## 3 Results and Discussion
### Bond-Dependent Coefficient \(k_{b}\) Prediction  
The experimental results of the measured crack widths for different load levels for tested beams were used to determine the coefficient \(k_{b}\). The coefficient \(k_{b}\) was calculated for the beams at the midspan and middle support for 35 kN, 50 kN, 70 kN, and 90 kN loads for beams series 1; and 25 kN, 35 kN, 45 kN, 60 kN, and 75 kN loads for beams series 2 using Equations (14) and (15), in accordance with ACI-06 [34] and ISIS-07 [35], respectively. These load levels included a wide range of service loads, ranging from 22-72% of the failure load, or 2-6 times the first crack load. Table 3 gives the maximal values of coefficient \(k_{b}\) for different load levels for the measured widths of three cracks in every critical section, in both the midspan and middle support sections. Additionally, Figure 10 shows the average values of the coefficient \(k_{b}\) for the measured widths of three cracks in every critical section for different load levels of each beam, using Equation (14) in accordance with ACI-06 [34]. Figure 9: (**a**) Experimental and predicted load–crack width relationships for tested beams series 1. (**b**) Experimental and predicted load–crack width relationships for tested beams series 2. From Table 3, it can be seen that similar maximum values for the coefficients \(k_{b}\) are obtained for the midspan for all beams series 1 using the applied codes. The values for coefficients \(k_{b}\) are \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Code** & **Beam** & **Midspan** & **Middle Support** & **Recommended Value** \\ \hline  & G1-0 & 0.75 & 0.65 & \\  & G1-15 & 0.74 & 1.02 & \\  & G1-25 & 0.75 & 1.33 & (ACI)—1.4 \\  & G2-0 & 2.07 & 2.17 & (CSA)—1.0 \\  & G2-15 & 2.51 & 3.59 & \\  & G2-25 & 2.50 & 4.05 & \\ \hline  & G1-0 & 0.63 & 0.55 & \\  & G1-15 & 0.62 & 0.85 & \\  & G1-25 & 0.62 & 1.01 & \\  & G2-0 & 1.58 & 1.65 & \\  & G2-15 & 1.91 & 2.73 & \\  & G2-25 & 1.90 & 3.08 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Coefficient \(k_{b}\) for GFR bars in the tested beams. Figure 10: Bond-dependent coefficient \(k_{b}\) for different load levels of tested beams: (**a**) midspan; (**b**) middle support. significantly less than the recommended values for the chosen codes. Additionally, these values are less than 1.0, the recommended value for the steel reinforcement, which indicates very good adhesion conditions between ribbed GFRP bars and the surrounding concrete. In Figure 10, uniform average coefficient values for different load levels can also be observed, except for beam G1-0, where the coefficient value increased with the 90 kN load. It can be concluded that for beams series 1, the designed internal force redistribution did not affect the variation of coefficient \(k_{b}\) in the midspan. As expected, higher \(k_{b}\) values were obtained for beams series 2, which also indicates poor adhesion conditions between wrapped GFRP bars and concrete. These values are greater than those recommended by the codes. Additionally, it can be observed that these coefficients are higher for beams G2-15 and G2-25, which were designed to achieve internal force redistribution, compared to beam G2-0. For the middle support, the \(k_{b}\) values are significantly different for the tested beams series 1. The highest values were obtained for the beam G1-25 (1.01 and 1.33), which had the smallest amount of reinforcement in the middle support section, while the smallest values were obtained for the beam G1-0 (0.55 and 0.65), which had the highest amount of reinforcement. For the beam G1-0, coefficient \(k_{b}\) gave similar values in the midspan and middle support sections. For beams G1-15 and G1-25, the \(k_{b}\) values increase in the support section, indicating that the internal force redistribution in the continuous GFRP-reinforced beams occurs with the slippage between bars and concrete in the middle support section.