# Analytical and Numerical Investigation of the Behavior of Engineered Cementitious Composite Members under Shear Loads

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## Abstract

**:**

_{w}) and shear span-to-depth ratio (a/d) on the behavior of ECC beams were also investigated. From a detailed parametric study, it was understood that a decreased a/d ratio exhibits enhanced load-carrying capacity for beams with and without stirrups for a particular cross-section. It was also observed that for the entire a/d ratio, the amount of stirrups had no substantial effect on the load-carrying capability of ECC beams.

## 1. Introduction

## 2. Research Significance

- To develop a reliable and robust three-dimensional FE procedure capable of predicting the shear behavior of ECC beams using existing models.
- To determine whether the existing AIJ A-method approach for determining the load-carrying capacity of ECC beams in shear is suitable.

## 3. Experimental Corroboration

## 4. Modeling of Specimens

#### 4.1. Characterization of the Material for Modeling

#### 4.2. Geometrical Model

_{x}, U

_{y}) and a hinge at the other end (U

_{x}, U

_{y}, U

_{z}). The loads were inputted as the vertical displacement at the two loading points. The loading and boundary conditions are displayed in Figure 6.

## 5. Results and Discussion

#### 5.1. Results on Relation between Load and Displacement

#### 5.2. Ultimate Capacity and Failure Pattern

_{u, num}/P

_{u, exp}for the investigated beams was 1.01, with a standard deviation and coefficient of variation of 0.01 and 0.47%, respectively. It is clear from the comparisons that the FE procedure adopted is accurate and may be used to estimate the behavior of an ECC beam under shear.

#### 5.3. Crack Pattern

#### 5.4. Ultimate Shear Capacity of ECC Beams

_{theo}/V,

_{exp}for a beam with varied a/d ratios and shear reinforcement was 0.952, with a standard deviation of 0.33. According to the findings, the AIJ A-method code could not estimate the ultimate shear capacity of the ECC beams, regardless of the quantity of shear reinforcement used, as stated by Zhang et al. [20].

## 6. Parametric Study

#### 6.1. Analysis of Load–Strain Relationship

#### 6.2. Shear Span-to-Depth Ratio against Particular Shear Reinforcement

#### 6.3. Effect of Shear Reinforcement against Particular Shear Span-to-Depth Ratio

#### 6.4. Crack Pattern and Failure Mode

#### 6.5. Shear Capacity of Beams

## 7. Conclusions

- Damage parameters and a damage plasticity model from the nonlinear finite element platform can predict the overall behavior of ECC under shear-dominant loads.
- The numerical study validates the results of other researchers’ experimental investigations into load, deflection, and failure modes, which were very similar. The obtained numerical and experimental load–deflection responses exhibited close agreement with each other. Furthermore, the difference in the peak load of the numerical modeling and experimental responses of all the beams was within the range of 3%, irrespective of the amount of reinforcement and a/d ratios, which shows the robustness of the procedure adopted in the FE analysis.
- The existing AIJ A-method fairly estimated the shear capacity of ECC beams as the beams demonstrated flexure-dominated shear failure, i.e., cracking in flexure with high longitudinal stress.
- Because of the dominant shear failure, simulated reinforced ECC beams with lower a/d ratios had higher load-carrying capacities, regardless of the degree of shear reinforcement.
- Stirrups did not affect the load-carrying capabilities of ECC beams for varied a/d ratios, regardless of the transverse reinforcement ratio.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 9.**Response of ECC beams comparison under load and deflection: (

**a**) P1, (

**b**) P2, (

**c**) P3, (

**d**) P4, (

**e**) P5, (

**f**) P6, and (

**g**) P7.

**Figure 10.**Comparison for component P4: the FE simulation’s plastic strain distribution and the experiment’s crack pattern were used.

