As a small town consulting engineer I am often asked to provide advice for relatively small remodel projects. Today was no different. The homeowner wished to take out a kitchen wall and wanted to know what size beam should be used, in its stead, to support the ceiling and roof overhead. His desire is to leave the ceiling-roof framing intact, installing the beam below the ceiling. Of concern, of course, was `how far down’ the beam would extend, into the newly open area. Neither he or I are particularly tall, but he wanted the work to `meet code’, giving me about a foot, of depth, to work with.
(Section 1208.3 of the 2006 International Building Code requires that occupiable, habitable spaces have ceiling heights of not less than 7 feet 6 inches. For one- and two- family dwellings, beams and girders spaced not less than 4 feet on center may project not more than 6 inches below the required ceiling height.)
I asked if the sheetrock ceiling was to remain. Yes. The reason I asked is that for roof members supporting `plaster’ and other crack-able materials, the `deflection’ (sag) limit set by building codes is the same as for floors, namely, that the beam, joist, whatever, be stiff enough to keep the deflection (due to `live’ load) less than the span divided by 360.
Having designed a `million’ similar beams in my lifetime, I was on-the-spot ready to give the owner some preliminary information. We measured the distance the new beam would span … 24 feet (ft). Knowing that a typical wood beam (subject to the sag-less-than-span/360 limit) will have a depth of 1/16th the span, I was able to say, … 24 x 12 inches / 16 “… about 16 inches.” He gulped, seeing such a deep beam being a headroom problem.
“Interestingly,” I added, wanting to somehow recover something from the previously designed million beams, ” … this ratio of 1/16 is true for cast-in-place concrete, and structural steel, but,” I (quickly) responded, … “we could get a lesser depth using steel.” (Though not as efficiently.)
We took one more measurement, the spans of the ceiling-roof members above … 25 ft.
I promised I would provide beam options in both wood (glulam) and steel. He asked which would be more expensive. I responded, “since they are both available, they are presumably competitive. The wood beams are probably `one day’ away, and the steel `two’.” I further added, “in general the steel and wood beams will weigh about the same, in any application,” but if we squeeze the depth with the steel, it will be less efficient, and thus weigh and cost more. Let’s see ….
Back at the office I ran the numbers. Since the roof-ceiling framing is already carrying the roof Dead load (dead weight of the roof), and that the new beam will be installed below the ceiling members, the load that the new member will carry will be only the `live’ load (superimposed onto the dead weight already being carried by the in-place members). The design `live’ load for this locale is 40 pounds per square foot (snow). Assuming the new beam will carry the `middle half’ of the roof framing (a term one of my students came up with), the load on the beam will be … ½ of 25 ft (of roof-ceiling) times 24 ft (of beam) times 40 pounds per square foot (of snow)… 12,000 pounds (lb). For steel beams we generally deal with 1000’s of pounds, or `kips’, or (just) `k’; so the total load on the beam will be 12k.
Using design aids provided by the American Institute of Steel Construction, the following standard beam sizes will work:
W12 x 26, W10 x 30, and W8 x 48,
where `W’ stands for `Wide-Flange’, the first number, 12, stands for how deep it is (12 in.), and the 26 stands for how much it weighs, 26 pounds per foot.
Note that, of the three, the 12 in. deep beam weighs the least; e.g., is the most efficient. The 8 in. deep beam gives us more room, but we `pay’ for it, with more steel! The 10 in. beam is in between.
Turning to Glulam options, the load on the beam is converted to a `line’ load by dividing the total by the length of the beam; 12,000 lb divided by 24 ft gives 500 lb per foot (plf).
Using design aids from the American Institute of Timber Construction (AITC) the following Glulam sizes are obtained:
5-1/2 in. (wide) x 18 in. deep, 6-3/4 x 16.5, and (gulp), 10-3/4 x 15.
The 18 in. deep beam is the most efficient, and weighs about 25 pounds per foot, for a total weight of about 600 pounds. The 16-1/2 in. deep beam gives more headroom, but weighs a bit more, 27 plf; the 10-3/4 x 15 is not much shallower, but way wider, and weighs 36 plf.
The steel beams solve the problem; they are stiff enough to keep the deflection within code limits and give us needed headroom. The steel and wood beam options weigh about the same, interestingly, though the depths are different. The shallowest beams are the heaviest (least efficient), and quite wide, for both wood and steel. In fact, if we look up the width of the W8 x 48, we find it is 8.5 in., wider than it is deep! … truly a WIDE-flange beam.
Summary: for floor beams and roof beams supporting crackable material such as sheetrock, plan on wood beam sizes on the order of the span divided by 16 for the beam depth. This `rule’ goes for joists and rafters as well. If headroom is a problem, then steel may offer a solution. Interestingly, wood and steel beams will weigh about the same, for any particular application, though the steel members will be shallower. If a very shallow member is desired, it will end up being quite fat, heavier, and thus more expensive.
References
International Building Code, International Code Council, Country Club Hills, IL.
Steel Construction Manual, ASD, Allowable Loads on Beams (Table), American Institute of Steel Construction, Chicago, IL.
Table DF-30, American Institute of Timber Construction (now maintained by the West Coast Lumber Inspection Bureau, Portland, OR).
Design Criteria for the City of Moscow, Moscow, ID.
