Nonlinear static analysis of reinforced concrete frames by network models

The simulation of reinforced concrete frames by networks, with bars obeying uniaxial stres-strain laws of concrete or steel, is proposed. Formulae for the determination of concrete bar sections are derived. Concrete σ-ε law, including cracking and plastic behavior, is described by 3 constitutive variables; steel σ-ε law, including plastic behavior, is described by 1 constitutive variable. A simple program is presented for the nonlinear static analysis of such network models based on the incremental loading technique. This program is used for the analysis of a plane, one story reinforced concrete frame under cyclic horizontal loading of its girder, for which experimental data are available. The computational results are found in good agreement with the experimental ones.     

Laterally braced wood beam-columns subjected to biaxial eccentric loading

This paper presents results of a study on the stability capacity and lateral bracing force of wood beam-columns subjected to biaxial eccentric compression loading. A numerical analysis model based on the column deflection curve method was developed. The model considers nonlinear parallel-to-wood-grain stress–strain relationship, size and stress distribution effects of wood strength, shear deformation, and the P-Delta effect of compression load. Material property tests and biaxial eccentric compression tests of wood beam-columns were conducted to provide input parameters and verification for the model. Good agreement was achieved. The adequacy of the 2% rule of thumb was also studied.     

Computerized modular ratio design of reinforced concrete members subjected to axial load and biaxial bending

A computerized method of analysis and design of reinforced concrete members of arbitrary cross-sections subjected to axial load and biaxial bending is proposed. The design process has been computerized to full automation—in the sense that given the concrete section and the applied loading, the program directly evaluates the amount of reinforcement required and the corresponding stress envelope. The strength of concrete in tension is neglected in the analysis. An iterative process which successively adjusts the section properties according to the stress state is employed. The design process is basically an iterative process of gradually increasing the amount of reinforcement till the permissible stresses are not exceeded. Reinforcement is added at locations of highest mean sequare stress in order to utilize fully the reinforcement added. Multiple loading cases are considered.     

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.     

Nonlinear and postbuckling analyses of curved composite panels subjected to combined temperature change and edge shear

The results of a detailed study of the nonlinear and postbuckling responses of curved unstiffened composite panels with central circular cutouts are presented. The panels are subjected to uniform temperature change and an applied in-plane edge shear loading. The analysis is based on a first-order shear-deformation Sanders-Budiansky type theory with the effects of large displacements, moderate rotations, transverse shear deformation and laminated anisotropic material behavior included. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. Numerical results are presented for cylindrical panels with central circular cutouts and are subjected to uniform temperature change and an applied in-plane edge shear loading. The results show the effects of variations in the panel curvature, hole diameter, laminate stacking sequence and fiber orientation, on the nonlinear and postbuckling panel responses, and their sensitivity to changes in the various panel, layer and micromechanical parameters.     

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.     

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.     

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.     

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.     

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.     

Strength and deformation of arbitrary beam sections using adaptive FEM

Still today, structural design is often based on simplified hand-calculation formulas for special cases, which is tedious to apply and do not cover more general situations. To improve the situation, the paper presents a FE-program for analysis of strength and deformation of arbitrary beam cross sections of steel and concrete loaded by all six force and moment components. The program is based on (1) an enhanced beam theory with three-dimensional state of stress, (2) multi-surface elasto-plasticity for modeling of the materials and (3) efficient numerical algorithms (mesh adaptive FEM, arc-length method, etc.). The paper presents the theory behind the program and some initial numerical testing to show how the program works. The initial numerical testing on steel and reinforced concrete beam sections loaded in bending, shear and torsion show promising results.     

预制裂隙岩石单轴压缩声发射特征研究

为了研究预制裂隙岩石失稳破坏过程中声发射特征,对预制不同倾角裂隙岩石进行了单轴压缩声发射试验,分析了预制裂隙岩石变形破坏特征及声发射信号变化规律。结果表明:随着预制裂隙倾角的减小,岩石试件的抗压强度逐渐降低,达到峰值应力的时间逐渐缩短,破坏时的轴向应变逐渐减小,试件由拉伸劈裂破坏向剪切滑移破坏转变;随着预制裂隙倾角减小,试件首次出现声发射能量和振铃计数峰值的时间提前、所需加载的轴向应力减小;声发射累计振铃计数随加载时间的增加呈非线性上升趋势,且预制裂隙倾角越小,声发射累计振铃计数上升速率越快。     

Artificial neural network models for FRP-repaired concrete subjected to pre-damaged effects

Confining damaged concrete columns using fibre-reinforced concrete (FRP) has proven to be effective in restoring strength and ductility. However, extensive experimental tests are generally required to fully understand the behaviour of such columns. This paper proposes the artificial neural networks (ANNs) models to simulate the FRP-repaired concrete subjected to pre-damaged loading. The models were developed based on two databases which contained the experimental results of 102 and 68 specimens for restored strength and strain, respectively. The proposed models agreed well with testing data with a general correlation factor of more than 97%. Subsequently, simplified equations in designing the restored strength and strain of FRP-repaired columns were proposed based on the trained ANN models. The proposed equations are simple but reasonably accurate and could be used directly in the design of such columns. The accuracy of the proposed equations is due to the incorporation of most affecting factors such as pre-damaged level, concrete compressive strength, confining pressure and ultimate confined concrete strength.

