In this paper, the performances of reinforced concrete (RC) beams strengthened in shear with steel fiber-reinforced concrete (SFRC) panels are investigated through experiment, analytical computation, and numerical analysis. An experimental program of RC beams strengthened by using SFRC panels, which were attached to both sides of the beams, is carried out to investigate the effects of fiber volume fraction, connection type, and number and diameter of bolts on the structural responses of the retrofitted beams. The current shear resisting model is also employed to discuss the test data considering shear contribution of SFRC panels. The experimental results indicate that the shear effectiveness of the beams strengthened by using SFRC panels is significantly improved. A three-dimensional (3D) nonlinear finite element (FE) analysis adopting ABAQUS is also conducted to simulate the beams strengthened in shear with SFRC panels. The investigation reveals the good agreement between the experimental and analytical results in terms of the mechanical behaviors. To complement the analytical study, a parametric study is performed to further evaluate the influences of panel thickness, compressive strength of SFRC, and bolt pattern on the performances of the beams. Based on the numerical and experimental analysis, a shear resisting model incorporating the simple formulation of average tensile strength perpendicular to the diagonal crack of the strengthened SFRC panels is proposed with the acceptable accuracy for predicting the shear contribution of the SFRC system under various effects.
Deterioration of reinforced concrete (RC) structures is increasing nowadays due to the degradation of structural materials, the increase in design load, and the damage arising from disasters such as earthquake and fire. One common strengthening technique for RC members is the use of fiber-reinforced polymer (FRP) composites, which aims to resist the tensile forces in the needed regions. Many researchers have investigated the performance of concrete beams strengthened by FRP composites under flexure, shear, and fatigue conditions [
On the contrary, strengthening by fiber-reinforced concrete (FRC) is one technique of interest since the addition of short discrete fibers to concrete could improve tensile strength, toughness, and ductility as discussed in the researches [
In this study, the new shear strengthening method for the RC beams is introduced. The steel fiber-reinforced concrete (SFRC) panels were attached to the shear zones through adhesive and bolts. These SFRC panels are precast members which can be prepared in advance and easily installed at site. In order to verify the effectiveness of this intervention technique, the experimental tests, finite element analysis, and analytical model of the RC beams strengthened by using SFRC panels are carried out as follows: (1) the structural responses of RC beams after strengthening is investigated to show the strengthening efficiency of the SFRC panels. (2) The applicability of the current shear resisting model proposed by JSCE 2006 [
The experimental program consisted of nine rectangular RC beams. The parameters investigated were (1) steel fiber volume fraction, (2) connection types, (3) number of bolts, and (4) diameter of bolt. Table
Experimental cases.
Beam name | Designation | Connection types | Fiber volume fraction (%) | Number of bolts | Diameter (mm) |
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Control beam | RC beam | — | — | — | — |
1.5F-Epoxy | Strengthened | Epoxy | 1.5 | — | — |
0F-8D12 | Strengthened | Epoxy + bolts | 0.0 | 8 | 12 |
1F-8D12 | Strengthened | Epoxy + bolts | 1.0 | 8 | 12 |
1.5F-8D12 | Strengthened | Epoxy + bolts | 1.5 | 8 | 12 |
1.5F-4D12 | Strengthened | Epoxy + bolts | 1.5 | 4 | 12 |
1.5F-6D12 | Strengthened | Epoxy + bolts | 1.5 | 6 | 12 |
1.5F-6D10 | Strengthened | Epoxy + bolts | 1.5 | 6 | 10 |
1.5F-8D10 | Strengthened | Epoxy + bolts | 1.5 | 8 | 10 |
All specimens had the same cross-sectional dimensions, longitudinal reinforcement ratio, and stirrup ratio. Figure
Geometry and reinforcement of RC beams (unit: mm).
The SFRC panels were used as external shear reinforcements. The panel dimensions were 300 × 700 × 10 mm3. Four SFRC panels were attached to shear span of the RC beams by using epoxy adhesive (i.e. two panels per side as shown in Figure
Details of the strengthened specimens and measurements (unit: mm).
Panel geometry and bolt arrangement (unit: mm). (a) No bolt. (b) 4 bolts. (c) 6 bolts. (d) 8 bolts.
Concrete with a design cylinder compressive strength of 30 MPa was used for all beams. The mix proportion of concrete is presented in Table
Mix proportion of concrete.
Water to binder ratio | Water (kg/m3) | Cementitious materials (kg/m3) | Fine aggregate (kg/m3) | Coarse aggregate (kg/m3) | Admixture (cc/m3) | Slump (cm) |
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0.54 | 185 | 342 | 770 | 1,150 | 1,710 | 12.5 |
Properties of steel fibers.
