# Neural-network-based approach to predict the deflection of plain, steel-reinforced, and bamboo-reinforced concrete beams from experimental data

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## Abstract

The necessity of providing low-cost housing to economically weaker sections of society has been recognised by the national government of India. In mountainous areas, the use of locally available construction material, such as bamboo, as concrete reinforcement has increased due its easy availability and economic benefit. However, due to the inadequate codal provisions for the design and detailing of bamboo-reinforced structures, evaluating the serviceability criteria for their deflection behaviour under different loads is difficult. Furthermore, factors such as bond failure between reinforcement and concrete, shrinkage and corrosion of reinforcing material, and uncertainty in material strength make the prediction of deflection even more cumbersome. This study presents an artificial neural network (ANN)-based method modelled using MATLAB for predicting the deflection behaviour of three types of beams, namely plain, steel-reinforced, and bamboo-reinforced beams. Experimental investigation is conducted to record data at regular load increments for the aforementioned three beam typologies fabricated in the laboratory under two-point loading for 28 days. A total of 122 laboratory test data are recorded for modelling the ANN. The used approach involves predicting the relationship among the applied load, tensile strength of the reinforcement, percentage (amount) of reinforcement (taken as input), and deflection of the beam (obtained as output). The present ANN approach exhibits gives satisfactory performance (coefficient of determination \((R^2) = 0.9983\) and mean square error = 0.00049) in predicting the deflection behaviour of beams. Hence, the ANN approach can be used as an efficient and robust tool in predicting serviceability behavior of different types of reinforced concrete beams.

## Keywords

Artificial neural network Bamboo reinforced concrete Low cost housing Deflection Sustainability## 1 Introduction

The limitations and concerns of civil engineers when using bamboo as a reinforcement material include the high deflection [13] of structural members. Hence, the deflection behaviour of bamboo with different magnitudes of applied loads must be understood and estimated in advance for civil engineering applications. The prediction of deflection is a key aspect for builders, civil engineers, and researchers because it governs the serviceability criteria. Therefore, predicting the deflection behaviour is crucial for the safety of building occupants and for judging the design of bamboo-reinforced structures. The level of deflection mainly depends on three factors, two of which are controllable and one of which is uncontrollable. The controllable factors include the percentage of reinforcement used and the tensile strength of the bamboo material, whereas the uncontrollable factor is the load acting on the bamboo structure. Moreover, bamboo material has a large range of varieties, shapes, sizes, density, strength, and other parameters. Therefore, due to a wide range of input variables, estimating a reliable deflection value for concrete beams in real-world engineering structures is challenging.

Several design codes based on empirical relations cannot be used to estimate the deflection because bamboo material is not homogeneous and no industry standard exists. Hence, the conventional approach for deriving a mathematical relationship between the load and deflection has not been very successful in the field due to the presence of many uncertainties, which make the modelling process difficult. Furthermore, the load-carrying ability and deflection of bamboo-reinforced members is compromised by the water absorption capacity and premature bond failure of bamboo strips [14]. In reality, the field testing data must be trained so that it can be practically used. There exist some empirical equations for predicting the deformation and loading behaviour of bamboo in a similar manner to that of steel-reinforced members. Numerical tools, such as the finite element method, are unable to predict the relationship between the load and deflection due to the aforementioned uncertainties in bamboo material. Moreover, finite-element-simulations are found to be marginally stiffer [15] than in modelling the load-deflection characteristics of bamboo-reinforced concrete beams, and these methods are computationally expensive. Currently, artificial-intelligence-based techniques are used in such types of applications.

