In this example we will obtain several beam size options for a specific set of conditions, specifically: 23 foot (ft) span from support to support; applied loading is 600 pounds per linear foot (plf) Snow load and 150 plf Dead load. The beam will be a common Western species Glued Laminated Timber (Glulam) beam. We will use the Beam Capacity Tables provided by the American Institute of Timber Construction as design aids. The total anticipated length is 24 ft. In particular we will find several commonly available beam sizes. For each size we will also calculate the beam weight and `Board Foot’ lumber input.
The total applied load to the beam is
… w TL = 600 plf Snow load + 150 plf Dead load = 750 plf Total load.
Whatever beams we pick must also, obviously, be able to also carry themselves. As such, we will use the AITC Beam Capacity Tables looking for beams that can carry 750, plus at least a little bit more. Using AITC Table DF-26, Roof Beam Capacity Table for Western Species Beams subject to Snow load we obtain the following options. Note that the beam weights are also provided by the Table.
3-1/8 in. x … nothing;
5-1/8 in. x 16-1/2 in., carries 776 plf, and weighs 20.6 plf;
6-3/4 in. 15 in., carries 830 plf, and weighs 24.6 plf.
Note: the 3-1/8 in. width cuts off at 19-1/2 in. for depth in the Table. It’s quite possible that a deeper beam would work, but the `Industry’ has chosen not to include the deeper 3-1/8 in. wide beams.
Let’s check the beam weights (self weights).
For the 5-1/8 in. x 16-1/2 in. beam: is the total load including self weight = 600 + 150 + 20.6 plf = 770.6 plf less than or equal to the `capacity’ of 776 plf? Yes. Good.
For the 6-3/4 x 15: is 750 + 25 = 775 Ã¢Â‰Â¤ 830? Yes. Good.
Now let’s see how much they each weigh.
Since the beam weights are provided, this is easy.
The 5-1/8 x 16.5 weighs 20.6 plf for 24 ft giving us 494 lb.
The 6-3/4 x 15 weighs 24.6 plf for 24 ft giving us 590 lb.
Note the footnotes to the Table indicating a Specific Weight of 35 pounds per cubic foot was used for the Table. Beams in various service conditions might indeed weight less (or maybe more) depending, particularly, on Moisture Content of the wood.
And now let’s calculate the `Board Footage’ for the beam options.
Western Species 5-1/8 in. wide beams are made from 2 by 6s. The `2 by’ is actually 1-1/2 in., giving us the lamination thickness. A 16.5 in. deep beam is thus made from 16.5 / 1.5 = 11 lams. Each lam has a board footage of 2 x 6 divided by 1 x 12 or 12 / 12 = 1.00 Board Foot per foot of length. The whole section is made from 11 of such lams, so, each foot of beam has 11 x 1.00 = 11.00 Board Feet (BF) per foot. The beam is 24 ft long, so, the total BF is 11.00 BF per foot x 24 ft = 264 BF.
Western Species 6-3/4 in. wide beams are made from 2 y 8s. A 15 in. deep beam is thus made from 15 / 1.5 = 10 lams. Each lam has a board footage of 2 x 8 divided by 1 x 12 or 16 / 12 = 1.333 Board Foot per foot of length. The whole section is made from 10 of such lams, so, each foot of beam has 10 x 13.33 = 13.33 Board Feet (BF) per foot. The beam is 24 ft long, so, the total BF is 13.33 BF per foot x 24 ft = 320 BF.
In terms of a formula:
BF = (nom. dim. of each lam / 12) x no. of lams x length of beam x no. of beams.
Gosh, we’re done!
Our beam options are:
5-1/8 in. x 16.5 in. x 24 ft, weighing 20.6 plf, total weight 494 lb, 264 BF; and
6-3/4 x 15 x 24, weighing 24.6 plf, total weight 590 lb, 320 BF.
The particular sizes of course are important for architectural considerations (clearance, etc.). The weights are important for shipping costs. And the BF values will probably drive the costs of the options.
Our final specifications for this example should also include the `grade’ of the beam. Table DF-26 indicates Fb = 2400 psi and E = 1.8 million psi. These are consistent with the commonly specified 24F-1.8E Douglas fir beam. Baby!
Table DF-26, Beam Capacity, Roof Beams – Snow Load, American Institute of Timber Construction, Centennial, CO.
Board Foot Measure, Jeff Filler, Yahoo! Contributor Network.