# Experimental Study on Evaluation of Replacing Minimum Web Reinforcement with Discrete Fibers in RC Deep Beams

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Minimum Web Reinforcement

_{s}. A β

_{s}of 0.75 is used if 0.25% of the orthogonal grid or 0.25% net effective reinforcement ratio normal to the strut axis exist. Suppose the designer chose not to provide any web reinforcement, reduction in the strut capacity and brittle failure is accounted for by using a low-efficiency factor (β

_{s}) of 0.45. Some researchers [11,12,13] have observed that inclined strut regions without web reinforcement in the deep beams should not be permitted regardless of the efficiency factor. Additionally, they suggested that minimum web reinforcement is also used to compensate for the effects of temperature, restrained shrinkage, and others which may not be explicitly considered. Though there is no consensus in the design codes [6,7,8,9] or the literature [12,13,14], the minimum web reinforcement seems essential.

#### 1.2. Discrete Fibers in Concrete

## 2. Research Significance and Objectives

- To evaluate the effect of minimum web reinforcement on the shear behavior of deep beams.
- To understand the effect of steel, macro-synthetic and hybrid fibers on the shear behavior of deep beams.
- To evaluate the possibility of completely replacing minimum web reinforcement with discrete fibers in concrete.
- To compare the change in the shear failure modes of deep beams reinforced with different fibers and minimum web shear reinforcement using the digital image correlation technique (DIC).

## 3. Experimental Program

#### 3.1. Test Specimen Details

#### 3.2. Materials

^{3}and 500 kg/m

^{3}, respectively. Table 3 shows the mix proportions of SCC used in this study. Ordinary Portland cement of grade 43 and Class-F Fly ash is used. The coarse aggregates were crushed gravel with a nominal particle size of 10 mm. Manufactured sand is used as fine aggregate. Polycarboxylate type superplasticizer used as an admixture to obtain the flow of concrete. Hooked-end steel and macro synthetic fibers are used in the study and are shown in Figure 5. Mechanical properties of the used fibers are summarized in Table 4. The SCC mix was thoroughly mixed using a drum mixer. The SCC was placed in the moulds in three lifts. The concrete was placed at one end of the moulds in each lift and allowed to flow along the length under its weight. No vibration was used in the entire casting process. Specimens were finished with light troweling. All the specimens were demoulded after 24 h of casting and water cured for a minimum of 28 days. The details of the compressive strength and density of the cubes for different fiber proportions are shown in Table 1. Thermomechanically treated (TMT) steel rebars of Fe 500 grade of different diameters of 20 mm, 12mm, and 8 mm were used as steel reinforcement.

#### 3.3. Test Setup and Instrumentation

#### 3.4. Digital Image Correlation (DIC)

## 4. Results and Discussion

#### 4.1. Load-Deflection Behavior

_{cm}bd to negate the influence of concrete compressive strength variation. Individual load-deflection responses are shown in Figure 9, along with points to indicate first crack, peak, and failure loads. Failure load is taken at a displacement of 8 mm for comparison and energy calculation as there is no change in load resistance after that.

#### 4.1.1. DB-F-0

#### 4.1.2. DB-S-0.3

#### 4.1.3. DB-SF-50

#### 4.1.4. DB-MSF-50

#### 4.1.5. DB-HB-50

_{cm}bd and plotted for comparison in Figure 10. Similarly, the energy absorption capacity of all the deep beams was calculated by the area under the load-deflection curve to compare the pseudo ductility of the different FRC beams and plotted in Figure 11.

#### 4.2. Strains in the Longitudinal Reinforcement

#### 4.3. Global Cracking Behavior of the Tested Beams

#### 4.4. Transverse Strain Variation at First Crack

#### 4.5. Stain Variation in Critical Crack

## 5. Summary and Conclusions

- The RC deep beams tested at an a/h ratio equal to one, primarily failed in the diagonal splitting mode in the bottle-shaped strut region by forming a diagonal crack between the inner edge of the support and the loading point. In plain concrete deep beams, the critical diagonal crack progressed to the entire beam depth at a faster rate leading to brittle failure. No resistance to the transverse tension led to low reserve capacity between the first crack and ultimate load.
- The addition of minimum web reinforcement in the deep beam effectively controlled the progress of the critical crack. Provision of web reinforcement led to higher reserve capacity after the first crack and higher peak load-carrying capacity. However, no change in the first crack load was observed in beams with web reinforcement compared to the plain concrete specimen.
- The addition of discrete steel fibers or macro synthetic fibers serves the purpose of arresting widening and propagation of the critical crack like conventional web reinforcement. Discrete fibers were more effective than conventional web reinforcement as the former can arrest the crack at every location, unlike web reinforcement.
- The addition of steel fibers in the concrete contributed to a higher first crack load in the deep beams, increasing the concrete tensile strength by arresting the micro cracks. Macro synthetic fibers were effective only at larger crack widths and could not improve the first crack load.
- The energy absorption capacity of the deep beams with 0.5% discrete fibers was on par with 0.3% conventional web reinforcement in both directions.
- Hybridization of steel and macro synthetic fibers resulted in higher ultimate load-carrying capacity compared to specimens reinforced with only steel or macro synthetic fibers. Hybridization also resulted in gradual load drop due to the effectiveness of synthetic fibers at larger crack widths.
- Limited test results from this study show that minimum web shear reinforcement of 0.3% in the diagonal strut region of deep beams can be replaced with 0.5% of either macro steel or macro synthetic or hybrid fibers. Fiber addition of 0.5% can provide similar or higher ultimate load carrying capacity, reserve capacity, and energy absorption.
- The provision of web reinforcement or discrete fibers in concrete did not change the final failure mode of deep beams with a low a/d ratio. All the specimens failed in diagonal splitting mode along the critical crack.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Details of the specimens: (

