# Research on Equivalent Static Load of High-Rise/Towering Structures Based on Wind-Induced Responses
## 1 Introduction  
Wind load is one of the loads that must be considered in engineering design. For highly flexible, low-damping and light-mass structures, such as high-rise buildings [1, 2], bridges [3, 4], circular cylinder structures [5, 6], wind turbines [7, 8, 9], railway catenary [10], cables [11, 12] and transmission towers [13], the wind vibration responses are very sensitive and highly susceptible to wind vibration disasters, and determining their wind vibration response and equivalent wind load is one of the core problems of structural wind engineering. Furthermore, the structural wind-induced response is the basis for the study of equivalent static wind loads. In the past, the wind loads of structures were mainly determined directly by anemometers. In the 1960s, Davenport AG [14, 15] first introduced random vibration theory into the analysis of the along-wind vibration response of high-rise buildings, divided the structure's total pulsation response into background and resonance components, and proposed the gust load factor method (GLF) based on the first-order displacement response, in order to calculate the equivalent static wind load of the structure. [PERSON] [16] argued that the equivalent pulsating wind load on the structure could instead be assessed by the inertial force of the first-order pulsating displacement response, and then proposed the inertial wind load method (IWL), which had been adopted into the Chinese code. [PERSON] et al. [17, 18] proposed an accurate assessment method for the structural background response of low-rise buildings with high stiffness, named the load-response correlation (LRC) method. [PERSON] et al. [19, 20] proposed the basalmoment array wind load factor (MGLF) method, which is characteristic of the advantages of LRC and IWL, and has been adopted by the American code. Subsequently, equivalent static wind load assessment methods were proposed by [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] and others [21; 22; 23; 24; 25; 26; 27; 28; 29]. The above-mentioned methods all take the responses at key locations, such as peak displacement and peak internal force, as the equivalent value, without considering other locations. However, with the development of building shape and height, considerations of only the first-order vibration mode cannot guarantee the security of the structure. On the other hand, with progress in the theory of the wind vibration response calculation, not only the higher-order mode of the wind vibration but also the background and resonant coupling components can be taken into consideration, so there is still a need to investigate the equivalent static wind loads. The main research methods of structural wind-induced response studies include theoretical analysis, field measurements, wind tunnel experiments and numerical simulations [1; 2; 5; 7; 30], and the theoretical analysis can be classified into two types: the time domain method and the frequency domain method. The advantage of the time domain method is that it has a wide range of applications, given its ability to obtain the dynamic response of the displacement, bending moment and shear force, and it can take into account the influence of material's nonlinearity, but the disadvantage is its time-consuming method of calculation. The advantage of the frequency domain method is that the concept is clear and the computational cost is small; the disadvantage is that it cannot consider nonlinear problems. In fact, with the development of computer hardware and frequency-domain computational theory, the disadvantages of the time domain method are gradually being overcome, and the results of the frequency domain method are becoming more and more accurate. [PERSON] et al. [31] proposed an along-wind vibration response analysis method that takes the higher-order modes and inter-modal coupling terms into consideration, and it is based on non-constant load tests performed in the frequency domain. [PERSON] et al.