## 3 Results and Discussion
### Load-Crack Width Relationship  
In this section, the obtained experimental maximal crack widths are compared to the provisions for calculation of crack widths with the chosen codes. EC2-13 [31] calculates the crack width \(w_{k}\) as the product of the maximal spacing of the cracks \(s_{r,max}\) and the average strain, which represents the difference in the average strain in the reinforcement, including the tension stiffening of the concrete \(\varepsilon_{fm}\) and the average strain in the concrete between the cracks \(\varepsilon_{cm}\):  
\[w_{k}=s_{r,max}\cdot\left(\varepsilon_{fm}-\varepsilon_{cm}\right) \tag{6}\]  
\[s_{r,max}=3.4\cdot c+0.425\cdot k_{1}\cdot k_{2}\cdot\frac{\varnothing}{ \rho_{peff}} \tag{7}\]  
\[\varepsilon_{fm}-\varepsilon_{cm}=\frac{\sigma_{f}-k_{t}\cdot\frac{f_{cutoff} }{\rho_{peff}}\cdot\left(1+\alpha_{e}\cdot\rho_{peff}\right)}{E_{f}}\geq 0.6 \cdot\frac{\sigma_{f}}{E_{f}} \tag{8}\]  
\[\rho_{p,eff}=\frac{A_{f}}{b\cdot h_{coeff}}\,h_{coeff}=\min[2.5(h-d),(h-x)/3,h/2] \tag{9}\]  
where \(c\) is concrete cover; \(k_{1}\) is a coefficient taking into account the bond properties (0.8 for high bond bars and 1.6 for smooth bars); \(k_{2}\) is a coefficient taking into account the distribution of the strain (0.5 for bending and 1 for pure tension); \(\varnothing\) is the bar diameter, \(\sigma_{f}\) is the stress in the tension reinforcement; \(E_{f}\) is the modulus of elasticity of the FRP reinforcement; \(\alpha_{e}\) is the modular ratio \(E_{f}/E_{c}\); \(k_{t}\) is a coefficient taking into account the load duration (0.6 for short term loads and 0.4 for long term loads); \(\rho_{p,eff}\) is the effective reinforcement ratio; \(A_{f}\) is the area of reinforcement; \(b\), \(h\), and \(d\) are the width, height, and effective depth of the beam, respectively; and \(x\) is the neutral axis depth. The Italian guideline CNR-DT-203/06 [33] for elements with FRP reinforcement calculates the crack width \(w_{k}\) as the product of the average distance between cracks \(s_{m}\) and the average strain accounting for tension stiffening \(\varepsilon_{fm}\):  
\[w_{k}=\beta\cdot s_{m}\cdot\varepsilon_{fm} \tag{10}\]  
\[s_{r,max}=50+0.25\cdot k_{1}\cdot k_{2}\cdot\frac{\varnothing}{\rho_{peff}} \tag{11}\]  
\[\varepsilon_{fm}=\frac{\sigma_{f}}{E_{f}}\cdot\left(1-\beta_{1}\cdot\beta_{2} \cdot\left(\frac{\sigma_{f}}{\sigma_{f}}\right)^{2}\right) \tag{12}\]  
\[\rho_{peff}=\frac{A_{f}}{b\cdot h_{coeff}}\,h_{coeff}=2.5(h-d) \tag{13}\]  
where \(k_{1}\) is a coefficient taking into account the bond properties (1.6 for the FRP bars), \(\sigma_{f}\) is the stress in the tension reinforcement of the cracked cross-section, \(\sigma_{f}\) is the stress in the tension reinforcement of the cracked cross-section when the first crack is observed, \(\beta\) is a coefficient relating the average crack width to the characteristic value (1.7 for cracking due to loads), \(\beta_{1}\) is a coefficient taking into account the bond properties (0.5 for the FRP bars), and \(\beta_{2}\) is a coefficient taking into account the load duration (1.0 for short-term loads and 0.5 for long-term loads). The maximal crack width \(w\) for an element with a FRP reinforcement according to ACI-06 [34] and CSA-12 [30], Annex S, can be obtained from:  
\[w=2\cdot\frac{f_{f}}{E_{f}}\cdot\beta\cdot k_{b}\cdot\sqrt{d_{c}^{2}+\left( \frac{s}{2}\right)^{2}} \tag{14}\]  
where\(f_{f}\) is the stress in the tension reinforcement, \(E_{f}\) is the modulus of elasticity of the FRP reinforcement, \(\beta=(h-x)/(d-x)\), \(d_{c}\) is the concrete cover from the center of the reinforcing bar, and \(s\) is the bar spacing. ISIS-07 [35] suggests a similar equation to calculate the maximal crack width \(w\) for FRP-reinforced sections:  
\[w=2.2\cdot\frac{f_{f}}{E_{f}}\cdot\beta\cdot k_{b}\cdot\sqrt[3]{d_{c}\cdot A} \tag{15}\]  
where \(A\) is an effective tension area of concrete surrounding the flexural tension reinforcement and having the same centroid as that reinforcement, divided by the number of the bars.