# Performance Prediction of Hybrid Bamboo-Reinforced Concrete Beams Using Gene Expression Programming for Sustainable Construction

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Constitutive Modeling of Material

- For tensile loading:

- For compressive loading:

#### 2.2. Description of Model

_{w}and d are the width and effective depth of beam, respectively. A 22 mm diameter steel bar was employed to provide the required steel reinforcement, and the same number of bars was provided in all the specimens. For the analysis of the BRC beams, corrugated bamboo with the size of 20 × 20 mm was utilized, as illustrated in Figure 4. This modification served to prevent the bond slip and enhance the overall performance, in line with past research practices [23].

#### 2.3. Boundary Conditions, Interactions, and Loading

#### 2.4. Meshing

#### 2.5. Validation of Model

## 3. GEP Algorithm

#### 3.1. Parametric Study

#### 3.2. Proposed GEP Model for Estimating Flexural Strength of Hybrid BRC Beams

_{c}represents the concrete compressive strength, and A

_{r}and A

_{c}denote the areas of reinforcements and cross-section, respectively. The graphical representation of the estimation model’s expression tree is also presented in Figure 10 along with the parameters for construction of the model listed in Table 6.

#### 3.3. Accuracy and Validation of Proposed GEP Model

^{2}), was employed to quantitatively gauge the model’s effectiveness. R

^{2}, which assesses the reliability of the model, can be calculated using the following equation:

^{2}value approaching 1 indicates a precise prediction. The statistical assessment of the model’s performance, in comparison to the numerical results referred to as ‘‘target’’, is illustrated in Figure 11. An examination of R

^{2}provided a value of 0.98 for the training dataset and 0.97 for the validation dataset.

^{2}, which quantifies the accuracy of the regression analysis, revealed that our results were highly precise. Moreover, the equation derived from the expression tree demonstrated its efficacy in accurately calculating the flexural strength. The similarity between the predicted magnitudes of the flexural strength obtained through GEP and those extracted from FEMs further validated the reliability of our approach. This breakthrough in accurately estimating the flexural strength not only saves time and resources but also offers a promising alternative to traditional experimental methods. These findings open up new avenues for leveraging GEP as a powerful tool for predicting and analyzing complex material properties in various engineering applications.

## 4. Results and Discussion

#### Load–Deflection Curves and Energy Absorption of All Models

## 5. Conclusions

- A hybrid beam configuration with 50% steel and 50% bamboo reinforcements in the tension region can achieve a competitive ultimate strength, with only the marginal 7% reduction compared to a conventional SRC beam. This proportion of bamboo replacement for steel in beam construction holds great promise for significantly reducing the reliance on steel resources in the building and construction industry.
- The proposed hybrid bamboo–steel beams revealed comparable serviceability performance while requiring less reinforcement. The energy absorption of the BRC and SRC beams proved to be quite similar, with the minimal difference of only 13%. This suggests that the BRC beams can meet the required performance standards while being an environmentally sustainable and cost-effective alternative.
- The developed GEP-based predictive model proved to be a robust tool for estimating the flexural strength of the BRC beams. By incorporating key parameters such as the cross-sectional area of concrete, area of reinforcements, concrete compressive strength, and span and depth of the beams, this model achieved an impressive 97% accuracy. This highlights its potential as a valuable tool for engineers and designers in the building and construction industry.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Concrete compressive stress–strain curve; (

