# Stability Evaluation of a Simplified Reclaimer Using Fluid-Structure Interaction
## 3 Results
This dual-level approach ensures that engineering design benefits from both computational efficiency and accuracy, aligning with the practical needs of the project development phases. For a wind speed of 52 m/s (Figure 15), the X force reached 1100 kN, 23% higher than the analytical force (850 kN), replicating the behavior of the 36 m/s analysis. The displacement was about 0.1 mm and the stability did not fail. For a wind speed of 68 m/s, considered critical in the analytical model (Figure 16), the ratio of the moments Em/Dm was still lower than 1.5. Similar to previous speeds, the forces predicted by the numerical model were higher than the forces predicted by the analytical model of 1450 kN; the numerical force was about 1900 kN, causing a maximum displacement of 0.17 mm. The stability did not fail in this case. For a wind speed of 84 m/s, the numerical predicted value for the force was about 2900 kN, 23% higher than the analytical predicted value. Although the destabilizing moment was higher than the stabilizing moment, the stability did not fail. Nevertheless, higher displacements were found, and a larger transient variation in the displacements. This may be attributed to differences in the real values of the stabilizing moment or phenomena not considered in the analytical evaluation. For a wind speed of 100 m/s (Figure 18), the general behavior of the previous results was repeated, with numerical forces higher than analytical forces. Also, the structure did not fail by stability. It can be seen that, after approximately 1 s of simulation, a higher displacement was reached. For a wind speed of 132 m/s (Figure 19), the average X force was about 7000 kN, 22% higher than the analytical value. In this case, the maximum displacement value was about 1.4 mm, and the stability failed due to reaction forces, as can be seen in Figure 6:4  
The system required 0.25 s to stabilize under a wind speed of 0 m/s. All the simulations were run by applying the prescribed wind velocity after this static analysis. The stability failure was defined by the determination of the reaction forces in the base of the reclaimer. The moment in the Z direction is caused by the misaligned wind forces on the mass center of the structure. The front part receives the dynamic pressure before the back part. The reaction forces in the supports of the reclaimer are shown in Figure 6:5 The forces are negative, indicating that the structure is being held by the supports. Stability fails when the reaction force over one of the supports reaches 0 N. In this case, the reaction force on the other support increases to the total dead load, and the reclaimer rotates to fall. As a summary, Table 2 presents a comparison between the analytical and numerical results for X forces at each evaluated wind speed. For all wind speeds, it is noticeable that the numerical results were higher than the analytical results. It is worth mentioning that the forces were not expected to be the same when comparing analytical and numerical results. This is because the analytical forces are predicted based on global parameters, such as the area of wind incidence, the distance between the wind load center and the support point, and the distance between the mass center and the support point. In contrast, the numerical forces were predicted for a specific reclaimer with defined dimensions. For the lower wind speeds (36, 52, 68, 84, and 100 m/s), an increase can be seen in the difference between the reaction forces on the front and back supports, but these forces \begin{table}
\begin{tabular}{c c c} \hline \hline
**Wind Speed (m/s)** & **Analytical X Force (kN)** & **Maximum X Force (kN)** \\ \hline
36 & 408 & 800 \\
52 & 850 & 1100 \\
68 & 1450 & 1900 \\
84 & 2233 & 2900 \\
100 & 3310 & 4300 \\
132 & 5460 & 7000 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison between analytical and numerical forces. stabilize over time. For the wind speed of 132 m/s, the reaction force on the front support reached 0 N and it was concluded that the structure failed by stability.