# Punching Shear Stress in Post-Tensioned Transfer Plate of Multi-Story Buildings
## 4 Analytical Model  
### Analytical Model Overview  
Since the purpose of this study was to analyze the shear behavior of the transfer plate, the height of the shear wall above the transfer plate was fixed to 20 stories and two representative apartment plans were selected as shown in Table 1. Table 1, (a) is a typical plan for the low-to-mid-rise apartment and Table 1, (b) is for high-rise apartments, respectively. Concrete strength was assumed to be 30 MPa for the transfer members, and 24 MPa for other members, such as shear walls and coupling beams.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Plan type** & & \\ \hline
**Column clear span** & 5.4–6.5 m & 3.5–6.6 m \\ \hline
**Column size** & & 1 m \(\times\) 1 m \\ \hline
**Concrete Strength** &
\begin{tabular}{c} Transfer members \\ (Transfer plate and columns) \\ Others \\ (Walls and beams) \\ \end{tabular} & 30 MPa \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of the analytic model.  
Figure 5: Calculation of direct shear and unbalanced moment at the slab-column connection.  
The thickness of the transfer plate is known to be proportional to the height of the superstructure [23]. The relationship between the thickness of the transfer plate and the height of the upper shear wall for seven design cases is shown in Figure 6. Since cases for post-tensioned transfer plate design are scarce, non-PT transfer plate cases are included in the relationship.  
The thickness of the transfer plate was assumed to be 1500 mm and 1300 mm for the post-tensioned transfer plates. For the post-tensioned transfer plate, a 15% reduction in thickness was assumed due to the application of prestress. The column span is commonly determined by the layout of the plan. In the case of an apartment, the underground portion is used for parking. Hence, the clear span is generally controlled by size of the parking module. In this study, a clear span of 3.5 to 6.6 m was assumed. To exclude the effect of column shape, a square column with a cross-section of 1 m by 1 m was also assumed.  
Since the purpose of this study was also to verify the analysis method for member design, linear-elastic analysis is conducted. In the numerical model, the columns and coupling beams are modeled with line element, and shear walls/core walls are modeled with thin shell element, which has in-plane and out-of-plane bending stiffness. The slab is also modeled with thin shell element and floor load of 3.0 kN/m\({}^{2}\) for superimposed dead load and 2.0 kN/m\({}^{2}\) for live load is applied on the slab.  
All elements, such as the shear wall, transfer plate and prestressing tendon, are modeled in the complete model (Figure 7a).  
Figure 6: Relationship between thickness of transfer plate and number of upper stories.  
Figure 7: Concept of two analysis modeling methods. (**a**) Complete model and (**b**) Separated model.  
Meanwhile, the separated model (Figure 7b) addresses only the transfer plate, prestressing tendon and the story of the transfer columns and core walls below. In the separated model, the shear wall above the transfer plate is replaced with an equivalent line load that is calculated based on axial force and in-plane moment of the shear walls.