NBCC 2020 Load Combinations Worked Example — Toronto 4-Storey Office

Complete worked example of NBCC 2020 Division B Part 4 load combinations for a 4-storey steel-framed office building in Toronto, Ontario. This example demonstrates dead, live, snow, wind, and seismic load calculation, all 8 ULS combinations, SLS combinations, and a column load takedown showing which combination governs at each floor level.

Quick access: CSA S16 Load Combinations → | CSA S16 Column Design → | CSA S16 Beam Design → | Canadian Wind Load →

PRELIMINARY — NOT FOR CONSTRUCTION. All results are for educational and reference use only. Must be independently verified by a licensed Professional Engineer (P.Eng.) before use in any project.

Problem Statement

Step 1 — Calculate Unfactored Loads

Dead Load D (Permanent)

Dead load includes structural self-weight and superimposed dead load (SDL):

Live Load L (Occupancy)

For column load takedown, use the tributary live load reduction per NBCC Cl. 4.1.5.8:

L_reduced = L * (0.3 + sqrt(9.8 / A_trib))

where A_trib is the tributary area in m^2 (capped at reduction to 0.5L for most occupancies).

For a column at the ground floor with A*trib = 4 * 7.5 _ 7.5 = 225 m^2:

L_reduced = 2.40 * (0.3 + sqrt(9.8 / 225)) = 2.40 * (0.3 + sqrt(0.0436)) = 2.40 * (0.3 + 0.209) = 1.22 kPa

This is less than 0.5 * 2.40 = 1.20 kPa — use 1.22 kPa reduced live load for column design.

Snow Load S (NBCC Cl. 4.1.6)

Snow load is calculated per the NBCC 2020 snow load formula:

S = Is * [ Ss * (Cb * Cw * Cs * Ca) + Sr ]

S = 1.0 * [ 1.8 * (0.80 * 1.0 * 1.0 * 1.0) + 0.3 ]
  = 1.0 * [ 1.8 * 0.80 + 0.3 ]
  = 1.0 * [ 1.44 + 0.3 ]
  = 1.74 kPa

The roof snow load is S = 1.74 kPa for the main roof. For the mechanical penthouse area, Ca = 1.3 (drift at step) giving a localised snow load of 2.64 kPa — check penthouse framing separately.

Wind Load W (NBCC Cl. 4.1.7)

The external wind pressure is:

p = Iw * q * Ce * Cp * Cg

where Iw = 1.0 (normal importance), q = 0.42 kPa (Toronto), Ce is the exposure factor (varies with height), Cp is the external pressure coefficient (windward/leeward/sidewall), and Cg = 2.0 (gust effect factor for the building as a whole).

For the windward wall at roof height (h = 16 m, Exposure B — urban terrain):

The total wind pressure on the MWFRS (windward + leeward) at roof level = 0.67 + 0.35 = 1.02 kPa, applied to the projected building area.

Seismic Load E (NBCC Cl. 4.1.8)

For a braced steel frame in Toronto (moderate seismicity), the base shear is:

V = S(Ta) * Mv * IE * W / (Rd * Ro)

W_per_storey = floor area * (D_floor + 0.25*L or companion snow)
Ground floor W ≈ 4 * 600 * (4.20 + 0.25*2.40) = 11,520 kN (approx total building weight)

V = 0.31 * 1.0 * 1.0 * 11,520 / (3.0 * 1.3) = 3,571 / 3.9 = 916 kN

The seismic base shear is V = 916 kN — distributed to each floor level proportional to height and mass per NBCC Cl. 4.1.8.11(6).

Step 2 — Factored ULS Load Combinations (NBCC Table 4.1.3.2.A)

Apply the 8 ULS combinations to the column at grid intersection B-2 (interior column) carrying roof + 3 floors. The column supports a tributary area of 7.5 m x 7.5 m = 56.25 m^2 per floor.

ULS-2 (1.25D + 1.5L) governs the column axial compression at 2,033 kN. This is typical for interior columns in braced frames in moderate seismic zones.

Step 3 — Column Load Takedown by Floor

The interior column B-2 accumulates load from floor to floor. Here's the factored axial load at each level for the governing ULS-2 combination:

The ground floor column sees Cf = 1,903 kN from ULS-2. This is the design axial load for the W250 column.

Step 4 — SLS Load Combinations (NBCC Cl. 4.1.3.4)

For serviceability (deflection, vibration), use unfactored loads:

Example — Floor beam deflection check (SLS-1):

For a W460x74 beam spanning 7.5 m, unfactored live load w_L = 2.40 kPa * 7.5 m (tributary width) = 18.0 kN/m:

delta_LL = 5 * w * L^4 / (384 * E * Ix)
         = 5 * 18.0 * 7,500^4 / (384 * 200,000 * 333e6)
         = 5 * 18.0 * 3.164e15 / (384 * 200,000 * 333e6)
         = 2.848e17 / 2.558e16
         = 11.1 mm

L/360 = 7,500 / 360 = 20.8 mm > 11.1 mm ✓

Step 5 — Which Combination Governs? Summary

Frequently Asked Questions

When does the seismic combination (ULS-8) govern over wind (ULS-6)?

ULS-8 (seismic) governs in regions where Sa(0.2) > 0.35g for short-period structures. In Canada, this includes: Vancouver and Victoria (Sa(0.2) = 0.95g), Montreal (0.69g), Quebec City (0.56g), and Ottawa (0.39g). For Toronto (0.33g), seismic is comparable to wind for braced frames with Rd = 3.0. The crossover point depends on the structural system — ductile moment frames (Rd = 5.0) reduce seismic forces by 40% relative to braced frames, making wind governing in more regions. Always check both ULS-6 and ULS-8. For low-rise buildings (h < 20 m) in moderate seismicity, wind governs lateral design; for taller buildings, seismic can govern due to higher mode effects.

How do I handle the companion load factors (0.5L, 0.5S) in practice?

The companion load factors (0.5 for live, 0.5 for snow when wind governs, 0.25 for snow when seismic governs) reflect the statistical probability that two extreme loads do not occur simultaneously. In the analysis model, these are applied as reduced load cases. For example, for ULS-6 (1.25D + 0.5L + 0.5S + 1.4W), you create a load combination that multiplies the full live load case by 0.5 and the full snow load case by 0.5. Most structural analysis software (ETABS, SAP2000, STAAD) handles this natively — you define load patterns (D, L, S, W, E) and then define combinations with the appropriate factors. The software automatically checks all combinations and reports the envelope.

Why does NBCC 2020 use a different wind load basis than ASCE 7?

NBCC 2020 uses the 1-in-50 year hourly mean wind speed as its reference (Cl. 4.1.7.1), while ASCE 7-22 uses the 3-second gust speed at a 1-in-700 year MRI for Risk Category II. The NBCC approach is a legacy of the Canadian wind climate (dominated by synoptic storms, not hurricanes) and the hourly mean basis better represents the sustained wind load on buildings. The gust effect factor Cg (typically 2.0) converts the hourly mean to an equivalent gust. The two approaches produce comparable design pressures for the same location when properly converted: a 1-in-50 year hourly mean of 120 km/h (Toronto) approximately equals a 1-in-700 year 3-second gust of 175 km/h for the same reliability. The NBCC wind map values cannot be directly compared to ASCE 7 wind map values without this conversion.

Related pages: CSA S16 Load Combinations → | CSA S16 Column Design → | CSA S16 Beam Design → | CSA S16 Frame Stability → | Canadian Wind Load Guide →