Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
Reference texts: Straube & Burnett, Building Science for Building Enclosures; ASHRAE Handbook — Fundamentals (Ch. 25 Thermal and Water Vapor Transmission Data, Ch. 26 Heat, Air, and Moisture Control in Building Assemblies); National Building Code of Canada (NBCC), Part 5 (Environmental Separation); ASTM C1472, Standard Guide for Calculating Movement and Other Effects When Establishing Sealant Joint Width; CMHC Best Practice Guides for Building Envelopes (brick veneer, shelf angles, thermal bridging, movement joints, flashing). This is a closed-book paper; the exam instructs that only the first five questions as they appear in the answer book are marked, but every question found in the source is answered in full below as a complete study resource.
Find. (1) The effective RSI of the wall by the parallel-path method; (2) whether interstitial condensation occurs, where, and at what rate; (3) the minimum vapour resistance a vapour retarder must have to prevent it.
Fig. 1 — Parallel-path sections through the brick veneer wall: insulation path (75% area, left) vs. wood-stud path (25% area, right).
Approach. (1) Sum series resistances along the insulation path and the stud path separately, then area-weight the two conductances (appendix Eq. 4); (2) build the steady-state temperature profile from the RSI's, find the indoor air's dew point, and see where that isotherm falls in the wall — then quantify the vapour flow into and out of that plane using standard permeance data for the significant vapour-resistant layers (gypsum, plywood, brick), since the appendix's Table 1 supplies only R-values, not permeances; (3) size a vapour retarder, placed on the warm side after the gypsum, so the vapour pressure downstream of it stays below the saturation pressure at the coldest point in the assembly.
Part (1) — Series resistance of each path. Layers common to both paths (ext. film, brick, air space, Tyvek, plywood, gypsum, int. film) total $R_{common}=0.03+0.15+0.22+0+0.11+0.08+0.12=0.71$ RSI. The stud's own resistance is $R_{stud}=l/k=0.140/0.11=1.273$ RSI. Adding the cavity fill to the common layers gives the insulation path:
$$R_{clear}=0.71+3.67=4.38\ \text{RSI}, \qquad R_{stud\ path}=0.71+1.273=1.983\ \text{RSI}$$
Part (1) — Area-weighted (parallel-path) U-value, Eq. (4). $U_{clear}=1/4.38=0.2283$, $U_{stud}=1/1.983=0.5044\ \text{W/(m}^2\text{K)}$. With a 25% framing factor:
$$U_{avg}=(1-0.25)(0.2283)+0.25(0.5044)=0.1712+0.1261=0.2973\ \text{W/(m}^2\text{K)}$$
$$\boxed{R_{eff}=1/U_{avg}=3.36\ \text{m}^2\text{K/W}}$$
about 23% below the simple series value (4.38 RSI) that ignores the thermal bridge through the studs.
Part (2) — Temperature profile (clear-field path). With $T_i=22^\circ$C, $T_o=-10^\circ$C ($\Delta T=32^\circ$C) and steady-state heat flow, the drop across each layer is proportional to its share of $R_{clear}=4.38$:
$$T(R_{cum})=T_i-\Delta T\cdot\frac{R_{cum}}{R_{clear}}$$
Evaluating at each interface gives 21.1°C after the interior film, 20.5°C after the gypsum, −6.3°C after the insulation (warm face of the plywood), −7.1°C after the plywood, −8.7°C after the air space, and −9.8°C after the brick (checks out at exactly −10°C after the exterior film).
