Pre-buckling Deflection Effects on stability of thin-walledBeamsWithopensections JSC 13, No. 1 (2012) 71-89 (original) (raw)
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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.
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.
Linear and non-linear stability analyses of thin-walled beams with monosymmetric I sections
Thin-Walled Structures, 2010
The paper investigates beam lateral buckling stability according to linear and non-linear models. First, the classical linear stability solutions are derived from the stability equation in the case of monosymmetric cross-sections. Bending distribution, load height parameter and Wagner's coefficient effects are taken into account. In the second step, they are extended to non-linear stability by considering pre-buckling deformation and improved solutions are then obtained. Based on a finite element model developed for large torsion of thin-walled beams with open sections, the stability of beams under gradient moments (M 0 , cM 0 , À 1 rc r 1) is particularly investigated. It is then concluded that beam lateral buckling resistance depends not only on pre-buckling deformation but also on section shape and load distribution. For bisymmetric I beam, closed form solutions are possible and prebuckling deformations have an incidence. In the case of beams with monosymmetric I and Tee sections, effects of pre-buckling deflections are important only when the largest flange is in compression under M 0 and positive gradient moment. Analytical solutions are possible. For negative gradient moments all available solutions fail and numerical solutions are more powerful. Effect of gradient moments on stability of redundant beams is investigated at the end. Under such boundary conditions, important axial forces are present due to non-linear beam deformation. These forces, omitted in literature, have an incidence on stability. The element is then concerned with beam-column behaviour rather than beam stability.
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.
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
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.
Buckling Resistance Criteria of Prismatic Beams Under Biaxial Moment Gradient
International Journal of Steel Structures
Laterally and torsionally unrestrained steel I-section beams are susceptible to torsional deformations between supports; therefore, according to Part 1-1 of Eurocode 3, they need to be designed to resist lateral-torsional buckling. Eurocode's steelwork design criteria require safety checking based on two stability interaction formulae utilizing the so-called equivalent uniform moment factors and the cross-section resistance formula that, in the case of moment gradient, refer to the beam end section. Uncoupling the beam stability resistance criterion and the cross-section resistance criterion may result in a nonuniform safety assessment of I-section beams. Finite element simulations of the beam resistance for different moment gradient ratios are performed. Verification of the buckling resistance is conducted by varying the following parameters: the slenderness ratio, the location of maximum end moments about both axes and the section depth-to-width ratio (i.e., considering rolled I-and H-sections). The variation in the accuracy of the current Eurocode resistance evaluation method is identified, and an approach for a better equalization of the safety predictions is suggested by considering different values of the most important factors influencing the stability performance of steel I-section beams.
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
Major axis in-plane buckling resistance of I-section beam-columns under moment gradient
Routledge eBooks, 2021
The inelastic second-order resistance of I-section beam-columns under arbi trary loading cases of one-directional bending is mainly dependent upon two factors, namely the direction of bending and the contribution of the web and flanges to the section moment of inertia in the plane of bending. Based on the concept of an approximate method of the evalu ation of inelastic second-order resistance of beam-columns presented by the authors else where, the objective of the present study is to develop the model parameters representing functions for accounting an approximate inclusion of distributed plasticity effects of plastic zones (stress redistribution along the member length) and within the member most stressed section (stress redistribution across the most stressed section depth). The model parameters for major axis bending are assessed for narrow flange I-section beam-columns (symbol I is used for the narrow flange section identification) on the basis of results obtained from a number of FEM simulations based on an accurate shell modelling technique and using Abaqus software. The concept of equivalent geometric imperfections is applied in compliance with the so-called Eurocode's general method in order to include globally the effect of geomet ric and material imperfections. The resulting model parameters evaluated for I-section steel work elements being laterally and torsionally restrained are compared with those developed elsewhere for hot-rolled wide flange HEB section members subjected to both compression and bending about the major principal axis. Additionally, results are compared with those obtained in previous studies and those of Eurocodes interaction criteria based on Methods 1 and 2. Concluding remarks with regard to the in-plane buckling resistance of double-tee sec tion beam-columns are presented.
Computers & Structures, 2007
This paper assesses the global performance and the underlying assumptions of a recently developed one-dimensional model characterising the elastic lateral-torsional buckling behaviour of singly symmetric tapered thin-walled open beams, which is able to account for the influence of the pre-buckling deflections. A comparative study involving the critical load factors and buckling modes yielded by (i) the one-dimensional model and (ii) two-dimensional shell finite element analyses (reference results) is presented and discussed. The results concern I-section cantilevers and simply supported beams (i) with uniform or linearly tapered webs, (ii) equal or unequal uniform flanges and (iii) acted by point loads applied at the free end or mid-span sections, respectively. In general, the one-dimensional predictions are found to agree well with the shell finite element results. Some significant discrepancies are also recorded (for the shorter beams), which are due to the occurrence of relevant cross-section distortion or localised buckling phenomena.