# Experimental Study on the Shear Behavior of Reinforced Highly Ductile Fiber-Reinforced Concrete Beams with Stirrups

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Programs

#### 2.1. Material Properties

#### 2.1.1. HDC

#### 2.1.2. Concrete and Steel Reinforcement

#### 2.2. Beam Specimens

#### 2.3. Test Apparatus

## 3. Test Results and Discussion

#### 3.1. Crack Patterns and Failure Modes

#### 3.1.1. RC Beam Specimens

- (1)
- Diagonal compression failure

- (2)
- Shear compression failure

#### 3.1.2. RHDC Beam Specimens

- (1)
- Diagonal compression failure

- (2)
- Shear compression failure

- (3)
- Diagonal tension failure

- (4)
- Flexural shear failure

#### 3.2. Discussion of Failure Modes

#### 3.2.1. Diagonal Compression Failure

#### 3.2.2. Shear-Compression Failure

#### 3.2.3. Diagonal Tension Failure

#### 3.2.4. Flexural Shear Failure

#### 3.3. Load–Deflection Behavior

#### 3.4. Deformation Capacity

#### 3.5. Shear Strength

#### 3.5.1. Shear Resistance Mechanisms

#### 3.5.2. Analysis of Shear Strength

#### 3.5.3. Prediction of Shear Strength According to the Code

## 4. Conclusions

- Unlike RC beams, RHDC beams failed in the shear mode with a gradual decrease in load-carrying capacity and higher residual strength. The modes of failure of RHDC beams included diagonal compression, shear-compression, flexural shear, and diagonal tension failures. When the shear span to effective depth ration was three, some RHDC beams failed in flexural shear mode with favorable ductility.
- Compared with RC beams, RHDC beams exhibited satisfactory integrity without the collapse and peeling-off of HDC. Stable crack propagation and multiple diagonal crack behavior were observed in RHDC beams, indicating that the fiber-bridging effect of HDC effectively restrained the development of shear cracks.
- Improvements in shear strength of RHDC beams ranged from 13.3% to 30.5% compared with RC beams; RHDC beams exhibited higher residual strength and deformation capacity, indicating that HDC significantly improved the brittle shear failure mode. Specimens H-1 and H-2 exhibited the largest improvement in shear strength and displacement ductility factor, respectively, compared with RC beams.
- The results proved that the shear span to effective depth ratio, stirrup ratio, and longitudinal reinforcement ratio of RHDC beams had a great influence on the shear failure modes. The shear strength of RHDC beams decreased as the shear span to effective depth ratio increased. For RHDC beams with the same shear span to effective depth ratio, the shear strength increased with the increase in longitudinal reinforcement ratio and stirrup ratio under shear compression failure.
- The calculated value of shear strength, according to GB 50010-2010, is conservative compared to the experimental values for shear strength of RHDC beams. The effect of material ductility on the shear strength of RHDC beams needs to be studied further, because shear failure modes and shear strength are closely related to the ultimate tensile strain and ultimate compressive strain of HDC.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Load–deflection curves. (

**a**) Diagonal compression failure, (

**b**) shear compression failure, (

**c**) diagonal tension failure, (

**d**) flexural shear failure.

**Figure 5.**Displacement factors. (

**a**) Deflection-clear span ratio corresponding to the peak load; (

**b**) Deflection-clear span ratio corresponding to the ultimate deflection; (

**c**) Displacement ductility factor.

**Figure 6.**Shear resistance mechanism of RHDC beams with stirrups: (

**a**) arch–truss model; (

**b**) main arch (I) and truss elements; (

**c**) secondary arch (II) and truss elements.

Fiber Type | Length/mm | $\mathbf{Diameter}/\mathsf{\mu}\mathbf{m}$ | Tensile Strength/MPa | Elastic Modulus/GPa | Elongation/% |
---|---|---|---|---|---|

PVA | 12 | 39 | 1600 | 40 | 7 |

Material | Cement | Fly Ash | Sand | Water | PVA Fibers |
---|---|---|---|---|---|