**Figure 11.**Truss and arch mechanisms based on the AIJ A-method: (

**a**) truss mechanisms; (

**b**) arch mechanisms.

**Figure 12.**Dimensions of the ECC beam used for parametric analysis (note: all dimensions are in mm).

Sl. No. | Specimen ID | Dimension (B × D × L) * (mm) | Shear Span (a) (mm) | Shear Span-to-Depth Ratio | Longitudinal Reinforcement Ratio ^{#} (%) | Transverse Reinforcement Ratio (p_{w}) ^{$} (%) | Stirrup Spacing (mm) |
---|---|---|---|---|---|---|---|

1. | P1 [20] | 150 × 300 ×2100 | 700 | 2.8 | 2.7 | 0 | 0 |

2. | P2 [20] | 150 × 300 ×2100 | 700 | 2.8 | 2.7 | 0.12 | 350 |

3. | P3 [20] | 150 × 300 ×2100 | 700 | 2.8 | 2.7 | 0.24 | 175 |

4. | P4 [20] | 150 × 300 ×2100 | 700 | 2.8 | 2.7 | 0.30 | 140 |

5. | P5 [20] | 150 × 300 ×2100 | 700 | 2.8 | 2.7 | 0.42 | 100 |

6. | P6 [24] | 100 × 200 ×1100 | 267 | 1.53 | 1.14 | 0 | 0 |

7. | P7 [24] | 100 × 200 ×1100 | 267 | 1.53 | 1.14 | 0.42 | 133.5 |

^{#}(longitudinal reinforcement ratio (%) = (area of steel reinforcement/(breadth × height)) × 100);

^{$}(shear reinforcement ratio (%) = (area of steel reinforcement/(breadth * spacing of stirrups)) × 100).

Specimen ID | Tensile Strength (MPa) | Tensile Strain (%) | Compressive Strength (MPa) | Compressive Strain (%) | Young’s Modulus (GPa) | Poisson’s Ratio |
---|---|---|---|---|---|---|

P1–P5 [20] | 4.0 | 1.2 | 32.7 | 0.8 | 18 | 0.19 |

P6–P7 [24] | 5.1 | 1.7 | 73.0 | 1.1 | 20.4 | 0.20 |

Notation | Value |
---|---|

Angle of dilation (Ψ) [28] | 20 |

Eccentricity ratio (ε) [29] | 0.1 |

Ratio of biaxial-to-axial compressive stress $({\sigma}_{b0}/{\sigma}_{c0}$) [30] | 1.16 |

${K}_{C}$ [31] | 0.67 |

Viscosity Coefficient (µ) [32] | 0.01 |

Sl. No. | Specimen ID | Experimental Results | FE Results | P_{u, num}/P_{u, exp} | % Difference in Ultimate Load | ||||
---|---|---|---|---|---|---|---|---|---|

P_{u, exp} (kN) | δ_{u, exp} (mm) | Mode of Failure | P_{u, num} (kN) | δ_{u, num} (mm) | Mode of Failure | ||||

1. | P1 [20] | 207.8 | 8.19 | ST | 208.6 | 6.4 | ST | 1.00 | 0.38 |

2. | P2 [20] | 250.2 | 10.02 | ST | 251.3 | 8.22 | ST | 1.00 | 0.44 |

3. | P3 [20] | 250.1 | 9.87 | ST | 252.4 | 6.93 | ST | 1.01 | 0.92 |

4. | P4 [20] | 260.4 | 10.55 | ST | 264.8 | 8.19 | ST | 1.02 | 1.69 |

5. | P5 [20] | 281.2 | 9.23 | ST | 284.1 | 8.18 | ST | 1.01 | 1.03 |

6. | P6 [24] | 115.7 | 3.00 | ST | 116.2 | 3.2 | ST | 1.00 | 0.43 |

7. | P7 [24] | 157.3 | 5.2 | ST | 158.2 | 4.9 | ST | 1.01 | 0.57 |

_{u}—ultimate load; δ

_{u}—ultimate deflection; ST—shear tension.

