# Research on Equivalent Static Load of High-Rise/Towering Structures Based on Wind-Induced Responses
## 4 Example and Analysis
Other values are also taken (\(f_{MAX}\) = 1 Hz, 3 Hz and 9 Hz; \(df\) = 1/500 Hz and 1/2000 Hz) for verification to ensure the calculation's accuracy. The results show that the resulting \(G_{\text{B}}\) decreases slightly when \(df\) = 1/500 Hz compared to \(df\) = 1/1000 Hz, but it remains unchanged when \(df\) = 1/2000 Hz, and the resulting \(G_{\text{B}}\) decreases slightly when \(f_{MAX}\) = 1 Hz and 3 Hz, compared to \(f_{MAX}\) = 6 Hz, while it remains unchanged when \(f_{MAX}\) = 9 Hz, which indicates that the \(df\) and \(f_{MAX}\) used in the numerical integration are reasonable. The values of the \(GLF\) of the tip displacement and its components \(G_{\text{YB}}\) and \(G_{\text{YR}}\), obtained under the four working conditions, are the results for condition 1. Since the effects of \(\beta\) and \(\lambda\) can all be considered when calculating the displacement response using the method in this paper, different results can be obtained under each of the four conditions, and because of that, the results under conditions 2, 3 and 4 will not be compared. From Table 2, it can be seen that under each working condition, the top displacement \(GLF\) is not less than the base bending moment \(GLF\), with a maximum deviation of about 3.1%, and the base bending moment \(GLF\) is greater than the base shear force \(GLF\), with a maximum deviation of 7.5%. The \(\sigma_{\text{B}}\) values of the base bending moment and shear force are obtained directly from the load and influence function (Equation (25)), which does not contain parameters \(\beta\) and \(\lambda\); therefore, the bending moment and shear force \(G_{\text{B}}\) are not affected by \(\beta\) and \(\lambda\), and \(G_{\text{B}}\) is constant under all four conditions. Further, the base bending moment \(G_{\text{B}}\) is slightly smaller than the base shear force \(G_{\text{B}}\), since the displacement influence function is obtained according to the assumption of the first-order vibration mode, and \(G_{\text{YB}}\) increases with the increase of \(\beta\). Since the \(\sigma_{\text{R}}\) values of the base bending moment and shear force are obtained according to the resonant displacement inertia force \(\hat{P}_{R}(z^{\prime})\) and the influence function (Equation (26)), and \(\hat{P}_{R}(z^{\prime})\) contains the effects of \(\beta\) and \(\lambda\), the \(\sigma_{R}\) response of each condition is not same, and both \(G_{\text{R}}\) values decrease with the increase in \(\beta\). For the displacement of \(\sigma_{R}\), although both \(\hat{P}_{R}(z^{\prime})\) and the influence function contain the parameters \(\beta\) and \(\lambda\), the parameter \(\lambda\) can be removed, so \(G_{\text{YR}}\) is not affected by parameter \(\lambda\), and only increases with the increase in \(\beta\). The \(G_{\text{MR}}\) decreases with the increase in \(\beta\), but remains unchanged or increases when \(\lambda\) increases from 0 to 0.2, which is mainly because \(\lambda\) can be approximately removed when \(\beta\) = 1. When only the first-order vibration mode is considered, the \(G_{\text{QR}}\) of base shear force decreases with the increase in \(\beta\), and increases with the increase in \(\lambda\).