# Punching Shear Stress in Post-Tensioned Transfer Plate of Multi-Story Buildings
## 5 Analysis Results according to the Modeling Method
### Punching Shear Stress under Seismic Load  
Figure 13 shows graphs of the ratio of maximum shear stress under lateral loads in global \(x\) and \(y\) directions at each column for the two modeling methods. In Figure 13, the ratio associated with the location of the column was shown as 0.23 to 7.4 at the exterior column, 1.3 to 6.7 at the corner column and 0.3 to 1.6 at the interior column for the Flat-shape plan. For the L-shape plan, the ratio was 0.1 to 3.9 at the exterior column, 0.6 to 4.4 at the corner column and 0.1 to 0.3 at the interior column. Figure 12: Example of column with/without shear wall within the critical section in L-shape plan. (a) Column no. 5, (b) Column no. 17, (c) Column no. 28 and (d) Column no. 27. Figure 13: Maximum punching shear ratio according to the modeling method (for lateral load only). (a) Flat-shape plan and (b) L-shape plan. In comparing the shear stress for the two plan shapes, the interior column, similar to the gravity load case, showed a relatively low ratio compared to other column locations. Especially in the L-shape plan, the shear stress at the interior column of the separated model was lower than that of the complete model. However, unlike the previous gravity load case, which had similar ratios according to the column location, the tendency under lateral load was not obvious. For columns without shear wall(s) within the critical section (red boxed point in Figure 13) that had shown large differences in the previous gravity load case, the punching shear stress ratio of the two modeling methods was less than 1.0. The implication is that lower shear stress was computed under the separated model in comparison to the complete model, which can lead to potentially insufficient shear design. Under lateral load, the moment occurs at the shear wall(s), which is transferred to the columns (Figure 14). If a shear wall exists within the critical section of the transfer column, the moment of the shear wall is transferred directly to the column, since the shear wall, transfer plate and column work as united structural system. So, a large moment could act on the transfer column, but the moment acting on the critical section could be small. Thus, the separated model, which does not consider the upper shear wall, may overestimate punching shear stress at the critical section. Whereas, if no shear wall exists within the critical section, the moment transferred from the nearby shear wall will act on the critical section and induce greater punching shear stress (Figure 14). In the eccentric shear stress model, the moment is transferred by eccentric shear acting on the critical section. The ratio is calculated according to Equation (2), and up to 44% of the moment can be transferred by eccentric shear. Since the eccentric shear stress model presented in ACI 318-19 is derived from the experiment of relatively thin flat plates [29], it does not accurately simulate eccentric shear caused by the moment. Moment acting on the critical section can be supported by bending in a thin slab, such as a flat plate, but the transfer plate is primarily supported by shear at the critical section rather than bending. Therefore, the eccentric shear stress model is less applicable to thick members, such as a transfer plate. Moment transferred to eccentric shear may be at a greater ratio than the ratio calculated in Equation (2). KBC 2016 requires the use of special seismic load (\(E_{m}\)) for load combination in designing components, such as transfer structures, which can change the flow of seismic loads drastically. The purpose is to ensure that the component and its supporting members are designed to be in the elastic state for seismic loads to prevent brittle failure [30]. As a result, seismic loads multiplied by the system overstrength factor (\(\Omega_{0}\)) are used as shown below. Figure 14: Moment transfer under later load.