## 1 Introduction  
Recently, owing to the rising labor costs in the construction market, precast concrete (PC) systems have been increasingly used in modular high-load long-span buildings (e.g., underground parking lots, logistics centers, and large shopping malls). To improve the construction and economic efficiency by reducing the number of PC structural members, one-way PC structure systems using prestressed PC girders and PC slabs are mainly used (Figure 0(a)). PC slabs make up most of this one-way PC structural system. Hence, reducing the PC slab volume has a great influence on the construction cost. The slabs used in the one-way PC method include hollow core slabs [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], double-tee slabs [13, 14, 15, 16, 17, 18, 19, 20], and inverted-tee slabs [21, 22, 23, 24, 25, 26, 27, 28]. The double-tee slab, which has a section with the largest distance between the compression zone in the concrete and the tensile reinforcing bar for flexural bending, has great section efficiency when compared with its member weight. However, in the double-tee slab, the depth of the slab is larger than that of other slab-system types, resulting in an increase in the total building height. To overcome this disadvantage, the Precast/Prestressed Concrete Institute (PCI) design handbook [29] allows the height of the member to be reduced to half the overall height of the slab in order to reduce the floor height of the double-tee slab. The structural strength is secured through the shear reinforcement of the deformed end, which is called a dapped end (see Figure 1b). However, unless it is appropriately designed, local damage may occur at the dapped end. To stably secure the structural performance of the dapped end of a double-tee slab, a multi-tee slab system, which uses a slab with an additional web installed on the outermost end of the double-tee slab [30], was developed (Figure 1c). In recent years, new construction methods have been proposed to combine structural and thermal insulation work by installing expanded polystyrene (EPS) between the webs of the multi-tee slab for improved constructability and to shorten the construction time (Figure 1c). However, technical issues should be addressed when applying this new construction method. In general, the dapped end can be severely stressed when the concentrated load is applied, and the cross-sectional shape changes rapidly. Thus, shear failure may occur at the dapped end, as shown in Figure 2a [31]. Special care should be taken to design the dapped end by providing appropriate shear reinforcement [29] when it is introduced in a multi-tee PC slab. Figure 1: One-way precast concrete (PC) slab with insulating materials. (**a**) Construction of a PC frame with a one-way PC slab. (**b**) PC slab with a dapped end. (**c**) Multi-tee PC slab with expanded polystyrene (EPS). Figure 2: Structural design of dapped end of the PC slab. (**a**) Crack pattern at the dapped end. (**b**) Strut–tie model for the dapped end. (**c**) Shear reinforcement for the dapped end. To analyze and improve the shear behavior of the dapped end of the PC slab, a strut-tie model was proposed in the existing literature [31] (Figure 2b). In the strut-tie model of the dapped end, the dotted line and solid line indicate the compressive force and tensile force, respectively, and the value on the line represents the magnitude of the load acting on the element. According to the strut-tie model, to prevent a diagonal tensile failure at the corner of the bent portion by the reaction force R, a tensile-resistant member that has the same force magnitude as the reaction force R should be placed at the BC element in Figure 2b. Therefore, in the design of the dapped end, shear reinforcing bars are generally placed to resist the tensile force loaded on the BC element (Figure 2c).