## 4 Conclusions  
The proposed method for the splicing of the FRP bar cut-off by both-sided overlapping, called \"double-strap joint NSM FRP\", showed very good results regarding providing mechanical characteristics of beams, compared to strengthening realized by a bar without a cut-off [16]. Non-linear numerical FEM models for the analysis of the behavior of beams strengthened via NSM FRP reinforcement with different overlapping splicing lengths have \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Splicing Method** & **FRP Length (m)** & **Groove Volume (m\({}^{3}\))** & **Groove Surface Area (m\({}^{2}\))** & **Epoxy (kg)** & **Primer (kg)** \\ \hline Double-strap joint & 7.20 (101.41\%) & 0.00276 (57.50\%) & 0.363 (75.63\%) & 4.278 (57.50\%) & 0.109 (75.63\%) \\ Classic lap splice & 7.10 (100\%) & 0.00480 (100\%) & 0.480 (100\%) & 7.440 (100\%) & 0.144 (100\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Economic analysis. Figure 24: Comparative analysis of the force-deflection diagram of the CFRP and GFRP model with a double-strap joint length of 60 cm. been presented. The influence of the diameter and type of NSM FRP bars on the strength and stiffness of the beams has been investigated as well. In the end, the practical and economic feasibility of the double-strap joint method has been shown in comparison to the classic lap splice method. Based on the presented results, the following conclusions can be drawn:  
* The results of the nonlinear numerical analysis of RC beams strengthened by the NSM FRP technique, loaded to bending according to the four-point load disposition, showed very good agreement with the experimental results regarding the load-deflection relationships, failure mechanisms, and strains in the GFRP bars. Therefore, the model is validated. * The concrete damage plasticity material model is suitable for a numerical analysis of concrete and epoxy with the appropriate definition of the parameters of the material mechanical properties (see Sections 2.2.2 and 2.2.3). * In most cases, beam failure occurs due to the exceeding of the shear stress between the concrete and the epoxy (bond stress) in the zone starting from the load application towards the supports as well as at the beginning of the groove for inserting the supplemental bars for splicing. * It has been shown that an overlapping length of 600 provides an increase in beam strength equal to the increase in strength in the case of an NSM FRP bar without a cut-off. * With an increase in the diameter of the FRP bars (\(\mathcal{O}8\), \(\mathcal{O}10\), and \(\mathcal{O}12\)), the strength of the strengthened beams increases for about 10% in the case of GFRP bars and about 5% in the case of CFRP bars. * Via the application of CFRP bars instead of GFRP bars, one achieves higher beam strength, but lower beam ductility, for the same diameters used. Therefore, choosing between CFRP and GFRP bars for the strengthening of the RC beam should be based on the load-bearing requirements, but with the limitation of preventing the brittle failure of the strengthened beam under the ultimate design loads. * The failure mechanism is qualitatively the same regardless of the material of FRP bars, but in the case of CFRP a more prominent peeling-off at the concrete-epoxy joint occurs. * Potential savings in the material and construction time are possible via the application of the proposed double-strap joint method compared to the classic lap splice method. A numerical analysis showed that, for an overlapping length of 600, the proposed way of splicing of FRP bars with a cut-off (\"double-strap joint NSM FRP\") achieves full beam strength, as in the case of FRP bars without a cut-off, regardless of the material used (GFRP or CFRP). This important conclusion is very significant for everyday engineering practices when the splicing of the additional FRP reinforcement in the NSM strengthening technique is necessary.