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Factor of Safety

Also known as FOS · safety factor

FS=σuσallowFS = \frac{\sigma_{u}}{\sigma_{allow}}

Worked example: 400 MPa ultimate at 160 MPa allowable → FS 2.5 — press Try an example to run it live, then adjust anything.

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See also
Von Mises Equivalent Stress (Plane Stress) — what to divide into when the stress state is biaxial rather than a single axial stress
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Factor of Safety explained

σuσallowFS

A factor of safety is the ratio between the stress that breaks the material and the stress you allow it to see in service. Structural steel with a 400 MPa ultimate strength worked at 160 MPa carries FS = 400 ÷ 160 = 2.5. American steel practice long used FS = 1.67 on yield for tension members, which is where the familiar 0.6Fy allowable comes from: 58 ksi ÷ 1.67 ≈ 34.7 ksi for A36. Elevator suspension ropes are held to 10 or 12, pressure-vessel plate to about 3.5, aircraft structure to a lean 1.5 — because on an aircraft, every extra kilogram of margin is a kilogram not carried.

Old engineers called it the "factor of ignorance", and the name is honest: it covers material scatter, corrosion, fabrication tolerance, overload and the sheer possibility that the analysis missed a load path. Two traps. First, always state what the numerator is — a factor of 2 on ultimate is a far thinner margin than a factor of 2 on yield, since steel's ultimate is well above its yield. Second, a factor of safety is not a licence to overload: it is consumed by the things you did not model, and a rope rated 5:1 that is jerked, shock-loaded and worn has already spent most of it.

Factor of Safety formula

FS=σuσallowFS = \frac{\sigma_{u}}{\sigma_{allow}}
Where
  • FSFS= Factor of safety
  • σu\sigma_{u}= Ultimate or yield strength (kPa)
  • σallow\sigma_{allow}= Allowable working stress (kPa)

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