Nonlinear analyses of thin-walled channel section columns

The paper presents a detailed comparison of nonlinear analyses of thin-walled channel section columns with tests. The columns are analysed as beam-columns having nonlinear constitutive relationships. The constitutive relationships are obtained firstly, by assuming elastic material behaviour and allowing local buckling of both flanges and web, and secondly, by assuming elastic-plastic material behaviour and confining local buckling deformations to the web. Based on the comparison, including theoretical and experimental load-shortening and load-deflection curves, it is concluded that the nonlinear theory generally closely agrees with the tests.The paper also investigates the applicability of combining an elastic nonlinear analysis with a spatial plastic mechanism analysis to describe the structural behaviour both before and after the ultimate load. The question of when this combination can be expected to accurately describe the column behaviour over the full loading range is discussed.A separate section compares theoretical ultimate loads with test strengths. The nonlinear analyses employed in the paper provide ultimate loads which agree with the test strengths to within 2% on average where primary local buckling occurs in the web of the channels, and 11% on average where primary local buckling occurs in the flanges of the channels.     

Identification of factor determining strength under compressive loads of steel members corrected by heating/pressing

By using cruciform columns, factors dominating behavior under compressive loads of steel structural members, whose locally buckled part was corrected by heating/pressing, have been elucidated. They were geometric residual imperfection resulted from incomplete correction and increase of yield stress due to large plastic deformation caused by local buckling and its correction process. For soundness diagnosis of the corrected member, the importance of these factors was investigated based on the results of the numerical simulation. Although the increase of yield stress did not affect the ultimate strength, that changed the deformation mode of the member after the ultimate situation. As the result, it was elucidated that the increase of yield stress was not important in the soundness diagnosis. The residual imperfection affected the buckling and ultimate strength of the corrected member. Rather the size of the region than the absolute value in the out-of-plane direction of the residual imperfection should be controlled as small as possible for ensuring the soundness of the corrected member.     

A numerical imperfection sensitivity study of cold-formed thin-walled tubular steel columns at uniform elevated temperatures

A numerical study is carried out on cold-formed rectangular hollow section columns to evaluate the sensitivity of column failure strength to initial imperfections, stress–strain relationships and to assess the existing design methods. It is shown that the magnitude of initial local buckling imperfection has a significant effect on the ultimate strength of short columns where failure is predominantly local buckling. Its effect on long columns is relatively small. Similarly the magnitude of initial global imperfection has more influence on the ultimate strength of a long column, whose failure is governed by global buckling, than on short columns, where local buckling controls. The shape of the stress–strain relationship of cold-formed steel will have noticeable effect on the column failure load. Current design methods, for high temperatures in ENV1993-1-2 and for ambient temperature in ENV1993-1-3, can provide a valid basis of calculation but modification will be necessary, depending on the exact model of stress–strain relationship of cold-formed steel at elevated temperatures.     

冷弯薄壁槽钢截面柱局部与整体相关屈曲

薄壁钢结构构件局部与整体稳定相关作用问题是一个相当复杂的研究课题,精确地分析必然要涉及到材料和几何非线性,给问题的解决增加了很大的难度。本文提出了一种有效的分析方法,把局部屈曲的薄壁压弯构件等效成若干个局部屈曲的小波段所组成的梁柱模型,通过建立短柱段超屈曲后的M-P-Φ曲线,用有限积分法获得压弯构件的相关屈曲承载能力。进行了冷弯槽钢截面柱的受压试验,试验与理论分析结果符合良好。     

Selection of the initial geometrical imperfection in nonlinear FE analysis of cold-formed steel rack columns

This paper presents three methodologies to predict the load carrying capacity of cold formed steel rack columns via nonlinear finite element analysis (FEA). The column lengths are chosen in the range where the main failure is due to distortional buckling. It is demonstrated that for this range, to derive an accurate prediction of the ultimate load is more complex than for lengths where the main failure is local or global. The nonlinear analysis is carried out introducing an initial geometric imperfection on the upright. The three methodologies presented here allow for different imperfection shapes. The first one uses the critical mode shape (the first buckling mode). The second corresponds to an iterative methodology in which the shape that leads to the lowest ultimate load is used. These two first methodologies use exclusively the finite element method (FEM). The third one combines the finite element analysis with the generalised beam theory (GBT) in order to determine the modal participation of the FEM buckling mode and generate a particular combined geometric imperfection. To validate the predicted loads, the results of the three methodologies are compared with values obtained in experimental tests.     

