# Wind Pressure Coefficient on a Multi-Storey Building with External Shading Louvers
## 4 Results and Discussion
### Impact of Shading Louvers on Average Wind Pressure Coefficient  
Some parameters are introduced to describe the characteristics of average \(C_{\text{P}}\) on outside surfaces of rooms. \(\overline{C_{\text{P}}}\) is the average \(C_{\text{P}}\) on outside surface of a room belongs to the intersection of one floor and one row, as given by Equation (10). \(\Delta\overline{C_{\text{P}}}\) is the difference of \(\overline{C_{\text{P}}}\) between a shaded condition and the non-shaded condition, as given by Equation (11). \(\overline{\Delta C_{\text{P-R}}}\) is the average difference of \(\overline{C_{\text{P}}}\) for all shaded conditions, compared with the non-shaded condition in a special row, as given by Equation (12). \(\overline{\Delta C_{\text{P-e}}}\) is the average difference of \(\overline{C_{\text{P}}}\) between a specific shaded condition and the non-shaded condition in a whole row, as given by Equation (13),  
\[\overline{C_{\text{P}}}=\frac{1}{A_{\text{R}}}\sum_{A_{\text{R}}}C_{\text{P}} \ \Delta S_{\text{R}} \tag{10}\]  
\[\Delta\overline{C_{\text{P}}}=\overline{C_{\text{P}}}-\overline{C_{\text{P-n}}} \tag{11}\]  
\[\overline{\Delta C_{\text{P-R}}}=\sum_{i=1}^{6}\bigl{|}\overline{C_{\text{P- e-i}}}-\overline{C_{\text{P-n}}}\bigr{|} \tag{12}\]  
Figure 13: Local range \(R\), local and average value of wind pressure coefficient \(C_{\text{P}}\) for different shaded conditions on the central lines of different floors along the windward, lateral and leeward surfaces. (**a**) Local value along F1; (**b**) Local range \(R\) and average value along F1; (**c**) Local value along F2; (**d**) Local range \(R\) and average value along F2; (**e**) Local value along F3; (**f**) Local range \(R\) and average value along F3; (**g**) Local value along F4; (**h**) Local range \(R\) and average value along F4; (**i**) Local value along F5; (**j**) Local range \(R\) and average value along F5. \[\overline{\Delta C_{\text{P-0}}}=\sum_{j=1}^{7}\overline{|C_{\text{P-R-j}}}-\overline{ C_{\text{P-n}}}| \tag{13}\]  
where \(A_{\text{R}}\) is the area of the outside surface of a room. In all simulation cases, the rooms in different floors and rows are assumed to have the same \(A_{\text{R}}\). Considering the usage of the symmetry model and symmetry domain in simulations, \(A_{\text{R}}\) in R1 and R7 are set as the half value of the real area. \(\Delta S_{\text{R}}\) is the area of a grid on the outside surface. \(\overline{C_{\text{P-0-}i}}\) is the \(\overline{C_{\text{P}}}\) for the shaded condition with a specific rotation angle \(\theta\), and \(i\) is set as 1-6 to represent \(\theta=0^{\circ}\), \(15^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), \(60^{\circ}\) and \(75^{\circ}\). \(\overline{C_{\text{P-n}}}\) is the \(\overline{C_{\text{P}}}\) in the non-shaded condition. \(\overline{C_{\text{P-R-j}}}\) is the \(\overline{C_{\text{P}}}\) in a specific row, and \(j\) is set as 1-7 to represent R1-R7. Figure 14: Local range \(R\), local and average value of wind pressure coefficient \(C_{\text{P}}\) for different shaded conditions on the central lines of different rows along the roof and lateral surfaces. (**a**) Local value along R3; (**b**) Local range \(R\) and average value along R3; (**c**) Local value along R4; (**d**) Local range \(R\) and average value along R4; (**e**) Local value along R5; (**f**) Local range \(R\) and average value along R5. Figure 15 presents \(\overline{C_{\rm P}}\) on five different floors along R1-R7. Figure 16 presents \(\Delta\overline{C_{\rm P}}\) between the non-shaded condition and other shaded conditions. In Figure 15, the \(\overline{C_{\rm P}}\) results of R1 and R2 show that the windward surface has the largest difference of \(\overline{C_{\rm P}}\) on different floors for most shaded conditions. On the windward R1 and R2, F4 has the highest \(\overline{C_{\rm P}}\) and F1 has the lowest \(\overline{C_{\rm P}}\) for most shaded conditions. \(\overline{C_{\rm P}}\) has the greatest reduction for all floors when \(\theta\) turns from \(60^{\circ}\) to \(75^{\circ}\).