Limit-State Function Reference
Quick reference for common limit-state functions in structural reliability — stress, displacement, fatigue, buckling, fracture and combined stress.
Common limit-state functions
| Failure mode | Limit-state function | Variables |
|---|---|---|
| Stress (yielding) | g = Sy - sigma | Sy: yield strength, sigma: applied stress |
| Displacement | g = delta_allow - delta | delta_allow: allowable, delta: computed |
| Fatigue life | g = N_failure - N_design | N_failure: fatigue life, N_design: design life |
| Buckling | g = P_critical - P_applied | P_critical: buckling load, P_applied: applied |
| Fracture | g = K_c - K_applied | K_c: toughness, K_applied: stress intensity |
| Combined stress | g = Sy - sqrt(sigma^2 + 3*tau^2) | sigma: normal, tau: shear |