## 2 Model of Beam-Column Subassemblage  
### Model Outline  
The PC beam-column connection focused on in this study is illustrated in Figure 2. It is an example taken from previous experimental specimens by the authors, which will be further covered in Section 4. The precast RC column and beam, which were separately fabricated, are attached by the interface mortar between them. The posttension forces are then applied to the debonded partial tendons located within a certain distance from the beam end, so the precast beam consists of a PC zone and an RC zone. Herein, the beam zone containing the prestressed debonded tendons is defined as the PC zone, and the beam zone without tendons is defined as the RC zone. By utilizing this type of connection, several benefits such as easier assembly, easier replacement of damaged members or tendons, and cost savings by the use of shorter tendons will be expectable.  
The strength and the deformation at the flexural ultimate state are calculated based on an analytical model, which is based on ideas from [21; 22] by the authors. The analytical  
Figure 2: Structural system of prestressed RC frame with debonded partial tendon.  
model shown in Figure 3 represents the beam and column member of an exterior beam-column connection of the PC frames with debonded partial tendons. As explained above, it is noted that the zone (\(l^{\prime}\)) with partial tendons is defined as the PC zone, and the zone (\(l\)-\(l^{\prime}\)) without tendons is defined as the RC zone. As shown in Figure 3, when a lateral force is applied to the frame, the beam rotates as a near-rigid body, while the main crack opening takes place at the beam-column interface. Minor cracks might also occur especially in the RC zone if the bending moment exceeds the cracking limit (\(M_{c}\)) of the RC zone. It is noted that in this study, the case of unyielding longitudinal reinforcement in the RC zone was mainly considered, because little residual deformation and self-centering behavior are desired.  
Focusing on the PC zone, resulting from the concrete strain in the extreme compression fiber along the PC zone (\(l^{\prime}\)), an axial shortening \(\Delta_{c,ex}\) concentrates at the beam-column interface. According to the condition of deformation compatibility, elongation of the tensile side tendon is equal to the crack-opening distance \(\delta_{d,tp}\) at the tendon location, and shortening of the compressive side tendon equals the concrete axial shortening \(\Delta_{c,tp}\) at the tendon location. In addition, according to the condition of force equilibrium, the tensile resultant force of the tendons at the beam end equals the compressive resultant force of the concrete.  
It is noted that, besides the debonded tendons, a small amount of longitudinal reinforcement is also arranged in the PC beams to hold the stirrups. In this study, for simplicity, the longitudinal bars are terminated at the beam end like the specimens described in Section 4.1. The effects of these bars on the bending moment at the beam end and the deflection of the PC beam are therefore ignored. In previous studies [18; 19; 20; 59], the longitudinal bars passed through the beam-column interface and were fixed inside the PC column, in order to improve energy dissipation capacity of the connection. In that case, the evaluation methods proposed in this study are also applicable by simple extensions.  
Figure 3: Analytical model of exterior beam–column connection subassemblage of PC frame with debonded partial tendons.  
The analytical model visualizes the distribution and interrelationship of various parameters at any beam section, including the deformations, internal forces, strains and stresses of concrete and tendons. As described in the later subsections, the deformation compatibility and force equilibrium conditions are established based on these parameters through this analytical model.