# Effects of Corner Set--Backs on Wind Loads and Wind Induced Responses of Rectangular Tall Buildings
## 3 Analysis of Test Results  
### Wind Pressure Coefficients at the Height of 2/3H for Models  
The measured pressure is normalized to calculate the wind pressure coefficient at the pressure tap \(i\) as follows:  
\[C_{pi}(t)=\frac{P_{i}(t)-P_{0}}{0.5\rho U_{H}^{2}} \tag{2}\]  
Figure 5: The corner set-back modifications and arrangement of measurement taps (Unit: mm).  
Figure 6: The definition of corner set-back (top view).  
where \(C_{pi}(t)\) is the time history of wind pressure coefficient at the pressure tap \(i\), \(P_{i}(t)\) is the time history of wind pressure at the pressure tap \(i\), \(P_{0}\) is the static pressure at the reference height of 0.609 m, \(\rho\) is the air density and \(U_{H}\) is the mean wind speed at 0.609 m.  
The mean wind pressure coefficient \(C_{pi,mean}\) is determined with the formula below:  
\[C_{pi,mean}=\frac{1}{N}\sum_{t=1}^{N}C_{pi}(t) \tag{3}\]  
in which, \(N\) is the number of sampling length.  
The RMS (root-mean-square) wind pressure coefficient \(C_{pi,rms}\) could be calculated by:  
\[C_{pi,rms}=\frac{1}{N-1}\sqrt{\sum_{t=1}^{N}\bigl{(}C_{pi}(t)-C_{pi,mean} \bigr{)}^{2}} \tag{4}\]  
Due to space, Figure 7 only displays the mean and the RMS wind pressure coefficients at the height of \(2/3\)H for all models. It is illustrated in Figure 7a that the mean wind pressure coefficients of tap No. 1 and tap No. 5 on the benchmark model and 5% corner set-back model are positive and symmetric with each other. As the corner set-back rate increases from 10% to 20%, the positions of tap No. 1 and tap No. 5 gradually moves to the corner set-backs, and the mean wind pressure coefficients of these two taps become negative. This is probably due to the influence of the corner set-backs, which reduces the width of the windward side, and leading to an accelerated flow separation at the windward corner. The maximum absolute value of mean negative pressure occurs at 10% corner set-back model. Taps No. 2, No. 3 and No. 4 are located at the center of the windward for all the corner set-back models, so their mean wind pressure coefficients are always positive and change slightly with the increasing of the corner set-back rate. For the leeward, the absolute values of the negative wind pressure coefficients decrease by increasing the rate of corner set-back. This is because the wake width on the leeward narrows due to the increase in corner set-back rate. The mean wind pressure coefficients vary more significantly on the side walls than with the windward and leeward, especially for tap No. 6. The absolute value of the mean wind pressure coefficients at the tap No. 6 and tap No. 20 of the models with the corner set-back rates of 5% and 10% are greater than the benchmark model.  
In Figure 7b, the RMS wind pressure coefficients of taps No. 1 and No. 5 of the 10%, 15% and 20% corner set-back models increase sharply. This may arise from the hit of shedding vortex on the leading edge of the windward. The corner set-backs do not affect the RMS wind pressure coefficients on the windward (taps No. 2, No. 3 and No. 4) much. The RMS wind pressure coefficients on leeward gradually decreases as the rate of corner set-back increases. For the side wall, the maximum RMS wind pressure coefficient of the benchmark model happens at tap No. 10, which results from the reattachment of flow. Similar phenomenon can be also observed at tap No. 10 of the 5% corner set-back model. However, with the increasing of the corner set-back rate from 0% to 20%, the RMS wind pressure coefficients of tap No. 10 decrease rapidly. The RMS wind pressure coefficients of taps No.6 and No.20 of the 10%, 15% and 20% corner set-back models are greater than those of the benchmark model. Notably, the 5% corner set-back model has greater RMS wind pressure coefficients on the side wall than other models.