Stress-strain Relationship Of Concrete Research Articles

Calculation of second-order bearing capacity of members subjected to axial load and biaxial bending

The second-order effects of biaxial bending members involve dual non-linear problems, namely material nonlinearity and geometric nonlinearity. These problems typically require iterative calculations and cannot be solved manually. To address this issue, this paper founded upon the strain-based resolution of stress and internal forces, deduces the formula for calculating the load-bearing capacity of the cross-section. The elastoplastic second-order deformation is then calculated at the member level, and the final result is presented in the form of a dimensionless nomogram for calculating the second-order biaxial bending members. In this paper, the limit range of section strain is determined based on the constitutive relationship of concrete and reinforcement. This range is divided into three limited strain areas, which enable the calculation of section bearing capacity and limit curvature, and subsequently the second-order bearing capacity of the member. The results are in good agreement with experimental data. The dimensionless nomogram in this paper considers the complete parabolic and rectangular of concrete stress-strain relationship and the ideal elastoplastic constitutive relationship of reinforcement and the second-order effect. It does not require iteration. It can quickly calculate the reinforcement or check the section bearing capacity by hand. It can be used to check the calculation results of engineering software and provides ideas for the design method of member subjected to axial load and biaxial bending based on seismic restoring force.

Analytical evaluation of stress–strain behavior of rubberized concrete incorporating waste tire crumb rubber

The advancement of rubberized concrete technology and its application in engineering can significantly promote the complete recycling and safe disposal of waste tire rubber. Integrating crumb rubber into concrete alters its compressive stress–strain behavior. This study investigated the stress–strain characteristics of rubberized concrete containing waste tire crumb rubber, addressing the absence of standard guidelines for the design of rubberized concrete. By examining the complete stress–strain curves of rubberized concrete, key parameters such as peak stress, initial elastic modulus, peak strain and secant modulus were meticulously evaluated. The study delved into the mechanisms through which crumb rubber influences the stress–strain behavior of concrete, considering factors including variations in rubber content and pretreatment methods. The experimental data were analyzed using conventional concrete constitutive theories to quantify the impact of crumb rubber on rubberized concrete's stress–strain relationship. Significant variations were observed, including a notable decline in strength with increasing rubber content. For instance, increasing the rubber content from 0.0% to 5.0% led to reductions of 44.2% in peak stress and 47.0% in secant modulus compared to the reference concrete. In addition, pretreating the crumb rubber markedly improved rubberized concrete strength, and the peak stress of concrete with 1.0%–5.0% pretreated crumb rubber increased by an average of 7.0% compared to that with untreated crumb rubber. The study identified that crumb rubber's inclusion significantly altered the coordination of stress and strain in concrete, thereby affecting its stress–strain behavior. A set of evaluation equations for the stress–strain relationship of rubberized concrete was developed, offering a reliable method for predicting its behavior. This research fills a critical gap in the analytical assessment of rubberized concrete and marks a significant stride towards its broader use in sustainable construction practices.

Axial behavior of square steel-tubed ultra-high-strength reinforced concrete columns

Steel-tubed reinforced concrete (STRC) columns with ultra-high-strength concrete (UHSC; compressive strength greater than 120 MPa) are currently used in some super high-rise buildings in Japan and other Asian countries. To properly evaluate the seismic performance of steel-tubed reinforced ultra-high-strength concrete (STR-UHSC) columns, it is necessary to understand their behavior under axial compression. However, there are few studies on the axial behavior of square STRC columns, particularly with UHSC. Therefore, axial compression tests were conducted on four square STR-UHSC columns with the test variables being the amount of transverse reinforcement and the presence of the steel tube. The concrete compressive strength used was over 170 MPa. The test result showed that the presence of the steel tube and the amount of the transverse reinforcement had no significant effect on the load-bearing capacity but greatly improved the post-peak behavior. To discuss the influence of the size effect and confining effect on the concrete compressive strength, a database of 56 plain and reinforced concrete columns with UHSC, including four specimens of this study was constructed. A new formula was proposed to evaluate the concrete compressive strength under the size effect and confining effect based on the regression analysis of the database. The proposed formula well simulated the measured peak load with a proper amount of contributions from concrete and longitudinal reinforcement. Finally, axial load-axial strain relationships were simulated using the proposed concrete stress–strain relationship. The axial behavior of each specimen was well simulated by considering the size effect and confining effect of the steel tube as well as the transverse reinforcement on the ultimate strain.

