# Analysis of Mechanical Properties of Air-Ribbed Skeleton Membrane Structure
## 5 Analysis of Calculation Results
### Analysis of Structural Mechanical Properties under Wind Load
#### 5.1.2 Analysis of Structural Displacement  
According to Figure 10, the maximum displacement of the tarpaulin under wind load appears at the middle of the end face. The maximum displacement values at 0\({}^{\circ}\) wind direction angle and 90\({}^{\circ}\) wind direction angle are 406.1 mm and 317.9 mm, respectively. The displacement of the tarpaulin at the lateral and roof are less than 110 mm. At a wind direction angle of 45\({}^{\circ}\), the maximum displacement is 439.4 mm. The maximum displacement of the roof is less than 110 mm, and the maximum displacement of the side reaches about 200 mm.  
Figure 10: The displacement of the tarpaulin in case 1, case 2, and case 3. (**a**) 0\({}^{\circ}\) wind direction angle; (**b**) 45\({}^{\circ}\) wind direction angle; (**c**) 90\({}^{\circ}\) wind direction angle. The data unit is mm.  
In the model, the edge of the air rib at the end and the tarpaulin on the end face are joined together. The top of parallelly arranged ribs is closely connected with the top of tarpaulins, and the stiffness of the ribs is greater than that of the flexible tarpaulins. The tarpaulin is supported by the ribs, which can minimize the displacement of the tarpaulin under wind load. As a result, the displacement of the tarpaulin is lowest on the top and end faces. However, there is a significant displacement in the center of the end face of the tarpaulin under wind load. This is the total displacement, which is the square root of the sum of squares of longitudinal displacement and lateral displacement. For the three cases (case 1, case 2, and case 3), the center of the end surface of the tarpaulin exhibits obvious displacement. The maximum displacement in case 2, specifically at the center of the end face of the tarpaulin, is larger than that in case 1 and case 3.  
The displacements of an air rib in case 1, case 2, and case 3 are shown in Figure 11. In case 1, the maximum displacement of the air rib appears at the top of the windward end face, and the maximum displacement is 182.7 mm. The displacements of the other air ribs remain within 100 mm. The maximum displacement of the air rib appearing at the top of the windward end face in case 2 is 247.1 mm, and the displacement of other air ribs are within the range of 140 mm and larger than that of case 1. In case 3, the load applied on the top of the tarpaulin has the greatest influence on the displacement of the air ribs, and the maximum displacement of the air ribs occurs at the top of the central air ribs, with a value of 100.3 mm. The lateral displacement of the air ribs is less than 50 mm. Comparing the three cases, the maximum displacement of the air ribs in case 2 is larger than that in case 1 and case 3. In case 1, the load applied on the windward end face is resisted by the air rib on the end face alone. The direction of the load is along the positive direction of the \(Z\) axis such that the air rib on the end face is unstable and the displacement of the air rib on the end face reaches the maximum. In case 2, the wind force affects both the end face and the top of the structure due to the comprehensive effect of wind direction at 45\({}^{\circ}\). In case 3, the wind load is transferred from the tarpaulin to the air ribs and all the air ribs resist the load. As a result, the influence of wind load on the rib on the end face is weak.  
According to the guidelines of the Chinese Technical Specification for Membrane Structures (CECS158:2015) [27], the maximum displacement of an air-ribbed membrane structure under load and normal working air pressure should be less than 0.5 times the clear distance between the surface of the air-ribbed membrane and any internal or external objects in the undistorted state. In this case, the horizontal distance between the membranes is 1 m; thus, the maximum horizontal displacement is limited to 0.5 m. The maximum displacements in all cases are less than the designated deformation limit, both satisfying the design criteria.