises criterion is most accurate for ductile materials. For brittle materials, consider maximum principal stress theory.