Question 1 of 6: Definitions

Question 1: Definitions (20 marks, mandatory)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

a) Importance factor. A code-prescribed multiplier (NBCC Table 4.1.6.2, denoted $I_S$, $I_W$, $I_E$ for snow, wind and seismic) that scales the specified environmental load up or down according to the consequence of the structure's failure — buildings that pose a high hazard to life or that must remain functional after an extreme event (post-disaster) get $I>1.0$; buildings whose failure poses low risk get $I<1.0$. It is the mechanism by which a code applies the same climatic load map to very different consequence-of-failure buildings. Example: the loose-housing barn in Figure 1 normally qualifies for the NBCC "low human occupancy" category, so its snow and wind loads (Q2's roof surface, Q5's girts) are multiplied by an importance factor below 1.0, letting the roof and wall framing be sized smaller than an occupied building of the same footprint would require.

b) Load combinations. NBCC Part 4 does not check dead, live, snow and wind loads one at a time — it requires the structure to be checked against a prescribed set of factored-load sums applied simultaneously (e.g. $1.25D+1.5L$, $1.25D+1.5S$, $1.25D+1.4W$, $0.9D+1.4W$, plus companion-load reduced versions), because the true worst case for a given member is rarely a single load acting alone. Example: Question 2's roof truss is checked under the combination that sums factored dead load and factored live (occupancy/snow-surrogate) load acting together at every joint, not dead load and live load in isolation.

c) Factored loads. The specified (nominal, service-level) load multiplied by its NBCC load factor ($\alpha>1$, e.g. $\alpha_D=1.25$, $\alpha_L=1.5$) to inflate it to the ultimate limit-states (ULS) design level, accounting for the possibility that the actual load exceeds the nominal value. Example: Question 2's truss joint loads are given as separate dead-load and live-load values; the factored joint load used in the analysis is $1.25D+1.5L$, e.g. $1.25(4)+1.5(10)=20.0$ kN at node 2.

d) Factored resistance. The nominal (characteristic) resistance of a material or member, $R$, multiplied by a resistance factor $\phi<1.0$ (e.g. $\phi_b=0.9$ for sawn-lumber bending, $\phi_c=0.65$ for concrete shear) to produce the design capacity $R_r=\phi R$, accounting for variability in material strength, member dimensions and workmanship. Limit-states design then requires $\text{factored load effect} \le \text{factored resistance}$ at every member. Example: Question 3's built-up timber lintel B1 is adequate only where its factored moment resistance $M_r=\phi_b F_b S$ meets or exceeds the factored applied moment $M_f$.

e) Low human occupancy. An NBCC/occupancy classification for a building or space where the density and duration of human occupancy are both low (Table 4.1.6.2 lists agricultural buildings, greenhouses and similar low-occupancy structures) — it is not the same as "unoccupied," but reflects that few people, for short periods, are present at any time. This classification lets the barn in Figure 1 use a reduced importance factor for snow, wind and seismic design, since a structural failure endangers far fewer occupants than an equivalent-size assembly or residential building.

f) Slope factor. The snow-load slope factor $C_s$ (NBCC Cl. 4.1.6.4) reduces the roof snow load as roof slope increases beyond about 15–30° (depending on roof surface and thermal condition), because snow increasingly slides or sloughs off a steep, slippery roof rather than accumulating; $C_s=1.0$ for slopes at or below the threshold and decreases roughly linearly to $C_s=0$ near 70°. Example: Figure 1's gable roof (rise 4 over run 12, i.e. slope $\approx 18.4\deg$) already sits close to the reduction threshold, so $C_s$ directly reduces the snow load feeding into Question 2's factored truss joint loads.

g) Hoop stress. The circumferential (tangential) tensile stress generated in the wall of a curved or cylindrical container by internal or lateral pressure acting radially outward, $\sigma_{hoop}=pr/t$ for a thin-walled cylinder of radius $r$ and wall thickness $t$ under pressure $p$ — the wall is stretched around its own circumference rather than bent. It governs the design of circular structures such as silos, grain bins and circular manure/liquid storage tanks; the rectangular manure tank of Question 6 instead resists its lateral pressure by out-of-plane bending of flat wall panels (no hoop action), which is precisely why a rectangular tank needs thicker walls and more reinforcement per unit volume than an equivalent circular one.

h) Uplift. A net upward force on a roof, member or whole structure that occurs when wind suction (negative external pressure on a roof or leeward wall) exceeds the counteracting factored dead load, or when hydrostatic/soil-water pressure exceeds a structure's self-weight. Roof and truss-to-wall connections must be explicitly designed for uplift using the load combination $0.9D+1.4W$ (the reduced dead-load factor deliberately makes it hard for dead weight to "hide" an uplift failure). Example: Figure 1's Q6 foundation must resist hydrostatic uplift on the empty manure tank base slab, and Q4's truss-to-column connections must resist wind uplift on the roof diaphragm.

i) Lateral force resisting system (LFRS). The complete structural system — typically shear walls, braced frames or moment frames working with horizontal diaphragms — that collects horizontal wind or seismic load applied to a building's surfaces and delivers it, as an unbroken load path, down to the foundation. Example: Question 4 designs the barn's LFRS as a plywood roof diaphragm spanning between the two 12 m end walls, each end wall acting as a plywood shearwall (Q5's girts and Q3's columns only carry the out-of-plane wind pressure into the diaphragm; the shearwalls carry the accumulated in-plane shear down to the Q6 foundation).

j) Type HS cement. A high-sulfate-resistant Portland cement (CSA A3001 Type HS, historically CSA Type 50) formulated with a restricted tricalcium-aluminate ($C_3A$) content, which limits the formation of expansive ettringite when the hardened concrete is exposed to sulfate-rich soils, groundwater, or aggressive organic acids — exactly the exposure a below-grade concrete manure storage tank experiences. Example: Question 6's manure tank concrete should specify Type HS cement (or an equivalent supplementary-cementing-material blend) as part of its durability design, discussed further in Question 6b.