Search

The present paper treats the lateral torsional buckling (LTB) of castellated rectangular hollow section (CRHS) beams. For the purpose, an analytical model was proposed to provide critical buckling loads in (LTB) resistance. In the present model two types of web openings are considered, referring to rectangular and hexagonal shape perforating. The sectional geometrical properties attributed to each type of opening are controlled by selecting the appropriate value of the reduction parameter. Ritz method is applied in order to found the governing equilibrium equations, following the critical buckling loads are determined from the eigenvalue problem imposed to the tangential stiffness matrix. The validity of the elastic lateral buckling resistances evaluated by the proposed method is checked with the finite element simulation using ABAQUS software. The numerical results for cantilevers and simply supported CRHS beams, with hexagonal and rectangular web openings, are presented for both short and long-span beams.

In this study, the finite element approach for linear vibration analysis of FGM beams under various thermal loads is investigated. The formulation is developed by using CPT, FSDT and HSDT kinematic...

This paper treats the distortional and shear deformation effects on the elastic lateral torsional buckling of thin-walled box beam elements, under combined bending and axial forces. For the purpose, a nonlinear kinematic model based on higher order theory is used applicable to both short and long thin-walled box beams. Because in the kinematic model of the higher order theory integrates additional flexibility terms related to shear, distortion and warping effects, it accurately predicts the lateral torsional buckling of the straight box beams. Ritz’s method is adopted as solution strategy in order to obtain the nonlinear governing equilibrium equations, then the buckling loads are computed by solving the eigenvalue problem basing on the singularity of the tangential stiffness matrix. Owing to flexural–torsional and distortional couplings, new matrices are obtained in both geometric and initial stress parts of the tangent stiffness matrix. The proposed method with the new stiffness terms, is efficient and accurate in lateral torsional buckling predictions, when compared with the commercial FEM code ABAQUS results. Based on the existing European guidelines EC3, an extensive numerical investigation is performed to demonstrate the effects of both shear and distortional deformations on the moment carrying capacity. The convenience of the model is outlined and the limit of models developed without shear and distortion deformation effects on lateral buckling loads evaluation is discussed.

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.

A general geometrically non-linear model for lateral-torsional buckling of thick and thin-walled FGM box beams is presented. In this model primary and secondary torsional warping and shear effects are taken into account. The coupled equilibrium equations obtained from Galerkin\'s method are derived and the corresponding tangent matrix is used to compute the critical moments. General expression is derived for the lateral-torsional buckling load of unshearable FGM beams. The results are validated by comparison with a 3D finite element simulation using the code ABAQUS. The influences of the geometrical characteristics and the shear effects on the buckling loads are demonstrated through several case studies.

The current investigation has been conducted to examine the effect of gravity loads on the seismic responses of the doubly asymmetric, three-dimensional structures comprising walls and frames. The proposed model includes the P- effects induced by the building weight. Based on the variational approach, a 3D finite element with two nodes and six DOF per node including P- effects is formulated. Dynamic and static governing equations are derived for dynamic and buckling analyzes of buildings braced by wall-frame systems. The influences of P- effects and height of the building on tip displacements under Hachinohe earthquake record are investigated through many structural examples.

International audience; General differential equations of motion in nonlinear forced vibration analysis of multilayered composite beams are derived by using the higher-order shear deformation theories (HSDT's). Viscoelastic properties of fiber-reinforced plastic composite materials are considered according to the Kelvin–Voigt viscoelastic model for transversely isotropic composite materials. The method of multiple scales is employed to perform analytical frequency amplitude relationships for superharmonic resonance. Parametric study is conducted by considering various geometrical and material parameters, employing HSDT's and first-order deformation theory (FSDT).

A finite-element analysis is used to calculate stresses in a CFRP plate- strengthened beam under mechanical loads. The FE results obtained are compared with those given by an analytical approach, and a parametric study is carried out to show how the maximum stresses are influenced by the thickness of the adhesive layer, the fiber volume fraction, and the hygrothermal effect.

