## 3 Results and Discussion
### Load-Deflection Relationship  
The deflection \(\Delta\) of continuously supported beams loaded with point midspan forces \(P\) could be calculated as:  
\[\Delta=\frac{7}{768}\cdot\frac{PL^{3}}{E_{c}I_{e}} \tag{16}\]  
where \(L\) is the span length, \(E_{c}\) is the modulus of elasticity of concrete, and \(I_{e}\) represents the effective moment of inertia. ACI-06 [34] suggests an equation to calculate the effective moment of inertia \(I_{e}\) based on [PERSON]'s pattern:  
\[I_{e}=\left(\frac{M_{cr}}{M_{a}}\right)^{3}\cdot\rho_{d}\cdot I_{g}+\left(1- \left(\frac{M_{cr}}{M_{a}}\right)^{3}\right)I_{cr}\leq I_{g} \tag{17}\]  
where \(M_{cr}\) is the cracking moment, \(M_{a}\) is the applied moment, \(I_{g}\) is the moment of inertia of the gross concrete section, and \(I_{cr}\) is the moment of inertia of the cracked section. Factor \(\beta_{d}\) is represented as:  
\[\beta_{d}=\frac{1}{5}\frac{\rho_{f}}{\rho_{fb}}\leq 1.0 \tag{18}\]  
where \(\rho_{f}\) is the FRP reinforcement ratio and \(\rho_{fb}\) is the balanced FRP reinforcement ratio. According to ISIS-07 [35], the effective moment of inertia can be expressed as:  
\[I_{e}=\frac{I_{g}I_{cr}}{I_{cr}+\left(1-0.5\cdot\left(\frac{M_{cr}}{M_{a}}\right) ^{2}\right)\cdot\left(I_{g}-I_{cr}\right)} \tag{19}\]  
which is very similar to the approach proposed in EC2-13 [31] when the coefficients for long-term durations are included. ACI-15 [29] suggests an equation to determine the effective moment of inertia based on research studies by [PERSON] and [PERSON] [11]:  
\[I_{e}=\frac{I_{cr}}{1-\gamma\cdot\left(\frac{M_{cr}}{M_{a}}\right)^{2}\cdot \left(1-\frac{I_{cr}}{I_{g}}\right)} \tag{20}\]  
where \(\gamma\) is integration factor, which considering beams loaded with midspan point forces, could be calculated as follows:  
\[\gamma=3-2\cdot\left(\frac{M_{cr}}{M_{a}}\right) \tag{21}\]  
Based on the obtained experimental results, [PERSON] and [PERSON] [23] suggested modification of the effective moment of inertia given in ACI-06 [34] for continuously supported GFRP-reinforced beams:  
\[I_{e}=\left(\frac{M_{cr}}{M_{a}}\right)^{3}\cdot\beta_{d}\cdot I_{g}+\left(1- \left(\frac{M_{cr}}{M_{a}}\right)^{3}\right)\cdot I_{cr}\cdot\gamma_{G}\leq I _{g} \tag{22}\]  
where \(\gamma_{G}=0.6\) is a reduction factor for the state after the cracks occur. In Figure 11, the deflections for experimental beams are compared to the calculated ones proposed by ACI-06 [34], ACI-15 [29], ISIS-07 [35], and [PERSON] and [PERSON] [23]. The experimental values for the cracking moment \(M_{cr}\) were used for all models. The specific load level deflections obtained through experiment are significantly higher than calculated values. Surely, the main reason for the mismatched diagrams is the fact that models used to calculate deflection are mainly based on research studies that were enforced on simple beams, which are calculated by the elastic analysis for uniform stiffness along the beam. The only match is for experimental and calculated deflections for the lower loads levels. The suggested model by [PERSON] and [PERSON] [23] shows much better fitting of deflection with experimental results, with slightly higher values. Within load levels close to failure, exceptions occur when the experimental deflection curve falls further. Similar observations and comparisons regarding deflection values for tested beams were also made [PERSON] in his experimental research [19]. Considering the experimental beams of a single series, deflections are fairly uniform, even for the different reinforcement axial stiffness in the middle of the beam span. This is a consequence of internal force redistribution, which occurs in the critical sections after formation of cracks. Since FRP-reinforced beams, due to the low modulus of elasticity of the FRP reinforcement, already show considerable deflection at service loads, eventual overload beyond these limits can cause damage to the structural members associated with these elements.