Type | Length (mm) | Diameter (mm) | Aspect ratio | Tensile strength (MPa) | Elastic modulus (GPa) | Shape of the end |
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Steel | 35 | 0.55 | 65 | 1050 | 210 | Hooked end |
The panels were bonded on the beams using a two-component epoxy adhesive (Sikadur-30) with a tensile strength of 29 MPa, shear strength of 18 MPa, and elastic modulus in tension of 11.2 GPa, as given by the manufacturer. In addition, 10 mm and 12 mm diameter chemical bolts (anchoring rod: HIT-V5.8 and injection mortar: HIT-HY 200-R) were used in this study.
After casting, the RC beams were sprayed by water daily and covered by wet cloth and plastic sheet for 28 days. Strengthening panels were cast of 10 mm thickness, and the locations of bolts on panels were fixed by providing holes on panels in the casting step. The panels were demolded after 24 hours and were cured in water for 7 days. Before strengthening, concrete and panel surfaces were roughened by using a concrete grinder and cleaned by using a air blower to remove dust. Then, the epoxy adhesive was applied on the concrete and panel surfaces. Next, the precast panels were attached to the side of the beams. For the specimens with bolt connections, after attaching the panels, RC beams were drilled to make holes. After cleaning the holes, adhesive was injected and anchoring rods were finally installed.
All beams were tested as simply supported beams under two symmetrical point loads as shown in Figure
Load-displacement responses of eight RC beams strengthened with SFRC panels were compared to that of the control beam without strengthening, and the load-deflection curves, referring to the total applied load and the midbeam deflection, are presented in Figures
Load-deflection curves for beams with different steel fiber volume fractions.
Load-deflection curves for beams with various connection details.
Load versus strain developed in the stirrups.
It is obvious from the test that a diagonal crack was clearly visible in the control beam. The diagonal crack was first observed at the middle height of the beam and then propagated to the support and loading point. The control beam failed when the concrete compression zone was crushed so that diagonal tension failure occurred.
To assess the cracking mechanism of the beams strengthened in shear with SFRC panels, Table
Crack pattern of the panels at ultimate load obtained from tests and FE analysis.
Beam | Crack pattern from experiments | Principal strain from FE analysis |
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1.5F-Epoxy |
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0F-8D12 |
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1F-8D12 |
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1.5F-8D12 |
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1.5F-4D12 |
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1.5F-6D12 |
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1.5F-6D10 |
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1.5F-8D10 |
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On the contrary, the debonding of the panels was not observed in the specimens with SFRC panels attached by using epoxy and bolt connections. In those beams, all panels remained in the beam sides until the test was completed since the bolts together with epoxy adhesive is responsible to hold the panels. Moreover, the local debonding between the bolts or at the free ends was not observed.
A number of cracks were observed in the mortar panels (specimen 0F-8D12) as shown in Table
Table
Comparison between experimental and analytical results.
Beam ID | Concrete | SFRC | Experimental results | Analytical results | ||||||
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Shear enhancement ratio |
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(MPa) | (MPa) | (MPa) | (kN) | (kN) | (kN) | (kN) | (kN) | |||
Control beam | 32.4 | — | — | 108.4 | 54.2 | — | 1.00 | 104.1 | 52.1 | 0.96 |
1.5F-Epoxy | 32.4 | 60.8 | 5.34 | 206.6 | 103.3 | 49.1 | 1.91 | 202.0 | 101.0 | 0.98 |
0F-8D12 | 32.4 | 56.8 | 3.77 | 206.0 | 103.0 | 48.8 | 1.90 | 207.4 | 103.7 | 1.01 |
1F-8D12 | 36.7 | 69.7 | 4.98 | 200.2 | 100.1 | 45.9 | 1.85 | 204.0 | 102.0 | 1.02 |
1.5F-8D12 | 32.4 | 60.8 | 5.34 | 222.7 | 111.4 | 57.2 | 2.05 | 218.1 | 109.1 | 0.98 |
1.5F-4D12 | 36.7 | 60.8 | 5.34 | 219.0 | 109.5 | 55.3 | 2.02 | 219.3 | 109.6 | 1.00 |
1.5F-6D12 | 36.7 | 60.8 | 5.34 | 202.8 | 101.4 | 47.2 | 1.87 | 204.0 | 102.0 | 1.01 |
1.5F-6D10 | 36.7 | 60.8 | 5.34 | 202.2 | 101.1 | 46.9 | 1.87 | 205.7 | 102.8 | 1.02 |
1.5F-8D10 | 36.7 | 60.8 | 5.34 | 217.8 | 108.9 | 54.7 | 2.01 | 204.7 | 102.4 | 0.94 |
Comparison of the shear capacity of four beams with different steel fiber volume fractions is exhibited in Figure
Shear enhancement of beams with different steel fiber volume fractions.
