MEASURED STRAINS

The installed gauges are capable to give interesting information about the behavior of the tested beams. Strain gauges installed in both, the longitudinal reinforcement and the traverse strengthening, gave quantitative information about strains and they were capable to show where the failure of the beam developed, and whether the beam failed in shear or bending.

Figures 5.21 and 5.22 show the strain measured in the gauges of the longitudinal

Experimental program for active shear strengthening of RC beams using Ni-Ti-Nb wires

reinforcement of all tests. A schematic drawing of the locations of the gauges is depicted on graph of beam 1.1 and in figs. 5.2 and 5.3. Almost all longitudinal strain gauges worked properly recording strains except for the gauge GLONG.02 of beam 5.1 where an unexpected rupture was detected close to the failure load of the test.

The approximate yielding strain is shown in the graphs by means of a vertical dashed line.

It is taken from the measured yielding strength of the tested steel rebars (fy = 513 MPa) as previously shown in subchapter 5.3 and it is given from Eq. 5.4:

𝜀 = 𝑓_𝑦

𝐸 = 513

200,000·= 0.002565 (5.4)

It can be seen that in beam 5.2 (which failed in bending), the longitudinal reinforcement yielded at mid-span (Gauge GLONG.02, see fig. 5.21). However, in the other beams, the longitudinal reinforcement did not yield at mid-span, but instead the longitudinal bar yielded close to the support in the shear span where the critical crack developed.

Figure 5.21a. Strains measured in the longitudinal reinforcement of beams 1.1, 1.2, 2.1 and 2.2. A schematic drawing of the locations of the gauges is depicted on graph of beam 1.1

GLONG1 GLONG2 GLONG3

Chapter 5

Figure 5.21b. Strains measured in the longitudinal reinforcement of beams: 3.1a, 3.1b, 3.2a, 3.2b, 4.1, 4.2, 5.1 and 5.2

Experimental program for active shear strengthening of RC beams using Ni-Ti-Nb wires

Figure 5.22. Strains measured in the longitudinal reinforcement of beams of the second phase

Chapter 5

The strain measured in the vertical links of the Ni-Ti-Nb pseudo-rectangular spiral are represented for the beam tests in fig. 5.23 and fig. 5.24. A schematic drawing of the locations of the gauges are depicted on graphs of beams 2.1 and 2.2, and in figs. 5.2 and 5.3. For clarity, only the strain measured in the gauges located in the critical span, where the failure took place, are represented.

The strain in the vertical links remained negligible until the shear cracks propagated. The values of the measured strains of the gauges were directly related to crack openings since the configuration of the spirals, with no adherence between concrete and Ni-Ti-Nb wires and only contact between them in the turn of the wires in each edge of the faces of the beams, made that all strain in each wire crossed by a crack, and consequently wire elongation, was a consequence of the opening of the crack.

At failure, different strain values were measured by the strain gauges attached at each vertical link. This ensures that there had been no general wire slippage around the corners of the cross sections. Visual inspection throughout all tests also confirmed that the slippage of the wires was avoided. Table 5.4 shows the strains at failure measured in all gauges of the beams.

Table 5.4. Strains () at beam failure measured in the gauges of the vertical links of the beams. In bold gauges in links of spans that failed in shear

Beam GTR.01

-No strain gauge used in positions GTR.01 and GTR.08

*Gauges did not provide proper data due to an error in the test set-up

Experimental program for active shear strengthening of RC beams using Ni-Ti-Nb wires

Figure 5.23. Strains measured in the spiral vertical links in beams 2.1, 2.2, 3.1a, 3.1b, 3.2a, 3.2b, 4.1, 4.2, 5.1, and 5.2. Schematic drawings of the locations of the gauges are depicted on graphs of beams 2.1and 2.2

GTR1 GTR2 GTR3 GTR4

GTR5 GTR6 GTR7 GTR8

Chapter 5

Figure 5.24. Strains measured in the vertical links of the spirals in beams 7.1, 7.2, 8.1, 8.2, 9.1, 9.2, 10.1 and 10.2

Experimental program for active shear strengthening of RC beams using Ni-Ti-Nb wires

For beams 3.1 and 3.2 some difficulties in the set-up for the strain gauges were encountered, since the gauges were installed previously to the activation process with a heat gun and, although the gauges were attached with special thermal adhesive (for temperatures up to 300 ºC), during the activation process some gauges were disabled and only one gauge in beam 3.2 worked correctly, measuring strains up to 3000 . This encountered difficulty was overcome with an additional protection of the gauges of beams 4.1 and 4.2, protecting them with special butyl wrap and external thermal tape (figure 5.25).

The stresses at failure in the vertical links may be obtained from the measured strains, taking into account the links crossing the first branch of the critical crack. For example, in beam 2.2, the first branch of the critical crack crossed the vertical link in which GTR.07 was attached (fig. 5.20d). Taking into account the tangent modulus of elasticity of Ni-Ti-Nb after the generation of recovery stresses (25 GPa), see table 4.8, the increase of stress in the Ni-Ti-Nb wire is given by Eq. 5.5:

𝜎 = 𝐸 · 𝜀 = 25,000 · 4,675 · 10⁻⁶= 116.87 𝑀𝑃𝑎 (5.5)

Figure 5.25. Beam 4.2 with shear strengthening ready to be activated after the application of a pre-load (highlighted fissures) with specially protected strain gauges

Chapter 5

This value will have to be added to the recovery stress developed due to activation when considering the stresses developed in the strengthening wires (for predicting the shear strength of the tested specimens, see Chapter 7). Also, crack opening in the first branch developed at failure can be approximated although the crack widths were not monitored during the tests. Considering, that the length of 150 mm of spiral link that developed such strain had an elongation of 0.70 mm (0.004675·150), all this elongation is due to the shear crack width in the vertical direction, which is a reasonable value. This aspect can be considered only in the cases where only one crack crosses the vertical link. This happens in most of the cases (see fig. 5.20).

To obtain a reasonable value of stresses developed at failure in all tested beams, the strains measured in the vertical cracks crossed by the first branch of critical crack have been analyzed and they are shown in table 5.5. Note that in some cases the first branch of critical crack did not develop exactly in the location of a vertical wire, and in those cases more than one strain gauge has been taken into account. Therefore, for modelling purposes, average values may be considered.

Considerable scatter had been encountered and values between 1000  and 5000  were obtained. Anyway, the average value of 3007  with a standard deviation of 1221  and covariance of 41 % for all tested beams are reasonable values in such test measurements.

The crack widths were not monitored during the tests. However, the considered average strain value of 3000  of Ni-Ti-Nb spiral link is equivalent, assuming one single shear crack (as may be seen in figure 5.20), leads to a shear crack width in the vertical direction of 0.45 mm at failure (length of 150 mm of spiral branch), what is a reasonable value. For reference:

2000  involves a shear crack width in the vertical direction of 0.30 mm at failure, and 5000

 involves a shear crack width in the vertical direction of 0.75 mm at failure.

Experimental program for active shear strengthening of RC beams using Ni-Ti-Nb wires

Table 5.5. Strains () measured in strain gauges attached to vertical links crossed by the first branch of the critical crack.

Gauges in links crossing the critical crack Beam Failure

* Second gauge crossed by first branch of critical crack

# Gauges did not provide proper data due to an error in the test set-up

$ Not considered strain and stress (bending failure)

Chapter 5