## 3 Experiments on Connections
### Connection Test Results  
The moment-rotation curves of each specimen are shown in Figure 8, and the experiment results, including maximum load, displacement, energy absorption, and failure modes, are listed in Table 2. The displacements were measured when the loads reached their peak, and the energy absorption was calculated by integrating the hysteresis curves in Figure 8. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Cycle** & **1–12** & **13–26** & **27–32** & **33–38** & **39–42** \\ \hline Displacement (mm) & \(\pm\)1.5\(\sim\)\(\pm\)9.0 & \(\pm\)12.0\(\sim\)\(\pm\)30.0 & \(\pm\)36.0\(\sim\)\(\pm\)48.0 & \(\pm\)57.0\(\sim\)\(\pm\)75.0 & \(\pm\)87.0\(\sim\)\(\pm\)99.0 \\ \hline Drift Ratio (\%) & \(\pm\)0.17\(\sim\)\(\pm\)1.01 & \(\pm\)1.35–\(\pm\)3.36 & \(\pm\)4.04–\(\pm\)5.38 & \(\pm\)6.39–\(\pm\)8.41 & \(\pm\)9.76–\(\pm\)11.1 \\ \hline Velocity Increment (mm/s) & \(\pm\)0.06 & \(\pm\)0.12 & \(\pm\)0.24 & \(\pm\)0.36 & \(\pm\)0.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Loading program of the component test. Figure 5: Components test setup. Figure 6: Stress contour of connection joints. Figure 7: Loading program. BC1 experienced premature failure owing to fatigue at 0.045 rad, displaying elastic behavior up to a lateral displacement of 4.86 mm before a fracture at the connection occurred at a displacement of 32.94 mm, with a maximum load of 93.20 kN. The energy absorption was 8580.68 kJ. BC2, with a connection of 105 mm longer than that of BC1, exhibited lateral buckling at a rotation of 0.024 rad without plastic hinge yielding, reaching a maximum displacement and load of 17.66 mm and 59.95 kN, respectively. The energy absorption was 5244.23 kJ which was a 38.88% decrease from BC1. BC3 was reinforced with stiffening plates from BC2 to enhance the circular tube section at the connection part. Local buckling was also observed on the connection plate when the curvature was 0.012 rad; however, plastic hinge yielding was observed. The maximum load was 52.39 kN, with both elastic and plastic behaviors observed in the lateral displacement up to 7.16 mm and 17.54 mm, respectively. The energy absorption was 1850.88 kJ. BC4 featured a dog bone-shaped detail design to induce a plastic hinge at the bracing member. Stiffeners with proper flexural stiffness were welded to this detail to prevent local buckling. While failure owing to fatigue at the connection point was not observed, plastic behavior was initiated at \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & **Max. Load** & **Displacement** & **Energy Absorption** & **Failure Mode** \\  & **(kN)** & **(mm)** & **(kJ)** & **Failure Mode** \\ \hline BC1 & 93.20 & 32.94 & 8580.68 & Fatigue failure of welding part \\ \hline BC2 & 59.95 & 17.66 & 5244.23 & Lateral buckling without plastic hinge yielding \\ \hline BC3 & 52.39 & 9.26 & 1850.88 & Lateral buckling after plastic hinge yielding \\ \hline BC4 & 14.14 & 74.44 & 4492.59 & No failure with plastic hinge yielding \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experiment results of connection specimens. Figure 8: Moment–rotation curves of the connections. a curvature of 0.106 rad. The specimen demonstrated ductile behavior until 74.44 mm of lateral displacement, with a maximum capacity of 14.14 kN. Utilizing the test results of the SMP shown in Figure 2(b), the rotation of the bracing was calculated by assuming a linear relationship between the lateral displacement and rotation. The strain history is based on the rotation from the lateral displacement of the SMP. The drift ratio is defined as the ratio of maximum lateral drift to the total height of the specimen. The strain history of the connection plate for all specimens based on the rotation of the bracing is shown in Figure 9. BC1 demonstrated a lower strain at the connection plate compared with that at the welded part of the column, resulting in column fracture.