HDC | 593 | 593 | 427 | 344 | 26 |

Chemical Composition | SiO_{2}/% | Al_{2}O_{3}/% | Fe_{2}O_{3}/% | Sum/% | MgO/% | SO_{3}/% | CaO/% |
---|---|---|---|---|---|---|---|

Cement | 19.56 | 5.79 | 3.60 | 28.95 | 0.97 | 2.43 | 64.22 |

Fly ash | 64.59 | 19.92 | 3.49 | 88.00 | 1.31 | 0.40 | 3.83 |

Type | Diameter (mm) | ${\mathit{f}}_{\mathbf{y}}\left(\mathbf{MPa}\right)$ | ${\mathit{f}}_{\mathbf{u}}\left(\mathbf{MPa}\right)$ | $\mathit{\mu}{\mathit{\epsilon}}_{\mathbf{y}}$ |
---|---|---|---|---|

HPB300 | 6 | 392 | 581 | 1910 |

8 | 355 | 508 | 1775 | |

HRB400 | 18 | 443 | 595 | 2215 |

20 | 423 | 585 | 2115 | |

22 | 445 | 613 | 2225 | |

25 | 437 | 605 | 2185 |

Specimen | Mixture Proportions | $\mathit{\lambda}$ | $\mathit{b}\times \mathit{h}/{\mathbf{mm}}^{2}$ | Length/mm | Stirrups | Stirrup Ratio/% | Longitudinal Steel Bars | Longitudinal Steel Bars Ratio/% |
---|---|---|---|---|---|---|---|---|

H-1 | H2 | 1 | 120 × 180 | 550 | ϕ6 @ 80 ϕ | 0.59 | 2 20 | 2.91 |

H-1a | H2 | 1 | 120 × 180 | 550 | ϕ6 @ 60 | 0.79 | 2 20 | 2.91 |

H-1b | H2 | 1 | 120 × 180 | 550 | ϕ6 @ 120 | 0.40 | 2 20 | 2.91 |

H-1c | H2 | 1 | 120 × 180 | 550 | ϕ6 @ 80 | 0.59 | 2 22 | 3.52 |

C-1 | C | 1 | 120 × 180 | 550 | ϕ6 @ 80 | 0.59 | 2 20 | 2.91 |

H-2 | H2 | 2 | 120 × 180 | 850 | ϕ6 @ 80 | 0.59 | 2 25 | 4.55 |

H-2a | H2 | 2 | 120 × 180 | 850 | ϕ6 @ 60 | 0.79 | 2 25 | 4.55 |

H-2b | H2 | 2 | 120 × 180 | 850 | ϕ6 @ 120 | 0.40 | 2 25 | 4.55 |

H-2c | H2 | 2 | 120 × 180 | 850 | ϕ6 @ 80 | 0.59 | 2 25 + 1 18 | 5.73 |

C-2 | C | 2 | 120 × 180 | 850 | ϕ6 @ 80 | 0.59 | 2 25 | 4.55 |

H-2.5 | H2 | 2.5 | 200 × 300 | 1740 | ϕ8 @ 80 | 0.63 | 6 25 | 4.91 |

H-3 | H2 | 3 | 200 × 300 | 1740 | ϕ8 @ 80 | 0.63 | 6 25 | 4.91 |

H-3a | H2 | 3 | 200 × 300 | 1740 | ϕ8 @ 60 | 0.84 | 6 25 | 4.91 |

H-3b | H2 | 3 | 200 × 300 | 1740 | ϕ8 @ 120 | 0.42 | 6 25 | 4.91 |

C-3 | C | 3 | 200 × 300 | 1740 | ϕ8 @ 80 | 0.63 | 6 25 | 4.91 |

Failure Modes | Crack Patterns | Failure Characteristic | Corresponding Beam Specimens |
---|---|---|---|

Diagonal compression failure | The stirrups did not attain the yield strength. The shear strength depends mainly on the compressive load-carrying capacity of the diagonal concrete compression struts. The beam failed in shear because of brittle behavior. | ||

Shear compression failure | The stirrups intersecting with diagonal cracks attained the yield strength. Shear strength depends mainly on the shear-compression composite strength of the concrete. The beam failed in brittle mode. |

