## 4 Results and Discussion  
Static Hoop Strains and Strengthening Effects of CFRP Layers on the Restraint of Static Strain Values  
The static hoop strains of the specimens were recorded from strain gauges and were read using the data logger after placing all the steel balls into the tanks. These experimental values were compared to the theoretical calculations to estimate the replacement ability of steel balls for a normal liquid in dynamic experiments. The static hoop stress and hoop strain of the non-strengthened tanks could be calculated using Equations (19) and (20); meanwhile, the values of the strengthened specimens could be determined using Equations (21) and (22). The static hoop stress in the specimens in Equations (19) and (21) were calculated similarly with a normal liquid and the density of the normal liquid (\(\rho_{l}\)) being replaced by the density of the steel balls and multiplying it by the volume fraction of the steel balls (\(v_{s}.\rho_{s}\)). Two parameters, \(\rho_{l}\) and \(v_{s}.\rho_{s}\), have equivalent meanings because there are clearances between the steel balls, while there are almost no distances between liquid molecular particles. \[\sigma_{h}=\frac{v_{s}.\rho_{s}.g.h_{l}.d}{2t_{a}} \tag{19}\]  
\[\varepsilon_{h}=\frac{\sigma_{h}}{E_{x}} \tag{20}\]  
\[\sigma_{h}=\frac{v_{s}.\rho_{s}.g.h_{l}.d}{2h} \tag{21}\]  
\[\varepsilon_{h}=\frac{\sigma_{h}}{E_{x}^{\prime}}, \tag{22}\]  
In Equations (19)-(22), \(\rho_{s}\) is the density of the steel balls (\(\rho_{s}=7850\) kg/m\({}^{3}\)), \(v_{s}\) is the volume fraction of the steel balls (\(v_{s}=58.8\%\)), \(g\) is the acceleration due to gravity (\(g=9.81\) m/s\({}^{2}\)), \(h_{l}\) is the distance from the free surface of the steel ball to the calculated point (see Figure 5), \(d\) is the inside diameter of the tanks (\(d=588.8\) mm), \(t_{a}\) is the thickness of the aluminum shells, \(h\) is the total thickness of the CFRP-aluminum lamination, \(E_{x}\) is the circumferential elastic modulus of the aluminum tanks, \(E^{{}^{\prime}}_{x}\) is the circumferential elastic modulus of the CFRP-aluminum lamination, \(\sigma_{h}\) is the hoop stress of the tanks, and \(\varepsilon_{h}\) is the hoop strain of the tanks. Figure 11 shows the static hoop strains in the vertical direction (strain gauges 1 to 11) and Figure 12 shows these values in the horizontal direction (strain gauges 6 and 12 to 21). The experimental strain values were compared to the theoretical values. In Figure 11, \(z\) is the distance from the bottom steel plate to the calculated points (\(z=0\) at the bottom steel plate). It can be seen that the static hoop strains obtained from the experiments matched well with the theoretical calculations. A few differences were apparent at the top and bottom of the SNS specimen. This was because the SNS specimen was very thin; therefore, geometrical imperfection occurred after connecting the aluminum tank with the test rings (cylinder 1 and 2). The initially calculated results show that the hoop strain/stress created by the steel balls could be evaluated by using the theory of a normal liquid. Therefore, the use of steel balls, as a replacement for a normal liquid, is an equivalent way to create a higher internal pressure in testing. Table 9 shows the effects of CFRP layers on the restraint of the static hoop strain values for all specimens that were tested. The values of static hoop strains decreased from about 35% to 62% when using 0\({}^{\circ}\)/90\({}^{\circ}\) CFRP strengthening, whereas these values decreased from 48% to 65% for 0\({}^{\circ}\) CFRP strengthening. The results of the two bottom strain gauges were excluded because the measured values were unstable, which were caused by geometrical imperfections. Strengthening Effects of the CFRP Layers on the Restraint of Strain Values on the Tanks Under Dynamic Excitation  
Figures 13 and 14 show the sloshing behaviors of all the specimens that were filled to heights of 530 mm and 265 mm with steel balls, respectively.