Mechanics of Materials — Stress & Strain

Factor of safety — the engineer's margin

continues from lesson 2 — values defined earlier in the course stay live here

ELI5: you never load a part to the edge of failure. The factor of safety = strength / actual stress tells you how much headroom you have. A FoS of 1 means "about to break"; engineers design for 2, 4, sometimes 10 depending on the stakes.

\sigma _{yield} := 250 MPa

= 250 MPa where steel starts to permanently deform

FoS = \frac{\sigma_{yield}}{\sigma_{axial}}

1.5708

safety factor ≈ 1.57

✓ pass

FoS > 1.5

enough margin for a static load (raise F_axial and watch it shrink)

Try it yourself: the factor of safety for a part stressed to 80 MPa in a material that yields at 240 MPa? (FoS = strength / stress.)

FoS_{you} := 240 MPa / 80 MPa

3

✏️ Your turn: divide the yield strength (240 MPa) by the applied stress (80 MPa).

✓ pass

\mathrm{abs}\left(FoS_{you} - 3\right) < 10^{-9}

green when your factor of safety is correct