Artificial neural networks (ANNs) and various soft computing tools have been widely adopted in civil engineering applications due to their excellent estimation capacity. Studies have predicted the output variable from the training data in cases where a mathematical relationship is not evident. Most studies in civil engineering use ANNs for predicting the concrete compressive strength [16, 17, 18, 19, 20, 21, 22, 23, 24]. Other applications of ANNs include damage detection in beams by utilising vibration measurements [25, 26, 27, 28, 29] and the assessment of shear resistance in concrete beams [30, 31, 32, 33, 34]. Several researchers have used ANNs to predict the deflection of structures and their members. Hegazy et al. [35] used an ANN for modelling the load–deflection characteristics of concrete slabs. Tadesse et al. [36] applied an ANN for anticipating the middle-span displacements of six composite bridges by using data generated from finite element modelling and experimental results. Sakr et al. [37] estimated the transient and longstanding displacements of composite beams, and Flood et al. [38] examined externally reinforced RC beams by using ANNs. Ud Darain et al. [39] evaluated the deflection and cracking behaviour of beams strengthened with various materials by using an adaptive neuro-fuzzy system. They used strengthening materials with variable bond lengths. The variable load is used as the input, whereas the crack width and deflection are the output. Nguyen et al. [40, 41] used an ANN model combined with the hierarchical k-means clustering algorithm [42, 43] to evaluate blast-triggered ground vibration in a coalmine situated in Vietnam. To estimate the blast-induced ground vibration, Bui et al. [44] used approaches such as random forest (RF), Bayesian additive regression trees, the Gaussian process, support vector regression, boosted regression trees, and k-nearest neighbours. Furthermore artificial intelligent tools are widely used in real world applications in various in different fields such as combination of ANN with random forest for estimating blast-induced air overpressure [45], ultimate bearing capacity of shallow footings [46]. In a previous study, a hybrid evolutionary-based algorithm was used to estimate the heating load of an energy-efficient building [47]. In [48], an ANN optimised with the particle swarm optimisation algorithm was used to predict the energy performance of a building. A literature review indicates that no studies have evaluated the serviceability behaviour of bamboo-reinforced beams by predicting the deflection through artificial intelligence techniques. The deflection behaviour governs the serviceability criteria on whether the structure would suffer damages due to cracks and excessive deformations. Thus, the current study aimed to fill this literature gap by determining the nonlinear correlation between the selected inputs in predicting the deflection of concrete beams through the application of an ANN.

## 2 Data acquisition and experimental setup

In this study, data is obtained from the experimental testing of rectangular concrete beams (three in each category) made of only plain concrete (PC), reinforced with steel (RC) and reinforced with bamboo (bamboo-reinforced concrete BRC). The bamboo strips used are made of Muli bamboo, which is locally procured. Before conducting experiments on BRC, tensile tests are performed on the bamboo specimen for evaluating its ultimate strength and engineering properties. The tensile test included the preparation of bamboo samples and the gripping arrangement for the specimen (Fig. 2a, b), for testing in the Universal Testing Machine (UTM). Normal bamboo consists of a round surface. Therefore, an aluminium tab is required to make a flat surface for attachment to the bamboo. First, the bamboo specimens were cut to the appropriate dimensions. The samples were between 9 and 12 inches long, and their widths were also suitably reduced. The bamboo used in the tensile test should have a strong grip, without which the bamboo tends to shift. The bamboo samples were loaded gradually with a moderate loading rate of 1 mm/min in the 60-tonne UTM machine until the bamboo strips broke (Fig. 2c). The average tensile strength of the three tested bamboo specimens was \(186\hbox { N/mm}^2\), and their average modulus of elasticity was 24.5 GPa. The experimental tests indicated that the failure points of the specimens consisted of nodes.

