The Glued Laminated Timber Industry provides a plethora of information to assist the designer in the selection of Structural Laminated Timber products. These aids include technical information that a designer can use in `calculations’, load-span `tables’ that allow the designer to select a beam based on span and design loads, software, and other. This article focuses on the use of tabular design aids (tables), generally available in print and on line. Users of such information range from design professionals such as licensed Professional Engineers and Architects, and their trainees, to Contractors, Owners, in fact just about anyone in the design and construction industries. This article explains by example how to use such tables. While I will not discriminate who you, the user, and reader of this article might be (amongst the list of possibilities above), I do demand that you `know what you are doing’ before you specify an actual structural member that becomes part of an actual structure that will be occupied by precious people. I am an Engineer, and my mandate as such is foremost that of public safety.
Let us consider the `Beam Capacity Tables’ provided by the American Institute of Timber Construction (AITC). These tables are easy to use, and available on line at AITC-Glulam.org. Tables provided elsewhere are in some cases similar, and others a bit different. In the end they should all give us about the same answer(s).
For the sake of example let’s consider a set of roof beams, all of which will span 24 feet, supported at their ends, carrying obviously the roof itself between the ends, and potentially a lot of snow. The weight of the roof we might obtain from the roof manufacturer or by calculation if we’re smart, from other design aids, or estimate based on experience. The amount of Snow we need to design for is generally provided by the local building department (unless, of course, there isn’t one). In areas of little or no snow the model building codes, for example the International Building Code, provide design loads for roofs.
In this example the roof weight has been estimated to be 15 pounds per square foot (psf) and the Snow load was obtained from the local building department to be 30 pounds per square foot. The beams will be spaced 4 ft apart, they will be exposed, and the roof construction is such that it can accommodate moderate deflections without cracking or damage. The beams will be exposed to view from below and the Owner desiring the best appearance possible.
The AITC tables are cast in terms of beam size, span, and Allowable load (`Beam Capacity’), where the Allowable load is in terms of pounds of loads per foot of beam, or plf. The loads are assumed to be `uniform’, which is an appropriate assumption for Snow loads (in the absence of drifting or other specific conditions that might cause otherwise) and `uniform’ roof construction materials. The tables show Beam Capacity for various size beams of various spans, the` idea’ being that a beam be selected with capacity at least as much as is required to carry the roof Snow and roof construction. And, the beam must additionally carry `itself’. (Obviously.) The weight of the roof construction is also called `Dead’ (D) load (dead weight) and Snow (S) is also called, in this context, a `Live’ load (as opposed to dead).
It is incumbent for the use of any design aid that the correct one is used. AITC provides six beam tables for the Douglas fir species and eight for Southern Pine. Around `here’ Douglas fir is used, so we will first narrow to the Douglas fir tables. Secondly, we will narrow to the four roof beam tables, and finally to the two that deal with `Snow’. Although not obvious in the list on the page from which they link, the first three are for beam widths of 3-1/8, 5-1/8, and 6-3/4 in. and the second three for 3-1/2, 5-1/2, and 6-3/4. The 3-1/8 and 5-1/8 in. widths are standard for Architectural and Premium Grade beams; the 3-1/2 and 5-1/2 typically for Framing and Industrial Grade. As such, in this application, we will use the first Snow load table (DF-26).
When we `open’ the Table (http://aitc-glulam.org/pdf/Capacity/DF_26.PDF) we find information such as: Simple Span, Fb 2400 psi, Fv 240 psi, E 1.8 million psi, CD 1.15, Deflection limit L/180 for TOTAL load. Before we use the (or any) table, we must make sure it is for conditions corresponding to our situation. Making sure,
Simple Span? … yes, our beams will `simply’ span 24 ft between support walls at both ends
Fb 2400 psi? … yes, this is the Bending Design Value for the most readily available 24F-V4 Douglas fir beam for our locale.
Fv 240 psi? … no, the current Design Value for shear is 265 psi; this table is slightly out of date; however, if the table is good for 240 it should also be good for 265; besides, shear seldom governs the design of moderate and long span beams, and our beams are certainly not short.
E 1.8 million? … yes.
CD 1.15? … yes; CD is the Load Duration factor and 1.15 is what is used for Snow load.
Deflection limit L/180 for Total load? … yes; L/180 corresponds to Total deflection limit for roof construction that is not easily damaged by deflections.
So, it looks like we can use this table.