Part (2) — Indoor dew point and condensation plane. Actual indoor vapour pressure $p_i=0.40\times2643=1057$ Pa. Interpolating Table 25 for the temperature at which $p_{sat}=1057$ Pa gives a dew point $T_{dp}\approx7.8^\circ$C. Mapping this isotherm into the wall using the temperature profile above places it $R_{cum}=1.94$ RSI from the inside — about 47% of the way through the 140 mm insulation from its warm face. Since the fiberglass batt itself is highly vapour-open (negligible resistance to vapour flow), moisture is not arrested until it reaches the first genuinely vapour-resistant material downstream, the plywood sheathing (warm face at $-6.3^\circ$C, $p_{sat}=382$ Pa there — far below the still-near-1057 Pa actual vapour pressure at that point, since only the gypsum offers any real vapour resistance upstream). Check: with no vapour retarder specified in the given assembly, the wall as-built WILL see interstitial condensation, concentrated at the insulation/plywood-sheathing interface (the classic cold-sheathing failure point in wood-frame brick veneer walls). $\boxed{\text{Condensation plane: back of insulation / warm face of plywood sheathing, }T\approx-6.3^\circ\text{C}}$
Part (2) — Condensation rate. The appendix's Table 1 gives only thermal R-values, not the vapour permeances needed for a flow calculation; standard published values (ASHRAE Fundamentals Ch. 26) are adopted for the layers with meaningful vapour resistance — gypsum board $M\approx2860$, plywood $M\approx57$, brick masonry $M\approx57\ \text{ng/(s}\cdot\text{m}^2\text{}\cdot\text{Pa)}$ (insulation, Tyvek, air space and the air films are all vapour-open and neglected). Vapour resistance upstream of the plane (through the gypsum only) $Z_{up}=1/2860=3.50\times10^{-4}$; downstream (plywood + brick) $Z_{down}=1/57+1/57=3.51\times10^{-2}\ \text{Pa}\cdot\text{s}\cdot\text{m}^2\text{/ng}$. With $p_{sat}$ at the plane $=382$ Pa and $p_o=0.80\times286.4=229$ Pa:
$$\text{Flow in}=\frac{p_i-p_{plane}}{Z_{up}}=\frac{1057-382}{3.50\times10^{-4}}\approx1.93\times10^{6}\ \text{ng/(s}\cdot\text{m}^2\text{)}$$
$$\text{Flow out}=\frac{p_{plane}-p_o}{Z_{down}}=\frac{382-229}{3.51\times10^{-2}}\approx4.4\times10^{3}\ \text{ng/(s}\cdot\text{m}^2\text{)}$$
$$\boxed{\text{Net condensation rate}\approx1.93\times10^{6}\ \text{ng/(s}\cdot\text{m}^2\text{)}\approx166\ \text{g/(day}\cdot\text{m}^2\text{)}}$$
a large uncontrolled rate, precisely because nothing upstream of the cold sheathing offers any meaningful resistance to the huge indoor-to-outdoor vapour pressure difference — the reason Part (3) sizes a retarder.
Part (3) — Minimum vapour retarder resistance. Placing a retarder of resistance $Z_v$ just behind the gypsum (warm side) makes the upstream resistance $Z_1=Z_{gyp}+Z_v$, with the same fixed downstream resistance $Z_2=Z_{ply}+Z_{brick}=3.51\times10^{-2}$. For the vapour pressure at the (still coldest, most restrictive) condensation plane to fall to exactly $p_{sat,plane}=382$ Pa — the threshold of no condensation — series-circuit algebra on the steady-state flow gives:
$$Z_1=Z_2\cdot\frac{p_i-p_{sat,plane}}{p_{sat,plane}-p_o}=3.51\times10^{-2}\times\frac{1057-382}{382-229}=0.155\ \text{Pa}\cdot\text{s}\cdot\text{m}^2\text{/ng}$$
$$\boxed{Z_{v,min}=Z_1-Z_{gyp}=0.155-0.00035\approx0.154\ \text{Pa}\cdot\text{s}\cdot\text{m}^2\text{/ng}}$$
equivalent to a maximum permeance of about 6.5 ng/(s·m2·Pa), i.e. roughly 0.11 US perms — well inside the range of an ordinary 6-mil polyethylene vapour barrier (typically 0.05–0.08 perm), confirming that a standard interior poly vapour barrier, correctly installed and sealed, is sufficient (and gives comfortable margin) for this assembly.
