24-Bld-A7 Building Envelope Design · May 2016

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.

Find. (1) The effective (parallel-path) RSI of the base wall. (2) An added continuous exterior insulation thickness that raises the effective RSI to 7.0.

Approach. Sum the two 1-D conduction paths (insulated cavity, solid stud) in series, area-weight their U-values by the framing factor to get the parallel-path effective U, then invert; for Part 2, add a continuous exterior insulation layer (a series resistance common to both paths) and solve for the thickness that drives the combined effective RSI up to 7.0.

1. Cavity-path resistance. Summing every layer the insulated 75% of the wall sees, in series: $$R_{cavity}=R_{si}+R_{brick}+R_{air}+R_{ply}+R_{batt}+R_{gyp}+R_{so}=0.12+0.13+0.22+0.11+3.67+0.08+0.03=\boxed{4.36\ \text{RSI}}$$ (the negligible-thickness Tyvek membrane and poly sheet contribute no measurable R.)
2. Stud-path resistance. The wood stud replaces the batt over the framing 25% of the area; its own conduction resistance is $R_{stud}=L/k=0.140/0.11=1.273$ RSI, so $$R_{stud\,path}=0.12+0.13+0.22+0.11+1.273+0.08+0.03=\boxed{1.963\ \text{RSI}}$$
3. Parallel-path (area-weighted) U-value. $$U_{cavity}=\frac{1}{4.36}=0.2294,\quad U_{stud}=\frac{1}{1.963}=0.5095\ \text{W/(m}^2\text{K)}$$ $$U_{avg}=0.75\,U_{cavity}+0.25\,U_{stud}=0.75(0.2294)+0.25(0.5095)=0.2994\ \text{W/(m}^2\text{K)}$$
4. Effective RSI of the base wall. $$R_{eff}=\frac{1}{U_{avg}}=\boxed{3.34\ \text{RSI}\ (\approx R19)}$$ — a conventional 2x6/16"o.c. wood-frame brick veneer wall, even with a full 140 mm cavity fill, only reaches about RSI 3.3 once the thermally-bridging studs are area-weighted in.

(2) Reaching RSI 7.0 (R40). A single continuous layer of exterior insulation, applied outboard of the sheathing (before the rainscreen cavity and brick), is added in series with both the cavity and stud paths equally — unlike cavity insulation, it does not see the framing factor at all, so it is the most efficient way to add R-value to a wood-frame wall without adding more thermal bridging.

1. Set up the target equation. With an added continuous RSI of $r$ on both paths, $$U_{avg}(r)=\frac{0.75}{4.36+r}+\frac{0.25}{1.963+r}=\frac{1}{7.0}=0.14286$$
2. Solve for $r$ (numerically, bisection). $$\boxed{r \approx 3.42\ \text{RSI}}$$
3. Convert to a board thickness. Using a typical continuous rigid mineral-wool insulation board (RSI ≈ 0.739 per 25 mm, i.e. ≈0.0296 RSI/mm): $$t=\frac{3.42}{0.0296}\approx 116\ \text{mm}$$ Specify a practical nominal thickness of $\boxed{120\ \text{mm mineral wool}}$ (two staggered 60 mm layers, through-fastened with long screws/clips through the sheathing to the studs), which delivers $r\approx3.55$ RSI and an effective wall RSI of $\boxed{\approx 7.13}$, comfortably clearing the RSI 7.0 target.

Configuration proposed: keep the base assembly as-is (brick veneer, existing 25 mm cavity, Tyvek WRB, plywood, 140 mm batt, poly, gypsum) and add 120 mm of continuous exterior mineral-wool board between the plywood sheathing and a new, deeper rainscreen cavity, supported on long screws or thermally-slotted clips through to the studs, with the brick ties extended through the added insulation thickness.

(3) Moisture performance vs. the conventional wall. Moving the majority of the wall's thermal resistance to the exterior side of the poly air/vapour barrier is the key improvement: in the conventional 2x6 wall almost all of the RSI (about 3.3 of 3.34, i.e. ~99%) sits inside the vapour barrier, so the plywood sheathing runs close to the outdoor temperature all winter and sits well below the interior dew point — the classic condensation-prone assembly. With 3.55 RSI of continuous insulation now outside the poly (roughly 3.55 of 6.89 RSI on the sheathing's cold side, i.e. over 50% of the total resistance), the sheathing temperature is pulled up close to room temperature, keeping it safely above the interior dew point through almost the entire heating season. This "exterior-to-total-resistance ratio" method (NBCC 9.25.5.2 / CSA S413 logic) is the standard check for condensation risk at the sheathing, and the proposed wall passes it comfortably where the conventional wall does not; the trade-off is a longer wall tie and a wider window/door jamb return to accommodate the added 120 mm.

(4) Floor/wall junction. The sketch below traces the continuity of all four control layers through the floor-slab intersection: the interior poly sheet (air and vapour barrier, since 6-mil poly performs both functions here) is lapped with a self-adhered membrane strip down over the floor-slab edge to keep it continuous where the platform framing would otherwise break it; the vapour-permeable Tyvek WRB stays outboard of the new mineral wool and is the water-resistive barrier that sheds incidental rainscreen moisture; and the outer face of the brick veneer is the rain-shedding surface that the rainscreen cavity is designed to drain behind.