## 1 Introduction  
The stationary random wind loads acting on each surface of a building structure have spatial correlation. The structural effect of the building structure under the action of wind load includes not only the downwind effect component, but also the cross-wind, vertical, and torsional effect components, and each maximum effect component does not occur concurrently [1; 2; 3]. It is unreasonable to consider only one or two of the effect components to evaluate the structural combination effect in the structural design, and it is also unreasonable to combine the maximum of each effect component to evaluate the structural combination effect. It is, therefore, critical to accurately calculate the combined effect of the extreme value of the effect component of the structural member under the action of wind load, which is of great significance for the study of the extreme value combination of the effect component of the building structure under the action of wind load. The load effect combination rules widely used today are mainly based on engineering experience and reliability theory. In the field of wind engineering, complete quadratic combination (CQC) and Turkstra (TR) rules are commonly used. For the scalar sum of the effect components of the stationary Gaussian wind load, when the components are uncorrelated and their peak factors vary only slightly, the combination extreme is equal to the square root of the sum of squares of the extremum of the effect components, which is also known as the square root of the sum of the squares (SRSS) rule; when the components are correlated, and the coupling of the cross terms between the components needs to be considered, the combination extreme is equal to the square root of the complete quadratic term of the extremum of each effect component, which is also known as the CQC rule. The CQC rule is based on the reliability theory, which is the statistical average of considerable samples. The accuracy is high when there are many samples, but the error may be large for a specific single sample [4]. The CQC rule is applied in the AS/NZS 1170.2:2011 wind load standard [5]. To facilitate application in engineering design, based on engineering experience, it is assumed that the wind load effect components obey a stable Gaussian distribution and are independent of each other. The maximum of one effect component and the accompanying values of the other effect components are combined sequentially, and the maximum is selected as the scalar sum of the effect components, which is also known as the TR rule. Based on the TR rule, [PERSON] et al. [6; 7; 8; 9; 10; 11] undertook intensive research on the combination extreme of wind load effects of low-rise and medium-rise building structures, and the results showed that the extreme value of wind load effect combination derived from the TR rule is related to the correlation coefficient of the effect component, the aspect ratio of the building plane, the building height, the wind direction angle, and the wind pressure distribution when the wind load combination effect reaches the maximum. [PERSON] [12] studied the combination of wind load effect components according to the TR rule, and the results showed that the combination extreme value is affected by the correlation coefficient of the effect component and its amplitude ratio, whereas the correlation coefficient of the wind load effect component differs from the correlation coefficient of the wind load component. The load component correlation coefficient, therefore, should not be used for effect component combination. TR rule is applied in GB50009-2012 [13] and AIJ-RLB-2004 [14; 15] codes. The theoretical solution of the probability distribution of the TR rule cannot be expressed, but the upper and lower bounds of its probability distribution can. [PERSON] et al. [14] obtained the minimum of the combination extreme according to the upper bound of the TR rule probability distribution. This rule is called the TR1 rule.