Design loads and load combinations

Before Owen can analyse a single truss for the operations centre, he needs to know what loads it must carry. Loads come from the weight of the structure itself, from people and contents, from snow, rain, wind and earthquakes, and from equipment such as the garage's bridge crane. In Canada, the minimum loads and the rules for combining them are set by the National Building Code of Canada (NBC), and by the provincial codes based on it. Ontario's Building Code follows the national structural provisions closely. This lesson uses the NBC 2020 format, which most provinces had adopted by 2026; the NBC 2025 (the sixteenth edition) keeps the same limit states framework but revises several climatic provisions, so always confirm which edition applies to your project.

Kinds of load

Loads are classified by how they arise and how variable they are, because the code treats them differently.

• Dead load (D) is the weight of the structure and everything permanently attached to it: members, deck, slabs, roofing, ceilings, ducts and partitions where their location is fixed. It is known fairly accurately and changes little over time.
• Live load (L) comes from the use of the building: people, furniture, stored goods, movable partitions and light vehicles. It is specified by occupancy as a uniform area load and, for some occupancies, a concentrated load that must be checked separately.
• Snow and rain loads (S, and R in US practice) depend on climate, roof shape, exposure and the possibility of drifting or ponding.
• Wind load (W) is a pressure or suction on the building surfaces that depends on the site's reference wind speed, terrain, height and building shape.
• Earthquake load (E) arises from ground shaking and depends on the seismic hazard, soil, building mass and the ductility of the lateral system.
• Other loads include soil and water pressure, thermal effects, settlement, impact, and the dynamic effects of moving equipment such as cranes.

Dead loads from unit weights

Dead loads are computed from member sizes and material unit weights. You will refine them as the design develops, because the member sizes you assumed at the start rarely survive unchanged.

Live loads and live load reduction

The NBC specifies live loads by use and occupancy. Examples include 1.9 kPa for residential areas, 2.4 kPa for offices above the first storey, 4.8 kPa for assembly areas without fixed seats, corridors and the first-storey floors of offices, and higher values for storage and vehicle repair areas. Roofs carry a minimum specified load of 1.0 kPa, but in most of Canada snow governs. Concentrated loads, such as 9 kN over a small area for office floors, must also be checked because they can govern for short members and slabs.

Large areas are unlikely to be fully loaded at once, so the NBC allows the live load on a member supporting a large tributary area to be reduced. For most occupancies other than assembly and storage, where the tributary area B exceeds 20 m², the specified live load may be multiplied by \(0.3 + \sqrt{9.8/B}\). For a column supporting 80 m² this factor is \(0.3 + 0.35 = 0.65\). Different rules apply for assembly and storage occupancies, where full load is more likely.

Snow loads

Snow is often the largest variable load on a Canadian roof. The NBC gives the specified snow load as \(S = I_S\,[S_s (C_b C_w C_s C_a) + S_r]\) where \(S_s\) is the ground snow load and \(S_r\) the associated rain load from the climatic table for the location, \(I_S\) is the importance factor (1.0 for normal buildings at ultimate limit states, higher for post-disaster buildings), \(C_b\) is the basic roof factor (usually 0.8), \(C_w\) a wind exposure factor, \(C_s\) a slope factor and \(C_a\) an accumulation factor that rises well above 1 where snow drifts against a higher roof or parapet. A municipal operations centre that houses emergency vehicles may be classed as a post-disaster building, which raises its importance factors, and Priya has asked the city to confirm the classification.

Wind and earthquake in brief

Wind pressure in the NBC takes the form \(p = I_W\,q\,C_e C_t C_g C_p\), where \(q\) is the reference velocity pressure for the site, \(C_e\) an exposure factor that grows with height and open terrain, \(C_t\) a topographic factor, \(C_g\) a gust factor and \(C_p\) a pressure coefficient that depends on the surface and wind direction. Earthquake loads come from the site's spectral accelerations, the building's period and the ductility of its lateral system. Both are covered in later design courses; here it is enough to know that each produces lateral loads applied at roof and floor levels.

