# Field Research on the Wind-Induced Response of a Super High-Rise Building under Typhoon
## 6 Wind-Induced Response Analysis  
### Acceleration Response  
The relationship between the structural acceleration response and wind speed is a subject of concern among wind engineering researchers. This paper analyses the relationship between the measured acceleration and average wind speed under typhoons by taking Typhoons Chan-hom and Dujuan as the research objects (Figure 19). The figure also shows the fitting curves based on the measured data, with a fitting equation of:  
\[\sigma_{a}=c_{1}\overline{U}^{2} \tag{14}\]  
where \(\sigma_{a}\) represents the root mean square (RMS) of the acceleration, \(\overline{U}\) is the 10 min mean wind speed at the top of the building and \(c_{1}\), \(c_{2}\) are the fitting parameters. Figure 18: Variation in the damping ratios against the peak acceleration response at the 41 st floor for the first three sway modes during the typhoons. (**a**) Mode 1; (**b**) Mode 2; and (**c**) Mode 3. Figure 19: _Cont._  
Figure 19 shows that the root mean square of the acceleration response of the building structure during Typhoons Chan-hom and Dujuan increases with the wind speed, but that the increase rate of Typhoon Chan-hom is smaller because the angle between the incoming flow and the building is 45\({}^{\circ}\), and because the acceleration response in the downwind and crosswind directions is not obvious. Table 6 shows that the fitting indexes of Typhoon Chan-hom are small, indicating a non-obvious dynamic response from this angle. The fitting indexes of the two directions of Typhoon Dujuan are at the same level, which is up to 1.634. Thus, the crosswind dynamic response should be considered in the design of high-rise buildings. Figure 19: Relation between the RMS of the acceleration and the 10-min mean wind speed on top of the building. (**a**) and (**b**) Chan-hom; (**c**) and (**d**) Dujuan. ### Acceleration Response  
High-rise buildings can generate vibrations under the wind load. When the vibrations exceed a certain limit, occupants can feel uncomfortable. This phenomenon is known as the occupant comfort problem. [PERSON] et al. [22] and [PERSON] et al. [23] have shown that factors that affect human comfort mainly include the vibration amplitude and frequency. When these two factors form a certain relationship, human bodies will feel uncomfortable. Many standards are applied for the measuring human comfort level. However, the most recognised standard is the use of the acceleration response amplitude. Therefore, many experts and specifications have given the calculation methods and limit values of the structural acceleration. The international standard organization (ISO 6897:1984) [24] for buildings with a frequency of 0.063-1.0 Hz, under a wind load with a return period of 5 years, gives the comfort limit value related to the natural vibration frequency in a horizontal direction:  
\[\sigma_{i}=0.026\times f_{i}^{-0.412}\ (\mathrm{m/s}^{2}) \tag{15}\]  
where \(\sigma_{i}(i=x,y)\) is  
where \(\omega_{0}\) is the basic wind pressure, \(\gamma\) is the unit weight of air, \(\gamma=0.012\) kN/m\({}^{3}\). \(g\) is the acceleration of gravity, \(g=9.8\) m/s, and \(v_{0}\) is the basic wind speed. The China Load Code (GB 5009-2012) indicates the basic wind pressures for the 10-, 50- and 100-year recurrence periods of the test building, which are 0.35, 0.6 and 0.7 kPa, respectively. The basic wind speeds of other recurrence periods T are calculated according to the following equation:  
\[\frac{U_{h}(z)}{U_{h}(10)}=\left(\frac{z}{10}\right)^{\alpha} \tag{20}\]  
\[U_{T}=U_{10}+(U_{100}-U_{10})(\ln T/\ln 10-1) \tag{21}\]  
where \(U_{T}\) is the basic wind speed of the recurrence period T, \(U_{h}(z)\) is the 10-min average wind speed at a height z, \(U_{h}(10)\) is the 10-min average wind speed at a height of 10 m, \(\alpha\) is the ground roughness index and \(\alpha=0.22\). The maximum mean wind speeds of Typhoons Chan-hom and Dujuan, measured in 10 min at a height of 177 metres, are 12.0 and 14.9 m/s, respectively.