# Investigating Load-Bearing Capabilities and Failure Mechanisms of Inflatable Air Ribs
## 3 The Load-Bearing Performance of Tents with Different Rise-Span Ratios
### The Analysis of the Distribution of Wind Pressure  
The distribution of the wind pressure on the tent is calculated by Fluent. To minimize the influence of boundaries on the wind pressure, the distance between the inlet and the boundary of the tent is set to five times the length of the tent, and the distance between the outlet and the boundary of the tent is set to ten times the length of the tent. The computational domain is set to be \(270\,\mathrm{m}\times 180\,\mathrm{m}\times 40\,\mathrm{m}\), ensuring the blockage ratio is lower than 3% [31, 32]. The inlet is configured as the velocity inlet, and symmetry conditions are applied to the top and side boundaries to maintain environmental continuity. The bottom boundary is treated as a non-slip wall to replicate ground interaction, while the outlet is free, preventing the back pressure. The flow field of the tent is meshed based on the study by [PERSON] et al. [33]. An unstructured grid is used in the immediate vicinity of the tent (\(20\,\mathrm{m}\times 20\,\mathrm{m}\times 20\,\mathrm{m}\)) to accurately capture the complex flow behavior around the structure. In contrast, a structured grid is used in the outer regions to enhance computational efficiency. The specific mesh configuration is illustrated in Figure 10. The simulation employs a total of approximately 4.6 million grids, achieving a balance between detailed accuracy and computational feasibility.  
According to the Technical Specification for Membrane Structures (CECS 2015) [28], the conditions for the inlet of the wind field are based on a 50-year return period. The wind velocity is 20.7 m/s at a height of 10 m, which corresponds to a fresh gate [34]. The environment is classified as Category B terrain, with a ground roughness coefficient of 0.15. A power function is used to simulate the variation of wind speed with height, which is defined as follows:  
\[U_{Z}=U_{G}\bigg{(}\frac{Z}{Z_{G}}\bigg{)}^{\beta} \tag{3}\]  
Figure 10: Mesh division for CFD analysis of the tent’s flow field ((**a**) shows the mesh distribution overview; (**b**) illustrates the mesh division within the tent’s flow field; (**c**) depicts the boundary layer mesh).  
Figure 9: The model of air-ribbed tents ((**a**) The original upright arched tent structure; (**b**) The improved tent model).  
where \(Z_{G}\) is the gradient wind height, \(\beta\) is the ground roughness coefficient, \(U_{G}\) is the gradient wind speed, and \(U_{z}\) is the wind speed at a height \(z\) above the ground.  
Figure 11 shows the distribution of wind pressure on the surface of the tents. The maximum pressure of Tent-0.333-S is 149.3 Pa, which is the smallest, while that of Tent-0.583-R is 202.19 Pa, the largest among the five structures. The maximum pressure appears at the upwind angle face, making the end rib the main component supporting the entire tent. Reducing the rise of the end ribs significantly affects the enlargement of the positive pressure area on the windward side, compared to reducing the span and creating negative pressure areas at the top of the tent. The top of the tent is under the wind suction, the end rib in the upwind direction is affected by the wind pressure, and the one in the downwind direction is affected by the wind suction. However, based on the wind pressure results alone, aside from slight changes in the distribution, the modifications of the end ribs have not effectively reduced the maximum wind pressure values on the tent.