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

*carry themselves. As such, we will use the AITC Beam Capacity Tables looking for beams that can carry 750,*__also__*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.
Beam
Options:

__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 ≤ 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!

References

Table DF-26, Beam
Capacity, Roof Beams – Snow Load, American Institute of Timber
Construction, Centennial, CO.

Board Foot Measure, Jeff Filler, Yahoo! Contributor Network.

Board Foot Measure, Jeff Filler, Yahoo! Contributor Network.

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