# Punching Shear Stress in Post-Tensioned Transfer Plate of Multi-Story Buildings
## 5 Analysis Results according to the Modeling Method
### Effect of Number of Stories below the Transfer Plate  
To analyze the differences in behavior according to the number of stories below, the results of an analytical model having four stories below the transfer plate were compared. The height of the shear wall above the transfer plate was fixed at 20 stories. In Figures 15-17, the results are marked according to the location of the column--exterior, corner and interior, as circle, triangle and square, respectively. According to the number of stories below, black, red and blue for the first story below, and grey, orange and purple for the fourth story below are used, respectively.  
Figure 15: Maximum punching shear stress ratio according to number of stories below transfer plate (for gravity load only). **(a)** Flat-shape plan and **(b)** L-shape plan.  
In Figure 15, the maximum shear stress ratio of two modeling methods under gravity load at each critical section of transfer columns are shown. In the case of the Flat-shape plan, the ratio changed for the exterior columns as the number of stories below increased in the range of \(-0.1\) to \(0.5\). It also changed in range of \(-0.2\) to \(-0.03\) at the corner columns and \(-0.1\) to \(0.2\) at the interior columns.  
Figure 16: Maximum punching shear stress ratio according to number of stories below transfer plate (for x-dir. lateral load only). (**a**) Flat-shape plan and (**b**) L-shape plan.  
Figure 17: Maximum punching shear stress ratio according to number of stories below the transfer plate (for y-dir. lateral load only). (**a**) Flat-shape plan and (**b**) L-shape plan.  
In the case of the L-shape plan, the ratio changed in the range of \(-0.3\) to \(0.05\) at the exterior columns, as the number of stories below increased. At the corner columns, the range was \(-0.2\) to \(0.13\), and at the interior columns, it was \(-0.02\) to \(0.4\).  
The results of the two planar shapes indicate that the separated model in comparison with the complete model overestimated punching shear stress under gravity load, despite increase in the number of stories below.  
Figures 16 and 17 show analysis results according to the increasing number of stories below under \(x\) and \(y\) directional lateral load. In the case of the Flat-shape plan under \(x\) directional lateral load, the ratio changed to \(-0.3\) to \(0.5\) at the exterior columns. It also changed to \(-0.55\) to \(0.05\) at the corner columns and to \(-0.4\) to \(0.13\) at the interior columns. Furthermore, it changed under \(y\) directional lateral load to \(-0.25\) to \(3.3\) at the exterior columns and \(-0.25\) to \(0.4\) at the interior columns. However, at the corner columns, it was \(-0.03\) to \(0.01\), which is significantly less than other columns.  
In the L-shape plan, the ratio changed under \(x\) directional lateral load as the number of stories below increased to \(-0.75\) to \(2.3\) at the exterior columns and \(0.7\) to \(2.5\) at the interior columns, respectively. At the corner columns, change was greater than the Flat-shape plan and ranged from \(0.3\) to \(0.3\). Under \(y\) directional lateral load, the ratio was \(-0.56\) to \(45.1\) at the exterior columns and \(0.3\) to \(2.3\) at the interior columns. At the corner columns, it changed to \(-0.6\) to \(0.02\).  
Figure 18: Maximum shear stress ratio vs. number of stories below (Flat-shape plan). (**a**) Corner and interior columns and (**b**) Exterior columns.