# Influence of Joint Strengthening on the Seismic Performance of Non-Engineered Buildings

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## Abstract

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## 1. Introduction

## 2. Materials

## 3. Methods

#### 3.1. RC Frame Structure Model

- An NEB portal model without joint strengthening (NEB-000);
- An NEB model with beam–column joint strengthening using a 75 mm wide plate (NEB-075);
- An NEB model with beam–column joint strengthening using a 100 mm wide steel plate (NEB-100).

#### 3.2. Loading Protocol

- Three complete cycles were applied for each drift ratio.
- The initial drift ratio was 0.002 (0.2%) in the test, and it was within the range of the linear elastic behavior of the specimen. The subsequent drift ratios were at least 1.25 times, but not more than 1.5 times, the previous drift ratio.
- The test was conducted by gradually increasing the drift ratio until a minimum drift ratio of 0.035 (3.5%) was achieved.

#### 3.3. Experimental Setup

## 4. Numerical Investigation

## 5. Results and Analysis

#### 5.1. Load Displacement

#### 5.2. Crack Pattern

#### 5.2.1. NEB-000 Model

#### 5.2.2. NEB-075 Model

#### 5.2.3. NEB-100 Model

#### 5.3. Energy Dissipation

#### 5.4. Damage State

#### 5.5. Structural Uncertainty

_{Sds}is the lognormal standard deviation that describes the total variability for the structural damage state, ds. β

_{C}is the lognormal standard deviation parameter that describes the variability of the capacity curve, calculated by Equation (1). β

_{D}is the lognormal standard deviation parameter that describes the variability of the demand spectrum. β

_{D}is set to 0.45 for a short period and 0.50 for a long period. ${\overline{S}}_{Sds}$ is the median value of the spectral displacement of structural components for the damage state, ds. ${\beta}_{M\left(Sds\right)}$ is the lognormal standard deviation parameter that describes the uncertainty in the estimated median value of the structural damage state threshold. β

_{M(Sds)}is taken as 0.40. The function “CONV” in Equation (1) implies a complex process of convolving probability distributions of the demand spectrum and capacity curve. From Equation (2), s is the standard deviation of the structure’s spectral acceleration capacity and m is the average of the structure’s spectral acceleration capacity. The results of the structural uncertainty calculation are presented in Table 9.

#### 5.6. Fragility Analysis

#### 5.6.1. Fragility Curve of NEBs

_{ds}is the standard deviation of the natural logarithm of spectral displacement for the damage state, ds. ${\overline{S}}_{d,ds}$ is the median value of the spectral displacement at which the building reaches the threshold of the damage state, ds. The resulting fragility curves of the NEBs are shown in Figure 13.

#### 5.6.2. Discrete Damage of NEBs

## 6. Conclusions

- The NEB model without joint strengthening tended to experience severe damage in the joint area. This joint damage could potentially cause the beam and column elements to break. The NEB model with joint strengthening using 75 mm wide steel plates reduced the level of joint damage, whereas the NEB model with 100 mm wide steel plates transferred the damage from the joint areas to the column sections at the end of the steel plates. These findings confirm that steel plates can maintain the integrity of beam and column elements and reduce the severity of damage.
- Strengthening the joints of the NEBs using 75 and 100 mm wide steel plates increased the load-bearing capacity by 68.92 and 68.31%, respectively. Compared to using 75 mm wide steel plates, strengthening the joints of NEBs with 100 mm wide steel plates was more effective in preserving the integrity of the beam–column elements. This improved the ductility and energy dissipation of the structure.
- Strengthening the joints of NEBs with 75 and 100 mm wide steel plates can change the damage limit states of NEBs. Subsequently, it also improves the seismic performance of the structure, as the structure exhibited higher undamaged values than the NEBs without joint strengthening.
- The use of steel plates as strengthening materials in NEB effectively improved the seismic performance and integrity of the structural elements. This material is relatively affordable for lower-class communities and easy to apply.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Insufficient reinforcement ratios of column in non-engineered building and (

**b**) inadequate shear reinforcement and development lengths/anchorage of longitudinal reinforcements.

**Figure 3.**Loading cycle based on displacement, controlled following ACI TI 374.1-05 [27].

**Figure 7.**(

**a**) Envelope curves obtained from the experimental investigation and (

**b**) comparison of the load-displacement curves obtained from the numerical investigation with the compressive envelop curves.

