## 3 Results and Discussion
### Parametric Study  
The validated numerical model presented in Section 2.2. has been applied for a parametric study of the influence of the diameter and type of FRP bars (glass and carbon) on the mechanical characteristics of the strengthened beams without a cut-off. Furthermore, a parametric analysis of the influence of the type of FRP bar on beam strength has been conducted for a constant length of double-strap joint splicing of 60\(\O\).  
Figure 21: Damage parameter in tension for a model with a double-strap joint length of 60 cm.  
Figure 22: Shear stress at the concrete–epoxy interface for a model with a double-strap joint length of 60 cm.  
Within the parametric analysis of the influence of the diameter of FRP bars without a cut-off on the characteristics of the strengthened beams, cases with diameters of \(\mathcal{O}8\), \(\mathcal{O}10\), and \(\mathcal{O}12\) have been analyzed. For all of the quoted bar diameters, an analysis with glass (GFRP) and carbon (CFRP) fibers has been conducted, taking the values of the modulus of elasticity, E = 148.10 GPa, and the ultimate tensile strength, f\({}_{\text{u}}\) = 1940 MPa, for the CFRP bars (Figure 9b). Although the different FRP types, reflected in different stress-strain relationships (Figure 9b), as well as surface treatments, influence the bond strength [14, 34], it is considered to be the case that the anchoring length of FRP bars in the first and third sections of the beam span is sufficient to provide composite action. Figure 23 presents force-deflection diagrams obtained numerically. One may conclude that, in cases of applications of GFRP without a cut-off, with an increase in the diameter from \(\mathcal{O}8\) to \(\mathcal{O}10\), and finally to \(\mathcal{O}12\), strength is increased by about 10%. Compared to the beams strengthened with GFRP bars, the beams strengthened with CFRP bars with the same diameter produce higher strength and stiffness of the beam, but lower beam ductility (ratio of the displacement at the ultimate load and the displacement at the yield of the primary steel reinforcement). The reason for this is the higher modulus of elasticity of the CFRP reinforcement, as well as the higher bond stress at the concrete-epoxy joint, which lead to more brittle failure compared to the case of beam strengthening with the GRFP bars. With an increase in the CFRP bar diameter, strength is increased for about 5%, which represents a slightly lower value compared to the strength increase in the case of the application of GFRP bars. It should be mentioned that, for the smallest diameter (\(\mathcal{O}8\)), the application of CFRP instead of GFRP bars provides higher beam strength for approximately 20%. This effectiveness decreases with an increasing FRP bar diameter. Nevertheless, the choice between the application of the GFRP and CFRP bars for RC beam strengthening should be protracted by cost analysis as well, considering the higher price of CFRP bars.  
The result of the analysis of the influence of the fiber type (GFRP, CFRP), for a constant bar diameter (\(\mathcal{O}10\)) and for an overlapping length of \(60\mathcal{O}\), is that it provides strength of a strengthened beam equal to the case of a beam with an FRP bar without a cut-off (Figure 24). This result fully confirms the conclusion that an overlapping length of \(60\mathcal{O}\) is required for the same strengthening effect as in the case of a beam without an FRP bar cut-off, regarding the FRP bar type.  
Figure 23: Influence of the diameter and type of FRP bar without a cut-off on the strength and stiffness of the strengthened beams.