# Impact of Openings on the In-Plane Strength of Confined and Unconfined Masonry Walls: A Sustainable Numerical Study

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. Numerical Modeling

#### 2.2. Experimental Tests and Validation

## 3. Results and Discussion

#### 3.1. Performance of Unconfined Masonry Walls against Lateral Loading

#### 3.1.1. MW AR1.78–0%

#### 3.1.2. MW AR1.78–1.85%

#### 3.1.3. MW AR1.78–3.66%

#### 3.1.4. MW AR1.78–10.91%

#### 3.1.5. MW AR1.78–16.5%

#### 3.2. Performance of Confined Masonry Walls against Lateral Loading

#### 3.2.1. CMW AR1.78–0%

#### 3.2.2. CMW AR1.78–1.85%

#### 3.2.3. CMW AR1.78–3.66%

#### 3.2.4. CMW AR1.78–10.91%

#### 3.2.5. CMW AR1.78–16.5%

#### 3.3. Impact of Openings on the Unconfined Masonry Walls

#### 3.3.1. Peak Load and Lateral Strength

#### 3.3.2. Stiffness Reduction

#### 3.3.3. Failure Type

#### 3.4. Impact of Openings on the Confined Masonry Walls

#### 3.4.1. Peak Load and Lateral Strength

#### 3.4.2. Stiffness Reduction

#### 3.4.3. Failure Type

#### 3.5. Benefits of Confinement

#### 3.5.1. Peak Load and Lateral Strength

#### 3.5.2. Stiffness

#### 3.5.3. Failure Type

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Finite Element Approaches. (

**a**) Macro-modeling approach, (

**b**) Simplified micro-modeling, (

**c**) Detailed micro-modeling approach.

**Figure 2.**Schematics of unconfined masonry walls with varying opening percentages. (

**a**) MW AR1.78–0%, (

**b**) MW AR1.78–1.85%, (

**c**) MW AR1.78–3.66%, (

**d**) MW AR1.78–10.91%, (

**e**) MW AR1.78–16.5%.

**Figure 3.**Schematics of confined masonry walls with varying opening percentages. (

**a**) CMW AR1.78–0%, (

**b**) CMW AR1.78–1.85%, (

**c**) CMW AR1.78–3.66%, (

**d**) CMW AR1.78–10.91%, (

**e**) CMW AR1.78–16.5%.

Maximum Compressive Strength of Brick = f_{b} = | 26,500 kN/m^{2} |

Maximum compressive strength of mortar = f_{m} = | 12,300 kN/m^{2} |

Initial elastic modulus of bricks = E_{b} = | 9,407,500 kN/m^{2} |

Initial elastic modulus of mortar = E_{m} = | 2,460,000 kN/m^{2} |

Poisson’s coefficient for brick elements = ν_{b} = | 0.2 |

Poisson’s coefficient for mortar = ν_{m} = | 0.15 |

Normal Stiffness = kN = | 66,727,500 kN/m |

Tangential Stiffness = Ks = | 28,973,783 kN/m |

Yield Strength of Reinforcement = σ_{y} = | 280 MPa |

Masonry Walls | Opening Size (m) | Peak Load (kN) | % Reduction in Strength | Initial Stiffness (kN/m) | % Reduction in Stiffness |
---|---|---|---|---|---|

MW AR1.78–0% | 0.00 | 117.17 | 0.00 | 43,448.24 | 0.00 |

MW AR1.78–1.85% | 0.25 × 0.25 | 84.44 | 27.93 | 31,049.80 | 28.54 |

MW AR1.78–3.66% | 0.25 × 0.5 | 59.89 | 48.88 | 21,365.52 | 50.83 |

MW AR1.78–10.91% | 0.5 × 0.75 | 33.22 | 71.65 | 16,538.58 | 61.93 |

MW AR1.78–16.5% | 0.75 × 0.75 | 23.32 | 80.10 | 10,253.75 | 76.40 |

Confined Masonry Walls | Opening Size (m) | Peak Load (kN) | % Reduction in Strength | Initial Stiffness (kN/m) | % Reduction in Stiffness |
---|---|---|---|---|---|

CMW AR1.78–0% | 0.00 | 193.17 | 0.00 | 52,808.06 | 0.00 |

CMW AR1.78–1.85% | 0.25 × 0.25 | 165.57 | 14.29 | 33,437.00 | 36.68 |

CMW AR1.78–3.66% | 0.25 × 0.5 | 162.35 | 15.95 | 25,165.07 | 52.35 |

CMW AR1.78–10.91% | 0.5 × 0.75 | 129.56 | 32.93 | 20,987.00 | 60.26 |

CMW AR1.78–16.5% | 0.75 × 0.75 | 120.87 | 37.43 | 16,412.80 | 68.92 |

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**MDPI and ACS Style**

Mughal, U.A.; Qazi, A.U.; Ahmed, A.; Abbass, W.; Abbas, S.; Salmi, A.; Sayed, M.M.
Impact of Openings on the In-Plane Strength of Confined and Unconfined Masonry Walls: A Sustainable Numerical Study. *Sustainability* **2022**, *14*, 7467.
https://doi.org/10.3390/su14127467

**AMA Style**

Mughal UA, Qazi AU, Ahmed A, Abbass W, Abbas S, Salmi A, Sayed MM.
Impact of Openings on the In-Plane Strength of Confined and Unconfined Masonry Walls: A Sustainable Numerical Study. *Sustainability*. 2022; 14(12):7467.
https://doi.org/10.3390/su14127467

**Chicago/Turabian Style**

Mughal, Ubaid Ahmad, Asad Ullah Qazi, Ali Ahmed, Wasim Abbass, Safeer Abbas, Abdelatif Salmi, and Mohamed Mahmoud Sayed.
2022. "Impact of Openings on the In-Plane Strength of Confined and Unconfined Masonry Walls: A Sustainable Numerical Study" *Sustainability* 14, no. 12: 7467.
https://doi.org/10.3390/su14127467