# Flexural Capacity of Concrete Beams with Basalt Fiber-Reinforced Polymer Bars and Stirrups

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

^{3}. Concrete with a ratio of w/c = 0.5 was selected for the test. The used aggregate was a mixture of sand with a grain size of up to 2 mm and a coarse natural aggregate with a grain size of up to 8 mm. The fraction of up to 2 mm was 51%, the 2–4 mm fraction 38%, while the 4–16 mm fraction was 62% of the crumb pile. Detailed mixture information is given in Table 2.

^{3}were used as dispersed reinforcement. These are thin basalt fibers with a fiber diameter of 20 µm, a tensile strength of 750 MPa, and a Young’s modulus of 89 GPa. Part of the aggregate was replaced by a volume of the dispersed reinforcement in Figure 1.

_{ck}of concrete were carried out pursuant to EN 12390-3:2011 [21] using cubic samples with a side of 100 mm, concrete flexural strength f

_{ctm}was tested on samples with dimensions of 100 × 100 × 400 mm pursuant to EN 12390-5:2011 [22], and elasticity modulus E

_{cm}was determined according to EN 12390-13:2014 [23] using cylindrical specimens with a diameter of 150 mm and a height of 300 mm. The results of concrete testing are presented in Table 3.

_{yk}= 500 MPa. The mechanical properties of BFRP bars were tested on a bar with a diameter of 6 mm, pursuant to ACI440.3R [24], i.e., the guaranteed tensile strength was f

_{u,ave}= 1180 MPa, the guaranteed modulus of elasticity was E

_{f}= 47.6 GPa, and the guaranteed strain at break was ε*

_{fu}= 2.0%. A detailed description of the research can be found in paper [25].

#### 2.2. Test Setup and Testing Procedure

_{eff}= 4200 mm were loaded in a four-point system. The beam support and loading scheme are shown in Figure 2. The beams were hinged at one end, free to roll at the other. The span length of the pure-bending region between the two load points was 1400 mm. The two-point load setup consisted of a wide flange beam spread on two steel plates covering its entire width. To enable their rotation, the steel plates had steel rollers. The test of the beams was load-controlled at a rate of 5 kN per minute. The load was generated by a hydraulic jack located at the center of the beam and applied to the broad flange. A load cell attached to the hydraulic jack measured the applied load. The mid-span and support deflections (U) were measured using a linear variable differential transformer. Mid-span deformations were measured using DIC (digital image correlation). The measurement set consists of two cooperating cameras and a control unit, enabling the recording of up to 5 million readings at a frequency of 15 Hz. The measurement procedure consists in the initial calibration of cameras for a given working area, applying a pattern, and ultimately recording the displacement of measurement points during the so-called facets.

## 3. Results

#### 3.1. Failure Modes

_{ult}. The first vertical flexural crack in BFRC RC beams was initiated in the middle of the constant moment region. The diagonal cracks formed when a load of approximately 0.5 P

_{ult}was applied. The first perpendicular cracks in RC and FRC reference beams developed when a load of 0.2 P

_{ult}was applied. Diagonal cracks formed much later in RC (0.45 P

_{ult}—A-I-W01, 0.45 P

_{ult}—A-I-W02) and FRC (0.60 P

_{ult}—A-I-W01, 0.52 P

_{ult}—A-I-W02) beams. This means that beams with steel reinforcement and basalt fibers had the highest scratch resistance. BFRC RC beams showed the lowest scratch resistance.

_{ult}and the ultimate flexural moments M

_{ult}, along with the average values of the failure force $\overline{{P}_{ult}}$, the ultimate bending moment $\overline{{M}_{ult}}$, and the change in the value of forces $\Delta {P}_{ult}$, with the destructive force specified for the reference A-I-W0 beams. The manner of beam failure and the maximum deflections are also shown.

#### 3.2. Moment-Deflection Behavior

#### 3.3. Strain in Concrete in Compression and Tension Zones

_{ult}and 60% in P

_{ult}compared to the series with steel reinforcement and basalt fibers, i.e., A-I-WB. On the other hand, the composite beam reaches the highest deformation value in the tensile zone of the beam under breaking load, equal to 8‰. This value is half that of the steel reinforcement or the basalt fibers series.

## 4. Comparison of the Calculated and Experimental Values of Flexural Capacity

_{n}is the flexural capacity, M

_{u}is the maximum moment due to external loads, while $\varphi $ is the reduction factor. The application of factor $\varphi $ is due to the lack of plastic deformation of BFRP reinforcement.

