Interactive buckling of beams in bending

A discrete model involving a limited number of degrees of freedom is presented, for analyzing the interaction between overall lateral-torsional buckling and local flange buckling, qualitatively. The results are compared with experiments and show a good qualitative agreement. The results suggest that a quantitative numerical analysis based on Koiter's asymptotic approach may have a wide range of validity.     

Local–global mode interaction in stringer-stiffened plates

A recently developed nonlinear analytical model for axially loaded thin-walled stringer-stiffened plates based on variational principles is extended to include local buckling of the main plate. Interaction between the weakly stable global buckling mode and the strongly stable local buckling mode is highlighted. Highly unstable post-buckling behaviour and a progressively changing wavelength in the local buckling mode profile are observed under increasing compressive deformation. The analytical model is compared against both physical experiments from the literature and finite element analysis conducted in the commercial code Abaqus; excellent agreement is found both in terms of the mechanical response and the predicted deflections.     

Influence of local postbuckling behaviour on bending of thin-walled beams

The influence of the local postbuckling behaviour on the bending of thinwalled beams is studied. The analysis of the postbuckling behaviour of a prismatic column-beam subject to compression and bending is employed in order to determine the overall flexural stiffness of a beam after local buckling. The asymptotic Koiter method is used in the second order approximation. The determination of post-buckling coefficients enables one to find the beam's flexural stiffness without the necessity of using hypotheses on effective widths of eccentrically compressed plates. It is shown that the post-buckling equilibrium branch in a bending moment-global curvature coordinate system for a perfectly elastic thin-walled beam is rectilinear (in the second order approximation of' the asymptotic method). Simple analytical relations are presented between the slope of the post-buckling equilibrium branch of global bending and post-buckling coefficients for local buckling mode. The results obtained are compared with data reported by other authors.     

Some thoughtd on mode interaction in thin-walled columns under uniform compression

Interaction of nearly simultaneous buckling modes in the presence of imperfections is studied. The investigation is concerned with thin-walled trapezoidal columns under uniform compression. The asymptotic expansion established by Byskov and Hutchinson is also used here. The present paper is devoted to an improved study of the equilibrium path in the initial post-buckling behaviour of imperfect structures. The results obtained include the effect of interaction of the ‘primary’ local mode and a ‘secondary’ local mode having the same wavelength as the primary. In this paper the analysis of a few buckling mode interactions is presented.     

The ultimate load sensitivity of lipped channel columns to column axis imperfection

An analytical investigation is made of the effect of column axis imperfection on the equilibrium behaviour and ultimate carrying capacity of thin-walled lipped channel columns. The Rayleigh-Ritz method is used to obtain local buckling loads and a semi-energy method is employed to describe post-buckling interaction behaviour. In the analysis a facility of allowing the locally deflected form to change after buckling is provided, resulting in asymptotic equilibrium curves tending towards continually changing reduced Euler loads as opposed to fixed reduced Euler loads based on an unchanging locally deflected form.The imperfection sensitivity of column designs which produce stable and unstable equilibrium behaviour after local buckling is investigated as is that of columns which exhibit neutral equilibrium behaviour before local buckling. Results are presented in the form of non-dimensional load-deflection equilibrium curves and ultimate load-slenderness plots covering these three equilibrium states. A comparison of the theory with independent experimental work is also included.     

外套增层结构体系抗震性能分析

根据现行的抗震规范,结合具体的工程实例,通过建立三维有限元模型,分别采用振型分解反应谱法和弹性时程分析法,对分离式和整体式两种外套增层结构体系进行了地震反应分析,比较了两种增层体系的抗震性能。计算结果表明:分离式结构易发生局部失稳,整体式结构抗侧刚度较大,新旧结构的协同工作,减小了上下层的刚度突变;当旧房抗侧刚度较强时,其整体抗震性能优于分离式结构。分析结论可为该类结构的抗震设计提供参考。     

Influence of load-non-uniformity and eccentricity on the stability and load carrying capacity of orthotropic tubular columns of regular hexagonal cross-section

The paper contains an analysis of the influence of non-uniformity and eccentricity of compressive loads on global and local buckling, on interactive buckling, and on the load-carrying capacity of thin-walled columns. Isotropic and orthotropic tubular columns of regular hexagonal cross-section have been examined. Equilibrium equations for the first and the second order non-linear approximation have been solved using the asymptotic Byskov–Hutchinson method. Numerical calculations have been performed for numerous different loading modes of isotropic columns and also for several loading modes of orthotropic columns. The results are presented in diagrams with some conclusions.     

