Accounting for Drifting Snow on Lower Roof Surfaces

On a recent consulting assignment I was asked to evaluate the effect of replacing an asphalt shingles with (slippery) steel would have on the snow accumulation on the roof. On a slippery sloped roof without obstruction(s) it makes sense that snow would slide off, and thus less accumulate. In `engineering' language we would anticipate a lesser snow `load' on the roof. And, in general, that is the case, and the Building Code provides the means of `calculating' the effect (for us engineers). And it was this reduced snow accumulation thing that was the subject of the previous article (here). What I didn't mention in that article is that the residence was added to through time resulting in a lower roof - upper roof situation. It (also) makes sense that snow could drift off the upper surface onto the lower. Anyone who lives very long in `snow country', and looks around at the snow on structures (as I presume most structural engineers do), notices that the drifting effect is real. And the Code provides us means of calculating the effect also.

Lower Roof of a Structure

Actually, most building codes provide the means of calculating the effect of drifting snow by reference, namely that Snow loads are to be determined in accordance with Chapter 7 of ASCE 7, Minimum Design Loads for Buildings and Other Structures, American Society of Civil Engineers, specifically Section 7.7.1 and Figures 7-7 through 7-9. There are two kinds of drifts: windward and leeward. (And both are real.) In this article we will look at two cases of (leeward) drifts: one from a roof that is 3 ft higher than the lower, and the other that is 8 ft higher, all other things equal.

Lower Roof (Only) a `bit' Lower than Upper

The first case is where the lower roof is a relatively short (vertical) distance below the upper. I use `bit' relatively; it depends on what kind of snow depths are involved, and whether or not the drift `fills in' what could be considered a `step'. In the particular example at hand the step (vertical difference) in surfaces is 3 ft; the ground snow load, pg, is 86 pound per square foot (psf), the (basic) roof snow load, pf, was calculated to be 60 psf, and in the case of asphalt shingles on a slope of 5/12 this value cannot be reduced for slope effect.

Section 7.7.1 directs us to determine the drift height, h_d, using Figure 7-9 which gives drift height as a function of ground snow load and upper roof width. For the example at hand the upper roof width is 24 ft, which along with p_g = 86 psf, gives h_d = 2.4 ft. This drift height is to be added to the balanced snow load depth, d_b.

Snow depths are determined using equation (7-3) for the specific weight of snow,

γ = 0.13 p_g + 14 (in pounds per cubic foot, pcf) (...) but not more than 30 pcf.

For our example, then,

γ = 0.13 (86) + 14 = 25 pcf (which is not more than 30 pcf).

Note that the specific weight of the snow in this case is 25/64 = 39% of that of water. And also note that though this equation looks exact, real life snow specific weights vary a lot. But, this equation does show the trend of increased snow depths also being denser.

So, from this we determine the balanced snow load depth,

h_b = p_b / γ = 60 psf / 25 pcf = 2.4 ft.

Interestingly the balanced load depth and the drift depth are the same in this example. Coincidence (I think).

But now we have a `problem'. The height of the snow on the lower roof now exceeds the level of the upper roof, from where we presume it came. In such cases we take the drift height to equal hc (the difference between the difference in heights of the roofs and the balanced snow load depth), and thus the drift comes right up to the (edge of) the upper roof. (Makes sense to me!) (And hd become hc.)

In our case hc = 3 ft - 2.4 ft = 0.6 ft. Then hd becomes hc = 0.6 ft.

The `surcharge' from the drift then becomes pd = γ h_d = 25 pcf (0.6 ft) = 15 psf. We add this to the balanced load of 60 psf to get 60 + 15 = 75 psf.

We'd get the same thing if we took the total depth at the drift and multiply it by the specific weight;

p _total = 25 pcf x 3 ft = 75 psf.

Note that in relative terms the total load didn't increase that much. In fact, if h_c/h_b is less than 0.2, we don't have to consider the drifting (but we're not prevented from considering it). Just for fun, let's see what our h_c/h_b value is ... 0.6 ft / 2.4 ft = 0.25; we are almost not required to take the drift into account.

Shape of Drift

The drift shape is assumed to be triangular, starting the deepest at the `step' and decreasing in a `straight line' fashion (to zero drift) across the drift width, w. In cases where the h_d is calculated to be greater than h_c, the width is given by the formula,

w = 4 h_d² / h_c ... but not greater than 8 h_c.

For the present example, then,

w = 4 (2.4 ft)² / 0.6 ft = 38 ft ... but not greater than 8 (0.6 ft) = 4.8 ft.

So, w = 4.8 ft.

So, the drift varies in depth from 0 ft deep 4.8 ft from the step to 0.6 ft deep right at the step. These depths add to the snow already there, so, the total depth varies from 2.4 ft at 4.8 ft from the step to 3.0 ft at the step.

And the snow load varies from 60 psf 4.8 ft away (and beyond) to 75 psf at the step.

Lower Roof `More Lower' Than Upper (or Upper `More Upper')

Now let's look at the case where the `step' (distance between the two roof surfaces) is 8 ft.

Other things equal, h_c = 8 - 2.4 = 5.6 ft; h_d ≤ h_c. So, the drift depth at the step is h_b + h_d = 2.4 + 2.4 = 4.8 ft. The total load (there) is ... 4.8 ft x 25 pcf = 120 psf.

Where h_d ≤ h_c the drift width is (from Sec. 7.7.1) ... w = 4 h_d. So, in this case, w = 4 x 2.4 = 9.6 ft.

We can now say that the `design' drift will go from zero at 9.6 ft from the step to 4.8 ft deep at the step, and the total (balanced plus drift surcharge) load on the roof will vary from 60 psf to 120 psf.

Concluding Remarks

Over the years it seems that ASCE 7 has evolved into a pretty accurate `scientific way' of determining how snow loads roofs. Future snow phenomena is assumed predictable from past experience and observation; but we know there is uncertainty involved (Global Cooling, Warming, or just Cycling), and thus we also incorporate factors of safety (not included in this article). And while I have observed a lot of snow falling, melting, drifting, and accumulating in ways suggested by this part of the `Code', I have also observed snow to drift and accumulate in ways quite opposite (especially where there is weird vortex action). So I never shy away from doing more robust designs, especially where I feel they are warranted. After all, ASCE 7 is titled Minimum Design Loads ...

One more thing, finally, is this: remember, the density (specific weight) equation above is only an `average' of how snow is observed. Falling snow density varies. I suppose it varies by region, and maybe elevation (humidity, temperature). And once on the ground, or roof, it varies. Warm weather and rain on snow make snow denser. By the end of a snow season the snow is denser than at earlier stages. The equation (7-3) is kind of a spatial, seasonal average but does reflect the tendency for snow to get denser at it gets deeper.

References

Mitigation of Increased Design Snow Loads on a Sloped Roof, Jeff Filler, Associated Content.

Minimum Design Loads for Buildings and Other Structures, ASCE Standard ASCE/SEI 7, American Society of Civil Engineers, www.asce.org.

See Also

Varying Snow Density (and similar articles), Jeff Filler, Associated Content.

Ground and Roof Snow Loads for Idaho, R.L. Sack, A. Sheikh-Taheri, 1986, University of Idaho, Department of Civil Engineering, Moscow, Idaho 83844.