## 3 Predictive Equations for Shear Spring Parameters
### Verification of Proposed Equations  
Figures 8 and 9 illustrate the application of the predicted parameters to the analysis of the collected column specimens. Figure 8 exhibits a close agreement between the predicted and experimental results, underscoring the efficacy of the predictive parameters in capturing the member response. The results using the proposed prediction equations simulate flexural (Figure 8a,d), flexural-shear (Figure 8f), and shear (Figure 8b,c,e) behaviors well. However, as shown in the statistical comparison in Figure 7, differences due to the errors in the degradation parameters were observed, but these errors are not considered significant enough to affect the performance evaluation results. Figure 9, on the other hand, presents cases where the predicted behavior deviates from the experimental results. Figure 9a represents a case where pinching behavior is not adequately captured, potentially due to limitations in predicting pinching parameters. In Figure 9b, the backbone curve parameters are computed with a notably low value, leading to an underestimation of maximum strength. Figure 9c-f show cases where the predicted performance degradation is more rapid than that observed in the experiments, resulting in a lower capacity. These discrepancies can be partly attributed to the higher variability associated with predicting pinching and degradation parameters, as evident in Figures 6 and 7. Figure 7: Statistical comparison of the errors between predicted and calibrated parameters. Note: The red cross represents an outlier. Figure 8: Comparison experimental results (gray solid line) with analytical predictions (blue solid line) using the proposed equations for well-matched cases: (**a**) tana90u5; (**b**) nag1063; (**c**) betrino11; (**d**) saatu3; (**e**) ly3 clh18; and (**f**) sezen2. Figure 9: Comparison experimental results (gray solid line) with analytical predictions (blue solid line) using the proposed equations for poorly matched cases: (**a**) oh4d13 rs; (**b**) tímai86; (**c**) zho11408; (**d**) umecus; (**e**) saatu4; and (**f**) ly2 clh18. Figure 10 and Table 1 present the statistical comparison between the experimental data, the calibrated model, and the predicted model. Many experimental studies on the seismic performance of structural members terminate testing when member strength decreases by 60% to 80% compared to its peak strength. However, for the calculation of performance metrics such as ductility ratio, the ultimate deformation is typically defined as the deformation when the reduced strength reaches 80% to 85% of the maximum strength on the backbone curve [32; 33; 34; 35; 36]. Additionally, in cases where significant strength reduction (up to 60%) is observed in the specimen, it is often assumed that the member has failed, and its subsequent behavior has negligible impact on the structural performance. Therefore, in this study, statistical comparisons between experimental and predicted results were primarily focused on data points up to 60 to 80% of the maximum strength of the specimen. The calibrated model exhibits good agreement with the experimental data for maximum and minimum forces as shown in Table 1 and Figure 10. The median values for maximum and minimum forces are 1.006 and 1.023, respectively, with relatively low standard deviations of 0.046 and 0.075. However, the median value of 0.868 for initial stiffness suggests a tendency for the calibrated model to underestimate the initial stiffness. The median for accumulated energy is 1.074, closely approaching unity. The predicted model, based on Equations (12)-(23), shows similar trends to the calibrated model for maximum and minimum forces, with median values of 0.981 and 0.971, respectively, when compared to the experiment data. However, the predicted model exhibits a more pronounced underestimation of accumulated energy, with a median value of