Stress–Strain Model of High-Strength Concrete Confined by Lateral Ties under Axial Compression

High-strength concrete can effectively reduce the cross-sectional size, increase space usage, and cut material costs. To analyze the mechanical properties of high-strength concrete vertical members, various confinement models have been proposed to define the ties-confined concrete stress–strain relationship. However, most existing models are divided into ascending and descending segments. These are continuous but not derivable at the peak point, which does not facilitate numerical calculations. Moreover, these models have a large number of parameters that are mostly obtained based on the fitting of experimental data, which may also lead to the limited applicability of the models. In this study, existing confinement models for high-strength concrete under axial compression are reviewed, and the differences between the models are discussed. Based on the results of normal triaxial experiments on high-strength concrete and the test data from other studies on ties-confined concrete columns, the effective confinement coefficient and empirical formula of ties strain at the peak stress of confined concrete are proposed. A confinement model is proposed based on the continuous derivable function, and it is validated based on the available experimental data. Results show that the proposed model can reflect the stress–strain relationship of the test specimens more simply while keeping the basic accuracy with other models.

Experimental, numerical and design investigations on the performance of axially-loaded ECFT stub columns with spherical-cap gaps

Elliptical concrete-filled steel tubular (ECFT) columns have been increasingly used in engineering practice in recent years due to their aesthetic appeal together with structural advantages. The spherical-cap gaps were generally found in the actual CFT structures based on the latest survey. However, related literatures on the ECFT stub columns with spherical-cap gaps (ECFT-SG) under axial load are rarely reported. Thus, this paper aims to reveal the effects of gaps on the performance of axially-loaded ECFT stub columns. In total, ten axially-loaded ECFT-SG specimens were tested to explore the effects of gap ratio (χsg) and steel yield strength (fy) on the failure modes, axial fore (N) – longitudinal shortening (Δ), strain responses, strength and ductility indexes, etc. Following this, a series of numerical models using a modified equivalent concrete stress-strain relationship were established to expand the parametric scope and further study the steel-concrete interaction stresses and the concrete longitudinal stress distribution. Finally, two strength prediction methods of ECFT-SG stub columns were presented. The results indicated that the initial concrete gaps would weaken the confinement effect provided by steel tube, thus decrease the initial stiffness, ultimate strength and ductility of the columns. With the χsg increasing, the overall bending and inward buckling phenomena would be observed because of the uneven damage of infill concrete. The two design methods proposed herein are expected to provide a reference to evaluate the safety of the existing CFT columns with initial gap imperfection.

Study on axial compressive behavior and damage constitutive model of manufactured sand concrete based on fluidity optimization

Due to the adsorption effect of manufactured sand on water reducer, the method of adding water reducer is often used to improve the fluidity of concrete mixture, which may change the strength of manufactured sand concrete. This paper systematically studies the manufactured sand concrete with different strength grades of C30, C40, C50, C60, C70, C80 prepared with basic water reducer dosage (1 time) and optimized water reducer dosage (1.65 times), and designs slump, slump loss, uniaxial compression and pore content tests for manufactured sand concretes with the same strength grade. The results show that optimized dosage of water reducer can significantly increase the fluidity, peak stress and elastic modulus of manufactured sand concretes with the same strength grade and reduce their slump loss, peak strain and pore content. Combined with Lemaitre damage mechanism, the total damage of manufactured sand concrete is divided into initial damage and load damage. The initial damage is caused by different fluidity of manufactured sand concrete. The greater the fluidity, the less initial damage will be. The influence of initial damage on the concrete stress-strain relationship is analyzed. As the initial damage increases, the total damage will increase, the strength and elastic modulus of the concrete will decrease. This is due to the fluidity changes the pore structure inside the concrete.

Unified Stress-Strain Model of FRP-Confined Square and Circle Rubber Concrete Columns.

Studying the stress–strain relationship of fiber-reinforced polymer (FRP)-confined rubber concrete (RuC) plays an important role in its application in engineering projects. Most of the existing stress–strain relationship models are established based on the test data of FRP-confined rubber concrete with circular cross-sections, and the effect of the section shape is not considered. Therefore, an analysis-oriented stress–strain model of FRP-confined circular and square rubber concrete columns was studied in this paper for the first time. A database that includes the rubber particle content and section shape on the peak stress-peak strain and axial–lateral strain relationship of FRP-confined rubber concrete was established by collecting 235 test data from the literature. By modifying the key parameters in the existing FRP-confined normal concrete stress–strain relationship model, a unified stress–strain relationship model of FRP-confined RuC with circular and square columns is established. The proposed model is verified, and a good accuracy of the model is proven.

