## 4 Test Results
### Demand and Capacity for Outward Force  
The outward-force-resisting capacity, considering both the outer and inner restrainers, was calculated and compared with the seismic demand of the restrainers, as presented in Table 4. The outward-force-resisting capacity was calculated by summing the resistances calculated using Equations (3) and (6). The outward force demand caused by the steel core was calculated using Equation (1), where the maximum compressive force measured for each test specimen was applied to \(N_{cut}\). The material strength was determined based on the results of the material tests. The ratio of the demand to the resisting capacity for the outward force is denoted as DCR (demand-capacity ratio) in Table 4. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{3}{*}{**Specimen**} & \multirow{3}{*}{\begin{tabular}{c} **Demand** \\ \(P_{d,w}\)**(kN)** \\ \end{tabular} } & \multicolumn{4}{c}{**Expected Resistance**} & \multirow{3}{*}{\begin{tabular}{c} **DCR** \\ **Restrainer** \\ \end{tabular} } \\  & & \begin{tabular}{c} **Outer** \\ **Restrainer** \\ \end{tabular} & \begin{tabular}{c} **Inner** \\ **Restrainer** \\ \end{tabular} & \begin{tabular}{c} **Sum** \\ \(P_{c,w}\)**(kN)** \\ \end{tabular} & \
\begin{tabular}{c} **Increase Rate** \\ **(\%)** \\ \end{tabular} &
\begin{tabular}{c} **\(P_{d,w}\)**/\(P_{c,w}\)** \\ \end{tabular} \\ \hline NR-T6 & 94 & 42.1 & NA (\({}^{1}\)) & 42.1 & NA & 2.23 \\ \hline R-T6S4 & 137 & 42.1 & 82.7 & 125 & 196 & 1.08 \\ \hline R-T6S4-G & 136 & 42.1 & 82.7 & 125 & 196 & 1.09 \\ \hline NR-T9 & 139 & 103 & NA (\({}^{1}\)) & 103 & NA & 1.35 \\ \hline R-T9S4 & 136 & 103 & 82.7 & 185 & 80 & 0.732 \\ \hline R-T9S2 & 150 & 103 & 30.7 & 133 & 30 & 1.13 \\ \hline R-T9S4-G & 103 & 103 & 82.7 & 185 & 80 & 0.558 \\ \hline R-T9S2-G & 133 & 103 & 30.7 & 133 & 30 & 0.994 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Outward force demand and resisting capacity of restrainers. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{3}{*}{**Specimen**} & \multicolumn{4}{c}{**For Completed Cycles**} & \multicolumn{4}{c}{**For Entire Test**} \\ \cline{2-5}  & **Compression (kN)** & **Tension (kN)** &
\begin{tabular}{c} **Compression** \\ **/Tension** \\ \end{tabular} & **Compression (kN)** & **Tension (kN)** \\ \hline R-T9S4 & 1484 & 989.7 & 1.50 & 1484 & 989.7 \\ \hline R-T9S4-G & 1439 & 992.6 & 1.45 & 1439 & 992.6 \\ \hline R-T9S2 & 1298 & 1029 & 1.26 & 1298 & 1029 \\ \hline R-T9S2-G & 1351 & 984.7 & 1.37 & 1351 & 984.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._Because bulging failure occurred in all of the specimens, the DCR should be close to 1. For NR-T6, the DCR was 2.75, which was significantly greater than 1 because the inner restrainer was not installed in the specimen. For NR-T9, the DCR was 1.26, which was also greater than 1 but considerably lower than that of NR-T6 owing to the increased thickness of the outer restrainer. The DCR was overestimated because of the following reasons. First, the outward force demand was overestimated upon neglecting the resistance of the bending moment against a couple caused by the higher-mode buckling of the steel core, as shown in Figure 1b. Second, the outward-force-resisting capacity was underestimated upon neglecting the contribution of the mortar filler. Most of the enhanced specimens exhibited a DCR greater than or close to 1; however, the DCRs of R-T9S4 and R-T9S4-G were significantly lower than 1. In these cases, the outward-force-resisting capacity might have been somewhat overestimated because bulging occurred at the end of the inner restrainer where the resistance to the outward force could not be fully achieved, as discussed in Section 4.2. The DCR would have been higher than or close to 1.0 if the bulging failure had occurred sufficiently far from the end of the inner restrainer.