Experimental load-deflection dataset used for ANN training

S.No. | Beam type | \(\rho\) % | Load (kN) | Disp. (mm) | S.No. | Beam type | \(\rho\) % | Load (kN) | Disp. (mm) |
---|---|---|---|---|---|---|---|---|---|

1 | PC | 0 | 0.00 | 0 | 62 | RC | 1.07 | 7.75 | 0.82 |

2 | PC | 0 | 0.30 | 0 | 63 | RC | 1.07 | 8.04 | 0.86 |

3 | PC | 0 | 0.60 | 0.01 | 64 | RC | 1.07 | 8.34 | 0.94 |

4 | PC | 0 | 0.89 | 0.02 | 65 | RC | 1.07 | 8.64 | 1.01 |

5 | PC | 0 | 1.19 | 0.03 | 66 | RC | 1.07 | 8.94 | 1.04 |

6 | PC | 0 | 1.49 | 0.04 | 67 | RC | 1.07 | 9.24 | 1.10 |

7 | PC | 0 | 1.79 | 0.05 | 68 | RC | 1.07 | 9.53 | 1.16 |

8 | PC | 0 | 2.09 | 0.06 | 69 | RC | 1.07 | 9.83 | 1.22 |

9 | PC | 0 | 2.38 | 0.07 | 70 | RC | 1.07 | 10.13 | 1.30 |

10 | PC | 0 | 2.68 | 0.08 | 71 | RC | 1.07 | 10.43 | 1.33 |

11 | PC | 0 | 2.98 | 0.09 | 72 | RC | 1.07 | 10.73 | 1.39 |

12 | PC | 0 | 3.28 | 0.1 | 73 | RC | 1.07 | 11.02 | 1.46 |

13 | PC | 0 | 3.58 | 0.11 | 74 | RC | 1.07 | 11.32 | 1.53 |

14 | PC | 0 | 3.87 | 0.12 | 75 | RC | 1.07 | 11.62 | 1.66 |

15 | PC | 0 | 4.17 | 0.13 | 76 | RC | 1.07 | 11.92 | 1.74 |

16 | PC | 0 | 4.47 | 0.14 | 77 | RC | 1.07 | 12.21 | 1.83 |

17 | PC | 0 | 4.77 | 0.15 | 78 | BRC | 1.49 | 0.00 | 0.00 |

18 | PC | 0 | 5.06 | 0.17 | 79 | BRC | 1.49 | 0.30 | 0.01 |

19 | PC | 0 | 5.36 | 0.18 | 80 | BRC | 1.49 | 0.60 | 0.03 |

20 | PC | 0 | 5.66 | 0.18 | 81 | BRC | 1.49 | 0.89 | 0.04 |

21 | PC | 0 | 5.96 | 0.2 | 82 | BRC | 1.49 | 1.19 | 0.05 |

22 | PC | 0 | 6.26 | 0.22 | 83 | BRC | 1.49 | 1.49 | 0.06 |

23 | PC | 0 | 6.55 | 0.22 | 84 | BRC | 1.49 | 1.79 | 0.07 |

24 | PC | 0 | 6.85 | 0.24 | 85 | BRC | 1.49 | 2.09 | 0.08 |

25 | PC | 0 | 7.15 | 0.25 | 86 | BRC | 1.49 | 2.38 | 0.11 |

26 | PC | 0 | 7.45 | 0.25 | 87 | BRC | 1.49 | 2.68 | 0.11 |

27 | PC | 0 | 7.75 | 0.27 | 88 | BRC | 1.49 | 2.98 | 0.12 |

28 | PC | 0 | 8.04 | 0.28 | 89 | BRC | 1.49 | 3.28 | 0.14 |

29 | PC | 0 | 8.34 | 0.3 | 90 | BRC | 1.49 | 3.58 | 0.15 |

30 | PC | 0 | 8.64 | 0.3 | 91 | BRC | 1.49 | 3.87 | 0.18 |

31 | PC | 0 | 8.94 | 0.31 | 92 | BRC | 1.49 | 4.17 | 0.20 |

32 | PC | 0 | 9.24 | 0.33 | 93 | BRC | 1.49 | 4.47 | 0.22 |

33 | PC | 0 | 9.53 | 0.34 | 94 | BRC | 1.49 | 4.77 | 0.25 |

34 | PC | 0 | 9.83 | 0.35 | 95 | BRC | 1.49 | 5.06 | 0.26 |

35 | PC | 0 | 10.13 | 0.36 | 96 | BRC | 1.49 | 5.36 | 0.32 |

36 | RC | 1.07 | 0.00 | 0.00 | 97 | BRC | 1.49 | 5.66 | 0.35 |

37 | RC | 1.07 | 0.30 | 0.03 | 98 | BRC | 1.49 | 5.96 | 0.38 |

38 | RC | 1.07 | 0.60 | 0.05 | 99 | BRC | 1.49 | 6.26 | 0.42 |

39 | RC | 1.07 | 0.89 | 0.07 | 100 | BRC | 1.49 | 6.55 | 0.45 |

40 | RC | 1.07 | 1.19 | 0.08 | 101 | BRC | 1.49 | 6.85 | 0.49 |

41 | RC | 1.07 | 1.49 | 0.09 | 102 | BRC | 1.49 | 7.15 | 0.52 |

42 | RC | 1.07 | 1.79 | 0.10 | 103 | BRC | 1.49 | 7.45 | 0.56 |

43 | RC | 1.07 | 2.09 | 0.12 | 104 | BRC | 1.49 | 7.75 | 0.61 |

44 | RC | 1.07 | 2.38 | 0.15 | 105 | BRC | 1.49 | 8.04 | 0.63 |

45 | RC | 1.07 | 2.68 | 0.15 | 106 | BRC | 1.49 | 8.34 | 0.70 |

46 | RC | 1.07 | 2.98 | 0.17 | 107 | BRC | 1.49 | 8.64 | 0.75 |

