Snow: A Weighty Matter

During the heavy snowfall of December, the Geophysical Institute received a number of calls requesting information on the amount of snow loading roofs should be able to support. It would have been prudent of me to have referred callers to the Department of Civil Engineering, but foolish pride prevailed, and now I might as well dust off the old engineering texts and stumble ahead, as it were, into the storm.

It should be understood that any figures given should only be interpreted in the broadest sense and treated as extremely rough guidelines (and with a good deal of suspicion).

First of all, only frame construction is considered, and only a flat roof at that. Only three sizes of rafters (or joists) will be considered (2" x 6", 2" x 8", and 2" x 10") with specific examples for only spans of 10 and 16 feet between supporting members. Average construction-grade lumber is assumed, with what is called in engineering handbooks an "extreme bending factor" of 1,500 pounds per square inch (psi). This broadly means that, if you bend a beam (rafter, joist) downward by placing a load along it, the fibers on the top half will be compressed and the fibers on the bottom will be stretched. The 1,500 psi is the maximum tension under which the fibers on the bottom can be placed before they tear and the beam breaks.

I will not present the calculations necessary to derive them, but the following figures are useful (and necessary) for what follows. In these expressions (all those extra digits are meaningless, of course--that's just the way they turned out), L is the length of the beam in inches, and W is the maximum evenly distributed load in pounds per inch along its length.

WxLxL for a 2"x 6" beam should not exceed 98,296.

WxLxL for a 2"x 8" beam should not exceed 182,815.

WxLxL for a 2"x 10" beam should not exceed 293,312.

These figures allow you to at least fake a good guess at how much a beam can support, and allow plenty of latitude for interpolation to different sizes. Using them for the examples of our 10-foot and 16-foot spans, we can construct the following simple table:

Now, to get back to snow-loading. A cubic foot of water weighs 62.36 pounds. A square foot of water one inch deep therefore weighs 5.197 pounds. Snow weighs about as much as an equal volume of water, so a square foot of snow one inch deep weighs about 1.04 pounds.

If our joists, or rafters, or whatever are placed on 2-foot centers, which is the common practice, each running foot will be supporting about 2.08 pounds for each inch of snow lying on the roof. Utilizing the figures given above then, we can construct one further table:

Obviously, the little 10-foot shed with the 2"x 10" rafters is grossly overdesigned, but the 2"x 6"'s get pretty spindly when you stretch them out.

There probably isn't an engineer in the state who wouldn't like to climb all over this, and rightfully so. It ignores many important design factors. Flat roofs are practically unheard of in Alaska, but they illustrate the principal. Obviously, as a rafter is "titled" more, as in a gable design, more and more of the stress is transmitted longitudinally along it (the horizontal component thus tending to push out the walls). If this were carried to its extreme where the rafter were tilted vertically, there would be no bending stress on it at all, only compression along its length.

There is a story told about the famous Dutch airplane designer, Anthony Fokker. When asked how he managed to arrive at his feared WWI fighter designs, he simply said that he made them so that they "looked right." That's the way many of us in Alaska build our houses. Usually it works just fine, but there are times when many of us wish that we had had just a little help with the engineering. I can attest to that from firsthand experience.