Top plates. Stud. Pre cut stud. 8 ft, 1 1/8 inch. 4 inch brick veneer ½ inch plywood sheathing. Insulation placed between the studs

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1 This example problem will illustrate the calculation of thermal resistance of a wall, calculation of heat flow through the wall, and how to obtain the temperature gradient through the wall. The elevation and section of a typical residential wall with a brick exterior are shown below. No windows are included in the example. values for the wall components are taken from the Colorado Energy web site, values.htm. The full table is given at the end of the example. residential wall is usually built with x4 wood studs. These studs actually measure.5 x 3.5 inches. There is one horizontal x4 at the bottom of the wall and two horizontal x4s at the top of the wall. These are called plates, the bottom or sole plate and the top plate. For an 8 foot high room, the wall is built 8 foot and /8 inch high. This allows for a inch thick ceiling and a /8 inch thick floor. ccounting for the top and bottom plates, this would require the vertical x4 studs to be 9 5/8 inch long. x4 studs that are 9 5/8 long can be bought at any building supply store, and are called pre cut studs. The studs are spaced at 6 inches on center. On center simply means the length between the centers of the studs. To make an 8 foot long wall, the center to center spacing of the two studs on either end will be slightly less than 6 inches. Batt fiberglass insulation is placed between the studs. There is ½ inch gypsum wallboard (drywall) on the interior, ½ inch plywood sheathing on the exterior stud face, a inch air space (to allow water drainage), and a 4 inch brick veneer. Top plates 8 ft, /8 inch Pre cut stud Insulation placed between the studs ½ inch gypsum wallboard (interior) Stud 4 inch brick veneer ½ inch plywood sheathing inch air space 8 ft ELEVTION SECTION The insulation and the studs will be a parallel system. This will then be in series with the brick, air space, sheathing, and interior dry wall finish. First consider the studs and insulation. The Colorado web site gives an value of 4.38 hr ft F/BTU. Many other sources give the value of wood as.0 hr ft F/BTU per inch of heat transfer, or an of 3.5 hr ft F/BTU for a x4 stud (actual heat length is 3.5 inches). We will use 4.38 hr ft F/BTU.

2 rea of wall: (8 ft)(8.09 ft) = rea of wood: (3 plates)(8 ft)(.5/ ft) + (7 studs)(9.65/ ft)(.5/ ft) = 9.75 ft % area of wood = 9.75/64.75 = 5.% rea of insulation: = ft Find the effective value of the insulation/wood stud parallel system. eff ins wood ins ins wood wood ft 9.75 ft hr ft F/BTU 4.38 hr ft F/BTU 8.96 hr ft F/BTU The value of the wall is obtained by adding the value of each component that is in series. Component value (hr ft F/BTU) Interior air film 0.68 ½ inch gypsum wallboard 0.45 Wood stud/ insulation 8.96 ½ inch plywood sheathing 0.63 inch air space.00 4 inch brick veneer 0.44 Exterior air film 0.7 TOTL.33 The air film is just a layer of dead air that provides additional insulating properties. Suppose on a winter day the exterior temperature is 0 F and the interior temperature is 68 F. The heat loss through this wall is: Q t.33 hr ft F/BTU T T 0F 68F 5. BTU/hr Determine the temperature at the inside of the air space, next to the sheathing. The reason for determining the temperature is to determine where condensation might form within the wall, and where to place a vapor barrier. To do this, we need to determine the value of everything to the exterior of the plane of interest. This is =.6 hr ft F/BTU. Now solve for the temperature, noting the heat flow is the same through all portions of the wall. Q T T t 5. BTU/hr.6 hr ft F/BTU 0F T