_{ult}is the bending resistance determined from scientific studies. The flexural capacity was determined according to the ACI M

_{ACI}and fib Model Code guidelines for M

_{fib}.

- -
- the methods for the determination of the tensile strength of FRP reinforcement, often depending on environmental factors;
- -
- the reduction coefficients of the load-bearing capacity, depending on the compressive strength of the concrete;
- -
- the methods for calculating the extent of the compression zone;
- -
- the different values of the ultimate deformation of concrete.

## 5. Conclusions

- As expected, the six beams with BFRP bars and stirrups failed by the crushing of concrete at mid-span in the compression fibers.
- The presence of composite reinforced bars increases the deformation value due to tensile stresses. Using the FRP reinforcement resulted in improving the flexural capacity of beams, regardless of the concrete type.
- Due to the relatively low value of Young’s modulus of BFRP reinforcement, the stiffness of the beam decreases significantly after scratching. After the drawing moment is exceeded, perpendicular cracks of considerable width are formed in the beam’s central section at the tension reinforcement level. Due to the corrosion resistance of BFRP bars, the crack width is not as important as in the case of reinforced concrete structures.
- BFRP basalt bars also influenced the nature of beam failure, which did not occur suddenly, but was rather associated with the forming of many cracks and significant deflection of the element.
- The methods for designing flexural capacity are based on the equations of the equilibrium of forces and moments in the cross section, as is the case with steel members.
- During the design, the differences resulting from the different physical and mechanical properties of the BFRP reinforcement compared to the steel should be considered. For this reason, rectangular stress distribution is assumed in the compression zone.
- The analysis showed differences of approximately 20% in the flexural capacity of the beams. The differences are mainly due to the use of different reduction factors. The difference in the results would have been much more significant when determining the flexural capacity using material factors that are ignored when compared with the test results.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Fiore, V.; Scalici, T.; Di Bella, G.; Valenza, A. A review on basalt fibre and its composites. Compos. Part B Eng.
**2015**, 74, 74–94. [Google Scholar] [CrossRef] - High, C.A.; Seliem, H.M.; El-Safty, A.R.; Rizkalla, S.H. Use of basalt fibers for concrete structures. Constr. Build. Mater.
**2015**, 96, 37–46. [Google Scholar] [CrossRef] - Pilakoutas, K.; Neocleous, K.; Guadagnini, M.; Matthys, S. Design guidelines for FRP reinforced concrete structures. Proc. Inst. Civ. Eng. Struct. Build.
**2011**, 164, 255–263. [Google Scholar] [CrossRef][Green Version] - Murad, Y.; Tarawneh, A.; Arar, F.; Al-Zu’bi, A.; Al-Ghwairi, A.; Al-Jaafreh, A.; Tarawneh, M. Flexural strength prediction for concrete beams reinforced with FRP bars using gene expression programming. Structures
**2021**, 33, 3163–3172. [Google Scholar] [CrossRef] - Szmigiera, E.D.; Protchenko, K.; Urbański, M.; Garbacz, A. Mechanical properties of hybrid FRP bars and nano-hybrid FRP bars. Arch. Civ. Eng.
**2019**, 65, 97–110. [Google Scholar] [CrossRef][Green Version] - Aydın, E.; Boru, E.; Aydın, F. Effects of FRP bar type and fiber reinforced concrete on the flexural behavior of hybrid beams. Constr. Build. Mater.
**2021**, 279, 122407. [Google Scholar] [CrossRef] - Brózda, K.; Selejdak, J. Analiza nośności na zginanie belki zbrojonej prętami GFRP na podstawie amerykańskich i włoskich zaleceń projektowych. Czasopismo Inżynierii Lądowej Środowiska i Architektury
**2017**, 64, 297–304. [Google Scholar] [CrossRef][Green Version] - Park, C.-G.; Jang, C.-I.; Lee, S.-W.; Won, J.-P. Microstructural investigation of long-term degradation mechanisms in GFRP dowel bars for jointed concrete pavement. J. Appl. Polym. Sci.
**2008**, 108, 3128–3137. [Google Scholar] [CrossRef] - Seręga, S.; Kotynia, R.; Lasek, K. Numerical modelling of preloaded RC beams strengthened with prestressed CFRP laminates. Eng. Struct.
**2018**, 176, 917–934. [Google Scholar] [CrossRef] - Bank, L.C. Design of FRP Reinforced and Strengthened Concrete; CRC Press: Boca Raton, FL, USA, 2008. [Google Scholar]
- Krassowska, J.; Kosior-Kazberuk, M. Pręty kompozytowe BFRP jako zbrojenie w prefabrykowanych belkach betonowych. Mater. Bud.
