# Shear Strength of HVFA-SCC Beams without Stirrups

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Parameters Affecting Shear

_{cc}), shear transfer at the interface due to aggregate interlock (V

_{ca}), dowel action of longitudinal reinforcement (V

_{d}), and the residual tensile stress across the crack (V

_{cr}). Several parameters have been identified as having a significant influence on the contribution to the shear resistance mechanism. The most-dominant, known mechanism influences are concrete strength, span to depth ratio (a/d), longitudinal reinforcement ratio, aggregate size, axial force, as well as other parameters such as bearing conditions, point of loading, etc.

^{0.33–0.5}, which indicates that the tensile strength of concrete is used as a governing parameter [23]. The strength of the concrete also affects the V

_{cc}component. Concrete with high compressive strength will be more resistant to preserve its compression zone. However, for concrete that is categorized as high strength (more than 50 MPa), diagonal cracking can pass through, instead of around, the aggregates due to the high strength of the cement paste. This condition will cause a smoother crack surface, which, in turn, can affect the shear transfer mechanism and result in an unconservative prediction [24,25,26].

_{s}factor of:

_{a}is the maximum aggregate size, and λ

_{0}is a constant. Meanwhile, ACI 318-19 [33] set the modification value as shown in Equation (2) to take into account the size effect:

## 3. Methods

#### 3.1. Experimental Investigation

#### 3.1.1. Materials and Properties

_{2}O

_{3}+ SiO

_{2}+ Fe

_{2}O

_{3}with 11.29% Al

_{2}O

_{3}, 31.76% SiO

_{2}, and 21.12% Fe

_{2}O

_{3}. Meanwhile, the level of SO

_{3}was 1.67% and CaO was 15.02%. Therefore, according to ASTM C-618, the fly ash used belonged to class C fly ash (which includes ‘C1′ type fly ash according to CSA A3001). This fly ash was mixed with Ordinary Portland Cement (OPC) to form the binder used in the HVFA-SCC mix design. The amount of fly ash content was 50% and 60% of the total weight of the binder.

#### 3.1.2. Beam Specimens

#### 3.1.3. Testing Beam Specimens

#### 3.2. Numerical Modeling

_{min}and ρ

_{max}. The effect of d was carried out by varying the beam depth but keeping the width and the reinforcement area.

#### 3.2.1. Materials Model

#### 3.2.2. Beam Model and Finite Element Meshing

#### 3.2.3. Loading

## 4. Results and Discussion

#### 4.1. Cracking Failure Modes

#### 4.2. Load-Deflection

#### 4.3. Experimental Results vs. Numerical Simulation

_{test}/V

_{atena}

_{,}and the mean maximum deflection of the test results and the numerical simulation, δ

_{test}/δ

_{atena,}are shown in Table 6. The V

_{test}/V

_{atena}of HVFA-SCC 50% is 1.06 and its corresponding δ

_{test}/δ

_{atena}is 1.08. The ratios indicate that the difference between the measured and numerical simulation is below 10%. For HVFA-SCC 60%, the difference is within 13%. Thus, the numerical modeling using 3D ATENA Engineering in this research is quite satisfactory, especially for 50% HVFA-SCC. On the basis of these results, beam modeling with 3D ATENA Engineering software can be further developed to conduct parametric studies in order to evaluate various parameter effects.

#### 4.4. Parametric Studies

#### 4.4.1. The Effect of the Reinforcement Ratio (ρ)

#### 4.4.2. The Effect of Shear Span to Beam Effective Depth Ratio (a/d)

#### 4.4.3. The Effect of Effective Beam Depth (d)

#### 4.5. Shear Strength of HVFA-SCC

^{2}while the HVFA-SCC beam in this research was 100 × 150 mm

^{2}. The ACI design code also recognizes this size effect by providing a modification factor whose value depends on the effective depth of the beam. The greater the beam size, the smaller the value of the modification factor.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The balance of forces at the formation of the primary diagonal crack before shear failure.

**Figure 17.**HVFA-SCC shear strength in the database of normalized shear strength vs. shear span to beam effective depth ratio.