Design of circular and rectangular hollow section columns

An analytical method for computing the ultimate failure loads of inelastic columns subjected to axial thrust and uniaxial bending moments is presented. As part of the computational procedure, a rapid method of calculating the moment thrust curvature relations is described. The procedure uses the well known Gauss quadrature formulae. With the aid of a mapping device, any quadrilateral part of the cross-section can be considered including any arbitrary residual stress pattern. This enables the analysis of a wide variety of cross-sections, including circular and rectangular hollow sections. The ultimate failure loads are obtained by finding the highest load for which an equilibrium deflected shape can be calculated. A generalised Newton-Raphson method has been adopted for the calculation of the deflected shape of the column. The computer program developed has been used to examine the validity of the newly proposed design curves in ECCS Recommendations as well as he draft BS 5400 : Part 3 applicable to circular and rectangular hollow sections. it is concluded that the ECCS recommendations are safe, but the proposals in BS 5400 : Part 3 are found to be unduly conservative.     

Finite element technique for design of stub columns

This paper presents a finite element analysis on the post-buckling behaviour of thin-walled cold-formed lipped channel and hat-section stub columns under axial compression. The specimens were modelled exactly as that used in the carefully controlled stub column tests conducted by Zaras and Rhodes. Numerical predictions on the load versus end-shortening characteristics and ultimate load capacity of the structures were obtained using a non-linear finite element analysis. The effect of the input parameters such as the degree of prescribed initial imperfection and the size of the element mesh, on the convergence of the solution is examined. The initial imperfection for post-buckling analysis is achieved by making use of the exact linear buckling wave form. Standard design procedures are developed for post-buckling analysis for thin-walled stub columns using finite element method. Results from the design procedure correlate well with experimental data and BS5950 predictions.     

厂房中吊车柱的稳定设计

讨论厂房中变截面柱设计中的屈曲问题。这些柱子的顶端和变截面处通常承受轴向偏心荷载,因此,柱子会产生弯矩。横向荷载产生的附加屈曲也必须考虑。基于这些因素,对几何非线性模型进行屈曲性能分析,并给出平衡微分方程。成功应用了两个柱段的等效(或有效)长度概念。考虑以下参数范围给出了有效长度系数:端部固定,端部与中间轴向荷载比,上、下段长度与惯性矩的比值以及连接处的力学性能。对临界荷载的缺陷敏感性进行研究。讨论不同偏心距和一次性施加横向荷载时柱的承载力变化。结果表明:上、下段可分别按照梁、柱单独处理。以交互方程的形式给出一些设计建议。     

The flexural behaviour of fixed-ended channel section columns

The paper presents a study of the behaviour of thin-walled channel sections compressed between fixed ends. The paper emphasises the differences between the behaviour of fixed-ended and pin-ended channel sections, arising mainly from the fact that the local buckling induces bending of pin-ended channel sections but not of fixed-ended channel sections.As a result of the different effects of local buckling, the strength of a fixed-ended channel section column exceeds that of a pin-ended column of the same effective length. The increase in strength is quantified for a particular channel section, and is studied through the transition from pinned to fixed-end support by analysing columns which are elastically restrained against rotations at the ends.The paper also investigates the imperfection sensitivity and post-ultimate behaviour of fixed-ended channel section columns. It is shown that fixed-ended columns are less sensitive to local imperfections and that they exhibit greater post-ultimate ductility than pin-ended columns.The study is confined to columns whose overall buckling mode is the flexural mode.     

Design of cold-formed steel unequal angle compression members

Cold-formed steel unequal angles are non-symmetric sections. The design procedure of non-symmetric sections subjected to axial compression load could be quite difficult. The unequal angle columns may fail by different buckling modes, such as local, flexural and flexural–torsional buckling as well as interaction of these buckling modes. The purpose of this study is to investigate the behaviour and design of cold-formed steel unequal angle columns. A nonlinear finite element analysis was conducted to investigate the strength and behaviour of unequal angle columns. The measured initial local and overall geometric imperfections as well as the material properties of the angle specimens were included in the finite element model. The finite element analysis was performed on fixed-ended columns for different lengths ranged from stub to long columns. It is demonstrated that the finite element model closely predicted the experimental ultimate loads and the behaviour of cold-formed steel unequal angle columns. Hence, the model was used for an extensive parametric study of cross-section geometries. The column strengths obtained from the parametric study were compared with the design strengths calculated using the North American Specification for cold-formed steel structural members. It is shown that the current design rules are generally unconservative for short and intermediate column lengths for the unequal angles. Therefore, design rules of cold-formed steel unequal angle columns are proposed.     

