Non-linear analysis of perforated steel plates subjected to localised symmetrical load

Although the literature contains a number of studies which have been developed to describe the non-linear behaviour of ordinary plates, few works are available on perforated plates, and studies on non-linear behaviour of perforated plates under localised symmetrical load are not studied in depth. The aim of this paper is to provide some insights into the elasto-plastic behaviour of plate girder web panels with circular holes under localised symmetrical load.Numerical analyses of square and rectangular perforated plates with centred and eccentric holes were developed. Results provide new insights into post-critical mechanisms in perforated plates subjected to localised loads when the length of the symmetrical compressive load, hole diameter and steel yield limit vary. An increase in the critical slenderness of the plate (a value at which transition from elastic to plastic collapse occurs) and a corresponding reduction in the elastic critical load occur when the dimensions of the hole increase. A further increase in the critical slenderness occurs when the length of the localised load is reduced. High-performance steel may be subject to buckling with a lower possibility of post-critical mechanisms: a reduction in critical slenderness occurs when the steel grade increases. Lastly, numerical analyses of slender and thick perforated plates were developed and their results compared.     

钢桥塔内部通行孔选型及有限元分析

钢桥塔内部通行孔对受压壁板力学性能产生不利影响。基于有限元分析,研究不同孔洞形状和孔洞大小对单轴受压开孔板弹性应力分布、弹性屈曲和弹塑性屈曲三方面性能的影响。结果表明:除圆孔外的其他各种孔型板,孔洞形状对开孔板弹性屈曲应力和弹塑性极限强度影响不大,但其对应力集中系数影响较大,其中,圆角矩形孔、长圆形孔和椭圆形孔板的应力集中系数较低。实际情况中,圆角矩形孔和长圆形孔板是钢桥塔内部通行孔的首选。但当孔径较大时,应采取孔洞补强措施来保证大孔径板件的力学性能满足设计要求。     

Elastic stability of uniformly compressed plates perforated in triangular patterns

Critical elastic buckling load of uniformly compressed isotropic plates perforated in equilateral triangular patterns was investigated using FEM. Stiffened and unstiffened square and rectangular elements with wide ranges of hole diameter-to-spacing ratio and plate slenderness were studied. The effect of perforations on the critical elastic buckling load was determined. Design formulas for predicting critical elastic buckling stress based on reduction coefficient approach and equivalent thickness approach were developed using multiple nonlinear regression analysis of FEM results. The obtained critical elastic buckling stress reductions and developed formulas were verified by comparison with results available in literature and with an extensive database of FEM results.     

Effect of aspect ratio on the elastic buckling of uniaxially loaded plates with eccentric holes

The Finite Element Method (FEM) has been employed to determine the elastic buckling load of uniaxially loaded rectangular perforated plates with length a and width b. Plates with simply supported edges in the out-of-plane direction and subjected to uniaxial end compression in their longitudinal direction are considered. Integer plate aspect ratios, a/b=1, 2, 3 and 4, have been chosen to assess the effect of aspect ratio on the plate buckling load. Two perforation shapes of different sizes are considered; circular, and rectangular with curved corners. The rectangular perforation is oriented such that either its long or its short side is parallel to the longitudinal direction of the plate. The center of perforation was chosen at different locations of the plate. The study shows that the buckling load of a rectangular perforated plate that could be divided into equal square panels is not the same as that of the square panel that contains the perforation when treated as a separate square plate. For rectangular plates, the study recommends not to have the center of a circular hole placed in a critical zone defined by the end half of the outer square panel, to try always to put the hole in an interior panel of the plate, and to have the distance between the edge of a circular hole and the nearest unloaded edge of the plate not less than 0.1b. The study concludes also that the use of a rectangular hole, with curved corners, with its short dimension positioned along the longitudinal direction of the plate is a better option than using a circular hole, from the plate stability point of view.     

Influence of central cracks on buckling and post-buckling behaviour of shear panels

It is generally accepted that cracks degrade the load bearing capacity of thin plates. The aim of the present paper is to investigate the influence of central cracks on the residual strength and stiffness degradation of shear panels using numerical finite element analysis. Various geometrical and mechanical characteristics of cracked panels such as the crack length, crack angle of inclination, panel aspect ratio, slenderness of panel, boundary conditions, Poisson's ratio, and Young's modulus are considered in the analyses. It is shown that the length and the angle of cracks may change the buckling behaviour of shear panels, and their combinational effects can result in substantial degradation.     

Elastic buckling of perforated plates under shear

Finite element studies aimed at computing the buckling coefficient for plates containing cut-outs and subjected to shear are reported. The cases considered are:

1. 1. Square and rectangular plates with central circular cut-outs.

