Reinforced Concrete Cross Sections Research Articles

Cracking in Reinforced Concrete Cross-Sections Due to Non-Uniformly Distributed Corrosion.

Corrosion affecting reinforced concrete (RC) structures generates safety and economical problems. This paper is focused on the simulation of corrosion-induced fractures in concrete, whereby non-uniform corrosion growth is taken into account. In particular, the volumetric expansion of rust accumulated around reinforcement bars causes cracking of the surrounding concrete. This phenomenon is simulated using the finite element (FE) method. In the analyses, concrete is described as a fracturing material by using a damage-plasticity model, steel is assumed to be elastic-plastic and rust is modeled as an interface between concrete and steel. The behavior of corrosion products is simulated as interface opening. Two-dimensional FE models of RC cross-sections with 2, 4 or 6 reinforcing bars are considered. Crack formation and propagation is examined. Moreover, interactions between cracks and patterns of possible failure are predicted. The most developed and complex crack pattern occurs around the side reinforcing bar. Conclusions concerning the comparison of results for uniform and non-uniform corrosion distribution as well as the prediction of concrete spalling are formulated.

Investigation of Nonlinear Behavior of the Reinforced Concrete Columns for Different Confined Concrete Models

Stress-strain and moment-curvature behavior of the reinforced concrete (RC) square columns have been analytically investigated according to different confined concrete models. The effect of transverse reinforcement diameter, transverse reinforcement spacing and concrete grade on the behavior of RC column models were investigated. For different confined concrete models, the confinement effectiveness coefficient, effective lateral confining stress, confined concrete compressive strength, strain at maximum concrete stress and ultimate concrete compressive strain values were calculated. In the second part, a parametric investigation was carried out for examining the effects of different design parameters on the moment-curvature relationships. Analytical moment-curvature relationships were obtained for RC cross-sections by using the TBEC (2018), Mander model (1988), Saatcioglu and Ravzi (1992) confined concrete models. The effects of the design parameters on the RC square column behavior were evaluated in terms of moment capacity and the curvature of the cross-section. In RC column models, stress-strain and moment-curvature relationships are obtained and compared according to different parameters. Confined concrete strength and the ultimate moment values obtained from the Mander model were higher than the Saatcioglu and Ravzi model when the transverse reinforcement close to the minimum spacing values. The results obtained from the Mander model and TBEC (2018) are close to each other.

Matrix equations models for nonlinear dynamic analysis of two-dimensional and three-dimensional RC structures with lateral load resisting cantilever elements

In control engineering and structural dynamics, mathematical models such as the state-space representation, equation of motion, and the phase plane are matrix equations describing the system equilibrium. This paper develops novel matrix equations models for linear/nonlinear dynamic analysis of reinforced concrete (RC) buildings with cantilever elements lateral load resisting systems (e.g., RC shear wall, RC core). The models offer a new approach for introducing two-dimensional and three-dimensional cantilever structures to control the theory’s state-space representation and structural dynamics’ equation of motion. The development primarily addresses the stiffness and mass matrices. The proposed displacement-related stiffness matrix of cantilever elements satisfies the necessary conditions of symmetricity and elemental boundary conditions. The nonlinear matrix structural analysis employs a smooth hysteretic model for deteriorating inelastic structures, referring to the relation between the bending moment and the bending curvature through the bending stiffness. The parameters controlling the cyclic behavior regard a composite RC cross section subject to gravitational load and bending simultaneously. The paper includes four examples that exemplify the practical utilization of the matrix equations models in analyzing two-dimensional and three-dimensional structures of linearly elastic and inelastic properties. The four examples demonstrated the idealized applicability of the matrix equations models for modal analysis, pushover analysis, and inelastic earthquake response analysis.

