3.1. Experimental Design and Method

A flexural experiment was planned to evaluate the effect of the reinforcing bar specifications such as steel bar, FRP bar, and the hybrid arrangement of steel and FRP bars on the flexural strength of FRC members. Table 1 lists the specimens and Fig. 1 shows the detailed diagrams of specimens. As shown in Table 1. a total of seven beam specimens were fabricated with the type of tensile reinforcing bar, mixing of PVA fiber, etc. as parameters.

Fig. 1

Detailed view of the beam and specimen cross-section

The specimens were planned in two types: single-layer and double-layer arrangements depending on the placement of tensile reinforcing bars. The double-layer specimens mixed PVA fibers at 0.5% and placed steel bars on top and CFRP, GFRP, and steel bar at the bottom as flexural tension members. The singlelayer specimens mixed PVA fibers in two ratios, 0.5% and 0%, to examine the effect of PVA fiber reinforcement, and placed CFRP and GFRP bars as flexural tension members. The specimens were designed with cross section of 200 mm×300 mm, length of 3000 mm, clear span of 2600 mm, depth of inner reinforcing bar as 200 mm, and the depth of outer reinforcing bar as 260 mm.

Every specimen was designed for failure by concrete crushing with an excessive reinforcement ratio. The D10 deformed bar was used for the shear reinforcing bar of the specimens, and the D13 deformed bar was used for the compressive bar and inner reinforcing bar. For the outer reinforcing bars, two pieces each of D16 deformed bar, GFRP D19, and CFRP D13 were arranged depending on the specimen.

The experiment was carried out using the universal testing machine (UTM) until every specimen was fractured by the compressive failure of concrete. Fig. 2 shows the installation of the specimens. For loading, the displacement control method was adopted for four-point support loading. Loading was ended when the load decreased by at least 30% after the maximum load. For the measurement of deflection and strain, the mid-span deflection was measured with a 100mm displacement meter and the strain of each reinforcing bar was measured by attaching a gauge to the center of every reinforcing bar.

Fig. 2

Specimen installation appearance

3.2. Experimental Design and Method

The PVA fibers of N Company in South Korea were used in the specimens, and the physical properties of the PVA fibers evaluated by the manufacturer are outlined in Table 2. The design criterion strength is 35 MPa and 100 mm×200 mm concrete specimens were fabricated to perform standard compressive strength test according to the existence or absence of fiber reinforcement. The experiment results showed that the compressive strength of specimen was 20.5 MPa for fiber-reinforced specimens and 21.4 MPa for other specimens. The concrete mixing ratio is shown in Table 3.

To examine the material properties of steel and FRP bars used in this experiment, the material experiment was conducted in accordance with KS B 0801. Three experiments were performed for each material, and their average values were calculated to derive the resultant value. Table 4. shows the material test results.

4.1. Crack and Failure Patterns

The crack pattern during the failure of every specimen is illustrated in Fig. 3 Failure of all the specimens was done by concrete crushing as planned at first except for P1-C, which is a member using CFRP bars only and mixed with fibers. The P1-C specimen showed an initial behavior similar to other specimens mixed with fibers, but was failed by the CFRP bar fracture in the end (Fig. 3(f)). This seems to be due to the increased extreme compressive strain of the concrete reinforced with fibers. Recent studies related to fiber-reinforced concrete have reported that the extreme compressive strain of fiberreinforced concrete was 0.0035 or higher. The concrete members reinforced with steel bars are generally designed around the yield point of steel bar. They do not consider the extreme compressive strain of concrete to be important during the member design because they assume that steel bars are yielded before the crushing failure of concrete. However, the extreme compressive strain of concrete plays a critical role in the prediction of the failure pattern for concrete members reinforced with FRP bars because they show linear elastic behavior with no yield point due to the nature of FRP. Therefore, when concrete reinforced with fibers and concrete reinforced with FRP bars are designed, the accurate extreme compressive strain of fiber-reinforced concrete is required to prevent the failure caused by the sudden fracture of FRP bars.

Fig. 3

Crack pattern of specimen

4.2. Load-Deflection Relationship

yielded before the crushing failure of concrete. However, the extreme compressive strain of concrete plays a critical role in the Fig. 4 shows the load-deflection relationship curve of the central part from the experimental results. Table 5. outlines the load and mid-span deflection at the first flexural crack and maximum load. In case of the specimens with the double-layer arrangement of steel and FRP bars (P1-SS, P1-SG, and P1-SC), the first cracking load of the P1-SS was greater by 26-34% than those of the P1-SG and P1-SC specimens. In case of the specimens with GFRP bar placed as the outermost reinforcing bar (P0-G, P1-G), the cracking load of the specimen with no fibers was higher by 16% than that of the specimen mixed with fibers. Furthermore, in the case of the specimens with CFRP bar placed as the outermost reinforcing bar (PO-C, P1-C), the first cracking load of the specimen with no fibers was higher by 18% than that of the specimen mixed with fibers. After cracking, the specimens with double-layer arrangement of FRP and steel bars showed a lower rigidity than the specimens reinforced with steel bars only.