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.

The effect of creep and shrinkage of reinforced concrete (RC) shear walls, strengthened with thin composite sheets, on their static and dynamic behavior is investigated. A finite-element model for their lateral stiffness and vibration characteristics is presented. Several test problems are examined to demonstrate the accuracy and effectiveness of the method proposed. Numerical results are obtained for four nonuniform distributions of graphite and boron fibers in epoxy matrices, and they demonstrate the significance of time-dependent effects on the lateral displacements and frequencies of the structures considered.

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 an alternative technological solution for passive earthquake control of shear building structures. For this purpose, new two nodes with ten DOF per node finite element is formulated for dynamic analysis of sandwich box column with viscoelastic material as core layer under torsion and bending effects. The viscoelastic material is modelled as a linear solid-type material to present the damping characteristics. Dynamic equilibrium equations are written in time domain and they are resolved numerically by adopting the time step-by-step Newmark numerical integration method, in conjunction with trapezoidal rule to compute the integration term of the dynamic equation. The influences of the boundary conditions to reduce the tip displacements and accelerations of a one storey building under seismic loads as far as possible are discussed.

External bonding of FRP plates or sheets has emerged as a popular method for strengthening reinforced concrete structures. Debonding along the FRP–concrete interface can lead to premature failure of the structures. Shear and normal stresses (in the thickness direction) at interfaces (referred to as interfacial shear and transverse normal stresses hereafter) have played a significant role in understanding this premature debonding failure of such hybrid structures. Extensive experimental and analytical analyses have been undertaken to investigate this problem. Large discrepancies have been found from various studies. This paper reports a closed-form formulation for interfacial stresses in plated beams. The analysis is based on the deformation compatibility approach developed by Tounsi and Benyoucef [8] where both the shear and normal stresses are assumed to be invariant across the adhesive layer thickness. The composite plate with variable fiber spacing bonded to reinforced concrete beam is considered in th...

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.

In this paper, a finite element model for static and free vibration analysis of reinforced concrete (RC) shear walls structures strengthened with thin composite plates having variable fibres spacing is presented. An efficient analysis method that can be used regardless to the sizes and location of the bonded plates is proposed in this study. In the numerical formulation, the adherents and the adhesives are all modelled as shear wall elements, using the mixed finite element method. Several test problems are examined to demonstrate the accuracy and effectiveness of the proposed method. Numerical results are obtained for six nonuniform distributions of E-glass, graphite and boron fibres in epoxy matrices. The fibre redistributions of the bonded plates are seen to increase the frequencies modes and reduce substantially the lateral displacements.

An analytical method is presented for the three-dimensional frequency analysis of buildings braced by shear walls and thin-walled open-section structures. Owing to the asymmetry of the structure, the centre of gravity and the centre of flexural rigidity of the floor plan do not coincide, and hence the flexural vibration in two mutually perpendicular directions and the warping torsional vibrations are all coupled. Based on the continuum approach and D'Alembert's principle, the governing differential equation of free vibration and its corresponding eigenvalue problem for asymmetric shear walls and thin-walled open-section structures are derived. Based on the theory of differential equations, an analytical method of solution is proposed to solve the eigenvalue problem and a general solution is derived for determining the natural frequencies of the structures. Results obtained from the proposed method for the example structure show good agreement with those of finite element analysis. It is also shown that the proposed analysis is efficient and accurate enough to be used both at the concept design stage and for final analysis. Copyright © 2007 John Wiley & Sons, Ltd.

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.

