Prediction of shear strength of FRP-reinforced concrete beams without stirrups based on genetic programming

The use of fibre reinforced polymer (FRP) bars to reinforce concrete structures has received a great deal of attention in recent years due to their excellent corrosion resistance, high tensile strength, and good non-magnetization properties. Due to the relatively low modulus of elasticity of FRP bars, concrete members reinforced longitudinally with FRP bars experience reduced shear strength compared to the shear strength of those reinforced with the same amounts of steel reinforcement. This paper presents a simple yet improved model to calculate the concrete shear strength of FRP-reinforced concrete slender beams (a/d > 2.5) without stirrups based on the gene expression programming (GEP) approach. The model produced by GEP is constructed directly from a set of experimental results available in the literature. The results of training, testing and validation sets of the model are compared with experimental results. All of the results show that GEP is a strong technique for the prediction of the shear capacity of FRP-reinforced concrete beams without stirrups. The performance of the GEP model is also compared to that of four commonly used shear design provisions for FRP-reinforced concrete beams. The proposed model produced by GEP provides the most accurate results in calculating the concrete shear strength of FRP-reinforced concrete beams among existing shear equations provided by current provisions. A parametric study is also carried out to evaluate the ability of the proposed GEP model and current shear design guidelines to quantitatively account for the effects of basic shear design parameters on the shear strength of FRP-reinforced concrete beams.     

Neural networks modeling of shear strength of SFRC corbels without stirrups

Based on developed semi-empirical characteristic equations an artificial neural network (ANN) model is presented to measure the ultimate shear strength of steel fibrous reinforced concrete (SFRC) corbels without shear reinforcement and tested under vertical loading. Backpropagation networks with Lavenberg–Marquardt algorithm is chosen for the proposed network, which is implemented using the programming package MATLAB. The model gives satisfactory predictions of the ultimate shear strength when compared with available test results and some existing models. Using the proposed networks results, a parametric study is also carried out to determine the influence of each parameter affecting the failure shear strength of SFRC corbels with wide range of variables. This shows the versatility of ANNs in constructing relationship among multiple variables of complex physical relationship.     

Effect of loading types and reinforcement ratio on an effective moment of inertia and deflection of a reinforced concrete beam

In the design of reinforced concrete structures, a designer must satisfy not only the strength requirements but also the serviceability requirements, and therefore the control of the deformation becomes more important. To ensure serviceability criterion, it is necessary to accurately predict the cracking and deflection of reinforced concrete structures under service loads. For accurate determination of the member deflections, cracked members in the reinforced concrete structures need to be identified and their effective flexural and shear rigidities determined. The effect of concrete cracking on the stiffness of a flexural member is largely dependent on both the magnitude and shape of the moment diagram, which is related to the type of applied loading. In the present study, the effects of the loading types and the reinforcement ratio on the flexural stiffness of beams has been investigated by using the computer program developed for the analysis of reinforced concrete frames with members in cracked state. In the program, the variation of the flexural stiffness of a cracked member has been obtained by using ACI, CEB and probability-based effective stiffness model. Shear deformation effect is also taken into account in the analysis and the variation of shear stiffness in the cracked regions of members has been considered by employing reduced shear stiffness model available in the literature. Comparisons of the different models for the effective moment of inertia have been made with the reinforced concrete test beams. The effect of shear deformation on the total deflection of reinforced concrete beams has also been investigated, and the contribution of shear deformation to the total deflection of beam have been theoretically obtained in the case of various loading case by using the developed computer program. The applicability of the proposed analytical procedure to the beams under different loading conditions has been tested by a comparison of the analytical and experimental results, and the analytical results have been found in good agreement with the test results.     