Failure Modes | Crack Patterns | Failure Characteristic | Corresponding Beam Specimens |
---|---|---|---|

Diagonal compression failure | The stirrups did not attain the yield strength. Shear strength depends mainly on the compressive load-carrying capacity of the diagonal HDC compression struts. The beam showed high residual strength. | ||

Shear compression failure | The stirrups intersecting with the diagonal cracks attained the yield strength at a slower rate. Shear strength depends mainly on the shear-compression composite strength of HDC. The beam has high residual strength. | ||

Diagonal tension failure | The stirrups attained the yield strength. The shear strength depends mainly on the tensile strength and ultimate tensile strain of HDC. | ||

Flexural shear failure | The stirrup and longitudinal reinforcement yielded successively. The yield point depends on the flexural capacity. The final failure depends mainly on the composite strength of HDC in the shear-compression zone. The beam failed in ductile mode. |

Specimen | ${\mathit{\lambda}}^{\prime}$ | Shear cracking | Yield | Major Diagonal Crack | Peak | $\frac{{\mathit{F}}_{\mathbf{m}}}{\mathit{b}{\mathit{h}}_{0}}$ | ${\Delta}_{\mathbf{u}}$ /mm | ${\Delta}_{\mathbf{u}}/\mathit{l}$ | $\mathit{\mu}$ | Failure Mode | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{F}}_{\mathbf{cr}}$/kN | ${\Delta}_{\mathbf{cr}}$ /mm | ${\Delta}_{\mathbf{cr}}/\mathit{l}$ | ${\mathit{F}}_{\mathbf{y}}$ /kN | ${\Delta}_{\mathbf{y}}$ /mm | ${\Delta}_{\mathbf{y}}/\mathit{l}$ | ${\mathit{F}}_{\mathbf{k}}$ /kN | ${\Delta}_{\mathbf{k}}$ /mm | ${\Delta}_{\mathbf{k}}/\mathit{l}$ | ${\mathit{F}}_{\mathbf{m}}$ /kN | ${\Delta}_{\mathbf{m}}$ /mm | ${\Delta}_{\mathbf{m}}/\mathit{l}$ | |||||||

H-1 | 0.97 | 119 | 0.42 | 1/714 | 465 | 1.92 | 1/156 | 473 | 2.12 | 1/142 | 497 | 2.48 | 1/121 | 30 | 3.58 | 1/84 | 1.86 | A |

H-1a | 0.97 | 140 | 0.66 | 1/455 | 496 | 2.12 | 1/142 | 476 | 3.21 | 1/94 | 520 | 2.7 | 1/111 | 31 | 3.48 | 1/86 | 1.64 | A |

H-1b | 0.97 | 130 | 0.7 | 1/429 | 515 | 3.39 | 1/89 | 454 | 5.12 | 1/59 | 520 | 3.92 | 1/77 | 31 | 5.41 | 1/55 | 1.60 | A |

H-1c | 0.98 | 165 | 0.53 | 1/567 | 462 | 2.2 | 1/136 | 434 | 2.86 | 1/105 | 471 | 2.38 | 1/126 | 28 | 3.60 | 1/83 | 1.64 | A |

C-1 | 0.97 | 149 | 0.4 | 1/750 | 385 | 0.92 | 1/435 | 386 | 0.88 | 1/341 | 393 | 0.99 | 1/303 | 23 | 1.44 | 1/208 | 1.56 | A |

H-2 | 1.98 | 131 | 1.18 | 1/254 | 275 | 3.3 | 1/182 | 227 | 9.53 | 1/63 | 285 | 4.02 | 1/149 | 17 | 8.43 | 1/71 | 2.55 | B |

H-2a | 1.98 | 157 | 1.42 | 1/211 | 308 | 4.11 | 1/146 | 282 | 5.38 | 1/112 | 326 | 5.3 | 1/113 | 19 | 18.86 | 1/32 | 4.59 | B |

H-2b | 1.98 | 91 | 0.66 | 1/455 | 320 | 3.47 | 1/173 | 260 | 10.9 | 1/55 | 354 | 4.29 | 1/140 | 21 | 4.69 | 1/128 | 1.35 | C |

