# Snow Load Shape Coefficients and Snow Prevention Method for Stepped Flat Roofs
###### Abstract  
Excessive snow load and nonuniform snow deposition are the main factors leading to building collapses. The snow load shape coefficient represents the dimensionless snow load, and its value is related to the unbalanced distribution of snow. The snow load shape coefficients for stepped flat roofs vary greatly in the codes of different regions, which always leads to underestimation of snow loads. We need a widely used standard for snow load shape coefficients. Therefore, through a combination of field measurements and numerical simulations, this study probes the snow accumulation processes and snow load shape coefficients on stepped flat roofs and proposes an equation to calculate snow load shape coefficients and the optimal slope of snow protection for lower roofs. It is found that the maximum snow load shape coefficient emerges at the roof junction with a value of 3.44. The nonuniform length of the snow accumulation is equal to two times the level difference. Based on these, the equation of the snow load shape coefficients is summarized, which is combined with the discrepancies between different codes and the regularity of snow distributions. In this study, the dynamic grid technology under the Eulerian framework is used to successfully predict snow accumulation on stepped flat roofs, and it is noted that snow erosion and deposition are closely related to the location and size of vortexes. Finally, we consider that the ideal slope for the lower roof to prevent snow should be \(11^{\circ}\). field measurements; numerical simulations; stepped flat roofs; snow load shape coefficients; snow accumulation processes; snow prevention Article  
Snow Load Shape Coefficients and Snow Detection Method for Stepped Flat Roofs  
flat roofs are mainly measured via the field measurements of full-size roofs [7; 8; 9; 10; 11]. Since 1956, the Division of Building Research of the National Research Council of Canada has carried out field measurements of snow loads on multiple structures with actual stepped flat roofs, whose results have become the main basis for the modification of snow load codes [11]. By establishing a snowdrift database to statistically explore stepped flat roofs, the USA revised the section on the snow load shape coefficient of stepped flat roofs [10]. The field measurement of the full-size roof is the most intuitive and accurate. However, due to the actual roof's large span and high snow storage, the final snow pattern is hard to obtain. As a result, reduced-scale field research has gradually developed [12; 13; 14; 15]. Compared with prototype measurement, scaled measurement requires less time and provides more valuable information. Nevertheless, the size effect of snow particles is not yet clear. Fortunately, investigations have shown that equilibrium drifts of models at a scale ratio greater than 1:30 are approximately proportional to the ones of prototype models [13; 14; 16], and provide suggestions for the snow load shape coefficients of stepped flat roofs [12; 16]. Due to the impact of the wind, a lower roof has a more easily unbalanced snow load, resulting in structurally weak areas. Therefore, different approaches are used to reduce the snow load on stepped flat roofs, such as manual operations for snow removal, roof heating systems, and improved roof structures. Manual operations for snow removal are only applicable to the roofs that one can set foot on. In addition, the cost of setting up roof heating systems is high, making them unsuitable for large-scale expansion. In contrast, improving the roof structure is relatively practical. The Guide to the Snow Load Provisions of ASCE 7-16 provides two suggestions for enhancing the structure of stepped flat roofs [17], as shown in Figure 1. The principle of both methods is to add components on the roof to reduce the space available for snowpack. Thus, it is necessary to clarify the snow accumulation processes and the final snow distribution on stepped flat roofs, to provide references and suggestions for the improvement of roof structures.