Formulation of shear strength of slender RC beams using gene expression programming, part II: With shear reinforcement

doi:10.1016/j.measurement.2016.10.024

Measurement

Volume 95, January 2017, Pages 367-376

https://doi.org/10.1016/j.measurement.2016.10.024 Get rights and content

Highlights

•
GEP is employed for the formulation of the shear capacity of RC slender beams.
•
A simplified formula is obtained for the shear capacity of beams with stirrups.
•
The GEP model has a better performance than the ACI, EC2, CSA and NZS codes.

Abstract

In this study, a new variant of genetic programming, namely gene expression programming (GEP) is utilized to predict the shear strength of reinforced concrete (RC) beams with stirrups. The derived model relates the shear strength to mechanical and geometrical properties. The model is developed using a database containing 466 experimental test results gathered from the literature. Sensitivity and parametric analyses are performed for further verification of the model. The comparative study proves the superior performance of the GEP model compared to the expressions developed in several codes of practice.

Introduction

The flexural behavior of concrete elements is relatively well-recognized. This has resulted in establishing consistent expressions for the design of these elements in several codes of practice. Some studies have also been conducted to investigate the shear mechanism of concrete members over the last couple of decades. However, the shear transfer mechanisms in concrete elements are not as straightforward as the flexural behavior of these elements and still needs more studies. Most of the expressions provided in the current code provisions are mainly based on experimental studies. They indeed follow both the sectional and strut and tie model to predict the shear capacity of concrete beams and significantly vary from code to code which provides a wide range of factor of safety against failure. Understanding the mechanism of the shear transfer in concrete elements has always been challenging over the past decades. Extensive research has been carried out in this field.

Ritter [1] and Morsch [2] proposed the first analytical model, i.e., truss analogy, to calculate the shear capacity of a reinforced concrete beam. Many other researchers have also published other expressions to predict the shear capacity of concrete beams. However, most of the currents standard codes of practice are using semi-empirical formulations. Recent analytical methods of determining the shear capacity of reinforced concrete beams, including the disturbed stress field model (DSFM) [3], [4], modified compression field theory (MCFT) [5], [6], [7], and the softened truss model [9], [10] are mainly developed based on the truss model assumption. Recently, Arslan [11] proposed two different formulas for normal and high strength reinforced concrete beams with stirrups.

Artificial neural networks (ANNs) have been recently utilized in many fields including engineering (e.g. [12]). ANNs has the ability of self-organization and self-learning. They can efficiently employ the prior acquired knowledge to respond to the new set of information quickly and automatically. There have been some researches with the specific objective of applying ANNs to the evaluation of the shear strength of RC beams with shear reinforcement (e.g. [13]). The ANNs were shown to be a powerful tool for predicting the shear strength of concrete beams. Despite the acceptable performance of ANNs, there is no efficient procedure for the selection of structures of such networks. Hence, many experiments have to be performed to obtain an appropriate configuration. Also, ANNs do not usually give a definite function to calculate the outcome using the input values.

Genetic programming (GP) [14] is a new alternative approach to ANNs for the aim of nonlinear modeling. The major advantage of GP lies in its powerful ability to generate prediction equation. GP follows the principle of Darwinian natural selection for evolving the models. It is known as an extension of genetic algorithms (GAs). The main difference between these two approaches is that in GP the evolving programs (individuals) are parse trees rather than fixed-length binary strings. GP and its variants have successfully been applied to various kinds of structural engineering problems (e.g. [15], [16], [17]).

Different variants of GP have been proposed to improve the traditional GP [18]. Gene expression programming (GEP) [19] is a robust variant of GP. The traditional GP representation is based on the evaluation of a single tree (model) expression. GEP evolves computer programs of different sizes and shapes encoded in linear chromosomes of fixed length. Some of the GEP applications to concrete structures modeling include prediction of the strength of concrete under triaxial compression [20] and prediction of the compressive strength of high-performance concrete [21].

This study investigates the feasibility of using GEP for simulating the complex behavior of the shear capacity of RC beams with stirrups. A new relationship is developed between the shear strength and several influencing parameters using a database gathered from 55 experimental studies. A comparative study is further conducted between the results obtained by the proposed model and those of the building codes. The GEP model is developed based on reliable experimental results collected from the literature.

Section snippets

Shear strength mechanisms

To determine the maximum shear capacity of reinforced concrete beams, the shear strength of the stirrups should be added to those provided by the concrete shear capacity.

