Shelf Sag Measurements

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.

Shelf Materials

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:

MDF
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.

Shelf Loading

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
Paperbacks	6
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 such as this shelf deflection chart, 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.

Comparison to Computed Sag Estimates

Relative to the theoretical sag values computed by the Sagulator, the empirical woodshop sag measurements agree reasonably well -- for floating shelves. However, for fixed shelves with no support edging, the Sagulator appears to considerably underestimate the actual sag values. As a result of these observed discrepancies, the formula used by the Sagulator will be examined in detail and updated, hopefully in the very near future.

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