KEVOS® MAKEOS · Strength
Principal Stresses and von Mises
What are the principal stresses, maximum shear and von Mises stress for this stress state?
Principal stresses, their direction, maximum shear stress, von Mises and Tresca equivalent stresses for a plane stress state, with safety factors against yield.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Normal stress σx | MPa | Normal stress in the X direction (tension positive) from your calculation. |
| Normal stress σy | MPa | Normal stress in the Y direction (tension positive). |
| Shear stress τxy | MPa | Shear stress on the X and Y faces. |
| Yield strength | MPa | Minimum yield strength from the material certificate or specification, not a typical value. |
| Required safety factor | Factor of safety required by your design code, customer specification or company standard. |
Method and formulas
- σ₁,₂ = (σx + σy) ÷ 2 ± √(((σx − σy) ÷ 2)² + τxy²); θp = ½ atan2(2τxy, σx − σy).
- von Mises σ′ = √(σ₁² − σ₁σ₂ + σ₂²); Tresca = max(|σ₁ − σ₂|, |σ₁|, |σ₂|) with σ₃ = 0.
- Safety factor = yield ÷ equivalent stress.
- Example: σx 120, σy -40, τ 50 MPa give σ₁ = 134.34 and σ₂ = -54.34 MPa, von Mises 168.23 MPa.
Limitations
- Plane stress (σz = 0); ductile, isotropic materials for the yield criteria.
- Stress concentrations must already be included in the entered stresses.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Combine bending, axial and torsional stresses at a critical point
- Check a hand calculation or FEA result
- Compare yield criteria
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Principal stresses σ1 and σ2
- Principal angle
- Maximum shear stress
- von Mises and Tresca equivalent stresses
- Safety factors
Interpreting the result
- Use von Mises for ductile metals; Tresca is slightly more conservative.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 212–218. Topic reference; no source tables or recommended settings are reproduced.
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