Prediction of the moment capacity of reinforced concrete slabs in fire using artificial neural networks

doi:10.1016/j.advengsoft.2009.07.006

Advances in Engineering Software

Volume 41, Issue 2, February 2010, Pages 270-276

https://doi.org/10.1016/j.advengsoft.2009.07.006 Get rights and content

Abstract

In this study, the application of artificial neural networks (ANN) to predict the ultimate moment capacity of reinforced concrete (RC) slabs in fire is investigated. An ANN model is built, trained and tested using 294 data for slabs exposed to fire. The data used in the ANN model consists of seven input parameters, which are the distance from the extreme fiber in tension to the centroid of the steel on the tension side of the slab (d′), the effective depth (d), the ratio of previous parameters (d′/d), the area of reinforcement on the tension face of the slab (A_s), the fire exposure time (t), the compressive strength of the concrete (f_cd), and the yield strength of the reinforcement (f_yd). It is shown that ANN model predicts the ultimate moment capacity (M_u) of RC slabs in fire with high degree of accuracy within the range of input parameters considered. The moment capacities predicted by ANN are in line with the results provided by the ultimate moment capacity equation. These results are important as ANN model alleviates the problem of computational complexity in determining M_u.

Introduction

Slabs are affected from fire as all other reinforced concrete (RC) members which are exposed to fire. As material strength of RC decreases with high temperature, the moment capacity (M_u) of RC slab decreases. In order to calculate the moment capacity of RC slab exposed to fire, the parameters such as the temperature increase depending on the fire exposure time, the temperature-distribution inside slab, the cross section and material properties, the tension and compression forces in slices, the depth equivalent rectangular stress block and the balance of the internal forces must be determined. As it is known, a large number of calculations are required to obtain these parameters. In order to avoid such computational complexity ANN approach may be used to predict effectively those parameters. However, to the best of author’s knowledge there is no research reported in literature on modeling of moment capacity using ANN method yet.

A neural network model is a computer model, whose architecture essentially mimics the learning capability of the human brain. ANN is a technique which can be applied to complex problems described with a large amount of data. It does not require knowledge of the physical processes involved. However, it identifies the relationships in a set of data. Therefore ANN approach may be applied to problems where conventional mathematical solutions are not applicable.

In recent years, ANN method has been used in variety of subjects in the structural engineering by many researchers. Some of these subjects are about prediction of the various properties of concrete [1], [2], [3], the properties of concrete aggregate [4], the strength of cements produced with pozzolans [5], the modeling of compressive strength of cement mortar [6], the rebar corrosion damage in RC structures [7], the performance of fiber reinforced RC beams and slabs [8], [9], [10], the moment and shear capacity [11], the shear strength [12], [13], [14], and the moment capacity and area of reinforcement [15] of RC beams, the ultimate deformation capacity of RC columns [16], the optimum cost [17] and the optimum depth [18] of RC slabs etc. Al-Khaleefi et al. [19] represented a functional relationship, using ANN method, between the fire resistance of a concrete filled steel column and the fire resistance parameters. However, there is no intensive research in determining the moment capacity of the RC slab using ANN yet.

In this study, a predictive model for the ultimate moment capacity of the RC slab in fire was developed by using ANN. The calculated moment capacities of the RC slabs in fire were compared with the moment capacities predicted by the ANN model to verify reliable application of the artificial neural network model. This research explores the applicability of using ANN to create an intelligent model for prediction of the ultimate moment capacity of RC slabs in fire.

Section snippets

Ultimate moment capacity of RC slabs in fire

In order to calculate the moment capacity of RC slab exposed to fire, the rising temperature by the fire exposure time, the temperature-distribution inside slab and the decrease in material strengths must be determined. After they are obtained, the tension and compression forces inside slab section are examined. The moment when the forces are balanced is the ultimate moment capacity of RC slab in fire. In the following subsections, these subjects are introduced.

Artificial neural network

Artificial neural networks are a computational tool that attempts to simulate the architecture and internal features of the human brain and nervous system. ANNs are consisting of a large number of simple processing elements called as neurons. Artificial neurons connected together form a network. The structure of artificial neural networks is layered. These are input, hidden and output layers. The back-propagation (BP) is one of the most popular learning algorithms. The back-propagation learns

ANN model used for the prediction of moment capacity

The objective of this work is to develop a neural network model for prediction of the ultimate moment capacity of slabs in fire. The data are obtained for different fire time, material and cross section properties. Temperature, concrete and steel material properties in each slice are obtained with slicing. Forces in all slices are determined by using the deteriorated properties of material. Heat transfer through slab is modeled as steady and one-dimensional. Heat transmission inside RC slab is

Analysis results

In this study, the ANN model has been developed to predict of the moment capacity of RC slabs in fire using the 294 data. The variation of Mean Squared Error (MSE) against the number of epochs for LM network training, validation and testing stages are shown in Fig. 5. It is evident that the MSE decreases rapidly with the increasing number of epochs. The result in terms of MSE here is reasonable, because the test set error and the validation set error have similar characteristics, and it does

Conclusions

The ultimate moment capacity of RC slabs exposed to fire for the different slab effective depths, the areas of reinforcement, the compressive strengths of the concrete and the yield strengths of the reinforcement is examined and predicted by using ANN method and the effect of these parameters are investigated. The calculated 294 data by author are used for this study. The correlation coefficient is obtained as 99.775% for training stage and 99.750% for testing stage. These values indicate that

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Prediction of the moment capacity of reinforced concrete slabs in fire using artificial neural networks

Abstract

Introduction

Section snippets

Ultimate moment capacity of RC slabs in fire

Artificial neural network

ANN model used for the prediction of moment capacity

Analysis results

Conclusions

Cem Concr Compos

Comput Mater Sci

Mater Des

Cem Concr Res

Comput Struct

Compos Part B: Eng

Eng Struct

Eng Struct

Eng Struct

Eng Appl Artif Intell

Comput Struct

Fire Safety J