2. 2. Square plates with centrally placed rectangular cut-outs.

3. 3. Square plates with eccentrically placed circular cut-outs.

4. 4. Square plates with reinforced circular cut-outs.

5. 5. Square plates with reinforced rectangular cut-outs.

Simply supported plates as well as clamped plates have been studied and approximate formulae for the use of designers have been suggested for the practical cases where the hole dimension is generally not greater than half the width of the plate.     

Strengthening of perforated plates under uniaxial compression: Buckling analysis

This paper focuses on the cutout-strengthening of perforated steel plates subjected to uniaxial compressive loads. The square plates considered each has a centrally placed circular hole and four simply supported edges in the out-of-plane direction. Four types of stiffeners named ringed stiffener (RS), flat stiffener (FS), longitudinal stiffener (LS) and transverse stiffener (TS) are mainly discussed. The finite element method (FEM) has been employed to analyse the elastic and elasto-plastic buckling behaviors of strengthened and unstrengthened perforated plates. The results show that the strengthened perforated plates have higher buckling strengths than those of the unstrengthened ones, while the elevations in elastic buckling stress and elasto-plastic ultimate strength are closely related to stiffener types (i.e., RS, FS, LS and TS) as well as plate geometric parameters (i.e., a plate slenderness ratio and a hole diameter ratio). Furthermore, comparisons of strengthening efficiency considering the variations of buckling stress with stiffener weight are carried out, and recommendations on the most efficient cutout-strengthening methods for the uniaxially compressed perforated square plates with centric circular holes are proposed.     

纯压圆弧形钢管桁架拱平面内稳定性能及设计方法

目前针对钢管桁架拱平面内稳定性能及承载力的研究较少,缺少相应的设计方法。提出了钢管桁架拱截面剪切刚度表达式,考虑剪切变形的影响推导了纯压两铰圆弧桁架拱屈曲荷载的简化计算公式以及换算长细比表达式。基于有限元方法,全面分析了截面高宽比、矢跨比、腹杆夹角及腹杆截面尺寸等不同参数对平面桁架拱和空间桁架拱弹性屈曲性能的影响,结果表明采用简化公式与有限元分析结果吻合良好。借鉴实腹拱和格构柱的稳定设计方法,采用大挠度弹塑性有限元法系统研究了平面及空间纯压桁架拱的相关稳定承载力,发现节间弦杆长细比与桁架拱整体长细比的比值是衡量局部稳定对整体稳定影响的关键参数,在此基础上提炼出纯压桁架拱的相关作用影响系数,并拟合得到了纯压桁架拱的稳定设计曲线,从而为一般荷载作用下压弯桁架拱的稳定承载力的设计奠定了基础。     

Numerical analysis of slender elliptical concrete filled columns under axial compression

This paper presents a non-linear finite element model (FEM) used to predict the behaviour of slender concrete filled steel tubular (CFST) columns with elliptical hollow sections subjected to axial compression. The accuracy of the FEM was validated by comparing the numerical prediction against experimental observation of eighteen elliptical CFST columns which carefully chosen to represent typical sectional sizes and member slenderness. The adaptability to apply the current design rules provided in Eurocode 4 for circular and rectangular CFST columns to elliptical CFST columns were discussed. A parametric study is carried out with various section sizes, lengths and concrete strength in order to cover a wider range of member cross-sections and slenderness which is currently used in practices to examine the important structural behaviour and design parameters, such as column imperfection, non-dimension slenderness and buckling reduction factor, etc. It is concluded that the design rules given in Eurocode 4 for circular and rectangular CFST columns may be adopted to calculate the axial buckling load of elliptical CFST columns although using the imperfection of length/300 specified in the Eurocode 4 might be over-conservative for elliptical CFST columns with lower non-dimensional slenderness.     

Buckling of plates with a hole under tension

An FEM analysis is made on the elastic buckling of plates, each of which has a hole and is subjected to tensile loading.In a general way, no attention is paid to the buckling of plates if they are subjected to a tensile load. However, when a plate has a hole, compressive stresses appear near the hole under a tensile load, and the stress may cause local buckling of the plate.In this paper, stress distributions and buckling behaviours of such plates under tension are studied. Aspect ratios, shapes of holes and so on, are adopted as parameters.Through the analysis, variations of buckling coefficients and buckling modes against aspect ratios are obtained. The effects of the hole shapes on the buckling strength are also discussed.     

