# Punching Shear Stress in Post-Tensioned Transfer Plate of Multi-Story Buildings
## 1 Introduction  
The need for vertical wall height and large open space on lower floors in buildings such as apartments and hotels exists [1]. Due to large vertical irregularity, stiffness changes dramatically at the transfer floor. In general, transfer structures refer to shear wall-frame systems, i.e., piloti structures.  
Transfer structures are susceptible to seismic forces, due to the concentration of stress at the transfer floor under seismic loading [2; 3]. Therefore, transfer structures are pragmatic at locations where moderate-to-low seismic zones exist, such as Korea and Hong Kong.  
Transfer girder and transfer plate systems are commonly adopted as transfer structures. Since the transfer plate system with post-tensioning tendons is effective in reducing member thickness [4], use has been widely adopted recently. However, research on post-tensioned transfer plate systems--compared to other transfer systems such as reinforced concrete transfer girder and plate systems, which have been studied for decades--is relatively scarce. Given that analysis software commonly used in industry, until recently, did not include the prestressing tendon element, the design of a post-tensioned transfer plate was performed using separate finite element analysis software with post-tensioning modeling features. This analysis method is done only with the transfer plate floor and one-story columns/walls below and internal forces in the shear walls above the plate are modeled with external forces, which are exerted on top of the transfer plate (the separate analysis method, hereafter). Hence, member design for vertical elements above and below the transfer plate is performed without the inclusion of theprestressing effect, and flexural and shear design of the post-tensioned transfer plate is conducted separately (Figure 1).  
There is no doubt that the separate analysis methodology is not applicable since it is not enough to simulate the actual behavior of overall structural systems. However, finite element analysis software with post-tensioning modeling features has not offered the multi-story building modeling until recently. The software that offers both the multi-story modeling and post-tensioning feature is developed, but in practice, the analysis and design of post-tensioned transfer plate are still carried out using the separate analysis method, without rigorous verification.  
In the separate analysis model, the shear wall above the transfer plate is replaced with an equivalent line load. As a result, the interaction between the shear wall and the transfer plate cannot be considered. Thus, compatibility, which is one of the fundamental assumptions of numerical analysis, is not satisfied. In addition, design codes present that secondary effects should be taken into account. However, secondary effects cannot be considered, since the elastic analysis model used for the design of the vertical members does not address the prestressing effect. The effect of the transfer floor height is also not considered, since the separate analysis used applies only to the floor of the transfer plate and columns/walls just below the plate, regardless of the number of stories below the transfer plate.