## 5 Conclusions  
This paper presents predictive equations for shear spring parameters that can be incorporated into fiber-section elements to more accurately capture the behavior of RC columns with non-conforming section details. In addition, seismic fragility assessments were conducted on an example structure utilizing the proposed shear spring model. The most important findings are summarized below.  
Predictive equations for shear spring parameters, encompassing shear behavior, cyclic degradation, and pinching effects, were developed based on the physical properties of RC columns. While the predictions for backbone curve parameters exhibited good accuracy, those for pinching and degradation parameters showed relatively lower accuracy.  
Comparative analysis with existing models revealed superior performance of the proposed model in predicting key hysteretic parameters, including peak force, initial stiffness, and cumulative energy dissipation. Notably, the highest accuracy and consistency were observed for peak force and initial stiffness predictions, demonstrated by the lowest standard deviations.  
Seismic fragility assessments of non-conforming RC frames revealed a significant disparity in damage probabilities between models with and without shear springs. Models without shear springs tended to overestimate structural performance, emphasizing the crucial role of shear springs in accurately assessing the seismic performance of non-conforming RC frames.  
Therefore, the proposed parameter prediction equations enable the simulation of the shear behavior of non-conforming RC columns with reasonable accuracy, forming a basis for more realistic seismic performance evaluations of RC frames. Furthermore, these equations could have practical applications in guiding the development of more reliable design and retrofitting strategies for non-conforming RC structures.  
However, the proposed model is based on a limited dataset of experimental results, which may constrain its predictive accuracy. Future research should prioritize expanding the experimental database, particularly for RC columns with diverse geometric properties. Additionally, refining data collection methodologies and incorporating advanced simulation techniques could further enhance the model's robustness and applicability. These efforts will be crucial for elevating the proposed model's utility and ensuring its practical contribution to the fields of structural performance evaluation and seismic design.  
Figure 19: Seismic fragility curves for shear and flexural models: (**a**) seismic fragility curves; (**b**) difference of probability in individual limit states.  
**Author Contributions:** Conceptualization, W.J.H. and S.J.K.; methodology, W.J.H. and S.J.K.; software, W.J.H.; validation, W.J.H. and S.J.K.; formal analysis, W.J.H. and S.J.K.; data curation, W.J.H.; writing--original draft preparation, W.J.H.; writing--review and editing, S.J.K.; visualization, W.J.H.; supervision, S.J.K.; project administration, S.J.K.; funding acquisition, S.J.K. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was supported by the Bisa Research Grant (No. 20220243) of Keimyung University in 2022.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Dataset available upon request from the authors.  
**Conflicts of Interest:** The authors declare no conflicts of interest.