铝合金方形和矩形管截面开孔梁受弯性能试验

对铝合金方形和矩形管截面开孔试件进行了受弯性能试验研究,试验共计13个试件,分别进行了三点弯曲试验和四点弯曲试验;试验材料分别为国产6061-T6和6063-T5铝合金挤压型材,主要对试件的破坏模式、抗弯承载力、弯矩 曲率曲线和应变分布曲线进行了研究,探讨了铝合金方形和矩形管截面梁在2种受弯状态下孔洞参数对受弯性能的影响。结果表明:试验中所有试件都发生了受压局部屈曲破坏;对于方形管截面梁,在2种受弯状态下,当孔洞的径高比为0.3时,孔洞对试件的抗弯承载力影响较小,当孔洞的径高比为0.6时,孔洞对试件的抗弯承载力有很大程度的影响;对于矩形管截面梁,在三点弯曲状态下,随着孔洞数目的增加,试件的抗弯承载力有很大程度的降低,在四点弯曲状态下,开孔数目对抗弯承载力影响较小;方形管截面梁在2种弯曲状态下的承载力相差较小,而矩形管截面梁在三点弯曲状态下的抗弯承载力比四点弯曲状态下的抗弯承载力有明显提高。     

Elastic buckling of uniaxially loaded skew plates containing openings

The paper is concerned with elastic buckling behavior of uniaxially loaded skew plates with openings. Simply supported and clamped plates subject to uniaxial compression in the longitudinal direction are studied. Two different shapes of openings, circular and skew of different sizes, are considered. The finite element software package ABAQUS has been employed to analyze the plates. Effects of parameters such as skew angle, size, shape and position of openings and aspect ratio of the plates are examined. Results are presented in the form of plots showing the variation of buckling coefficient against the parameters studied.     

Slenderness classification of unstiffened metal plates under shear loading

Buckling behavior of slender and compact carbon steel, stainless steel and aluminum plates under the action of in-plane shear is investigated. Unstiffened shear plates with respect to their slenderness parameter and buckling behavior are qualitatively and quantitatively divided into slender, moderate and stocky categories. Accordingly, slender plates have a low buckling capacity, followed by a large postbuckling reserve. Their ultimate load coincides with the formation of inclined yield bands. Stocky plates yield before buckling. They have some post-yield capacity, buckle plastically and their ultimate and critical loads are equivalent. Moderate plates have concurrent material yielding and geometrical buckling followed by a sudden loss of stiffness. They neither have post-yield nor postbuckling reserves. Since the proportional limit stress is observed to be the cause of bifurcation in stocky plates, it is suggested that in dealing with the slenderness parameter, the yield stress be replaced by the proportional limit stress.     

全加劲两侧开缝钢板剪力墙弹性屈曲研究

采用有限元方法对全加劲两侧开缝钢板剪力墙在面内水平荷载作用下的弹性屈曲临界荷载、屈曲模态进行了研究。对影响其弹性屈曲性能的参数进行了分析,包括两侧和中部加劲肋与墙板的刚度比、两侧和中部加劲肋宽厚比以及墙板高厚比和边长比。给出了全加劲两侧开缝钢板剪力墙加劲肋的弹性屈曲设计参考公式,为开缝钢板剪力墙的应用提供依据。     

Stiffened steel plates under uniaxial compression

The stability of steel plates stiffened with tee-shape sections under uniaxial compression and combined uniaxial compression and bending was investigated using a finite element model. The emphasis of the work presented in this paper was to find the parameters that uniquely describe the strength and behaviour of stiffened steel plates. A finite element model, validated using the results of tests on full-size stiffened plate panels, was used to investigate the scale effect for five dimensionless parameters. The parameters investigated were: the transverse slenderness of the plate, the slenderness of the web and flange of the stiffener, the ratio of torsional slenderness of the stiffener to the transverse slenderness of the plate, and the stiffener-to-plate area ratio. Average magnitude residual stresses and initial imperfections were assumed for this study.A parametric study covering a wide range of dimensionless parameters indicated that stiffened steel plates do not fail by stiffener tripping unless a bending moment is applied to create flexural compressive stresses in the stiffener. Although plate buckling and overall buckling were found to lead to a very stable post-buckling behaviour, the interaction between these two buckling modes was found to give rise to a sudden loss of capacity following initial plate buckling. The plate transverse slenderness, the stiffener slenderness-to-plate slenderness ratio, and the stiffener-to-plate area ratio were found to have a significant effect on this behaviour.A comparison of the numerical analysis results with API and DnV design guidelines indicates that the guidelines predict stiffened steel plate capacity with various degrees of success, depending on the governing mode of failure. Neither guidelines address the potential interaction-buckling phenomenon.     