Linear genetic programming for shear strength prediction of reinforced concrete beams without stirrups

A new design equation is proposed for the prediction of shear strength of reinforced concrete (RC) beams without stirrups using an innovative linear genetic programming methodology. The shear strength was formulated in terms of several effective parameters such as shear span to depth ratio, concrete cylinder strength at date of testing, amount of longitudinal reinforcement, lever arm, and maximum specified size of coarse aggregate. A comprehensive database containing 1938 experimental test results for the RC beams was gathered from the literature to develop the model. The performance and validity of the model were further tested using several criteria. An efficient strategy was considered to guarantee the generalization of the proposed design equation. For more verification, sensitivity and parametric analysis were conducted. The results indicate that the derived model is an effective tool for the estimation of the shear capacity of members without stirrups (R = 0.921). The prediction performance of the proposed model was found to be better than that of several existing buildings codes.     

Propagation of a cohesive crack through adherent reinforcement layers

This paper analyzes the propagation of a cohesive crack crossing one or several reinforcement layers by a simple model valid for any specimen or loading condition. In this instance the case of reinforced concrete beams loaded at three points is considered. In this approach steel bars do not constitute a physical barrier to the propagation of the crack, as concrete continuity is preserved by a computational strategy consisting of overlapping both materials in the same spatial position. The model uses cohesive elements to represent the crack and interface elements to simulate the decohesion and shear generated in the steel-concrete debonding process. The results given by this model are compared to experimental results on rectangular and T-shaped beams reinforced by bars arranged in one or several layers. The model closely follows the experimental trends when changing the parameters that control the type of fracture; such as the steel ratio, the bond strength, the position and arrangement of the bars, the size of the specimen and the shape of the beam cross-section. In spite of its simplicity, this model can be useful when studying local fracture and decohesion phenomena wherever they may take place within a reinforced or prestressed concrete structure.     

Prediction of deflection of reinforced concrete shear walls

Reinforced concrete shear walls are used in tall buildings for efficiently resisting lateral loads. Due to the low tensile strength of concrete, reinforced concrete shear walls tend to behave in a nonlinear manner with a significant reduction in stiffness, even under service loads. To accurately assess the lateral deflection of shear walls, the prediction of flexural and shear stiffness of these members after cracking becomes important. In the present study, an iterative analytical procedure which considers the cracking in the reinforced concrete shear walls has been presented. The effect of concrete cracking on the stiffness and deflection of shear walls have also been investigated by the developed computer program based on the iterative procedure. In the program, the variation of the flexural stiffness of a cracked member has been evaluated by ACI and probability-based effective stiffness model. In the analysis, shear deformation which can be large and significant after development of cracks is also taken into account and the variation of shear stiffness in the cracked regions of members has been considered by using effective shear stiffness model available in the literature. Verification of the proposed procedure has been confirmed from series of reinforced concrete shear wall tests available in the literature. Comparison between the analytical and experimental results shows that the proposed analytical procedure can provide an accurate and efficient prediction of both the deflection and flexural stiffness reduction of shear walls with different height to width ratio and vertical load. The results of the analytical procedure also indicate that the percentage of shear deflection in the total deflection increases with decreasing height to width ratio of the shear wall.     

Empirical modelling of shear strength of RC deep beams by genetic programming

This paper investigates the feasibility of using genetic programming (GP) to create an empirical model for the complicated non-linear relationship between various input parameters associated with reinforced concrete (RC) deep beams and their ultimate shear strength. GP is a relatively new form of artificial intelligence, and is based on the ideas of Darwinian theory of evolution and genetics. The size and structural complexity of the empirical model are not specified in advance, but these characteristics evolve as part of the prediction. The engineering knowledge on RC deep beams is also included in the search process through the use of appropriate mathematical functions.The model produced by GP is constructed directly from a set of experimental results available in the literature. The validity of the obtained model is examined by comparing its response with the shear strength of the training and other additional datasets. The developed model is then used to study the relationships between the shear strength and different influencing parameters. The predictions obtained from GP agree well with experimental observations.     