The Threshold for Under-Reinforced Concrete Sections Proposed by ACI 318, EC 2 and BS 8110

The ductile behavior of reinforced concrete (RC) cross-sections has always been desirable for building codes and standards. However, the threshold to distinguish ductile and brittle behavior of RC cross-sections proposed by building codes has yet to be evaluated [1-4]. This behavior mainly depends on the type of RC cross-section whether it is under- or over-reinforced. While there is not much research conducted on general comparison of the three codes of ACI 318-19, BS 8110 and Eurocode 2 (EC2) regarding design and analysis of RC structural elements, the specific detailed investigation on the threshold for under- and over-reinforced RC cross-sections has yet to be conducted. This article aims to determine the most accurate threshold used to distinguish under- and over-reinforced RC cross-sections amongst the three aforesaid codes by scrutinizing fundamentals and assumptions. A RC cross-section with strain distribution diagram over the section for the three statuses of under-reinforced, balanced, and over-reinforced cross-section is discussed in this research. A theoretical approach is adopted to compare the threshold through the depth of neutral axis of balanced steel concrete cross-sections. The method of calculation is associated with the maximum tensile strain of longitudinal steel bars at the cross-section. The depth of neutral axis is considered to be equal to effective depth of the cross-section multiple by a coefficient. This coefficient is the focus of the comparison. The coefficient is directly given as a number by BS 8110 and EC2. In ACI 318-19 there is no direct value given for the threshold, which leaves no choice other than the accurate calculation of depth of neutral axis for the balanced reinforcement which is in form of an equation. The article concludes that ACI 318-19 provides the most accurate threshold to classify under- and over-reinforced RC cross-sections while EC2 provides the least accurate threshold. The accuracy of threshold proposed by BS 8110 is between those of ACI318-19 and EC2. The scope of this research is confined to singly- and doubly-reinforced concrete cross-sections with any shape using ordinary concrete.

Modified Time-Dependent Model for Flexural Capacity Assessment of Corroded RC Elements

The corrosion of embedded steel bars in concrete is one of the severe deterioration processes that can escalate the risk and reduce the durability and lifetime of concrete structures. Based on the literature, simultaneous corrosion of longitudinal and transverse bar is considered to estimate section capacity. In this research, a flexible multi-stage approach is proposed to differentiate between corrosion levels on longitudinal and transverse reinforcement based on their corrosion initiating time. The result indicated that the multi-stage approach provides higher capacity and curvature for the sections. A significant reduction in reinforced concrete (RC) sections’ ductility after corrosion of confining bars and before starting corrosion of longitudinal rebars was observed, which illustrates the importance of stirrups corrosion effects on the sections’ ductility. In the higher values of corrosion intensity, confined concrete’s ultimate strain tends to reach the unconfined state. Using the energy-based method of calculating ultimate concrete compressive strain instead of approximate methods, a higher value of curvature ductility of corroded RC cross-sections is obtained.

A corrosion model for the interpretation of cyclic behavior of reinforced concrete sections

AbstractA generalized cyclic steel model characterized by isotropic and kinematic hardening, inelastic buckling in compression and corrosion of rebars in reinforced concrete (RC) structures is presented. The model has been implemented in a fiber code, to perform seismic analyses of RC sections. The model is particularly accurate with respect to experimental cyclic behavior of rebars with buckling in compression when the strain does not exceed 1.5%. Twelve configurations of RC cross sections were selected as case studies for three geometries and different steel arrangements, assumed representative of RC columns or bridge piers (in a suitable scale). Each section was subjected to two groups of cyclic curvature histories representative of severe seismic loads, not far from collapse. Different axial loads and corrosion percentages (no corrosion, moderate, or high) have been selected to perform cyclic parametric analyses. One of the cases was taken from an experimental test on columns, deriving also steel characteristics used in all numerical cases. The results of the comparison among RC sections have been discussed. Numerical results show that the maximum compressive strain for steel rebars is always smaller than 1.5%, therefore the proposed steel model is accurate and represents a valid tool for structural assessment. Corrosion reduces RC section capacity, affecting various rebar mechanical characteristics, in particular buckling behavior.

Numerical evaluation of core concrete quality on the response of concrete jacketed columns

Reinforced concrete jacketing is one of the most frequently used methods for strengthening of reinforced concrete (RC) columns. A large number of experimental studies have been carried out to investigate the effectiveness of repair and strengthening techniques and interface treatment on the response of concrete jacketed columns. However, the effects of potential damage in existing column and quality of core concrete on the response of jacketed RC columns have not been investigated. One of the main goals of this study is to examine how the material properties of the existing column affect the overall response of the jacketed RC columns. Two computer models were developed and nonlinear analyses were performed to determine the moment-curvature relationships and axial load-moment interaction diagrams of concrete jacketed RC cross sections. The effects of material strength and magnitude of axial loads were investigated. It is determined that the strength of core concrete has no effect on the response of concrete jacketed RC columns under lower axial loads while it increases the strength and reduces the ductility under higher axial load levels

