# Snow Load Shape Coefficients and Snow Prevention Method for Stepped Flat Roofs
## 4 Results and Discussion
### Snow Prevention Method for Stepped Flat Roofs  
According to the results of the measurements and numerical simulation, the final shape of the windward snow accumulation on the lower roof is approximated as a triangle. It can be predicted that increasing the angle of the lower roof can reduce the snow depth. Therefore, when the angle of the lower roof \(\beta\) is 1\({}^{\circ}\)-14\({}^{\circ}\), the final snow distribution of the lower roof is obtained as shown in Figure 16. As the angle of the lower roof increases, the snow profile on the lower roof is virtually unchanged, but the amount of snow accumulation significantly decreases. To quantitatively analyze the change in snow accumulation, the snow removal rate \(\sigma\) is defined as Equation (22):  
\[\sigma=\frac{A_{0}-A_{\beta}}{A_{0}}, \tag{22}\]  
where \(A_{\beta}\) is the snow accumulation on the lower roof at different angles, and \(A_{0}\) represents the initial amount of snow on the lower roof.  
The snow removal rate \(\sigma\) and the maximum snow depth \(D\) on the lower roof are depicted in Figure 17. When \(\beta\) = 0\({}^{\circ}\)-3\({}^{\circ}\), the amount of snow accumulation on the lower roof decreases by more than 10%, and the snow depth significantly decreases with the reduction in the snow accumulation. Subsequently, the snow removal rate and snow depth show a linear trend in the range of \(\beta\) = 3\({}^{\circ}\)-11\({}^{\circ}\). When \(\beta\) > 11\({}^{\circ}\), as the snow removal rate increases, the snow depth decreases slowly. The snow removal on the lower roof is more than 90% at \(\beta\) = 12\({}^{\circ}\), and the maximum dimensionless snow depth is less than 0.2. When \(\beta\) increases from 13\({}^{\circ}\) to 14\({}^{\circ}\), the snow accumulation on the lower roof reduces by only 1.8%, with the snow depth less than 0.1H.  
As the angle gradually increases, the amount of snow accumulation on the roof decreases. However, the increase in the slope angle will extend the roof, which results in higher construction costs and resource waste. Therefore, the snow load shape coefficients of the lower roof are calculated as shown in Figure 18. The maximum snow load shape coefficient of the lower roof gradually decreases with the increase in the roof slope angle. When the slope increases by 1\({}^{\circ}\), the maximum snow load shape coefficient decreases by about 0.2. The snow load on the lower roof is less than the ground snow load at \(\beta\) = 11\({}^{\circ}\). When \(\beta\) \(\geq\) 13\({}^{\circ}\), the maximum snow load shape coefficient of the lower roof has reached below 0.5.  
Figure 15: Comparison between the snow simulation and the actual measurement on stepped flat roofs [12; 14; 22].  
Finally, compositing the snow removal rate \(\sigma\), maximum snow depth \(D\), and snow load shape coefficient \(\mu\) on the lower roof, the slope of the lower roof is suggested to be \(11^{\circ}\). When \(\beta=11^{\circ}\), the snow removal rate on the lower roof is more than 85%, the maximum snow depth is about 0.25H, and the maximum snow load shape coefficient is about 0.85.