Determining Wood Joist Size and Spacing
Outline
1. Problem Statement
2. Prescriptive Design
3. The Internet
4. Design Software
5. Basic Principles
6. Conclusion
7. References
1. Problem Statement
In the previous example (here) we had a 2 x 12 dimension lumber floor joist system, joists @ 16 in. o.c., spanning approximately 16 ft. The loads being carried were 40 psf Occupancy Live load and 11 psf Dead load (including the weights of the joists). But I didn’t say how we came up with the joists. Now I will. The easy way would be `to hire an engineer’. But that is the expensive way. Plus, I’d rather be doing something else (playing). So, unless you are involved in a project that `requires’ certification by a professional engineer, there are a number of legitimate ways for you yourself to determine the required joists. And these are ways we (engineers) often employ likewise. Or, even if you will hire an engineer, it may be beneficial to do some `pre-engineering’ on your own, for cost estimation purposes, or to minimize or streamline the scope of work for the engineer. So, here goes.
2. Prescriptive Design – Building Codes
For Conventional Light-Frame (wood) Construction the International Building Code (IBC) provides tables showing the maximum spans for various size, species, and grades of dimension lumber, as a function of joist spacing, and Live load. Two tables are provided: one uses an Occupancy Live load of 40 psf; the other uses 30 psf (applicable to residential sleeping areas). Joist spacing options are: 12 in. o.c., 16 in. o.c., 19.2 in. o.c., and 24 in. o.c. Integer multiples of each of these spacings `fit’ into common 8 ft long sheets of floor sheathing. For floor applications, 16 in. o.c. is common; for heavier loads sometimes 12 in. o.c. is used. The Tables (Table 2308.8(1) and 2308.8(2) also indicate that the deflection due to live load (for the Tables) is limited to span (L) / 360, which is the maximum allowable deflection according to the building code. Both Tables have 10 psf and 20 psf Dead load options.
For our particular problem we will use Table 2308.8(2), which is for 40 psf Live load. For a species we will use Douglas Fir-Larch, which is commonly available in my area. (For your area of practice you will need to find out what species and grades are commonly available.) In our problem we know our joists are going to need to be `about’ 16 ft long. Actually they will be a bit shorter, since they will frame to the sides of the beam and lap some distance onto the side walls. For now we will simply look for allowable spans of 16 ft or more, and split hairs later if we need to. (After all, we don’t know the beam width yet.) And let’s limit our investigation to Grade # 2.
So, using the Table we find the following … (Douglas Fir-Larch)
Dead load 10 psf
2 x 8 will carry the loads out to … 12-7 (ft-in.) … NOT good.
2 x 10 will carry the loads out to … 15-5 (ft-in.) … maybe good.
2 x 12 will carry the loads out to … 17-10 … probably good.
(I say `maybe’ since we have a bit more Dead load (11 psf), but once we deduct half the width of the beam, and some of the wall, our span will be a bit less than 16 ft, and it might indeed work.)
(I say `probably’ above since strictly speaking we have a 11 psf Dead load in our problem).
Dead load 20 psf
2 x 10 … 14-1 … not good.
2 x 12 … 16-3 … good.
So, we could go back to our original example and argue that 2 x 10s would be adequate. (And, note, it would also cut the Dead load down a bit.) If 2 x 12s were a `guess’ in the original example, then the `guess’ was a bit robust. HOWEVER, if the 2 x 12s were specified by another designer, it could be that the designer had some more stringent requirements in mind. For example, many floors are designed with deflection limits more stringent than the L/360.
3. The Internet (GASP!)
Much of what we do these days directly or indirectly involves the Internet. And the amount of information on the `Net’ no doubt is growing faster than any (one) of us can keep track of. In structural design the Internet should be considered a tool, however, and not a source. But through the Internet I can, for example, go to the American Forest and Paper Association / American Wood Council Website and find a Maximum Span Calculator. This is not all that far-fetched, really, since the IBC references the AF&PA span tables for joists and rafters. So, instead of going to Washington, D.C., and knocking on their door, I’m just visiting their website. I need to know what I am doing when I use their website, but likewise I would need to know what I am doing with any paper they give (or sell) me if I go to their door. So, let’s do it … the link is … www.awc.org/calculators/span/calc/timbercalcstyle.asp
If we put in Douglas Fir-Larch, # 2, 2 x 10, 16 in. o.c., Live load 40 psf and Dead load 10 psf … we get … a max span of 18-1. The site allows us to use a Dead load of 15 psf … let’s put that in, and we get … a max span of 17-3. Good!
Alternately we can go to their `Span Options Calculator’ and put in … Douglas Fir-Larch, span of 16 ft, Live load of 40 psf, Dead load of 15 psf … and it gives the following options:
2 x 10 in Grade SS (Select Structural)
2 x 12 in Grade # 1
2 x 12 in Grade # 2
… basically the same thing.
And note all the disclaimers. You need to know what you are doing.
I think once you know what you are doing, you can play around on their site a bit and discover that the deflection limitation is on Live load, even though it isn’t explicitly said.
4. Design Software
Proprietary wood design software is available that can be used to `crank out’ required joist grades, sizes, etc. Proprietary means that the owners of the software probably want money for their software, but often free trial versions are available. Anyone in the wood design business will generally end up purchasing such software. And, or but, even though you pay for it, there are still plethora of disclaimers. You need to know what you are doing with it. Commercially available software will generally let you put in any values you want to for Dead load, Live load, etc.
5. Basic Principles
Or we can determine our joist size, species and grade, etc. required, by basic mechanics. In my opinion it’s a lot of fun, and you should certainly be able to follow along before you venture into using design software, but it is also time consuming. We will solve this problem using basic design principles (and calculations) in another lesson.
6. Conclusion
In this lesson we have looked at several ways of determining the required floor joist species, grade, and size for a particular floor system. More attention was given to the `prescriptive’ approach and some attention to a viable resource on the Internet. The nice thing about following the prescriptive part of the code is that the code is what the building official uses in review of your design. The nice thing about the `AF&PA way’ is that there are more options for Dead load and deflection limits. Also mentioned was the use of commercially available design software. Since I am not in the business (here) of promoting one software over another, I have not expanded on this aspect. We will, as I mentioned, however, spend a chunk of time on determining the required joists by basic principles, reserved for a later lesson.
7. References
American Forest & Paper Association / American Wood Council, 1111 Nineteenth St., NW, Suite 800, Washington, D.C., 20036, www.awc.org.
International Building Code, International Code Council, 4051 West Flossmoor Road, Country Club Hills, IL 60478.