Closed-form approximation of the axial force-bending moment interaction diagram for hollow circular reinforced concrete cross-sections

This paper proposes a simple closed-form approximation of the axial force-bending moment interaction diagram for solid and hollow circular reinforced concrete (RC) cross-sections with an arbitrary number of layers of longitudinal reinforcement. The implemented nonlinear material models are those of the European building code. Specifically, the parabola-rectangular strain-stress relation and the stress-block model are considered for the concrete in compression. On the other hand, the elastic-perfectly plastic behavior is assumed for the reinforcing steel bars. The proposed semi-exact closed-form approximation involves one parameter only, which is calibrated by means of a numerical optimization procedure taking into account a large database of cross-sections. Moreover, an efficient procedure is developed for the design of the outer layer of longitudinal reinforcement in solid or hollow circular RC cross-sections under combined axial force and bending moment (the mechanical ratio of any other layers of longitudinal reinforcement is considered as known function of the mechanical ratio of the outer layer of longitudinal reinforcement). Finally, several numerical examples are included to demonstrate the accuracy of the approximated axial force-bending moment interaction diagram and the effectiveness of the derived design procedure.

Resistance of Reinforced Concrete Columns Subjected to Axial Force and Bending

The paper presents a method for determining the resistance of cross-sections of reinforced concrete (RC) columns subjected to the axial force and bending. It takes account of the effect of concrete softening in plastic range and the mean compressive strength of concrete fcm. Such members are frequently encountered in engineering practice (pillars, bridges, viaducts). The stress-strain relationship for concrete in compression for short term uniaxial loading is assumed according to Eurocode 2 for nonlinear analysis. This stress-strain relation adequately represents the behaviour of the concrete by introducing four parameters. For reinforcing steel characterized by yield stress fyk, linear-elastic model with hardening in plastic range is applied. In the derivation of the resistance of the cross-sections of columns under consideration the following assumptions are introduced:•plane cross-sections remain plane•elasto-plastic stress/strain relationships for concrete and reinforcing steel are used•the tensile strength of concrete is ignored•the ultimate strains for concrete and reinforcing steel are determined a priori.The resistance of the RC cross-section is reached when either ultimate compressive strain in concrete or ultimate tensile strain in steel is reached anywhere in that section. The analytical formulae for the resistance NRm relating to the axial force and MRm relating to the bending moment are derived by integrating the equilibrium equations of the cross-section, taking account of physical and geometrical relationships as well as the condition of the ultimate limit state. On the basis of a combinatorial approach, twelve possible forms of the stress distribution in the section are considered. Using the derived formulae the interaction curves with the values of the normalized, cross-sectional forces nRm = NRm /(b t fcm) and mRm = MRm /(b t2fcm) for the rectangular cross-section have been obtained (b, t – dimensions of the rectangle). The obtained formulae describe the cross-section under consideration in the phase of failure. Replacing the mean values fcm and fyk by the corresponding design values fcd and fyd one obtains formulae determining the design values of the normalized cross-sectional forces nR = NR /(b t fcd) and mR = NR /(b t2fcd). For presentation of the proposed deformation model numerical calculations have been performed. They are presented in the form of interaction diagrams for rectangular cross-sections. Each curve refers to the corresponding value of the reinforcement ratio. The maximum compressive strain in concrete is calculated at the extreme fibre in the compression zone of the section. The points located on the nRm axis are related to pure compression, while on the mRm axis – to pure bending. The occurrence of the tensile strains in the cross-section leads to the crack formation in the concrete. Moreover, these solutions have been compared with those based on the parabolic-rectangular diagram for concrete under compression and with those obtained experimentally by other authors. In a similar way one may obtain interaction diagrams for ring cross-sections. Based on this analysis conclusions are drawn concerning application possibilities of the proposed approach.

