Lateral–torsional buckling analysis of thin-walled beams including shear and pre-buckling deformation effects (original) (raw)
Related papers
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.
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.
Lateral-torsional buckling of tapered thin-walled beams with arbitrary cross-sections
Thin-Walled Structures, 2013
In this paper, a theoretical and numerical model based on the power series method is investigated for the lateral buckling stability of tapered thin-walled beams with arbitrary cross-sections and boundary conditions. Total potential energy is derived for an elastic behavior from strain energy and work of the applied loads. The effects of the initial stresses and load eccentricities are also considered in the study. The lateral-torsional equilibrium equations and the associated boundary conditions are obtained from the stationary condition. In presence of tapering, all stiffness coefficients are not constant. The power series approximation is then used to solve the fourth-order differential equations of tapered thinwalled beam with variable geometric parameters having generalized end conditions. Displacement components and cross-section properties are expanded in terms of power series of a known degree. The lateral buckling loads are determined by solving the eigenvalue problem of the obtained algebraic system. Several numerical examples of tapered thin-walled beams are presented to investigate the accuracy and the efficiency of the method. The obtained results are compared with finite element solutions using Ansys software and other available numerical or analytical approaches. It is observed that suggested method can be applied to stability of beams with constant cross-sections as well as tapered beams.
Buckling of thin-walled beams by a refined theory
Journal of Zhejiang University SCIENCE A, 2012
The buckling of thin-walled structures is presented using the 1D finite element based refined beam theory formulation that permits us to obtain N -order expansions for the three displacement fields over the section domain. These higher-order models are obtained in the framework of the Carrera unified formulation (CUF). CUF is a hierarchical formulation in which the refined models are obtained with no need for ad hoc formulations. Beam theories are obtained on the basis of Taylor-type and Lagrange polynomial expansions. Assessments of these theories have been carried out by their applications to studies related to the buckling of various beam structures, like the beams with square cross section, I-section, thin rectangular cross section, and annular beams. The results obtained match very well with those from commercial finite element softwares with a significantly less computational cost. Further, various types of modes like the bending modes, axial modes, torsional modes, and circumferential shell-type modes are observed.
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
A direct one-dimensional beam model for the flexural-torsional buckling of thin-walled beams
Journal of Mechanics of Materials and Structures, 2006
In this paper, the direct one-dimensional beam model introduced by one of the authors is refined to take into account nonsymmetrical beam cross-sections. Two different beam axes are considered, and the strain is described with respect to both. Two inner constraints are assumed: a vanishing shearing strain between the cross-section and one of the two axes, and a linear relationship between the warping and twisting of the cross-section. Considering a grade one mechanical theory and nonlinear hyperelastic constitutive relations, the balance of power, and standard localization and static perturbation procedures lead to field equations suitable to describe the flexural-torsional buckling. Some examples are given to determine the critical load for initially compressed beams and to evaluate their post-buckling behavior.
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.
Applied Mathematical Modelling, 2013
Effects of axial forces on beam lateral buckling strength are investigated here in the case of elements with mono-symmetric cross sections. A unique compact closed-form is established for the interaction of lateral buckling moment with axial forces. This new equation is derived from a non-linear stability model. It includes first order bending distribution, load height level and effect of mono-symmetry terms (Wagner's coefficient and shear point position). Compared to the so-called three-factors (C 1 -C 3 ) formula commonly employed in beam lateral buckling stability, another factor C 4 is added in presence of axial loads. Prebuckling deflection effects are considered in the study and the case of doubly-symmetric cross sections is easily recovered. The proposed solutions are validated and compared to finite element simulations where 3D beam elements including warping are used. The agreement of the proposed solutions with bifurcations observed on the non-linear equilibrium paths is good. Dimensionless interaction curves are dressed for the beam lateral buckling strength and the applied axial load, where the flexural-torsional buckling axial force is a taken as reference.
2017
Lateral torsional buckling is a limit state for I-shaped steel beams that may often be a controlling issue in structural steel design. When these members are not appropriately braced so as to prevent lateral deformations and torsion, they are subjected to risk of failure by lateral torsional buckling before reaching their ultimate capacity. This paper investigates elastic lateral torsional buckling of simply supported I-shaped steel beams under concentrated load and linear moment gradient using design standards and codes, approaches from the literature and finite element analysis. Several unbraced member lengths and end moment values are taken into account to compare and evaluate these approaches in terms of elastic critical moment and end moment ratios. Analysis results show that lateral torsional buckling is a crucial stability problem for I-shaped steel members that are under flexure and it is reflected with adequate safety in the design codes and standards considering finite element analysis outcomes.
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.