**b**) concrete compressive damage; (

**c**) concrete tensile stress–strain curve; (

**d**) concrete tensile damage.

**Figure 3.**Typical concrete beam specimen with different reinforcement configurations, as detailed in Table 3.

**Figure 8.**Flow chart representing steps of GEP [64].

**Figure 9.**Parametric study: (

**a**) capacity vs. f’

_{c}; (

**b**) capacity vs. A

_{r}; (

**c**) capacity vs. L; (

**d**) capacity vs. A

_{c}; (

**e**) capacity vs. D.

**Figure 10.**Gene expression tree for calculation of flexural strength: (

**a**) sub-ET 1; (

**b**) sub-ET 2; (

**c**) sub-ET 3.

**Figure 11.**Comparisons of model and target results for flexural strength of hybrid BRC beams: (

**a**) training dataset; (

**b**) validation dataset.

**Figure 13.**(

**a**) Comparison of strength reduction percentage for all beams in comparison to control beam (B1-4SB-SS); (

**b**) comparison of energy reduction of all models with respect to B1-4SB-SS.

**Figure 14.**Tensile damage in beams: (

**a**) B1-4SB-SS (control); (

**b**) B2-4BB; (

**c**) B3-4BB-BS; (

**d**) B4-4BB-SS; (

**e**) B5-2BB-2SB-SS.

**Table 1.**Mechanical and material properties [55].

Material | Density (kg/m ^{3}) | Young’s Modulus (MPa) | Poisson’s Ratio | Compressive Strength (MPa) | Tensile Strength (MPa) |
---|---|---|---|---|---|

Bamboo | 700 | 18,475 | 0.20 | 90 | 90 |

Steel | 7850 | 200,000 | 0.30 | 400 | 400 |

Concrete | 2300 | 33,600 | 0.15 | 31.31 | 3.13 |

Plasticity Parameter | Notation | Value |
---|---|---|

Dilation angle | ψ | 40 |

Eccentricity | ϵ | 0.1 |

Stress ratio | $\frac{{\sigma}_{b0}}{{\sigma}_{c0}}$ | 1.16 |

Shape factor | K | 0.66 |

Viscosity | μ | 0 |

Designation | Reinforcement Type | Description |
---|---|---|

B1-4SB-SS (Control) | Steel | Reference beam with steel bars and steel stirrups |

B2-4BB | Bamboo | Beam only with bamboo bars |

B3-4BB-BS | Bamboo | Beam with bamboo bars and bamboo stirrups |

B4-4BB-SS | Bamboo and steel | Beam with bamboo bars and steel stirrups |

B5-2BB-2SB-SS | Bamboo and steel | Beam with 50% steel bars, 50% bamboo bars, and steel stirrups |

Beam | P_{u} (kN) | ||
---|---|---|---|

Experiment | FEM | Experiment/FEM | |

SRC | 51 | 49.6 | 1.028 |

BRC | 35 | 34.22 | 1.023 |

Parameter | Range |
---|---|

Concrete compressive strength (f’_{c}) | 10–50 MPa |

Span length (L) | 100–140% |

Area of reinforcement (A_{r}) | 2–8% |

Area of cross-section (A_{c}) | 100–150% |

Depth of beam (D) | 200–350 mm |

Function Set | +, −, /, x |
---|---|

Number of chromosomes | 50 |

Head size | 10 |

Number of genes | 3 |

Linking function | Addition |

One-point recombination | 0.0027 |

Two-point recombination | 0.0027 |

Constants per gene | 10 |

Gene recombination | 0.0027 |

Gene transposition | 0.0027 |

Lower/upper bound of constants | −10/10 |

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**MDPI and ACS Style**

Waqas, H.A.; Bahrami, A.; Sahil, M.; Poshad Khan, A.; Ejaz, A.; Shafique, T.; Tariq, Z.; Ahmad, S.; Özkılıç, Y.O.
Performance Prediction of Hybrid Bamboo-Reinforced Concrete Beams Using Gene Expression Programming for Sustainable Construction. *Materials* **2023**, *16*, 6788.
https://doi.org/10.3390/ma16206788

**AMA Style**

Waqas HA, Bahrami A, Sahil M, Poshad Khan A, Ejaz A, Shafique T, Tariq Z, Ahmad S, Özkılıç YO.
Performance Prediction of Hybrid Bamboo-Reinforced Concrete Beams Using Gene Expression Programming for Sustainable Construction. *Materials*. 2023; 16(20):6788.
https://doi.org/10.3390/ma16206788

**Chicago/Turabian Style**

Waqas, Hafiz Ahmed, Alireza Bahrami, Mehran Sahil, Adil Poshad Khan, Ali Ejaz, Taimoor Shafique, Zain Tariq, Sajeel Ahmad, and Yasin Onuralp Özkılıç.
2023. "Performance Prediction of Hybrid Bamboo-Reinforced Concrete Beams Using Gene Expression Programming for Sustainable Construction" *Materials* 16, no. 20: 6788.
https://doi.org/10.3390/ma16206788