Lessons · Engineering · factor of safety
Factor of safety: how far the material is from its limit
Factor of safety is the material's strength divided by the working stress, FS = σ_strength / σ_working. Turned round, the allowable stress is strength over the factor.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
The load on a lifting lug is never exactly the number on the drawing. The crane jerks, the steel has a flaw, the weight was guessed. The factor is the room for all of that, and a lug designed at a factor of 1.0 is a lug designed to fail on an ordinary day.
How to think about it
Ask which strength the factor is against: yield, where the part bends for good, or ultimate, where it breaks. Divide that strength by the factor to get the stress you may design to, then size the area from the load.
Worked example
FS = strength / stress, or σ_allow = strength / FSTwo forms of the same idea.
Mild steel yields at 250 MPa; the design calls for FS = 2 on yieldThe rule, from the code or the client.
σ_allow = 250 / 2 = 125 MPaThe most stress the part is allowed to see.
A bar of 400 mm² may then carry F = 125 × 400 = 50,000 N = 50 kNAllowable stress times area gives the allowable load.
Your turn
Ultimate strength 400 MPa, FS = 4. Write the allowable stress.
σ_allow = 400 / = 100 MPa
Solve one, graded on the server
The trap
Taking the factor against the wrong strength. A factor of 2 on ultimate can still be past yield on a ductile steel, and the part is permanently bent while the calculation says it is safe.