## 4 Wind Simulation  
In simplicity, it is assumed that the wind direction is constant and always perpendicular to the structural lateral surface and only along-wind response is taken into account. Since this building is in China, the selection of design basic wind speed refers to Chinese specifications. Actually, if other specifications are selected, the corresponding design basic wind speed can be transformed from that in Chinese specifications by converting the standard height, terrain roughness, etc. The fatigue assessment procedure stated in this paper keeps the same. According to Chinese specifications [13], in this city, when the terrain roughness is defined as Area B, which means the outskirts area of the city, return period is 100 years, standard height is 10 m and average time interval is 10 min, the standard mean wind pressure is \(p_{0}=0.45\) kPa and the mean wind speed can be calculated as \(v_{0}=\sqrt{1600p_{0}}=26.83\) m/s. Since this structure is located in a downtown area (the terrain roughness is defined as Area C which means the downtown area with intensive buildings nearby), the mean wind speed is transformed into \(v_{a0}=20.23\) m/s. The mean wind speed profile takes the form of a power law as:  
\[U(z)=U_{0}\left(\frac{z}{z_{0}}\right)^{\alpha} \tag{4}\]  
where \(z_{0}\) is the reference height which is taken as 10 m; \(U_{0}\) is the wind speed at the reference height; which is taken as 20.23 m/s as stated above; and \(\alpha\) is the exponent of the velocity profile, which is 0.22 for this case. The harmonic superposition method is used to generate the random fluctuating wind time series, and Davenport spectrum is adopted as the power spectrum of velocity fluctuation [14], as shown in Equations (5) and (6):  
\[\frac{nS_{v}(n)}{\overline{v}_{10}^{2}}=\frac{4 kx^{2}}{n{(1+x^{2})}^{3/4}} \tag{5}\]  
\[x=1200\frac{n}{\overline{v}_{10}} \tag{6}\]  
where \(\overline{v}_{10}\) is the mean wind speed in the standard height of 10 m, which is taken as 20.23 m/s as stated above; \(n\) is the frequency of the fluctuating wind; \(k\) is the terrain roughness factor of this area, which is 0.03; and \(S_{v}(n)\) is the power spectrum of velocity fluctuation. Due to the large height and width of the high-rise structure, the horizontal and vertical spatial coherence of velocity fluctuation needs to be taken into consideration simultaneously, the square root of the coherence function \(Coh(d,n)\) is as shown in Equations (7) and (8):  
\[Coh(d,n)=\frac{S_{u_{1}u_{2}}(d,n)}{\sqrt{S_{u_{1}}(l,n)S_{u_{2}}(k,n)}}=e^{-c} \tag{7}\]  
Figure 2: Beam-to-column connection. \[c=\frac{n\Big{[}c_{x}(x-x^{\prime})^{2}+c_{z}(z-z^{\prime})^{2}\Big{]}^{\frac{1}{2}} }{\frac{1}{2}[\overline{v}(z)+\overline{v}(z^{\prime})]} \tag{8}\]  
where \(l\) and \(k\) are two points on the structural surface and their coordinates are (\(x\), \(z\)) and (\(x^{\prime}\), \(z^{\prime}\)), respectively; the distance between them is \(d\); \(S_{u_{1}u_{2}}(d,n)\) is the cross spectrum; \(S_{u_{1}}(l,n)\) and \(S_{u_{2}}(k,n)\) are the self-power spectrum of these two points; \(\overline{v}(z)\)and \(\overline{v}(z^{\prime})\) are the mean wind speed in the height of \(z\) and \(z^{\prime}\); and \(c_{z}\) and \(c_{x}\) are constants, 10 and 16, respectively. Because of the large computing amount involved in harmonic superposition method, during the generation of wind field it is not realistic to consider the horizontal and vertical spatial coherence of each beam-to-column connection. Therefore, in order to simplify the procedure, a total of 17 height reference points located at the height of each layer are selected in the vertical direction, and in the horizontal direction along the width, three reference points in each layer is selected every 35 m. Thus, a total of 51 wind time series are generated, whose duration is 50 s and the time interval is 0.1 s. Figure 3 is a typical fluctuating wind time-history obtained.