This document describes using neural networks and genetic algorithms to design one-way reinforced concrete slabs. A neural network model with an input layer of 6 nodes, two hidden layers of 10 nodes each, and an output layer of 3 nodes was developed. The model was trained using 100 design examples from experts. The neural network was able to accurately predict slab depth, main reinforcement spacing, and distribution reinforcement spacing for 25 new design examples not used in training, demonstrating it can be used to design one-way slabs that satisfy code requirements.

1. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
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NEURAL NETWORK MODEL FOR DESIGN OF ONE-WAY R.C.C SLABS
USING GA/BPN
Dr. B. Ramesh Babu
Principal
Anantha Lakshmi Institute of Technology & Sciences
Anantapur, Andhra Pradesh, India.
ABSTRACT
The design of R.C.C slabs involves many constraints like different edge conditions, loading,
geometry and I.S. 456-2000 code provisions. The design has to satisfy all the constraints. This paper
demonstrates the applicability of artificial neural networks and genetic algorithms for the design of
one –way slabs to satisfy all the design constraints.
KEYWORDS: Artificial Neural Networks, Genetic Algorithms, One-Way Slabs, R.C.C. Slabs.
1. INTRODUCTION
Due to different edge conditions, the designer has to design many number of one way slabs in
any given building which becomes cumbersome. The present investigation proposes an alternative
method for the easy design of one-way slabs using the principles of Genetic Algorithms and Neural
Networks. Thus, the objective of the present work is to demonstrate the applicability of Genetic
algorithms and Artificial Neural Networks for the structural design of one-way slabs. The networks
have been trained with design data obtained from design experts in the field.
2. DESIGN OF ONE- WAY SLABS
2.1 Development of Simple and Genetic Algorithm Based Neural Network Models
The development of simple Artificial Neural network model and Genetic Algorithm based
neural network model for design of two-way slabs involves various steps such as
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1. Generation of exemplar patterns.
2. Selection of network type.
3. Selection of input and output for the network.
4. Arriving at a suitable network configuration.
5. Training of a network.
6. Validation of the resulting network.
These stages are addressed in the following sections.
2.1.1 Generation of Exemplar Patterns
The objective of this work is to develop neural network models for the design of one-way
slabs. This requires a comprehensive set of examples that cover various parameters influencing the
design of one-way slabs. All the training examples should invariably satisfy I.S. 456-2000 code
provisions. For the present work, all the training examples have been developed by presenting
different one-way slab problems to various design experts. The experts were asked to provide
designs satisfying I.S. code provisions. The design variables considered are the span, live load,
grades of concrete and steel and diameters of reinforcements. The design values are obtained for
different spans viz., 3.0m, 3.5m, 4.0m, 4.5m and 5.0m. Three different live load intensities viz., 1.5,
2.0 and 4.0 KN/m2
are considered. M20 and M25 grades of concretes have been used. Reinforcement
steel of three different grades viz. FE 250, FE 415 and FE 500 have been used. For main
reinforcement, two diameters viz., 8.0mm and10.0 mm are considered. For distribution
reinforcement only 8.0mm diameter has been considered. For each set, the overall depth of slab
required, main reinforcement spacing and distribution steel spacing are obtained.
For the present problem, a total of hundred samples training examples are obtained from
different experts such that these examples cover all the possible combinations of design variables
considered. Out of these, seventy five examples have been used for training and twenty five
examples are used for validation.
2.1.2 Selection of Network Type
The present problem considered for the neural network application involves the mapping of
the known parameters such as span lengths, loading, reinforcement details, So as to design the RCC
slabs. The design is highly dependent on these parameters as they interact among themselves in a
non-linear fashion. Therefore, while selecting a network type its ability for mapping complex non-
linear relationships must be considered for application. From the literature available, it is observed
that feed forward neural networks have the ability to map such non-linear relationships. Hence, the
feed forward form of neural architecture is used for the design of slabs.
2.1.3 Selection of Input and Output
In the present work, it is required to develop neural network models for the design of one-
way slabs. This means, the models should be able to predict the values of the depth of the section,
spacing of both main and distribution reinforcements for a given live load, grade of steel and
concrete. The input layer for the network has been configured taking in to account the possible
parameters that may influence the output. As the network is supposed to map the functional
relationship between the input and output parameters, the performance of the network is highly

3. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
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sensitive to the input information. In addition, proper choice of input parameters improves the net
performance for unseen problems i.e. the generalization capability. Accordingly the input to the
network is chosen as follows:
• span of the section (L)
• Live load (wl)
• Grade of concrete (fck)
• Grade of steel (fy)
• Diameter of main reinforcement (D1)
• Diameter of distribution reinforcement (d1)
Thus the input vector selected for this model is
IP = {L, wl, fck, fy, D,d } ------------ (1)
Although the relationship between the input parameters and macroscopic behavior of the
material is highly non-linear, the quantitative degree of non-linearity is not clearly known. Hence,
only the linear terms have been induced in the input vector. The network is expected to establish the
degree of non-linearity through the training examples in an implicit manner.
The designer would like to know the depth of the section and the areas of reinforcement for
the given grade of concrete, grade of steel, live load and Edge condition. Thus the model should be
able to predict the following.
• Overall Depth of slab (D)
• Spacing of main reinforcement (S1)
• Spacing of distribution reinforcement (S2)
Accordingly, the output vector for the neural network model is selected as
OP = { D, S1,S2 } ---------------- (2)
From the literature available it is learnt that computers work better for the values lying in
between 0 and 1. So the input and output parameters have been normalized in the range (0, +1) using
suitable normalization or scaling factors. This has been done by dividing the greatest entry at a node
by a scale factor slightly greater than it.

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2.1.4 Selecting a Suitable Network Configuration
2.1.4.1 GA/ BPN Model
After doing a few trials, it is observed that the network with 10 neurons each in two hidden
layer is behaving well. Accordingly a configuration of (6-10-3) has been selected for this network
model. The architecture is depicted in Figure 1.
Input layer Hidden layer Output layer
(6Neurons) (10 Neurons) (3 Neurons)
Figure 1. The Final GA/ BPN Configuration for one way slabs.
2.1.5 Training of the Network
2.1.5.1 Training of GA/BPN Model
The training of the present network has been accomplished using the Back Propagation
algorithm (BP). Conventionally, a BPN determines its weights based on a gradient search technique
and hence runs the risk of encountering a local-minima . GA on the other hand is found to be good at
finding ‘acceptably good’ solutions. The idea to hybridize the two networks has been successful to
D
S1
S2
L
wl
fck
fy
D1
d1
▪
▪

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enhance the speed of training . In the present work, the weights for the BPN have been obtained by
using a GA. Genetic Algorithms (GAs) which use a direct analogy of natural behavior work with a
population of individual strings, each representing a possible solution to the problem considered.
Each individual string is assigned a fitness value which is an assessment of how good a solution is to
a problem. The high-fit individuals participate in “reproduction” by cross-breeding with other
individuals in the population. This yields new individual strings as offspring which share some
features with each parent. The least-fit individuals are kept out from reproduction and so they “die
out”. A whole new population of possible solutions to the problem is generated by selecting the high-
fit individuals from the current generation. This new generation contains characteristics which are
better than their ancestors. The parameters which represent a potential solution to the problem,
genes, are joined together to form a string of values referred as a chromosome. A decimal coding
system has been adopted for coding the chromosomes in the present work. The network
configuration chosen for the present work is 6-10-3. Therefore, the number of weights (genes) that
are to be determined are 6X10+10X3= 90. With each gene being a real number, and taking the gene
length as 5, the string representing the chromosomes of weights will have a length of 90X5=450.
This string represents the weight matrices of the input-hidden layer-output layers. An initial
population of chromosomes is randomly generated. Weights from each chromosome have been
extracted then using the procedure suggested in reference. The fitness function has been devised
using FITGEN algorithm. A constant learning rate of 0.6 and a momentum factor of 0.9 have been
adopted during the training. Satisfactory training has been obtained after just 1500 training cycles.
This indicates the efficiency of the Genetic Algorithm. The progress of the learning of the network is
presented in Table 4.4. The training of the network accepted at this stage is depicted in figures 4(a-c).
From these figures, it is observed that, the ANN model predicted the output which closely matches
with analytical results.
Fig 2. (a). Learning of GA/BPN Model for Overall Depth of Slab, (b). Learning of GA/BPN Model
for Spacing of Main Reinforcement, (c). Learning of GA/ BPN Model for Spacing of Distribution
Reinforcement
(a) (b) (c)

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2.1.6 Validation of the Network Models
2.1.6.1validation of GA/BPN Model
Validation of the network is to test the network for the parameters that are not used in
training of the network. The network was asked to predict the overall depth, main reinforcement
spacing and distribution steel spacing of 25 sets which are not included in the training set. It can be
seen from the figures 6 (a-c) that the values predicted by GA/BPN model for new sets match
satisfactorily with results of design experts. It can also be noticed that the designs provided by the
neural network model satisfy all the provisions of I.S. 456-2000. Hence it can be concluded that this
neural network model can be successfully used to design different one-way slabs
Fig 3. (a). Validation of GA/BPN Model for Overall Depth of Slab, (b).Validation of GA/BPN
Model for Spacing of Main Reinforcement, (c). Validation of GA/BPN Model for Spacing of
Distribution Reinforcement
3. CONCLUSION
In this chapter the application of Genetic Algorithm based Neural Network model for the
design of two-way slab problem have been demonstrated. The network model have been trained
using one hundred examples obtained from different design experts. The training examples are so
chosen that they will cover all the design variables involved in the problem. It is observed that both
the model learned the design of one way slabs with good accuracy satisfying I.S. 456-2000
provisions.
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