LRFD balances capacity reduction against load amplification — slide φ and γ to see how the safety margin responds.
Design codes define limit states — strength and serviceability. For strength: φRn ≥ Ru. The resistance factor φ accounts for material variability and analysis uncertainty. LRFD multiplies loads up (γ) and capacity down (φ) to create a reliable safety margin. ASD divides capacity by a safety factor Ω instead.
The strength limit state asks: will it break? It uses factored loads to check that members can resist the most extreme forces they might realistically see. The serviceability limit state asks: will it function? It uses unfactored loads to check deflection, vibration, and cracking. Both must be satisfied.
LRFD separates uncertainty into two places. Load factors (γ) account for how much actual load might exceed predicted load. Resistance factors (φ) account for material variability. Dead load is well-known (γ=1.2). Live load is unpredictable (γ=1.6). A single safety factor can't distinguish between these.
Start with Rn — what the member can theoretically resist. Multiply by φ to get design strength. Compare to γRu, the service load amplified for uncertainty. If design strength meets or exceeds factored demand, the check passes.
φ=0.90 flexure/tension yielding. φ=0.75 tension fracture, bolts. φ=0.85 columns. φ=0.65 bearing on concrete. Lower φ = more abrupt failure mode = larger required margin.