Structural Design Basis, Loads, and Limit States
Design philosophy
Every structure must satisfy two families of limit states. Ultimate limit states (ULS) concern safety: collapse, buckling, overturning, and rupture. Serviceability limit states (SLS) concern function: excessive deflection, vibration, and cracking. Design checks compare a factored resistance to a factored effect: φR ≥ ΣγQ, where φ is a resistance factor and γ a load factor. The load factors differ between load combinations because dead load is more predictable than live or environmental load.
Load combinations and probability
Combination rules recognize that not all loads peak simultaneously. A typical strength combination is 1.2D + 1.6L + 0.5S, while wind and seismic combinations use companion-load factors (often 0.5 for live load) on the non-governing loads. The 0.9D + 1.0W combination exists to catch uplift and overturning, where less dead load is unfavorable. Recognizing which variable is the "principal" action is the core skill.
Traps candidates fall into
- Forgetting that the minimum gravity combination (0.9D) governs stability checks.
- Mixing ASD and LRFD: never combine unfactored loads with factored resistances.
- Confusing nominal, specified, and factored values when reading a table.
- Treating a companion load as additive at full magnitude.
Worked rule of thumb
For a roof with D = 20 psf, L = 20 psf, S = 30 psf, the strength demand is 1.2(20) + 1.6(20) + 0.5(30) = 24 + 32 + 15 = 71 psf. If uplift from wind gives −15 psf, check 0.9(20) − 15 = +3 psf; a positive result means the roof stays down, so anchorage may still be needed for the net reaction.