# Fatigue Analysis of Greenhouse Structure under Wind Load and Self-Weight
## 3 Results and Discussion  
To verify the accuracy of fluid dynamics analysis, the pressure coefficients obtained through experiments [24] and the analysis of a single-span greenhouse with the dimensions provided in Table 1 are compared as shown in Figure 6. As shown in this figure, the experimental and analysis results are in good agreement, with a correlation coefficient of 0.99. Furthermore, a fluid dynamics analysis is conducted for the actual model, and the pressure coefficient for wind load is compared with the EN1991-1-4 standard, as shown in Table 4. The pressure coefficient is calculated using Equation (4) [6]  
\[C_{p}=p(t)/(\frac{1}{2}\rho U_{ref}^{2}) \tag{4}\]  
where \(C_{p}\) is the pressure coefficient, \(p(t)\) is pressure, \(\rho\) is air density, and \(U_{ref}\) is the reference velocity at ridge height. Figure 5: S–N curve of greenhouse structure: (a) S–N curve of SPSR400, (b) S–N curve of aluminum. \(S_{a}\): an applied alternating stress; \(N_{f}\): cycles of failure. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & **Loading Condition for Stress** & **Stress Compensate** & **Wind Speed** & **Remark** \\  & **Normalized Model** & **for Self-Weight** & **Distribution** & **Remark** \\ \hline
1 & Only wind load & X & \(k=1.664\), \(c=5.129\) & \\
2 & Only wind load & O & \(k=1.664\), \(c=5.129\) & \\
3 & Wind load with self-weight at 12 m/s & X & \(k=1.664\), \(c=5.129\) & Korea island wind speeds data \\
4 & Wind load with self-weight at 21 m/s & X & \(k=1.664\), \(c=5.129\) & speeds data \\
5 & Wind load with self-weight at 30 m/s & X & \(k=1.664\), \(c=5.129\) & \\ \hline \hline \end{tabular} Remark: X: No apply, O: apply.  
\end{table} 
Table 3: Fatigue analysis model construction case of stress normalized and wind load condition. As shown in Table 4, the pressure coefficient is similar to that in the EN1991-1-4 design guide. Thus, the analysis results can be considered to be reasonable. Figure 7 shows the strain and stress obtained through structural analysis under each load condition of self-weight and wind load. The effects of self-weight show a horizontally symmetrical shape, where stress is large at the center of the greenhouse structure, and the maximum stress is 85.9 MPa. In addition, owing to the effect of wind at 30 m/s, stress is high at the front of the greenhouse under upwind conditions and at the first and second roofs, where the speed is the highest. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(C_{p}\)} & \multicolumn{3}{c}{**Road Face**} & \multicolumn{10}{c}{**Front Face**} & \multicolumn{10}{c}{**Face  
To examine the relationship with stress when self-weight and wind speed are applied simultaneously, the changes in stress were examined according to wind speed. Figure 8 shows the stress distribution according to wind speed. As wind speed increases, the part with concentrated stress moves to the front of the greenhouse under upwind conditions. In other words, as wind speed increases, the contribution ratio of self-weight decreases. Figure 9 shows the changes in stress according to wind speed and the square of wind speed. Stress is proportional to the square of wind speed when only wind load is applied. However, when self-weight and wind load are applied simultaneously, nonlinear characteristics appear if the wind speed is low and linear characteristics appear when the wind speed is high. This is because the effect of self-weight is negligible compared to that of wind load at high wind speed. First, normal mode analysis was performed to check if resonance occurs for the dynamic load of the structure to determine whether the dynamic characteristics of the structure should be considered in the fatigue analysis. The result is shown in Figure 10. As seen in the figure, the fundamental mode appears above 4 Hz. This is higher than 2 Hz, which is the frequency band for wind speed. Thus, the effect of resonance on fatigue life can be considered to be negligible.