Designing sag-proof shelves.
By Tom Caspar
Have you ever heard a shelf groan? Well, maybe not, but some shelves look like they would if they could. So much stuff gets piled on them that they end up sagging like a limp noodle. It’s not a pretty sight. A span that holds up weight should look strong and sturdy. Even a slight sag sends an unappealing visual message.
A shelf sags in two stages. There’s a small sag when you first put weight on the shelf. This sag, or deflection, increases as more stuff is loaded on the shelf over the years. The shelf keeps on sagging, a little more each year, because wood slowly but surely changes shape under a load. This characteristic of wood is called “creep.” Arm yourself for the fight against creep with common sense engineering knowledge about how each dimension of a shelf affects its strength, or rigidity (Fig. A).
The most important dimensional factor is a shelf’s thickness. The effect of the other two dimensions, width and length, is straightforward; add 10 percent to the width of a shelf, and it’s 10-percent more rigid; add 10 percent to the length, and it’s 10-percent less rigid. However, add 10 percent to the thickness of a shelf and it’s 21-percent stronger! Strength increases at an exponential rate as you add thickness. That’s why wooden joists and steel beams stand on edge. A shelf that’s 7/8-in. thick is about 36-percent stronger than a 3/4-in. thick shelf. If you’re careful, you should be able to get 7/8-in. thick boards from 4/4 lumber. With such a substantial increase in rigidity, it’s definitely worth the effort.
Let’s put our common sense engineering to the test. How wide or long does a cherry shelf have to be to hold up, say, a set of encyclopedias? We can use standard dimensions that have proven themselves reliable over the years to answer this question (Fig. B).
Encyclopedias are large books, so we need a shelf that’s at least 12-in. deep. (Books look best when they sit 1-in. or so back from the front edge of a shelf.) How heavy are they? It wouldn’t be a bad idea to place them on a bathroom scale and find out. Books and magazines can be surprisingly heavy. These standards suggest they’ll weigh up to 50 lbs. per running foot.
How long should a 3/4-in. cherry shelf be to hold up these books? The standards tell us that a wide hardwood shelf that carries a heavy load should be no more than 36-in. long. But this doesn’t tell us the whole story, and that’s why we have to look at one more variable before we can build this shelf with confidence.
How strong is the wood?
Some species of wood are much more rigid than others. In terms of deflection under a load, hickory is about twice as strong as butternut. If we make similar shelves out of hickory and butternut, and apply the same load, the butternut shelf will sag twice as much. If we cut the butternut shelf in half, it will sag the same amount as the hickory shelf.
The shelving standards are based on averages. Is our cherry encyclopedia shelf average? No, cherry is more than 10 percent weaker than an average wood like walnut or soft maple (Fig. C). Thus, the shelf has to be shorter or thicker.
Plywood and composite woods
Manufactured wood products are not as strong as solid wood. Plywood is only about half as rigid as the average hardwood because it’s made of alternating layers of thick veneer. Wood is not as rigid across the grain as along the grain. In a shelf, the grain of some of the veneer layers runs the long way, but almost half runs the short way.
Particleboard and MDF (medium density fiberboard), collectively called composite woods, do not have the grain structure of solid wood or of plywood veneers. These products have a hard time holding up their own weight. They have about onequarter of the strength of an average wood. Nevertheless, composite wood is widely used for shelving. Comprehensive information on sizing composite wood shelves is available from an industry trade association.
The rigidity of plywood and composite wood can be improved by gluing on solid wood edges or plastic laminate faces (Fig. D.)
How to strengthen a shelf
After weighing the encyclopedias, you may find that they exceed the limits of the standards. In that case, we need to make a more rigid shelf. We could widen the shelf from 12-in. to 16-in., an increase of 25 percent. That would make the shelf 25-percent stronger. It’s an option, but for the sake of argument let’s say that a 16-in. shelf is too deep for our design. What else could we do?
We could shorten the shelf. Like width, it’s a straight percentage reduction. A shelf that is 25 percent shorter will also hold up 25 percent more weight.
A shorter shelf for our encyclopedias isn’t going to work, however. With all the supplements added to it, there’s more than three feet of books! How about making the shelf thicker? If we’ve already purchased 3/4-in. stock, this option is out.
It’s time to be creative about building a shelf that will be stronger than just one solid board. The simplest solution is to add a lip or two to the shelf. Rip some of the 3/4-in. stock into 1-1/2-in. wide strips, turn them on edge, and glue them onto the front and back edges of the shelf (Fig. E). If you need considerably more strength, make the rear strip several inches deep.
Another way to add thickness to a shelf without using expensive thick lumber is to make a hollow shelf 1- to 1-1/2-in. thick from thin plywood and strips of solid wood (Fig. F). This type of shelf is based on the engineering principles of a torsion box. It’s light in weight but very strong. Use it to carry very heavy loads.
Housing a shelf into the sides of a case will enable the shelf to carry more weight. A fixed shelf is more rigid than a loose shelf because its ends are joined to the sides at a stiff right angle (Fig. G). Some joints are stronger than others, so choosing one kind over another can also effect the strength of a shelf. A plain dado works fine, but a sliding dovetail is stronger because it has more mechanical strength and a larger glue surface area.
Supporting a shelf in the middle strengthens a shelf more than you might think (Fig. H). Weight on one side of a middle support helps hold up weight on the other side, like kids on a see-saw. The net effect is that one long shelf with a center support can hold up more weight than two shorter shelves.
Click any image to view a larger version.
Fig. A: The ABCs of Holding Up Weight
Changing any dimension affects the rigidity of a shelf. The biggest returns come with adding thickness and choosing a strong material. These two factors are the foundation of sag-proof shelf design.
Fig. B: Standard Shelving Dimensions
Here are some guidelines for sizing shelves that are supported at the ends by brackets. The maximum length of a shelf increases when you use thicker stock and stronger material.
Fig. C: Rigidity of Common Wood Species
Wood species vary dramatically in rigidity. Standard shelving dimensions are based on using a wood of average strength, such as walnut. To find out how much shorter or longer a shelf of another wood should be, multiply the suggested length by the percentages above.
Fig. D: Strengthening Plywood and Composite Shelves
Each of these shelves is the same thickness, length and width. The solid wood shelf holds up four times the weight of the plain particleboard shelf. If the shelves were narrower, adding solid wood and laminate would help even more.
Add a lip to take advantage of the thickness multiplier effect. If the shelf is made of relatively weak wood, consider using stronger wood for a back lip.
Build a torsion-box shelf for lightweight rigidity. All the parts are glued together. It will almost be as rigid as if it were built of solid wood of the same thickness.
House a shelf to take advantage of the strength of a glued joint. The sides of a case hold a fixed shelf at a rigid right angle. Fasten a fixed shelf to the case’s back for even more rigidity.
Multiply strength by adding a center support. The shelf can then hold up more than twice the weight of two shorter shelves.
This story originally appeared in American Woodworker October 1999, issue #75.