3 Solving, the temperature is 6.3 F. s a check, we could look towards the interior. The value of everything to the interior of the plane of interest is = 0.7 hr ft F/BTU. Solve for the temperature. Q T T t 5. BTU/hr 0.7 hr ft F/BTU T 68F Solving, the temperature is 6.3 F, which checks with what we obtained by looking at the exterior. In a similar manner we can obtain the temperature gradient through the wall as follows. Component Interface Temperature ( F) Interior air film/wallboard 65.4 Wallboard/stud 63.6 Stud/sheathing 8.7 Sheathing/air space 6.3 ir space/brick.4 Brick/exterior air film 0.6

4 Value Table English (US) Units Material Insulation Materials Inch hr ft F/Btu Fiberglass Batts Thickness hr ft F/Btu 3 /" Fiberglass Batt /8" Fiberglass Batt /" Fiberglass Batt (high density) /" Fiberglass Batt /4" Fiberglass Batt (high density).00 8" Fiberglass Batt " Fiberglass Batt (high density) /" Fiberglass Batt " Fiberglass Batt Fiberglass Blown (attic) Fiberglass Blown (wall) ock Wool Batt ock Wool Blown (attic) ock Wool Blown (wall) Cellulose Blown (attic) Cellulose Blown (wall) Vermiculite.3 utoclaved erated Concrete.05 Urea Terpolymer Foam 4.48 igid Fiberglass (> 4lb/ft3) 4.00 Expanded Polystyrene (beadboard) 4.00 Extruded Polystyrene 5.00 Polyurethane (foamed-in-place) 6.5 Polyisocyanurate (foil-faced) 7.0 Construction Materials Concrete Block 4" 0.80 Concrete Block 8". Concrete Block ".8 Brick 4" common 0.80 Brick 4" face 0.44 Poured Concrete 0.08 Soft Wood Lumber.5 " nominal ( /").88 x4 (3 /") 4.38 x6 (5 /") 6.88

5 Material Inch hr ft F/Btu Cedar Logs and Lumber.33 Sheathing Materials Plywood.5 Thickness hr ft F/Btu /4" 0.3 3/8" 0.47 /" /8" /4" 0.94 Fiberboard.64 /".3 5/3".06 Fiberglass (3/4") 3.00 (") 4.00 ( /") 6.00 Extruded Polystyrene (3/4") 3.75 (") 5.00 ( /") 7.50 Foil-faced Polyisocyanurate (3/4") (") 7.0 ( /") 0.80 Siding Materials Hardboard (/") 0.34 Plywood (5/8") 0.77 (3/4") 0.93 Wood Bevel Lapped 0.80 luminum, Steel, Vinyl (hollow backed) (w/ /" Insulating board).80 Brick 4" 0.44 Interior Finish Materials Gypsum Board (drywall /") 0.45 (5/8") 0.56 Paneling (3/8") 0.47 Flooring Materials Plywood.5 (3/4") 0.93 Particle Board (underlayment).3 (5/8") 0.8 Hardwood Flooring

6 Material Inch hr ft F/Btu Thickness hr ft F/Btu (3/4") 0.68 Tile, Linoleum 0.05 Carpet (fibrous pad).08 (rubber pad).3 oofing Materials sphalt Shingles 0.44 Wood Shingles 0.97 Windows Single Glass 0.9 w/storm.00 Double insulating glass (3/6") air space (/4" air space).69 (/" air space).04 (3/4" air space).38 (/" w/ Low-E 0.0) 3.3 (w/ suspended film).77 (w/ suspended films) 3.85 (w/ suspended film and low-e) 4.05 Triple insulating glass (/4" air spaces) (/" air spaces) 3.3 ddition for tight fitting drapes or shades, or closed blinds 0.9 Doors Wood Hollow Core Flush ( 3/4") Solid Core Flush ( 3/4") 3.03 Solid Core Flush ( /4") 3.70 Panel Door w/ 7/6" Panels ( 3/4") Storm Door (wood 50% glass).5 (metal).00 Metal Insulating (" w/ urethane) ir Films Interior Ceiling 0.6 Interior Wall 0.68 Exterior 0.7 ir Spaces /" to 4" approximately.00