## 4 Numerical Modeling and Methodology
### Case-Study Frames
The current investigation reveals that, even within these material constraints, the ACPH mechanism is proficient in redirecting inelastic deformation away from the concrete and into the replaceable steel plates. Consequently, the structural integrity of the frame is maintained. Although the present modeling framework is focused on deficient systems, the ACPH concept is not limited to these parameters and can be easily adapted to modern frames by modifying the steel grade hierarchy and plate thickness to align with improved base material characteristics. The design of the columns features symmetrical arrangements of longitudinal steel positioned around the edges of the cross section. This approach facilitates a homogeneous confinement zone, mitigates flexural distortion resulting from eccentric axial loads, and maintains uniform stiffness in relation to each principal axis. Specifically, twelve longitudinal bars, each measuring 20 mm in diameter, are distributed in evenly spaced clusters along the perimeter. Conversely, the beams within these precast frames incorporate three longitudinal reinforcements of 20 mm diameter at both the top and bottom, along with four additional 20 mm bars situated in the middle segment. A schematic illustration of the reinforcements is given in Figure 7. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Concrete Class**} & **Characteristic Compressive Strength (MPa)** & **Equivalent Cube** & **Characteristic Axial** & **Modulus of** \\  & **Compressive Strength (MPa)** & **Compressive Strength (MPa)** & **Tensile Strength (MPa)** & **Elasticity at 28 Days (MPa)** \\ \hline C20 & 20 & 25 & 1.4 & 27,386 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical properties of the concrete. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Steel Class**} & **Minimum Yield Strength (MPa)** & **Minimum Tensile Strength (MPa)** & **Minimum Elongation at Failure (\%)** & **Modulus of Elasticity (MPa)** \\ \hline B250 & 250 & 300 & 0.08 & 200,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mechanical properties of the reinforcing steel. The design methodology has yielded the specified ACPH configuration. The cross-sectional dimensions of the ACPH element are 25 cm by 40 cm, aligning with the measurements of the beam. Additionally, the length of the ACPH element and its placement concerning the column surface were determined based on the height of the beam, following the guidelines established in the cited article. This analysis aims to evaluate the efficacy of the ACPH method in enhancing the seismic performance of PRC frames subjected to significant ground motions. This is achieved by modeling and analyzing four distinct frame configurations: 1B1S, 1B2S, 2B1S, and 2B2S, both with and without the installation of the replaceable hinge connectors at the beam-column junction. Figure 8 depicts four distinct finite element models (FEMs) that exclude the ACPH, each showcasing a unique arrangement of precast frames with varying structural configurations. The same figure also includes an FEM representation of the same frames integrated with the ACPH. Conversely, a meshed depiction of the ACPH is presented in Figure 9. By comparing the dynamic responses and deterioration between frames that utilize ACPHs and those with conventional precast joints, the research elucidates the capability of this specialized hinge subassembly to localize damage more effectively while improving the overall ductility of the structures during intense seismic activity. This comparative methodology allows for the precise identification of whether the ACPH successfully redistributes plastic deformations away from critical elements such as beams or columns into a replaceable segment, thereby reducing the long-term damage potential to the primary concrete components.