# Structural Framing of a Deck for a Mountain Cabin

Consider the deck plan illustrated. It is 32′ x 12′ and will be attached to the gable end of a mountain cabin.

The cabin is to be located in Valley County, Idaho, in a location for which the local building authority has established a design roof snow load of 150 psf (pounds per square foot). (This is about 12 to 15 feet of snow!)

The design load provided by the local building authority is presumed to be a `roof’ design snow load (since not indicated otherwise). In general, snow accumulations on elevated roof surfaces, particularly those that are heated, are about 70% of what occurs naturally on the `ground’. To design the deck, a `ground’ and `unheated’ value of, say, 250 psf will be used, which will also accommodate some drifting.

The joists will be `designed’ first, since they drive the design of the decking boards. Spacing of joists for floor applications is generally is 16 inches (in.) on-center (o.c.). Due to the robust snow load in this application it may be necessary space the joists closer; we shall see!

The joists planned will span 11 feet (ft) from ledger to support beam and then overhang 1 ft more to get the full deck width. To simplify the design of the joists they will be treated as simple, single span joists of 11 ft. Structurally, the 1 ft overhangs will provide a bit of counter bending, making the single 11 ft span assumption conservative. Using the American Wood Council `Maximum Span Calculator for Joists and Rafters‘ (Span Options tab), 11 ft span, 250 psf Snow load, 16 in. o.c. spacing, and an assumed 5 psf Dead load, the following design options are provided: __Douglas Fir, Select Structural (Grade), 2 x 12 (Size)__. This design assumes that the Wet Service factor is not applicable (moisture content of wood less than 19%), and that the joists have not been incised for Preservative treatment. In situations where high moisture content in wood * is* expected (during the design loading condition) it would be appropriate to apply the Wet Service factor (`Yes’ on the Wet Service option). Note further that a deflection limit of L/240 was used. For floors in general a value of L/360 is usually set, primarily for walking comfort and to protect crack-able materials. Since comfort will not be an issue for a deck with 12 to 15 feet of snow on it (unless it is some other kind of comfort), and since the deck will not be constructed of crack-able materials such as concrete or gypsum, the deflection limit was relaxed (similar to that of a ROOF with non-crackable ceiling materials).

Once the joist spacing is obtained the required decking thickness may be determined. The cabin ROOF will be constructed of Douglas fir `Select’ grade heavy timber decking. Let us use this material for the attached deck also. __The decking for the roof will have a tongue and groove profile, whereas the decking for the `deck’ will be S-4-S, meaning `surfaced (straight) four sides’.__ In fact, the decking *for the deck* will be specified to be installed with __Ã‚Â¼ in. gaps between courses__ (adjacent pieces) to allow for drainage (rain, snowmelt, various forest litter).

Using the American Institute of Timber Construction *Standard for Tongue-and-Groove Roof Decking*, AITC 112-93, Table 3, the design values for Douglas Fir (Douglas Fir – Larch) `Select’ are: Bending Stress (F_{b}) = 2000 psi (pounds per square inch) and Modulus of Elasticity (E) = 1,800,000 psi. Pages 11 and 13 of the Standard provide adjustment values for the Bending design value as follows: multiply by 1.15 for Snow and 1.10 for 2 in. thickness or 1.04 for 3 in. thickness. (The latter adjustments are based on the published design values based on 4 in. decking). Thus, assuming we will use 2 in. decking, __F _{b} (adjusted)__ = 2000 psi x 1.15 x 1.10 =

__2530 psi__, and

__E = 1,800,000 psi__(doesn’t get adjusted).

The load and span tables provided in the Standard aren’t going to work for our deck design since our joist spacing is way less than those published, and our applied load is too high. Hence, we are going to have to do some design-check calculations `by hand’ (hand calculations), as follows.

A single piece (strip) of decking will carry a `line’ load of,

w = ÃÂƒ x S = (250 psf Snow + 5 psf Dead + 5 more Dead for decking itself) x (5-1/2 in. actual width + Ã‚Â¼ in. gap) / 12 in. per foot = 260 psf x (5.75/12 ft) = __125 pounds per linear foot (plf)__, where ÃÂƒ is the load in psf, and S is the tributary width (`swath’) of deck that each piece supports.

Assuming any particular piece will span 4 or more joist spaces, the associated bending moment, M, and deflections, ÃŽÂ”, are M = 0.107 w L^{2} and ÃŽÂ” = 0.0065 w L^{4}/EI (Item 42, Table B.1, American Institute of Timber Construction *Timber Construction Manual*).

To check bending: M = 0.107 w L^{2} = 0.107 (125 plf) (16/12 ft)^{2} = 23__.8 pound-ft (lb-ft) or 285 lb-in.,__ where L is the structural span length of the decking which is equal to the joist spacing.

