## 5 Calculations and Evaluation  
The diameter of the reinforcing bars was taken as d. Calculations were performed to quantitatively evaluate the constraint stress of the concrete due to changes in the coating thickness. As shown in Figure 16, when a compression force C was applied to a reinforcing bar with a diameter of \(d\), it was transferred to the concrete via the compression stress of the reinforcing bar with an adhesion length of \(l\). Formula (14) is obtained when the unit average adhesion stress \(\tau_{b}\) acts on the surface area \(\pi dl\) of the reinforcement. \[C=\pi d\l\tau_{b} \tag{14}\]  
where \(C\) is the compressive force acting on the reinforcement, \(D\) the Rebar diameter, \(L\) is the length of specimen, and \(\tau_{b}\) is the unit average adhesion stress. (d) Experimental results and considerations  
When using D19 reinforcing steel as shown in Figure 17a, the reference specimen that was not induction-heated was compared with the specimen that was induction-heated on the entire surface according to the length direction of the reinforcing steel as shown Table 7. Further, when conducting induction heating, it was determined that the thermal expansion pressure generated in the reinforcing steel caused cracks in the ribs of the rebar \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **a/c** & **Calculated Value** \\ \hline D10 & 0.6/6.7 & 0.0896 \\ D19 & 1.5/13.4 & 0.112 \\ D25 & 1.95/17.8 & 0.1096 \\ D32 & 2.4/22.3 & 0.1076 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Calculation of fracture aspects of deformed reinforcing bars by ribs. Figure 15: Adhesive tensile test and distribution of adhesive stress [57]. with the largest surface area, thereby reducing the adhesion strength. Furthermore, when comparing non-heated reference specimens with only the center heated specimens, it is assumed that the total load is the same in the area below the reinforcement ribs of the entire specimen, and thus, the adhesion strength due to induction heating was evaluated. Figure 16: Rebar force transition structure [57]. Figure 17: Reinforced concrete extraction experiment results (D00-000: D reinforcement type-distance mm-heating-all heating). Consequently, the test specimen heated only by the center showed 58, 8.3, and 11.5% reduction rates in the order of 30, 40, and 50 mm, respectively, while 58, 8.9, and 12 reduction rates were observed in the concrete stress. In the case of test specimens heated entirely by reinforcing steel, the reduction rates were 61, 29, and 11.5% in the order of 30, 40, and 50 mm, respectively, and 63, 27.8, and 12%, respectively. The 30 mm specimen with high heating efficiency showed a reduction of more than 60% in the adhesion strength, and the overall temperature of the reinforcing steel increased owing to the heat conduction of the reinforcing steel, and showed no significant difference compared to the total heating specimen. In addition, on reducing the heating efficiency, the difference between local heating and total heating is approximately 20% or greater, and further, if the heating efficiency is reduced by distance, the range of expansion pressure generation on reinforcing bars due to heat conduction is significantly reduced. Furthermore, when cracks from the reinforced ribs are connected to the surface of the concrete, the stress of the concrete is reduced by the same width in proportion to the stress reduction difference for which the ribs are responsible. For the test specimen using D25 as shown in Figure 17c reinforcement, the adhesion strength reduction rates were 27.3, 23.2, and 17.4% in the order of 30, 40, and 50 mm, respectively. Although the rib stress and concrete constraint stress were proportionally reduced, the rib constraint stress reduction rate was observed to be slightly higher. For a test specimen using D32 as shown in Figure 16d, the reduction rates of 15.4, 17, and 17% are shown in the order of 30, 40, and 50 mm, respectively.