Mode interaction in thin-walled equal-leg angle columns

This paper presents and discusses numerical results, obtained through Ansys shell finite element analyses, dealing with the post-buckling behaviour (mostly elastic, but also elastic–plastic), ultimate strength and failure mode nature of fixed-ended and pin-ended thin-walled equal-leg angle steel columns with coincident critical flexural-torsional and minor-axis flexural buckling loads (i.e., experiencing very strong coupling effects between these two global instability phenomena) – for comparative purposes, columns that are buckling in pure flexural-torsional and flexural modes are also analysed. Since the main aim of the work is to investigate the column imperfection-sensitivity, the analyses concern otherwise identical columns containing initial geometrical imperfections with different shapes and amplitudes, combining the competing critical buckling modes – particular attention is paid to the sign of the minor-axis flexural component. The results reported consist of column (i) elastic equilibrium paths and the corresponding peak loads and deformed configurations and (ii) elastic–plastic collapse loads and mechanisms, making it possible to assess how they are influenced by the initial geometrical imperfections.     

Nonlinear analysis of concrete-filled thin-walled steel box columns with local buckling effects

Local buckling of steel plates reduces the ultimate loads of concrete-filled thin-walled steel box columns under axial compression. The effects of local buckling have not been considered in advanced analysis methods that lead to the overestimates of the ultimate loads of composite columns and frames. This paper presents a nonlinear fiber element analysis method for predicting the ultimate strengths and behavior of short concrete-filled thin-walled steel box columns with local buckling effects. The fiber element method considers nonlinear constitutive models for confined concrete and structural steel. Effective width formulas for steel plates with geometric imperfections and residual stresses are incorporated in the fiber element analysis program to account for local buckling effects. The progressive local and post-local buckling is simulated by gradually redistributing the normal stresses within the steel plates. Two performance indices are proposed for evaluating the section and ductility performance of concrete-filled steel box columns. The computational technique developed is used to investigate the effects of the width-to-thickness ratios and concrete compressive strengths on the ultimate strength and ductility of concrete-filled steel box columns. It is demonstrated that the nonlinear fiber element method developed predicts well the ultimate loads and behavior of concrete-filled thin-walled steel box columns and can be implemented in advanced analysis programs for the nonlinear analysis of composite frames.     

Experimental investigation concerning lipped channel columns undergoing local–distortional–global buckling mode interaction

This work deals with the structural behaviour and ultimate strength of fixed-ended cold-formed steel lipped channel columns experiencing local–distortional–global buckling mode interaction, due to the closeness between the critical buckling stresses associated with these three buckling mode types. After briefly addressing the column specimen geometry selection and showing a few numerical elastic post-buckling results, the paper reports the results of an experimental investigation involving a set of 12 columns with several cross-section dimensions and yield stresses, which is aimed at (i) providing experimental evidence of the occurrence of the triple mode interaction under consideration and (ii) quantifying its effect on the column deformed configuration evolution and failure load erosion (drop). Various aspects concerning the test set-up and procedure are described in some detail before presenting and discussing the obtained column experimental results, which basically consist of (i) measured cross-section dimensions, lengths and initial displacements (geometrical imperfections), (ii) stress–strain curves and yield stresses determined from tensile coupon tests, (iii) recorded non-linear equilibrium paths (applied load vs. various relevant displacements) and ultimate strength values, and (iv) observed deformed configurations and collapse mechanisms.     

Y形柱稳定性分析研究

Y形柱是机场航站楼屋盖支承体系中常采用的一种构件形式,作为主要承重构件,其稳定性决定了屋盖结构的整体承载能力。利用荷载-位移全过程跟踪技术,考虑几何非线性、材料非线性和初始几何缺陷,研究了在竖向和水平风、地震作用下薄壁Y形柱的稳定性。研究表明:竖向荷载作用下Y形柱以分叉段平面外屈曲为主要失稳模式;Y形柱对初始几何缺陷不敏感;水平风荷载对Y形柱稳定性不起控制作用;竖向和水平荷载作用下,发生面外失稳前柱子分叉处已经进入塑性变形,柱子强度问题先于整体失稳。     

