Proposed soft computing models for moment capacity prediction of reinforced concrete columns


Computational intelligence (CI) is a powerful approach to determine the response values of complex systems. Despite their benefits, the way to reach the solution in these approaches is difficult and cannot be expressed in a clear and simple formulation. In recent years, some methods have been proposed to provide simple and efficient mathematical forms in such approaches. In this paper, five of these methods are investigated to estimate the amount of moment capacity in rectangular concrete columns based on the extracted equations of CI. To train, validate and also test the proposed equations, a set of experimental laboratory tests of RC columns were collected from PEER database, and then mathematical frameworks for calculating the target were extracted. The obtained results of the proposed structures are also compared with each other, and it was concluded that all methods with high accuracy were able to estimate the moment capacity, but equation-based neuro-fuzzy system had better results than other presented models. The proposed equations are very powerful tools for determining the final capacity of RC columns as a key element in concrete structures.

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A :

Coefficient of linear function

A s :

Area of longitudinal reinforcement

b :

Bias value

\( b_{1} \) :

Bias for the hidden layer

\( b_{2} \) :

Bias for the output layer

C :

Membership function

c :

Mean for x


Correction factor for As

C(\( f'_{c} \)):

Correction factor for \( f'_{c} \)

C(\( f_{y,l} \)):

Correction factor for \( f_{y,l} \)


Correction factor for L/r

D :

Depth or longer side of the column

f :

Linear function

\( f'_{c} \) :

Compressive strength of concrete

\( f_{y,t} \) :

Yield stress of longitudinal reinforcement

\( f_{y,l} \) :

Yield stress of transverse reinforcement

I :

Moment of inertia of the cross section

IW :

Input weights of hidden layer

L :

Length of equivalent cantilever

L/r :

Length of column to gyration ratio

LW :

Layer weights of output layer

M :

Moment capacity of concrete column

\( M_{0} \) :

ANFIS output


Mean of error

N :

Number of data


Standard deviation

V :

Output layer for ANN-8-Purelin

W :

Width or shorter side of the column

w :


X :

Input parameter

\( x_{ \hbox{max} } \) :

Maximum value for x

\( x_{ \hbox{min} } \) :

Minimum value for x

\( x_{n} \) :

Normal value of x

\( x_{r} \) :

Real value of x

Y :

Polynomial equation

Z :

Output layer for ANN-1-Tansig

\( \rho_{l} \) :

Longitudinal reinforcement ratio

\( \rho_{t} \) :

Transverse reinforcement ratio

σ :

Variance for x


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Naderpour, H., Mirrashid, M. Proposed soft computing models for moment capacity prediction of reinforced concrete columns. Soft Comput 24, 11715–11729 (2020).

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  • Flexure failure
  • Moment capacity
  • Reinforced concrete columns
  • Soft computing
  • Structural capacity