Buckling and lateral buckling interaction in thin-walled beam-column elements with mono-symmetric cross sections (original) (raw)
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Lateral buckling of thin-walled beam-column elements under combined axial and bending loads
Based on a non-linear stability model, analytical solutions are derived for simply supported beam-column elements with bi-symmetric I sections under combined bending and axial forces. An unique compact closed-form is used for some representative load cases needed in design. It includes first-order bending distribution, load height level, pre-buckling deflection effects and presence of axial loads. The proposed solutions are validated by recourse to non-linear FEM software where shell elements are used in mesh process. The agreement of the proposed solutions with bifurcations observed on non-linear equilibrium paths is good. It is proved that classical linear stability solutions underestimate the real resistance of such element in lateral buckling stability especially for I section with large flanges. Numerical study of incidence of axial forces on lateral buckling resistance of redundant beams is carried out. When axial displacements of a beam are prevented important tension axial forces are generated in the beam. This results in important reduction of displacements and for some sections, the beam behaviour becomes non-linear without any bifurcation. r
International Journal of Mechanical Sciences, 2011
In this paper, lateral-torsional buckling behavior of open-section thin-walled beams is investigated based on a geometrically nonlinear formulation, which considers the effects of shear deformations. A finite element numerical solution along with an incremental-iterative solution procedure is adopted to trace the pre-buckling as well as the post-buckling equilibrium paths. Formulation is applicable to a general type of open-section and load position effects are also included. Numerical results are validated through comparisons with experimental results and those based on other formulations presented in the literature. Comparisons have also been made between the results based on fully nonlinear analysis and linearized buckling analysis in order to illustrate the effects of pre-buckling deformations as well as the shear deformations on the buckling load predictions. Examples illustrate the influence of beam slenderness and moment gradient on the effects of pre-buckling deformations in predicting bucking loads.
Pre-buckling deflection effects on stability of thin-walled beams with open sections
2012
The paper investigates beam lateral buckling stability according to linear and non-linear models. Closed form solutions for single-symmetric cross sections are first derived according to a non-linear model considering flexural-torsional coupling and pre-buckling deformation effects. The closed form solutions are compared to a beam finite element developed in large torsion. Effects of pre-buckling deflection and gradient moment on beam stability are not well known in the literature. The strength of singly symmetric I-beams under gradient moments is particularly investigated. Beams with T and I cross-sections are considered in the study. It is concluded that pre-buckling deflections effects are important for I-section with large flanges and analytical solutions are possible. For beams with T-sections, lateral buckling resistance depends not only on pre-buckling deflection but also on cross section shape, load distribution and buckling modes. Effects of prebuckling deflections are important only when the largest flange is under compressive stresses and positive gradient moments. For negative gradient moments, all available solutions fail and overestimate the beam strength. Numerical solutions are more powerful. Other load cases are investigated as the stability of continuous beams. Under arbitrary loads, all available solutions fail, and recourse to finite element simulation is more efficient.
2014
The paper investigates beam lateral buckling stability according to linear and non-linear models. Closed form solutions for single-symmetric cross sections are first derived according to a non-linear model considering flexural-torsional coupling and pre-buckling deformation effects. The closed form solutions are compared to a beam finite element developed in large torsion. Effects of pre-buckling deflection and gradient moment on beam stability are not well known in the literature. The strength of singly symmetric I-beams under gradient moments is particularly investigated. Beams with T and I cross-sections are considered in the study. It is concluded that pre-buckling deflections effects are important for I-section with large flanges and analytical solutions are possible. For beams with T-sections, lateral buckling resistance depends not only on pre-buckling deflection but also on cross section shape, load distribution and buckling modes. Effects of prebuckling deflections are important only when the largest flange is under compressive stresses and positive gradient moments. For negative gradient moments, all available solutions fail and overestimate the beam strength. Numerical solutions are more powerful. Other load cases are investigated as the stability of continuous beams. Under arbitrary loads, all available solutions fail, and recourse to finite element simulation is more efficient.
