The Science of Simple Spans
How the various code provisions for joist span, blocking, notching, and bearing lengths work together to prevent floors from deflecting.
Synopsis: Span is just one of many rules relating to joists; there are others for blocking, notching, and bearing lengths. When taken together, these rules offer paths to design a floor system that will support the calculated loads with minimal deflection. In this installment of Know the Code, Glenn Mathewson explains the code-maximum deflection limit, and how joist thickness as well as blocking, rim joists, and hangers at the ends and bearing locations combine to keep joists upright and stressed.
Maximum joist span seems like a pretty simple concept to grasp. There’s obviously a natural limit to how far wood can span without breaking under a particular load. But when building a house, we don’t want to get anywhere near that breaking point. We don’t even want a joist to bend all that much. So when we talk about maximum joist spans as the IRC defines them, we’re not really talking about pushing things to the limit; we’re largely talking about what it takes to build a serviceable floor—one that isn’t overly bouncy and won’t rattle the dishes when we walk on it.
The IRC’s span tables make it easy to pick a joist to bridge a simple span—one without intermediate supports or cantilevers— or to work the other way around to get the biggest simple span out of the wood available. But span is just one of many rules relating to joists; there are others for blocking, notching, and bearing lengths. All these rules can be read alone, but when taken together and sprinkled with a little science, they start to make sense not as arbitrary rules but as the means to reach the expected ends. We don’t need an engineering degree to understand how these various joist-related provisions work together, so let’s discuss them casually.
The first step in designing a floor system is to determine how much you expect it to support— the load. The higher the load imposed on a joist or beam, the shorter the distance it can safely and serviceably span. This shortening isn’t because the code is concerned about the floor breaking; it doesn’t want it to bend too much. Deflection, rather than strength, is the foremost limiter to span in conventional wood-frame construction.
Maximum deflection is the most a building system or component is allowed to bend under its maximum design load. Floors have historically been held to L/360—divide the joist length in inches by 360, and you get the maximum deflection allowed for a given span (table R301.7 in the 2021 IRC). For any 14-ft. joist, for example, the deflection limit is about 1/2 in. (168 in./360 = 15/32 in.).
The L/360 deflection limit for residential floors exists for at least two good reasons. One, it should prevent the drywall or plaster ceiling below from cracking. It’s also about how stiff you, as an occupant, expect the floor to feel when you walk on it. While a trampoline can support the 40-lb.-per-sq.-ft. (psf) live load prescribed for residential living areas, it would make a rather impractical kitchen floor. If more deflection than L/360 were allowed, the allowable spans would increase, but the floor wouldn’t be as stiff. If you span less than the max allowed for a given joist, it will deflect less and feel stiffer.
So, what gives a joist stiffness? When a load is put on a joist, the fibers in the top of the joist compress, and those in bottom are put under tension. In the middle, what engineers call the “neutral plane,” these forces diminish to zero. The ability of the wood fibers to resist being scrunched by compression or stretched out by tension directly translates to how much a joist deflects, and is why denser wood species can span farther: they’re better at resisting the stretching and scrunching and therefore deflect less. Still, height can make up for the deficiencies of a species. The more mass is distributed away from the center of a joist—or toward the tension and compression edges (in other words, the taller the joist)—the better it resists deflection. Thus a 2×10 can span farther than a 2×8 of the same grade and species. This is also why I-joists can span extreme distances without a major increase in depth: Much if not most of their mass is in the top and bottom flanges.
These tension and compression stresses are also what moves the load to the ends of the joist for transfer to whatever’s below—typically beams, hangers, or plates. For this transfer to work, the joist must be held in a state of stress. A joist not stressing is a joist deflecting. Joists will lay down on the job if permitted to, and a joist laid flat, like decking, can’t span very far without bending along its thickness. Given the way houses are built, that isn’t what happens. Instead, joists, especially when overspanned or overloaded, try to flop over in the middle of the span.