Buckling behavior of cold-formed zed-purlins partially restrained by steel sheeting

This paper presents a study on the buckling behaviour of purlin-sheeting systems under wind uplift loading. The restraint provided by the sheeting to the purlin is modeled by using two springs representing the translational and rotational restraints. The analysis is performed using finite strip methods in which the pre-buckling stress is calculated based on the same model used for the buckling analysis rather than taken as the ‘pure bending’ stress. The results obtained from this study show that, for both local and distortional buckling, the restraints have significant influence on the critical loads through their influence on the pre-buckling stress rather than directly on the buckling modes. While for lateral-torsional buckling, the influence of the restraints on the critical loads is mainly due to their influence on the buckling modes rather than the pre-buckling stress.     

Towards a rationally based elastic-plastic shell buckling design methodology

The ‘reduced stiffness method’ for the analysis of shell buckling was developed to overcome a trend towards increasingly sophisticated analysis that has become divorced from its basically simple underlying physics. This paper outlines the developments of the reduced stiffness method from its origins in the late 1960s, through its experimental confirmation, generalisation and elaboration over the past 20 years, to its more recent consolidation using carefully controlled non-linear numerical experiments. It is suggested that the method has now reached a stage where it could profitably be adopted as a basis for an improved shell buckling design methodology.     

Cellular buckling in I-section struts

An analytical model that describes the interactive buckling of a thin-walled I-section strut under pure compression based on variational principles is presented. A formulation combining the Rayleigh–Ritz method and continuous displacement functions is used to derive a system of differential and integral equilibrium equations for the structural component. Numerical continuation reveals progressive cellular buckling (or snaking) arising from the nonlinear interaction between the weakly stable global buckling mode and the strongly stable local buckling mode. The resulting behaviour is highly unstable and when the model is extended to include geometric imperfections it compares excellently with some recently published experiments.     

Flexural buckling of fire exposed aluminium columns

In order to study buckling of fire exposed aluminium columns, a finite element model is developed. The results of this model are verified with experiments. Based on a parametric study with the finite element model, it is concluded that the simple calculation model for flexural buckling of fire exposed aluminium columns in EN 1999-1-2 does not give an accurate prediction of the buckling resistance in fire. This paper proposes an alternative design model, which takes into account the shape of the stress–strain relationships of aluminium alloys at elevated temperatures. Predictions of this model agree well with that of the finite element model.     

Buckling of thin-walled orthotropic cylindrical shells under uniform external pressure.: Application to corrugated tin cans

The general instability of thin-walled orthotropic circular cylindrical shells under external pressure is investigated. The buckling pressure can be predicted with the use of simple analytical formulae derived from an asymptotic analysis of the corresponding eigenvalue problems. The results predicted by these formulae are compared with finite element solutions and the four types of experimental models investigated by Ross (Thin Walled Structures 1996;26(3):179–93). The comparison proved to be accurate enough for practical purpose except for experimental model 1.     

A semi-analytical model for global buckling and postbuckling analysis of stiffened panels

A computational model for global buckling and postbuckling analysis of stiffened panels is derived. The loads considered are biaxial in-plane compression or tension, shear, and lateral pressure. Deflections are assumed in the form of trigonometric function series, and the principle of stationary potential energy is used for deriving the equilibrium equations. Lateral pressure is accounted for by taking the deflection as a combination of a clamped and a simply supported deflection mode. The global buckling model is based on Marguerre’s nonlinear plate theory, by deriving a set of anisotropic stiffness coefficients to account for the plate stiffening. Local buckling is treated in a separate local model developed previously. The anisotropic stiffness coefficients used in the global model are derived from the local analysis. Together, the two models provide a tool for buckling assessment of stiffened panels. Implemented in the computer code PULS, developed at Det Norske Veritas, local and global stresses are combined in an incremental procedure. Ultimate limit state estimates for design are obtained by calculating the stresses at certain critical points, and using the onset of yielding due to membrane stress as the limiting criterion.     

High strength thin-walled rectangular concrete-filled steel tubular slender beam-columns,Part I: Modeling

High strength thin-walled rectangular concrete-filled steel tubular (CFST) slender beam-columns under eccentric loading may undergo local and overall buckling. The modeling of the interaction between local and overall buckling is highly complicated. There is relatively little numerical study on the interaction buckling of high strength thin-walled rectangular CFST slender beam-columns. This paper presents a new numerical model for simulating the nonlinear inelastic behavior of uniaxially loaded high strength thin-walled rectangular CFST slender beam-columns with local buckling effects. The cross-section strengths of CFST beam-columns are modeled using the fiber element method. The progressive local and post-local buckling of thin steel tube walls under stress gradients is simulated by gradually redistributing normal stresses within the steel tube walls. New efficient Müller's method algorithms are developed to iterate the neutral axis depth in the cross-sectional analysis and to adjust the curvature at the columns ends in the axial load–moment interaction strength analysis of a slender beam-column to satisfy equilibrium conditions. Analysis procedures for determining the load–deflection and axial load–moment interaction curves for high strength thin-walled rectangular CFST slender beam-columns incorporating progressive local bucking and initial geometric imperfections are presented. The new numerical model developed is shown to be efficient for predicting axial load–deflection and axial load–moment interaction curves for high strength thin-walled rectangular CFST slender beam-columns. The verification of the numerical model and parametric studies is given in a companion paper.     

