ASCE 7-22 load combinations for structural design: LRFD and ASD equations explained
Every structural member must resist the worst realistic demand from multiple load types acting together. ASCE 7-22 prescribes the combinations that engineers must check: Section 2.3.1 for LRFD (strength design) and Section 2.4.1 for ASD (allowable stress design). ACI 318-19 Table 5.3.1 adopts the ASCE 7 LRFD set for reinforced concrete. This page covers all equations, companion factors, seismic resolution, and a worked example.
What are load combinations?
A load combination is a prescribed sum of individual load types (dead, live, wind, snow, seismic, etc.), each multiplied by a load factor that accounts for the probability of simultaneous occurrence and the uncertainty in the load magnitude. The structure must be designed for the most critical effect from all applicable combinations.
In the United States, ASCE 7 (Minimum Design Loads and Associated Criteria for Buildings and Other Structures) defines these combinations. Material-specific codes such as ACI 318 (concrete), AISC 360 (steel), and NDS (wood) reference ASCE 7 for the load side and add their own resistance factors or allowable stresses.
LRFD combinations (Section 2.3.1)
LRFD (Load and Resistance Factor Design) applies load factors greater than 1.0 to amplify the expected loads, then compares the factored demand to the reduced nominal strength (φRn). ASCE 7-22 Section 2.3.1 defines 7 basic equations:
| Eq | Combination | Governs when |
|---|---|---|
| 1 | 1.4D | Dead load only (no live, wind, or snow) |
| 2 | 1.2D + 1.6L + 0.5(Lr or S or R) | Live load dominant |
| 3 | 1.2D + 1.6(Lr or S or R) + (f1L or 0.5W) | Roof load dominant |
| 4 | 1.2D + 1.0W + f1L + 0.5(Lr or S or R) | Wind dominant |
| 5 | 1.2D + 1.0E + f1L + 0.2S | Seismic dominant (gravity + Eh + Ev) |
| 6 | 0.9D + 1.0W | Wind uplift (minimum gravity) |
| 7 | 0.9D + 1.0E | Seismic uplift (minimum gravity) |
Companion load factor f1. In Equations 3 through 5, f1 = 0.5 for most occupancies. For garages, places of public assembly, and areas where the live load exceeds 100 psf, f1 = 1.0 because these spaces are more likely to carry full live load simultaneously with the primary environmental load.
Companion roof load. Where roof live load (Lr), snow (S), and rain (R) appear together, each generates its own combination because they are mutually exclusive maximums: you check 0.5Lr, 0.5S, and 0.5R separately and take the worst result. The factors 1.6 (primary, Eq 3) and 0.5 (companion, Eq 2/4) reflect the relative probability that the roof load is the dominant versus the secondary effect.
ASD combinations (Section 2.4.1)
ASD (Allowable Stress Design) uses unfactored or lightly factored loads and compares the resulting demand to an allowable capacity that already includes a safety factor. ASCE 7-22 Section 2.4.1 defines 8 basic equations:
| Eq | Combination | Governs when |
|---|---|---|
| 1 | D | Dead load only |
| 2 | D + L | Gravity (floor live load active) |
| 3 | D + (Lr or S or R) | Roof load dominant |
| 4 | D + f1aL + 0.75(Lr or S or R) | Gravity + roof (reduced) |
| 5 | D + (0.6W or 0.7E) | Lateral dominant |
| 6a | D + f1aL + 0.75(0.6W) + 0.75(Lr or S or R) | Wind + gravity + roof (all reduced) |
| 6b | D + f1aL + 0.75(0.7E) + 0.75S | Seismic + gravity + snow (all reduced) |
| 7 | 0.6D + 0.6W | Wind uplift (minimum gravity) |
| 8 | 0.6D + 0.7E | Seismic uplift (minimum gravity) |
Companion load factor f1a. The ASD counterpart of f1. In Equations 4, 6a, and 6b, the live load factor is 0.5 for standard occupancies and 0.75 for garages, assembly, and high-live-load areas. The 0.75 multiplier on all companion loads in Equations 4 and 6 reflects the reduced probability that full dead, live, and environmental loads act simultaneously at service level.