Modeling of transfer length of prestressing strands using genetic programming and neuro-fuzzy

In this study, the efficiency of neuro-fuzzy inference system (ANFIS) and genetic expression programming (GEP) in predicting the transfer length of prestressing strands in prestressed concrete beams was investigated. Many models suggested for the transfer length of prestressing strands usually consider one or two parameters and do not provide consistent accurate prediction. The alternative approaches such as GEP and ANFIS have been recently used to model spatially complex systems. The transfer length data from various researches have been collected to use in training and testing ANFIS and GEP models. Six basic parameters affecting the transfer length of strands were selected as input parameters. These parameters are ratio of strand cross-sectional area to concrete area, surface condition of strands, diameter of strands, percentage of debonded strands, effective prestress and concrete strength at the time of measurement. Results showed that the ANFIS and GEP models are capable of accurately predicting the transfer lengths used in the training and testing phase of the study. The GEP model results better prediction compared to ANFIS model.     

A plastic damage approach for confined concrete

There are many situations in which it is necessary to increase the capacity of structures in use. This need maybe either for a change of use or because the structures have suffered some damage or have shown little resistance in case of extreme loads such as earthquakes. The most common methods for repair and retrofit of reinforced concrete columns are concrete jacketing, steel jacketing and fiber wrapping. This last type of reinforcement has many advantages as it offers a high-strength, low-weight and corrosion-resistant jacket with easy and rapid installation. The reinforcement with composite materials improves shear and compression strength and ductility as a result of concrete core confinement. The present analytical and numerical ability to quantify the efficiency of fiber confinement is rather limited, especially with respect to ductility.A constitutive model that approximately reproduces the behavior of structural concrete elements under confinement is developed in this paper. The model allows the assessment of concrete columns and bridge piles repaired and/or reinforced with fiber reinforced composites (FRP). The model presented is a modification of an existing coupled plastic damage model. A new definition for the plastic hardening variable and a new yielding surface with curved meridians are proposed. Both improvements enable the adequate reproduction of concrete behavior in high confinement conditions.The comparison of numerical and experimental results shows the model capacity to simulate concrete behavior under triaxial compression conditions like the ones present in concrete columns confined with fiber reinforced composites.     

Efficient finite element modelling of reinforced concrete beams retrofitted with fibre reinforced polymers

This paper presents a new simple and efficient two-dimensional frame finite element (FE) able to accurately estimate the load-carrying capacity of reinforced concrete (RC) beams flexurally strengthened with externally bonded fibre reinforced polymer (FRP) strips and plates. The proposed FE, denoted as FRP–FB-beam, considers distributed plasticity with layer-discretization of the cross-sections in the context of a force-based (FB) formulation. The FRP–FB-beam element is able to model collapse due to concrete crushing, reinforcing steel yielding, FRP rupture and FRP debonding.The FRP–FB-beam is used to predict the load-carrying capacity and the applied load-midspan deflection response of RC beams subjected to three- and four-point bending loading. Numerical simulations and experimental measurements are compared based on numerous tests available in the literature and published by different authors. The numerically simulated responses agree remarkably well with the corresponding experimental results. The major features of this frame FE are its simplicity, computational efficiency and weak requirements in terms of FE mesh refinement. These useful features are obtained together with accuracy in the response simulation comparable to more complex, advanced and computationally expensive FEs. Thus, the FRP–FB-beam is suitable for efficient and accurate modelling and analysis of flexural strengthening of RC frame structures with externally bonded FRP sheets/plates and for practical use in design-oriented parametric studies.     

A new predictive model for compressive strength of HPC using gene expression programming

In this study, gene expression programming (GEP) is utilized to derive a new model for the prediction of compressive strength of high performance concrete (HPC) mixes. The model is developed using a comprehensive database obtained from the literature. The validity of the proposed model is verified by applying it to estimate the compressive strength of a portion of test results that are not included in the analysis. Linear and nonlinear least squares regression analyses are performed to benchmark the GEP model. Contributions of the parameters affecting the compressive strength are evaluated through a sensitivity analysis. GEP is found to be an effective method for evaluating the compressive strength of HPC mixes. The prediction performance of the optimal GEP model is better than the regression models.     

