*2.2. Material Properties*

The beam testing was accompanied by the determination of the average compressive strength and the average modulus of elasticity of the concrete. The mechanical properties of the concrete were determined in cylindrical samples with a diameter of 150 mm and a height of 300 mm. The average compressive strength of the concrete for beams B-1, B-2, B-3, and B-4 was 68.94 MPa, 70.13 MPa, 65.47 MPa, and 71.39 MPa, respectively. The average modulus of the concrete elasticity under compression in the case of beams B-1, B-2, B-3, and B-4 was 35.47 GPa, 36.63 GPa, 35.97 GPa, and 38.07 GPa, respectively.

As longitudinal reinforcement, steel bars with a diameter of 20 mm and a characteristic yield strength of 500 MPa and GFRP bars with a diameter of 20 mm and an average tensile strength > 1100 MPa, as declared by the manufacturer, were used. The modulus of elasticity of the steel bars and GFRP bars was 200 GPa and 57 GPa, respectively, as declared by the manufacturer. GFRP stirrups with a diameter of 12 mm and headed bars with a diameter of 12 mm were used as shear reinforcement.

Both stirrups and headed bars were a Schöck product described as Schöck Combar. The bars used were made of E-CR (Electrical/Chemical Resistance) glass fiber composite with a diameter of approximately 20 μm and vinyl ester resin. The head anchorage was a fiber reinforced polymer mortar. The anchor head was 60 mm long, and the maximum diameter was 30 mm (Figure 3a). In order to compare the mode of failure and tensile strength of GFRP bars, five samples of Φ12 headed bars and five samples of Φ12 straight bars were tested. The bar tests were carried out in accordance with Annex A of the American standard ACI 440.3R-04 [32] and the instruction ISO 10406-1:2015 [33]. Test samples were made by embedding the bar ends in Sikadur-330 epoxy resin filling internally screwed steel pipes (Figure 3b). The head anchorage was at one end of the test bar. The end of the head anchoring was embedded in a steel element with a special flange (Figure 3c) to eliminate clamping forces that could distort the test results. For the tensile test, samples with a multiplicity of 10 (measuring base length 120 mm for bars Φ12) were used. The modulus of elasticity was determined on the basis of strain results based on a 60 mm long measurement base.

**Figure 3.** Samples for determining the tensile behavior of GFRP bars: (**a**) dimensions of the head anchorage of GFRP Schöck Combar; (**b**) straight bar sample; (**c**) headed bar sample.

Tensile strength *f* u, modulus of elasticity *E*f, and ultimate strain εu were determined by the procedure in [32] using the following relationships:

$$f\_{\mathbf{u}} = \frac{F\_{\mathbf{u}}}{A} \tag{1}$$

$$E\_{\rm f} = \frac{F\_1 - F\_2}{(\varepsilon\_1 - \varepsilon\_2)A} \tag{2}$$

$$
\varepsilon\_{\mathbf{u}} = \frac{F\_{\mathbf{u}}}{E\_{\mathbf{f}}A} \tag{3}
$$

where: *F*u, the tensile capacity of FRP bar; *A*, the cross-sectional area of FRP bar; *F*1, the tensile load at approximately 50% of the ultimate load capacity; ε1, the tensile strain at approximately 50% of the ultimate load capacity; *F*2, the tensile load at approximately 20% of the ultimate load capacity; ε2, the tensile strain at approximately 20% of the ultimate load capacity.

Straight bars were stretched in a testing machine using classic jaws used for the tensile test (Figure 4a), steel bars among others. The end in the form of a steel flange was fixed in a special jaw shown in Figure 4b. The use of this type of jaw, with an appropriate wall thickness of the steel tube, eliminated clamping forces that might have distorted the result of the actual anchoring strength.

**Figure 4.** The method of fixing the sample in the testing machine: (**a**) fixing the straight steel pipe; (**b**) fixing of a flanged steel pipe.

Based on the data provided by the manufacturer and by Kurth [24], the average tensile strength of the stirrups used was set at *f* bend = 770 MPa and the mean value of modulus of elasticity at *E* = 57 GPa. The stirrups used in this study were bent during manufacture, and the bending diameter was seven times the diameter of the bar (84 mm). The stirrups shaped in the same way were the subject of research by the manufacturer and Kurth in [24]. In this study, the stress-strain characteristics of GFRP stirrups were not experimentally determined, and the values of the tensile strength and modulus of elasticity of GFRP stirrups were taken from the manufacturer's data, which were consistent with Kurth's results [24].

### *2.3. Instrumentation, Test Setup and Procedure*

The examination of each beam consisted of two stages. In the first stage, the beam was subjected to a 4-point bending until one of the support zones was damaged (Figure 5). In the second stage, the support at which damage occurred was moved directly under the force, obtaining a 3-point bending scheme.