Influence of sulfuric acid corrosion on concrete stress–strain relationship under uniaxial compression

This study aims to provide some references on understanding the uniaxial compression behaviors of concrete corroded by sulfuric acid. Six groups of concrete cylinder specimens were immersed in sulfuric acid solution with pH≈0.95 for different days. 3D laser scanning technology was applicated to obtain 3D coordinates of the points on the corroded cylindrical surface. The irregular cross sectional areas of each specimen were calculated at intervals of 1 mm along the longitudinal axis by MATLAB. The elastic modulus, peak strain, ultimate strain and peak stress were calculated through the experimental complete stress–strain curves. It showed that as the corrosion time increased, the elastic modulus, peak strain and peak stress gradually decreased. The ultimate strain decreased first and then increased over time. The parameters of the stress–strain model including the ascending and descending stages were obtained by fitting the experimental data. The relationship between the mechanical properties and mass loss was explored.

A deep learning framework for constitutive modeling based on temporal convolutional network

A novel and efficient deep learning framework adopting the Temporal Convolutional Network (TCN) model is proposed to simulate the ultra-long-history-dependent stress-strain constitutive model. First, the practical requirements for the constitutive models of stress-strain relationship with ultra-long-history-memory are summarized, which is favorable for adopting the TCN model in sequence modeling. The traditional Recurrent Neural Networks (RNNs) for sequence modeling are compared with the TCN model and the advantages of the TCN model for constitutive modeling are illustrated. Subsequently, the architecture of the TCN model for the constitutive modeling of steel and concrete material is illustrated in detail. In the TCN model, multiple dilated convolutional layers achieve long-term history dependence, while the causal convolution guarantees the stress is only updated based on historical strain history instead of the whole loading process. Third, a one-dimensional (1D) concrete stress-strain relationship dataset is established with significant stiffness degradation, strength degradation, and pinching effect. Two 1D reinforced concrete (RC) stress-strain datasets are established with steel content ratios of 1% and 10%. A two-dimensional (2D) low-yield-point steel dataset is also established. Fourth, the performance of the TCN model is evaluated for 1D concrete, steel, and RC datasets and 2D steel dataset. The TCN model achieves higher prediction accuracy and efficiency compared to the traditional RNN model for constitutive modeling. The influence of kernel size, hidden dimension of convolutional filter, and the number of convolutional layers on the test set performance are reported in detail. Finally, three prospective implementations of the proposed TCN model in solid mechanics are proposed, including the physics-informed machine learning, the multi-scale transfer learning framework, and the finite element force method.

PARÁMETROS RELEVANTES DE LA CURVA ESFUERZO-DEFORMACIÓN EN COMPRESIÓN DE CONCRETOS NO CONFINADOS PRODUCIDOS EN MÉXICO

Las Normas Técnicas Complementarias para Diseño por Sismo para la Ciudad de México especifica por primera vez, métodos de análisis sísmico no lineal de estructuras, para los cuales es necesario conocer, entre otros, los parámetros que definen la curva-esfuerzo-deformación en compresión del concreto sin confinar. En esta investigación se llevaron a cabo estudios analíticos y experimentales de concretos producidos recientemente en México. Con base en los resultados encontrados se dan recomendaciones para estimar parámetros que definen de manera importante la curva esfuerzo-deformación del concreto sin confinar. Los estudios experimentales de los especímenes de concreto se realizaron en el Instituto de Ingeniería de la UNAM, aplicando ciclos de carga en compresión de acuerdo con las normas ASTM y NMX correspondientes y tomando como resultado un promedio de las muestras ensayadas. Se proponen expresiones para obtener el módulo de elasticidad del concreto, Ec, parámetro que es relevante en el cómputo de desplazamientos laterales de estructuras en zonas sísmicas, así como en el cómputo de los periodos de vibrar de una estructura en estas zonas. También en esta investigación se dan expresiones para obtener valores de parámetros importantes de la curva esfuerzo-deformación del concreto no confinado en compresión, los cuales se emplean en el modelado de articulaciones plásticas para el análisis no lineal. Estos parámetros son la relación de Ec y el módulo secante, Esec, Ec/Esec y la deformación del concreto en f’c, e’c. Con base en los resultados de estos ensayes se dan recomendaciones para la estimación de estos parámetros para concretos producidos recientemente en México.

