Canadian Load Combinations — NBCC 2020 ULS and SLS for Steel Design
Complete reference for load combinations per NBCC 2020 Division B for Canadian structural steel design with CSA S16-19. Covers Ultimate Limit States (ULS) combinations, Serviceability Limit States (SLS) combinations, importance factors for snow/wind/earthquake, companion load factors, and a step-by-step worked example for a steel building frame.
Quick access: Beam design | Column design | Combined loading
NBCC 2020 Load Combination Framework
Per NBCC 2020 Division B Clause 4.1.3.2, steel structures must be designed for:
Ultimate Limit States (ULS): Strength and stability — factored loads
Serviceability Limit States (SLS): Deflection, vibration, drift — specified loads
Ultimate Limit States (ULS) Combinations
Per NBCC 2020 Table 4.1.3.2:
| Comb | Load Combination | Principal Load | Companion Loads |
|---|---|---|---|
| 1 | 1.4 × D | Dead | — |
| 2 | 1.25 × D + 1.5 × L | Live | — |
| 3 | 1.25 × D + 1.5 × L + 0.4 × (S or W) | Live + Dead | Snow or Wind |
| 4 | 1.25 × D + 1.5 × S + 0.5 × L | Snow | Live |
| 5 | 1.25 × D + 1.4 × W + 0.5 × L | Wind | Live |
| 6 | 1.25 × D + 1.4 × W + 0.5 × S | Wind | Snow |
| 7 | 1.25 × D + 1.0 × E + 0.5 × L | Earthquake | Live |
| 8 | 1.25 × D + 1.0 × E + 0.25 × S | Earthquake | Snow |
Where:
- D = dead load
- L = live load (including roof live and snow loads where applicable)
- S = snow load (ground snow × CBS × shape factor)
- W = wind load
- E = earthquake load (per NBCC 2020 Clause 4.1.8)
- T = temperature effects (not shown — see NBCC for temperature combinations)
ULS Combinations with Temperature
When temperature effects T are significant:
| Comb | Load Combination |
|---|---|
| 9 | 1.0 × D + 1.0 × T + 0.5 × L |
| 10 | 1.0 × D + 1.0 × T + 0.5 × S |
Importance Factors
Per NBCC 2020 Table 4.1.3.3:
| Building Category | I_E (Earthquake) | I_W (Wind) | I_S (Snow) |
|---|---|---|---|
| Low (ULS) — farm buildings, storage | 0.80 | 0.80 | 0.80 |
| Normal — offices, residential, schools | 1.00 | 1.00 | 1.00 |
| High — schools, community centres | 1.25 | 1.15 | 1.15 |
| Post-Disaster — hospitals, fire stations | 1.50 | 1.25 | 1.25 |
Importance factors multiply the corresponding loads in the combination:
- Wind load in Comb 5: 1.4 × I_W × W
- Snow load in Comb 4: 1.5 × I_S × S
- Earthquake in Comb 7: 1.0 × I_E × E
Serviceability Limit States (SLS) Combinations
Per NBCC 2020 Clause 4.1.3.3 for deflection and drift:
| Comb | Load Combination | Application |
|---|---|---|
| 1 | 1.0 × D + 1.0 × L | Total deflection (floor beams) |
| 2 | 1.0 × D + 0.5 × L + 0.5 × S | Total deflection (roof beams with snow) |
| 3 | 1.0 × L | Live load deflection only |
| 4 | 1.0 × W | Wind drift (interstorey) |
| 5 | 1.0 × D + 0.5 × L + 0.4 × W | Wind-induced vibration |
Deflection Limits per CSA S16
Per CSA S16-19 Clause 25.3 (Serviceability):
| Element | Limit | Load Case |
|---|---|---|
| Roof beams — live load | L/180 | 1.0 × L |
| Roof beams — total load | L/240 | 1.0 × D + 0.5 × L + 0.5 × S |
| Floor beams — live load | L/300 to L/360 | 1.0 × L |
| Floor beams — total load | L/300 | 1.0 × D + 1.0 × L |
| Cantilevers — live load | L/180 | 1.0 × L |
| Crane girders — live load | L/600 to L/1000 | 1.0 × L |
| Interstorey drift (wind) | H/400 | 1.0 × W |
Load Combination Factors Summary
| Load | ULS Factor (Principal) | ULS Factor (Companion) | SLS Factor |
|---|---|---|---|
| Dead load D | 1.25 (or 1.0) | 1.0 | 1.0 |
| Live load L | 1.5 | 0.5 | 0.5-1.0 |
| Snow S | 1.5 | 0.4 | 0.5 |
| Wind W | 1.4 | 0.4 | 1.0 (drift) |
| Earthquake E | 1.0 | — | — (not checked) |
| Temperature T | 1.0 | — | 1.0 |
Snow Load Calculation
Per NBCC 2020 Clause 4.1.6:
Ground snow load S_s — from NBCC 2020 Appendix C (location-specific)
Roof snow load: S = S_s × C_b × C_w × C_s × C_a × S_r
Where:
- C_b = basic roof snow load factor (0.8 for most roofs)
- C_w = wind exposure factor (1.0 for normal, 0.75 for exposed, 1.25 for sheltered)
- C_s = slope factor (1.0 for flat roofs, reduces with slope)
- C_a = accumulation factor (for drifts, sliding snow)
- S_r = 1.0 kPa for most of Canada (rain-on-snow surcharge)
Worked Example — Load Combinations for Steel Frame
Given: Steel building frame in Toronto. Bay width = 9.0 m, tributary width = 9.0 m. Normal importance (I_S = I_W = I_E = 1.0). Calculate factored loads for a roof beam.
