# Fatigue Analysis of Greenhouse Structure under Wind Load and Self-Weight
## 2 Description of Model and Analysis Method
### Description of Model and Analysis Condition  
In this study, a three-span Venlo-peach-type ventilated greenhouse with a floor area of approximately 560 m\({}^{2}\) is used, as shown in Figure 3 [19]. This model is designed to withstand a wind speed of 30 m/s. The detailed dimensions are shown in Table 1. The dimensions of the flow field domain for fluid dynamics analysis are shown in Figure 3 and Table 1. The flow analysis space is configured to have least eight times the length and at least four times the height of the greenhouse to minimize the effects of interfaces. The mass and momentum equations were solved for flow analysis, and the standard \(\kappa\)-\(\varepsilon\) model was solved to consider the turbulence model analysis with a high Reynolds number [20; 21]. The air temperature in the flow field was assumed to be 20 \({}^{\circ}\)C, the density of air was set as 1.207 kg/m\({}^{3}\), and the viscosity of air was set as 1.85 \(\times\) 10\({}^{-5}\) kg/ms. As the boundary conditions of the analytical model, the entrance was selected as a velocity inlet, the outlet was selected as a pressure outlet, and non-slip conditions were applied to the bottom area. Inlet velocity varied with height to reflect the fact that wind speed varies according to the roughness of the ground surface. The average velocity distribution according to the height of the entrance is  
\[u=0.186\times\text{log}\left(100\times h\right)+2.393 \tag{2}\]  
Figure 2: Probability density function and time series data of Korean island wind speeds: (a) frequency of wind speed with Weibull distribution (\(k\) is 1.664, \(c\) is 5.129); (b) time series data of wind speed (0.5 year data). Structural analysis is performed by applying self-weight and wind load independently and by applying self-weight and wind load simultaneously. Here, self-weight is a static load and wind is a dynamic load. When the combined force of wind and self-weight is applied, the stress generated in each can be written in the principle of superposition as  
\[\sigma_{etotal}=\sigma_{s}+\sigma_{w} \tag{3}\]  
where \(\sigma_{etotal}\) is compensated stress to fatigue estimation, \(\sigma_{s}\) is stress due to self-weight, \(\sigma_{w}\) is stress due to wind load. The stress due to the self-weight (\(\sigma_{s}\)) has a constant static stress, independent of time. Wind load, on the other hand, is a dynamic load (\(\sigma_{w}\)) that varies with time. Therefore, it is reasonable to compensation the stress due to the self-weight (\(\sigma_{s}\)) to the pre-stress because it is independent of the fatigue load data when the stress due to the dynamic load and the stress due to the static load act simultaneously. The structural stress model for fatigue analysis is configured by normalizing the structural analysis results by the square of wind speed. Fatigue is analyzed using the S-N (Stress versus the Number of cycles to failure) curve, which consists of a log-log plot. The S-N curve of zinc-plated SPSR 400, which is used in this study, is shown in Figure 5[22]. Furthermore, the Goodman method is used for mean stress compensation [23]. Typically, residual stress and local pre-stress are modified using material properties; however, this method is inappropriate when stress is distributed in a broad range, such as self-weight. In life estimation analysis, the wind induced stress can directly effect on calculate \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Part** & **Material** & **Density (kg/m3)** & **Elastic Modulus (MPa)** & **Poisson’s Ratio** \\ \hline Frame & SPSR400 & 7.85 \(\times\) 10\({}^{-6}\) & 203,000 & 0.30 \\ Al-Frame & Al alloy (BS1490) & 2.70 \(\times\) 10\({}^{-6}\) & 72,000 & 0.33 \\ Footing & Concrete & 2.40 \(\times\) 10\({}^{-6}\) & 28,600 & 0.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material properties of greenhouse structure. Figure 4: Finite element model of baseline design the three-span Venlo-peach-type greenhouse. the damage by rainflow counting of varying dynamic load.