Gene expression programming

GP may be defined as a supervised machine learning technique that searches a program space instead of a data space. Symbolic regression is typically carried out through the standard GP to evolve a population of computer programs. The GP-based methods are substantially useful in cases where traditional methods are fairly complicated to be carried out, or the specific models of mathematical physics do not exist in detail. GEP is a natural development of GP first invented by Ferreira [19]. A basic

Model development

The primary objective of this paper is to develop a new formulation for the shear strength of slender RC beams with stirrups using the GEP approach. The GEP model was developed using six influencing input parameters as follows: $V = f (b_{w}, d, f_{c}, ρ_{l,} ρ_{w,} \frac{a}{d})$ where V (kN) is the shear strength of RC beam without stirrups, b_w (mm) is the web width, d (mm) is the effective depth, a/d represents the shear span to depth ratio, f_c (MPa) is the concrete compressive strength, ρ_l (%) shows the amount of longitudinal

Performance analysis and comparative study

According to Smith [80], if a model gives R > 0.8, and the error value is at the minimum, there is a strong correlation between the predicted and measured values. The model can, therefore, be judged as good. It can be observed from Fig. 4 and Table 3 that the GEP model with high R and low MAE and RMSE values precisely predicts the shear strength. The proposed model has both predictive ability (low MAE and RMSE values) and generalization performance (similar MAE and RMSEvalues) [81].

The proposed

Conclusions

In this study, a robust variant of GP, namely GEP is employed to assess the shear resistance of RC beam with stirrups. The shear strength was formulated in terms of several affecting factors (b, d, f_c, a/d, ρ_l, ρ_w) representing the behavior of the shear strength. A widely dispersed database including both the HSC and NSC reinforced beams was used for the model development. It was observed that the GEP-based model is capable of predicting the shear strength of RC beam with stirrups to a high

References (84)

R. Perera et al.
Strut-and-tie modelling of reinforced concrete beams using genetic algorithms optimization
Constr. Build. Mater.
(2009)
A.H. Alavi et al.
Prediction of principal ground-motion parameters using a hybrid method coupling artificial neural networks and simulated annealing
Comput. Struct.
(2011)
H. Tanyildizi et al.
Modeling mechanical performance of lightweight concrete containing silica fume exposed to high temperature using genetic programming
Constr. Build. Mater.
(2010)
A.H. Gandomi et al.
Multi-stage genetic programming: a new strategy to nonlinear system modeling
Inf. Sci.
(2011)
S.M. Mousavi et al.
A new predictive model for compressive strength of HPC using gene expression programming
Adv. Eng. Softw.
(2012)
A.H. Gandomi et al.
Formulation of shear strength of slender RC beams using gene expression programming, part I: without shear reinforcement
Automat. Constr.
(2014)
A. Baykasoglu et al.
Prediction of compressive and tensile strength of limestone via genetic programming
Expert Syst. Appl.
(2008)
A.H. Gandomi et al.
A hybrid computational approach to derive new ground-motion attenuation models
Eng. Appl. Artif. Intell.
(2011)
A. Cladera et al.
Experimental study on high-strength concrete beams failing in shear
Eng. Struct.
(2005)
Y. Pan et al.
A novel QSPR model for prediction of lower flammability limits of organic compounds based on support vector machine
J. Hazard. Mater.
(2009)

W. Ritter

Die Bauweise Hennebique

Schweiz. Bauzeitung

(1899)

E. Morsch, Concrete Steel Construction, English Translation E.P.Goodrich, McGraw-Hill, New York, from 3rd edn of Der...

F.J. Vecchio

Disturbed stress field model for reinforced concrete: formulation

ASCE J. Struct. Eng.

(2000)

F.J. Vecchio

Disturbed stress field model for reinforced concrete: implementation

ASCE J. Struct. Eng.

(2001)

E.C. Bentz et al.

Development of the 2004 CSA A23.3 shear provisions for reinforced concrete

Can. J. Civ. Eng.

(2005)

F.J. Vecchio et al.

The modified compression field theory for reinforced concrete elements subjected to shear

J. Am. Concr. Inst.

(1986)

F.J. Vecchio et al.

Predicting the response of reinforced concrete beams subjected to shear using the modified compression field theory

ACI Struct. J.

(1988)

S.T. Mau et al.

Shear strength prediction for deep beams with web reinforcement

Struct. J. Am. Concr. Inst.

(1987)

X.B. Pang et al.

Behavior of reinforced concrete membrane elements in shear

Struct. J. Am. Concr. Inst.

(1995)

G. Arslan

Shear strength of reinforced concrete beams with stirrups

Mater. Struct.

(2008)

J.A. Abdallaa et al.

