Library / Mechanical / MEC-38
Mechanical
Factor of safety
Ratio of the material’s yield strength to the working equivalent stress.
- Ref
- MEC-38
- Rev
- v1
- Field
- Mechanical
- Result
- n
σ_y is the yield strength of the material in MPa and σ_eq the equivalent stress (such as von Mises or Tresca) found for the worst load case. n is how many times the load could rise before first yield. A value of 1 means the part is at the point of yielding.
Ratio of the material’s yield strength to the working equivalent stress. A value of 1 means the part is at the point of yielding.
Calculator
- Stress margin σy − σeq150 MPa
- Load increase possible before yield150 %
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- n = 2.5 at the defaults leaves a 150 MPa margin below yield. Typical design values lie between about 1.5 and 3, depending on how well the loads and material are known.
- n counts only against yield. For brittle materials, fatigue or buckling, a different strength measure is needed.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| σeq Equivalent stress | 1 to 2,000 MPa | 0.125 | 250 | 249.9 | +10% | −9.09 % |
| σy Yield strength | 10 to 2,000 MPa | 0.1 | 20 | 19.9 | +10% | +10 % |
Sweep of Equivalent stress
| Equivalent stress (MPa) | Factor of safety |
|---|---|
| 1 | 250 |
| 2.586 | 96.67 |
| 6.687 | 37.38 |
| 17.29 | 14.46 |
| 44.72 | 5.59 |
| 115.6 | 2.162 |
| 299.1 | 0.8359 |
| 773.4 | 0.3233 |
| 2,000 | 0.125 |
Sweep one variable
Variables and how each one contributes
Factor of safety
What the equation gives you. Everything else feeds it.
Yield strength
The yield strength of the material, in MPa. Directly proportional: a stronger material raises the factor by the same proportion.
Equivalent stress
The equivalent working stress, in MPa. Inverse: halving the stress doubles the factor. A 10 % rise in σeq lowers n by about 9 %.
Worked example with the values above
- Yield strength: σy = 250 MPa. Equivalent stress: σeq = 100 MPa.
- Divide: 250 / 100.
- n = 2.5, so the load could rise 150 % before first yield.
Assumptions and limits
- The equivalent stress was found from the worst realistic load case.
- Yield is the limit that matters; the material is ductile.
Common mistakes
- Dividing the ultimate tensile strength by the stress when yield is the limit.
- Treating n = 1 as safe. At that value any overload causes permanent deformation.
Statistics and uncertainty
The factor of safety guards against scatter in both the load and the material strength. With a 10 % scatter in yield strength and 20 % in the load, n = 2.5 reduces the chance of yielding to a very small value, but n = 1.2 would not. The factor does not say how likely failure is, only how far away the mean values are.
Where it is used
- Deciding whether a design margin is adequate.
- Comparing two materials for the same load.
Maths you need
- Yield strength: the stress at which permanent deformation starts
- Ratios: strength over stress