The bending *stress* caused by this bending moment is,

f_{b} = M/S,

where

S is the Section Modulus, bh^{2}/6.

Making sure we take into account the decking is oriented flat,

__S =__ (5.5 in.)(1.5 in.)^{2}/6 = __2.06 in. ^{3}__. (Of course the actual thickness of the `2 X’ decking is 1-1/2 in.).

So,

__f _{b} =__ M/S = 285 lb-in. / 2.06 in.

^{3}=

__138 psi__.

The so-called bending design check is, (is) f_{b} = 138 psi Ã¢Â‰Â¤ F_{b} (adjusted) = 2530 psi (?). Yes! Way yes! The 2 x 6 DF decking is way strong enough to carry all that snow `in bending’.

Checking deflection; ÃŽÂ” = 0.0065 w L^{4}/EI where I is the Moment of Inertia, bh^{3}/12.

Remembering that the decking is flat,

I = (5.5 in.)(1.5 in.)^{3}/12 = __1.55 in. ^{4}__.

First dividing w by 12 to get it into a pounds per inch line load, and leaving L in inches for span,

ÃŽÂ” = 0.0065 (125 / 12 pounds per inch) (16 in.)^{4} / [(1,800,000 psi) (1.55 in.^{4})] = __0.0016 in__. (only about 1/600^{th} of an inch).

In terms of a ratio with the span, 0.0016 in. / 16 in. = .0001 = 1/10,000.

If we apply a limit to the decking pieces similar to what we did for the joists, L/240 or 1/240th of the span, we see that the __2 x 6 DF Select__ decking is *plenty stiff enough* also*.*

For determining the outboard deck beams we will use the Wood Beam Capacity Calculator by J. Ochshorn at Cornell. It is not `Code’ per se, but is noted to be based on the 2005 NDS, which *is* Code.

The beams will carry approximately half of the 11 ft spans plus the 1 ft overhang, for a tributary width of about Ã‚Â½ of 11 + 1 = 6.5 ft. We wil use Douglas Fir for Species, and Select Structural grade. Further, let us use 4 beams, 8′-0″ long each, with the two `interior’ spans being `simple’, and the two end spans with the supports brought in 1 ft (for looks), giving 1′ overhangs. We will model all four beams as 8′ simple span, presuming the 7 ft + 1 ft to be a bit conservation (as we did with the joists). (Besides, the Ochshorn Calculator doesn’t handle overhangs.)

Using the Calculator with Span = 8 ft, Spacing = 6.5 ft (the tributary width), Snow load duration, not wet service, Select Structural grade, Live load deflection limit L/240, we get 4 x 14 or 3-ply 2 x 12. Since the deck is pretty close to the ground and the support beams not real visible, a solid beam-like look is not essential; let’s use __3-ply 2 x 12 built-up beams__ (and utilizing the same lumber as for the joists).

To determine the support posts it is necessary to obtain the `Reactions’ from the support beams. Using a `one-size-fits-all’ approach for the support posts, the three `inner’ posts will carry, each, 8 ft x 6.5 ft or 52 square feet of deck, resulting in design loads of, each, 52 square feet x (250 psf snow + say 10 psf materials weight) = __13,520 lb__.

Using the `Capacity of a Wood Column’ Calculator, J. Ochshorn, Cornell University, assuming our posts (columns) are relatively short (~ 1 ft tall), we find that a 3-ply 2 x 6 DF No. 2 built up column will carry nearly 28,000 lb; more than adequate!

Summary:

Decking: 2 x 6 `Select’ Grade, S4S.

Joists: 2 x 12 DF Select Structural Grade @ 16 in. o.c.

Outer Support Beams: four 3 – Ply 2 x 12 Select Structural, 8 ft length each (outer beams 7 ft + 1 ft overhang).

Support posts: 3 ply 2 x 6 DF No. 2.

Notes:

1) we will deal with the fasteners, connections, and ledger later (another article); and

2) instead of four 8-ft outboard beams, two 16-ft continuous spanning beams could be arguably better. The calculations for two 16-ft beams will be handled in another article.

References

*Standard for Tongue-and-Groove Roof Decking*, AITC 112-93, and Errata, American Institute of Timber Construction, West Coast Lumber Inspection Bureau (Custodian), Portland, Oregon.

`Maximum Span Calculator for Joists and Rafters‘, American Wood Council, Washington, D.C.

`Wood Beam Capacity Calculator‘ and `Wood Column Capacity Calculator‘, J. Ochshorn, Cornell University, Ithaca, New York.

Step-by-Step Calculations for a (Continuous) Wood Beam for a Deck, Jeff Filler, Associated Content.