# Snow Load Shape Coefficients and Snow Prevention Method for Stepped Flat Roofs
## 4 Results and Discussion
### Snow Load Shape Coefficients
Additionally, the maximum snow load shape coefficient in this paper is higher than that of other codes. The snow load shape coefficients of the AIJ code are the lowest in the snow load codes, with a maximum of only about 1. The ASCE code states that the unbalanced length of the snowpack only accounts for 1/6 of the roof span with snow load shape coefficients of less than 2. The snow load shape coefficients in NBCC are the highest among the other codes, whose maximum value is 2.7, but the nonuniform length of the snow accumulation is equal to the level difference (H). The EN and GB codes all consider that the length for the nonuniform area is 2/3 (2H) of the roof span, and the maximum snow load shape coefficient in the two codes is 2.5. The maximum snow load shape coefficients and the unbalanced length of snow are summarized in Table 4. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Code** & **Calculation Formula of \(\mu\)** & **Parameter Description** \\ \hline GB50009 2012 [9] & \(\begin{array}{c}\mu=(L_{1}+L_{2})/2H\quad(2.0\leq\mu\leq 4.0)\\ x_{d}=2H\quad(4\;\text{m}\leq x_{d}\leq 8\;\text{m})\end{array}\) \\ \hline ASCE 2017 [10] & \(\begin{array}{c}\mu=\gamma\frac{(h_{d}+h_{s})}{50}\\ \frac{h_{c}}{\sqrt{L_{1}}}\sqrt[]{5_{0}+10}-1.5\quad(h_{d}\leq h_{c})\\ h_{b}=S_{b}/\gamma\\ \gamma=0.13S_{0}+14\quad\left(\gamma\leq 301\text{b}/\text{ft}^{3}\right)\\ x_{d}=\begin{cases}4h_{d}\quad(h_{d}\leq h_{c})\\ 4h_{d}^{2}/h_{c}\quad(h_{d}>h_{c})\end{cases}\quad(x_{d}\leq 8h_{c})\end{cases}\) \\ \hline EN 1991-1-3 2003 [8] & \(\begin{array}{c}\mu=\mu_{i}\text{Ce}_{c}t\\ \mu_{2}=\mu_{w}+\mu_{s}\\ \mu_{w}=(b_{1}+b_{2})/2h\quad(\mu_{w}\leq\gamma H/S_{0})\\ \mu_{s}=\begin{cases}0&\alpha<15^{\circ}\\ 0.5\mu_{1}\quad\alpha\geq 15^{\circ}\\ x_{d}=2H\quad(5\;\text{m}\leq x_{d}\leq 15\;\text{m})\end{cases}\) \\ \hline NBCC 2015 [11] & \(\mu_{b}=\begin{cases}0.8\quad l_{c}\leq\left(\frac{20}{C_{c}}\right)\\ \frac{1}{C_{c}}\left[1-(1-0.8C_{c})\exp\left(-\frac{l_{c}-70}{100}\right) \right]\\ C_{a}=\begin{cases}C_{a0}-(C_{a0}-1)(x/x_{d})\quad 0\leq x\leq x_{d}\\ 1.0\quad x>x_{d}\end{cases}\end{cases}\) \\ \hline AIJ 2004 [7] & \(\begin{array}{c}\mu=\mu_{b}+\mu_{w}+\mu_{s}\\ \mu_{s}=\begin{cases}0\quad\alpha<10^{\circ}\\ \mu_{b}\quad\alpha\geq 25^{\circ}\end{cases}\end{array}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Formulas of snow load shape coefficients in the codes of different countries. Figure 13: Comparisons of the empirical formula in this paper with different countries’ codes. It is evident that the values of the snow load shape coefficients in different codes vary significantly due to the differences in the environmental and geographical characteristics of each country. This poses challenges in identifying the snow load of stepped flat roofs in practical projects. Therefore, the maximum snow load shape coefficients at each position and the maximum nonuniform length of deposition are summarized in Equation (21), which refers to the codes of different countries, and Equation (20). \[\mu=\left\{ \begin{matrix}-1.22(x/\mathrm{H})+3.44&0\leq x/\mathrm{H}\leq 2\\ 1&x/\mathrm{H}>2\end{matrix} \right. \tag{21}\]  
Equation (20) states that the unbalanced length of the snow load on the lower roof is twice the level difference. The values of the snow load shape coefficient conform to linear regularity, with the maximum located at \(x=0\), and the maximum is about 3.44.