Analytical solution for the resistance of composite beams subjected to bending

The paper deals with the resistance of steel and concrete composite beams, named BH beams, subjected to bending. They are structurally connected with prefabricated or castin situslabs, forming floor slab system. The beams under consideration consist of the reinforced concrete (RC) rectangular core placed inside a reversed TT welded profile. The stress-strain relationship for concrete in compression of the RC core is assumed for nonlinear analysis according to Eurocode 2. For reinforcing and profile steels linear elastic – ideal plastic model is applied. The normalized ultimate bending moment determining the resistance of the BH beam is derived by integrating the equilibrium equations of the bending moments about the horizontal axis of the RC core rectangle, taking into account the physical and geometrical relationships. The presented model was verified by tests carried out on two BH beams subjected to bending. The comparisons made indicated good convergence between the analytical solution and the experimental results in ultimate bending moments.

Finite element model for bolted shear connectors in concrete-filled steel tubular columns

This research presents a study on the numerical simulation of the structural behavior of bolted shear connectors used as force transfer device in concrete-filled composite columns. The numerical model was developed in ABAQUS software, using the constitutive model named Concrete Damaged Plasticity. In the study, the influence of different concrete stress-strain relationships on tensile and compressive strengths was analyzed, as well as the influence of the use of damage variables. Three different stress-strain relationships on concrete compressive strength were tested, and another three on concrete tensile strength, distinguished by the crack opening displacement. The obtained results were calibrated with the experimental results of four experimental models, and, next, the proposed calibration was compared with twelve other experimental results. Finally, the proposed parameters showed to be suitable to represent the structural behavior of bolted shear connectors applied in force transfer in concrete-filled composite columns.

Curvilinear Stress-Strain Relationship for Concrete of EN-2 Regulation in the ZI Method and the Calculation of Beam Strength

The article illustrates the possibilities of the practical application of the ZI method [1 and 2] when calculating the strength of reinforced concrete beams. The article presents variants of description of the EN-2 regulation curvilinear diagram for concrete with reliability of 50 % by the ZI method with reliability of 50 %, 95 % and ~100 %. The article demonstrates how, when calculating the strength of normally and abundantly reinforced concrete beams by the ZI method, it is possible to do without the calculation of the limit value of the thickness of the concrete layer of the beam compression zone. This is important in the case of the calculation of the strength of abundantly reinforced beams. The method for calculating the strength of abundantly reinforced beams has been improved. When calculating strength, we also obtain actual values of stress-strain parameters at the crack. The tables provide data supporting the proposed innovations and facilitating calculations.

Pozzolanic Potential and Mechanical Performance of Wheat Straw Ash Incorporated Sustainable Concrete

The pozzolanic potential, mechanical strength, and stress-strain behavior of a locally available wheat straw ash (WSA) as a partial substitute of cement was evaluated in this study. Various samples of a locally available wheat straw were burnt to ashes at three distinct temperatures and characterized through X-ray powder diffraction and energy dispersive X-ray spectroscopy. The WSA obtained from burning at 550 °C was found highly amorphous and possessed suitable chemical composition to be used as pozzolanic material. The burned WSA was grounded to achieve the desired fineness and mortar cubes and concrete cylinders were cast by substituting 15%, 20%, 25%, and 30% cement with it. The strength of mortar and concrete decreased with increasing amounts of WSA except for those containing 15% WSA, where it slightly increased than the respective control samples at later ages, i.e., 28 and 91 days. Despite reduced strength at high replacements (20%, 25%, and 30%), the strength activity index values met ASTM C618 requirements for pozzolanic materials. Moreover, the compressive strength of concrete containing 20% WSA exceeded to that of control concrete at 91 days. The stress-strain relation of concrete containing 15% to 20% WSA also showed comparable stiffness and toughness to those of control samples at all ages. Particularly, the concrete containing 15% WSA showed significant improvement of strength, stiffness, toughness, and ductility at 91 days. Lastly, the results of mechanical strengths and pozzolanic reactivity were successfully validated indirectly by measuring the porosity of mortars and thermo-gravimetric analysis of cement pastes, respectively. Based on current findings and their validation, WSA can be used as a substitute of cement up to 20% in the production of sustainable normal strength concrete for their application in common domestic building projects.

