## 5 Conclusions  
Liquid storage tanks are an essential category in the infrastructure of our modern society and industries. Damage to a liquid storage tank can be a major concern because it can lead to serious social and economic losses. Therefore, many researchers have investigated the dynamic responses of liquid storage tanks. Many studies have sought to investigate the fluid-structure interaction effects on the seismic performance of a liquid storage tank. However, the effects of fluid-structure interaction with the nonlinearity of the material have not been widely considered in seismic performance assessment, while determinations of the maximum hydrodynamic pressures induced by earthquake ground motion require, in principle, the use of a nonlinear dynamic (time-history) analysis, as specified in Eurocode 8 [25]. In this study, the earthquake responses of a concrete rectangular liquid storage on the surface of rigid soil were investigated with material nonlinearity taken into consideration. The material nonlinearity in concrete was considered using the concrete damage plasticity model. Because the rectangular structure has geometric asymmetry and given that the corresponding earthquake responses depend on the incident angle of three-directional earthquake ground motion, directional effects were examined in this study. From the dynamic analyses of a rectangular liquid storage tank subjected to three-directional earthquake ground motion, the following can be concluded:  
* The effects of material nonlinearity are significant when considering the earthquake responses of the system considered here. The displacement increases significantly due to the material nonlinearity. With the increased displacement, inclined cracks, which are typical for concrete structures such as slabs and plates, arise on the long-sided walls. The evolution of the tensile damage reflects the inclined cracks. The distributions of the section moments are also influenced by the inclined cracks. Reinforcing bars should be optimally placed in these areas after taking the inclined cracks into account. * The hydrodynamic pressure can be reduced significantly by the material nonlinearity. This reduction can also modify the base shear and overturning moment due to the hydrodynamic pressure and the resulting impulsive mass and its height in a simplified dynamic analysis of a liquid storage tank. Therefore, the material nonlinearity should be taken into account to ensure more accurate predictions of the hydrodynamic pressure applied to such a structure. * The time history of the sloshing height from the nonlinear analysis is nearly identical to that from the linear analysis. This is due to the fact that the convective mode of the fluid motion is adequately separated from its impulsive mode. Therefore, the material nonlinearity in the structure has negligible effects on the sloshing height. * The earthquake responses of a rectangular liquid storage tank are affected significantly by the incident angle of the earthquake ground motion. However, no consistent trend was noted in the responses of the displacement, hydrodynamic pressure, or sloshing height. Therefore, it is necessary to consider the directionality of the input ground motion for reliable predictions of the earthquake responses of such a system. * The evolution of the tensile damage shows very similar patterns in the analyses at various incident angles of earthquake ground motion. However, it should be noted that the times at which one or both long-sided walls become damaged strongly depend on the incident angle. It can be concluded from these observations that a rigorous inelastic analysis must be considered to predict accurately the earthquake responses of a rectangular liquid storage tank. * The profiles of the hydrodynamic pressure are significantly influenced by the incident angle of the input ground motion.