The links above reference tables of shelf sag measurements for shelves that range in width from 30″ to 54″ in 6″ increments. The objective was to collect real-life sag values for shelves that are representative of common bookshelf construction in terms of materials, shelf dimensions, and support/stiffening mechanisms. I was also curious to see how the real-life values would compare to the theoretical values computed by the Sagulator. The measurements were collected with a shop-built shelf deflectometer.
Six types of shelving materials were used (all 3/4″ thick) including sheet stock, softwood, and hardwoods. These materials which range in stiffness from low to high, are:
- Pine Plywood
- White Pine
- Yellow Poplar
- Black Cherry
- Red Oak (Northern?)
To get an idea of how these materials stack up to other materials in terms of stiffness (and hence sag), take a look at this table of wood strength properties, in particular the Static Bending, Modulus of Elasticity column. As an example, you can see that Sugar Maple is approximately the same stiffness as Northern Red Oak. If your favorite wood is not represented in these sag tables, you have a decent shot of extrapolating its sag performance if you can locate a species with a comparable stiffness rating.
Three different shelf depths were used – 8″, 12″, and 16″ – representing narrow, standard, and extra wide bookshelves. An 8″ deep shelf would be appropriate for paperbacks and small hardcover books. A 12″ shelf is perhaps the most common size for bookcases since it can accommodate magazines and the majority of textbooks. 16″ deep shelves are less common although they are ideal for oversized books, newspaper storage, and other odd-sized reading materials.
Shelf Stiffening Techniques
The following shelf stiffening and support techniques were tested.
- Free floating – ends of shelf not screwed or otherwise secured to support ledges
- Fixed – ends of shelf clamped to support ledges
- Fixed with front support – ends secured with clamps, 1-1/2″ edging screwed to underside of front edge of shelf
- Fixed with rear support – ends secured with clamps, rear edge supported by wooden beam underneath
- Fixed with front and rear support – ends secured with clamps, front edging, rear beam support
The idea was to start with a shelf with the least amount of support (a floating shelf) and go to progressively greater support levels. For the solid wood shelves, the front edging was made from the same type of wood as the shelf. For the plywood and MDF shelves, pine edging was used. The thinking here was that these types of materials are typically used for utility shelves so why not use utility grade wood for the edging.
Three different shelf load levels were tested, representing light, moderate, and heavy loads:
- Light – 20 pounds per linear foot
- Moderate – 30 pounds per linear foot
- Heavy – 40 pounds per linear foot
The objective was to simulate a uniformly loaded bookshelf with typical loads placed on it. This involved arranging cement blocks and steel weights as evenly as possible across the shelf span. This turned out to be something of an inexact science; if one particular weight is shifted a couple inches in any direction, this can result in a slightly different deflection measurement. But, these differences were usually on the order of one to two hundredths of an inch so I didn’t fret too much over them. Note that no attempt was made to simulate a centrally loaded bookshelf — I felt that this scenario was less common plus I didn’t have the energy to run hundreds of additional tests.
To help decide which load levels to test, I weighed various items in the home library. The results are shown in the table below. For what it’s worth, most of the weighed text books were woodworking related. I also came across a design guideline in a book by Jim Tolpin (Built-in Furniture: A Gallery of Design Ideas) of 35 pounds per linear foot for library shelving.
|Shelf Items||Weight – lbs per linear foot|
|Small hardcover text books||20|
|Large (9″x11″) hardcover text books||32|
|Fine Woodworking magazines||40|
Optimal Versus Excessive Sag
The headings for the shelf sag tables display optimal versus sag values. How were these values derived? Well, there are published references that say the eye will notice a deflection of 1/32″ (0.03″) per running foot. If we go with this guideline and then factor in an additional 50% sag over time beyond the initial sag, this results in a target sag of 0.02″ per foot or less. That’s 0.06″ for a 3′ wide bookshelf. The optimal sag figures in the shelf sag tables are based on this 0.02″ (1/50″) maximum sag per foot specification. Note that all of the optimal sag figures are under 1/10″ regardless of shelf span.
Other sources that I have come across indicate that shelf sag should be less than 1/4″. For a 4-1/2′ wide bookshelf (about the widest most would consider building), a sag of 0.06″ per foot results in 0.27″ for the full span. For a 4′ shelf, the sag would be 0.24″. So, I opted to use this 0.06″ (1/16″) sag per foot specification to derive the excessive sag figures.
Personally, I think that shelf sag approaching 1/4″ is way too much – unless the shelf is hidden in a closet or back room where the aesthetics (or stability) of the shelf aren’t a concern. But for a bookshelf in a highly visible location, one should strive for a maximum sag closer to the optimal values displayed in the shelf sag tables. To simplify things, call the target sag 1/10″ or less. This is close to the 3/32″ allowable sag that Jim Tolpin uses for his shelf construction.
For floating shelves, the theoretical sag estimates computed by the Sagulator agree reasonably well with the empirical woodshop sag measurements for shelves that have a relatively short span (under 32″) and for shelves that are 12″ or deeper. For wider span shelves that have a depth of 8″ or less, the Sagulator values tend to overshoot the shop values – by as much as 35%.
For fixed shelves with no support edging, the Sagulator estimates considerably undershoot the shop measurements. The measurements are approximately 2.5 to 3.5 times greater than the calculated values, depending on shelf span and depth. The disparity is smallest for shelves that have a short span (under 32″) or that are 12″ or deeper. The disparity increases as shelf span increases and depth decreases.
For fixed shelves with a support edging, the shop measurements are approximately 1.5 to 3 times greater than the Sagulator estimates. Once again, the disparity is smallest for shelves that span 32″ or less or that are 12″ or greater in depth. The disparity increases as shelf span increases and depth decreases.
It’s not entirely clear why the Sagulator estimates are not in closer agreement to the shop sag measurements but I suspect a big part of the answer is that some of the assumptions made by the beam deflection formulas do not hold up in the real world. One of these is that the shelf support structure is completely rigid; in reality, some degree of racking and movement will occur in a shelf, especially for one that is free-standing. Another assumption is that the shelf material has a fixed elasticity, known as the modulus of elasticity, and that the elasticity remains constant along the length of the shelf. The reality is that the elasticity of lumber can vary considerably from piece to piece and even within a piece depending on the grain of the wood, moisture content, and any internal defects in the wood.
Though disconcerting, the computed versus empirical shelf sag disparities are well under an order of magnitude (10x). For a shelf with an observed sag of 0.15″, an estimated sag of 0.05″ is off by a factor of three, but for all practical purposes, it’s probably not a big deal given the small magnitude of the sag. However, when dealing with sag of 0.25″ or more, a 3x difference could be crucial.