# Understanding the Seismic Resilience of Metallic Cylindrical Tanks Through Parametric Analysis
## 6 Conclusions  
To determine the transition zone between rigid and flexible tank idealizations, the trend of hydrodynamic pressures exerted by the fluid on the tank wall during an earthquake has been extensively studied. Specifically, the seismic response of open-top steel tanks, both with rigid and deformable walls, fully anchored at the base, is analyzed. Understanding hydrodynamic pressures is critical because they directly influence the circumferential stresses in the steel shell, which can lead to shell buckling. The importance of selecting a rigid or flexible tank idealization lies in the potential for under- or over-estimating hydrodynamic pressures compared to actual values, which impacts the accuracy of the seismic analysis. After calibrating the model with two experimental tests, 50 transient explicit analyses were performed using LS-DYNA software ver. 9 to generate the envelopes of hydrodynamic pressure profiles for ten different configurations of \(H/R\) slenderness ratios and five configurations of \(R/t\) ratios. The seismic responses obtained from the numerical analyses were then compared with the design predictions from the AWWA, EC8-4, and NZSEE standards. Given the differences in assumptions regarding rigid or flexible tanks and the complexity of the design methodologies in the international standards, the goal of this research was to investigate the prediction of hydrodynamic pressures to provide more accurate seismic analysis and design recommendations for above-ground cylindrical tanks. Key conclusions from the study are outlined below:  
1. NZSEE Method: This method is relatively complex as it requires the use of advanced mathematical tools such as Bessel functions and the solution of \"heavy\" equations. While initially developed for rigid tanks, the NZSEE method was extended to flexible tanks with minimal modification, resulting in discrepancies between predicted and observed responses. 2. EC8-4 Method: This method is the only one that accounts for the influence of tank wall deformability. However, it is highly complex, as it requires an iterative procedure, and FE analyses are always necessary for accurate results. 3. AWWA Method: This is the simplest of the three methods but does not account for the flexibility of the tank wall. Additionally, it is based on an admissible stress design approach, and the choice of the force reduction factor used in the calculations remains debatable, as no unanimous consensus can be gathered on it. 4. The comparison of the methods proposed in the three standards reveals that differences between the results can be quite large when considering the various contributions. However, these differences become less significant when evaluating the total pressures. This is due to the fact that the amplitude of hydrodynamic pressures is generally lower than that of the hydrostatic pressures. Specifically, for slender tanks, the influence of hydrodynamic pressures is sufficiently diminished. While variations of around 10% were observed between the total pressure profiles computed using the different methods, variations in the order of 25-30% were found in the impulsive contributions. 5. The previous comments, along with the subsequent considerations regarding the parametric sensitivities and the various ratios involved in the analyses, such as radius, height, thickness, as well as rigid vs. flexible and slender vs. squat configurations, lead to the most important result summarized in Figure 13. This figure provides guidance on the selection of flexible versus rigid tanks, depending on the \(H/R\) (height-to-radius) and \(R/t\) (radius-to-thickness) ratios. The figure offers valuable insights into how the tank's geometric properties influence the decision to adopt a flexible or rigid model for seismic design, helping to optimize safety and performance based on the tank's specific characteristics. 6. Explicit dynamic nonlinear analyses were conducted to accurately reproduce the FSI problem.