## 5 Peak Factors and Extreme Values of Wind Pressure  
The peak factor for each tap is calculated by averaging the largest values selected from each of the 360 segments of the normalized wind pressure coefficient data of \(\beta=90^{\circ}\). As shown in Figure 10, test results are compared with the determination via the HPM given in Section 2, i.e., Equation (15). It is observed that the HPM provides excellent estimations for most wind pressures, with a relative error of no more than 5%. Hence, the HPM is employed to determine peak factors in this study. Figure 10: Comparison for \(g_{\text{peak}}\) between experimental results and the HPM method at \(\beta=90^{\circ}\). Figure 9: Statistical analysis for kurtosis \(m_{4}\) of wind pressure coefficient. (**a**) Histogram of \(m_{4}-3\), (**b**) distribution of \(m_{4,\,\max}\). The distribution of peak factors for three representative wind azimuths, \(\beta=210^{\circ}\), \(225^{\circ}\), and \(240^{\circ}\), is shown in Figure 11a-c, respectively. Peak factors are all larger than 3.5. Furthermore, every contour has a small region with peak factors even larger than 8.5. As presented in Figure 12a, the histogram is the peak factors for all measurements, in which the purple line is the exceedance probability of peak factors. About 60% of them are larger than 5.0, and 20% exceed 7.0. Figure 12: Statistical distribution of peak factor. (**a**) All measurements, (**b**) maximum of each tap. The histogram of maximal peak factor \(g_{\text{peak, max}}\) is presented in Figure 12b, in which all the \(g_{\text{peak, max}}\) values are larger than 5.5, and even 60% of them are larger than 9.0. It can be concluded that peak factors for such roofs are much more considerable than 2.5 and others following the Gaussian assumption. Additionally, the spatial distribution of \(g_{\text{peak, max}}\) is presented in Figure 11d. Peak factors are predominant around edge \(ab\) and edge \(cd\) of the BCR as well as edge \(ef\) of the SCR. As presented in Figure 7c, \(C_{p,\text{ mean, min}}\) also exhibit their minimums around these regions which are deemed to have predominant wind suctions and be the most sensitive. For the wind-resistant design of the roof, extreme wind pressures are important parameters. Accordingly, the influence of the non-Gaussian property on the extreme wind pressures is investigated hereafter. Considering that most of the mean values of wind pressure coefficients are negative, only negative extreme wind pressures are included. As shown in Table 1, the extreme wind pressure coefficients for six taps are collected based on \(g_{\text{peak, max}}\). For comparison, peak factors \(g_{\text{peak, G}}\), following Gaussian assumption, and a constant peak factor of 2.5 are also considered for extreme wind pressure calculation, namely \(C_{p,\text{ peak, G}}\) and \(C_{p,\text{ peak, 2.5}}\). According to Table 1, \(g_{\text{peak, NG}}\) is about three times \(g_{\text{peak, G}}\), leading to the discrepancy between \(C_{p,\text{ peak, NG}}\) and \(C_{p,\text{ peak, G}}\) being significant. The influence of the non-Gaussian property on the resulting extreme wind pressure is considerable. Therefore, the use of \(g_{\text{peak, G}}\), or 2.5 is not suitable for the calculation of extreme wind pressures on the combined long-span cylindrical roofs. Generally, the envelope of wind pressure coefficients among all azimuths is important for designers. However, the maximum \(g_{\text{peak}}\) does not always indicate the maximum extreme wind pressure. Thus, the influence of the non-Gaussian property on the maximums of wind pressure coefficients among all azimuths is also investigated. The wind pressure coefficients when the extreme value at each tap is maximum among the tested azimuths, i.e., \(C_{p,\text{ peak, max}}\), are listed in Table 2. The difference between \(C_{p,\text{ peak}}\) and \(C_{p,\text{ peak, G}}\) is dramatic, as well as \(C_{p,\text{ peak}}\) and \(C_{p,\text{ peak, 2.5}}\).