Michael J O Rourke. American Scientist. Volume 85, Issue 1. Jan/Feb 1997.
The snow-covered scenes depicted on holiday cards suggest that people like a little snow during the wintertime. Nevertheless, a lot of snow can cause serious problems. The blizzard of March 1993, for instance, left much of the eastern United States covered in snow: 15 inches in Birmingham, Alabama, more than 2 feet around Albany, New York, and 8-foot drifts in eastern Kentucky. That snowfall resulted in more than 200 deaths, 3 million people without power because of downed power lines and the closure of six major airports between Atlanta and Boston. Blizzards can be even worse. The biggest U.S. snowstorm on record-the blizzard of March 1888-blanketed Albany, New York, in about 4 feet of snow and caused around 400 deaths.
Such large snowstorms can also cause structural damage to buildings. After the blizzard in March 1993, one large insurer of industrial facilities reported more than 100 losses with a total damage of about $200 million to buildings and their contents. The same insurer reported that in an average year-during the period from 1977 through 1989-it paid for 78 snowand ice-related losses with a total value (property damage and business disruption) of about $23 million.
Consequently, rooftop snow is an important consideration for the design of buildings in many parts of the United States. This article describes the various types of snow hazards for building structures, the methods currently used by engineers to quantify these hazards and emerging laboratorybased techniques for evaluating snow loading on buildings.
Estimating Snow Loads
Structural engineers design buildings for two types of loads: vertical loads, which are downward-directed loads caused by the weight supported by a structure, and lateral loads, which are horizontally directed loads caused by wind or earthquakes. Perhaps surprisingly, snow loads on a roof influence both vertical–and lateral–load design. For vertical loads, the design constraints seem fairly obvious: Structural members must be capable of supporting the weight of snow on a roof. But the magnitude of lateral loads–specifically earthquake loads-can also be influenced by roof snow loads, because a lateral load generated during an earthquake is proportional to the total weight of the structure, which includes the weight of snow on the roof.
Snow on a roof may produce a load with a distribution that is uniform-the same load over the whole roof-or nonuniform-a varying load caused by wind-induced drifting, or melting and refreezing of snow. In the United States, engineers determine potential roof-snow loads from site-specific estimates of the weight of snow that may accumulate on the ground. A uniform load caused by snow on a roof can be estimated as some fraction of the site-specific ground-snow load, thereby accounting for the influence of wind, roof slope and the roof’s thermal characteristics. A nonuniform load can be estimated by increasing the site-specific ground-snow load to account for snow drifting and other similar effects.
Imagine a building with a two-level roof, both surfaces flat but one higher than the other. Wind of a sufficient velocity would remove snow from the upper-level roof. If the lower-level roof is downwind, some of the blowing snow would land on it, resulting in a nonuniform load caused by a triangular drift that would grow where the lower-level roof meets the wall supporting the upper-level roof. Insurance records suggest that roughly 75 percent of snow-related structural damage comes from drift loads on two-level roofs.
How much snow should a building be able to support? To answer that question engineers must balance safety and economy. For example, designing a building to support a larger than expected load of snow would result in a smaller probability of structural collapse but also in a more expensive building. In the United States, buildings of average importance, including office buildings and shopping malls, are designed to survive roof-snow loads that can develop from the largest likely site-specific-ground-snow load with a 50-year mean recurrence interval (MRI). In other words, there is 1 chance in 50 (or 2 percent) that the ground-snow load in a given year will exceed the 50-year MRI value. For essential facilities-including fire and police stations, emergency shelters and some health-care facilitiess now loads are based on the 100-year MRI value, which has a 1 percent probability of being exceeded in any given year. At the other end of the spectrum, snow loads for buildings that represent a low risk to human life, including agricultural facilities, are based on a 25-year MRI, which has a 4 percent annual probability of being exceeded. Most engineers agree that this probabilistic approach, coupled with the safety factors used in the design of engineered materials, reduces the risk of a snow-load-induced failure to acceptably low levels.
