Design loads and load combinations

Before Owen can analyze a single truss for the operations center, 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 the United States, building codes are adopted by states and cities, and nearly all are based on the International Building Code (IBC), which refers to ASCE/SEI 7, Minimum Design Loads and Associated Criteria for Buildings and Other Structures, for loads and load combinations. This lesson uses ASCE 7-22. Check which edition your jurisdiction has adopted, because state adoption lags the newest edition by several years.

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

ASCE 7 specifies live loads by occupancy. Examples include 40 psf for residential areas, 50 psf for offices, 80 psf for office corridors above the first floor, 100 psf for lobbies, first-floor corridors and assembly areas without fixed seats, and higher values for storage and garages. Ordinary flat roofs carry a roof live load (Lr) of 20 psf, which can be reduced for large tributary areas and steep slopes, but in northern states snow usually governs. Concentrated loads, such as 2,000 lb on a small area for office floors, must also be checked.

Large areas are unlikely to be fully loaded at once, so ASCE 7 allows the live load on members supporting a large area to be reduced. The reduced load is \(L = L_o\,(0.25 + 15/\sqrt{K_{LL} A_T})\) where \(A_T\) is the tributary area in square feet and \(K_{LL}\) is a live load element factor (4 for interior columns, 2 for interior beams). Reduction applies when \(K_{LL} A_T \ge 400\ \text{ft}^2\), and the result may not be less than 0.50\(L_o\) for members supporting one floor or 0.40\(L_o\) for members supporting two or more. Loads over 100 psf, garages and assembly areas have stricter rules.

Snow loads

Snow is often the largest variable load on a roof in the northern United States. ASCE 7-22 computes a flat roof snow load from the ground snow load \(p_g\) as \(p_f = 0.7\,C_e C_t\,p_g\), with an exposure factor \(C_e\) and a thermal factor \(C_t\), then adjusts it for roof slope and adds drifts at steps and parapets and unbalanced loads on gable roofs. A notable change in ASCE 7-22 is that ground snow loads are now risk-targeted and mapped separately for each risk category, so the importance factor of earlier editions no longer appears in the formula. A municipal operations center that houses emergency vehicles may fall in Risk Category IV, and Priya has asked the city to confirm the category.

Wind and earthquake in brief

Wind pressure in ASCE 7 starts from the velocity pressure \(q_z = 0.00256\,K_z K_{zt} K_e V^2\) (psf, with V in mph), where V is the basic wind speed for the risk category and the K factors account for height and exposure, topography and ground elevation. Pressures on each surface then follow from gust and pressure coefficients. Earthquake loads come from mapped spectral accelerations, the building's period and a response modification coefficient for the 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

US structural design uses either load and resistance factor design (LRFD), also called strength design, or allowable stress design (ASD). In LRFD the design strength of each member must equal or exceed the required strength from factored loads: \(\phi R_n \ge \sum \gamma_i Q_i\). Load factors above 1 cover the chance that loads exceed their nominal values; resistance factors below 1 cover variability in strength and workmanship. ASD instead combines nominal loads with factors of 1.0 or less and compares them with allowable strengths, \(R_n/\Omega\). Serviceability checks such as deflection use unfactored loads.

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.

# ASCE 7-22 LRFD combinations (simplified) for one member; loads in kip/ft, downward +
D, L, Lr, S, W = 0.52, 0.0, 0.50, 1.05, -0.25   # no floor live load on a roof; wind uplift negative

combos = {
    "1: 1.4D":                1.4 * D,
    "2: 1.2D+1.6L+0.5S":      1.2 * D + 1.6 * L + 0.5 * max(Lr, S),
    "3: 1.2D+1.6S+0.5W":      1.2 * D + 1.6 * S + 0.5 * max(W, 0),
    "3: 1.2D+1.6Lr":          1.2 * D + 1.6 * Lr,
    "4: 1.2D+1.0W+L+0.5S":    1.2 * D + 1.0 * max(W, 0) + L + 0.5 * S,
    "5: 0.9D+1.0W":           0.9 * D + 1.0 * W,
}
for name, w in combos.items():
    print(f"{name:22s} {w:7.3f} kip/ft")
gov = max(combos, key=combos.get)
low = min(combos, key=combos.get)
print("Governing downward:", gov, f"{combos[gov]:.2f} kip/ft")
print("Least downward (uplift check):", low, f"{combos[low]:.2f} kip/ft")

1: 1.4D                  0.728 kip/ft
2: 1.2D+1.6L+0.5S        1.149 kip/ft
3: 1.2D+1.6S+0.5W        2.304 kip/ft
3: 1.2D+1.6Lr            1.424 kip/ft
4: 1.2D+1.0W+L+0.5S      1.149 kip/ft
5: 0.9D+1.0W             0.218 kip/ft
Governing downward: 3: 1.2D+1.6S+0.5W 2.30 kip/ft
Least downward (uplift check): 5: 0.9D+1.0W 0.22 kip/ft

Crane and impact loads

The garage's 5-ton bridge crane runs on runway beams carried by brackets on the columns. Moving loads like this are increased for dynamic effects: ASCE 7 requires vertical wheel loads to be increased by an impact percentage that depends on the crane type, and lateral and longitudinal forces from trolley movement and braking to be added. 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 percent and can lead to members that are heavier than they need to be. Labeling every load as specified or factored, and noting which combination it comes from, avoids the confusion.