Fig. 4

Loads-deflection relationship of specimens

As shown in Fig. 4(a), all the three specimens showed similar behavior of rigidity during the early cracking. After the first cracking, the rigidity of all specimens decreased. The specimen reinforced with steel bar only (P1-SS) showed a greater rigidity than the specimens reinforced with FRP bar as the outermost reinforcing bar (P1-SG, P1-SC). However, the P1-SS specimen showed a rapid decrease in rigidity after the steel bar yielded. When the maximum strengths of specimens were compared, the specimen where CFRP bar was arranged as the bottom tensile reinforcing bar (P1-SC) showed the greatest maximum strength among the specimens with a double-layer arrangement of steel and FRP bars. The other specimens did not show significant differences in rigidity and flexural strength depending on the mixing of fibers as shown in Fig. 4(b) and (c). However, the specimens mixed with fibers (P1-C, P1-G) showed a greater deflection under the maximum load than the specimens with no fibers (P0-C, P0-G), suggesting excellent strain performance. This difference was greater in the specimens using CFRP.

5.1. Finite Element Analysis Model

The VecTor2 program was used for finite element analysis. VecTor2 is a nonlinear finite element analysis program based on the modified compression field theory of concrete members. The finite element model is shown in Fig. 5 The external constraint of specimens was set as simple support and a vertical concentrated load was applied to the corresponding joint.

Fig. 5

FE model

5.1.1. Concrete model

For the nonlinear material model of concrete used in this analysis, the stress-strain diagram Eq. (1) of general strength concrete range proposed by Popovics was used. The graphs (Fig. 6) reflect the fact that as the rigidity increases, the rising part shows linearity, and as the maximum compressive stress increases, the ductility of concrete decreases.

Fig. 6

FE model(concrete)

(1)

f c i = ε c i ε P f P n n − 1 ( ε c i ε P )   for   ε c i < 0

Where f_P = corresponding to the peak compressive stress, ε_P = less compressive than the strain, n = The curve fitting parameter.

5.1.2. Reinforcing bar model

For steel bars, a model consisting of three parts of stressstrain curves (Fig. 7) was used. This analysis model shows a linear behavior until the steel bar reaches the yield point. Until fracture, the phase shows linear or nonlinear behavior depending on the parameter of hardening phenomenon. The tension and compressive reinforcement stress fs are determined by Eq. (2).

Fig. 7

FE model(reinforcement steel bar)

(2)

f s = [ E s ε s for   ε s < ε y f y for   ε y < ε s < ε s h f u + ( f y − f u ) ( ε u − ε s ε u − ε s h ) P for   ε s h < ε s < ε u 0 for   ε u < ε s ]

Where ε_s is the reinforcement strain, ε_y is the yield strain, ε_sh is the strain at the onset of the strain hardening, ε_u is the ultimate strain, P is the strain-hardening parameter.

5.2. Comparison and Analysis of Finite Element Analysis Results

Fig. 8 shows graphs comparing the load-deflection relationship curves from the experiments of specimens and the finite element analysis results. In the case of specimens with a double-layer arrangement of steel and FRP bars (P1-SS, P1-SG, P1-SC), the graph from analysis showed somewhat greater initial rigidity compared to the graph from the experiment. In the case of the other four specimens (P0-G, P1-G, P0-C, P1-C), the time when the first crack occurs and the initial elastic zone section was predicted relatively accurately. For the specimen with a singlelayer arrangement of GFRP bar as tensile reinforcing bar, the graph from analysis showed a smaller rigidity than the graph from experiment after the initial crack, but the difference is not large. For the specimen with a single-layer arrangement of CFRP bar as tensile reinforcing bar, the graph from analysis showed a somewhat greater rigidity than the graph from experiment after the initial crack, but the rigidity tended to decrease as it approached the maximum load. This difference in rigidity seems to be caused by the fact that the upward trend of extreme compressive strain of concrete depending on the mixing of PVA fibers affected the experimental results.

Fig. 8

Loads-deflection relationship of specimens

The experimental and analysis values of the crack moment and maximum moment of each specimen are outlined in Table 6. In the case of crack moment, the total error rate ranged between 0.97 and 1.07, indicating small variations. When the maximum moment values obtained through experiments were compared with the values obtained through finite element analysis, the ratio was 1.2 on average, the standard deviation was 0.085, and the maximum error rate was within 22%. These results suggest that the flexural reinforcing bar and PVA fibers had large effect on the crack and contraction of concrete, resulting in somewhat large maximum moment values. Based on this, it was concluded that the finite element analysis model proposed in this study simulates the actual behavior of the beams reinforced with FRP bars and PVA fibers relatively accurately. However, further research is necessary to attain the reliability of the analysis model results in the case of various parameter analyses in future.