The probabilistic approach begins with a statistical analysis of yearly data for a site’s maximum ground-snow load. First, more than 250 first-order National Weather Service stations-facilities that take hourly or daily recordings of wind speed and direction, temperature, snowfall and so on-make frequent “water equivalent” measurements each winter. Second, the water equivalent, given in inches, can be translated to the weight of snow on the ground. For example, 6 inches of water equivalent corresponds to a load of 31.2 pounds per square foot of ground snow. The resulting data can be used to determine the maximum load from ground snow at a site. Finally, the 25, 50 and 100 MRI ground-snow loads can be determined by modeling the probability of a particular maximum load at a particular site. Unfortunately, the 250 first-order weather stations provide rather sparse coverage of the United States. For example, New York’s 47,000 square miles are covered by only seven stations, two of which are in the New York City metropolitan area. As a result, the direct water-equivalent data are often supplemented with maximum annual snowdepth data available from a much larger number of cooperative stations.
Uniform Roof Loading
In the United States, all engineered structures except those built in places where it hardly ever snows, including Florida and low-elevation sites in southern California-are designed to withstand some uniform roof-snow load. A site-specific uniform roof load from snow can be calculated from the groundsnow load and one or more related factors, including the slope of the roof. Engineers use that approach because there are numerous direct measurements of ground snow but relatively few direct measurements of roof load. In the American Society of Civil Engineers (ASCE) Standard 7-95, which provides information on structural design loads for buildings, the uniform roof load is taken as the ground load multiplied by a generalized ground-to-roof conversion factor of 0.70 and modified by site- and structure-specific exposure and thermal factors. The generalized ground-to-roof factor accounts for the reduction in roof load over time caused by the effects of wind, melting and so on for an “average” structure. Moreover, the ground-toroof conversion factor of 0.70 applies to structures in colder areas, where the ground-snow load is likely caused by a number of snow storms over a winter and the roof load gets reduced by wind and thermal effects between storms. In warmer areas, where the ground-snow load is more likely caused by a single large storm, the conversion factor and site- and structure-specific factors are omitted. Instead, a roof is designed to withstand a load equal to the maximum expected ground-snow load-assuming an appropriate MRI.
The site- and structure-specific factors account for “nonaverage” conditions. The site-specific-exposure factor, which ranges from 0.7 to 1.3, is a function of the terrain around a site-ranging from large city centers to areas above the tree line-and the wind exposure of the roof-ranging from roofs exposed on all sides (with no shelter) to roofs nestled among tall trees. The lowest value corresponds to exposed roofs above the tree line, where wind is more likely than average to remove snow from a roof; the highest value corresponds to sheltered roofs in large city centers, where wind removal is less likely than average. The structure-specific-thermal factor, which ranges from 1.0 to 1.2, accounts for nonaverage thermal conditions. The lowest value is for typical heated structures, where heat flow up through the roof results in some melting of the roof snow; the highest value is for unheated structures, which lack such thermal effects.
Using these factors, an engineer can calculate how heavy a load-the socalled design load-a building must be able to hold. The design load for a heated structure with a nominally flat roof ranges from 49 percent (0.7 x 0.7 x 1.0 = 0.49) of the ground-snow load for an exposed structure in open terrain to 91 percent (0.7 x 1.3 x 1.0 = 0.91) of the ground-snow load for a sheltered structure in a heavily built-up terrain. The corresponding range for an unheated structure is from 59 to 109 percent. At the level of 109 percent, the design load exceeds the ground load for unheated structures where wind removal is not likely, because an engineer expects the ground-snow load to decrease over time because of heat from the ground and the snow on the roof will not.
A sloped roof requires an additional factor to calculate its uniform roof load. The slope-modification factor accounts for the likelihood of snow sliding off the roof over time. The slope factor, as given in the ASCE Standard 7-95, depends on a roof’s slope, slipperiness and thermal conditions. The uniform roof load decreases with a roof’s slope, and it becomes zero for roofs with slopes of 70 degrees or more. For a given slope, the roof load is less for a warm and slippery roof surface.
The generalized ground-to-roof conversion factor, as well as the exposure-, thermal- and slope-modification factors, come from observations and engineering judgment. For example, my colleagues and I measured roof and ground loads for about 200 structures in the Northeast, the Midwest and the Northwest to determine the actual exposure- and thermal-modification factors. Despite a fair amount of scatter, the observed data reveal that both increasing wind and building heat reduce the roof-snow load in comparison with the ground-snow load. In addition, Ron Sack of the University of Oklahoma measured the slope-modification factor on six specially constructed unheated test roofs and 10 full-sized unheated structures; the data, also scattered, show that a larger slope leads to a smaller roof load, in part because of snow sliding off the roof.