Key differences from LRFD. ASD loads are unfactored (factor = 1.0 on D and L) or lightly factored (0.6W, 0.7E). The 0.75 combination factor in Equations 4 and 6 has no LRFD equivalent because LRFD encodes the joint-probability reduction directly in the individual load factors. ASD has 8 equations versus LRFD's 7 because ASD splits wind (Eq 7) and seismic (Eq 8) uplift into separate equations, while LRFD's Eq 6 and Eq 7 parallel the same split.
LRFD vs ASD: when each method applies
| LRFD (Sec 2.3) | ASD (Sec 2.4) | |
|---|---|---|
| Philosophy | Factored demand ≤ φRn | Service demand ≤ Rn/Ω |
| Load factors | > 1.0 (1.2D, 1.6L, ...) | 1.0 or < 1.0 (0.6W, 0.7E) |
| Concrete (ACI 318-19) | Required (Table 5.3.1) | Not used for strength |
| Steel (AISC 360) | Permitted | Permitted |
| Soil bearing | Less common | Typically used |
| Reliability target | Both are calibrated to the same target reliability index (β ≈ 3.0 for gravity, 2.5 for wind) | |
LRFD and ASD are not competing methods. They are two presentations of the same probabilistic reliability framework, calibrated to produce equivalent safety levels. For reinforced concrete, ACI 318-19 mandates LRFD. For structural steel, AISC 360 permits either. For soil bearing, geotechnical practice typically uses ASD (service-level) pressures.
Seismic load effect resolution
In ASCE 7-22 Section 12.4.2, the seismic load effect E is resolved into horizontal and vertical components before substitution into the combination equations:
Ev = 0.2 · SDS · D
Substituting into LRFD Eq 5: U = (1.2 + 0.2SDS)D ± ρQE + f1L + 0.2S. The vertical seismic effect increases (or decreases) the effective dead load factor from 1.2 to (1.2 + 0.2SDS). Both positive and negative horizontal directions must be checked.
For ASD Eq 5 (seismic): D + 0.7E resolves to (1.0 ± 0.14SDS)D ± 0.7ρQE. The 0.7 factor on E is the ASD-to-LRFD conversion for seismic.
Overstrength combinations. Where ASCE 7 Section 12.4.3 applies (collector elements, foundations, certain connections), the seismic overstrength factor Ω0 replaces ρ in the horizontal effect: Emh = Ω0 · QE. These produce the most demanding combinations in high-seismic designs.
calcnote's load combination calculator resolves all seismic permutations automatically: enter ρ, SDS, and optionally Ω0, and every resolved LRFD and ASD combination appears with the effective D factor shown explicitly.
Worked example: gravity-only building
Consider a floor beam with the following unfactored loads: D = 100 psf, L = 50 psf, S = 30 psf, Lr = 20 psf (no wind, no seismic). Standard occupancy (f1 = 0.5).
| Eq | Expression | U (psf) |
|---|---|---|
| 1 | 1.4(100) | 140 |
| 2 | 1.2(100) + 1.6(50) + 0.5(30) | 215 |
| 2 | 1.2(100) + 1.6(50) + 0.5(20) | 210 |
| 3 | 1.2(100) + 1.6(30) + 0.5(50) | 193 |
| 3 | 1.2(100) + 1.6(20) + 0.5(50) | 177 |
Eq 2 with S = 30 governs at U = 215 psf. Eq 1 (dead-only) is lower; Eq 3 inverts the primary/companion roles and is also lower. Equations 4 through 7 do not apply because wind and seismic are absent. The calculator generates all applicable permutations and highlights the maximum automatically.
Sources
- ASCE 7-22: Minimum Design Loads and Associated Criteria for Buildings and Other Structures, Sections 2.3 (LRFD) and 2.4 (ASD).
- ACI 318-19: Building Code Requirements for Structural Concrete, Table 5.3.1 (required strength combinations).
- Glossary: load combination, LRFD, ASD, factored load, seismic overstrength factor.