In this example we will calculate the weight and Board Foot Measure quantities of decking for a proposed patio roof. The roof itself is 28 feet (ft) by 15 ft in plan view, single ridge, with 5/12 slopes, as sketched. The decking proposed is 2 x 6 Ponderosa Pine tongue-and-groove decking. The `layup’ proposed is `Random Length Controlled’ (RLC). Along the way we will also calculate the `square footage’ of roof (decking) surface. Also, to accommodate `trim waste’ with the RLC layup the quantities will, in the end, be increased 10%.
First we will calculate the `length’ of each slope. The plan length of each sloped surface, L, is 28 ft / 2 = 14 ft. The slope length, L’, may be calculated by
L’ = L / cos θ,
θ is the roof slope angle, which may be obtained from the roof slope rise/run by,
θ = tan -1 (rise/run) = tan -1 (5/12) = 22.6˚.
L’ = 14 ft / cos 22.6˚ = 15.17 ft.
The sloped area, A’, is obtained by
A’ = 15.17 ft x 15 ft (the other dimension) = 227.5 square ft (sq. ft.).
The total sloped area surface (both slopes) is, thus, 2 x 227.5 = 455 sq. ft.
Now let’s get the weight.
For design purposes Ponderosa Pine may be taken to have a specific weight, γ, of 29 pounds per cubic feet (pcf). The `area’ weight, σ, of 1-7/16 inches (in.) thickness of Ponderosa Pine may be calculated as (in general)
σ = γ x t,
t is the thickness,
σ = 29 pcf x (1-7/16 in. x 1 ft / 12 in.) = 3.5 pounds per square foot (psf).
The total weight of the decking for the roof is thus,
W = σ x A’ (total) = 3.6 psf x 455 psf = 1593 lb.
Now let’s get Board Footage.
The decking joints will be about every 5 in. (see sketch). That means that for each of the slopes there will be
15.17 ft x 12 in. / ft divided by 5 in. = 36.4 pieces (courses).
The `.4′ means that one coarse will be of `ripped’ boards (or, perhaps, the pieces will be placed with small gaps to make up the fraction). To illustrate the Board Footage calculation I will simply round off the 0.4, and assume the difference is `absorbed’ by the increase of 10% for trim waste.
Each nominal 2 x 6 deck pieces is made from a nominal 2 x 6 piece of lumber. It probably arrives at the manufacturing plant at about 1-1/2 by 5-1/2, and then if planed, etc. to the final dimensions 1-7/16 x 5 (not counting the tongue). Each piece has a board foot measure of 2 x 12 / 1 x 12 or 1.0 Board Foot per foot of length. Each piece (course) is 15 ft long, so each piece (course) has 1.0 Board Foot per foot x 15 ft = 15 Board Feet. Then, there are 36 per side, and 2 sides, so the total calculated Board Footage (BF) is 15 x 36 x 2 = 1080 BF.
To account for trim waste let’s increase the above calculated quantities by 10 percent. The `area of decking’ is 455 x 110% = 500 square feet. The weight is 1593 x 1.1 = 1752 lb. And the Board Footage is 1080 x 1.1 = 1188 BF, or about 1200 BF.
Wood prices are often quoted in Board Foot measure, or thousand Board Feet (MBF), thus the calculation. Total weight quantities are important for shipping. Some manufacturers provide information such as ‘weight per square foot’ and `Board Foot per square foot’. That would have saved us some of the above calculations, but wouldn’t have been as interesting.
Note: there are a number of layup types for timber decking. The RLC layup allows the manufacturer to provide pieces of `random’ length; thus the allowance for `trim waste’. Alternately, the decking pieces may be ordered to specific lengths. In the present example the pieces could be ordered in 15 ft lengths, resulting in very little trim waste. Or, the pieces could be ordered in multiples of the rafter spacing, also reducing trim waste.
Timber Construction Manual, Sixth Edition, John Wiley & Sons and the American Institute of Timber Construction, 2012.
Standard for Tongue-and-Groove Heavy Timber Decking, AITC (Standard) 112-93, American Institute of Timber Construction, Centennial, CO.
Board Foot Measure, Jeff Filler, Yahoo! Contributor Network.