# Analysis of Mechanical Properties of Air-Ribbed Skeleton Membrane Structure
## 5 Analysis of Calculation Results
### Angle of Cable Wind Rope Effect on Mechanical and Structural Properties
#### 5.3.2 Structural Displacement Analysis  
Figure 16 shows the displacement of the tarpaulin under different wind rope setting angles. The displacement of the tarpaulin is similar in case 5 and case 6. The maximum  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Working Condition**} & \multirow{2}{*}{**Maximum Stress (MPa)**} & \multicolumn{2}{c}{**Average Stress of Stress Band**} & \multicolumn{2}{c}{**Stress between End Face and Air**} \\  & & **(MPa)** & **Frame (MPa)** \\ \hline case 5 & 23.28 & 11.80 & 2.24 \\ case 6 & 31.52 & 15.96 & 2.99 \\ case 7 & 53.75 & 17.05 & 3.88 \\ case 8 & 54.73 & 13.84 & 3.85 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The maximum and average stress of the tarpaulin in case 4 and case 5.  
Figure 14: The stress of the tarpaulin in case 5, case 6, case 7, and case 8. (a) Case 5. (b) Case 6. (c) Case 7. (d) Case 8. The data unit is MPa.  
displacement occurs at the center of the tarpaulin's end face. Specifically, the maximum displacement is 325.9 mm in case 5 and 318.6 mm in case 6, indicating that the displacement of the end face is not significantly affected by the change in the setting angle of the wind rope. The deformation of the leeward side and the top of the tarpaulin in case 6 closely resembles that of case 5. The wind ropes at 30\({}^{\circ}\) are better than those set at 45\({}^{\circ}\) in terms of reducing the deformation area range and the influence of the combination of snow and wind loads on the normal use of the membrane structure.  
The displacements of tarpaulin in case 7 and case 8 are similar, with the maximum displacement occurring at the end face of the tarpaulin. Specifically, case 7 exhibits a maximum displacement of 622 mm, while case 8 has a maximum displacement of 467 mm. These values indicate that the structural deformation is relatively small when the cable wind rope is set at 30\({}^{\circ}\) under a wind angle of 0\({}^{\circ}\). This finding aligns with the results obtained when the wind angle is 90\({}^{\circ}\).  
The displacements of the air ribs in case 5 and case 6 are shown in Figure 17. The maximum displacement of the air ribs occurs in the bending zone of the leeward side. The maximum displacement of the air ribs in case 5 is 99.24 mm, and the value in case 6 is 105.8 mm. There is a slight difference in the results of the two cases, primarily due to the similar reduction effect of the wind ropes on the windward side and the equal load applied to the leeward side and top of the air ribs. Consequently, the setting angle of the wind ropes has minimal influence on the displacement of air ribs.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Working Condition** & **Maximum Stress** & **Average Stress** \\ \hline case 5 & 20.66 & 12.29 \\ case 6 & 18.99 & 11.85 \\ case 7 & 21.60 & 13.53 \\ case 8 & 13.75 & 9.42 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The maximum and average stress of the air ribs in case 5, case 6, case 7, and case 8.  
Figure 15: The stress of the air ribs in case 5, case 6, case 7, and case 8. (**a**) Case 5. (**b**) Case 6. (**c**) Case 7. (**d**) Case 8. The data unit is MPa.  
Figure 16: The displacement of the tarpaulin in case 5, case 6, case 7, and case 8. (**a**) Case 5. (**b**) Case 6. (**c**) Case 7. (**d**) Case 8. The data unit is mm.  
Figure 17: The displacement of the air ribs in in case 5, case 6, case 7, and case 8. (**a**) Case 5. (**b**) Case 6. (**c**) Case 7. (**d**) Case 8. The data unit is mm.  
The maximum displacements of the air ribs in case 7 and case 8 both occur at the center of the end face, and the maximum displacement of the air ribs in case 7 is about 435.9 mm. The displacements at other positions of the air ribs in case 8 are minimal and the average value is less than 89.69 mm. This shows that when the wind rope is arranged at 30\({}^{\circ}\), the displacement of the air ribs is small. Therefore, it can be concluded that a wind rope angle of 30\({}^{\circ}\) is preferable for all cases.