H-2c | 1.98 | 83 | 0.95 | 1/315 | 346 | 4.38 | 1/137 | 267 | 16.42 | 1/37 | 355 | 5.16 | 1/116 | 21 | 5.62 | 1/107 | 1.28 | B |

C-2 | 1.98 | 89 | 0.70 | 1/429 | 256 | 2.06 | 1/291 | 192 | 4.61 | 1/131 | 256 | 2.06 | 1/291 | 15 | 3.61 | 1/167 | 1.75 | B |

H-2.5 | 2.42 | 260 | 2.87 | 1/418 | 738 | 7.33 | 3/491 | 548 | 24.2 | 1/50 | 747 | 7.51 | 1/160 | 16 | 8.56 | 1/140 | 1.17 | B |

H-3 | 2.90 | 201 | 2.2 | 1/655 | 633 | 7.83 | 1/184 | 564 | 23.91 | 1/60 | 696 | 12.38 | 1/116 | 15 | 21.08 | 1/68 | 2.69 | D |

H-3a | 2.90 | 250 | 2.64 | 1/545 | 625 | 7.36 | 1/196 | 553 | 24.8 | 1/58 | 711 | 12.18 | 1/118 | 15 | 20.02 | 1/72 | 2.72 | D |

H-3b | 2.90 | 221 | 2.44 | 1/590 | 635 | 7.5 | 1/192 | 454 | 19.76 | 1/73 | 666 | 9.23 | 1/156 | 14 | 9.91 | 1/145 | 1.32 | B |

C-3 | 2.90 | 318 | 2.17 | 1/664 | 542 | 4.82 | 1/299 | 486 | 12.35 | 1/117 | 624 | 8.04 | 1/179 | 13 | 10.39 | 1/139 | 2.16 | B |

Specimen | ${\mathit{V}}_{\mathbf{exp}}/\mathbf{kN}$ | ${\mathit{V}}_{\mathbf{cal}}/\mathbf{kN}$ | ${\mathit{V}}_{\mathbf{exp}}/{\mathit{V}}_{\mathbf{cal}}$ | Failure Mode |
---|---|---|---|---|

H-1 | 248.500 | 107.120 | 2.320 | A |

H-1a | 259.750 | 118.346 | 2.195 | A |

H-1b | 259.900 | 95.902 | 2.710 | A |

H-1c | 235.450 | 107.124 | 2.198 | A |

C-1 | 196.500 | 77.766 | 2.527 | A |

H-2 | 142.550 | 94.881 | 1.502 | B |

H-2a | 162.800 | 106.103 | 1.534 | B |

H-2b | 176.950 | 83.659 | 2.115 | C |

H-2c | 177.500 | 94.881 | 1.871 | B |

C-2 | 128.000 | 70.416 | 1.818 | B |

H-2.5 | 373.480 | 235.365 | 1.587 | B |

H-3 | 348.150 | 217.875 | 1.598 | D |

H-3a | 357.480 | 249.690 | 1.432 | D |

H-3b | 333.230 | 186.060 | 1.791 | B |

C-3 | 312.000 | 168.945 | 1.847 | B |

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## Share and Cite

**MDPI and ACS Style**

Zhang, M.; Deng, M.; Yang, J.; Zhang, Y.
Experimental Study on the Shear Behavior of Reinforced Highly Ductile Fiber-Reinforced Concrete Beams with Stirrups. *Buildings* **2022**, *12*, 1264.
https://doi.org/10.3390/buildings12081264

**AMA Style**

Zhang M, Deng M, Yang J, Zhang Y.
Experimental Study on the Shear Behavior of Reinforced Highly Ductile Fiber-Reinforced Concrete Beams with Stirrups. *Buildings*. 2022; 12(8):1264.
https://doi.org/10.3390/buildings12081264

**Chicago/Turabian Style**

Zhang, Min, Mingke Deng, Jiasheng Yang, and Yangxi Zhang.
2022. "Experimental Study on the Shear Behavior of Reinforced Highly Ductile Fiber-Reinforced Concrete Beams with Stirrups" *Buildings* 12, no. 8: 1264.
https://doi.org/10.3390/buildings12081264