## 1 Introduction  
Wind loads on long-span roofs are always critical concerns at the structural design stage. Therefore, an accurate evaluation of the extreme wind pressure on the roof is essential. At present, the peak factor following classical Gaussian assumption is often accepted to determine extreme values of wind pressures. In most codes [1; 2; 3; 4; 5], peak factors are suggested as 2-4. For example, a peak factor of 2.5 is used in the Chinese standard GB50009-2019 [5]. However, this is not the case for actual peak factors for wind pressures on long-span roofs.  
Generally, most regions of the long-span roof are immersed in flow separation. Pressures for these regions tend to exhibit non-Gaussian properties whose distribution tails are wider than Gaussian distribution [6; 7]. Peak factors for non-Gaussian processes are often larger than those for Gaussian processes [8]. Still, using peak factors following the Gaussian assumption will underestimate the extreme values of wind pressures which leads to risky design or even undesirable roof damage [9; 10; 11].  
There are two major ways to determine the peak factors and extreme values for non-Gaussian processes. One is the observed peak method [12; 13; 14; 15]. This method relies on a large number of repeated samples to ensure accurate and precise data fitting, which is time-consuming and uneconomical in wind tunnel tests. The other is the translation process method, which uses a monotonic translation process to realize the translation of a non-Gaussian process to a standard Gaussian process. It establishes a point-to-point relationship between the non-Gaussian and Gaussian processes. The accuracy of the translation process method based on the Hermite polynomial model (HPM) and using short-term time histories to calculate peak factors has been verified by several studies [16; 17; 18].  
There are relevant studies about non-Gaussian peak factors and extreme wind pressures for tall buildings [19; 20; 21; 22; 23] and small-size low buildings [24; 25; 26; 27], while few studies are available for long-span structures with spans of hundreds of meters [28]. The cylindrical long-span roof is a very common building envelope for industrial structures. As shown in Figure 1, an L-shaped structure is the combination of a big cylindrical roof (BCR) and a small cylindrical roof (SCR). Nevertheless, the wind flow over a combined cylindrical roof considerably differs from that over a single cylindrical roof [29; 30]. However, comprehensive statistical and spatial information about the non-Gaussian property and peak factors for the entire wind pressure field on the long-span roof is still not available but is critical for identifying the most sensitive regions on the roof.  
This study focuses on the non-Gaussian property and its influences on peak factors and extreme values of wind pressure on the combined L-shaped long-span cylindrical roof and is organized as follows: the translation process method based on the HPM is first introduced. Then, wind tunnel tests are conducted to measure wind pressure histories for the roof. Subsequently, the non-Gaussian property of wind pressures is analyzed by the statistical and spatial distribution for mean value, skewness, and kurtosis of wind pressures. Finally, the peak factors and extreme values of wind pressures are investigated by different methods to illustrate the influence of the non-Gaussian property.