方形钢管混凝土钢管壁弹性屈曲分析

对方形钢管混凝土钢管壁局部屈曲行为进行弹性分析,推导钢管壁发生局部屈曲时的屈曲系数、屈曲半波长及临界屈曲应力表达式,并与局部屈曲试验研究成果进行比较,提出更为合理的计算公式,为后续的进一步研究打下基础。     

方形钢管混凝土钢管壁弹性屈曲分析

对方形钢管混凝土钢管壁局部屈曲行为进行弹性分析,推导钢管壁发生局部屈曲时的屈曲系数、屈曲半波长及临界屈曲应力表达式,并与局部屈曲试验研究成果进行比较,提出更为合理的计算公式,为后续的进一步研究打下基础.     

Elasto-plastic buckling of compression members as a coupled instability

In the paper the author shows that plastic deformations can be considered as a bifurcational instability of the atomic lattice. Thus, the plastic buckling of a compression bar is examined like a coupled instability between the general buckling by flexural and the local buckling by plastic deformations. The modified Hunt-Burgan model is studied and an interaction relationship between the elastic buckling load and the plastic collapse load is determined. Although this relationship is obtained in an elastic field, the form corresponds to the Ayrton-Perry relationship for plastic buckling, used by Maquoi and Rondal for the analytical expressions of the ECCS buckling curves. However, one can see that the general imperfections corresponding to Eulerian buckling and local imperfection due to residual stresses have different effects, in opposition to Maquoi-Randal relationships. A new relationship for the simple plastic buckling and coupled plastic buckling are proposed.     

Local buckling analysis of pultruded FRP structural shapes subjected to eccentric compression

An analytical stability model for the local buckling of pultruded fiber reinforced polymer (FRP) structural shapes subjected to eccentric compression is presented. The model is based on considering each of these shapes as being composed of a group of orthotropic plates that are linked together. The differential equations that describe the buckling behavior of each of the plates comprising the shape were defined and solved using the Levy's solution. The presented model was used to conduct a parametric study to investigate the effect of the main parameters governing the local buckling behavior of such shapes.     

Tests and finite element analysis of pin-ended channel columns with inclined simple edge stiffeners

This paper presents an experimental investigation and a finite element analysis on cold-formed channels with inclined simple edge stiffeners compressed between pinned ends. Compression tests of pin-ended channel columns with inclined simple edge stiffeners have not been performed till now. A total of 36 channel specimens including three different cross sections with different edge stiffener inclined angles and column lengths were tested. Detailed measurements of initial geometric imperfections and material properties of the specimens were also conducted before the above tests. Failure modes include local buckling, distortional buckling, flexural buckling and interaction among these buckling modes were observed in tests. The results indicate that inclined angle and loading position significantly affect the ultimate load-carrying capacity and failure mode of specimens. Moreover, a non-linear finite element model was developed and verified against tests. Geometric and material non-linearities were included in the model. Results from the finite element analysis agree well with experimentally ultimate loads and failure modes. However, it should be improved on prediction for certain displacement.     

Behavior of beam web panel under opposite patch loading

Elastic buckling is studied for a panel with various boundary conditions including simple supports, fixed supports and elastic restraints. The panel is subjected to opposite patch loading. Following a review of existing work on the effects of localized compression, also known as patch loading, a study is conducted to take into account the restraints provided by the flanges of the I beam in a realistic manner. This study is based on a finite element model implemented in the CAST3M software. A new equation is proposed to calculate the buckling critical coefficient for a beam web panel considering the rotational stiffness provided by the flanges. The model is then applied to longitudinally stiffened web panels which are subjected to opposite patch loading.A parametric analysis is performed to determine the transition from a global buckling mode to a local buckling mode where the sub-panels on each side of the stiffener behave separately. The numerical results show that the flexural rigidity of the stiffener is the appropriate parameter that governs the buckling mode. From these results, a formula is proposed to calculate the buckling critical coefficient of stiffened web panels.