**Figure 18.**HVFA-SCC shear strength in the database of normalized shear strength vs. longitudinal reinforcement ratio.

**Figure 20.**Normalized shear strength of non-conventional concrete vs. longitudinal reinforcement ratio.

Oxide | SiO_{2} | Fe_{2}O_{3} | Al_{2}O_{3} | CaO | MgO | K_{2}O | SO_{3} | TiO_{2} | P_{2}O_{5} | Cl | MnO | SrO | BaO | Nd_{2}O_{3} |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Concentration (%) | 31.76 | 21.12 | 11.29 | 15.02 | 3.85 | 2.35 | 1.67 | 1.59 | 1.01 | 0.56 | 0.27 | 0.14 | 0.15 | 0.12 |

Composition | Type | Unit | Mixtures | |
---|---|---|---|---|

HVFA-SCC 50% | HVFA-SCC 60% | |||

Cement | type 1 | kg/m^{3} | 250 | 200 |

Fly Ash | type C | kg/m^{3} | 250 | 300 |

Fine Aggregate | river sand | kg/m^{3} | 870.3 | 877.6 |

Coarse Aggregate | crushed stone | kg/m^{3} | 787.7 | 781.3 |

Water | NA | L/m^{3} | 150 | 150 |

HRWR | m-glenium sky 8614 | L/m^{3} | 10 | 10 |

% of fly ash replacement | 50 | 60 |

Property | Unit | Mix ID | Target Value | |
---|---|---|---|---|

HVFA-SCC 50% | HVFA-SCC 60% | |||

Slump flow | mm | 700 | 700 | 650–800 |

T50 | s | 3.16 | 3.11 | 2–5 |

L-Box | mm/mm | 0.90 | 0.94 | 0.8–1.0 |

V funnel | s | 9.34 | 9.50 | 6–12 |

Material | Cylinder Compressive Strength * (MPa) | Cube Compressive Strength ** (MPa) | Tensile Strength * (MPa) | Yield Strength * (MPa) | Modulus of Elasticity *** (MPa) | Material Model |
---|---|---|---|---|---|---|

HVFA-SCC 50% | 35.18 (2.35) | 41.38 | 2.06 (0.05) | NA | 34,470 | 3D NonLinear Cementitious Material 2 |

HVFA-SCC 60% | 31.84 (2.32) | 37.46 | 2.21 (0.11) | NA | 33,170 | |

Reinforcement φ 16 | NA | NA | NA | 402.9 (10.3) | 200,000 | Reinforcement-Bilinear |

Steel Plate | NA | NA | NA | NA | 200,000 | 3D Elastic Isotropic |

Beam ID | fc’ (MPa) | * First Flexural Crack (kN) | * First Primary Diagonal Crack (kN) | Ultimate Shear (kN) | Maximum Deflection (mm) |
---|---|---|---|---|---|

HVFA-SCC 50%-1 | 32.68 | 3.00 | 23.13 | 26.13 | 6.55 |

HVFA-SCC 50%-2 | 37.34 | 4.00 | 25.25 | 29.50 | 7.27 |

HVFA-SCC 50%-3 | 35.51 | 4.25 | 25.75 | 28.63 | 7.39 |

HVFA-SCC 60%-1 | 30.45 | 4.00 | 22.50 | 25.75 | 7.90 |

HVFA-SCC 60%-2 | 30.56 | 4.50 | 23.50 | 26.00 | 6.64 |

HVFA-SCC 60%-3 | 34.52 | 3.50 | 21.88 | 25.63 | 7.13 |

Beam ID | ft (MPa) | ATENA | V_{test}/V_{atena} | δ_{test}/δ_{atena} | |
---|---|---|---|---|---|

Vult (kN) | δ (mm) | ||||

HVFA-SCC 50% | 2.06 | 26.58 | 6.63 | 1.06 | 1.08 |

HVFA-SCC 60% | 2.21 | 25.66 | 6.42 | 1.01 | 1.13 |

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**MDPI and ACS Style**

Budi, A.S.; Safitri, E.; Sangadji, S.; Kristiawan, S.A.
Shear Strength of HVFA-SCC Beams without Stirrups. *Buildings* **2021**, *11*, 177.
https://doi.org/10.3390/buildings11040177

**AMA Style**

Budi AS, Safitri E, Sangadji S, Kristiawan SA.
Shear Strength of HVFA-SCC Beams without Stirrups. *Buildings*. 2021; 11(4):177.
https://doi.org/10.3390/buildings11040177

**Chicago/Turabian Style**

Budi, Agus Setiya, Endah Safitri, Senot Sangadji, and Stefanus Adi Kristiawan.
2021. "Shear Strength of HVFA-SCC Beams without Stirrups" *Buildings* 11, no. 4: 177.
https://doi.org/10.3390/buildings11040177