## 4 Results and Discussion
### Effects of the Higher Sloshing Modes on the Sloshing Response
#### 4.4.5 Sloshing Response at the Corner of the Tank  
It has been demonstrated in the previous sections that at different sloshing frequencies of the tank, the sloshing response in the middle of the tank walls (\"a\" and \"b\") is highly sensitive to the value of the spectral acceleration of the external load. Accordingly, extending the results to the corner of the tank, the critical sloshing location [38] is of great importance. It is worth noting that the maximum sloshing response in the liquid storage tank occurred at the corner of the tank under both loading conditions (Table 11 and Figure 8). Unlike the vertical earthquake component, which has been shown to have a negligible effect on the sloshing response [72], the two horizontal components, the major and the minor components, accounted for the sloshing response at the corner of the tank. Therefore, it seems to be essential to study the sensitivity of the sloshing response at the corner of the tank to the major and minor horizontal components and their combination. As shown in the previous sections, under both loading conditions, the spectral acceleration at the first sloshing period (1 st mode) was closely related to the maximum sloshing response for both major and minor earthquake horizontal components. Regarding S1, it has also been indicated that increasing the value of the spectral acceleration of the major earthquake components at the first three odd sloshing periods of vibration (1, 3, 5) increased the maximum sloshing response in the middle of the shorter wall (\"a\"), perpendicular to the direction of the major component. It should also be considered that for S1 (major component), the R\({}^{2}\) scores for the first and the third sloshing periods were equal (0.95), indicating that these convective modes play an important role in the maximum sloshing response. In order to extend the results to the corner of the tank, the critical sloshing location, it is important to determine the predominant excitation component by which corner sloshing is most affected. Since the horizontal earthquake components were applied to the tank under two different loading conditions, S1 and S2, there are two different R\({}_{\text{dir}}\) ratios, one for each loading condition. The effect of changing this ratio, as well as the value of spectral acceleration at the first five sloshing periods on the maximum corner sloshing for both major and minor components under both loading conditions, is presented in this section. Corner Sloshing and Spectral Acceleration--S1  
According to Section 4.4.5, the three scatter plots, shown in Figure 14, show the relationship between the maximum sloshing response at the corner of the tank as a function of spectral accelerations at the first sloshing period of vibration for the major, minor, and combined components. The square root of the sum of squares (SRSS) method was used to combine spectral accelerations of the major and minor components. This combination method was recommended by [73] to estimate corner sloshing according to the sloshing height of each orthogonal direction. At first, the maximum sloshing responses of the tank under the selected earthquakes and their spectral accelerations were normalized, similar to the previous sections. A regression line was drawn for each scatter plot, and finally, the coefficient of determination (R\({}^{2}\)-Score) was calculated. Figure 14 shows the relationship between the maximum sloshing response at the corner of the tank and the spectral accelerations at the first sloshing period for the major, minor, and combined components under the first loading condition (S1). As shown in Figure 14, while there is an approximately linear relationship between the maximum corner sloshing and the spectral accelerations for the major and the combined components, the spectral acceleration for the minor component seems to have an insignificant effect on the corner sloshing. In this case, the ratio between the length of the major earthquake action and the minor one, R\({}_{\text{dirr}}\), is equal to 1.29.