Modeling and simulation of shear resistance of R/C beams using artificial neural network

J. Franklin Inst.

(2007)

J. Koza

Genetic Programming, on the Programming of Computers by Means of Natural Selection

(1992)

A.H. Gandomi et al.

A linear genetic programming application to CFRP confined concrete cylinders

Mater. Struct.

(2010)

A.H. Gandomi et al.

Expression programming techniques for formulation of structural engineering systems

C. Ferreira

Gene expression programming: a new adaptive algorithm for solving problems

Complex Syst.

(2001)

A.H. Gandomi et al.

A novel approach to strength modeling of concrete under triaxial compression

J. Mater. Civil Eng. – ASCE

(2012)

American Concrete Institute, ACI Building Code Requirements for Reinforced Concrete, ACI 318-02,...

Eurocode 2: Design of concrete structures - Part 1–1: General rules and rules for buildings, Brussels,...

CSA, Design of Concrete Structures A23.3-94, Canadian Standards Association, Rexdale, Ontario,...

NZS 3101, the Design of Concrete Structures. Part 1, New Zealand Standards, Wellington,...

C. Ferreira

Gene Expression Programming: Mathematical Modeling by an Artificial Intelligence

(2006)

GEPSOFT. GeneXproTools. Version 4.0. Available online; 2006,...

P. Adebar et al.

Shear strength of members without transverse reinforcement

Can. J. Civ. Eng.

(1996)

S.H. Ahmad et al.

Shear strength of reinforced lightweight concrete beams of normal and high strength concrete

Mag. Concr. Res.

(1994)

N.S. Anderson et al.

Detailing of stirrup reinforcement

ACI Struct. J.

(1989)

D. Angelakos et al.

Effect of concrete strength and minimum stirrups on shear strength of large members

ACI Struct. J.

(2001)

F. Bach, M.P. Nielson, MW. Braestrup, Shear tests on reinforced concrete T-beams series V, U, X, B and S. Structural...

B. Bresler et al.

Shear strength of reinforced concrete beams

ACI J. Proc.

(1963)

L.M. Cerruti et al.

Staggered shear design of concrete beams: large scale tests

Can. J. Civ. Eng.

(1987)

A.P. Clark

Diagonal tension in reinforcedconcrete beams

ACI J. Proc.

(1951)

M.P. Collins et al.

How safe are our large, lightly reinforced concrete beams, slabs and footings?

ACI Struct. J.

(1999)

S.Y. Debaiky et al.

Behavior and strength of reinforced haunched beams using high strength concrete

ACI J. Proc.

(1982)

Cited by (43)

