# Bond Characteristics of a Deformed Steel Bar Embedded in Donut-Type Voided Slab
## 4 Calculation of the Bond Strength of the Donut-Type Voided Slab
### The Method of Calculating the Bond Strength of the Donut-Type Voided Slab  
As the bond strength of the donut-type voided slab of each region (A, B, and C) was found to be different in the experimental results. The equation for calculating the bond strength considering the contribution to the bond strength by region, which was derived from the experimental results, was proposed to consider the bond characteristics by region, as shown in Equation (7). This equation is used to estimate the bond strength of the donut-type voided slab according to the entire embedded length by calculating the average bond stress by region based on the bond stress-slip relationship by region, which is derived through the short bond experiment.  
\[\tau_{avg}=\frac{\sum\tau_{avg,reg}\times l_{reg}}{l_{total}} \tag{7}\]  
\(\tau_{avg,reg}\): Average bond stress of each region;  
\(l_{reg}\): Embedded length of each region;  
\(l_{total}\): Total embedded length of re-bar.  
The average bond stress of each region, \(\tau_{avg,reg}\), was obtained through the Rilem standard [23] method and the KS calculation method of the average bond stress [18]. The Rilem standard method calculates the average bond stress by calculating the average bond stress of each slip (0.01, 0.10, and 1.0 mm) in the bond stress-slip curve as shown in Equation (8). Similarly, in terms of the KS F 2441 method of calculating the average bond stress, it was also stated that the nominal average bond stress can be calculated by dividing the slipping distance at the loaded end into five equal intervals. At this time, the slipping distance at the loaded end is limited to be less than 0.25 mm. Thus, the average bond stress of each region was calculated using Equations (8) and (9) in this study, and the average bond strength of the donut-type voided slab specimen derived through the calculation is shown in Table 6.  
\[\tau_{avg,Rilem}=\frac{\tau_{0.01}+\tau_{0.10}+\tau_{1.0}}{3} \tag{8}\]  
\[\tau_{avg,KS}=\frac{\tau_{0.05}+\tau_{0.10}+\tau_{0.15}+\tau_{0.20}+\tau_{0.2 5}}{5} \tag{9}\]  
\(\tau_{0.01}\)/ 0.10/ 1.0 : the bond stress of each slip in the bond stress-slip curve;  
\(\tau_{0.05}\)/ 0.10/ 0.15 / 0.20 /0.25 : the bond stress of each slip in the bond stress-slip curve.  
As indicated in Table 6, the conventionally proposed equation for bond strength underestimated the bond strength of the donut-type voided slab by over 25% when the inner cover thickness was not 2.5 \(d_{b}\). However, when Equation (7), which was proposed considering the bond characteristics of each region, was applied, the estimated bond strength of the donut-type voided slab was highly accurate within the error range of 5%. In terms of the GB-270-26-E specimen, the value estimated through the proposed equation was found to be 20% higher than the experimental value. That is because the experiment  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multicolumn{2}{c}{**Test Result**} & \multicolumn{2}{c}{**Conventional Method**} & \multicolumn{2}{c}{**Suggested Method**} \\ \cline{2-7}  & \(P_{test}\) & \(P_{[PERSON]}\) & \(P_{Zuo}\) & \(P_{CEB-FIP}\) & \(P_{Rillem}\) & \(P_{ks}\) \\  & [**kh**] & [**kh**] & [**kh**] & [**kh**] & [**kh**] & [**kh**] \\ \hline GB-270-0-E & 60.27 & 26.85 & 20.23 & 45.61 & 52.25 & 61.68 \\ \hline GB-270-10-E & 72.93 & 42.78 & 28.88 & 56.50 & 76.61 & 77.30 \\ \hline GB-270-26-E & 89.60 & 60.04 & 43.27 & 66.04 & 114.51 & 110.47 \\ \hline \hline \end{tabular} Note. _P_: The ultimate bond force.  
\end{table}
Table 6: Test results vs. suggested method.  
was ended before the bond failure of the GB-270-26-E specimen due to the rupture of the deformed steel bar.