**2022**, 30–32. [Google Scholar] [CrossRef] - Tang, Y.; Jiang, T.; Wan, Y. Structural monitoring method for RC column with distributed self-sensing BFRP bars. Case Stud. Constr. Mater.
**2022**, 17, e01616. [Google Scholar] [CrossRef] - Tang, Y.; Sun, Z.; Wei, Y.; Zou, X. Compressive behavior and design method of BFRP bars constrained with a BFRP spiral with different spacings in concrete members. Eng. Struct.
**2022**, 268, 114757. [Google Scholar] [CrossRef] - Pawłowski, D.; Szumigała, M. An experimental and theoretical study of deflections of BFRP RC beams. Czasopismo Techniczne. Budownictwo
**2015**, 112, 63–70. [Google Scholar] [CrossRef] - Qureshi, J. A Review of Fibre Reinforced Polymer Structures. Fibers
**2022**, 10, 27. [Google Scholar] [CrossRef] - Li, C.; Zhu, H.; Niu, G.; Cheng, S.; Gu, Z.; Yang, L. Flexural behavior and a new model for flexural design of concrete beams hybridly reinforced by continuous FRP bars and discrete steel fibers. Structures
**2022**, 38, 949–960. [Google Scholar] [CrossRef] - Abed, F.; Alhafiz, A.R. Effect of basalt fibers on the flexural behavior of concrete beams reinforced with BFRP bars. Compos. Struct.
**2019**, 215, 23–34. [Google Scholar] [CrossRef] - Kosior-Kazberuk, M.; Krassowska, J.; Vidales Barriguete, A.; Ramirez, C.P. Fracture parameters of basalt fiber reinforced concrete. Anales de Edificación
**2018**, 4, 52–58. [Google Scholar] [CrossRef][Green Version] - EN 12350-2:2019—Testing Fresh Concrete. Slump Test. Available online: https://shop.bsigroup.com/ProductDetail?pid=000000000030360058 (accessed on 20 April 2021).
- EN 12350-7:2019—TC—Tracked Changes. Testing Fresh Concrete. Air Content. Pressure Methods. Available online: https://shop.bsigroup.com/ProductDetail?pid=000000000030407441 (accessed on 20 April 2021).
- EN 12390-3:2009—Testing Hardened Concrete—Part 3: Compressive Strength of Test Specimens. Available online: https://standards.iteh.ai/catalog/standards/cen/d1d94876-958b-4941-ade0-780076fc330a/en-12390-3-2009 (accessed on 20 April 2021).
- EN 12390-5:2019—Testing Hardened Concrete—Part 5: Flexural Strength of Test Specimens. Available online: https://standards.iteh.ai/catalog/standards/cen/5653c2c7-55a9-4bcb-8e13-5b1dfb0e3baf/en-12390-5-2019 (accessed on 20 April 2021).
- EN 12390-13:2013—Testing Hardened Concrete. Determination of Secant Modulus of Elasticity in Compression. Available online: https://shop.bsigroup.com/ProductDetail/?pid=000000000030398745 (accessed on 20 April 2021).
- ACI Committee 440. Guide Test Methods for Fiberreinforced Polymers (FRPs) for Reinforcing or Strengthening Concrete Structures; American Concrete Institute: Farmington Hills, MI, USA, 2004. [Google Scholar]
- Kosior-Kazberuk, M.; Wasilczyk, R. Analiza ugięć i zarysowania betonowych belek ze zbrojeniem niemetalicznym. Budownictwo i Inżynieria Środowiska
**2017**, 8, 173–183. [Google Scholar] [CrossRef] - ACI Committee 440. Guide for the Design and Connstruction of Structural Concrete Reinforced with Fiber-Reinforced Polymer (FRP) Bars; American Concrete Institute: Farmington Hills, MI, USA, 2015. [Google Scholar]
- Fédération Internationale du Béton (FIB). Model Code for Concrete Structures 2010—Ernst-und-Sohn.de; Ernst & Sohn, a Wiley Brand: Lausanne, Switzerland, 2013; Available online: https://www.ernst-und-sohn.de/index.php?q=en/fib-model-code-for-concrete-structures-2010 (accessed on 14 March 2021).

