## 3 Test Results and Analysis
### Stiffness Degradation  
The internal damage of concrete accumulates under cyclic loads, resulting in cracks. The slip between concrete and reinforcement increases gradually, and the stiffness of the specimen continues to decrease. The stiffness of the beam-column connections was represented using the secant stiffness (\(K_{\text{i}}\)):  
\[K_{\text{i}}=(F_{\text{i}}{}^{+}-F_{\text{i}}{}^{-})/(\Delta_{\text{i}}{}^{+}- \Delta_{\text{i}}{}^{-}) \tag{2}\]  
where \(F_{\text{i}}{}^{+}\) and \(F_{\text{i}}{}^{-}\) are the positive and negative peak load in the ith cycle, and \(\Delta_{\text{i}}{}^{+}\) and \(\Delta_{\text{i}}{}^{-}\) are the positive and negative peak displacement in the ith cycle.  
The five specimens' stiffness degradation trends were similar, as shown in Figure 15. Due to the tightening of the actuator anchor rod and ground anchor bolt during the test process, specimens showed rapid increases in stiffness after the actuator loading surface was in close contact with the loading beam surface. Before specimens yielded, many cracks initiated and developed, and the stiffness decreased rapidly with the increase in displacement. After the specimens yielded, the stiffness degradation gradually slowed, there were fewer new cracks, and the specimens' stiffness curves tended to be consistent.  
Although the assembled specimens had weak regions due to secondary pouring, their initial stiffness was higher than that of XJ. This showed that the integrity of MRPC-assembled connections was excellent. The initial stiffness of SFZP-3 and SFZP-2 was relatively large, indicating that MRPC with end-bent steel fibers had relatively good resistance to deformation. SFZP-3's initial stiffness was the largest because SF-3 was easier to stir, and its distribution of fibers was more uniform. In the later loading stage, because it was short, the steel fiber pulled out and withdrew from the sample, and the rate of stiffness decline obviously increased. The stiffness degradation of the MRPC with 30 mm end-bent steel fibers more effectively delayed crack development during the entire loading process and, to a certain extent, reduced damage accumulation. SFZP-4's initial stiffness was only slightly higher than that of XJ. It might be that the interface bonding between MRPC and the assembled beam was relatively poor, which reduced the specimen's stiffness.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Specimen Number**} & \multirow{2}{*}{
\begin{tabular}{c} **Loading** \\ **Direction** \\ \end{tabular} } & \multicolumn{2}{c}{**Yield Point**} & \multicolumn{2}{c}{**Ultimate Point**} & \multirow{2}{*}{\(\mu\)} \\ \cline{3-3} \cline{5-6}  & & \(P_{\mathbf{y}}\) & \(\Delta_{\mathbf{y}}\) & \(P_{\mathbf{u}}\) & \(\Delta_{\mathbf{u}}\) & \\  & & **(kN)** & **(mm)** & **(kN)** & **(mm)** & \\ \hline \multirow{4}{*}{XJ} & + & 25.3 & 19.3 & 24.6 & 81.9 & 5.1 \\  & \(-\) & 25.3 & 11.2 & 19.8 & 81.9 & 6.8 \\  & Average & 25.3 & 15.3 & 22.2 & 81.9 & 6.0 \\  & \(+\) & 21.6 & 13.2 & 37.8 & 148.7 & 11.3 \\ SFZP-1 & \(-\) & 26.6 & 22.1 & 29.9 & 148.1 & 6.9 \\  & Average & 24.1 & 17.7 & 33.9 & 148.4 & 9.1 \\  & \(+\) & 21.4 & 13.0 & 34.2 & 163.8 & 12.6 \\ SFZP-2 & \(-\) & 23.9 & 14.2 & 37.6 & 163.2 & 11.4 \\  & Average & 22.7 & 13.6 & 35.9 & 163.5 & 12.0 \\  & \(+\) & 23.3 & 11.7 & 38.6 & 143.7 & 12.2 \\ SFZP-3 & \(-\) & 24.8 & 16.8 & 30.1 & 143.7 & 8.5 \\  & Average & 24.1 & 14.3 & 34.3 & 143.7 & 10.4 \\  & \(+\) & 21.9 & 14.9 & 36.4 & 142.7 & 9.5 \\ SFZP-4 & \(-\) & 22.9 & 19.6 & 28.7 & 142.7 & 7.3 \\  & Average & 22.4 & 17.3 & 32.5 & 142.7 & 8.4 \\ \hline \end{tabular}
\end{table}
Table 8: Loads and displacements of specimens at feature points.  
The end-bent steel fibers will increase the initial stiffness of MRPC assembled connections, while the wavy steel fibers will slow down the stiffness degradation rate of MRPC specimens before yielding.