Joist thickness, though, is a large part of what prevents this kind of flop. While the height handles the stress, the thickness of the joist helps keep it upright and handling said stress. The ratio between thickness and height is important, and most obvious in beams, where additional plies and larger-sawn thicknesses are common. Sawn joists, on the other hand, no matter how tall, are always 1-1/2 in. thick. So even though a sawn joist can handle more stress as it gets taller, it also gets harder to keep it upright.
Thanks to other code provisions (and common sense), the width of the joist doesn’t have to do the job alone; blocking, rim joists, or hangers at the ends and bearing locations are what ultimately keep the joist upright and stressed (R502.7). Other than hangers, which also support vertical load, these features do almost exclusively that: resist rotation. When the height of the joist compared to its width is greater than a 2×12, the width can’t hold the joists upright along their length and bridge blocking is required within the span to prevent the joist from rolling over (R502.7.1).
Let’s get out of the code and look at the science. If you want a stiffer floor with less deflection, you just need better stress management. You could use larger joists (height), denser wood (species), or closer joist spacing, or you could add bridge blocking within the span to reduce midspan joist rotation. But let’s say you have a 2×10 joist that’s slightly overspanned; its primary failure is excessive deflection, and the usual reason for that is it wants to flop over midspan. The same principles that stiffen a floor to above-code deflection limits can stiffen an overspanned floor up to the deflection limit. The code won’t tell you this, but I will. Bridge blocking can bring slightly overspanned joists to within deflection limits, and that’s a more reasonable alternative to replacing the 2x10s with 2x12s.
After deflection, shear is the next stress joists need to be able to handle, but it isn’t typically a major consideration in wood joists. Shear stresses are distributed opposite of bending stresses; they are greatest along the horizontal center of the joist (the neutral plane), and increase toward the ends. Shear failures in sawn joists typically appear as cracks that start at the ends and propagate along the neutral plane—in other words, along the grain. This kind of failure would be problematic because two small joists aren’t equivalent to one big joist; each smaller piece deflects more than one big one would. But it’s highly unusual for a sawn joist to fail in shear along its length. Shear across the grain is even rarer if not unheard of because of the way the grain is oriented (it’s much easier to split wood along the grain than it is to chop across the grain). Research has shown joists will fail in bending long before they fail in shear, which is why, despite shear stresses being largest at the ends of joists, the IRC allows joist ends to be notched up to one-quarter the depth of the joist. No notches are allowed in the middle third, where the bending stresses are greatest, and in the rest of the joist, where bending stresses are smaller, they’re limited to one-sixth of the joist’s depth. Holes, meanwhile, are allowed 2 in. away from the edges, anywhere in the span, which tells you how little there is to worry about when it comes to shear stresses.
We also have to think about bearing. Once joists are loaded, they have to transfer the load vertically. The key here is preventing the joist or the member it’s bearing on from crushing. Wood crushes more easily across the grain, as it is in joist ends, than it does parallel to the grain, as in a post. The size of the bearing area required to prevent crushing is directly related to the strength of the joist and what it’s bearing on, and the total load being transferred. Distributing the load over a greater area reduces the load on any one point, which can in turn allow for greater loads (just like snowshoes distribute your weight to keep you from post-holing in the snow). This is another engineering fundamental the IRC simplifies. For joists bearing on wood or metal, section R502.6 requires the full width to bear with at least 1-1/2 in. of length. This is the minimum area of wood necessary to transfer the loads that a floor designed using the IRC’s prescriptive tables can generate without overstressing the joist and crushing its ends. The minimum bearing length on concrete or masonry is 3 in., but this increased length isn’t about the wood, it’s about the concrete. A joist bearing on concrete creates stresses that can cause the corner of the concrete or masonry to spall off under the joist. The 3 in. of required bearing spreads the load over a greater area to reduce the chance of spalling, and leaves enough area behind the compromised edge for the joist to bear safely if it does spall.
Glenn Mathewson is a consultant and educator with buildingcodecollege.com.
Drawing: Kate Francis
Published in Fine Homebuilding issue #302