     

Numerical method for analysing open thin-walled structures under interaction of bending and torsion

A computer program is developed to analyse concrete beams of open thin-walled sections, at different stages of loading from zero load to failure. The program is divided into two parts; the first part deals with the beam from zero load to cracking. Of course, loading is combined bending, shear and torsion (warping torsion and St Venant's torsion). In this part of the program, Vlassov's theory has been used. The cracking load is defined as that load which causes principal tensile stresses equal to the tensile strength of concrete. The second part of the program deals with all post-cracking stages of loading from cracking point to failure. An iteration procedure is used until full convergence occurs at a particular cross-section. The geometrical properties are calculated; these include the contribution of steel in the cross-section and that of concrete in the compressive zones. The mathematical model is given. The computer results are compared with earlier experimental results, and the two sets of results show reasonable agreement. The program is written in FORTRAN.     

CDM based finite element code for concrete in 3-D

This paper presents a three dimensional finite element code DAMAG3D for nonlinear analysis of concrete type materials modeled as elastic-damage. The CDM model adopted is the one as proposed by SUARIS W, OUYANG C, FERNANDO V. M. Damage model for cyclic loading of concrete. J Engng Mech, American Society of Civil Engineers 1990; 116(5): 1020-35. for monotonic and cyclic loading of concrete structures. Code DAMAG3D is applied to simulate response of concrete under monotonically increasing load paths of uniaxial compression, Brazilian test, strip loading and patch loading, with reasonable correlation established with experimental results and results from other nonlinear constitutive models.     

On choice of optimal anisotropy of composite plates against buckling, with special attention to bending-twisting coupling

The lay-up optimization problems of composite plates against buckling are studied. The plate has symmetric lay-up and is loaded by an in-plane loading. The Classical Lamination Plate Theory is used. The necessary optimality conditions for the plate orthotropy/anisotropy optimization problems are considered, with special attention to bending-twisting coupling. The purpose of the optimization is to maximize the (lowest) buckling eigen value. The varied lay-up/layer orientation angles are considered both as smooth functions of the location coordinates and as having the same values at every point. It is shown that the twisting moment (calculated in the principal curvature axes) plays an important role in the conditions. Two example problems for a thin composite plate, loaded by shear, are considered. The first one corresponds to the case of one shear loading direction. The details of some known numerical solutions are studied. The obtained numerical results are in agreement with the theoretical results. The maximal lowest eigen values are 2-folded ones. A schematic model for treatment of the known optimal numerical solution (60° unidirectional lay-up for a long plate loaded by shear) is proposed. The second example problem corresponds to the case of shear loading acting in two opposite directions. The ways of equalizing the lowest buckling values corresponding to both loading directions are proposed. Numerical results for various aspect ratio and plate thickness values are presented. The potential of weight saving is demonstrated.     

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.     

Evaluating shakedown under proportional loading by non-linear static analysis

A lower bound method for calculating shakedown loads under proportional loading by static non-linear finite element analysis is presented. Stress fields obtained by static analysis and stress superposition are substituted into Melan’s lower bound shakedown theorem. The proposed method is applied to two sample problems: a thick cylinder under internal pressure and a square plate with a central hole under proportional biaxial loading. The results indicate that the method gives accurate lower bound shakedown loads for these problems.     

Statistical analysis and predictions of fracture and fatigue of micro-components

A number of materials typically used in MEMS technology exhibit brittle fracture behaviour which leads to a scatter in strength and a size effect as a consequence. Furthermore, some of these materials, e.g. polycrystalline silicon, show fatigue effects which limit the lifetime under cyclic loading conditions. Probabilistic methods based on the Weibull theory have been established successfully in predicting the strength of micro-components under static loading. However, the consequence of fatigue on reliability predictions has not yet been studied extensively. We present strength as well as lifetime predictions for poly-silicon components with stress concentrations based on experimental data published in the literature. Our results show that while strength predictions for components with stress concentrations based on scaling procedures works well, lifetime prediction is a challenging task associated with large prediction uncertainties. Finally, we relate the crack propagation approach used for our lifetime predictions with micro-mechanical fatigue models that are discussed for poly-silicon.