## 3 Results and Discussion
### Numerical Analysis of the Required Splicing Length of the GFRP  
Based on the experimentally obtained results and linear extrapolation [16], it has been determined that the length of the supplement of 600 (60 cm) provided beam strength equal to the beam without a GFRP cut-off. An NSM GFRP bar spliced in this way has the same strengthening effect as a GFRP reinforcement without a cut-off. The extrapolation method is not reliable enough; therefore, one of the main goals of this paper was to confirm this conclusion completely, based on a developed and validated numerical model. According to the postulates presented in Section 2.2., a numerical model of a beam strengthened by GFRP reinforcement with both-sided overlapping at the cut-off location with a length of 60 cm has been created. The ground for determining the efficiency of the strengthening was a comparative analysis of a load-deflection diagram. Figure 20 presents, side-by-side, the experimental and numerical load-deflection diagram for the beam without a cut-off of GFRP reinforcement (B-G1), and for the beam with splicing overlapping of 60 cm. Based on the results, one may conclude that elastic stiffness and stiffness after crack occurrence coincide completely. The stiffness of the beam after the yielding of the basic reinforcement is in good correlation with the experimental results. One may notice that the beam with a double-strap joint of 60 cm exhibits an approx. 5% greater force value at the occurrence of the yield of the basic reinforcement. Additionally, at the ultimate load the deflection in the midspan is about 10% lower. The reason for such results is the increase in the overlapping length, i.e., of the groove, which contains the epoxy and two inserted FRP bars, and thus exhibits higher stiffness and lower beam ductility. An increased groove length increases the adhesion at the joint between the concrete and the epoxy, and, at the same time, the epoxy also has a higher tensile strength compared to that of concrete. This is manifested after the occurrence of the yielding of the basic reinforcement (steel), which can be seen on the diagram in Figure 20.  
The confirmation of the conclusion regarding the failure mechanism has been conducted through the analysis of the crack pattern, expressed as the damage parameter in tension, as well as through observing the shear (bond) stress at the concrete-epoxy interface. The results of the analyzed model with a GFRP splicing length of 60 cm (Figures 21 and 22) have been compared with the results of model B-G1 (Figures 14 and 15). The analysis results show that the crack pattern is uniform, similar to beam B-G1. The obtained shear (bond) stresses at the concrete-epoxy interface confirm that this stress has been exceeded at the beginning of the widening of the groove for cut-off bypassing, as well as in the zone starting from the load application towards the supports. This indicates that the failure mode of the concrete beam with a GFRP splicing of 60 cm is the same as in the remained splicing cases (B-G3 and B-G4). It is worth mentioning that, in the numerical models, the  
Figure 20: Comparative analysis of the force–deflection diagram of model B-G1 and the model with a double-strap joint length of 60 cm. tensile strength of the GFRP reinforcement is also achieved at the ultimate load, which is in concordance with the experimentally measured strains in the GFRP reinforcement of beam B-G1 [16]. Based on these results, one may confirm that the complete splicing of a GFRP reinforcement with a cut-off in the system double-strap joint can be achieved via the use of supplemental bars with a length of 60\(\O\). Compared to the required overlapping length of 110\(\O\) in the classic lap splice method [28], it can be concluded that the proposed splicing method requires less overlapping length to achieve the same bearing capacity as in the case of NSM FRP strengthening without a cut-off of the additional FRP bar.