**Figure 5.** Test setup of two stages. Dimensions in mm.

For the first stage, the load causing the appearance of diagonal and perpendicular cracks was determined. The angle of inclination of the compressed concrete strut was also established for each stage. The element was loaded until the appearance of cracks, and the load was then increased at a speed of about 0.2 kN/s, stopping at ca. every 50 kN; each time the crack pattern and the load at which it occurred was monitored. For each beam, strain measurements of concrete were made in the compression zone and the tension bars. Concrete strains were measured using RL300/50 resistivity strain gauges. Strain gauges were glued onto the concrete around the stirrups (on both sides of the

web). Beam deflections were recorded in the middle of the span and under concentrated forces using inductive sensors. Displacement of supports was also measured using inductive sensors located next to the support points. The strains of steel bars and GFRP bars were measured with the use of RL120/20 strain gauges. Strain gauges on bars were placed in the middle of the length of the vertical arms of stirrups/bars with head anchoring. Strain gauges were also glued to longitudinal bars in the middle of the span and in cross-sections under applied forces.

### **3. Experimental Results and Discussion**

### *3.1. Rebar Test*

The failure mode of straight bars was of an explosive nature, and all bars were characterized by linear-elastic behavior over the entire strength range. The average tensile strength of a straight GFRP bar was 1299 MPa with a standard deviation *s* = 69 MPa. The mean modulus of elasticity was 58.1 GPa, with a standard deviation of *s* = 3.4 GPa. The mean value of the ultimate strain was 22.4‰ with a standard deviation *s* = 0.7‰. The damaged sample after the test is shown in Figure 6a, while the static equilibrium paths of the tested bars are shown in Figure 6c.

**Figure 6.** Rebar test results: (**a**) straight bar sample failure; (**b**) headed bar sample failure; (**c**) static equilibrium paths in the tensile test of various types of GFRP bars. \* Based on the manufacturer's data and Kurth's tests [24].

Headed bars were characterized by linear-elastic behavior until stress initiating the loss of bar adhesion to the anchor head was reached. The failure mode consisted of the slipping of the bar from the anchor head and was radically less violent than bar rupture. Vint tested the anchoring of GFRP headed bars in concrete and came to similar conclusions [21]. A relatively high value of bar displacement relative to the anchor head was achieved, at which the sample was still able to carry the load. The average value of the tensile strength of the GFRP headed bar was 545 MPa with a standard deviation *s* = 15 MPa. The average modulus of elasticity was 61.9 GPa, with a standard deviation of *s* = 3.0 GPa. The damaged sample after the test is shown in Figure 6b, while the static equilibrium paths of the tested bars are shown in Figure 6c.

Before the test, the bar diameter was measured with an accuracy of 0.1 mm. The diameter was measured taking into account the ribs, then the thickness of the ribs was measured, and the core diameter of the bar cross-section *d*f,i was calculated. Fifteen diameter measurements were made for each bar over a distance of 200 mm. The average value of the diameter *d*f is given in Table 2. The tensile strength *f* u, modulus of elasticity *E*f, and ultimate strain εu were determined based on Formulas (1)–(3), and the results are shown in Table 2.


**Table 2.** Samples details and test results.

The short-term tensile strength of headed bars was lower than that of straight bars. The strength of headed bars was about 42% of the tensile strength of straight bars. In addition, based on data from the manufacturer, it was found that the strength of headed bars constituted about 71% of the strength of the bent stirrup section (Figure 6c). The modulus of elasticity for both straight bars and headed bars was similar and amounted to about 60 GPa, which roughly corresponded to the manufacturer's data, including the research by Kurth [24]. Similarly to the paper [24], where GFRP Φ16 headed bars were tested, the modulus of elasticity obtained as a result of testing headed bars was slightly larger than that obtained in the tensile test of bars without anchoring. The average ultimate strain recorded for the tensile test of straight bars was about 22.4 ‰, which corresponded to an elongation of about 1.3 mm (on a measuring base of 60 mm). In the case of stirrups, based on the assumption of linear-elastic behavior in the tensile test and the value of the average tensile strength and modulus of elasticity declared by the manufacturer, the estimated ultimate strain was about 13.5 ‰, which corresponded to an elongation of about 0.8 mm (based on measurement equal to 60 mm). The head length of 60 mm introduced the possibility of transferring the force of almost equal tensile strength of the anchorage at an elongation of about 2.5 mm. It could be concluded that a single bar with a head anchorage had a lower tensile strength than a straight bar or stirrup. In the case of a support zone reinforced with headed bars, greater stress redistribution could be expected than in the case of the corresponding reinforcement in the form of frame stirrups.
