Load Combinations — ASCE 7, AS/NZS 1170, EN 1990, NBCC Reference
Load combinations define how individual loads are combined for structural design. Each code specifies factors reflecting the probability of simultaneous maximum occurrence. This page covers LRFD and ASD combinations from the major international standards.
ASCE 7-22 LRFD load combinations (IBC)
| Combo | Expression | Controls For |
|---|---|---|
| LC1 | 1.4D | Heavy dead load |
| LC2 | 1.2D + 1.6L + 0.5(Lr or S or R) | Gravity floors |
| LC3 | 1.2D + 1.6(Lr or S or R) + (L or 0.5W) | Gravity roofs |
| LC4 | 1.2D + 1.0W + L + 0.5(Lr or S or R) | Wind + gravity |
| LC5 | 1.2D + 1.0E + L + 0.2S | Seismic + gravity |
| LC6 | 0.9D + 1.0W | Wind uplift |
| LC7 | 0.9D + 1.0E | Seismic overturning |
D = dead, L = live (0.5L when L<=100 psf except garages/assembly), Lr = roof live, S = snow, R = rain, W = wind (strength-level in ASCE 7-16+), E = seismic = rho*QE + 0.2*SDS*D.
ASCE 7-22 ASD load combinations
| Combo | Expression |
|---|---|
| LC1 | D |
| LC2 | D + L |
| LC3 | D + (Lr or S or R) |
| LC4 | D + 0.75L + 0.75(Lr or S or R) |
| LC5 | D + (0.6W or 0.7E) |
| LC6 | D + 0.75L + 0.75(0.6W) + 0.75(Lr or S or R) |
| LC7 | 0.6D + 0.6W |
| LC8 | 0.6D + 0.7E |
ASCE 7-22 key definitions
| Symbol | Name | Typical Values |
|---|---|---|
| D | Dead load | Self-weight, fixed equipment |
| L | Live load | 40-100 psf (floors), per ASCE 7 Table 4-1 |
| Lr | Roof live load | 12-20 psf per ASCE 7 Table 4-2 |
| S | Snow load | Site-specific, pf + ps per ASCE 7 Ch. 7 |
| R | Rain load | Per ASCE 7 Ch. 8 (ponding) |
| W | Wind load | Strength-level per ASCE 7 Ch. 26-31 |
| E | Seismic load | E = rho*QE + 0.2*SDS*D |
LRFD vs ASD equivalent factors
| Load Type | LRFD Factor | ASD Factor | LRFD/ASD Ratio |
|---|---|---|---|
| Dead (favorable) | 1.2 | 1.0 | 1.20 |
| Dead (unfavorable) | 0.9 | 0.6 | 1.50 |
| Live | 1.6 | 1.0 | 1.60 |
| Wind | 1.0 | 0.6 | 1.67 |
| Seismic | 1.0 | 0.7 | 1.43 |
| Snow | 1.6 | 1.0 | 1.60 |
The LRFD factors are calibrated to produce equivalent reliability as ASD. For a typical floor beam, the LRFD demand is about 1.4-1.5x the ASD demand, offset by the phi factor (0.90 for bending) vs Omega (1.67 for bending).
AS/NZS 1170.0 ULS combinations
| Combo | Expression |
|---|---|
| 1 | 1.35G |
| 2 | 1.2G + 1.5Q |
| 3 | 1.2G + Wu + psi_c*Q |
| 4 | G + Eu + psi_c*Q |
| 5 | 0.9G + Wu |
| 6 | 0.9G + Eu |
psi_c = combination factor: 0.4 for floors, 0.6 for storage, 0.0 for roofs.
AS/NZS 1170 combination factors
| Action | psi_c (short-term) | psi_c (long-term) | psi_s (serviceability) |
|---|---|---|---|
| Floor live load | 0.4 | 0.4 | 0.6 |
| Storage live load | 0.6 | 0.6 | 0.9 |
| Roof live load | 0.0 | 0.0 | 0.0 |
| Wind | 0.0 | 0.0 | 0.0 |
| Earthquake | 0.0 | 0.0 | 0.0 |
EN 1990 fundamental combination (ULS)
sum(gamma_G*Gk) + gamma_Q1*Qk1 + sum(gamma_Qi*psi_0i*Qki), where gamma_G = 1.35 (unfavorable), gamma_Q = 1.50.
