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In this paper, the effect of shear deformations on elastic lateral buckling of tapered thin-walled open and closed bi-symmetric section beams under combined bending and axial forces is investigated. For the purpose, a geometrical non-linear beam theory is presented according to a new kinematic model that incorporates shear flexibility components. Ritz method is applied to obtain the governing equilibrium equations, then the buckling loads are computed by solving the eigenvalue problem basing on the singularity of the tangential stiffness matrix. The elastic lateral buckling resistances given by the proposed method are generally in good agreement with the finite element simulation using Abaqus software. The numerical results for cantilevers and simply supported thin walled beams with open and box sections reveal that the classical stability solution tends to overestimate the real lateral buckling resistance of short tapered box cantilever beams.

This paper proposes a new model for thin-walled open profiles able to predict bending-torsion buckling of thermally restrained steel I beams with bi- and mono-symmetric cross-sections. Refined nonlinear kinematics accounts for the shifts of the centroid and shear centre generated by the thermal gradient. The eigenvalue problem derived from geometrically nonlinear balance equations is solved via power series and Newton-Raphson technique. Several examples are presented; the results are compared with those provided by Abaqus simulation and the literature.

An analytical method to predict the thermal buckling of simply supported and clamped-clamped FGM box beams is presented in this paper. By means of Galerkin’s method, a new expression of the critical moment inducing lateral buckling for simply supported beams under thermo-mechanical loads is established. The beam thermo-mechanical properties are graded along the wall thickness according to a power law of the porous volume fraction. The critical temperature gradients given by the present method are compared to those provided by the commercial FEM code Abaqus, and the difference among the results is quite small. To investigate the effects of temperature and porosity on the instabilities of beams, some numerical examples are presented.

Simply supported steel beams with rectangular hollow section (RHS) are investigated, taking into account large twist and cross-sections distortions. A closed-form expression for the critical value of the external couple inducing lateral torsional buckling is found; homotopy perturbation method (HPM) is used to investigate the post-buckling non-linear path. The linear and non-linear paths given by HPM are compared to those of: i) a Newton–Raphson algorithm with arc length; and ii) the commercial FEM code Abaqus. Some numerical examples are presented.

International audience; The elastic lateral torsional buckling behavior of doubly symmetric web tapered thin-walled beams is investigated in this work. For the purpose, a non-linear model is developed in large torsion context according to a new kinematics proposed model. Firstly, the elastic equilibrium governing equations are carried out from the stationary condition. Secondly, the Ritz's method is deployed in order to derive the algebraic equilibrium equations. From this system, an analytical formula is proposed for the lateral buckling strength of web tapered beams in function of the classical stiffness terms, the load height position and the tapering parameter. The proposed formula is simple and gives accurate results when compared to finite element simulations. For this aim some numerical examples are considered in the validation process.

Free vibration of FGM box beam is investigated by the formulation of an exact dynamic stiffness matrix on the basis of first-order shear deformation theory (FSDT). Primary and secondary torsional warping, shear and bending deformations are incorporated in the one-dimensional beam model. Material properties of the beam are assumed to be graded across the wall-thickness. A recent function characterising the distribution of shear stresses is introduced. The present model is validated by comparison with finite element analysis for various boundary conditions. Good correlation exists between the values of Abaqus analysis and those calculated with the present method.

This paper presents a theoretical investigation in free vibration of a functionally graded beam (FGB) which has a variable cross-section. It is assumed that material properties vary along the beam thickness only according to exponential distributions (it is simply called E-FGB). The governing equation is reduced to an ordinary differential equation in spatial coordinate for a family of cross-section geometries with exponentially varying width. Analytical solutions of the natural frequencies are obtained for E-FG beams with clamped-free, hinged-hinged, and clamped-clamped end supports. Results show that the non-uniformity in the cross-section and the inhomogeneity in material properties influence the natural frequencies. It is also shown that, all other parameters remaining the same, the natural frequencies of E-FG beams are always proportional to those of homogeneous isotropic beams. Therefore, one can predict the behaviour of E-FG beams knowing that of similar homogeneous beams.

This paper deal with the seismic analysis of reinforced concrete (RC) coupled shear wall structures strengthened by bonded composite plates. In the analytical formulation of the present study, the adherent and the adhesive layers are modeled as shear wall elements, using the mixed finite element method. In the validation process of the proposal model, static and free vibration analyses of coupled shear walls are firstly studied. Comparisons with theoretical results reported in the literature are made and good agreement is observed. After this stage, numerical results are presented that relate to the performance of RC coupled shear walls bonded with composite plates under several different earthquake scenarios, in which an RC coupled shear wall strengthened by steel plates is treated as a limiting case.