This paper deals with the bending and vibration analysis of moderately damaged coupled shear wall structures with externally bonded carbon fiber-reinforced polymer (CFRP) sheets. In the analytical formulation, the adherent and the adhesive layers are all modelled as shear walls, using the mixed finite-element method (FEM). The anisotropic damage model is adopted to describe the damage extent of the RC coupled shear walls. A free vibration analysis is carried out to determine the frequencies of multi-storey strengthened shear wall structures with openings. Test problems are conducted to demonstrate the accuracy and effectiveness of the proposed method. Numerical results are presented to show the performance of reinforced concrete coupled shear wall structures bonded with composite plates in which a damaged RC shear wall with openings strengthened by a thin steel sheets is treated as a comparator. The effects of damage extent and of the bonded sheets on the bending and vibration characteristics of damaged RC coupled shear wall structures are also studied.

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.

The paper considers the seismic analysis of reinforced concrete (RC) coupled shear walls structures strengthened by bonded composite plates having variable fibers spacing. An efficient analysis method that can be used regardless of the sizes and location of the bonded plates is proposed in this study. In the numerical formulation, the adherents and the adhesives layers are all modeled as shear walls elements, using the mixed finite element method. Dynamic analysis was performed to investigates the influence of the fibers redistribution of the bonded plates on the lateral deflections of RC coupled shear walls. This conceptual study has demonstrated the feasibility of mitigating the seismic response of RC coupled shear walls building structures by using composites plates having variable fibers spacing.

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.

The free vibration of stiffened and damaged coupled shear walls is investigated using the mixed finite element method. The anisotropic damage model is adopted to describe the damage extent of the reinforced concrete shear wall element. The internal energy of a locally damaged shear wall element is derived. Polynomial shape functions established by Kwan are used to present the component of displacements vector on each point within the wall element. The principle of virtual work is employed to deduce the stiffness matrix of a damaged shear wall element. The stiffened system is reinforced by an additional stiffening beam at some level of the structure. This induces additional axial forces, and thus reduces the bending moments in the walls and the lateral deflection, and increases the natural frequencies. The effects of the damage extent and the stiffening beam on the free vibration characteristics of the structure are studied. The optimal location of the stiffening beam for increasing as far as possible the first natural frequency of vibration is presented.

In this paper an approximate analytical method is proposed to predict the distribution of interfacial stresses in FRP–RC hybrid beams. The theoretical results are compared, and show close agreement, with other rigorous theoretical analyses. A parametrical study is carried out to show the effects of some design variables, e.g. thickness of adhesive layer, thickness of FRP plate and the distance from support to cut-off end of bonded plates.

The use of aircraft structural parts made of polymer matrix composites subjected to severe environment conditions calls for better knowledge of their long – term behaviour, with an emphasis on their ability to withstand important cyclic variations of moisture and temperature. The influence of temperature and moisture on such structures is receiving special attention, because it induces transient residual stresses within the plies. Such stresses must be taken into account in the design of composite materials, particularly aerospace structures, e.g. aircraft. In the present paper the transient hygroscopic stresses induced by cyclic and unsymmetric environmental loadings which simulate an aeronautical application are investigated. It is shown that the heterogeneity and anisotropy of such plates generally result in transient stress distributions which are very different from the equilibrium stress distribution. Some stacking sequences exhibit important stresses within the plies. These stresses have to be taken into account in the design of composite structures submitted to a moist environment.

International audience; The present study investigates the dynamic analysis of Reinforced Concrete (RC) coupled shear walls strengthened by bonded Carbon Fibre Reinforced Polymer (CFRP) composite plates applied on both sides of the coupling beams. For this purpose, new finite element models are developed for both the walls and strengthened coupling beams. In the validation process of the proposed model, static and free vibration analyses of coupled shear walls were firstly studied. Comparisons with ABAQUS code using shell elements were made and good agreement was observed. After this stage, dynamic analysis was carried out under El Centro and Northridge earthquake records. In these conceptual studies, the maximum top lateral deflection responses of strengthened and unstrengthened RC coupled shear walls are computed. The obtained results showed that mitigation of seismic behaviour of RC coupled shear walls by using CFRP bonded composite plates depends on the geometrical characteristics of shear wall structure and dominant range frequencies of the input earthquake records.

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