Modeling of Internally or externally prestressed concrete beams until fracture in nonlinear elasticity

In this paper, we present an analytical model to analyze reinforced and prestressed concrete beams loaded in combined bending, axial load and shear, in the frame of non linear elasticity. In this model, the equilibrium of the beam is expressed by solving a system of equations, governing beams equilibrium, based on the stiffness matrix of the beam, which connects the load vector to the node displacements vector of the beam. It is built from the stiffness matrix of the section which takes into account a variation of the shearing modulus (depending on the shear variation) instead of assuming a constant shearing modulus as in linear elasticity. For the internal tendons, the stiffness matrix is completed by the terms due to the prestress effect in flexural equilibrium and by the balancing of one part of the shear by the transverse component of the force in the inclined cables. A computing method is then developed and applied to the calculus of some internally or externally prestressed concrete beams. The comparison of the results predicted by the model with several experimental results show that, on the one hand, the model predictions give a good agreement with the experimental behavior in any field of the behavior (after cracking, post cracking, post steel yielding and fracture of the beam); and, on the second hand, that the model leads to the prediction of tendons slipping at deviators and to the tension increase in the tendons

Reliability assessment of the behavior of reinforced and/or prestressed concrete beams sections in shear failure

The object of this article is to be able to simulate the behavior of reinforced and/or prestressed concrete beam’s section in the shear loading through a model allowing the evaluation of nonlinear strains caused by shear, while taking into account the real behavior of the materials. In this approach, we are often confronted with problems of modeling uncertainties linked to some insufficiencies of the mechanical model allowing to describe the physical phenomena in a realistic way. For that, it is necessary to use a reliability model making it possible to evaluate their probability of failure, by establishing failure curves according to the different transition zones of the limit state curve of the nonlinear behavior in the shear loading up to at section failure of reinforced and/or prestressed concrete beams. In this work, we also propose a coupling of the reliability method by response surface to carry out the reliability optimization on complex mechanical models, where the mechanical and reliability models developed have been implemented on the Fortran. This allows the estimation in an efficient way of the different reliability characteristics according to each transition zone from the limit state curve to the real behavior until failure in the shear loading

Numerical simulation and reliability of behaviour until the rupture of reinforced concrete spacial structure members with circular cross section

Numerical simulation of simple and composed bending behaviour of reinforced concrete spatial structure elements with circular cross section in the field of nonlinear elasticity, require a particular modeling’s technique of the cross section shape by a subdivision of the latter into trapezoids to best approximate the contour of the cross section. The input and output parameters of the materials behaviour modeling are simulated by random and deterministic variables. The present study aims at proposing a technique of the behaviour’s simulation up to failure taking into account the material non-linearity on the reinforced concrete structural elements with a circular cross section; a comparison was made between our simulation results and the experimental results. On the other hand, a numerical method has been modeled which makes it possible to estimate the reliability and the probability of failure of our simulation. To validate this modeling, we performed another comparison of the results obtained from our mechanical model by a Monte Carlo simulation with a reliable Hasofer-Lind metho

Modeling of Internally or externally prestressed concrete beams until fracture in nonlinear elasticity

In this paper, we present an analytical model to analyze reinforced and prestressed concrete beams loaded in combined bending, axial load and shear, in the frame of non linear elasticity. In this model, the equilibrium of the beam is expressed by solving a system of equations, governing beams equilibrium, based on the stiffness matrix of the beam, which connects the load vector to the node displacements vector of the beam. It is built from the stiffness matrix of the section which takes into account a variation of the shearing modulus (depending on the shear variation) instead of assuming a constant shearing modulus as in linear elasticity. For the internal tendons, the stiffness matrix is completed by the terms due to the prestress effect in flexural equilibrium and by the balancing of one part of the shear by the transverse component of the force in the inclined cables. A computing method is then developed and applied to the calculus of some internally or externally prestressed concrete beams. The comparison of the results predicted by the model with several experimental results show that, on the one hand, the model predictions give a good agreement with the experimental behavior in any field of the behavior (after cracking, post cracking, post steel yielding and fracture of the beam); and, on the second hand, that the model leads to the prediction of tendons slipping at deviators and to the tension increase in the tendons

Numerical simulation and reliability of behaviour until the rupture of reinforced concrete spacial structure members with circular cross section

Numerical simulation of simple and composed bending behaviour of reinforced concrete spatial structure elements with circular cross section in the field of nonlinear elasticity, require a particular modeling’s technique of the cross section shape by a subdivision of the latter into trapezoids to best approximate the contour of the cross section. The input and output parameters of the materials behaviour modeling are simulated by random and deterministic variables. The present study aims at proposing a technique of the behaviour’s simulation up to failure taking into account the material non-linearity on the reinforced concrete structural elements with a circular cross section; a comparison was made between our simulation results and the experimental results. On the other hand, a numerical method has been modeled which makes it possible to estimate the reliability and the probability of failure of our simulation. To validate this modeling, we performed another comparison of the results obtained from our mechanical model by a Monte Carlo simulation with a reliable Hasofer-Lind metho

Compressive study on recycled concrete: experiment and numerical homogenization modelling

This paper describes a study of recycled concrete under compressive loads. The study was conducted in two main parts. In the first part, experimental tests were carried out on concrete samples with varying levels of substitution (25%, 50%, and 75%) with recycled aggregate in order to measure the mechanical properties of the recycled concrete. In the second part of the study, a nonlinear homogenization model was developed on the basis of a classical secant approach to predict the behavior of recycled concrete. In this model, we assume that the behavior of the mortar phase, the concrete, and the recycled aggregates follow Mazars damage law. Comparison with the experimental data shows that the proposed homogenization model is accurate and efficient in predicting the correct nonlinear behavior of the recycled concrete. By better understanding the properties and behavior of recycled concrete, it will be possible to develop more effective methods for incorporating recycled materials into concrete structures

Verification of asymptotic homogenization method developed for periodic architected materials in strain gradient continuum

Strain gradient theory is an accurate model for capturing the size effect and localization phenomena. However, the challenge in identification of corresponding constitutive parameters limits the practical application of the theory. We present and utilize asymptotic homogenization herein. All parameters in rank four, five, and six tensors are determined with the demonstrated computational approach. Examples for epoxy carbon fiber composite, metal matrix composite, and aluminum foam illustrate the effectiveness and versatility of the proposed method. The influences of volume fraction of matrix, the stack of RVEs, and the varying unit cell lengths on the identified parameters are investigated. The homogenization computational tool is applicable to a wide class materials and makes use of open-source codes in FEniCS. We make all of the codes publicly available in order to encourage a transparent scientific exchange