# Effect of the Openings on the Seismic Response of an Infilled Reinforced Concrete Structure

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation and Literature Review

#### 1.2. Research Significance and Objectives

## 2. Modeling Strategy and Calibration

^{2}). The experimental tests were conducted by Furtado et al. [22].

#### 2.1. Description of the Numerical Modeling Strategy

#### 2.2. Calibration of the Modeling Strategy

#### 2.2.1. Methodology

^{2}(length and width, respectively), representing those existing in the Portuguese building stock [30], and are shown in Figure 2. The specimen Inf_12 is a wall without openings, no strengthening, no reinforcement, and with no gaps in the wall–frame interface. The specimen Inf_14 was built with the same geometry and the remaining details. The only difference was the introduction of a central opening, of 1150 × 1250 mm

^{2}. The opening construction process was carried out according to typical construction practices. Moreover, an RC lintel on the top of the window was built, as shown in Figure 2. The cross-section of the RC lintel is 100 × 150 mm

^{2}. The longitudinal reinforcement used in the RC lintel comprises 3ø6 mm with a total length of 1650 mm.

^{2}with longitudinal reinforcement of 4ø16 + 2ø12 and a transversal reinforcement of ø8//50 mm, along with the plastic regions, and ø8//150 mm in the remaining column extension. Concerning the beams, the cross-section is 300 × 500 mm

^{2}with a longitudinal reinforcement of 5ø16 + 5ø16. The geometry and reinforcement detailing are shown in Figure 2.

#### 2.2.2. Definition of the Modeling Parameters

#### 2.2.3. Validation of the Modeling Strategy

#### 2.3. Preliminary Conclusions on Modeling Calibration

## 3. Case Study

#### 3.1. General Description

^{2}and has five bays, 6 m long, along the longitudinal direction and three bays, 5 m long, in its transverse direction, as shown in Figure 6a. The building inter-story height is 3 m, as shown in Figure 6b. The cross-section of the columns is: 400 × 300 mm

^{2}(Stories 1 and 2) and 300 × 300 mm

^{2}(Stories 3 and 4). The columns’ cross-section is presented in Figure 6c. All the beams have a rectangular section of 200 × 500 mm

^{2}, and their reinforcement detailing is shown in Figure 6d. The slab thickness was designed to be 150 mm thick.

^{2}plus a variable load of 2.5 kN/m

^{2}. The concrete class is C25/30, and the steel reinforcement grade is A400 [34]. Three 3D models were generated in SeismoStruct [23], considering different configurations, namely: (i) “BF model” is the model that simulates a bare frame configuration (only infills’ gravity load was considered); (ii) “FI model” is the model that simulates the RC structure with infill walls without openings, shown in Figure 6e; and (iii) “PI model” is the model that simulates the RC structure with the walls with a central opening, shown in Figure 6f.

#### 3.2. Modal Analyses

#### 3.3. Nonlinear Pushover Analyses

#### 3.4. Nonlinear Dynamic Analyses

## 4. Parametric Study

#### 4.1. Effect of Irregular Vertical Distribution (Scenario A)

#### 4.2. Effect of In-Plan Irregular Distribution (Scenario B)

#### 4.3. Effect of Openings Ratio (Scenario C)

## 5. Conclusions

- The vertical irregularity due to the distribution of openings changes the dynamic characteristics of the building structure, namely, the natural frequencies are reduced by 66%. It also modifies the initial stiffness values and maximum resistance by between 10 and 25%. It was also observed that the collapse mechanisms vary due to the openings.
- The in-plane irregularity in the opening distribution caused similar effects to those observed in Scenario A. The conclusions are identical to the previous case. In particular, the irregular horizontal distribution of the opening increases the potential for the torsional phenomena of the building. Reductions in the initial stiffness by between 32% and 56%, and in the maximum strength by around 7–18%, were also observed.
- The importance of the area of the openings was studied and it was found that this variable also influences the dynamic response of the building. The increase in the openings area makes the model response more similar to that without masonry infill walls. A relevant aspect to consider is the way in which the numerical input properties are defined for the masonry infill walls, since they cannot be directly extrapolated.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Modeling strategy adopted for the masonry infill walls: (

