# Bond Characteristics of a Deformed Steel Bar Embedded in Donut-Type Voided Slab
## 1 Introduction
### Research Background  
A voided slab is a slab with voids created by inserting void-shapers between the top and bottom layers of rebar in flat plate slabs [2]. By replacing the concrete inside the slab, which has a small influence on the flexural performance, with a void-shaper, the voided slab can maintain flexural strength and sound insulation as well as general RC slabs of the same thickness while reducing the weight by approximately 30%, thus being regarded as an effective structural system [2; 3; 4]. By applying the advantages of voided slabs, several voided slabs with various void shapes and details were developed, and many studies have been conducted to verify its structural performance in terms of the flexure, shear, and punching shear [3; 4; 5; 6]. The donut-type voided slab is one of the developed voided slabs; [PERSON] et al. [7] proposed a donut-type void as the optimum shape for a void-shaper by conducting analytical studies in which various shapes of void were used as variables, and  
Figure 1: Donut-type void-shaper. Figure 2: Regions of the donut-type voided slab. Note—I: Insufficient region, T: Transition region, S: Sufficient region. they also evaluated the structural performance of the voided slab in terms of the flexure, shear, and punching shear through empirical and analytical studies [8; 9; 10; 11]. Meanwhile, the bonding performance between the rebar and the concrete is a crucial factor in the deflection, crack, and tension stiffening effect of the slab [12; 13]. According to [PERSON] et al. [14], bond behaviors between concrete and rebars are influenced by the diameter of the deformed steel bar, rib shape, rib spacing, the degree of the surface roughness, the cover thickness of the concrete and tensile strength of deformed steel bars. According to [PERSON] et al. [15], bond failure mechanism between the concrete and the rebar is divided into pull-out failure and splitting failure, and bond strength of tensile rebar is greatly reduced when a splitting failure occurs. In addition, the splitting failure should be considered when the ratio of the rebar diameter to the minimum cover thickness is less than 2.5. The donut-type void-shaper, which is mainly examined in this study, has an externally convex curved surface on the parts corresponding to corners and vertices of a rectangle and an inner hole connected through the center of the upper and bottom parts, as shown in Figure 1. As the void-shaper is placed in the web of the donut-type voided slab, a concrete cover is formed between the void-shaper and the rebar. Moreover, as the various cross-sections are generated depending on shapes of the void-shaper, the cover thickness between the void-shaper and the rebar varies along the longitudinal direction of the rebar as shown in Figure 2. The donut-type voided slab ensures a sufficient cover thickness in that the distance from the center of the rebar to the bottom surface of slab is more than 2.5 \(d_{b}\). However, as the inner cover thickness varies along the longitudinal direction of the rebar, a sufficient cover thickness of 2.5 \(d_{b}\) is not satisfied in some part of the donut-type voided slab. Therefore, the rebar bond conditions of the donut-type voided slab are divided into three regions (sufficient, transition, and insufficient regions) as shown in Figure 2.  
In the case of voided slabs, [PERSON] [16] argued that the amount of the concrete surrounding the bottom tension rebar in a voided slab can decrease because of the void, subsequently reducing the bond strength of the rebar. The experimental results indicated that the maximum bond strength of the voided slab using round plastic balls as void-shapers decreased by 45% compared to that of a general RC slab. According to [PERSON] et al. [17], the bond stress-slip relationship and the bond stress distribution of a steel wire in the deck type voided slab are different from that in general RC slabs by the concrete inner cover thickness, and the bond stress-strain model for one module of the deck type voided slab was proposed.