47 | RC | 1.07 | 3.28 | 0.19 | 108 | BRC | 1.49 | 8.94 | 0.78 |

48 | RC | 1.07 | 3.58 | 0.21 | 109 | BRC | 1.49 | 9.24 | 0.82 |

49 | RC | 1.07 | 3.87 | 0.25 | 110 | BRC | 1.49 | 9.53 | 0.86 |

50 | RC | 1.07 | 4.17 | 0.28 | 111 | BRC | 1.49 | 9.83 | 0.91 |

51 | RC | 1.07 | 4.47 | 0.30 | 112 | BRC | 1.49 | 10.13 | 0.97 |

52 | RC | 1.07 | 4.77 | 0.34 | 113 | BRC | 1.49 | 10.43 | 1.00 |

53 | RC | 1.07 | 5.06 | 0.36 | 114 | BRC | 1.49 | 10.73 | 1.03 |

54 | RC | 1.07 | 5.36 | 0.43 | 115 | BRC | 1.49 | 11.02 | 1.09 |

55 | RC | 1.07 | 5.66 | 0.47 | 116 | BRC | 1.49 | 11.32 | 1.14 |

56 | RC | 1.07 | 5.96 | 0.52 | 117 | BRC | 1.49 | 11.62 | 1.24 |

57 | RC | 1.07 | 6.26 | 0.56 | 118 | BRC | 1.49 | 11.92 | 1.30 |

58 | RC | 1.07 | 6.55 | 0.60 | 119 | BRC | 1.49 | 12.21 | 1.38 |

59 | RC | 1.07 | 6.85 | 0.65 | 120 | BRC | 1.49 | 12.51 | 1.48 |

60 | RC | 1.07 | 7.15 | 0.70 | 121 | BRC | 1.49 | 12.81 | 1.70 |

61 | RC | 1.07 | 7.45 | 0.75 | 122 | BRC | 1.49 | 13.11 | 2.05 |

Table 1 presents the dataset obtained from the experimental testing. The three input parameters (\(\rho\), \(f_y\), and the applied load) are employed as input vectors of the ANN. The load-displacement behaviour of all the beams is then compared. The selection of parameters is crucial because it has a direct influence on the evaluation of the deflection of the structural member. The load-displacement behaviour of all the beams was then compared. The output was selected as the member deflection governing the serviceability criteria. In addition to the selected three inputs, other factors such as the compressive strength of concrete; dimensions of the structural member; corrosion of rebars; clear cover remaining in the beam; aggregate type; and degradation of the bond between the reinforcement, water–cement ratio, and concrete [49, 50] also affect the long-term deflection of the structural member. The long-term effects of creep, shrinkage, and the environmental conditions on the deflection were also not considered in the experimentation. Paulson et al. [49] investigated the behaviour of reinforced concrete beams by examining the deflection over 12 months. Val and Chernin [50] considered the effect of rebar corrosion on the deflections of steel-reinforced beams by modelling the uncertainties in material properties, loads, and the bond between the reinforcing member and concrete. The dataset in this study indicates that the bamboo-reinforced beams can sustain larger deflections than the PC and steel-reinforced beams. Hence, in contrast to plain reinforced beams, bamboo-reinforced beams exhibit ductile failure.

## 3 ANNs

*O*is the output linked with

*i*th input node, \(w_i\) is the weight linked with the

*i*th input node, and \(I_i\) is the input at node

*i*.

*N*denote the estimated value of observation

*i*, observed value of observation

*i*, and total number of datasets, respectively. The RMSE is defined as follows:

*E*(

*x*) taken over