Carbonated recycled coarse aggregate and uniaxial compressive stress-strain relation of recycled aggregate concrete

Carbonation treatment was employed to improve the quality of recycled coarse aggregate (RCA), and the RCA or carbonated RCA (CRCA) was used to prepare recycled aggregate concrete (RAC or RAC-C). The influence of the RCA replacement rate and CRCA on the mechanical properties and stress-strain relation of concrete was investigated. The results have shown that carbonation treatment enhances the physical properties and interfacial transition zone (ITZ) of CRCA, and effectively prevents the degradation in mechanical properties of concrete. Increased RCA or CRCA replacement rate reduces the peak stress and ascending slope and increases the peak strain of RAC or RAC-C. The stress-strain curve of RAC-C has higher ascending slope, peak stress and lower peak strain than that of RAC and is closer to that of natural aggregate concrete (NAC) due to the improved new ITZ. The stress-strain relation result agrees well with the proposed model.

Analytical modeling of reinforced concrete columns subjected to bidirectional shear

Under general seismic loading, reinforced concrete columns may be subjected to lateral loads in more than one direction. Available experimental data on columns subjected to bidirectional forces indicate that higher levels of damage and a higher loss of ductility and strength have been observed compared to similar tests under unidirectional shear forces. In this study, an experimental program was conducted in which six lightly reinforced concrete columns were subjected to unidirectional and bidirectional cyclic shear forces. This observation was used to identify the mechanisms and parameters governing the behavior of columns subjected to cyclic bidirectional lateral loads. Hence, a new conceptual model was developed to obtain the capacity of member. The shear forces were analyzed and an analytical formulation was derived to account for the effects in the concrete stress-strain relationship, the moment-curvature diagram and the plastic hinge length. These equations were used along with a structural model with concentrated plastic hinges to obtain the capacity curve of the column. The results of the formulations developed were verified using the results of the experiments performed on columns subjected to unidirectional and bidirectional cyclic lateral forces.

Generic Model Stress-Strain Relationship for Concrete in Compression at Elevated Temperatures

Generic Model Stress-Strain Relationship for Concrete in Compression at Elevated Temperatures

A Close to Reality Method for Determining the Resistance of RC Structures under Eccentric Compression

The paper presents the derivation of analytical formulae determining the resistance of the cross-sections of RC structures subjected to eccentric compression. It takes account of the effect of the concrete softening and the mean compressive strength of concrete. The stress-strain relationship for concrete in compression for uniaxial loading is assumed according to Eurocode 2 for nonlinear analysis. This stress-strain relation closely to reality represents the behavior of the concrete by introducing four parameters. For reinforcing steel linear-elastic model with hardening in the plastic range is applied. The resistance of the cross-section of RC structure is reached when either the ultimate compressive strain in concrete or the ultimate tensile strain in steel is reached anywhere in that section. The formulae determining the section resistance are derived by integrating the equilibrium equations of the cross-section taking account of the physical and geometrical relations as well as the conditions of the ultimate state. Using the derived formulae the interaction diagrams with the values of the ultimate normalized cross-sectional forces have been obtained for the ring cross-sections. The calculated results have been compared with those obtained by testing on RC columns with ring cross-sections subjected to the eccentric compression. The performed analysis confirmed a good conformity between theoretical and experimental results.

The Effect of Aggregate Shape and Configuration to the Concrete Behavior

It has long been acknowledged that the behaviour of concrete is influenced by the properties of its constitutive materials. The geometry of aggregates is believed to contribute to the strength and stress-strain relationship of concrete. However, advanced studies are still required to quantify the effect of such factor in determining the behaviour of concrete. This research was aimed at investigating the effect of aggregate shape and configuration on the stress-strain relationship of concrete. Four types of specimens were investigated. There was one single coarse aggregate with different shape placed in the centre part of the specimens. The specimens were subject to uni-axial compression and both the load and displacement were measured. The experiments were conducted at the Structural and Material Laboratory of Diponegoro University in Semarang . The results show that the specimen with a diamond shaped aggregate results in the lowest compressive strength. However, the initial tangent stiffness of all specimens is almost identical up to 25% of its ultimate strength. Finite element analyses were carried out to study stress distribution in the specimens. The results show that the stresses are concentrated at the corner of the aggregates. This stress concentration initiates cracks at the Interfacial Transition Zone (ITZ) around the corner of the aggregates. The cracks then propagate and spread to the mortar which then reduce the stiffness of the specimens.

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.