# Punching Shear Stress in Post-Tensioned Transfer Plate of Multi-Story Buildings
## 4 Analytical Model
### Seismic Load  
ASCE 41-17 [26] (also the KBC 2016 [18]) recommends performing linear dynamic analysis for a structure with large vertical and soft story irregularity to consider the dynamic behaviors. However, for this study, a simple lateral force profile using equivalent static loads was applied to compare behavior according to the modeling method. The equivalent static load (\(F_{x}\)) was calculated based on KBC 2016 (same as ASCE 7-16 [27]) and applied at the center of mass of each floor. The equivalent static load is calculated as follows:  
\[F_{x}=C_{vx}V \tag{7}\]  
\[C_{vx}=\frac{w_{x}h_{x}^{k}}{\sum\limits_{i=1}^{n}w_{i}h_{i}^{k}} \tag{8}\]  
\[V=C_{s}W \tag{9}\]  
\[0.01\leq C_{s}=\frac{S_{D1}}{\left(\frac{R}{k_{c}}\right)T}\leq\frac{S_{DS}}{ \left(\frac{R}{k_{c}}\right)} \tag{10}\]  
where \(V\) is the base shear force; \(C_{s}\) is the seismic response coefficient; \(W\) is the effective seismic weight of the building, including the total dead load and other loads; \(S_{D1}\) and \(S_{DS}\) are the design effective ground  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & Tendon section & 7-strand wire (\(A_{p}\) = 15.2 mm\({}^{2}\)) \\  & Bonding type & Bonded \\
**Prestress tendon** & Wobble Coefficient & 0.002/m \\  & Curvature coefficient (\(K\)) & 0.15/rad. \\  & Anchorage slip (\(\mu\)) & 6 mm \\ \hline \hline \end{tabular}
\end{table}
Table 2: Prestress tendon modeling parameters.  
acceleration at 1 s period and short periods, respectively; \(R\) is the response modification factor; \(I_{E}\) is the occupancy importance factor; \(T\) is the fundamental period of the building (s); \(F_{x}\) is the equivalent static load at each level; \(C_{vx}\) is the vertical distribution factor; \(w_{i}\) or \(w_{x}\) is the effective seismic weight of story level \(i\) or \(x\); \(h_{i}\) or \(h_{x}\) is the height from the base to story level \(i\) or \(x\); \(k\) is the exponent related to the fundamental period of the structure, which is 1.0 and 2.0 for structures having a period of 0.5 s or less and period of 2.5 s or more, respectively; and \(n\) is the number of stories.  
The design effective ground acceleration at 1 s period (\(S_{D1}\)) and short periods (\(S_{DS}\)) can be calculated as follows:  
\[S_{DS}=S\times 2.5\times F_{a}\times 2/3 \tag{11}\]  
\[S_{D1}=S\times F_{v}\times 2/3 \tag{12}\]  
where \(S\) is the effective ground acceleration; and \(F_{a}\) and \(F_{v}\) are the site coefficients for short periods and 1 s period, respectively.  
The effective ground acceleration, Site classification and response modification factor are summarized in Table 3. The effective ground acceleration is assumed to be 0.22 g, which is the effective acceleration of the maximum considered earthquake (MCE) level in Korea.  
The site coefficient can be determined according to site classification. In this study, site classification is assumed as \(S_{D}\), which is commonly selected when there are no soil test results (Table 3). For site classification of \(S_{D}\), \(F_{a}\) and \(F_{v}\) are determined according to KBC 2016 as 1.6 and 1.8, respectively.  
In buildings with a transfer structure, two structural systems are mixed. The building of this study has a frame system and shear wall system together, and it is a better strategy to induce deformation to occur in the upper shear wall, rather than in lower frame structure. Thus, the response modification factor, \(R\), is determined as 4.0, which is for the conventional reinforced concrete shear wall system. Furthermore, occupancy important factor, \(I_{E}\), is determined as 1.2, which is the value for residential building regulated in KBC 2016.