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.     

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.     

Numerical simulation of the shear behaviour of reinforced concrete rectangular beam specimens with or without FRP-strip shear reinforcement

The successful validation of a numerical model is presented that can realistically approximate the shear behaviour of reinforced concrete (R/C) rectangular beams strengthened against shear with externally applied open hoop fibre reinforcing polymer (FRP) strips. For this purpose, the measured load-deformation response of ten (10) full-scale R/C beam specimens is utilised. These specimens were loaded monotonically in a four-point bending arrangement up to failure. Open hoop FRP strip shear reinforcement was applied externally to upgrade the shear capacity of eight (8) R/C beam specimens. Four of these specimens had these FRP strips without anchorage, whereas for the other four the FRP strips were attached together with novel anchoring devices. This successful numerical simulation predicts with a very good degree of approximation the observed load-deformation behaviour and the ultimate shear capacity of all these specimens as well as the observed modes of failure including diagonal concrete cracking, debonding of the FRP strips in the case of no anchoring, or the plastification of parts of the anchoring devices plus the adjacent crushing of the concrete.     

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.     

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.     

Empirical modeling of shear strength of steel fiber reinforced concrete beams by gene expression programming

The addition of steel fibers into concrete improves the postcracking tensile strength of hardened concrete and hence significantly enhances the shear strength of reinforced concrete reinforced concrete beams. However, developing an accurate model for predicting the shear strength of steel fiber reinforced concrete (SFRC) beams is a challenging task as there are several parameters such as the concrete compressive strength, shear span to depth ratio, reinforcement ratio and fiber content that affect the ultimate shear resistance of FRC beams. This paper investigates the feasibility of using gene expression programming (GEP) to create an empirical model for the ultimate shear strength of SFRC beams without stirrups. 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 model is fairly promising approach for the prediction of shear strength of SFRC beams. The performance of the GEP model is also compared with different proposed formulas available in the literature. It was found that the GEP model provides the most accurate results in calculating the shear strength of SFRC beams among existing shear strength formulas. Parametric studies are also carried out to evaluate the ability of the proposed GEP model to quantitatively account for the effects of shear design parameters on the shear strength of SFRC beams.     

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.     

A fibre model for push-over analysis of underdesigned reinforced concrete frames

Most of the existing reinforced concrete buildings were designed according to early seismic provisions or, sometimes, without applying any seismic provision. Some problems of strength and ductility, like insufficient shear strength, pull-out of rebars, local mechanisms, etc., could characterize their structural behaviour. The above mentioned topics lead to a number of problems in the evaluation of the seismic behaviour of reinforced concrete (RC) frames. Therefore the assessment of existing RC structures requires advanced tools. A refined model and numerical procedure for the non-linear analysis of reinforced concrete frames is presented. The current version of the model proposed is capable of describing the non-linear behaviour of underdesigned reinforced concrete frames including brittle modes of failure. Selected results of an experimental–theoretical comparison are presented to show the capabilities of this model. The results show the capacity of the model of describing both the global behaviour and the local deformation at service and ultimate state.     

Proposition of new computer artificial intelligence models for shear strength prediction of reinforced concrete beams

Engineering with Computers - The study is investigated the capacity of new artificial intelligence (AI) methodologies for shear strength (Vs) computation of reinforced concrete (RC) beams. The...     

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.     

Design optimization of 3D reinforced concrete structures having shear walls

This paper presents a computer-based method for the optimal design of three-dimensional Reinforced Concrete (RC) structures having beams subjected to shear force and bending moment, columns subjected to biaxial moments, biaxial shears and axial loads, and shear walls subjected to pure shear. Regarding the beams and columns, the design variables are the width, depth and area of longitudinal reinforcement of member sections. The design variables for the shear walls are the thickness of the wall, the area of vertical reinforcement, horizontal distance between the vertical stirrups, the area of horizontal reinforcement, vertical space between the horizontal stirrups, and the area of vertical flexural reinforcement. The Optimality Criteria (OC) method is applied to minimize the cost of the concrete, steel and formwork for the structure. ACI code [1] provisions concerning the strength and ductility of beams, columns and shear walls are taken as constraints. The constraints also impose upper and lower bounds on the dimensions of beams and columns, and on shear wall thickness, reinforcement area and the maximum and minimum vertical and horizontal spaces between the stirrups of the shear walls. Sensitivity analysis is conducted for both internal forces and the capacities of the sections of the beams, columns and shear walls. The features of the design method are illustrated by a solved example.     

Numerical modeling of masonry-infilled RC frames subjected to seismic loads

The behavior of masonry-infilled reinforced concrete frames under cyclic lateral loading is complicated because a number of different failure mechanisms can be induced by the frame-infill interaction, including brittle shear failures of the concrete columns and damage of the infill walls. In this study, nonlinear finite element models have been used to simulate the behavior of these structures. Diffused cracking and crushing in concrete and masonry are described by a smeared-crack continuum model, while dominant cracks as well as masonry mortar joints are modeled with a cohesive crack interface model. The interface model adopts an elasto-plastic formulation to describe the mixed-mode fracture of concrete and masonry. The model accounts for cyclic crack opening and closing, reversible shear dilatation, and joint compaction due to damage. The constitutive models have been validated with experimental data and successfully applied to the dynamic analysis of a three-story, two-bay, masonry-infilled, non-ductile, reinforced concrete frame tested on a shake table. The results have demonstrated the capabilities of the finite element method in capturing the nonlinear cyclic load–displacement response and failure mechanisms of the structure, and indicated the important contribution of infill walls to the seismic resistance of a non-ductile reinforced concrete frame.     

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.

