## 5 Demonstration of Machine Learning Model
### Shear Demand Curve  
The shear demand curves for reinforced concrete columns are derived through nonlinear static pushover analysis, considering flexural behavior without shear failure. The model depicting flexural behavior incorporates the non-elastic response of the material, the effect of the confinement pressure resulting from transverse reinforcement, and the effects of bond-slip failure. To calculate shear demand curves for different failure types, a process to determine the bond-slip failure parameters is essential. Therefore, we developed models based on different failure types and validated the modeling methodology using results from past experimental studies [1; 2; 3]. In this study, the column models reproduced three failure modes (flexural, flexure-shear, and shear failure) and assumed the bond-slip failure at the ends of the column regardless of the failure modes. The column failure modes are classified into flexural failure, flexural-shear failure, and shear failure, and bond-slip failure occurs regardless of the failure type. After application of an axial load that was the same as in previous experimental studies of the column model, the lateral cyclic load at the top of the column was set using the displacement control option. Figure 6 shows the details of the flexural behavior model. If using the double bending model, the boundary conditions were specified as fixed and sliding; for the single bending model, they were set as fixed and free. Columns were modeled using elastic beam-column elements, and plastic hinge regions were represented using displacement-based nonlinear beam-column elements with four integration points. The length of the plastic hinge region was set equal to the height of the column cross section, based on the analytical model by [PERSON] et al. [23]. Emphasis was placed on incorporating the deformation in the column into the analytical results by establishing the plastic hinge. The Concrete02 material model was used to construct the fiber sections of the nonlinear beam-column elements. To account for the enhanced concrete compressive strength and ductility in areas confined by transverse reinforcement (confined concrete), the model proposed by [PERSON] et al. [24] was utilized. The material model for the longitudinal reinforcement was the Steel02 material model, which allows for strain hardening. Figure 6: Flexure-governed column modeling method. Bonding failure in RC columns occurs when the bonding stress between the rebar and concrete exceeds the allowable bonding stress, leading to failure, which typically occurs at the top and bottom of the column where lap splices are located. In the flexure failure model, zero-length section elements were applied at the top and bottom of the column to incorporate bonding failure. The fiber sections of these zero-length section elements are identical to those in the column, but the material model is changed from a stress-strain relationship to a stress-slip relationship. The stress-slip relationship was applied using Equations (7) and (8), as presented by [PERSON] [25]. \[slip_{y}=\frac{e_{y}f_{y}\phi_{c}}{8u_{e}} \tag{7}\]  
\[SF_{slip}=\frac{slip_{y}}{e_{y}} \tag{8}\]  
Here, \(slip_{y}\) is the yield slip for bonding failure (mm), \(\epsilon_{y}\) is the yield strain of the longitudinal reinforcement, \(f_{y}\) is the yield stress of the longitudinal reinforcement (MPa), \(\Phi_{c}\) is the diameter of the longitudinal reinforcement (mm), \(u_{e}\) is the elastic bonding stress (MPa), \(f_{c}\) is the concrete compressive strength (MPa), and \(SF_{slip}\) is the bonding failure variable. The strain in the rebar and concrete material models is multiplied by the bonding failure variable (\(SF_{slip}\)) to enable the use of the stress-slip relationship material model in the zero-length fiber sections. Figure 7 depicts the details of the model used to determine shear failure.