## 4 Results and Discussion
### Comparison of Bending and Tensile Test  
The structural concrete Standards [8; 12] adopt residual strength values supplied by bending tests, \(f_{R1}\) and \(f_{R3}\), as structural designing values of fiber reinforced concrete. Equation (2) shows the relation between the force applied by the test machine and the residual strength of the material in the bending test [23].  
\[f_{R}=\frac{3 Fl}{bl_{sp}^{2}} \tag{2}\]  
where \(f_{R}\) is the stress, \(Fl\) the applied force, \(l\) the span between supports, \(b\) the width of the specimen and \(l_{sp}\) the height of the ligament in the notched section.  
In tensile tests the applied force of the testing machine is transformed to stress by dividing the load by the resistant transversal cross section.  
Figure 10 shows the \(f_{R}\) stress-CMOD curves for bending and tensile tests. Figure 10a shows the result for SCCP6, Figure 10b VCCP6, and Figure 10c for VCLP6 concrete. For SCCP6 and VCCP6 concretes it can be seen that the results obtained by traditional strain gauges and by video-extensometry are very similar for displacements of 0.02 mm. On the other hand, in the case of VCLP6, with a weaker resistant matrix, the values of both measurement types are only comparable for displacements larger than 0.2 mm.  
Figure 9: Load-displacement curves obtained by the LVDTs extensometers and by video-extensometry in the tensile tests: (**a**) SCCP6, (**b**) VCCP6 and (**c**) VCLP6 concretes.  
A similar behavior is observed for both, bending and tensile tests, for each type of concrete. A first linear branch appears from the test onset up to the limit of proportionality, \(f_{LOP}\), when the matrix of concrete cracks. The \(f_{LOP}\) is associated with the strength of the concrete matrix. In the case of bending tests, the low-strength concrete, VCLP6, \(f_{LOP}\) value was 2.80 MPa, compared with 5.98 MPa and 5.37 MPa, corresponding to SCCP6 and VCCP6, respectively. In the case of tensile tests \(f_{LOP}\) ranged from 1.63 MPa to 2.27 MPa, values representing 42% of the strength of the equivalent bending results.  
After \(f_{LOP}\), stress decreases until the minimum resistance point,\(f_{MIN}\). Then, the remaining stress increases until \(f_{REM}\) due to the contribution of the fibers. This remaining part of the stress-CMOD curve increases in all concretes, being the increment more subtle in VCLP6. The maximum residual strength for bending tests were: 3.60, 3.24 and 3.89 MPa for SCCP6, VCCP6 and VCLP6, respectively. These values were reduced to 0.87, 1.45 and 0.39 MPa for each type of concrete, respectively, being 31% the average reduction in remaining resistance in comparison with the bending test.  
In addition, Figure 10 includes a continuous black line marked as 0.33\(f_{R3}\). This line corresponds to the simplified stress-deformation diagram proposed by EHE-08 [12] for designing structural fiber reinforced concrete. In the case of SCCP6 and VCLP6 concrete, the value 0.33\(f_{R3}\) is higher than the entire residual stress branch, so the standard would overestimate the strength of the fiber reinforced under tensile testing. On the contrary, in the case of VCCP6, from 1 mm of CMOD, the experimental residual stress is higher than the one prescribed by the EHE-08. The main contribution of tensile tests in relation to bending tests is that they directly show the behavior of fiber reinforced concrete and directly provide values that can be used in the structural design.  
Figure 10: \(f_{R}\) stress-CMOD curves for bending and tensile tests: (**a**) SCCP6, (**b**) VCCP6 and (c) VCLP6 concretes.