Sl. No. | Specimen ID | Experimental Load (V, _{exp}) (kN) | V_{su}(V, _{theo}) (kN) | Shear Strength Shared by | V, _{theo}/V, _{exp} | ||
---|---|---|---|---|---|---|---|

Truss Mechanism (V_{t}) (%) | Arch Mechanism (V_{a}) (%) | Fiber Bridging Mechanism (V_{f}) (%) | |||||

1. | P1 [20] | 207.8 | 171.8 | 0 | 47 | 53 | 1.21 |

2. | P2 [20] | 250.2 | 188.5 | 12 | 40 | 48 | 1.32 |

3. | P3 [20] | 250.1 | 214.7 | 24 | 32 | 44 | 1.31 |

4. | P4 [20] | 260.4 | 231.9 | 28 | 29 | 43 | 1.27 |

5. | P5 [20] | 281.2 | 216.9 | 38 | 21 | 42 | 1.30 |

6. | P6 [24] | 115.7 | 170.1 | 0 | 58 | 42 | 0.68 |

7. | P7 [24] | 157.3 | 202.8 | 32 | 33 | 35 | 0.78 |

Beam | Shear Span, a (mm) | Shear Span-to-Depth Ratio (a/d) | Transverse Reinforcement Ratio (%) |
---|---|---|---|

S-1 | 250 | 1 | 0 |

S-2 | 250 | 1 | 0.3 |

S-3 | 375 | 1.5 | 0 |

S-4 | 375 | 1.5 | 0.1 |

S-5 | 375 | 1.5 | 0.2 |

S-6 | 250 | 2 | 0 |

S-7 | 250 | 2 | 0.2 |

S-8 | 250 | 2 | 0.3 |

S-9 | 250 | 2 | 0.4 |

S-10 | 625 | 2.5 | 0 |

S-11 | 625 | 2.5 | 0.1 |

S-12 | 625 | 2.5 | 0.2 |

S-13 | 625 | 2.5 | 0.3 |

S-14 | 625 | 2.5 | 0.4 |

S-15 | 750 | 3 | 0 |

S-16 | 750 | 3 | 0.1 |

S-17 | 750 | 3 | 0.2 |

S-18 | 750 | 3 | 0.3 |

Beam | Total Shear Capacity (kN) | Shear Load Carried by | |
---|---|---|---|

ECC Matrix (%) | Stirrups (%) | ||

S-1 | 256.5 | 100 | - |

S-2 | 255.9 | 89.4 | 10.6 |

S-3 | 158.9 | 100 | - |

S-4 | 158.7 | 94.3 | 5.7 |

S-5 | 158.7 | 91.5 | 8.5 |

S-6 | 113.7 | 100 | - |

S-7 | 113.7 | 88.1 | 11.9 |

S-8 | 113.7 | 76.1 | 23.9 |

S-9 | 113.7 | 70.2 | 29.8 |

S-10 | 97.2 | 100 | - |

S-11 | 97.2 | 90.7 | 9.3 |

S-12 | 97.2 | 81.4 | 18.6 |

S-13 | 97.3 | 76.8 | 23.2 |

S-14 | 97.3 | 72.1 | 27.9 |

S-15 | 85.5 | 100 | - |

S-16 | 85.4 | 94.7 | 5.3 |

S-17 | 85.5 | 89.4 | 10.6 |

S-18 | 85.4 | 86.8 | 13.2 |

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**MDPI and ACS Style**

Arulanandam, P.M.; Sivasubramnaian, M.V.; Chellapandian, M.; Murali, G.; Vatin, N.I.
Analytical and Numerical Investigation of the Behavior of Engineered Cementitious Composite Members under Shear Loads. *Materials* **2022**, *15*, 4640.
https://doi.org/10.3390/ma15134640

**AMA Style**

Arulanandam PM, Sivasubramnaian MV, Chellapandian M, Murali G, Vatin NI.
Analytical and Numerical Investigation of the Behavior of Engineered Cementitious Composite Members under Shear Loads. *Materials*. 2022; 15(13):4640.
https://doi.org/10.3390/ma15134640

**Chicago/Turabian Style**

Arulanandam, Preethy Mary, Madappa VR Sivasubramnaian, Maheswaran Chellapandian, Gunasekaran Murali, and Nikolai Ivanovich Vatin.
2022. "Analytical and Numerical Investigation of the Behavior of Engineered Cementitious Composite Members under Shear Loads" *Materials* 15, no. 13: 4640.
https://doi.org/10.3390/ma15134640