# 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 Average Bond Strength of the Conventional Methods  
[PERSON] [20] proposed the the equation for calculating the average bond stress of the deformed steel bar as shown Equation (3). In this equation, the minimum thicknesses of the cover surrounding the deformed steel bar and embedded length and diameter of deformed steel bar were considered in order to estimate the average bond stress of the deformed steel bar (\(\tau_{avg}\)).  
\[\tau_{avg}=5.17(f_{c})^{\frac{1}{3}}(\frac{d_{b}}{l_{b}})^{\frac{1}{2}}(\frac{ c_{\min}}{d_{b}})^{\frac{1}{2}} \tag{3}\]  
\(f_{c}\) : The compressive strength of concrete (MPa);  
\(d_{b}\): Diameter of the deformed steel bar (mm);  
\(l_{b}\): The embedded length of a deformed steel bar (mm);  
\(c_{\min}\): The minimum thicknesses of the cover surrounding the deformed steel bar [mm].  
[PERSON] and [PERSON] [21] proposed the equation for calculating the ultimate bond force of the deformed steel bar as shown Equation (4). It is insisted that the maximum and minimum thicknesses of the cover surrounding the deformed steel bar were considered in order to estimate the ultimate bond force of the deformed steel bar (\(T_{c}\)).  
\[T_{c}=f_{c}^{\frac{1}{3}}[1.44l_{b}(c_{\min}+0.5d_{b})+56.3A_{b}](0.1\frac{c_ {\min}}{c_{\max}}+0.9) \tag{4}\]  
\(f_{c}\) : The compressive strength of concrete (MPa);  
\(d_{b}\): Diameter of the deformed steel bar (mm);  
\(A_{b}\): Cross sectional area of the deformed steel bar (mm\({}^{2}\));  
\(l_{b}\): The embedded length of a deformed steel bar (mm);  
\(c_{\min}\): The minimum thicknesses of the cover surrounding the deformed steel bar [mm];  
\(c_{\max}\): The maximum thicknesses of the cover surrounding the deformed steel bar [mm].  
In the CEB-FIP MC2010 [22], the equation for calculating the average bond strength of the deformed steel bar is not directly proposed, while the equation for calculating the development length (\(l_{d}\)) of the deformed steel bar is shown in Equation (5), which is derived based on Equation (6), which is the equation for calculating the tensile stress of the deformed steel bar (\(f_{stm}\)) according to the bond length.  
\[l_{d}=\frac{d_{b}}{4}\frac{f_{y}}{f_{bd}} \tag{5}\]  
\[f_{stm}=54\bigg{(}\frac{f_{c}}{20}\bigg{)}^{0.25}\bigg{(}\frac{20}{d_{b}} \bigg{)}^{0.2}\bigg{(}\frac{l_{b}}{d_{b}}\bigg{)}^{0.55}\bigg{[}\bigg{(}\frac{ c_{\min}}{d_{b}}\bigg{)}^{0.33}\bigg{(}\frac{c_{\max}}{c_{\min}}\bigg{)}^{0.1}+8K_{tr} \bigg{]} \tag{6}\]  
\(f_{c}\) : The compressive strength of concrete (MPa);  
\(f_{c}\) : The yield strength of the deformed steel bar (MPa);  
\(f_{bd}\) : The average bond stress of the deformed steel bar (MPa);  
\(d_{b}\): Diameter of the deformed steel bar (mm);  
\(A_{b}\): Cross sectional area of the deformed steel bar (mm\({}^{2}\));  
\(l_{b}\): The embedded length of a deformed steel bar (mm);  
\(K_{tr}\): Transverse reinforcement index;  
\(c_{\min}\): The minimum thicknesses of the cover surrounding the deformed steel bar (mm);  
\(c_{\max}\): The maximum thicknesses of the cover surrounding the deformed steel bar (mm).  
In these equations, the maximum and minimum thicknesses of the cover surrounding the deformed steel bar were considered in order to estimate the bond stress of the deformed steel bar. However, even in these equations for estimating the average bond strength of the deformed steel bar, the bond characteristics of the donut-type voided slab by region, for which minimum inner cover thickness varied according to the longitudinal direction of thedeformed steel bar, were not reflected. Thus, as shown in Table 6, the bond strength of the donut-type voided slab was found to be underestimated when the average bond stress was calculated using Equations (3)-(6).