Nonuniform Roof Loading
Although uniform loading is the governing design snow load for nominally flat single-level roofs, it infrequently leads to structural collapse. As noted above, structural damage and collapse usually arise from heavier, localized roof loads caused by drifted snow. In the winter of 1978, for example, a Jordan Marsh department-store warehouse in eastern Massachusetts was subjected to one snowstorm in late January and an even larger one in February. In combination, the storms produced four large drifts on the store’s roof. Although the ground-snow depth was only about 3 inches before the early February storm, which added about 27 inches, the largest drift on the roof surpassed 15 feet. Forming such a drift requires three elements: a source of driftable snow to feed the drift; wind of sufficient speed-above the threshold velocity for snow transport; and a downwind geometric irregularity around which the drift can grow.
Consider the two-level flat roof mentioned above. If the lower-level roof is downwind, the upper-level roof is the snow source, and the roof step is the geometric irregularity. My colleagues and I examined 350 case histories of drift formation on such a roof, and the results are incorporated in the ASCE Standard 7-95. We found that the total height of a drift on a downwind lower roof equals the sum of the surcharge height from drifting plus the depth of the initial underlying uniform snow load on the roof. The surcharge height increases with the ground-snow load and the length of the upper-level roof-a longer roof provides a larger source of driftable snow. More recently, Peter Irwin of Rowan, Williams, Davies and Irwin, Incorporated, in Guelph, Ontario, described a similar relation, which is being used in the National Building Code of Canada.
A gable roof can also lead to drifted or unbalanced roof loads. For such a roof, the ASCE Standard 7-95 considers two separate cases: a uniform case, wherein both sides of the ridge line have the same load, and an unbalanced load case, in which the upwind roof has no snow load and the downwind roof’s load is calculated as 1.3ps/Ce, where ps represents the uniform load and Ce represents the wind-exposure factor. The ASCE Standard 7-95 only requires that a building’s roof be designed to withstand the unbalanced load if its slope lies between 15 and 70 degrees. That constraint assumes that less-steep roofs would not provide a sufficient downwind geometric irregularity and that snow would slide off of steeper slopes.
Nevertheless, my former graduate student, Mike Auren, and I found that substantial unbalanced loads can develop on low-sloped roofs (less than 15 degrees). Our model of gable-roof drifting assumes a substantial snowfall, with ground-snow depth and initial uniform roof load represented by hg. Then a strong wind from one side of the ridge to the other carries a percentage of the upwind-side snow across the ridge line, thereby forming a triangular drift on the downwind side. The height of the surcharge drift at the eave is the product of hg and BETA, in which 0 represents how much of the snow from the upwind side ends up in the drift on the downwind side. The value of could range from 0 to 2, where 0 means that none of the windward snow ended up in the drift and 2 means that all of the windward snow blew into the drift. So the total height of the drift at the eave is the sum of the uniform load hg and the drift BETA h g, or (hg + 0 h) = (1 + hg. If all of the snow from the upwind part of the roof ends up in a downwind drift, such that P = 2, this generates the deepest possible drift, where (1 + 2)hp. = 3hQ.
Our analysis of gable-roof case histories suggests that an appropriate range of 0 is from 0.5 to 1.0. Our recommended value for depends on a roof’s aspect ratio: roof length (end wall to end wall) divided by width (ridge line to eave). For an aspect ratio of one or less, we recommend P = 0.5. For an aspect ratio of 4 or more, I =1.0. The increase in fi with increasing aspect ratio reflects expected wind-directionality effects. That is, a roof with an aspect ratio much less than 1 should produce a substantial drift on the downwind roof only if the wind blows essentially perpendicular to the ridge line. On the other hand, roofs with an aspect ratio much greater than 1 can experience substantial drifts from a relatively wide range of wind directions, from perpendicular to the ridge line to diagonal across the roof.
Current North American approaches for characterizing drift loads use only one environmental factor, the ground-snow load. Although drift formation also requires wind, provisions of the current code do not explicitly use wind speed at the site in formulating load provisions. This inconsistency arises largely from the lack of available maps for blizzards-joint occurrences of snowfall and strong winds.