**Figure 5.**Load-deflection curves for the tested beams. (

**a**) Relationship until ultimate deflection; (

**b**) Relationship between the development of the first crack and deflection limits.

**Figure 6.**Strains in concrete in series A-I-W01, A-I-WB1, and B-I-WB1. (

**a**) The position of longitudinal reinforcement in tension and compression zones; (

**b**) Strains in the DIC area.

**Figure 7.**Three operating states of the structure with BFRP reinforcement: (

**a**) cross section with the optimal degree of reinforcement, (

**b**) rearmed cross section—failure by the crushing of concrete, (

**c**) underreinforced cross section—failure by bars breaking.

Beam No. | Bar Diameter, mm | No. of Bars | Materials of Bars | Basalt Fibers, kg/m^{3} | |
---|---|---|---|---|---|

RC | A-I-WO1 | 14 | 4 | steel | 0 |

A-I-WO2 | 14 | 4 | steel | 0 | |

FRC | A-I-WB1 | 14 | 4 | steel | 8 |

A-I-WB2 | 14 | 4 | steel | 8 | |

BFRC | B-I-WB1 | 14 | 4 | basalt | 8 |

B-I-WB2 | 14 | 4 | basalt | 8 |

Mixture Proportions | Quantity |
---|---|

Cement 42.5R, kg/m^{3} | 320 |

Water, kg/m^{3} | 160 |

Sand 0.125–4 mm, kg/m^{3} | 732 |

Aggregate, kg/m^{3} | 1203 |

Fiber Content [kg/m^{3}] | Slump | Air Content | f_{ck} | σ | ν | f_{ctm} | σ | ν | E_{cm} |
---|---|---|---|---|---|---|---|---|---|

mm | % | MPa | MPa | % | MPa | MPa | % | GPa | |

0 | 19 | 3.1 | 43.78 | 0.6 | 0.96 | 5.55 | 0.85 | 15.28 | 40.64 |

8 | 2 | 3.8 | 44.52 | 2.75 | 6.17 | 6.11 | 0.68 | 12.14 | 42.02 |

Beam No. | Max. Load P_{ult} | $\overline{{\mathit{P}}_{\mathit{u}\mathit{l}\mathit{t}}}$ | Moment M _{ult} | $\overline{{\mathit{M}}_{\mathit{u}\mathit{l}\mathit{t}}}$ | Failure Mode | Ultimate Deflection ∆a_{lim} | |
---|---|---|---|---|---|---|---|

kN | kN | kNm | kNm | - | mm | ||

RC | A-I-W01 | 110 | 110 | 77 | 77 | F | 59.67 |

A-I-W02 | 110 | 77 | F + CC | 73.97 | |||

FRC | A-I-WB1 | 137 | 126 | 95.9 | 88.2 | F + CC | 68.04 |

A-I-WB2 | 115 | 80.5 | F + CC | 76.52 | |||

BFRP | B-I-WB1 | 110 | 97 | 58.8 | 67.9 | F | 52.21 |

B-I-WB2 | 84 | 77 | F + BR | 52.06 |

Beam No. | Load | Strain in Concrete on the Position of Longitudinal Reinforced | ||
---|---|---|---|---|

In compression ε | In tension ε | |||

[-] | [‰] | [‰] | ||

RC | A-I-W0 | 0.5 P_{ult} | −1.050 | 1.513 |

P_{ult} | −3.443 | 5.420 | ||

FRC | A-I-WB | 0.5 P_{ult} | −1.153 | 1.339 |

P_{ult} | −3.632 | 4.076 | ||

BFRP | B-I-WB | 0.5 P_{ult} | −0.332 | 2.356 |

P_{ult} | −1.533 | 8.838 |

Load-Bearing Capacity | RC | BFRC | |
---|---|---|---|

M_{ult} | kNm | 82.50 | 76.50 |

M_{ACI} | kNm | 107.98 | 66.82 |

M_{ult}/M_{ACI} | - | 1.31 | 0.87 |

M_{fib} | kNm | 76.97 | 52.01 |

M_{ult}/M_{fib} | - | 0.93 | 0.68 |

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**MDPI and ACS Style**

Krassowska, J.; Piña Ramírez, C.
Flexural Capacity of Concrete Beams with Basalt Fiber-Reinforced Polymer Bars and Stirrups. *Materials* **2022**, *15*, 8270.
https://doi.org/10.3390/ma15228270

**AMA Style**

Krassowska J, Piña Ramírez C.
Flexural Capacity of Concrete Beams with Basalt Fiber-Reinforced Polymer Bars and Stirrups. *Materials*. 2022; 15(22):8270.
https://doi.org/10.3390/ma15228270

**Chicago/Turabian Style**

Krassowska, Julita, and Carolina Piña Ramírez.
2022. "Flexural Capacity of Concrete Beams with Basalt Fiber-Reinforced Polymer Bars and Stirrups" *Materials* 15, no. 22: 8270.
https://doi.org/10.3390/ma15228270