Impact of fine lightweight aggregates and coal waste on structural lightweight concrete: Experimental study and gene expression programming
2024, Structures
Light Expanded Clay Aggregate (LECA) is one of the materials used to make lightweight concrete. In this study, two types of lightweight aggregates including LECA in both coarse and fine aggregate forms and pumice in fine aggregate form have been used to produce lightweight aggregate concrete. Coal waste is also used as partial replacement for cement. The results show that the usage of pumice as partial replacement for sand and LECA as coarse aggregate is applicable and can used for producing structural lightweight aggregate concrete. Furthermore, by using and increasing in the amount of LECA as fine aggregate, the slump of lightweight concrete in comparison to using sand, is also increased. The mixtures with LECA in both fine and coarse aggregate forms have the best results. Also, the results show that adding the coal waste improves the properties of lightweight concrete, and the optimal ratio is about 15% as partial replacement for cement by weight. In addition, gene expression programming is employed to establish empirical connections derived from experimental outcomes. In this regard, a relationship is proposed to determine the compressive strength of lightweight aggregate concrete based on the experimental data. The outcomes of gene expression programming demonstrate that the suggested formula exhibits good accuracy and efficiency in forecasting the specified parameter.
Prediction of compressive strength of brick columns confined with FRP, FRCM, and SRG system using GEP and ANN methods
2024, Journal of Engineering Research (Kuwait)
This study assesses the strength capacity of brick columns under various confinement materials, including fiber-reinforced polymer (FRP), fiber-reinforced cementitious matrix (FRCM), and steel-reinforced grout (SRG) using gene expression programming (GEP) and artificial neural networks (ANN) models. To achieve this, a comprehensive database of masonry column test results from existing scientific literature is compiled. The models' performance is evaluated using statistical errors like the coefficient of linear correlation (R²), mean absolute error (MAE), mean square error (MSE), and root mean square error (RMSE). Additionally, sensitivity analysis is carried out to assess the significance of individual parameters in the models. The findings reveal that ANN predictions closely match empirical data, demonstrating a strong correlation coefficient of 0.95. The accuracy of the ANN approach is reasonably high, with only 26% of the predicted values deviating by more than 20% from the actual data. Based on the statistical analyses, the correlation coefficient between the actual and estimated data was 0.88, for GEP method. Also, the GEP model yields outcomes, with roughly 43% of the predicted values differing by 20–50% from the actual data. In a comparison of the two models, the ANN model outperforms the GEP model, displaying a 40% reduction in error when estimating the compressive strength of masonry columns. The data estimated by the GEP were sparser than those estimated by the ANN. Nevertheless, the GEP model still maintains an acceptable correlation coefficient and error rate, making it a viable choice for precise predictions. It offers a user-friendly formula and meets the needs of both customers and builders.
Prediction of shear strength of RC slender beams based on interpretable machine learning
2023, Structures
The purpose of this paper is to explore a prediction model of the shear strength of reinforced concrete (RC) slender beams driven by experimental data and mechanisms. An experimental database containing 774 shear test specimens of RC slender beams with and without stirrups is collected. According to that, six machine learning models are applied and compared, and the interpretability of these models is further explored. Through the comparison of six machine learning models, namely k-nearest neighbor, decision tree, random forests, Adaboost, gradient boosting decision tree, and XGBoost, the XGBoost model performs well in prediction accuracy (R² = 0.999 and 0.953 in the training set and testing set). The XGBoost model is also significantly better than the mechanism-driven model in terms of prediction accuracy and variance, which is selected for further interpretation analysis. The interpretation analysis consists of three steps: (i) to identify the importance of features, (ii) to analyze feature dependence, (iii) to explore a novel interpretable idea combined the shear mechanism and SHapley Additive exPlanations (SHAP) method. It is the novel interpretable idea that the shear contribution distribution of the RC slender beam obtained by the SHAP value is further discussed. Through the comparison and discussion of the two mechanism models, the results of interpretable analysis indicate that the contribution distribution of the model conforms to the mechanism. Finally, the proposed interpretable approach is feasible and the developed XGBoost model is recommended for predicting the shear strength of RC beams and even similar questions.
Improved-GEP-based models for predicting distortion control indices of curved composite box girders
2023, Structures
Curved steel-concrete composite box girders are subjected to complex torsional actions under vertical loads, which may generate excessive distortional warping stresses. However, the complexity of the distortional warping stresses makes it challenging to obtain a quantitative prediction method, which may result in the adoption of potentially unsafe or uneconomical diaphragm designs. In this paper, improved-GEP (gene expression programming)-based models for predicting two distortion control indices of curved composite girder bridges are proposed. The key parameters in distortion equation for the curved composite box girder bridges are derived first, and then a comprehensive parametric analysis is conducted. Subsequently, an improved GEP algorithm is proposed to establish the formulas for calculating two distortion control indices. Compared to the traditional GEP, the proposed algorithm can markedly improve the mining ability of the constant terms and coefficients and enhance the global search ability by introducing a least squares algorithm and a new-generation and quasi-offspring mixed competitive strategy. In addition, with the operative and terminal symbols determined based on distortion theory, the efficiency and physical significance of the GEP models are effectively enhanced. The statistical indices and sensitivity analysis demonstrate that the proposed models for predicting the two distortion control indices agree with the finite element analysis results and distortion theory.
Mapping the strength of agro-ecological lightweight concrete containing oil palm by-product using artificial intelligence techniques
2023, Structures
The critical challenge for the cement production industry is the high emission of greenhouse gases. For the sustainability in a cycling economy context civil and environmental engineers should reconsider future generations and should redesign and manufacturing in a safe and eco-friendly alternative. Previous experimental studies have shown, that using oil palm by-product in the production of sustainable lightweight structural concrete, (SLSC) presents good life cycle, land-use efficiency and economic benefits. In this work a formula-based model is proposed to evaluate the strength of SLSC, knowledge-aided modeling based on machine learning methods (e. g., for further development, Multivariate Adaptive Regression Splines (MARS), Gene Expression Programming (GEP), M5P Model Tree (M5P) and Extreme Learning Machine (ELM)) were selected. A comprehensive and reliable experimental record comprising of 449 data of SLSC containing oil palm by-product was utilized to formulate strength predictive models. The proposed models were investigated, in terms of assessment criteria, error measurements, and performance evaluation. The efficiency of the MARS model was shown by comparing its performance with GEP, M5P and ELM. As well as Monte-Carlo simulation approach was conducted to verify the proposed models. Evaluation of the relative importance of effective variables presented that the gravel (11.84%), oil palm waste aggregate (11.38%) and water to binder ratio (11.15%) were the most influential features in the strength prediction of the SLSC. Also, a parametric study is developed to provide robustness of the proposed predictive model. Results of the modeling provide a new understanding of the provision of an auto-estimated strength evaluation of SLSC incorporating oil palm by-product with superiority promotion of knowledge-aided modeling mechanism.
Prediction of moment redistribution capacity in reinforced concrete beams using gene expression programming
2023, Structures
Citation Excerpt :
Gene expression programming (GEP) is one of the soft computing modelling tool that has been frequently used in many civil engineering studies to predict mathematical relations based on experimental studies as an efficient alternative to traditional regression. There are many studies in the literature performed on RC beams using GEP such as, prediction of flexural strength for beams reinforced with FRP bars [8], proposing a formulation for shear strength of slender RC beams [9], and proposing a model for shear strength of steel fibers RC beams [10]. However, in the literature review, it is not available any study regarding the determination of the moment redistribution with the GEP model.
Moment redistribution can play an important role in making the design of reinforced concrete (RC) structures more realistic and economical. In this paper, a new comprehensive formula has been proposed that considers four input parameters that are thought to influence moment redistribution the most in statically indeterminate RC beams using gene expression programming (GEP). For this reason, an experimental database of 108 data points was collected from experimental studies in the literature to predict the moment redistribution of the RC beams using genetic programming. All of these collected data points belong to two-span RC continuous beams. The results of the GEP formulation were statistically compared with the experimental results obtained from the literature and the results from the equations provided by the current design code provisions. The results of the comparison revealed that the proposed GEP-based formulation has the best performance and accuracy among the proposed models. Moreover, the sensitivity analysis and parametric study were also carried out to evaluate the most critical parameters affecting on moment redistribution of RC continuous beams.