Common psi factors (EN 1990, Annex A1)
| Action | psi_0 | psi_1 | psi_2 |
|---|---|---|---|
| Domestic (Cat. A) | 0.7 | 0.5 | 0.3 |
| Offices (Cat. B) | 0.7 | 0.5 | 0.3 |
| Assembly (Cat. C) | 0.7 | 0.7 | 0.6 |
| Shopping (Cat. D) | 0.7 | 0.7 | 0.6 |
| Storage (Cat. E) | 1.0 | 0.9 | 0.8 |
| Vehicle < 30kN | 0.7 | 0.7 | 0.6 |
| Vehicle > 30kN | 0.6 | 0.6 | 0.3 |
| Snow (< 1000m) | 0.5 | 0.2 | 0.0 |
| Snow (> 1000m) | 0.7 | 0.5 | 0.2 |
| Wind | 0.6 | 0.2 | 0.0 |
EN 1990 ULS combinations for a typical office building
| Combo | Expression |
|---|---|
| 1 | 1.35*Gk + 1.50*Qk (gravity) |
| 2 | 1.35*Gk + 1.50*Qk + 0.6*1.50*Wk (gravity + wind) |
| 3 | 1.35*Gk + 1.50*Wk + 0.7*1.50*Qk (wind + gravity) |
| 4 | 1.00*Gk + 1.50*Wk (wind uplift) |
| 5 | 1.00*Gk + 1.50*Ek + 0.7*1.50*Qk (seismic) |
NBCC 2020 ULS combinations (Canada)
| Combo | Expression |
|---|---|
| 1 | 1.4D |
| 2 | 1.25D + 1.5L |
| 3 | 1.25D + 1.5S |
| 4 | 1.25D + 1.4W |
| 5 | 1.0D + 1.0E |
Key differences from ASCE 7: dead load factor 1.25 (not 1.2), live load factor 1.5 (not 1.6), wind factor 1.4 (not 1.0). NBCC uses factored wind (1-in-50 year), whereas ASCE 7-22 uses strength-level wind directly.
Governing combination guide
| Scenario | Typical Governing Combo |
|---|---|
| Floor beams | 1.2D + 1.6L |
| Roof beams (snow) | 1.2D + 1.6S |
| Interior columns | 1.2D + 1.6L |
| Exterior columns (wind) | 1.2D + 1.0W + L |
| Foundations (uplift) | 0.9D + 1.0W |
| Lateral system | 1.2D + 1.0E + L |
| Cantilever (overturning) | 0.9D + 1.0W |
| Heavy equipment support | 1.4D |
Worked example: which combination governs for a floor beam?
Given: Floor beam with D = 20 kip-ft, L = 40 kip-ft (office, L > 100 psf rule does not apply), no wind/seismic.
| Combo | Factored Moment (kip-ft) |
|---|---|
| LC1 | 1.4 * 20 = 28 |
| LC2 | 1.2*20 + 1.6*40 = 88 |
| LC6 | 0.9*20 = 18 (not applicable, no W) |
LC2 governs at 88 kip-ft. This is the most common governing combination for interior gravity framing.
Worked example: roof beam in wind zone
Given: Roof beam with D = 8 kip-ft, Lr = 12 kip-ft, W = +/-15 kip-ft (uplift case), no snow.
| Combo | Factored Moment (kip-ft) |
|---|---|
| LC1 | 1.4 * 8 = 11.2 |
| LC3 | 1.2*8 + 1.6*12 = 29.6 (gravity) |
| LC4 | 1.2*8 + 1.0*0 + 0.5*12 = 15.6 |
| LC6 | 0.9*8 + 1.0*(-15) = -7.8 (uplift!) |
LC3 governs for gravity at 29.6 kip-ft. LC6 causes uplift at -7.8 kip-ft (dead load alone must exceed wind uplift for stability). If 0.9D < W, the roof needs hold-down connections.
Cross-code comparison of critical load factors
| Parameter | ASCE 7 (US) | AS/NZS 1170 (AU) | EN 1990 (EU) | NBCC (CA) |
|---|---|---|---|---|
| Dead (unfavorable) | 1.2 | 1.2 | 1.35 | 1.25 |
| Dead (favorable) | 0.9 | 0.9 | 1.00 | 1.00 |
| Live | 1.6 | 1.5 | 1.50 | 1.5 |
| Wind | 1.0* | 1.0* | 1.50 | 1.4 |
| Seismic | 1.0 | 1.0 | 1.00 | 1.0 |
| Snow | 1.6 | 1.5 | 1.50 | 1.5 |
| Max dead only | 1.4 | 1.35 | 1.35 | 1.4 |
* ASCE 7 and AS/NZS 1170 use strength-level wind, so the factor is 1.0. EN 1990 and NBCC apply factors to characteristic/service-level wind.
Live load reduction (ASCE 7-22)
Tributary area reduction for members supporting floor live load:
| Influence Area KLL*At (ft^2) | Reduction Factor |
|---|---|
| <= 400 | 1.00 (no reduction) |
| 800 | 0.82 |
| 1200 | 0.72 |
| 1600 | 0.66 |
| 2000 | 0.61 |
| 2400 | 0.58 |
| 2800+ | 0.50 (minimum) |
KLL = live load element factor (4 for interior columns, 2 for edge columns, 2 for beams). Does not apply to heavy live loads (L > 100 psf), garages, or assembly occupancies.