When a deep layer of snow accumulates on the roof of a heated building, it can lead to ice amassing at the eave. When the outside air temperature is below freezing and the indoor temperature is well above freezing, a deep layer of snow and/or a poorly insulated roof can allow enough heat to escape into the snow near the roof that its temperature exceeds freezing. The above-freezing snow near the roof surface will melt, and the meltwater will travel, by gravity, toward the eaves. At the overhanging eave, which is cold because there is no warm building below it, the meltwater refreezes and forms an ice dam and eave icicles. Additional meltwater then pools behind the ice dam. Although roofs are designed to shed water, they are not usually watertight, particularly when subject to standing water. So the pooled water behind the ice dam often seeps into the buildingwetting interior walls and the ceiling near the eaves. This problem can even cause structural collapse.
Builders have fought eave icing with various methods: keeping the roof snow cold, keeping the eave warm or making the eave area impervious to water. All the roof snow can be kept below freezing by incorporating a properly sized air space in the roof system with air vents at both the eaves and the ridge line; cold air enters at the eave vents and flows up and out of the ridge vent. Alternatively, heat tape has been used on the eave to prevent a buildup of ice, but warmer temperatures can lead to sliding snow that can strip off the tape. The third approach uses metal flashing or a membrane near the edge of the roof, which can be designed to make the surface more or less impermeable to the water pooled behind an eave ice dam.
In terms of structural strength, the current ASCE Standard 7-95 standard requires that overhanging eaves of warm roofs be designed for twice the uniform roof load to account for the weight of potential ice dams. Cold roofs are excluded from this requirement, because eave icing would not be expected. Small-Scale Simulations
The current approaches for quantifying snow loading on building roofs rely almost exclusively on analyses of full-scale case histories in combination with engineering judgment. In addition, procedures for establishing drift loads, which account for the majority of snow-related collapses, are based on a probabilistic characterization of the ground-snow loads, as opposed to a characterization of the joint probability of the occurrence of snowfall and wind. Future improvements will utilize information obtained from small-scale laboratory studies.
The full-scale case-history approach can be applied only when a sufficient number of case histories can be analyzed. For example, it would be impossible to use the case-history approach for a one-of-a-kind sports stadium, because the stadium would have to be completed before full-scale measurements could be made. Similarly, available full-scale measurements for many common roof geometries, including saw-tooth and mansard roofs, can be limited. In addition, case histories cannot be repeated, and they rely on Mother Nature to provide snow and wind.
Laboratory studies, on the other hand, may prove particularly useful for new or unusual roof geometries and for properly accounting for the relation between wind speed and drift formation. Small-scale laboratory studies have been used to determine the structural loads on buildings for at least 25 years. Wind tunnels have been used to measure wind loading on a structure’s main frame and more-localized wind pressure on exterior walls and windows for high-rise buildings. To a lesser extent, small-scale laboratory studies-specifically shake tables-have been used to determine seismic loads.
Engineers can use wind tunnels and water flumes to perform small-scale studies of snow loads on roofs. Nick Isyumov and his colleagues at the University of Western Ontario were among the first to use wind-tunnel techniques to study snow loading on buildings. The flow of air in a tunnel simulates wind, and particles, such as bran, can be used to model snow. Irwin and his colleagues, as well as a group of my colleagues at Rensselaer, have used the water-flume technique, in which the flow of water in a flume simulates wind, and particles, such as commercially available crushed walnut shells, model the snow.
These techniques facilitate a morethorough understanding of snow-loading problems, because parameters of interest can be isolated and manipulated. For example, Peter Wrenn of John G. Waite and Associates in Albany, New York, and I completed a flume study of snow drifts on a structure with the two-level roof described above. This study showed that in a simulated suburban-wind environment the snow that gets blown off the upper roof and the percentage of that snow that settles on the lower roof both depend on wind (actually water in the experiment) velocity. As expected, more snow is blown off the upperlevel roof in stronger wind. On the other hand, a smaller percentage settles on the lower-level roof in stronger wind, because more snow particles blow beyond the drift area. Using these kind of relations plus measurements of the amount of snow on the upper-level roof and the strength and duration of a wind storm, an engineer can estimate the drift-induced snow load.
In the future, small-scale simulations should improve our knowledge of the interactions between structures and snow storms. With that knowledge, engineers will generate more accurate models of snow loads on the roofs of buildings. Consequently, we will build stronger structures where required and safer, more economical structures overall.