## 3 A Demonstration of the Proposed Framework: A Case Study
### Prototype Building Description  
A comparative case study was performed on three four-story PC frame buildings located in Sendai, Japan. These buildings differ in their level of prefabrication and are labeled as follows:  
1. A cast-in situ PC frame;
2. A partially precast PC frame (50% PCa, with only precast stair components);
3. A fully precast PCaPC frame with MT connection (100% PCa). All three buildings were based on a common prototype layout adapted from [PERSON] and [PERSON] [33], and were designed according to Japanese seismic provisions. The buildings  
Figure 8: Configuration of PCaPC joint with MT connection. are assumed to be located on stiff soil with a ground amplification factor of 0.85, as obtained from the J-SHIS database. Each frame shares the same structural plan, consisting of a longitudinal span of 7.5 m and a floor height of 4.0 m. The boundary frame members are identical across the three models in terms of cross-sectional dimensions, concrete strength, and prestressing parameters. This ensures that any differences in recovery performance are attributable solely to the degree of prefabrication and connection type, rather than structural or material variations. In particular, the PCA 50% PC structure incorporates precast stair elements while all other components remain cast in place. An elevation view illustrating the geometric configuration of the prototype structure is provided in Figure 9.  
The seismic analysis focused on the structural response in the north-south direction, modeled as a two-dimensional frame. To capture the behavior of MT joints under seismic loading, a nonlinear component-end spring model was developed. This spring model idealizes the restoring force characteristics of the MT joint, which were derived from previous finite element analyses by [PERSON] and [PERSON] [33]. These analyses demonstrated that the MT joint exhibits a three-stage behavior involving joint closure, hinge relocation, and self-centering. Critical nonlinearities, including localized concrete crushing, gap opening, and frictional slip, were captured and translated into equivalent hysteretic parameters for the spring model. Structural response simulations were performed using the Newmark-\(\upbeta\) method in a time-history framework, where restoring force curves were assigned to each component based on either simplified elastic-plastic assumptions or nonlinear hysteretic input depending on the connection type. This modeling strategy enables the efficient simulation of time-dependent functional recovery while preserving the essential nonlinear characteristics required for accurate seismic loss estimation. The structural response results, particularly inter-story drifts and floor accelerations, served as EDPs to evaluate component-level damage. These damage assessments formed the basis for grouping components into performance groups and modeling their time-dependent functional recovery. To evaluate post-earthquake building functionality, the major components of the prototype structure were grouped into 22 distinct performance groups, as summarized in Table 3. These groups included both structural elements (e.g., columns, beams, and MT connections) and nonstructural systems (e.g., prefabricated stairs, electrical panels, HVAC units, elevators, and ceiling components), and were categorized based on their primary functional role (e.g., structural safety, vertical access, or environmental control). Figure 9: The geometric elevation of the prototype structure. Each performance group is associated with a specific engineering demand parameter (EDP) such as the inter-story drift ratio or floor acceleration, depending on whether the component is displacement-sensitive or acceleration-sensitive. The median thresholds listed in the table represent the typical onset of damage at a particular demand level and were derived by referencing fragility parameters available in FEMA P-58, complemented by recent experimental [47] findings on PCaPC components with MT connections.