ASCE 7-22 Load Combinations: Sections 2.3 and 2.4
ASCE 7-22 Section 2.3 provides LRFD (strength) load combinations and Section 2.4 provides ASD (allowable stress) load combinations. Both sets must be considered; the governing combination produces the most critical demand on each structural member.
ASCE 7-22 LRFD Combinations (Section 2.3.1)
| Combination | Formula | Typical Application |
|---|---|---|
| LC1 | 1.4D | Dead load only (minimum; concrete self-weight check) |
| LC2 | 1.2D + 1.6L + 0.5(Lr or S or R) | Floor beam gravity (most common interior) |
| LC3 | 1.2D + 1.6(Lr or S or R) + (L or 0.5W) | Roof beam with snow/live |
| LC4 | 1.2D + 1.0W + L + 0.5(Lr or S or R) | Wind + gravity |
| LC5 | 0.9D + 1.0W | Wind uplift / overturning |
| LC6 | 1.2D + 1.0E + L + 0.2S | Seismic + gravity |
| LC7 | 0.9D + 1.0E | Seismic overturning |
Where D = dead, L = live, Lr = roof live, S = snow, R = rain, W = wind, E = seismic. All loads are at strength level (no additional conversion needed for wind since ASCE 7-10).
ASCE 7-22 ASD Combinations (Section 2.4.1)
| Combination | Formula | Typical Application |
|---|---|---|
| LC1 | D | Dead only |
| LC2 | D + L | Gravity (service level) |
| LC3 | D + (Lr or S or R) | Roof loading |
| LC4 | D + 0.75L + 0.75(Lr or S or R) | Full gravity |
| LC5 | D + 0.6W | Wind (service) |
| LC6 | D + 0.75L + 0.75(0.6W) + 0.75(Lr or S or R) | Combined gravity + wind |
| LC7 | 0.6D + 0.6W | Wind uplift (ASD) |
| LC8 | D + 0.7E | Seismic (service) |
| LC9 | 0.6D + 0.7E | Seismic overturning (ASD) |
LRFD vs ASD: Key Differences
| Aspect | LRFD | ASD |
|---|---|---|
| Load level | Factored (amplified) | Service (unfactored) |
| Resistance | phi * Rn (resistance factor) | Rn / Omega (safety factor) |
| Target reliability | beta ~ 3.0 (members), 2.5 (connections) | Same target (different calibration) |
| Wind treatment | 1.0W (strength-level wind) | 0.6W (converts to service level) |
| Seismic (E) | 1.0E | 0.7E |
| Typical governing combination | 1.2D + 1.6L (floor beams) | D + L (floor beams) |
| phi for flexure | 0.90 | Omega = 1.67 |
| phi for shear | 0.90 | Omega = 1.67 (1.5 for bolts) |
| phi for connections | 0.75 | Omega = 2.00 |
Controlling Load Combinations by Member Type
Not every combination governs every member. The following guide identifies which combinations typically control for common structural members.
| Member Type | Controlling LRFD Combination | Controlling ASD Combination | Notes |
|---|---|---|---|
| Floor beam (gravity) | LC2: 1.2D + 1.6L | LC2: D + L | Live load dominates |
| Roof beam (gravity) | LC3: 1.2D + 1.6S | LC3: D + S | Snow on roof |
| Column (gravity) | LC2: 1.2D + 1.6L | LC2: D + L | Cumulative floor loads |
| Lateral frame (wind) | LC4: 1.2D + 1.0W + L | LC6: D + 0.75L + 0.45W | Combined gravity + lateral |
| Lateral frame (seismic) | LC6: 1.2D + 1.0E + L | LC8: D + 0.7E | Seismic + gravity |
| Foundation uplift | LC5: 0.9D + 1.0W | LC7: 0.6D + 0.6W | Minimum dead, maximum wind |
| Anchor bolts (tension) | LC5: 0.9D + 1.0W | LC7: 0.6D + 0.6W | Overturning at base |
| Connection (gravity) | LC2: 1.2D + 1.6L | LC2: D + L | Same as beam but phi=0.75 |
Worked Example: Load Combinations for a Roof Beam
Given: A roof beam supports the following unfactored loads:
- Dead load: D = 0.80 klf (beam self-weight + deck + roofing)
- Snow load: S = 1.20 klf (balanced snow)
- Wind (uplift): W = -0.60 klf (net uplift on roof)
- Roof live load: Lr = 0.40 klf (maintenance)
- Seismic: E = 0.30 klf (vertical component not shown for simplicity)
Beam span: L = 30 ft. Compute factored moments for each LRFD combination.