**Figure 11.**Capacity curve of the NEBs with points representing the load or displacement in various damage states.

**Figure 12.**Spectrum capacity of the NEBs with points representing Sa or Sd in various damage states.

Material | Properties |
---|---|

Concrete for column | f′c = 14.72 MPa |

Concrete for beam | f′c =10.81 MPa |

Flexural reinforcement | fy = 479.99 MPa and fu = 659.01 MPa |

Shear reinforcement | fy = 426.74 MPa and fu = 560.76 MPa |

Steel plate | fy = 399.77 MPa and fu = 589.02 MPa |

Specimen ID | Beam 15 × 20 × 300 | Column 15 × 15 × 250 | Steel Plate T:W:L (mm) | ||
---|---|---|---|---|---|

Longitudinal Reinforcement | Shear Reinforcement | Longitudinal Reinforcement | Shear Reinforcement | ||

NEB-000 | 4D10 | D6-200 | 4D10 | D6-200 | NA |

NEB-075 | 4D10 | D6-200 | 4D10 | D6-200 | 5:75:500 |

NEB-100 | 4D10 | D6-200 | 4D10 | D6-200 | 5:100:500 |

**Table 3.**Parameters of concrete material according to ATENA (adapted from ATENA Program Documentation Part 1 Theory [30] (p. 33)).

Parameter | Value of Parameter |
---|---|

Cylinder strength | f′c = −0.85 f′cu |

Tensile strength | f′t = 0.24 f′cu^{2/3} |

Initial elastic modulus | Ec = (6000 15.5f′cu) √f′cu |

Poisson’s ratio | ν = 0.2 |

Softening compression | w_{d} = −0.0005 mm |

Type of tension softening | 1—exponential, based on G_{F} |

Compressive strength in cracked concrete | c = 0.8 |

Tension stiffening stress | σ st = 0.4 |

Shear retention factor | variable |

Tension–compression function type | linear |

Fracture energy Gf according to VOS 1983 | G_{F} = 0.000025 f′t^{ef} [MN/m] |

Orientation factor for strain localization | γ max = 1.5 |

Specimen ID | Maximum Load (kN) | Displacement (mm) | ||||
---|---|---|---|---|---|---|

Compressive | Tensile | Compressive | Drift Ratio (%) | Tensile | Drift Ratio (%) | |

NEB-000 | 6.50 | −5.91 | 69.90 | 2.91 | −69.90 | 2.91 |

NEB-075 | 10.98 | −11.09 | 55.90 | 2.33 | −55.90 | 2.33 |

NEB-100 | 10.94 | −11.13 | 69.90 | 2.91 | −69.90 | 2.91 |

Specimen | Energy Dissipation (Joule) | Increase in Value (%) |
---|---|---|

NEB-000 | 1556.00 | 0.00 |

NEB-075 | 2131.98 | 37.02 |

NEB-100 | 2741.44 | 76.19 |

**Table 6.**Description of the structural damage states of a reinforced concrete frame (C1) (adapted from Hazus Earthquake Model Technical Manual [32] (pp. 5–15)).

Damage State | Description of the Structural Damage |
---|---|

Slight (DS1) | Flexural or shear type hairline cracks in some beams and columns near joints or within joints. |

Moderate (DS2) | Most beams and columns exhibit hairline cracks. In ductile frames, some of the frame elements have reached yield capacity, indicated by larger flexural cracks and some concrete spalling. Nonductile frames exhibit larger shear cracks and spalling. |

Extensive (DS3) | In ductile frames, some of the frame elements have reached their ultimate capacity, as indicated by large flexural cracks, spalled concrete, and buckled main reinforcement; nonductile frame elements may have suffered shear or bond failures at reinforcement splices, broken ties, or buckled main reinforcement in columns, which can result in partial collapse. |

Complete (DS4) | Structure is either collapsed or in imminent danger of collapse due to brittle failure of the nonductile frame elements or loss of frame stability. Approximately 13% of low-rise, and 10% of mid-rise, and 5% of high-rise of the total area of C1 buildings with complete damage are expected to be collapsed. |

Model | Load (kN) | Displacement (mm) | ||||||
---|---|---|---|---|---|---|---|---|

First Crack | Yield | Peak | Ultimate | First Crack | Yield | Peak | Ultimate | |

NEB-000 | 1.37 | 3.80 | 6.50 | 3.69 | 7.50 | 14.70 | 22.90 | 69.90 |

NEB-075 | 2.25 | 4.30 | 9.04 | 10.39 | 7.50 | 14.70 | 22.90 | 55.90 |

NEB-100 | 2.66 | 4.72 | 8.21 | 7.98 | 7.50 | 14.70 | 22.90 | 69.90 |

Model | DS1 (Slight) | DS2 (Medium) | DS3 (Extensive) | DS4 (Complete) | ||||
---|---|---|---|---|---|---|---|---|

