24-Bld-A7 Building Envelope Design · December 2017

Question 2 of 6

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Question 2 (20 marks)

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.

Given. Base wall assembly (exterior to interior) and film resistances:

Stud spacing 16" o.c., framing factor 25%. Target for the improved design: RSI 7.0 (R40, imperial).

Find. (1) The effective RSI of the base wall by the parallel-path method; (2) a wall configuration reaching RSI 7.0; (3) a comparison of interstitial-condensation risk between the two walls; (4) a labelled floor/wall junction sketch for the proposed wall.

Approach. (1) Sum series resistances along the insulation path and the framing path separately, then area-weight the two conductances (Eq. 4 of the appendix); (2) add a layer of CONTINUOUS exterior insulation — outboard of the sheathing, so it is not interrupted by the studs — sized to make up the RSI shortfall; (3) compare the fraction of total wall resistance that sits outboard of the vapour-sensitive plywood sheathing in each design, since a higher outboard fraction keeps the sheathing warmer and further from its winter dew point.

1. Part (1) — Series resistance of each parallel path. The common layers (exterior air film, brick, air space, plywood sheathing, gypsum, interior air film) total $R_{common}=0.03+0.13+0.22+0.11+0.08+0.12=0.69\ \text{RSI}$. The stud thermal resistance is $R_{stud}=l/k=0.140/0.11=1.273\ \text{RSI}$. Adding the cavity fill to each: $$R_{insulation\ path}=0.69+3.67=4.36\ \text{RSI}, \quad R_{framing\ path}=0.69+1.273=1.963\ \text{RSI}$$
2. Part (1) — Area-weighted (parallel-path) U-value, Eq. (4). $U_{ins}=1/4.36=0.2294$, $U_{frame}=1/1.963=0.5095\ \text{W/(m}^2\text{}\cdot\text{K)}$. With a 25% framing factor, $$U_{avg}=(1-0.25)(0.2294)+0.25(0.5095)=0.1720+0.1274=0.2994\ \text{W/(m}^2\text{}\cdot\text{K)}$$ Substituting, $\boxed{R_{eff,base}=1/U_{avg}=3.34\ \text{RSI (m}^2\text{}\cdot\text{K/W)}}$ — about 23% below the simple series value (4.36 RSI) that ignores the thermal bridge through the studs, and well short of the RSI 7.0 target.
3. Part (2) — Where to add resistance. Adding more batt insulation between the same studs would only widen the gap between the insulation path and the (unchanged) framing path — the stud remains the bottleneck. The standard fix is a layer of CONTINUOUS insulation outside the sheathing, in the rainscreen cavity, where it is not bridged by the studs at all (only by occasional point fasteners/girts, neglected here — see the check note). Isolating the stud-cavity parallel combination on its own (before adding the new layer): $$R_{stud\text{-}cavity}=\frac{1}{(1-0.25)(1/3.67)+0.25(1/1.273)}=\frac{1}{0.2044+0.1964}=2.495\ \text{RSI}$$ Summing every OTHER fixed layer (ext. film, brick, rainscreen cavity, sheathing, stud-cavity combination, gypsum, int. film): $$R_{fixed}=0.03+0.13+0.22+0.11+2.495+0.08+0.12=3.185\ \text{RSI}$$
4. Part (2) — Size the new continuous layer. The shortfall to close is $R_{needed}=7.0-3.185=3.815\ \text{RSI}$. Using a semi-rigid mineral-wool exterior insulation board, $k\approx0.035\ \text{W/(m}\cdot\text{K)}$: $t=R_{needed}\times k=3.815\times0.035=0.134\ \text{m}=134\ \text{mm}$. Rounding up to a standard, joint-staggering installation of two 70 mm boards (140 mm total, joints offset to avoid a through-thickness seam): $$\begin{aligned} R_{added} &= 0.140/0.035=4.00\ \text{RSI} \\ R_{total} &= 3.185+4.00=\boxed{7.19\ \text{RSI (m}^2\text{}\cdot\text{K/W)}\approx\text{R41}} \end{aligned}$$ This clears the RSI 7.0 (R40) target with margin, which is deliberate: point thermal bridging through the girts/clips that carry the brick ties across the new insulation layer is not modelled in this hand calculation and typically derates a continuous-insulation wall by 5–10%, so the design is sized to stay above R40 after that derate. Check: assumes semi-rigid mineral-wool exterior insulation at k = 0.035 W/(m·K) and neglects point thermal bridging from brick-tie fasteners through the new layer — a full assessment would use a 2-D/3-D thermal model (e.g. THERM) or a manufacturer's tested clip-system derating.
