# Bond Characteristics of a Deformed Steel Bar Embedded in Donut-Type Voided Slab
## 3 Experimental Results and Analysis
### The Bond Stress Distribution of the Donut-Type Voided Slab  
In terms of the bond stress distribution, the following Equations (1) and (2) were derived from the strain difference between two adjacent measurement points by strain gauges placed at a certain interval in the axial direction of the deformed steel bar. After the elastic region of the deformed steel bar (\(\varepsilon_{s}>0.0028\)), the bond stress was calculated using the results of the deformed steel bar tension test (\(F_{s}\)) and Equation (2). \[\mu=\frac{d_{b}E_{s}\Delta\varepsilon_{s}}{4\Delta x} \tag{1}\]  
\[\mu=\frac{d_{b}F_{s}}{4\Delta x} \tag{2}\]  
\(E_{s}\): Elastic modulus of the deformed steel bar (MPa);  
\(d_{b}\): Diameter of the deformed steel bar (mm);  
\(F_{s}\): The deformed steel bar strength at the non-elastic region (kN);  
\(\Delta\varepsilon_{s}\): The difference of the deformed steel bar strain between measurement points;  
\(\Delta\): Distance between measurements points (mm). [PERSON] [19] argued that when the embedded length of the rebar was long, the bond stress distribution varied according to the embedded length. He also insisted that the bond stress was generated mainly near the loaded end in the initial load step, and that the concrete gradually distributed the stress in the longitudinal direction of the deformed steel bar since the bond stress moved inwards as the load increased. However, bond conditions of the donut-type voided slab vary in the longitudinal direction of the rebar, as found in the experimental results of the short bond specimen, the bond stress-slip relationship changes. As such, to evaluate the bond strength by regions, the bond stress distribution by load step was investigated by using the entire-type specimen, which considered all the shapes of  
Figure 8: The bond force by wedging action of deformed steel bar. (a) A-type specimen; (b) C-type specimen. Figure 9: The spalling of concrete at C-type region in GB-270-0-E.  
the void shaper. According to the deformed steel bar strain of the entire-type specimen by load step shown in Figure 10, the closer it was to the free end of the specimen, the more the deformed steel bar strain decreased because the concrete partially bore the tensile force of deformed steel bar through the bond strength between the deformed steel bar and concrete. As indicated in the cases of the S-270-S-E and GB-270-26-E, under the condition of an inner cover thickness of 2.5 \(d_{b}\), the deformed steel bar strain increased linearly as the load increased. On the contrary, regarding the deformed steel bar strain of the specimens of GB-270-0-E and GB-270-10-E whose inner cover thickness was not satisfied as 2.5 \(d_{b}\), the strain at the C and D points was found to be higher than that of S-270-S-E as loads increased, unlike the results shown in Figure 10c. It seems that the amount of tensile force on the deformed steel bar borne by the concrete decreased due to the low inner cover thickness between points B and D, thus leading to the increased slip of the deformed steel bar. Subsequently, the bond stress of the deformed steel bar that was to be borne by the concrete in the B-D region was transferred to the concrete in the D-E region, which was a transition region. Figure 10: Strain distribution of deformed steel bar; (**a**) GB-270-0-E vs. S-270-S-E; (**b**) GB-270-10-E vs. S-270-S-E; (**c**) GB-270-26-E vs. S-270-S-E. These behaviors can be confirmed more clearly through the bond stress distribution by load step shown in Figure 11. In the case of the GB-270-26-E specimen, whose inner cover thickness of 2.5 \(d_{b}\) was satisfied, the bond stress distribution according to the load increase was quite similar to that of the S-270-S-E specimen. Furthermore, as shown in the study by [PERSON] [19], the maximum bond stress point was generated mainly near the loaded end in the initial load step, and the concrete was found to have distributed the stress in the longitudinal direction of the deformed steel bar gradually as the load increased.