FEM simulations of cracking in RC beams due to corrosion progress

This paper presents a two-dimensional model of a reinforced concrete (RC) element with rust introduced as interface between steel and concrete. The aim of the simulation is to represent the influence of reinforcement corrosion on the concrete cover. The analysis brings information about cracking of concrete, which is considered as the main aspect of failure of a structural element. The simulation is performed using Abaqus, a computational code based on the finite element method (FEM). The damage-plasticity and the cracking models are employed to describe the concrete response to chloride corrosion effects. In particular an RC cross-section is analyzed using two alternative algorithms of nonlinear computations: implicit and explicit solution. Moreover, a three-dimensional test of a beam subject to corrosion and static loading is analyzed.

Flexural performance of functionally graded RC cross-section with steel and PP fibres

Many studies have been conducted on the behaviour of reinforced concrete (RC) to determine the effects of different fibre types on the mechanical properties of concrete. Tests such as flexural and shear tests are used to evaluate the behaviour of RC. Most previous studies have focused on reinforcement of the entire cross-section with one fibre type, but the use of double-type reinforcement is growing and the lower cost of polypropylene (PP) fibres can be a significant factor in the use of double-type reinforcement. Therefore, in this work, experimental tests and numerical simulations were carried out to study reinforcement of the cross-section with steel fibres, PP fibres or both, in two separate layers. Beams were reinforced using 0·5%, 1% and 2% fibre volume fractions of steel and PP fibres. The beams with a reinforced cross-section with one or two fibre types were evaluated under flexural loading. The results showed that reinforcement of the entire cross-section with steel fibres led to a higher load-carrying capacity than reinforcement of the cross-section with two fibre types in two separate layers.

Damage Evaluation of Reinforced Concrete Cross-Section under Compression and Bending

By using the simple stiffness matrix formula of reinforced concrete (RC) cross-section under bending and compression, some RC cross-sections under bending and compression were traced through full path. Based on the numerical analysis, the damage of each point was calculated in a cross section, and the damage distribution of one member under the ultimate load was analyzed. This was agreement with experimental phenomena. In cross-section level, cross-section whole damage index was given and researched; and it could well explain cross-section mechanical behaviors.

Influence of strain rate on the seismic response of RC structures

At the strain rate levels induced by seismic excitations, dynamic properties of concrete and reinforcing steel exhibit non-negligible increases if compared with the values exhibited under quasi-static properties. This is expected to change the mechanical behavior of structural systems, under seismic loading conditions. The work here presented aims to appreciate the influence of strain rate sensitivity of concrete and reinforcing steel on the global seismic response of reinforced concrete (RC) structures. In order to assess the influence of the strain-rate, first (a) the modified material properties are used to derive moment–curvature relationships of a generic RC cross section, then (b) the seismic fragility of a 2D RC frame structure is derived accounting for seismic strain rate modified material properties, and (c) the seismic assessment of a real 3D RC frame structure at the significant damage (SD) limit state is conducted in both cases of quasi-static material properties and strain rate modified material properties. The results shows that considering updated material properties, to account for earthquake induced strain rate, a strength reserve of the structural system is experienced when only ductile failure mechanisms are accounted for; on the other hand, a reduction of the structural capacity is obtained when brittle failure mechanisms are included.

A simplified method for flexural capacity assessment of circular RC cross-sections

A simplified method for the assessment of bending moment resistance for reinforced concrete (RC) members with circular cross-sections is presented. In the proposed method longitudinal rebars arrangement is replaced with a thin steel ring equivalent to the steel total area; moreover, according to modern codes, simplified stress–strain relationships for concrete and reinforcing steel are used. The performed analyses demonstrate that the value of flexural capacity determined by the proposed approach, is very close to the results obtained by applying rigorous methods based on analytical and numerical algorithms. The study also proves that in members subjected to bending moment without axial load, the flexural strength depends on the geometry of the section (i.e. radius and concrete cover) and on mechanical ratio of steel reinforcement by a very simple formula.

Shrinkage-induced strains on cross-sections of reinforced concrete prisms

This paper describes experimental testing to investigate the effects of steel reinforcement on the distribution of shrinkage strains over cross-sections of reinforced concrete (RC) prisms. Measurements were taken in a harsh environment (50°C and 5% relative humidity (RH) and a moderate environment (28°C and 50% RH) on prisms of dimensions (80 × 150 × 500 mm). The research provides experimental measurements that supplement the scarce database for the distribution of induced drying shrinkage strains over RC cross-sections. As expected, the presence of steel restrains the development of shrinkage strains and the degree of restraint depends on the amount of steel. The effect of reinforcing steel on induced strains at the upper levels of the cross-sections increases as the steel ratio increases, particularly for specimens cured in the harsh environment. Over time, the distributions of total strains over cross-sections were found to approach linearity, with a higher rate towards linearity as the steel ratio was increased.