(Note: if the roof construction is of more easily damageable material, such as gypsum, a more stringent deflection limitation would be required and the Table not applicable.)
The trick now is to get the pounds-per-square-foot (`area’) loads above into `pounds-per-foot-of-beam (`line’) loads. Some design aids help with this step. The AITC aids don’t, so I will show you a couple ways to do it. One way is by use of an `equation’. (Engineers love equations.)
w = σ x S (or σ x s),
where
w is the `line’ load,
σ is the `area’ load,
S is the tributary width for each beam, and
s is the beam spacing.
In many cases S and s end up being the same thing, particularly for wood construction, where the width (say, of roof) contributing to each beam, being half the distance to each adjacent beam, is identical to the spacing itself.
For this example,
wD = 15 psf x 4 ft = 60 plf,
wS = 30 psf x 4 ft = 120 plf.
Another way to get the `line’ load on each beam is as follows: each beam supports an area of roof 4 ft by 24 ft or 96 square feet. Each square foot weighs 15 pounds. The total weight of roof each beam must carry is, thus, 96 x 15 = 1440 lb. This amount divided by the beam length is (1440 / 24) … 60 plf. Similarly for Snow, or other loads.
The weight of the beam itself is not determined yet, since we don’t have its size.
The Total load, excluding the beam weight, is 120 + 60 = 180 plf.
Following down the column for a span of 24 ft in Table DF-26 (last column on the right, first page) we find that the smallest size in the 3-1/8 in. width that will carry 180 plf is the … 3-1/8 x 13.5. The Table says it will carry 247 plf. The 247 is followed by `D’ which, in this case means Deflection controls (not to be confused with D for Dead load). Further, over on the left the weight of this beam is provided; it weighs 10 plf.
A formal Design Check may be expressed,
(is) the load on the beam = 180 plf (total load) + 10 plf (self weight) = 190 plf ≤ the capacity = 247 plf? The answer is … yes! The 3-1/8 x 13.5 beam is `good’.
Further down the Table we find that the 5-1/8 x 10.5 carries 191 plf (controlled by deflection). It weighs 13 plf.
Is load = 180 + 13 = 193 ≤ capacity = 191? … No; we need to go bigger. But we were close! Some designers would say `close enough’. I won’t take up that argument, here.
Trying the 5-1/8 x 12 … which has a capacity of 285 and weighs 15 plf,
(is) 180 + 15 = 195 ≤ 285? … (way) yes!
We can go farther down the Table and also find that a 6-3/4 x 10.5 beam also works. Note that it weighs 17 plf. More wood, at probably greater cost. In general, the narrower beams tend to be more efficient. At some point, however, narrow beams become too narrow and become unstable. From the Table we might present an `answer’ something like this:
Suitable beam: 3-1/8 x 13.5 or 5-1/8 x 12 24F-V4 Douglas fir, Premium Appearance Grade. (The Owner, it turns out, is a practicing Architect.)
In a previous article a suitable beam for exact same conditions was determined by brute calculations to be 3-1/8 x 12 (smaller). In that example a slightly smaller section was found utilizing a provision in the International Building Code that allows for not counting all the Dead load in the total load deflection. Had that example not utilized that provision, the same size section would have been determined as in this example.
The above example illustrates the use of an Industry-provided load-span table for specifying a Glued Laminated Timber beam. Note all the warnings, disclaimers, etc. at the bottom of the page. Obviously the information in such tables is not 100% guaranteed to be perfect. However, such information is generally formulated with a great deal of care – no one in the Industry wants a structural failure. Further, they are only applicable to situations exactly matching those used to formulate them. Correct use of such tables is incumbent on the user.
As a practicing engineer I often use such tables. As an educator I invite non-engineers to use the tables, as long as they `know what they are doing’. Building officials often accept design solutions provided by non-engineers for Residential and other light framing construction applications. Use of tables such as the one described above may constitute an adequate design to some officials. Others may require a certified (`stamped’) design, regardless.
In any case where the applicability of a table or other design aid is in question, or where designs are more complicated, the service of a licensed professional should be obtained.
References
American Institute of Timber Construction, Centennial, CO, www.aitc-glulam.org.
Example Specification of a Glulam Roof Beam, Jeff Filler, Associated Content.
International Building Code, International Code Council, Country Club Hills, IL.
Table DF-26, Roof Beams – Snow Loads, Douglas Fir – Larch, American Institute of Timber Construction, Centennial, CO.