View all citing articles on Scopus

View full text

Formulation of shear strength of slender RC beams using gene expression programming, part II: With shear reinforcement

Highlights

Abstract

Introduction

Section snippets

Shear strength mechanisms

Gene expression programming

Model development

Performance analysis and comparative study

Conclusions

Constr. Build. Mater.

Comput. Struct.

Constr. Build. Mater.

Inf. Sci.

Adv. Eng. Softw.

Automat. Constr.

Expert Syst. Appl.

Eng. Appl. Artif. Intell.

Eng. Struct.

J. Hazard. Mater.

Die Bauweise Hennebique

Schweiz. Bauzeitung

Disturbed stress field model for reinforced concrete: formulation

ASCE J. Struct. Eng.

Disturbed stress field model for reinforced concrete: implementation

ASCE J. Struct. Eng.

Development of the 2004 CSA A23.3 shear provisions for reinforced concrete

Can. J. Civ. Eng.

The modified compression field theory for reinforced concrete elements subjected to shear

J. Am. Concr. Inst.

Predicting the response of reinforced concrete beams subjected to shear using the modified compression field theory

ACI Struct. J.

Shear strength prediction for deep beams with web reinforcement

Struct. J. Am. Concr. Inst.

Behavior of reinforced concrete membrane elements in shear

Struct. J. Am. Concr. Inst.

Shear strength of reinforced concrete beams with stirrups

Mater. Struct.

Modeling and simulation of shear resistance of R/C beams using artificial neural network

J. Franklin Inst.

Genetic Programming, on the Programming of Computers by Means of Natural Selection

A linear genetic programming application to CFRP confined concrete cylinders

Mater. Struct.

Expression programming techniques for formulation of structural engineering systems

Gene expression programming: a new adaptive algorithm for solving problems

Complex Syst.

A novel approach to strength modeling of concrete under triaxial compression

J. Mater. Civil Eng. – ASCE

Gene Expression Programming: Mathematical Modeling by an Artificial Intelligence

Shear strength of members without transverse reinforcement

Can. J. Civ. Eng.

Shear strength of reinforced lightweight concrete beams of normal and high strength concrete

Mag. Concr. Res.

Detailing of stirrup reinforcement

ACI Struct. J.

Effect of concrete strength and minimum stirrups on shear strength of large members

ACI Struct. J.

Shear strength of reinforced concrete beams

ACI J. Proc.

Staggered shear design of concrete beams: large scale tests

Can. J. Civ. Eng.

Diagonal tension in reinforcedconcrete beams

ACI J. Proc.

How safe are our large, lightly reinforced concrete beams, slabs and footings?

ACI Struct. J.

Behavior and strength of reinforced haunched beams using high strength concrete

ACI J. Proc.