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Enhancement of multifiber beam elements in the case of reinforced concrete structures for taking into account the lateral confinement of concrete due to stirrups

Abstract : In order to determine the seismic vulnerability of reinforced concrete structures, effective and sufficiently accurate numerical methods are required. Two-dimensional or three-dimensional finite element methods, widely used, provide reliable results. However, these types of methods involve a large number of degrees of freedom and robust 3D behavioral laws for concrete and steel to accurately capture the non-linearities in slender reinforced concrete elements. Another more practical method, in the field of structural engineering, is the use of multifiber beam elements.By using multifiber beam elements, the structure can be discretized with linear elements that carry a section discretized in the transversal direction based on the kinematic assumption of Euler Bernoulli or Timoshenko. The discretization of the section makes it possible to simply use nonlinear behavior laws and to model composite sections such as reinforced concrete. Nevertheless, there are limitations to this kind of model. Therefore, several researches have been conducted in the past few years to enhance the kinematics of the beam elements in order to correctly reproduce the shearing effects, especially in the case of short beams where the latter effect is not negligible. Several approaches have been developed in this field, as the one proposed by [VEC 88] adequate for two-dimensional case studies but doesn’t reproduce the torsional effect, the approach presented by [LEC 12], but whose model can not be applied to reinforced concrete elements, and the formulation proposed by [MOH 10] which is suitable for reinforced concrete applications but works only in 2D. More recently ([CAP 16b]; [CAP 16a]) have developed an enhanced multifiber beam model adapted to reinforced concrete elements and takes into account the warping of the section. The combination of this beam element with a concrete behavior model such as the µ model [MAZ 13], provides robust results with interesting computational speed. However, as shown by some experimental tests [CUS 95], the amount of transverse reinforcement triggers significantly the behavior of the beam elements, especially under cyclic loading . In the previous works, these reinforcements are neglected or considered in an approximative manner.Based on the work of [LEC 12] and [CAP 16a], this thesis aims to model the effect of transversal reinforcement. The approach proposed herein is to enhance the multifiber beam elements in order to take into account the distortion of the section. For this purpose, additional transverse displacements are introduced. The application of the principle of virtual powers on the field of associated virtual velocity leads to project the equilibrium equations of the element and thus to obtain the classical equilibrium equation of the element as well as the equilibrium of the section. The latter one allows to take into account the effect of the transverse reinforcements and to correctly calculate the lateral stresses applied to each concrete fiber. Moreover, in order to be able to reproduce the confinement effect due to the presence of stirrups, a dilatant constitutive law has to be attributed to the concrete fibers at the section level. In this context, the Mu model has been chosen even though it’s not a dilatant model. For this reason, a method of introducing dilatancy at the level of the Poisson’s coefficient is presented in this work. The 2D and 3D enhanced multifiber displacement beam models are formulated based on the Caillerie beam element [CAI 15] with higher order interpolation functions. The performance of these two approaches is also demonstrated by comparing the numerical model response to different experimental results of the literature.
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Natalia Khoder. Enhancement of multifiber beam elements in the case of reinforced concrete structures for taking into account the lateral confinement of concrete due to stirrups. Mechanics of materials [physics.class-ph]. Université Grenoble Alpes, 2018. English. ⟨NNT : 2018GREAI096⟩. ⟨tel-02058755⟩

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