## 2. CQC Combination Rules and Simplified Combination Coefficients  
The CQC rule takes into account cross-term coupling between components. The calculation of the square root of the complete quadratic term of the extreme value of each effect component is complex, especially for the case of multiple effect components. To facilitate engineering applications, in this section, the extreme value probability distribution functions of the wind load effect components scalar sum are used to obtain the expression of the extreme value of the combined effect, by which the simplified combination coefficient of the extreme value of the effect component is given. The extreme value of the effect component and its combination coefficient are used to express the extreme value of the combined effect, and a simplified Equation for the combination of wind load effect components' extreme value is given according to the CQC rule. It is straightforward to expand the two-effect component extreme value combination to a multi-effect component extreme value combination, and the simplified Equation can then be derived according to CQC rule. Assuming that the wind load effect components \(R_{1}(t)\) and \(R_{2}(t)\) obey the Gaussian distribution, the scalar sum is:  
\[R(t)=R_{1}(t)+R_{2}(t), \tag{1}\]  
This also obeys the Gaussian distribution, and the extreme probability distribution function of the scalar sum is as follows:  
\[F(R)=\exp\left[-v_{0,R}^{+}T\cdot\exp\left(-\frac{(R-\mu_{1}-\mu_{2})^{2}}{2 \sigma_{R}^{2}}\right)\right], \tag{2}\]  
In the Equation, \(\mu_{1}\) and \(\mu_{2}\) respectively represent the mean value of \(R_{1}(t)\) and \(R_{2}(t)\); \(T\) represents the given duration; \(v_{0,R}^{+}\) is the mean upcrossing rate of the extreme value of \(R(t)\), and the expression is as follows. The expression is different from the mean upcrossing rate in EN 1991-1-4 [23] which corresponds to the natural frequency of the structure, the background factor, and the resonance response factor. Furthermore, when calculating the total wind load of the structure according to EN 1991-1-4, the reduction effect on the wind action due to the non-simultaneity of occurrence of the peak wind pressures on the surface is taken into account by the size factor Cs. The resulting force is multiplied by 0.85-1 according to the ratio of the height to the depth of the structure. \[v_{0,R}^{+}=\frac{1}{2\pi}\cdot\frac{\dot{\sigma}_{R}}{\sigma_{R}}, \tag{3}\]In the Equation, \(\sigma_{R}\) represents the standard deviation of \(R(t)\), and \(\dot{\sigma}_{R}\) represents the standard deviation of the derivative of \(R(t)\); the expressions of \(\sigma_{R}\) and \(\dot{\sigma}_{R}\) are, respectively, Equations (4) and (5). \[\sigma_{R}=\sqrt{\sigma_{1}^{2}+2\rho_{12}\sigma_{1}\sigma_{2}+\sigma_{2}^{2}}, \tag{4}\]  
\[\dot{\sigma}_{R}=\sqrt{\dot{\sigma_{1}}^{2}+2\rho_{12}\dot{\sigma_{1}}\dot{ \sigma_{2}}+\dot{\sigma_{2}}^{2}}, \tag{5}\]  
In the Equation, \(\sigma_{1}\) and \(\sigma_{2}\) represent the standard deviations of \(R_{1}(t)\) and \(R_{2}(t)\) respectively; \(\dot{\sigma_{1}}\) and \(\dot{\sigma_{2}}\) represent the standard deviations of the derivatives of \(R_{1}(t)\) and \(R_{2}(t)\) respectively; \(\rho_{12}\) represents the correlation coefficient of \(R_{1}(t)\) and \(R_{2}(t)\). Substituting Equations (4) and (5) into Equation (3), we get:  
\[v_{0,R}^{+}=\sqrt{\frac{1+2\rho\cdot\frac{v_{0,1}^{+}}{v_{0,2}^{+}}\cdot c_{2 1}+\left(\frac{v_{0,2}^{+}}{v_{0,1}^{0}}\right)^{2}\cdot c_{21}^{2}}{1+2\rho _{12}\cdot c_{21}+c_{21}^{2}}\cdot v_{0,1}^{+}}, \tag{6}\]  
In the Equation, \(c_{21}\) is the ratio of \(\sigma_{2}\) to \(\sigma_{1}\); \(v_{0,1}^{+}\) and \(v_{0,2}^{+}\) are the mean upcrossing rate of the extreme values of \(R_{1}(t)\) and \(R_{2}(t)\), respectively. If \(v_{0,1}^{+}\) and \(v_{0,2}^{+}\) are equal, \(v_{0,R}^{+}\) and \(v_{0,1}^{+}\) are equal.