## 3 Results and Discussion
### Load-Deflection Relationship
For this reason, it is important to know the deflection response of the structural member during the entire loading process, not only at service loads. Hence, a modified model for calculation of deflection for continuously supported GFRP-reinforced beams for each load level is proposed. The model is based on the expression given in ACI-15 [29], with a modification factor value of 0.7, in accordance with the previous study by [PERSON] et al. [26] and as shown in Equation (23), to reduce the moment of inertia after cracking. Additionally, in Equation (24) a non-linear parameter \(P\) is used in accordance with [PERSON] et al. [9] for higher load levels:  
\[I_{e}=\frac{0.7\cdot I_{cr}\cdot P}{1-\gamma\cdot\left(\frac{M_{cr}}{M_{a}} \right)^{2}\cdot\left(1-\frac{0.7\cdot I_{cr}}{I_{g}}\right)} \tag{23}\]\[P=1-\left(1/11\left(\frac{M_{cr}}{M_{a}}\right)\right)^{4} \tag{24}\]  
The U.S. standard ACI-318-14 [36] for concrete structures with steel reinforcement suggests that the effective moment of inertia \(I_{e}\) for continuous beams should be calculated by the expression:  
\[I_{e}=0.85I_{em}+0.15I_{ec} \tag{25}\]  
where \(I_{em}\) and \(I_{ac}\) are the effective moment of inertia in the midspan and middle support sections, respectively. In this way, the effects of internal force redistribution are introduced into the calculation of the effective moment of inertia. Considering the significant contribution of elastic moment redistribution in GFRP-reinforced continuous beams [26], the stiffness ratio between the critical cross-sections depends mainly on the stiffness ratio of the GFRP reinforcement in these cross-sections. Therefore, the influence of the cross-section stiffness in the middle support area on the deflection in the midspan for continuously supported GFRP-reinforced beams is more significant than for beams with steel reinforcement. For this reason, the authors applied a more appropriate expression for the calculation of the effective moment  
\[I_{e}=\left(\frac{M_{cr}}{M_{a}}\right)^{3}\cdot\rho_{d}\cdot I_{g}+\left(1- \left(\frac{M_{cr}}{M_{a}}\right)^{3}\right)I_{cr}\leq I_{g} \tag{17}\]0 Experimental and predicted load–deflection relationships for tested beams. of inertia for these beams, with a more significant contribution of the cross-section stiffness in the middle support area:  
\[I_{e}=\left(\frac{M_{cr}}{M_{a}}\right)^{3}\cdot\rho_{d}\cdot I_{g}+\left(1- \left(\frac{M_{cr}}{M_{a}}\right)^{3}\right)I_{cr}\leq I_{g} \tag{17}\]1  
The very good prediction of the experimental results with the proposed model is shown in Figure 11 over the entire loading process, where the effective moment of inertia \(I_{e}\) is less than the cracked moment of inertia \(I_{cr}\). Using the coefficient \(P\), the proposed model shows a good development of deflection for higher load levels. Immediately after cracks occur, a large increase in deflections in accordance with ISIS-07 [35] is noticed. This sudden reduction in stiffness was not observed during testing of the beams series 1, as can be seen in Figure 11, which again indicates very good adhesion conditions between ribbed GFRP bars and concrete. Further experimental results would better confirm the proposed model.