| Combination | Factored Load (klf) | Moment Mu = wL^2/8 (ft-kips) | Governs? |
|---|---|---|---|
| LC1: 1.4D | 1.4 * 0.80 = 1.12 | 1.12 * 900 / 8 = 126.0 | No |
| LC2: 1.2D + 1.6S + 0.5Lr | 1.2(0.80) + 1.6(1.20) + 0.5(0.40) = 0.96 + 1.92 + 0.20 = 3.08 | 3.08 * 112.5 = 346.5 | YES (gravity) |
| LC3: 1.2D + 1.6Lr + 0.5S | 0.96 + 0.64 + 0.60 = 2.20 | 2.20 * 112.5 = 247.5 | No |
| LC4: 1.2D + 1.0W + Lr | 0.96 + (-0.60) + 0.40 = 0.76 | 0.76 * 112.5 = 85.5 | No |
| LC5: 0.9D + 1.0W | 0.72 + (-0.60) = 0.12 | 0.12 * 112.5 = 13.5 | Check (uplift, net positive here) |
| LC6: 1.2D + 1.0E + 0.2S | 0.96 + 0.30 + 0.24 = 1.50 | 1.50 * 112.5 = 168.8 | No |
| LC7: 0.9D + 1.0E | 0.72 + 0.30 = 1.02 | 1.02 * 112.5 = 114.8 | No |
For LC5 with negative result: 0.9(0.80) + 1.0(-0.60) = 0.72 - 0.60 = +0.12 klf (net downward, no uplift). If W were -1.0 klf, then 0.72 - 1.0 = -0.28 klf (net uplift), producing a negative moment of -0.28 * 112.5 = -31.5 ft-kips. The beam bottom flange must be checked for compression under this uplift condition.
Result: LC2 governs at Mu = 346.5 ft-kips. The required beam plastic section modulus:
Zx_required = Mu / (phi * Fy) = 346.5 * 12 / (0.90 * 50) = 92.4 in3
A W21x44 (Zx = 95.4 in3) would work.
Common mistakes
Not checking minimum gravity combinations. LC6 (0.9D+W) and LC7 (0.9D+E) govern for uplift and overturning. Missing these can result in unconservative foundation design.
Applying live load reduction incorrectly. The 0.5L factor only applies when L<=100 psf and not in garages/assembly. Reduction applies to floor live load only, not roof or snow.
Mixing LRFD and ASD. Never mix factored loads with ASD capacities or vice versa. LRFD loads go with phi*Rn, ASD loads go with Rn/Omega.
Forgetting companion loads. In LC3, the companion load (L or 0.5W) must be included. Leaving it out underestimates the combination.
Omitting vertical seismic component. E includes 0.2*SDS*D, which increases the effective dead load factor. For SDS = 0.4, this adds 0.08D to the seismic combination.
Using service-level wind with LRFD factors. ASCE 7-16+ uses strength-level wind (Vult). Do NOT apply the 1.6 wind conversion factor that older codes required.
Not considering pattern loading. For continuous beams and frames, live load should be placed on alternate spans to maximize positive and negative moments.
Frequently asked questions
What is the most common governing combination? For most interior floor beams and columns: 1.2D + 1.6L. For lateral system members: seismic or wind combinations.
Factored vs. unfactored loads? LRFD uses factored loads and phi factors. ASD uses service loads and Omega factors. Both target the same reliability index (beta ~ 3.0 for members, 2.5 for connections).
Why so many combinations? Different scenarios of simultaneous loading. The probability that all loads are at maximum simultaneously is very low. Factors reflect the statistical likelihood of joint occurrence.
When does 0.9D + W govern? When wind uplift on a roof or horizontal wind pressure creates a net overturning moment. The 0.9 factor on dead load reflects the minimum likely dead weight, ensuring the structure does not become unstable from overestimated dead load.
Do I need to check all combinations for every member? Technically yes. In practice, experienced engineers identify the likely governing combinations for each member type and check those first, then spot-check others. Missing a critical combination is a design error.
How do load combinations work with seismic overstrength? For certain elements (collector, cantilever column systems), ASCE 7 requires using E = Omega_0 * QE, which amplifies the seismic effect. This overrides the standard E in the combination.
What about notional loads in AISC? AISC Chapter C requires notional loads (Ni = 0.002*Yi) when the ratio of second-order to first-order drift exceeds 1.7, or when using the Effective Length Method. Notional loads are combined with gravity load combinations.
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Related references
- Load Combinations ASCE 7 (detailed)
- Live Load Reference
- Snow Load Calculation
- Wind Load Calculation
- Seismic Design Categories
- Beam Formulas
- Deflection Limits
- Steel Grades
- How to Verify Calculations
Disclaimer
This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against the governing building code and project specification. The site operator disclaims liability for any loss arising from the use of this information.
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