Snow load

Apart from wind loads, snow loads play an important part in the design of struc-tures. Many modern buildings have moved away from traditional shapes and their behaviour with respect to snow accumulation is not known well enough [41]. When constructing a tension roof, the load corresponding to the expected intensity of snow has to be considered. As for the wind loads this is more or less straightforward for ordinary types of roofs, and is found in national building codes. For cable and membrane roofs this is considerably more difficult.

Snow distribution

The snow intensity is measured at meteorological weather stations as the ground snow depth. Prior to 1970, many buildings were designed and built assuming uni-formly distributed snow loads [118]. After a number of failures, attention was given

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2.7. ROOF LOADS

to unbalanced loads, due to snow drift. Therefore, surveys of actual snow loads were started to determine the difference between ground and roof snow load. The results from the surveys showed that, in cold and windy areas, the roof snow load was considerably lower than the ground snow load. Nonetheless, on certain parts of some roofs the load was significantly higher.

Today, building codes make provision for drifting of snow by specifying a number of snow load cases for the type of roof considered. Some shapes of roofs tend to accumulate more unbalanced loads than others, and the load cases try to cover the possible snow distributions over the roof. Unfortunately, the roof types covered by the codes are usually traditional. Tension structures, such as cable and membrane roofs, with sculptural forms are not covered by the codes. Due to the flexibility of tension roofs, ponding of snow can occur in flat areas or under heavy snow loads.

This requires consideration in design and can only be analysed with the aid of wind tunnel or water flume experiments.

Wind tunnel and water flume testing

Like wind tunnel experiments, some model laws has to be followed when modelling the snow in air or water. In wind tunnels, granular materials, such as tea, glass, and nut shells, are used to simulate dry snow, while sand is used in water flume experi-ments, Figure 2.23. One limitation in modelling, which cannot easily be overcome, concerns the great variation in snow properties. Common simulation materials can-not model sticky snow. For example, sand will can-not stay on steep surfaces which makes it difficult to simulate snow accumulations on steep slopes where snow will accumulate before eventually sliding off. Another limitation in model studies is that only one wind direction is considered at a time but the overall seasonal environment consists of a sequence of snow storms and high winds from different directions. In reality, the final snow accumulation depends on the chronological order and dura-tion of the storms and on temperature, sunshine, humidity, etc. Surrounding terrain may also affect total snow accumulation and drift patterns on structures. Whether air or water is the medium, a model can provide a good simulation of the flow around structures. However, the state-of-the-art of snow drift modelling prevents the measurement of quantitative results [50, 118].

Recently a water flume test was used to determine the snow loads on a large tension roof at Denver International Airport, U.S.A. [10]. Denver is known for its heavy snow falls, and the shape of the roof leads to high snow load intensities being expected.

The tests also showed that in the valleys of the roof the design snow intensity was very high, 3.8 kN/m², Figure 2.23. The predicted snow pattern from the model test agreed well to that seen on the roof after the first snow falls, confirming the reliability of the test.

CHAPTER 2. LITERATURE REVIEW

Figure 2.23: Investigation of snow drift with the help of a model test, where water replaces air and sand represents snow. Reproduced from [10].

Computer simulations

In the design of the tension roof of Denver International Airport, the water flume experiments were supplemented by a computer program based on the Finite Area Element (FAE) method (not to be confused with the Finite Element Method) [38].

This is a so-called hybrid method, which means that the wind velocity field is ob-tained from wind tunnel experiments. A brief description of the FAE method and its properties is given below. First, the roof is divided into many area elements by a grid. The wind velocities are measured at grid intersection points. Time histories of meteorological data concerning the wind direction and speed are used as input for the computations. Snow drift is computed using empirical relationships for snow flux versus wind velocity. By computing the mass fluxes into and out of each ele-ment, the rate of build up or depletion of snow mass in the element due to drifting is determined. The mass balance computations at each time step include the addi-tional mass from snow fall and the depletion due to melting. The method also takes into consideration the less significant drift of snow that has been rained upon, or that has experienced a melting episode. Some surfaces, which are rough or ribbed, have high snow storage capacities and can trap snow permanently (at least until it melts). Therefore, the area elements are assigned with a certain storage capacity for snow depending on surface roughness. Also included in the FAE method is a heat balance used to calculate the melting rate of the snow pack inside each element, and the ability of snow to store liquid water and thereby increasing the snow density.

The FAE method has proved to be a good tool to supplement the model studies, and overcome the limitations associated with them. With this method quantitative results can be obtained with higher accuracy [38].

A purely computational method for predicting snow accumulation, called SNOW-SIM, has been developed under a research project at Narvik Institute of Technology in Norway [7]. The method includes a commercial CFD program, combined with a simplified drift-flux model to simulate snow drift. A computer simulation of snow drift has the advantage over wind tunnel or water flume experiments that it can be more available and less expensive. Simulations can be done with snow drifts

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from different directions and with variations in velocity and intensity. Simulations in three dimensions were presented, but due to limitations in computer power only small buildings of regular shape with a coarse mesh resolution, and simulation times of up to 50 seconds could be studied. Therefore, the simulations could only be re-garded as an indication of where the snow will deposit, not as an exact quantity calculation. Compared with real measurements the simulations gave similar snow drift patterns. Bang et al. [7] gave a number of problems that have to be resolved before quantitative results can be available. These included the proper treatment of turbulence in the CFD program, evaluation of different drift-flux models, and modelling of structures with their local terrain. Thus, a complete computer simula-tion of snow drift magnitude is today not available even for buildings of tradisimula-tional shape [7].

As in the case with wind loads on tension structures with complex shapes, Tabarrok and Qin [115] have proposed a simplified method to calculate the snow load distri-bution. In their method, vertical snow loads are generated based on the horizontal projection of each elemental area and a snow load magnitude per unit horizontal area specified by the designer. This means that there is full snow load on a hor-izontal surface and zero load on a vertical surface. This method is of course very approximative as it cannot handle snow drift.

It has been seen that the determination of snow load magnitude and distribution is a task of equal difficulty as that for wind load. For a roof with a complex shape the only way to find the sought quantities, i.e. magnitude and distribution, is through model tests. This procedure is expensive, time consuming and requires special knowledge and experience.