International audience; The effect of distortional deformation on the elastic lateral buckling of thin-walled box beam elements under combined bending and axial forces is investigated in this paper. For the purpose, an analytical model is developed for the stability of laterally unrestrained box beams according to higher order theory. Ritz and Galerkin's methods are applied in order to discretize the governing equilibrium equations and then the buckling loads are obtained by requiring the singularity of the tangential stiffness matrix. The different solutions are discussed and then compared to the finite element simulation using Abaqus software where shell elements are used in the mesh process. The numerical results reveal that classical stability solutions as those adopted in Eurocode 3 overestimate the real lateral buckling resistance of thin-walled box beam members, particularly for the ones with high ratios between the height and the thickness of the cross-section. Numerical study of incidence of compressive forces on lateral buckling resistance of thin-walled box beam is investigated.

In this paper an approximate hand-method for seismic analysis of an asymmetric building structure having constant properties along its height is presented. The building is stiffened by a combination of shear walls and thin-walled open section structures. Based on the continuum technique and d’Alembert’s principle, the governing equations of free vibration and the corresponding eigenvalue problem are derived. By applying the Galerkin technique, a generalized method is proposed for the free vibration analysis of coupled vibration of a building braced by shear walls and thin-walled open section structures. Simplified formulae are given to calculate the circular frequencies and internal forces of a building structure subjected to earthquakes. The utility and accuracy of the method is demonstrated by an numerical example, in which the proposed method is compared with finite element calculations.

In this paper, a closed-form solution for interfacial stresses in externally FRP plated RC beam including creep and shrinkage effect is presented. In such plated beams, tensile forces develop in the bonded plate, and these have to be transferred to the original beam via interfacial shear and normal stresses. Consequently, debonding failure may occur at the plate ends due to a combination of high shear and normal interfacial stresses. These stresses between a beam and a soffit plate, within the linear elastic range, have been addressed by numerous analytical investigations. Surprisingly, none of these investigations has examined interfacial stresses while taking the creep and shrinkage effect into account. This paper presents an analytical model for the interfacial stresses between RC beam and a thin FRP plate bonded to its soffit. The influence of creep and shrinkage effect relative to the time of the casting, and the time of the loading of the beams is taken into account. Numerical examples of a typical RC beam strengthened with an externally bonded FRP plate are discussed with emphasis on the shear and normal stresses at the edge of the plate.

International audience; A 3D finite element beam element model is investigated for the behavior, the buckling and the post-buckling analyses of thin-walled tapered beams with open cross sections. For the purpose, a non-linear model is performed in large torsion context according to a new kinematics that accounts for large torsion, flexural-torsional coupling and the presence of tapering terms in bending and torsion. The equilibrium equations are carried out and new tapering stress resultants are then present. This model is extended to finite element formulation in the same circumstances. 3D beams elements with two nodes and seven degrees of freedom per node are adopted. Due to large torsion assumption and flexural torsional coupling, new matrices are established in both the geometric and the initial stress parts of the tangent stiffness matrix. The Arclength method is adopted as solution strategy of the non-linear equations. Many applications are presented that deal with the behavior, the buckling and the post-buckling equilibrium. Comparisons are made with some available solutions and with shell elements of a commercial code. The bifurcation points are in accordance with non-linear stability solutions. Moreover, the present element is also compared to similar tapered beam finite element without the new tapering terms. The proposed beam element is efficient and accurate in both linear and non-linear behavior analyses. It follows a non negligible gain in computation time especially when the post-buckling behavior is performed.

International audience; The purpose of the present work it to study the damping and forced vibrations of three-layered, symmetric laminated composite beams. In the analytical formulation, both normal and shear deformations are considered in the core by using the higher-order zig-zag theories. The harmonic balance method is coupled with a one mode Galerkin procedure for a simply supported beam. The geometrically nonlinear coupling leads to a nonlinear frequency amplitude equation governed by several complex coefficients. In the first part of the paper, linear and nonlinear damping parameters of laminated composite beams are obtained. In the second part, nonlinear forced vibration analysis is carried out for small and large vibration amplitudes. The frequency response curves are presented and discussed for various geometric and material properties.

The present paper deals with the effect of deformation delayed creep and shrinkage of the concrete on the seismic response of shear walls reinforced concrete strengthened with composite materials having a sinusoidal distribution of fibers. The lateral stiffness of shear walls RC, adhesives and composite material taking into account the phenomenon of creep and shrinkage of concrete described by the Eurocode 2, and widthwise varying fiber volume fraction of the composite plate has been determined by a finite element model. Large earthquakes recorded in Algeria (El-Asnam and Boumerdes) have been tested to demonstrate the accuracy of the proposed method. Numerical results obtained are discussed and the factors influencing the seismic response of reinforced concrete shear walls strengthened taking account the effects of the delay mechanism creep and shrinkage of concrete are highlighted. Prospects are being studied