## 4 Phenomenological and Statistical Analysis of Results
### Analysis of Stiffness Degradation and Strength Degradation  
Under cyclic loads, when the same peak load is maintained, the phenomenon that the peak displacement increases with the increase of the number of cycles is called stiffness degradation [27]. Stiffness is measurable via secant stiffness, represented using the equation of secant stiffness, denoted as K:  
\[K_{i}=\frac{\left|+P_{i}\mid+\right|-P_{i}\mid}{\left|+\Delta_{i}\mid+\right| -\Delta_{i}\mid} \tag{3}\]  
In this equation, \(+P_{i}\) is indicative of the load present at the forward peak point during the i-th cycle, while \(-P_{i}\) the load at the negative peak point under the same cycle.\(+\Delta_{i}\) and \(-\Delta_{i}\) represent the forward-peak-point displacement and the negative-peak-point displacement at the i-th level of loading respectively. Post-calculation, the stiffness degradation curve can be visualized in Figure 9.  
Our findings from five specimens were near-congruous in terms of overall stiffness and the degradation trends. The XJ-1 joint's complete stiffness smoothly transitions, with the initial stiffness of ZP-4 proving greater due to the inherent pipe, albeit with a high attenuation rate. ZP-2 demonstrates lower overall stiffness than the remaining joints, attributable to its shorter reinforcement length L, leading to shear failure in its core area. This outcome culminates in a lesser overall stiffness than that of the ZP-1 with longer L bars. Preservation of the steel pipe in the column can notably enhance the initial joint stiffness.  
Under cyclic loading, with the increase of the number of load cycles at the same level, the strength of the specimen decreases continuously, which is called strength degradation [28], typically estimated by the strength degradation coefficient \(\lambda_{i}\). The equation is as follows:  
\[\lambda_{i}=\frac{P_{j,max}^{i}}{P_{j,max}^{i-1}} \tag{4}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Joint Number** & \(\mathbf{S}_{(EFCH)}\) **(kN\(\cdot\)mm)** & \(\mathbf{S}_{(\Delta\)**OFM)** & \(\mathbf{S}_{(\Delta\)**OFN)** & **(kN\(\cdot\)mm)** & \(\mathbf{h_{e}}\) \\ \hline XJ-1 & 995.61 & 911.47 & 0.17 \\ ZP-1 & 696.83 & 839.81 & 0.13 \\ ZP-2 & 820.81 & 1065.43 & 0.12 \\ ZP-3 & 632.49 & 945.18 & 0.11 \\ ZP-4 & 890.53 & 919.56 & 0.15 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Equivalent viscous damping coefficient.  
Figure 9: Stiffness degradation curve.  
where \(P_{j,\ max}^{i}\) is indicative of the peak load of the hysteresis curve for the \(i\)-th cycle when the specimen load is at the j-th level. \(P_{j,max}^{i-1}\) represents the hysteresis curve's peak load for the \(i\)-1 cycle when the specimen is under load at the \(j\)-th stage. The strength degradation curve is shown in Figure 10.  
As displacement and load cycles amplify, the reinforcement of all specimens begins to yield. Periodically, characteristics such as the substantial fracturing of the concrete in the core area, serious damage in the plastic beam hinge area at the beam ends, and partial retreat from work lead to a decrease in joint strength. Additionally, due to the relative slip between concrete and longitudinal reinforcement, the joint strength proves irregular. Despite this, the strength of the five joints is stably maintained above 0.75. The strength degradation trend of cast-in-site joints and newly assembled joints show similar patterns, suggesting that the novel type of assembled joints possesses an excellent resistance to damage. However, the joint XJ-1 displays the most stable strength degradation. The new ZP-2 joint's strength experiences a sudden drop due to a large concrete wedge collapsing.