Bifurcation of locally buckled point symmetric columns—Analytical developments

The paper derives the differential equations for the overall bifurcation of locally buckled point-symmetric columns. It is shown that flexural buckling about the minor and major principal axes are coupled in a locally buckled point-symmetric column whereas the buckling modes are uncoupled in a non-locally buckled column. The governing equations are solved for simply supported and fixed-ended columns and applied to Z-sections. Overall bifurcation curves are obtained for five Z-sections with increasingly slender flanges. It is shown that local buckling reduces the elastic torsional buckling load more so than the flexural buckling load for Z-sections, and that local buckling can cause a mode switch from the flexural to the torsional mode in Z-sections with very slender flanges.     

冷弯薄壁钢柱在一致升温情况下的失效分析

采用ANSYS软件对在一致升温情况下的冷弯薄壁短柱进行有限元数值模拟分析。分析结果表明:随着温度的升高,理想短柱的极限承载力的退化速度高于材料极限强度的下降速度,低于钢材弹性模量高温软化速度。研究表明:柱截面的宽厚比影响柱在高温下的极限承载力退化速度;长细比对柱影响较小。通过对比初始局部缺陷柱与理想柱的极限承载力,得到了升温过程中具有初始局部缺陷柱相对于理想轴压柱的极限承载力修正系数曲线。对于求出的柱高温下极限承载力退化系数曲线,给出了冷弯薄壁短柱抗火设计和验算方法。     

Postbuckling analysis of stiffened cylindrical shells under combined external pressure and axial compression

A new approach is extended to investigate the buckling and postbuckling behaviour of perfect and imperfect, stringer and ring stiffened cylindrical shells of finite length subject to combined loading of external pressure and axial compression. The formulations are based on a boundary layer theory which includes the edge effect in the postbuckling analysis of a thin shell. The analysis uses a singular perturbation technique to determine the buckling loads and the postbuckling equilibrium paths. Some interaction curves for perfect and imperfect stiffened cylindrical shells are given and compared well with experimental data. The effects of initial imperfection on the interactive buckling load and postbuckling behaviour of stiffened cylindrical shells have also been discussed.     

On the Direct Strength Method (DSM) design of cold-formed steel columns against distortional failure

This work reports the results of a numerical investigation on the influence of the cross-section geometry and end support conditions on the post-buckling behaviour and Direct Strength Method (DSM) design of cold-formed steel columns buckling and failing in distortional modes. The columns analysed exhibit (i) four end support conditions, (ii) different cross-section shapes, dimensions and lengths, and (iii) several yield stresses. These features were carefully selected in order to ensure, as much as possible, that all columns (i) buckle and fail in “pure” distortional modes and (ii) cover a wide (distortional) slenderness range. The post-buckling equilibrium paths and ultimate loads presented and discussed were obtained through Ansys elastic and elastic-plastic shell finite element analyses. Moreover, the ultimate strength data acquired are used to show that, regardless of the column geometry, the current DSM distortional design curve is not able to predict adequately (safely and accurately) the ultimate loads of columns with other than fixed end supports. The paper also includes a preliminary assessment/proposal of the modifications that must be included into this DSM design curve in order to overcome the above limitation.     

Design of thin-walled plain channel section columns against flexural buckling

The paper presents a comparison of design strengths of thin-walled plain channel section columns, which have slender flanges and may undergo local buckling, with tests and analytical ultimate loads. The design strengths are obtained using the British, American and Australian specifications for cold-formed steel structure. The comparison is shown for fixed-ended and pin-ended columns.

A simple design procedure is presented for plain channel section columns. By introducing a ‘pin-ended stub column strength’, it is possible to calculate accurately the strength of concentrically loaded pin-ended columns without resorting to a beam-column design approach. It is also possible to account for the different effects of local buckling on the strengths of pin-ended and fixed-ended columns.     

高温下轴心受压高强Q690钢柱的局部稳定

现行《建筑钢结构防火技术规范》(GB 51249-2017)未给出火灾下钢结构的局部稳定设计方法,为了获得轴心受压焊接H形高强Q690钢柱高温下的局部稳定性能,考虑钢材高温下力学性能退化、截面高温下焊接残余应力降低及初始几何缺陷,采用ABAQUS软件建立经试验验证的高温局部稳定分析有限元模型,得到焊接H形高强Q690钢...