5. Part (2) — Proposed configuration (exterior to interior). Exterior air film (0.03) → brick veneer, 100 mm (0.13) → vented rainscreen air cavity on adjustable ties, 25 mm (0.22) → continuous mineral-wool exterior insulation, 140 mm in two staggered 70 mm layers (4.00, NEW) → Tyvek WRB (≈0) → plywood sheathing, 12.5 mm (0.11) → 2x6 stud wall with 140 mm glass-fibre batt in the cavity, 25% framing factor (2.495 parallel-path) → gypsum board, 12.5 mm (0.08) → interior air film (0.12).
6. Part (3) — Where does the sheathing sit, thermally? Interstitial condensation risk is governed by how cold the vapour-sensitive plywood sheathing gets relative to its winter dew point, which in turn depends on what SHARE of the wall's total resistance lies outboard of it (between the sheathing and the exterior air). In the conventional wall, only the exterior film + brick + air space sit outboard of the sheathing: $$\text{fraction}_{base}=\frac{0.03+0.13+0.22}{R_{ins\ path}}=\frac{0.38}{4.36}=\boxed{8.7\%}$$ almost the entire wall's resistance (91.3%) sits INBOARD of the sheathing, so the sheathing runs close to the outdoor temperature all winter — exactly the cold, condensation-prone location.
7. Part (3) — Same check for the proposed wall. In the proposed wall, the new continuous layer sits OUTBOARD of the sheathing along with the film/brick/cavity: $$\text{fraction}_{new}=\frac{0.03+0.13+0.22+4.00}{R_{total}}=\frac{4.38}{7.185}=\boxed{61.0\%}$$ Moving 61% of the wall's total resistance outboard of the sheathing (versus 8.7% in the conventional wall) keeps the sheathing much closer to the warm interior temperature all winter, comfortably above the prescriptive minimum-outboard-ratio guidance ASHRAE/NBCC give for avoiding interstitial condensation in Vancouver/Toronto-severity climates (typically ≈30–40% of total R needed outboard of the first vapour-sensitive/vapour-retarding layer). The proposed wall is therefore markedly LESS prone to interstitial condensation at the sheathing than the conventional wall, without needing a full Glaser-diagram calculation to make the comparison — it is the same "warm sheathing" strategy used in exterior-insulated ("perfect wall") retrofits. A secondary benefit: because most of the insulation is now continuous rather than interrupted by framing, the wall also has far less risk of a localized cold spot (and surface condensation) directly behind each stud.

Fig. 2 traces the four control layers through the floor/wall junction of the proposed wall: the air barrier (red) is the sealed exterior face of the new continuous mineral-wool insulation (taped joints, lapped to the window/floor-line details); the vapour barrier (blue, dotted) stays on the interior, warm side of the stud-cavity insulation (the 6-mil poly named in the base assembly, or an equivalent vapour-retarder paint); the water-resistive barrier (green) is the same sealed face of the continuous insulation, lapped shingle-fashion over the shelf angle and any flashing at the floor line; and the rainwater-shedding surface (orange, dashed) is the brick veneer face together with the drained/vented rainscreen cavity behind it. At the floor line, a shelf angle carries the veneer with a soft (compressible) joint left below it, and the through-wall flashing beneath the angle ties into the WRB with a positive lap so drainage from the cavity above is shed clear of the angle.