Compatibility between the RC beam and panels is also analyzed. Figure
Load versus vertical displacement of the RC beam and panel of specimens with different fiber volume fractions. (a) 0F-8D12. (b) 1F-8D12. (c) 1.5F-8D12.
The effect of connection types is presented in Figure
Shear enhancement of beams with various connection details.
Load versus vertical displacement of the RC beam and SFRC panel with various connection details. (a) 1.5F-Epoxy. (b) 1.5F-4D12. (c) 1.5F-6D12. (d) 1.5F-6D10. (e) 1.5F-8D10.
Besides, the number of bolts per panel affects the shear capacity of the strengthened beams. The shear enhancement ratio decreased from 2.05 to 1.87 for 12 mm bolts and from 2.01 to 1.87 for 10 mm bolts as the number of bolts decreased from 8 to 6 bolts per panel. However, the different tendency was found when the number of bolts was reduced to 4 bolts per panel and the bolt arrangement was changed to the diagonal pattern (Figure
To calculate the shear contribution of SFRC panels (
Based on the equations above, the calculation of shear contribution of SFRC panels in the seven beams excluding the control beam and the beam 1.5F-Epoxy is carried out. Figure
Comparison in shear contribution of SFRC panels between experiment and calculation.
In conclusion, since the JSCE equations [
Finite element (FE) modeling of strengthened RC beams was carried out using the available commercial software package ABAQUS. The tested beams were simulated first to validate the effectiveness of the FE tool. Then, FE analysis was performed to investigate the response of the strengthened beams under various effects as a parametric study. Table
Summary of experimental and analytical results.
Series | Name | SFRC panels | No. of bolts |
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Shear enhancement ratio | |||
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Thickness (mm) |
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I | B1 | 15 | 70 | 5.24 | 1.5 | 8 | 222.8 | 111.4 | 2.06 |
B2 | 20 | 70 | 5.24 | 1.5 | 8 | 227.3 | 113.6 | 2.10 | |
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II | B3 | 10 | 50 | 4.95 | 1.5 | 8 | 202.8 | 101.4 | 1.87 |
B4 | 10 | 90 | 6.64 | 1.5 | 8 | 221.4 | 110.7 | 2.04 | |
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III | B5 | 10 | 70 | 5.24 | 1.5 | 4 | 186.4 | 93.2 | 1.72 |
B6 | 10 | 70 | 5.24 | 1.5 | 10 | 208.8 | 104.4 | 1.93 |
Bolt patterns of specimens in series III (unit: mm). (a) B5. (b) B6.
A three-dimensional (3D) FE model was developed. Due to the symmetry of the beams, half of the specimens was modeled as shown in Figure
FE model. (a) FE model of 1.5F-8D12. (b) Loading and boundary condition.
A mesh convergence study was carried out to examine the optimal mesh size. The results show that further decrease in the mesh size has little effect on the numerical results. Consequently, the mesh sizes of the concrete and panels were 20 mm in general and 5 mm for the region near the bolts as presented in Figure
FE mesh discretization. (a) Concrete beam. (b) SFRC panel. (c) Bolts.
Figure
In order to model the behavior of concrete, concrete damage plasticity (CDP) was used. The stress-strain curve of concrete in compression was simulated by the model proposed by Hognestad [
For the strengthening panels, concrete damage plasticity was also used to simulate the behavior of steel fiber-reinforced concrete. The behavior of SFRC in compression was expressed by the model proposed by Lee et al. [
Material model of SFRC. (a) Compression (Lee et al. [
The longitudinal and shear reinforcements were modeled by a bilinear elastic-perfectly plastic model. The stress-strain behavior of bolts is that of linear elastic material until yielding, followed by plastic behavior. In addition, the modulus of elasticity and yield stress for bolts were taken as 200 GPa and 520 MPa, respectively. On the contrary, as mentioned in the section of element models, a cohesive surface model was used as shown in Figure
Traction-separation cohesive material law.
Figure
Load-midspan deflection comparison for tested beams. (a) Control beam. (b) 1.5F-Epoxy. (c) 0F-8D12. (d) 1F-8D12. (e) 1.5F-8D12. (f) 1.5F-4D12. (g) 1.5F-6D12. (h) 1.5F-6D10. (i) 1.5F-8D10.
The maximum principal strain at the peak load of the panels obtained from FE analysis is plotted in Table
The numerical analysis was extended to investigate the effects of panel thickness, the compressive strength of SFRC, the number of bolts, and bolt arrangement on the performances of the strengthened beams. The shear capacity of all analytical beams is listed in Table
Load-deflection curves of the parametric study. Effect of (a) panel thickness; (b) compressive strength of SFRC; (c) number of bolts (symmetrical pattern); (d) bolt pattern.