     

Dynamic response simulation for reinforced concrete slabs

Present investigation comprises development of a new finite element numerical formulation for nonlinear transient dynamic analysis of reinforced concrete slab structures. Depending on many experimental data, new material constitutive relationships for concrete material have been formulated. A regression analysis of available experimental data in the SPSS-statistical program has been employed for formulating the proposed material finite element models, and the appropriateness of the models are confirmed through the histograms and measured indices of determination. Concrete slab structures were analyzed using eight-node serendipity degenerated plate elements. The constitutive models of the nonlinear materials are introduced to take into account the nonlinear stress–strain relationships of concrete. For studying the stress profile of the concrete slab through its thickness, a layered approach is adopted. Elastic perfectly plastic and strain hardening plasticity approaches have been employed to model the compressive behavior of concrete. Assumptions for strain rate effect were included in dynamic analysis by supposing the dynamic yield function as a function of the strain rate, in addition to be the total plastic strain. The yield condition is formulated in terms of the first two stress invariants. Geometrical nonlinearity was considered in analysis as a mathematical model based on the total lagrangian approach taking into account Von Karman assumptions. Implicit Newmark with corrector–predictor algorithm was used for time integration solution of the equation of the motion for slab structures. An incremental and iterative procedure is adopted to trace the entire response of the structure; a displacement convergence criterion is adopted in the present study. A computer program coded in FORTRAN has been developed and used for the dynamic analysis of reinforced concrete slabs. The numerical results show good agreement with other published studies’ results which include deflections.     

Parametric modelling and evolutionary optimization for cost-optimal and low-carbon design of high-rise reinforced concrete buildings

Design optimization of reinforced concrete structures helps reducing the global carbon emissions and the construction cost in buildings. Previous studies mainly targeted at the optimization of individual structural elements in low-rise buildings. High-rise reinforced concrete buildings have complicated structural designs and consume tremendous amounts of resources, but the corresponding optimization techniques were not fully explored in literature. Furthermore, the relationship between the optimization of individual structural elements and the topological arrangement of the entire structure is highly interactive, which calls for new optimization methods. Therefore, this study aims to develop a novel optimization approach for cost-optimal and low-carbon design of high-rise reinforced concrete structures, considering both the structural topology and individual element optimizations. Parametric modelling is applied to define the relationship between individual structural members and the behavior of the entire building structure. A novel evolutionary optimization technique using the genetic algorithm is proposed to optimize concrete building structures, by first establishing the optimal structural topology and then optimizing individual member sizes. In an illustrative example, a high-rise reinforced concrete building is used to examine the proposed optimization approach, which can systematically explore alternative structural designs and identify the optimal solution. It is shown that the carbon emissions and material cost are both reduced by 18–24% after performing optimization. The proposed approach can be extended to optimize other types of buildings (such as steel framework) with a similar problem nature, thereby improving the cost efficiency and environmental sustainability of the built environment.     

Analysis of cyclic loading of plane RC structures

A numerical procedure for cyclic loading response of planar reinforced concrete structures is presented. A nonlinear orthotropic stress strain law for biaxially loaded plain concrete is developed and compared with experimental results for monotonic biaxial loading and uniaxial cyclic loading. The stress-strain law recognizes strength and ductility changes due to biaxial stress, and strength and stiffness degradation with cycles of loading. The stress strain law is incorporated into a finite element computer program which utilizes isoparametric quadrilaterals with extra non-conforming deformation modes. Numerical and experimental results are presented for a monotonically loaded shear wall-frame system and a cyclically loaded shear wall.     

Design optimization of 3D reinforced concrete structures

This paper presents a computer-based method for the optimal design of three-dimensional reinforced concrete (RC) skeletal structures having members subjected to biaxial moments, biaxial shears and axial loads. The width, depth and area of longitudinal reinforcement of member sections are taken as the design variables. The optimality criteria (OC) method is applied to minimize the cost of the concrete, steel and formwork for the structure. The primary focus of the paper concerns fundamental issues related to the formulation of design performance constraints on combined axial load, biaxial moments and biaxial shears. An example problem is solved with and without account for biaxial shear constraints to illustrate their influence on the design.     

Shear-Bending-Torsion Interaction in Structural Concrete Members: A Nonlinear Coupled Sectional Approach

Inclined cracks that take place in reinforced concrete elements due to tangential internal forces, such as shear and torsion, produce a non-isotropic response on the structure in the post-cracked regime and up to failure, also known as crack-induced-anisotropy. The result is that all six internal forces acting in a cross-section are generally coupled. A generalized beam formulation for the nonlinear coupled analysis of non-isotropic elements under six internal forces is presented. The theory is based on a cross-section analysis approach with both warping and distortion capabilities, which were proved necessary to correctly handle the problem with frame element analysis. In this paper, the non-linear mechanical aspects of cracked concrete structures under tangential forces are summarized. A state of the art review of beam formulations for the non-linear analysis of concrete structures is presented, and the approaches followed to account for the interaction of shear and torsion forces are discussed. After presenting the proposed formulation, its capabilities are shown by means of an application example of a cross section under coupled bending-shear and torsion, finally main conclusions are drawn.     

Nonlinear analysis of reinforced concrete hyperboloid cooling towers—I. Material model, finite element model and validation

This is the first part of a two-part series of papers in which the constitutive material modelling of reinforced concrete, in shell structures, which resist applied loads predominantly through membrane action, is presented. The material model includes the effects of tensile cracking, tension stiffening, compression softening, interface shear transfer, and change in material stiffness due to crack rotation. A four-noded isoparametric curved shell element has been used in the nonlinear finite element analysis. The results obtained by using the model for analysis of a shear wall panel subjected to in-plane loading have been compared with those from experimental investigation.