INELASTIC LATERAL BUCKLING OF BEAM-COLUMNS
An accurate line model based on the finite-element method is developed for analyzing the inelastic lateral buckling of I-section beams and beam-columns. The prebuckling in-plane bending is analyzed using a geometrically nonlinear finite-element method that accounts for the effects of prebuckling displacements and residual stresses on yielding. The results of the prebuckling analysis allow the distributions of yielding and strain-hardening throughout the beam to be determined. The out-of-plane flexural-torsional buckling of the inelastic beam is analyzed by adapting an elastic tapered monosymmetric finite element. For this element, the deflections and twists are referred to an arbitrary straight-line axis along the midheight of the web, instead of the shear center or centroidal axes. The elastic element is adapted for inelastic buckling by using reduced out-of-plane stiffnesses that allow for yielding and strain-hardening. The method is used to give some indications of the accuracy of earlier studies based on less accurate assumptions.
Lateral post-buckling analysis of thin-walled open section beams
Thin-Walled Structures, 2002
Thin-walled beams with open sections are studied using a nonlinear model. This model is developed in the context of large displacements and small deformations, by accounting for bending-bending and bending-torsion couplings. The warping and shortening effects are considered in the torsion equilibrium equation. The governing coupled equilibrium equations obtained from Galerkin's method are solved by a Newton-Raphson iterative process. It is established that the buckling loads are highly dependent on the pre-buckling deformations of the beam. The bifurcated branches are unstable and strongly influenced by shortening effects. Some comparisons are presented with the solutions commonly used in linear stability, like in the standard European steel code (Eurocode 3). The regular solutions appear to be very conservative, especially for I sections with large flanges.
Interactive buckling of thin-walled beam-columns with open and closed cross-sections
Thin-Walled Structures, 1993
The influence of interactive buckling on the postbuckling behaviour of thinwalled elastic beams with imperfections is studied. The investigation is concerned with thin-walled closed and open cross-section beam-columns under axial compression and a constant bending moment. The beams are assumed to be simply supported at the ends. The asymptotic expansion established by Byskov and Hutchinson is employed in the numerical calculations in the form of the transition matrix method. The paper's aim is to achieve the improved study of the equilibrium path in the postbuckling behaviour of imperfect structures with regard to the second-order approximation. The calculations are carried out for several types of beams. NOTATION aoJ, bo~ aj bi 19, E hi Three-and four-index coefficients in the nonlinear equilibrium equations by eqn (15) I Coefficients accompanying linear terms in the system by eqn (15) Width of the ith wall of beam (m) Plate rigidity of the ith wall (Nm) Young's modulus (Nm-2) Thickness of the ith wall of the beam (m)
IJERT-Flexural Buckling Analysis of Thin Walled T Cross Section Beams with Variable Geometry
International Journal of Engineering Research and Technology (IJERT), 2014
https://www.ijert.org/flexural-buckling-analysis-of-thin-walled-t-cross-section-beams-with-variable-geometry https://www.ijert.org/research/flexural-buckling-analysis-of-thin-walled-t-cross-section-beams-with-variable-geometry-IJERTV3IS031854.pdf Thin walled structure is a structure whose thickness is small compared to its other dimensions but which is capable of resisting bending in addition to membrane forces. Which is basic part of an aircraft structure, the structural components of an aircraft consist mainly of thin plates stiffened by arrangements of ribs and stringers. Thin plates (or thin sections or thin walled structures) under relatively small compressive loads are prone to buckle and so must be stiffened to prevent this. The determination of buckling loads for thin plates in isolation is relatively straightforward but when stiffened by ribs and stringers, the problem becomes complex and frequently relies on an empirical solution. The buckling of the thin plates is a phenomenon which could lead to destabilizing and failure of the aircraft; in this paper it is considered T cross section with variable geometry and length. The critical buckling stresses have been studied for several combinations of the geometry parameters of the beam with the help of ANSYS and drown the result plots Keywords: Thin walled beams, buckling analysis, Finite element analysis I INTRODUCTION A great deal of attention has been focused on plates subjected to shear loading over the past decades. One main fact in design of such elements, which fall in the category of thin-walled structures, is their buckling behavior. Plate girders and recently shear walls are being widely used by structural engineers, as well as ship and aircraft designers. The role of stiffeners is proved to be vital in design of such structures to minimize their weight and cost. Xiao-ting et al [1] presented an analytical model for predicting the lateral torsional buckling of thin walled channel section beams restrained by metal sheeting when subjected to an uplift load. And calculated the critical load from critical energy theory and showed that the critical buckling moment in the pure bending case is less than half