## 1 Introduction  
Seismic design standards have been continuously improved to mitigate potential earthquake damage to buildings in seismically active regions. Despite these efforts, a significant number of reinforced concrete (RC) structures, particularly those constructed before the implementation of modern seismic codes, remain vulnerable due to inadequate seismic design and detailing. In South Korea, for instance, seismic design codes were first mandated for new buildings in 1988 and have since undergone continuous revisions and expansions [1]. Consequently, RC members in older buildings often exhibit non-conforming cross-sectional details, such as widely spaced transverse reinforcements, the absence of seismic hooks, and insufficient anchorage length of stirrups [2, 3, 4]. These deficiencies can significantly compromise the ductility of RC members under seismic loads, increasing their susceptibility to brittle failure modes such as reinforcing bar rupture and shear failure [5]. Past earthquake damage consistently underscores the risks associated with such structures. To enhance the seismic performance of existing buildings and improve future designs, significant research efforts have been dedicated to developing effective retrofitting strategies and refining seismic design methodologies [6; 7; 8; 9]. Successful mitigation of earthquake damage necessitates a comprehensive understanding of the seismic behavior of such structures. This requires an accurate assessment of seismic demands and the identification of critical members that are most susceptible to damage through reliable analysis. However, accurately simulating the nonlinear shear behavior of RC members in analysis programs remains a challenge, which could significantly affect the accuracy of structural performance evaluations such as seismic fragility analysis. Seismic fragility analysis is a methodology used to evaluate a structure's vulnerability to specific ground motion levels by assessing the likelihood of the structure surpassing predefined damage thresholds [10; 11; 12]. The concept of seismic fragility functions was initially introduced in the 1970s for nuclear power plant containment structures and was further refined by [PERSON] and [PERSON] (1984) [11]. Subsequent research has extended this concept to various structures, including buildings and bridges [10; 12]. Seismic fragility functions serve as performance evaluation tools, quantifying the probability of specific damage states occurring in a target structure based on various ground motion parameters like peak ground acceleration (PGA), spectral acceleration (SA), and others. By evaluating a structure's seismic performance considering diverse ground motion parameters, it becomes possible to rapidly anticipate potential damage to the structure during random seismic events. In general, seismic fragility functions provide a quantitative assessment of the response to ground motion using damage probability, offering predictions as they leverage nonlinear numerical models of the target structure. However, it is crucial to note that the probability of exceeding a damaged state relies on the outcomes of time history analysis with detailed nonlinear numerical models, which can be computationally expensive and challenging to generate with high fidelity. These limitations are particularly acute for RC structures with non-conforming details, where shear behavior plays a predominant role. To accurately evaluate the response of such structures, a reliable nonlinear numerical model for members exhibiting predominantly shear-critical behavior is crucial. While existing nonlinear analysis programs often face challenges in modeling this behavior, extensive research has been dedicated to developing shear spring models applicable to fiber-section and finite-length models [13; 14; 15; 16; 17; 18; 19; 20]. [PERSON] (2004) [13] proposed a model using a limit state material model to simulate the behavior of shear-critical RC columns.