*N*datasets. The ANN data were divided into three datasets for training, testing, and validating the model.

## 4 Results and discussion

Results of statistical analyses of the 3-5-1 ANN architecture over five sample runs

\(R^2\) | MSE | Rank | |||
---|---|---|---|---|---|

Training | Validation | Testing | All | ||

0.99977 | 0.99913 | 0.99505 | 0.9983 | 0.000417 | 1 |

0.99985 | 0.99482 | 0.99903 | 0.99821 | 0.001002 | 2 |

0.99863 | 0.99173 | 0.99857 | 0.99652 | 0.005964 | 3 |

0.99754 | 0.98426 | 0.99487 | 0.99378 | 0.006271 | 4 |

0.99815 | 0.9909 | 0.99893 | 0.99584 | 0.006883 | 5 |

## 5 Conclusions

In this research, the deflection of several concrete beams is predicted under varying loads in short term, different types of reinforcement material, and different percentages of reinforcement by using an ANN. A sequence of experimental tests are performed to validate the usage of bamboo as a potential reinforcement material for concrete beams. The ANN results closely matched with the experimental values of deflection for the different beam typologies tested. The regression values of the ANN for training, validation and testing are 0.9997, 0.9991 and 0.9950 respectively with the best validation performance being obtained at epoch 31. The results indicate that the ANN can be utilised as a powerful and reliable tool for estimating the deflection behaviour of concrete beams in the considered loading conditions. It can be applied in civil engineering structures by engineers to quickly estimate the deflection of reinforced concrete beams without performing any complex analysis. The ANN and experimental results indicate that bamboo-reinforced beams can be used a substitute in place of traditionally used steel rebars. The ultimate load and maximum deflection are comparable for the two typologies of reinforced beams tested in this study. The bamboo-reinforced beam exhibited a 30% increase in the load-carrying capacity compared with the plain reinforced concrete beam for a 1.5% area of reinforcement. For a 1.1% area of steel reinforcement, the bamboo-reinforced beam exhibited an 8% increase in the load-carrying capacity.

In future studies, the database can be expanded by using different percentages of reinforcement and different varieties of bamboo. Furthermore, experimental data can be obtained for large-scale beams and columns to determine the actual site conditions. The present study evaluated the deflection of beams under loading only for predicting the short-term service life. Hence the time-dependent behaviour of reinforcing material, which affects the long-term serviceability, can also be investigated by performing further experimentation. Experimental studies can also be performed on other structural elements (i.e., concrete columns and slabs) that use bamboo strips as inherent reinforcement

## Notes

### Compliance with ethical standards

### Conflict of interest

The Authors declare that they have no conflict of interest.

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