## 1 Introduction
This approach combines fiber-section elements for flexural behavior, elastic rotational spring elements to represent bar-slip behavior, and translational spring based on the limit state material model to capture shear behavior. The degradation in axial capacity due to damage from shear behavior is simulated by applying the limit state material as an axial spring. [PERSON] et al. (2016) [21] presented a concentrated plasticity model utilizing the modified Ibarra-Medina-Krawinkler deterioration model [22] to represent member behavior through a rotational spring. [PERSON] and [PERSON] (2014) [15] proposed a model to capture the initial lateral strength degradation using rotation of the plastic hinge region at the column end. The flexural behavior of the column can be simulated using a fiber-section-based element model capable of representing both strength damage and stiffness damage. [PERSON] et al. (2015) [17] investigated the seismic fragility of RC frames, considering shear deformation in beam-column joints. Five different joint models were studied: rigid joint model, joint shear response without anchorage failure, joint shear response with anchorage failure, column shear response, and joint and column shear response. The rotational deformation of the joint panel zone was modeled using the Pinching4 material model [23] as a rotational spring. The shear behavior in the column was captured by the [PERSON] (2004) [13] model, implemented as a translational limit state model. To account for bar slip, a zero-length fiber-section element was employed in the model, effectively capturing the bond-slip behavior between reinforcing bars and concrete. [PERSON] and [PERSON] (2021) [18] conducted a seismic vulnerability assessment of RC bridges considering the influence of chloride-induced corrosion of shear-critical RC piers. The flexural behavior of the RC piers was modeled using a force-based beam-column element [24], which is based on the iterative force-based formulation. The bond-slip effect of the longitudinal rebar was represented using a rotational zero-length spring element. The behavior for three failure modes (flexural, flexural-shear, and shear failure) was implemented using translational spring elements, modifying the [PERSON] (2004) [13] model of the limit state material model [19; 20]. The aforementioned models aim to capture complex behaviors in RC members under cyclic loading, including strength and stiffness degradation, pinching effects, and other phenomena that are challenging to represent in traditional models. Effective implementation of shear springs relies on accurate parameters tailored to each RC member's characteristics. While many researchers have proposed equations to predict these parameters based on the properties of RC columns, limitations exist. These limitations encompass the inability to account for pinching effects [13; 14], difficulty in modeling stiffness or strength degradation due to cyclic loading [14; 15], and predictions that are often based on experimental data from flexural failure mode [14]. Consequently, these limitations can significantly hinder the accurate prediction of member behavior under seismic loads, especially for non-conforming RC columns. Hence, to address these challenges, this study proposes predictive equations for shear spring parameters to enhance the simulation accuracy of capacity degradation and pinching effect simulations in RC columns subjected to cyclic loading. Regression equations utilizing fundamental physical properties are provided to streamline parameter derivation for the Pinching4 [23] model within OpenSees [25], thereby reducing computational effort compared to existing methods. The effectiveness of the proposed predictive equations is validated through two numerical models: one incorporating the new shear spring parameters and another baseline model without them. These models are employed to evaluate the impact of shear deformation in vertical members on the seismic fragility of a non-conforming RC frame.