Load Data:
- Dead load: D = 3.0 kPa (roofing + steel + mechanical)
- Roof live load: L_r = 1.0 kPa (NBCC minimum for access)
- Snow load: S_s = 1.8 kPa (Toronto ground snow), C_b = 0.8, C_w = 1.0, C_s = 1.0 S = 1.8 × 0.8 × 1.0 × 1.0 = 1.44 kPa
- Wind load: W = 0.6 kPa (from NBCC 2020 static wind procedure, q_30 × C_p × C_e)
Factored Load per Metre of Beam (9.0 m tributary):
| Comb | Load Combination | w_f (kN/m) |
|---|---|---|
| 1 | 1.4 × D = 1.4 × 27.0 = | 37.8 |
| 2 | 1.25 × D + 1.5 × L_r = 1.25 × 27.0 + 1.5 × 9.0 = | 47.3 |
| 3 | 1.25 × D + 1.5 × L_r + 0.4 × S = 33.75 + 13.5 + 0.4 × 13.0 = | 52.4 |
| 4 | 1.25 × D + 1.5 × S + 0.5 × L_r = 33.75 + 19.5 + 4.5 = | 57.8 |
| 5 | 1.25 × D + 1.4 × W + 0.5 × L_r = 33.75 + 7.56 + 4.5 = | 45.8 |
| 6 | 1.25 × D + 1.4 × W + 0.5 × S = 33.75 + 7.56 + 6.5 = | 47.8 |
Governing ULS combination: Comb 4 (snow principal) = 57.8 kN/m
SLS deflection check: Live load only: w = 1.0 × L_r = 9.0 kN/m Delta = 5 × 9.0 × 9000^4 / (384 × 200,000 × I_x) For W410×60 (I_x = 216 × 10^6 mm^4): Delta = 39.3 mm L/360 = 9000/360 = 25 mm. 39.3 > 25 mm. NOT OK.
Increase to W530×82 (I_x = 485 × 10^6 mm^4): Delta = 39.3 × (216/485) = 17.5 mm. 17.5 < 25 mm. OK.
Result: W530×82, 350W. Governed by SLS deflection, not strength.
Design Resources
- CSA S16 Beam Design — Flexural Guide
- Canadian Deflection Limits — CSA S16
- CSA S16 Combined Loading
- Canadian Wind Load Guide
- Canadian Snow Load Guide
- Beam Capacity Calculator
- All Canadian References
Frequently Asked Questions
What is the difference between ULS and SLS load combinations per NBCC 2020? ULS (Ultimate Limit States) combinations apply load factors > 1.0 to account for the probability of exceedance and are used for strength design of members and connections. SLS (Serviceability Limit States) combinations use specified (unfactored or partially factored) loads for deflection, drift, and vibration checks. For a typical steel beam: ULS combination 2 (1.25D + 1.5L) governs strength, while SLS (1.0L) governs deflection.
How do NBCC 2020 load combinations differ from ASCE 7? NBCC 2020 uses a principal load / companion load framework where only one load at a time is considered the principal load with its full factor. Companion loads receive reduced factors (0.5 for L, 0.4 for S/W). ASCE 7 applies full factors to all loads simultaneously. The dead load factor is 1.25 in NBCC vs 1.2 in ASCE 7. Live load is 1.5 vs 1.6. Wind is 1.4 vs 1.0 (ASD) or 1.0 (LRFD with wind directionality). These differences matter for cross-border projects.
What is the importance factor I_E and when does it apply? I_E is the earthquake importance factor that multiplies the seismic base shear per NBCC 2020 Clause 4.1.8. It ranges from 0.80 (low importance) to 1.50 (post-disaster). I_W (wind importance) and I_S (snow importance) are separate factors applied in combinations 5-6 and 4 respectively. A normal importance building uses I_E = I_W = I_S = 1.0. A post-disaster hospital uses I_E = 1.50, I_W = I_S = 1.25.
When does SLS govern over ULS for steel beam design? SLS (deflection) often governs for steel floor beams with longer spans (L > 8 m), especially where L/360 live load limits apply. A beam that satisfies strength with Cf/Cr = 0.5-0.7 may still deflect L/250 > L/360, requiring a deeper section. For roof beams in heavy snow regions (S_s > 2.5 kPa), SLS also frequently governs. Always run both ULS and SLS checks — do not assume strength governs.
Educational reference only. Load combinations per NBCC 2020 Division B Clause 4.1.3.2. Verify importance factors and load data with the project structural engineer. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent PE/SE verification.