Limit states design and load factors

Canadian structural design uses limit states design. At the ultimate limit states (ULS), the factored resistance of each member must equal or exceed the effect of factored loads: \(\phi R \ge \sum \alpha_i S_i\). Load factors above 1 cover the chance that loads exceed their specified values and the uncertainties of analysis; resistance factors below 1 cover variability in material strength and workmanship. At serviceability limit states (SLS), such as deflection and vibration, specified (unfactored) loads are used.

Because the maximum values of different variable loads are unlikely to occur at the same moment, the codes combine a principal load at its full factored value with companion loads at reduced factors.

You must check every combination and use the one that produces the largest effect in each member. Different members, and even different points in the same member, can be governed by different combinations. A roof truss is usually governed by dead plus snow; a column base or anchor rods by dead plus wind with the low dead load factor, because wind uplift tries to lift the roof off.

Sofia automates the combination check so that it can be repeated whenever the loads change. Writing the combinations as data, rather than as separate formulas, makes them easy to review against the code table.

# NBC 2020 ULS combinations (simplified) for one member; loads in kN/m, downward +
D, L, S, W = 7.7, 7.5, 19.7, -4.0      # roof live load treated as L; wind uplift negative

combos = {
    "1: 1.4D":            1.4 * D,
    "2: 1.25D+1.5L":      1.25 * D + 1.5 * L,
    "2: 1.25D+1.5L+1.0S": 1.25 * D + 1.5 * L + 1.0 * S,   # a roof cannot carry both; shown for comparison
    "3: 1.25D+1.5S":      1.25 * D + 1.5 * S,
    "3: 1.25D+1.5S+0.4W": 1.25 * D + 1.5 * S + 0.4 * max(W, 0),
    "4: 0.9D+1.4W":       0.9 * D + 1.4 * W,
    "4: 1.25D+1.4W+0.5S": 1.25 * D + 1.4 * max(W, 0) + 0.5 * S,
}
for name, w in combos.items():
    print(f"{name:22s} {w:7.2f} kN/m")
realistic = {k: v for k, v in combos.items() if "1.5L+1.0S" not in k}
gov = max(realistic, key=realistic.get)
low = min(realistic, key=realistic.get)
print("Governing downward:", gov, f"{realistic[gov]:.1f} kN/m")
print("Least downward (uplift check):", low, f"{realistic[low]:.1f} kN/m")

1: 1.4D                  10.78 kN/m
2: 1.25D+1.5L            20.88 kN/m
2: 1.25D+1.5L+1.0S       40.58 kN/m
3: 1.25D+1.5S            39.17 kN/m
3: 1.25D+1.5S+0.4W       39.17 kN/m
4: 0.9D+1.4W              1.33 kN/m
4: 1.25D+1.4W+0.5S       19.48 kN/m
Governing downward: 3: 1.25D+1.5S 39.2 kN/m
Least downward (uplift check): 4: 0.9D+1.4W 1.3 kN/m

Crane and impact loads

The garage's 5-tonne bridge crane runs on runway beams carried by brackets on the columns. Moving loads like this are increased for dynamic effects: the wheel loads are multiplied by an impact allowance, and lateral and longitudinal forces from acceleration and braking are added. CSA S16, the steel design standard, and the crane manufacturer's data give the values. Lesson 9 shows how to find the position of moving wheel loads that produces the largest moment in a runway beam.

Serviceability load cases

Strength is not the only requirement. A roof that sags enough to pond water, a floor that bounces when people walk, or a frame that sways enough to crack the cladding has failed its users even if no member is close to breaking. Serviceability checks use specified loads without load factors, and usually only the variable load that causes the movement being checked. Typical deflection limits for beams are span/360 under live or snow load where ceilings or brittle finishes are attached, and span/240 or span/180 where they are not, with stricter limits for members supporting masonry or crane rails. Lessons 10 and 11 develop the methods for computing these deflections.

Keep the two sets of numbers separate in your calculations. A common source of error in hand calculations is carrying factored loads into a deflection check, which overestimates the deflection by roughly 40 to 60 per cent and can lead to members that are heavier than they need to be. Labelling every load as specified or factored, and noting which combination it comes from, avoids the confusion.