A practical ANN model for predicting the PSS of two-way reinforced concrete slabs

This paper aims to develop a practical artificial neural network (ANN) model for predicting the punching shear strength (PSS) of two-way reinforced concrete slabs. In this regard, a total of 218 test results collected from the literature were used to develop the ANN models. Accordingly, the slab thickness, the width of the column section, the effective depth of the slab, the reinforcement ratio, the compressive strength of concrete, and the yield strength of reinforcement were considered as input variables. Meanwhile, the PSS was considered as the output variable. Several ANN models were developed, but the best model with the highest coefficient of determination (R²) and the smallest root mean square errors was retained. The performance of the best ANN model was compared with multiple linear regression and existing design code equations. The comparative results showed that the proposed ANN model was provided the most accurate prediction of PSS of two-way reinforced concrete slabs. The parametric study was carried out using the proposed ANN model to assess the effect of each input parameter on the PSS of two-way reinforced concrete slabs. Finally, a graphical user interface was developed to apply for practical design of PSS of two-way reinforced concrete slabs.

     

Nonlinear finite element analysis of concrete structures using new constitutive models

Nonlinear finite element analysis was applied to various types of reinforced concrete structures using a new set of constitutive models established in the fixed-angle softened-truss model (FA-STM). A computer code FEAPRC was developed specifically for application to reinforced concrete structures by modifying the general-purpose program FEAP. FEAPRC can take care of the four important characteristics of cracked reinforced concrete: (1) the softening effect of concrete in compression, (2) the tension-stiffening effect by concrete in tension, (3) the average (or smeared) stress–strain curve of steel bars embedded in concrete, and (4) the new, rational shear modulus of concrete. The predictions made by FEAPRC are in good agreement with the experimental results of beams, panels, and framed shear walls.     

Support vector regression based shear strength modelling of deep beams

Support vector regression based modelling approach was used to predict the shear strength of reinforced and prestressed concrete deep beams. To compare its performance, a back-propagation neural network and the three empirical relations was used with reinforced concrete deep beams. For prestressed deep beams, one empirical relation was used. Results suggest an improved performance by the SVR in terms of prediction capabilities in comparison to the empirical relations and back propagation neural network. Parametric studies with SVR suggest the importance of concrete cylinder strength and ratio of shear span to effective depth of beam on strength prediction of deep beams.     

Improving analytical models of circular concrete columns with genetic programming polynomials

This study improves weighted genetic programming and uses proposed novel genetic programming polynomials (GPP) for accurate prediction and visible formulas/polynomials. Representing confined compressive strength and strain of circular concrete columns in meaningful representations makes parameter studies, sensitivity analysis, and application of pruning techniques easy. Furthermore, the proposed GPP is utilized to improve existing analytical models of circular concrete columns. Analytical results demonstrate that the GPP performs well in prediction accuracy and provides simple polynomials as well. Three identified parameters improve the analytical models—the lateral steel ratio improves both compressive strength and strain of the target models of circular concrete columns; compressive strength of unconfined concrete specimen improves the strength equation; and tie spacing improves the strain equation.     

Reinforced concrete deep beam shear strength capacity modelling using an integrative bio-inspired algorithm with an artificial intelligence model