Figure
Strain at peak load of the panels with different numbers of bolts. (a) 4 bolts (B5). (b) 6 bolts (1.5F-6D12). (c) 8 bolts (1.5F-8D12). (d) 10 bolts (B6).
In the previous section, the analysis indicated that the current shear resisting model underestimated the actual values since the connecting bolts are not considered in the calculation. Also, the JSCE equations [
Calculation for the regressing equation of average tensile strength perpendicular to the diagonal crack.
Name | SFRC panels |
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Stiffness of fiber fraction, |
Stiffness of bolt group, |
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Thickness (mm) |
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(MPa) | (MPa) | ||||||
B1 | 15 | 70 | 5.24 | 8.30 | 3.15 | 0.86 | 1.58 |
B2 | 20 | 70 | 5.24 | 3.72 | 3.15 | 0.86 | 0.71 |
B3 | 10 | 50 | 4.95 | 6.90 | 3.15 | 0.86 | 1.39 |
B4 | 10 | 90 | 6.64 | 8.59 | 3.15 | 0.86 | 1.29 |
B5 | 10 | 70 | 5.24 | 3.67 | 3.15 | 0.43 | 0.70 |
B6 | 10 | 70 | 5.24 | 8.53 | 3.15 | 1.08 | 1.63 |
1.5F-epoxy | 10 | 60.8 | 5.34 | 7.74 | 3.15 | 0.00 | 1.45 |
0F-8D12 | 10 | 56.8 | 3.77 | 12.39 | 0 | 0.86 | 3.29 |
1F-8D12 | 10 | 69.7 | 4.98 | 9.32 | 2.1 | 0.86 | 1.87 |
1.5F-8D12 | 10 | 60.8 | 5.34 | 5.81 | 3.15 | 0.86 | 1.09 |
1.5F-4D12 | 10 | 60.8 | 5.34 | 5.37 | 3.15 | 0.43 | 1.00 |
1.5F-6D12 | 10 | 60.8 | 5.34 | 4.44 | 3.15 | 0.65 | 0.83 |
1.5F-6D10 | 10 | 60.8 | 5.34 | 4.58 | 3.15 | 0.45 | 0.86 |
1.5F-8D10 | 10 | 60.8 | 5.34 | 8.22 | 3.15 | 0.60 | 1.54 |
By substituting equation (
Comparison in shear contribution of SFRC panels between investigation and calculation using the developed model.
This study indicated the importance of the SFRC panels in the shear strengthening effectiveness for the existing RC beams. Based on the experimental and numerical investigations, the following conclusions could be drawn: Shear capacity of RC beams significantly increased as the RC beams were strengthened using SFRC panels. The effect of the steel fibers was pronounced when the volume fraction of fiber was 1.5%. The resistance to cracks in the panels increased due to the addition of steel fibers. The shear capacity of the specimens with epoxy combined with bolts connection was slightly higher than that with the specimens with only epoxy connection. However, sudden debonding of the SFRC panel was observed at the ultimate load in the case of the specimen with epoxy connection. It is noted that since only one strengthened specimen with the epoxy connection has been tested in this study, further investigation shall be carried out to confirm the behavior of using only epoxy as connection. However, using epoxy combined with bolts connection can prevent debonding and improve stiffness of strengthened beams under service load. The load-displacement relationships obtained from FE analysis were in close agreement with the experimental results in terms of the ultimate load, crack patterns, and failure mode. This indicates that the presented numerical modeling procedure can be used for predicting the behavior of RC beams strengthened in shear with SFRC precast panels. The experimental and numerical results showed that the shear capacity increased with the increase in number of bolts up to 8 bolts per panel and compressive strength of SFRC up to 70 MPa. Bolt patterns (also called bolt arrangement) strongly affected the shear behavior of the beams. The diameter of the bolts and panel thickness insignificantly influenced the shear effectiveness of the SFRC strengthened beams. The shear resisting model of JSCE [ For the proposed strengthening method, it is suggested to prepare the panels’ holes during casting process. In addition, the drilling of the holes for the bolts on existing RC beams shall be carefully done to avoid the microcraking on the substrate and the possible damage of existing reinforcement. However, some investigations should be conducted in the future such as onsite implementation and the comprehensive evaluation of the current design models.
The data used to support the findings of this study are included within the article. Requests for access of the experimental and analytical data should be made to Dr. Pitcha Jongvivatsakul via email:
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was financially supported by the Thailand Research Fund (TRG5880231) and Grants for Development of New Faculty Staff, Ratchadaphiseksomphot Endowment Fund, Chulalongkorn University. The authors would like to acknowledge SR. Fiber Co., Ltd., Hilti (Thailand) Ltd., and Retrofit Structure Specialist Co., Ltd. for providing materials and installation assistance.