**a**) plain concrete with no web reinforcement; (

**b**) plain concrete with 0.3% web reinforcement; (

**c**) fiber reinforced concrete with no web reinforcement.

**Figure 6.**(

**a**) Test setup and instrumentation of deep beams, (1. controller, 2. UTM of 2000 kN capacity, 3. test specimen, 4. light source, 5. data acquisition system (DAQ), 6. data storage (DIC+DAQ), 7. DIC camera). (

**b**) Schematic diagram of the test set-up, (1. fixed head, 2. loading plate, 3. connecting posts, 4. test specimens, 5. support plate, 6. movable head, 7. hydraulic cylinder). (

**c**) Instrumentation on the rear face of deep beam.

**Figure 7.**(

**a**) Comparison of strain measured using DIC and LVDT, (

**b**) Location of virtual gauge in DIC, (

**c**) Location of LVDT.

**Figure 9.**Load-deflection curves of tested specimens: (

**a**) control beam (

**b**) beam with web reinforcement (

**c**) SF 50 beam (

**d**) MSF 50 beam (

**e**) hybrid 50 beam (

**f**) summary.

**Figure 13.**Principal strain contours of tested deep beams at key load points (+ve: tension, −ve: compression).

**Figure 14.**Final failure modes of deep beams: (

**a**) DB-F-0, (

**b**) DB-S-0.3, (

**c**) DB-SF-50, (

**d**) DB-MSF-50, (

**e**) DB-HB-50.

Specimen ID | V_{f} (%) | Avg. Cube Strength f _{cm} (MPa) | Standard Deviation (SD) (MPa) | Avg. Bulk Density (kg/m^{3}) |
---|---|---|---|---|

DB-F-0 | 0.0 | 55.6 | 2.01 | 2256 |

DB-SF-50 | 0.5 | 52.5 | 2.37 | 2279 |

DB-MSF-50 | 0.5 | 52.1 | 2.40 | 2267 |

DB-HB-50 | 0.5 | 60.2 | 2.17 | 2284 |

DB-S-0.3 | 0.0 | 52.9 | 1.90 | 2247 |

Beam ID | Fiber Volume Fraction (%) | Vertical Web Reinforcement (%) | Horizontal Web Reinforcement (%) |
---|---|---|---|

DB-F-0 | 0 | 0 | 0 |

DB-E-0.3W | 0 | 0.3 | 0.3 |

DB-SF-50 | 0.5 | 0 | 0 |

DB-MSF-50 | 0.5 | 0 | 0 |

DB-HB-50 | 0.5 | 0 | 0 |

Cement | Fly Ash | Water | Fine Aggregate | Coarse Aggregate | SP ^{a} | W/B ^{b} |
---|---|---|---|---|---|---|

340 | 160 | 215 | 827 | 790 | 1.75 | 0.43 |

^{a}superplasticizer,

^{b}water to binder ratio (binder = cement + fly ash).

Specification | Hooked End Steel Fibers | Macro-Synthetic Fibers |
---|---|---|

Specific gravity | 7.85 | 0.91 |

Length (mm) | 30 | 50 |

Diameter (mm) | 0.6 | 0.5 |

Tensile strength (MPa) | 1000 | 618 |

Modulus of Elasticity (GPa) | 200 | 10 |

Aspect ratio | 50 | 100 |

Beam ID | f_{cm}(MPa) | P_{cr}(kN) | Δ_{cr}(mm) | P_{u}(kN) | Δ_{u}(mm) | P_{cr}/P_{u} | EAC (kN-mm) | Failure Mode |
---|---|---|---|---|---|---|---|---|

DB-F-0 | 55.6 | 511.5 | 2.24 | 812.5 | 3.48 | 0.63 | 2863.8 | Diagonal Splitting |

DB-SF-50 | 52.5 | 677.7 | 2.60 | 1140.3 | 4.65 | 0.59 | 4562.8 | Diagonal Splitting |

DB-MSF-50 | 52.1 | 432.9 | 2.07 | 1078.5 | 4.93 | 0.40 | 4344.1 | Diagonal Splitting |

DB-HB-50 | 60.2 | 544.2 | 1.93 | 1437.6 | 5.46 | 0.38 | 4991.4 | Diagonal Splitting |

DB-S-0.3 | 52.9 | 524.7 | 2.21 | 970.8 | 4.35 | 0.54 | 4666.2 | Diagonal Splitting |

_{cm}= compressive strength of concrete in MPa, P

_{cr}= first diagonal crack load in kN, Δ

_{cr}= deflection at the first diagonal crack in mm, P

_{u}= ultimate load in kN, Δ

_{u}= deflection at ultimate load in mm, EAC= energy absorption capacity in kN-mm.

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**MDPI and ACS Style**

Sagi, M.S.V.; Lakavath, C.; Prakash, S.S.; Sharma, A.
Experimental Study on Evaluation of Replacing Minimum Web Reinforcement with Discrete Fibers in RC Deep Beams. *Fibers* **2021**, *9*, 73.
https://doi.org/10.3390/fib9110073

**AMA Style**

Sagi MSV, Lakavath C, Prakash SS, Sharma A.
Experimental Study on Evaluation of Replacing Minimum Web Reinforcement with Discrete Fibers in RC Deep Beams. *Fibers*. 2021; 9(11):73.
https://doi.org/10.3390/fib9110073

**Chicago/Turabian Style**

Sagi, Murali Sagar Varma, Chandrashekhar Lakavath, S. Suriya Prakash, and Akanshu Sharma.
2021. "Experimental Study on Evaluation of Replacing Minimum Web Reinforcement with Discrete Fibers in RC Deep Beams" *Fibers* 9, no. 11: 73.
https://doi.org/10.3390/fib9110073