The design and sustainability of reinforced concrete deep beam are still the main issues in the sector of structural engineering despite the existence of modern advancements in this area. Proper understanding of shear stress characteristics can assist in providing safer design and prevent failure in deep beams which consequently lead to saving lives and properties. In this investigation, a new intelligent model depending on the hybridization of support vector regression with bio-inspired optimization approach called genetic algorithm (SVR-GA) is employed to predict the shear strength of reinforced concrete (RC) deep beams based on dimensional, mechanical and material parameters properties. The adopted SVR-GA modelling approach is validated against three different well established artificial intelligent (AI) models, including classical SVR, artificial neural network (ANN) and gradient boosted decision trees (GBDTs). The comparison assessments provide a clear impression of the superior capability of the proposed SVR-GA model in the prediction of shear strength capability of simply supported deep beams. The simulated results gained by SVR-GA model are very close to the experimental ones. In quantitative results, the coefficient of determination (R²) during the testing phase (R² = 0.95), whereas the other comparable models generated relatively lower values of R² ranging from 0.884 to 0.941. All in all, the proposed SVR-GA model showed an applicable and robust computer aid technology for modelling RC deep beam shear strength that contributes to the base knowledge of material and structural engineering perspective.

     

Prediction of splitting tensile strength from the compressive strength of concrete using GEP

Splitting tensile strength is one of the important mechanical properties of concrete that is used in structural design. In this paper, it is aimed to propose formulation for predicting cylinder splitting tensile strength of concrete by using gene expression programming (GEP). The database used for training, testing, and validation sets of the GEP models is obtained from the literature. The GEP formulations are developed for prediction of splitting tensile strength of concrete as a function of water-binder ratio, age of specimen, and 100-mm cube compressive strength. The training and testing sets of the GEP models are randomly selected from the complete experimental data. The GEP formulations are also validated with additional experimental data except from the data used in training and testing sets of the GEP models. GEP formulations’ results are compared with experimental results. Results of this study revealed that GEP formulations exhibited better performance to predict the splitting tensile strength of concrete.     

Flexural buckling load prediction of aluminium alloy columns using soft computing techniques

This paper presents the application of soft computing techniques for strength prediction of heat-treated extruded aluminium alloy columns failing by flexural buckling. Neural networks (NN) and genetic programming (GP) are presented as soft computing techniques used in the study. Gene-expression programming (GEP) which is an extension to GP is used. The training and test sets for soft computing models are obtained from experimental results available in literature. An algorithm is also developed for the optimal NN model selection process. The proposed NN and GEP models are presented in explicit form to be used in practical applications. The accuracy of the proposed soft computing models are compared with existing codes and are found to be more accurate.     

Embedded fiber optic sensor for characterization of interface strains in FRP composite

Fiber reinforced polymer composites (FRP) have found widespread usage in repair and strengthening of concrete structures. FRP composites exhibit high strength to weight ratio, corrosion resistance, and convenient to use in repair applications. Several methods have been devised for repair of concrete beams with FRP fabrics, including wrapping of the cracked members, or adhesion of the fabric to the tension face of the members. A common cause of failure in such members is associated with debonding of the FRP substrate from the concrete in an abrupt manner. The mechanism of debonding is investigated through embedment of a distributed optical fiber sensor at the interface between the cracked concrete and the FRP fabric during repair of reinforced concrete beams under load. The fiber optic system consists of segmented long gauge length sensors along the length of an embedded optical fiber. This arrangement allows for complete interrogation of the interface deformations and debonding phenomenon. Experimental results pertaining to the load testing of FRP-repaired reinforced concrete beams are reported.     

Time-dependent creep and shrinkage analysis of composite beams curved in-plan

This paper develops a numerical formulation for the time-dependent creep and shrinkage analysis of steel–concrete composite beams that are curved in-plan under conditions of service load. The creep behaviour of the concrete is considered by using the viscoelastic Wiechert model, in which the aging effect of the concrete is taken into account. The curved composite beam model that is developed also accounts for the partial shear interaction at the deck-girder interface in the tangential (or longitudinal) direction, as well as in the radial (or horizontal) direction, due to the flexibility of the shear connectors. Models based on the developed formulation are validated by comparisons with sophisticated and computationally intensive ABAQUS shell element models, and with available results reported in the literature. The effects of initial curvature and partial interaction on the time-dependent behaviour of curved composite beams are also illustrated in the examples.