# Research on Equivalent Static Load of High-Rise/Towering Structures Based on Wind-Induced Responses
## 4 Example and Analysis
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Top Displacement**} & \multicolumn{3}{c}{**Basal Bend Moment**} & \multicolumn{3}{c}{**Basal Shear Force**} \\ \hline
**Condition** & \(G_{\text{YB}}\) & \(G_{\text{YR}}\) & \(DGLF\) & \(G_{\text{MB}}\) & \(G_{\text{MR}}\) & \(MGLF\) & \(G_{\text{QB}}\) & \(G_{\text{QR}}\) & \(QGLF\) \\ \hline
1 & 0.6520 & 0.9761 & 2.1738 & 0.6520 & 0.9761 & 2.1738 & 0.6560 & 0.8275 & 2.0560 \\  & (1.000) & (0.998) & (0.999) & (1.000) & (1.000) & (1.000) & (0.994) & (1.002) & (1.000) \\
2 & 0.6591 & 1.0302 & 2.2230 & 0.6520 & 0.9532 & 2.1549 & 0.6560 & 0.7460 & 1.9934 \\  & & & & (1.000) & (1.000) & (1.000) & (0.994) & (1.003) & (0.999) \\
3 & 0.6520 & 0.9761 & 2.1738 & 0.6520 & 0.9761 & 2.1738 & 0.6560 & 0.8438 & 2.0688 \\  & & & & (1.000) & (1.000) & (1.000) & (0.994) & (1.001) & (0.999) \\
4 & 0.6591 & 1.0302 & 2.2230 & 0.6520 & 0.9589 & 2.1596 & 0.6560 & 0.7612 & 2.0049 \\  & & & & (1.000) & (1.000) & (1.000) & (0.994) & (1.002) & (1.000) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: \(GLF\) of feature locations obtained in this paper. Taking the above high-rise building as an example, the _GLF_ values of each response at any position of the structure under different working conditions are obtained, and the different MGLF values and QGLF values relative to DGLF for each working condition are given in terms of DGLF values. The results are shown in Figure 3.  
From Figure 3, it can be seen that with the increase in building height, the _MGLF_ and _QGLF_ corresponding to the four working conditions increase significantly, and the _DGLF_ remains unchanged along the height. This is mainly because this paper uses the influence function based on the first-order vibration mode to calculate the _DGLF_, so the total pulsation response and the average response are in the form of the first-order vibration mode, and for _MGLF_ and _QGLF_, the increase rate increases with the increase in \(\beta\) and decreases with the increase in \(\lambda\). Under the same working conditions, the _MGLF_ is larger than both the _QGLF_ and the _DGLF_, and only the value of _DGLF_ at the basal level is larger (slightly) than the _MGLF_, but the deviation is within 3%. Therefore, if _DGLF_ and _QGLF_ are used as the equivalent wind load in the structural design, the moment response of the structure may be underestimated; however, the use of the _MGLF_ value for the equivalent wind load calculation is more important, because the design of the structure is biased towards safety, which is corroborated by the popular idea of using the bending moment as the control parameter for towering structures. Under the same working conditions, the basal _QGLF_ value is the smallest, but as the building's height increases, the _QGLF_ value gradually increases, and when the height is above 100 m, the _QGLF_ under each working condition is greater than the DGLF. As the building's height increases, the difference between the _MGLF_ and _QGLF_ gradually decreases, until the tops tend to be equal, and the MGLF is greater than the _DGLF_. Until the top is reached, the difference between the _MGLF_ value and the _DGLF_ value gradually increases, and the maximum deviation between the _MGLF_ and _QGLF_ is about 22%, compared with _DGLF_. The position of maximum deviation is the top of the structure, so the wind effect of the structure will be seriously underestimated when the wind load design is based only on the base moment _GLF_.