Limits to Plastic Analysis due to Size-Scale Effects on the Rotational Capacity of Reinforced Concrete Cross Sections

Reinforced concrete (RC) structures are usually designed to provide a ductile response under bending loadings. To this aim, most codes of practice impose lower and upper limits to the steel ratio in order to prevent unstable crack propagation and to avoid brittle failure due to concrete crushing without steel yielding. Within these limitations, elastic analysis with moment redistribution or even plastic analysis can be adopted for RC structures. In this context, size-scale effects are usually disregarded, leading to unsafe design conditions in the case of large structures.In the present study, the limitations of the prescriptions provided by the European and American building codes concerning the admissible plastic rotation and moment redistribution are highlighted. In particular, using a numerical algorithm based on the finite element method and on nonlinear fracture mechanics concepts recently developed by the present authors, the mechanical behaviour of the plastic hinge region of RC beams in bending is simulated. The results show that the effect of the structural dimension should be explicitly introduced in the code prescriptions for a safe structural design, by considering different design curves depending on the size-scale of the beams.

Stiffness and ductility of fibre-reinforced polymer-strengthened reinforced concrete members

The use of fibre-reinforced polymer (FRP) composites for repair and strengthening of civil engineering structures is gaining increasing acceptance worldwide and can be considered close to achieving the status of mainstream technology. Especially widespread is the application of externally bonded FRP laminates and bars for flexural strengthening of reinforced concrete (RC) members. Although a vast amount of experimental and theoretical research has been devoted to quantifying the strength of FRP-strengthened beams, less attention has been paid to stiffness and ductility aspects. The aim of this work is to carry out a systematic numerical analysis of the influence of the most relevant parameters on stiffness and ductility of FRP-strengthened RC cross-sections. As far as stiffness is concerned, the substantial advantages related to the use of active (i.e. pre- or post-tensioned) strengthening systems are quantified. For evaluation of ductility, an energy-based index is proposed which allows comparison of cross-sections with different amounts and types of FRP reinforcement accounting implicitly for their different moment–curvature behaviour. The damage accumulation of the cross-section is also addressed by means of an energy-based index and of the Park–Ang damage index.

Behavior of Precracked RC Beams Strengthened with Carbon FRP Sheets

Experimental data obtained from strengthened, precracked, reinforced concrete (RC) specimens are presented together with the results of material characterization. Strengthening was attained with the adhesion of carbon fiber-reinforced plastic (CFRP) sheets to the concrete surface. The CFRP was applied as in situ (i.e., working under the beam). Several variables were investigated, including: two CFRP material systems, two concrete surface preparations, two RC cross sections, and the number and location of CFRP plies. For two specimens, the presence of applied load (simulating the total service load) as well as external prestressing during the adhesion of the CFRP reinforcement, were investigated. It is shown that the effect of CFRP strengthening was considerable, but the effect of some of the tested variables was modest. An existing analytical model has been extended to simulate the load-deflection behavior as well as the failure mode of the precracked RC specimens. Different failure mechanisms from ductile to brittle were simulated and verified, adopting the mechanical properties of the constituent materials obtained via standard tests or using a simple test for the concrete-adhesive interface.

Study of Layering Procedures in Finite-Element Analysis of RC Flexural and Torsional Elements

A new postcracking formulation for concrete, along with both implicit and explicit layering procedures, is used in the analysis of reinforced-concrete (RC) flexural and torsional elements. The postcracking formulation accounts for tension stiffening in concrete along the rebar directions, compression softening in cracked concrete based on either stresses or strains, and aggregate interlock based on crack-confining normal stresses. Transverse shear stresses computed using the layering procedures are included in material model considerations that permit the development of inclined cracks through the RC cross section. Examples of a beam analyzed by both the layering techniques, a torsional element, and a column-slab connection region analyzed by the implicit layering procedure are presented here. The study highlights the primary advantages and disadvantages of each layering approach, identifying the class of problems where the application of either procedure is more suitable.