## 4 Test on Beams
### Failure Tests on the Retrofitted Beams
#### 4.3.4 Experimental Contributions to the Beam Shear Resistance  
The experimental contributions to the beam shear resistance due to the transverse steel reinforcement (V\({}_{\text{Rd,s exp}}\)), the CFRP reinforcement (V\({}_{\text{Rd,f exp}}\)) and the concrete (V\({}_{\text{Rd,c exp}}\)), were estimated for the tested beams DB1-R and DB2-R in Table 4 when the maximum experimental shear was recorded. The shear crack with an inclination angle \(\theta\) equal to about 45\({}^{\circ}\) extended along each beam for about 800 mm (Figure 8a,b). The experimental transverse steel contribution was evaluated by Equation (7):  
\[\text{V}_{\text{Rd,s exp}}=\text{n}_{\text{sw}}\cdot\text{A}_{\text{sw}} \cdot\text{f}_{\text{0.2\%, m}} \tag{7}\]  
in which n\({}_{\text{sw}}\) is the number of the stirrups crossing the shear crack, A\({}_{\text{sw}}\) is the cross-section area of the stirrups and f\({}_{\text{0.2\%,m}}\) is the mean value of the yield stress of the stirrups from the data in Table 1.  
The spacing of the stirrups was irregular along each beam (SS2.1) and therefore n\({}_{\text{sw}}\) was calculated by the ratio between the length of the beam part crossed by the shear crack (800 mm) and the mean spacing of the stirrups. The values of n\({}_{\text{sw}}\) were 3.5 and 3.4 for the beam DB1-R and DB2-R. The CFRP reinforcement contribution was estimated by Equation (8):  
\[\text{V}_{\text{Rd,f exp}}=\text{n}_{\text{f,strips}}\cdot\text{2}\cdot\text{ t}_{\text{f}}\cdot\text{b}_{\text{f}}\cdot\text{E}_{\text{f}}\cdot\text{ \varepsilon}_{\text{f exp}} \tag{8}\]  
where n\({}_{\text{f,strips}}\) is the number of the CFRP strips crossing the shear crack, t\({}_{\text{f}}\) is the CFRP fabric thickness, b\({}_{\text{f}}\) is the CFRP strip width, E\({}_{\text{f}}\) is the CFRP fabric Young's modulus and \(\text{\varepsilon}_{\text{f exp}}\) is the strain measured on the CFRP U-strips at beam failure (SS4.3.3). The CFRP fabric characteristics and the strip geometries are given in SS3. The evaluation of the number of the U-strips, which gave a contribution to the shear resistance, is not simple because debonding of the strips was evident and the brittle failure of the CFRP reinforcement did not permitted plastic force distribution. However, n\({}_{\text{f,strips}}\) equal to 3 is used to evaluate the CFRP contribution in Table 4 because this is the number of the strips crossing the shear crack in Figure 8a,b for each beam. The value of the experimental CFRP strain \(\text{\varepsilon}_{\text{f exp}}\) was about equal to 0.3% for the beam DB1-R (Figure 9) and 0.25% for the beam DB2-R. The experimental concrete contribution was obtained by the subtraction of the experimental shear contribution of the CFRP and the steel reinforcements from the maximum experimental shear recorded on the retrofitted beams (Figure 7a,b). After the CFRP reinforcement failure, the experimental shear was about 157 kN and 114 kN for the beam DB1-R and DB2-R (Figure 7a,b). The beams could sustain these shear forces thanks to the transverse steel reinforcement and the concrete contributions. In fact, the sum of the transverse steel reinforcement and the concrete contributions in Table 4 is equal to 142 kN and 153 kN for the beams DB1-R and DB2-R: these values are very similar to the ones recorded after CFRP reinforcement failure. However, the evaluation of the steel contribution is uncertain because: 1. The stirrups spacing was irregular; 2. The plastic force distribution was reduced by the CFRP reinforcement and so some stirrups could give a smaller contribution; 3. The CFRP reinforcement limited the crack width and the stress in the stirrups could be smaller than the yield stress depending on the actual steel strain. For the tested beams, the experimental strain measured on the CFRP strips were about 0.3% (SS4.3.3) and therefore the stirrups more probably yielded because the steel yield strain is 0.2%. The evaluation of the CFRP contribution is also uncertain because: 1.