of the critical moment, it is more effective to use the anti sag bars in the simply supported beams than in the fixed beams, the closer the loading point to the centre the lower the critical load. M.Ma et al [2] developed energy method for analyzing the lateral buckling behavior of the monosymmetric I beams subjected to distributed vertical load, with full allowance for distortion of web. the method assumes that the flanges buckle as rigid the rectangular section beams, but the web distorts as an elastic plate during buckling. it is shown that the disparity between the distortional and classical critical load increases as h/l increases and that for short beams the classical method seriously over estimates the critical load. B. W. Schafer [3] worked on cold-formed thin-walled open cross-section steel columns and provided local, distortional, and flexural-torsional buckling. Experimental and numerical studies indicated that post buckling strength in the distortional mode is less than in the local mode. In pin-ended lipped channel and zed columns, local and Euler interaction is well established. A direct strength method is proposed for column design. The method uses separate column curves for local buckling and distortional buckling with the slenderness and maximum capacity in each mode controlled by consideration of Euler equation. Attard Mario et al [4] investigated lateral-torsional buckling behavior of open-section thin-walled beams based on a geometrically nonlinear formulation, which considers the effects of shear deformations, also made Comparisons between the results based on fully nonlinear analysis and linearized buckling analysis in order to illustrate the effects of pre-buckling deformations as well as the shear deformations on the buckling load predictions. Ing. Antonin pistek,[5] analytical method for limit load capacity Calculation Of thin walled aircraft structures focused on description and Comparison of different methods for limit load Capacity calculation of thin walled aircraft Structures-considering all possible forms of Buckling and failures on nonlinear behavior of The structure under gradually increased Loading. Carine Louise Nilsen, et al [6] found that the behavior of thin-walled steel sections, including local buckling, distortional buckling, global buckling and shear buckling have been well understood and appropriate design methods existed. Foudil Mohria et al [7] derived analytical solutions Based on a non-linear stability model, for simply supported beam-column elements with bi-symmetric I sections under combined bending and axial forces. Jaehong Lee et al [8] explained lateral buckling of thin-walled composite beams with monosymmetric sections. A general geometrically nonlinear model for thin walled laminated
Elastic buckling of thin-walled beam-columns based on a refined energy formulation
Modern Trends in Research on Steel, Aluminium and Composite Structures, 2021
The paper discusses the effects of both in-plane displacements and second order P-δ bending on the elastic flexural-torsional buckling of beam-columns. An energy based solution of the elastic flexural-torsional buckling limit curves under arbitrary proportion between the major axis bending moment and the axial force is presented. The novelty of the approach is related to the development of an improved closed-form solution, in which the equivalent uniform moment modi fication factor should vary not only with the minor axis buckling force utilization ratio N/N z but also with that of major axis buckling N/N y represented by the factored ratio N/N z (1-k 1). Investiga tions include the effect of in-plane displacements resulting from an arbitrary moment gradient on the elastic flexural-torsional buckling of thin-walled narrow flange and wide flange double-tee sec tion members. The obtained solution is illustrated by elastic flexural-torsional buckling curves for different values of the factor k 1 of a beam-column subjected to unequal end moments.
Journal of Constructional Steel Research, 2019
The present study investigates the flexural-torsional struts buckling and beam lateral buckling analyses. In the highlight of braced structures, analytical solutions are derived for higher 3D buckling modes of simply supported struts with arbitrary cross-sections. Closed-form solutions are also investigated for lateral buckling strength of beams with doubly symmetric cross-sections. For more general cases, the finite element approach is adopted. In presence of torsion, warping is of primary importance. For this aim, 3D beams with 7 degrees of freedom (DOFs) per node are adopted in the analysis. The model is able to carry out higher buckling modes of bars under compression or lateral buckling modes of beams initially in bending. The analytical and the numerical results of the present model are compared to some available benchmark solutions of the literature and to finite element simulations of some commercial codes (Abaqus, Adina). The efficiency of the closed form solutions and the numerical approach is successfully verified. Applications of higher buckling modes in design of braced structures are considered according to Eurocode 3 code. A particular attention is pointed out to torsion and flexuraltorsional buckling modes not considered in bar strength. At the end, some solutions are proposed in order to cover the full strength of columns and beams in presence of instabilities. This proposal makes steel structures more performant and attractive when effects of instabilities are limited at a minimum.