## 3 Results and Discussion
### Load Capacity and Moment Redistribution  
Measured applied loads in the middle of both spans and end reactions were used to determine internal forces along the length of the beam and to calculate the moment redistribution (Figure 6). Figure 5: Modes of failure of experimental beams. Figure 6: Experimental versus elastic bending moments at failure. Figure 7 shows the relationship between the percentage of moment redistribution in the middle support and the applied load. Beams G1-0 and G2-0 achieved negative moment redistribution at failure of 16.4% and 0.5%, respectively. However, the beams had completely different behavior. At first, beam G1-0 had a positive moment redistribution and beam G2-0 had a negative moment redistribution. With the further development of cracks, the trend of the moment redistribution changed in both beams. For beam G1-0, the negative moment redistribution appeared and increased with further loading, while for beam G2-0 the negative moment redistribution decreased. Beams G1-15, G1-25, G2-15, and G2-25 reached high percentages of moment redistribution at failure of 18.5%, 26.7%, 26.9%, and 18.5%, respectively. Positive moment redistribution started soon after cracking and stabilized as the propagation of cracks stabilized. This was a consequence of the \"setup\" of the tested beams due to the ratios of axial stiffness of reinforcement between the midspan and middle support sections. At failure, an increase of moment redistribution was observed as a result of the slippage between GFRP bars and surrounding concrete, especially for beams series 1. It can be concluded that moment redistribution in continuous beams with GFRP reinforcement occurs with a great influence from the ratio of reinforcement axial stiffness between critical sections. Further details of the results for moment redistribution can be found in previously published work [26]. All tested continuous beams were designed according to ACI-15 [29], while CSA-12 [30] and EC2-13 [31] were used as controls. As the moment redistribution is not allowed by actual codes for FRP-reinforced beams, for adopted reinforcement, failure loads are calculated by use of elastic analysis, i.e., based on bending moments, which are obtained as 0.156 Pl for the moment at the midspan and 0.188 Pl for the moment in the middle support section for continuous beams. The failure load was calculated as a lower load at which one of the critical sections (in the midspan or the middle support) reached flexural strength, using actual material properties. It should be noted that the bending behavior of the tested beams can be successfully described with simple equivalent-section-based analytical approaches, which can be used for different structural elements and materials with FRP bars [32]. In Figure 8, calculated failure loads according to ACI-15 [29], CSA-12 [30], and EC2-13 [31] are given in comparison to experimental failure loads. The ultimate bending moment \(M_{n}\) is calculated by the following equations when the reinforcement ratio \(\rho_{f}\) is greater than the balanced reinforcement ratio \(\rho_{\beta}\):  
\[M_{n}=\rho_{f}\cdot f_{f}\cdot\left(1-\frac{0.5}{\alpha_{1}}\cdot\frac{\rho \cdot f_{f}}{f_{c}}\right)\cdot b\cdot d^{2} \tag{1}\]  
Figure 7: Load–moment redistribution relationship in the middle support section for experimental beams: (**a**) series 1; (**b**) series 2. \[f_{f}=\sqrt{\frac{\left(E_{f}\cdot\varepsilon_{cu}\right)^{2}}{4}+\frac{\alpha_{1} \cdot\beta_{1}\cdot f_{c}}{\rho_{f}}\cdot E_{f}\cdot\varepsilon_{cu}-0.5\cdot E _{f}\cdot\varepsilon_{cu}} \tag{2}\]  
where _fj_ is the stress in the tension FRP reinforcement; \(E_{f}\) is the modulus of elasticity of the FRP reinforcement; \(\varepsilon_{cu}\) is the ultimate strain of concrete; \(f_{c}\) is concrete compressive strength; \(b\) and \(d\) are the width and effective depth of the beam, respectively; \(\alpha_{1}\) and \(\beta_{1}\) are the strength reduction factors for concrete:  
\[