# Analysis of Mechanical Properties of Air-Ribbed Skeleton Membrane Structure
## 5 Analysis of Calculation Results  
### Analysis of Structural Mechanical Properties under Wind Load  
#### 5.1.1 Structural Stress Analysis  
The air ribs are placed evenly and connected with others by the flexible tarpaulin. The air ribs have a higher stiffness compared to the tarpaulin due to their internal pressure. Flexible tarpaulins are prone to significant deformation under the influence of wind loads. The deformation of tarpaulin and air ribs is different. The stress distribution of tarpaulin under wind load is shown in Figure 8. The analysis results indicate that high stress occurs at the connection area between the air ribs and the tarpaulin. Specifically, the maximum stress appears at the connection between the air ribs and the end face of tarpaulin. The value of maximum stress is 80.40 MPa when the wind angle is 0\({}^{\circ}\), 109.00 MPa at a wind angle of 45\({}^{\circ}\), and 22.02 MPa at a wind angle of 90\({}^{\circ}\). It should be noted that the maximum stress of the tarpaulin is higher at a wind angle of 45\({}^{\circ}\) compared with both 0\({}^{\circ}\) and 90\({}^{\circ}\) wind angles.  
Figure 9 presents the stress distribution of the air ribs under wind load. The maximum stress is observed at the point of the deformation bending section. The angle between the point and the ground is 45\({}^{\circ}\), and the distribution of stress is the same in all cases. The maximum stress values are as follows: 17.35 MPa at a wind angle of 0\({}^{\circ}\), 19.61 MPa at a wind angle of 45\({}^{\circ}\), and 17.97 MPa at a wind angle of 90\({}^{\circ}\). The stress of other components is uniform, and the average stress of the air ribs in three cases is 11.34 MPa, 13.38 MPa, and 11.99 MPa, respectively. Based on these results, it can be concluded that the air-ribbed skeleton membrane structure is safe under the action of wind load because the stress is less than the fracture strength.  
Figure 8: The stress 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 MPa.  
Figure 9: The stress of the air ribs 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 MPa.  
The air ribs are made of annular film material, which is utilized to hold high-pressure air. The thickness of the film is much smaller than the average diameter of the air rib; so, it can be simplified to a thin-walled ring. The internal pressure of the air rib is 0.2 MPa (relative pressure). Many scholars have utilized the formula for thin-walled ring structures, as mentioned in references [25; 26].  
The axial and circumferential stresses of the air rib can be calculated as follows:  
\[\sigma_{c}=\frac{pbd}{2 bt}=12.095\;\text{MPa} \tag{3}\]  
\[\sigma_{a}=\frac{p\pi d^{2}/4}{\pi(D^{2}-d^{2})/4}=5.998\;\text{MPa} \tag{4}\]  
where the variables are as follows:  
\(\sigma_{c}\)--circumferential stress (Pa);  
\(\sigma_{a}\)--axial stress (Pa);  
\(p\)--relative pressure inside and outside the air rib (Pa);  
\(b\)--length of single air rib (m);  
\(D\)--outer diameter of air rib (m);  
\(d\)--inner diameter of air rib (m);  
\(t\)--wall thickness of air rib (m).  
The primary stresses are calculated to be 13.72 MPa and 4.73 MPa, respectively, using Formulas (5) and (6):  
\[\sigma_{1}=\frac{\sigma_{c}+\sigma_{a}}{2}+\sqrt{\frac{\left(\sigma_{c}-\sigma _{a}\right)^{2}}{2}}=13.72\;\text{MPa} \tag{5}\]  
\[\sigma_{2}=\frac{\sigma_{c}+\sigma_{a}}{2}+\sqrt{\frac{\left(\sigma_{c}-\sigma _{a}\right)^{2}}{2}}=4.73\;\text{MPa} \tag{6}\]  
The stress calculated by the simulation is in the same range as the theoretical calculations. In the model, the stress transferred from the tarpaulin is applied on the air ribs; thus, the simulation results typically match the maximum theoretical calculation value.