**a**) under compression; and (

**b**) under shear.

**Figure 3.**Test setup of the in-plane experimental tests: (

**a**) detail of the hydraulic actuator; and (

**b**) lateral view.

**Figure 4.**Numerical simulation of the specimen Inf_12 (wall w/o opening): (

**a**) force–displacement curves; and (

**b**) cumulative energy dissipation.

**Figure 5.**Numerical simulation of the specimen Inf_14 (wall w/ opening): (

**a**) force–displacement curves; and (

**b**) cumulative energy dissipation.

**Figure 6.**Case study: (

**a**) plan view; and (

**b**) general view of the BF model; (

**c**) columns’ cross-section; (

**d**) beams’ cross-section; (

**e**) FI model; and (

**f**) PI model.

**Figure 7.**Numerical results. (

**a**) Natural frequencies. Capacity curve (pushover analysis): (

**b**) longitudinal direction; and (

**c**) transverse direction.

**Figure 9.**Nonlinear dynamic analyses: maximum inter-story drift ratio: (

**a**) longitudinal and (

**b**) transverse direction. Maximum base shear: (

**c**) longitudinal and (

**d**) transverse direction.

**Figure 11.**Parametric study A: (

**a**) natural frequencies; (

**b**) capacity curve (longitudinal direction); and (

**c**) capacity curve (transverse direction).

**Figure 13.**Parametric study B: (

**a**) natural frequencies; (

**b**) capacity curve (longitudinal direction); and (

**c**) capacity curve (transverse direction).

**Figure 15.**Parametric study C: (

**a**) natural frequencies; (

**b**) capacity curve (longitudinal direction); and (

**c**) capacity curve (transverse direction).

Input Parameters | Inf_12 (Panel w/o Opening) | Inf_14 (Panel w/ Opening) | Percentage of Reduction (%) | |
---|---|---|---|---|

Strut Elements | E_{m} (Kpa) | 2,500,000 | 2,000,000 | 20 |

f_{mθ} (Kpa) | 470 | 376 | 20 | |

f_{t} (kPa) | 100 | 100 | 0 | |

ε_{m} (%) | 0.00006 | 0.00006 | 0 | |

ε_{u} (%) | 0.03 | 0.03 | 0 | |

ε_{cl} (%) | 0.003 | 0.003 | 0 | |

ε_{1} (%) | 0.00038 | 0.00038 | 0 | |

ε_{2} (%) | 0.00295 | 0.00295 | 0 | |

γ_{un} | 1.50 | 1.50 | 0 | |

α_{re} | 0.30 | 0.30 | 0 | |

α_{ch} | 0.45 | 0.45 | 0 | |

β_{a} | 1.75 | 1.75 | 0 | |

β_{ch} | 0.65 | 0.65 | 0 | |

γ_{plu} | 0.60 | 0.60 | 0 | |

γ_{plr} | 1.25 | 1.25 | 0 | |

e_{x1} | 1.75 | 1.75 | 0 | |

e_{x2} | 1.25 | 1.25 | 0 | |

Shear Elements | τ_{o} | 100 | 80 | 20 |

Μ | 0.70 | 0.7 | 0 | |

τ_{max} | 200 | 200 | 0 | |

α_{s} | 1.5 | 1.5 | 0 | |

General properties | t (m) | 0.15 | 0.15 | 0 |

OOP failure drift (%) | 5 | 5 | 0 | |

A_{ms1} (m^{2}) | 0.19 | 0.15 | 20 | |

A_{ms2} (% of A_{ms1}) | 50 | 40 | 20 | |

h_{z} (% of vertical panel side) | 0.55 | 0.55 | 0 | |

K_{s} (kN/m) | 15 | 12 | 20 | |

Self-weight (N/m^{3}) | 98.5 | 84.4 | 15 |

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**MDPI and ACS Style**

Furtado, A.; Rodrigues, H.; Arêde, A.
Effect of the Openings on the Seismic Response of an Infilled Reinforced Concrete Structure. *Buildings* **2022**, *12*, 2020.
https://doi.org/10.3390/buildings12112020

**AMA Style**

Furtado A, Rodrigues H, Arêde A.
Effect of the Openings on the Seismic Response of an Infilled Reinforced Concrete Structure. *Buildings*. 2022; 12(11):2020.
https://doi.org/10.3390/buildings12112020

**Chicago/Turabian Style**

Furtado, André, Hugo Rodrigues, and António Arêde.
2022. "Effect of the Openings on the Seismic Response of an Infilled Reinforced Concrete Structure" *Buildings* 12, no. 11: 2020.
https://doi.org/10.3390/buildings12112020