Sd | Sa | Sd | Sa | Sd | Sa | Sd | Sa | |

NEB-000 | 0.5243 | 0.1698 | 1.0275 | 0.4693 | 1.6007 | 0.8039 | 4.8860 | 0.4559 |

NEB-075 | 0.8178 | 0.4717 | 1.9991 | 1.2005 | 3.1245 | 1.3581 | 3.9074 | 1.2853 |

NEB-100 | 1.0275 | 0.5833 | 1.9991 | 1.1993 | 2.5024 | 1.3532 | 4.8860 | 0.9870 |

Model | Limit State | S_{d} (m) | β_{C} | β_{D} | β_{M(Sds)} | β_{Sds} |
---|---|---|---|---|---|---|

NEB-000 | DS1 | 0.5243 | 2.3981 | 0.4500 | 0.400 | 1.1509 |

DS2 | 1.0275 | 2.3981 | 0.4500 | 0.400 | 1.1509 | |

DS3 | 1.6007 | 2.3981 | 0.4500 | 0.400 | 1.1509 | |

DS4 | 4.8860 | 2.3981 | 0.4500 | 0.400 | 1.1509 | |

NEB-075 | DS1 | 0.8178 | 2.2248 | 0.4500 | 0.400 | 1.0781 |

DS2 | 1.9991 | 2.3981 | 0.4500 | 0.400 | 1.0781 | |

DS3 | 3.1245 | 2.3981 | 0.4500 | 0.400 | 1.0781 | |

DS4 | 3.9074 | 2.3981 | 0.4500 | 0.400 | 1.0781 | |

NEB-100 | DS1 | 1.0275 | 2.3836 | 0.4500 | 0.400 | 1.1448 |

DS2 | 1.9991 | 2.3836 | 0.4500 | 0.400 | 1.1448 | |

DS3 | 2.5024 | 2.3836 | 0.4500 | 0.400 | 1.1448 | |

DS4 | 4.8860 | 2.3836 | 0.4500 | 0.400 | 1.1448 |

Model | Limit State | DBE = 0.255124 g | MCE = 0.382686 g | ||
---|---|---|---|---|---|

Probability | Discrete Damage | Probability | Discrete Damage | ||

NEB-000 | Undamaged | 56.49% | 29.61% | ||

Slight | 26.44% | 30.04% | 39.16% | 9.55% | |

Medium | 11.16% | 15.28% | 19.39% | 19.77% | |

Extensive | 5.42% | 5.74% | 10.54% | 8.85% | |

Complete | 0.49% | 4.93% | 1.30% | 9.25% | |

NEB-075 | Undamaged | 81.54% | 65.44% | ||

Slight | 14.04% | 67.50% | 24.10% | 41.35% | |

Medium | 2.83% | 11.21% | 6.29% | 17.81% | |

Extensive | 1.02% | 1.81% | 2.59% | 3.70% | |

Complete | 0.58% | 0.44% | 1.57% | 1.02% | |

NEB-100 | Undamaged | 82.46% | 66.86% | ||

Slight | 11.16% | 71.30% | 19.39% | 47.47% | |

Medium | 3.59% | 7.57% | 7.42% | 11.98% | |

Extensive | 2.30% | 1.30% | 5.03% | 2.38% | |

Complete | 0.49% | 1.80% | 1.30% | 3.73% |

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## Share and Cite

**MDPI and ACS Style**

Purwanto, E.; Kristiawan, S.A.; Sangadji, S.; Saifullah, H.A.
Influence of Joint Strengthening on the Seismic Performance of Non-Engineered Buildings. *Buildings* **2024**, *14*, 488.
https://doi.org/10.3390/buildings14020488

**AMA Style**

Purwanto E, Kristiawan SA, Sangadji S, Saifullah HA.
Influence of Joint Strengthening on the Seismic Performance of Non-Engineered Buildings. *Buildings*. 2024; 14(2):488.
https://doi.org/10.3390/buildings14020488

**Chicago/Turabian Style**

Purwanto, Edy, Stefanus Adi Kristiawan, Senot Sangadji, and Halwan Alfisa Saifullah.
2024. "Influence of Joint Strengthening on the Seismic Performance of Non-Engineered Buildings" *Buildings* 14, no. 2: 488.
https://doi.org/10.3390/buildings14020488