# Optimization of Fiber-Reinforced Polymer Bars for Reinforced Concrete Column Using Nonlinear Finite Element Algorithms

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Finite Element Modeling and Experimental Verification

#### 2.2. Numerical Development of the Models

## 3. Seismic Parameters Model Development

_{y}) and detect the corresponding displacement in order to confirm the boundary of the elastic and non-elastic zone (the parts of the bilinear graph) [53].

_{s}is the yield force based on the first plastic hinge [55].

## 4. Results (Finite-Element Analysis)

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Group | $\mathit{D}\mathit{o}\mathit{r}$ $\mathit{b}\times \mathit{h}$ $\left(\mathit{m}\mathit{m}\right)\text{}$ | $\mathit{h}/\mathit{b}\text{}$ | $\mathit{H}\left(\mathit{m}\mathit{m}\right)$ | ${\mathit{f}}_{\mathit{c}}^{\prime}\text{}\left(\mathbf{MPa}\right)$ | Number of Longitudinal Bars | Number of Stirrups at Ordinary Zones | Number of Stirrups at Specific Zones |
---|---|---|---|---|---|---|---|

A1 | $508$ | N/A * | 1.1 | 31.7 | 6 | 2 | 9 |

B1 | $315\times 635$ | 2.0 | 1.4 | 30.2 | 6 | 3 | 9 |

C1 | $457\times 457$ | 1.0 | 1.0 | 32.1 | 8 | 3 | 8 |

D1 | $648\times 648$ | 1.0 | 1.4 | 30.7 | 12 | 4 | 13 |

E1 | $324\times 324$ | 1.0 | 0.7 | 32.3 | 4 | 3 | 7 |

F1 | $324\times 324$ | 1.0 | 1.4 | 31.5 | 4 | 5 | 12 |

G1 | $914\times 914$ | 1.0 | 2.0 | 31.6 | 26 | 3 | 17 |

H1 | $635\times 1270$ | 2.0 | 2.7 | 30.3 | 24 | 5 | 15 |

Laboratory Results | Finite Element Results | Difference (FEM vs. Laboratory) | ||||
---|---|---|---|---|---|---|

Specimen | Compressive Strength (MPa) | Maximum Axial Strain (mm/mm) | Compressive Strength (MPa) | Maximum Axial Strain (mm/mm) | Compressive Strength (%) | Maximum Axial Strain (%) |

A1 | 26 | 2.94 × 10^{−3}. | 29 | 3.00 × 10^{−3} | 11.9 | 2.5 |

B1 | 23.94 | 1.60 × 10^{−3} | 25.1 | 1.50 × 10^{−3} | 4.9 | −6.6 |

C1 | 26.6 | 3.25 × 10^{−3} | 27.3 | 3.30 × 10^{−3} | 2.5 | 1.6 |

D1 | 24.5 | 3.16 × 10^{−3} | 24.7 | 3.12 × 10^{−3} | 0.6 | −2.0 |

E1 | 20.4 | 2.20 × 10^{−3} | 20.55 | 2.13 × 10^{−3} | 0.4 | 5.3 |

F1 | 26.2 | 7.70 × 10^{−3} | 24.7 | 7.40 × 10^{−3} | −7 | −4 |

G1 | 28.5 | 6.99 × 10^{−3} | 30 | 7.11 × 10^{−3} | 5.2 | 2.5 |

H1 | - | - | 22.35 | 7.20 × 10^{−3} | - | - |

Name | Ultimate Stress (MPa) | Failure Strain | Modulus of Elasticity [1] |
---|---|---|---|

CFRP | 3690 | 0.031 | 580 |

GFRP | 1600 | 0.17 | 51 |

Group of Specimens | Steel (S) | CFRP Bars (C) | GFRP Bars (G) | Number of Longitudinal Bars #25 | Optimized CFRP with #12 Bars |
---|---|---|---|---|---|

A | AS | AC | AG | 6 | AO |

B | BS | BC | BG | 6 | BO |

C | CS | CC | CG | 8 | CO |

D | DS | DC | DG | 12 | DO |

E | ES | EC | EG | 4 | EO |

F | FS | FC | FG | 4 | FO |

G | GS | GC | GG | 26 | GO |

H | HS | HC | HG | 24 | HO |

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**MDPI and ACS Style**

Roudsari, S.S.; Ungureanu, L.M.; Soroushnia, S.; Abu-Lebdeh, T.; Petrescu, F.I.T.
Optimization of Fiber-Reinforced Polymer Bars for Reinforced Concrete Column Using Nonlinear Finite Element Algorithms. *Algorithms* **2022**, *15*, 12.
https://doi.org/10.3390/a15010012

**AMA Style**

Roudsari SS, Ungureanu LM, Soroushnia S, Abu-Lebdeh T, Petrescu FIT.
Optimization of Fiber-Reinforced Polymer Bars for Reinforced Concrete Column Using Nonlinear Finite Element Algorithms. *Algorithms*. 2022; 15(1):12.
https://doi.org/10.3390/a15010012

**Chicago/Turabian Style**

Roudsari, Sajjad Sayyar, Liviu Marian Ungureanu, Soheil Soroushnia, Taher Abu-Lebdeh, and Florian Ion Tiberiu Petrescu.
2022. "Optimization of Fiber-Reinforced Polymer Bars for Reinforced Concrete Column Using Nonlinear Finite Element Algorithms" *Algorithms* 15, no. 1: 12.
https://doi.org/10.3390/a15010012