工形截面钢拱考虑腹板局部屈曲的承载力设计方法研究

把工形截面钢拱的腹板做高做薄是提高其承载力的有效方法之一。该文采用大挠度弹塑性壳单元模型,研究焊接工形截面两铰圆弧钢拱在允许腹板局部屈曲条件下的平面内稳定承载力及其设计方法,其中考虑钢拱几何初始缺陷和残余应力的影响。首先,对钢拱在均匀轴压力作用下的承载力和破坏机理进行有限元数值分析和参数研究,考察拱截面腹板高厚比、钢拱几何长细比、截面翼缘腹板板厚比和翼缘宽厚比对钢拱稳定系数的影响。在设定的钢拱翼缘宽厚比范围内,基于大量的钢拱承载力数值分析结果,提炼出腹板高厚比和翼缘腹板板厚比组合效应的等效正则化腹板高厚比,进而获得钢拱稳定系数与等效正则化腹板高厚比以及钢拱正则化长细比之间关系的计算公式。其次,研究压弯组合作用下钢拱腹板高厚比变化对钢拱整体稳定承载力的影响,揭示钢拱压弯组合作用下的破坏机理及稳定承载力。最后通过对大量钢拱算例进行不同压弯组合工况下的极限承载力分析,提出了钢拱在一般荷载或组合荷载作用下承载力设计的计算公式。     

两边连接交叉加劲钢板剪力墙弹性屈曲分析

采用ANSYS有限元软件对两边连接交叉加劲钢板剪力墙进行了弹性屈曲分析,重点研究了加劲肋与墙板的刚度比、墙板高厚比、边长比以及加劲肋宽厚比对弹性屈曲系数的影响,并将分析结果与十字加劲板进行了比较.研究表明,交叉加劲肋能够显著提高钢板剪力墙的弹性屈曲荷载,其远大于十字加劲肋;随着墙板边长比和高厚比的增大,屈曲系数趋于减小;而较小的加劲肋宽厚比能使墙板获得较大的屈曲系数;最后给出了两边连接交叉加劲板弹性屈曲系数的计算公式.     

Imperfections in steel girder webs with and without perforations under patch loading

In this paper, the problem of stability of web plates with imperfections, subjected to patch load, is studied. The aim is to give some insights about the best way to take into account real imperfections in non-linear stability analyses of plates with and without perforations. In this context, the study is developed on the basis of the measured imperfections or numerically deriving the deformed model (theoretical imperfections). The influence of the patch load length, out-of-plane imperfection amplitude, dimension and position of the hole on stability behaviour and buckling strength are studied comparing some theoretical deformed configurations corresponding to different modal shapes. The results obtained with a three-dimensional model of the whole real beam with stiffeners, with experimentally measured imperfections, and each corresponding single web panel are compared and discussed obtaining some insights about the accuracy of the simplified (and conservative) model of the single panel.The main insights of this work are as follows. The deformed shape, corresponding to the first buckling mode, can be assumed as the initial configuration of the panels with and without holes to study post-critical behaviour until ultimate condition. The shape of the imperfection does not severely change the critical buckling stress. A longer patch load reduces the ultimate stress in the panel. An initial imperfection amplitude of less than 1% of the height of the panel does not reduce the ultimate load by more than about 5%.     

Buckling of centerline-stiffened plates subjected to uniaxial eccentric compression

A solution for the elastic buckling of flat rectangular plates with centerline boundary conditions subjected to non-uniform in-plane axial compression is presented. The loaded edges are simply supported, the non-loaded edges are free, and the centerline is simply supported with a variable rotational stiffness. The Galerkin method is used to establish an eigenvalue problem and a series solution for plate buckling coefficients is obtained by using combined trigonometric and polynomial functions that satisfy the boundary conditions. It is demonstrated that the formulation approaches the classical solution of a plate with a clamped edge as the variable rotational stiffness is increased. The variation of buckling coefficient with aspect ratio is presented for various stress gradient ratios. The coupling between plate aspect ratio, centerline rotational stiffness, and gradient of applied compressive stress is illustrated and discussed. The solution is applicable to stiffened plates and I-shaped beams that are subjected to biaxial bending or combined flexure and torsion, and is important to estimate the reduction in elastic buckling capacity due to stress gradient.     

Flexural behaviour of stainless steel oval hollow sections

Structural hollow sections are predominantly square, rectangular or circular in profile. While square and circular hollow sections are often the most effective in resisting axial loads, rectangular hollow sections, with greater stiffness about one principal axis than the other, are generally more suitable in bending. Oval or elliptical hollow sections (EHS) combine the aesthetic external profile of circular hollow sections with the suitability for resisting flexure of rectangular sections, whilst also retaining the inherent torsional stiffness offered by all tubular sections. This paper examines the structural response of recently introduced stainless steel oval hollow sections (OHS) in bending and presents design recommendations. In-plane bending tests in the three-point configuration about both the major and minor axes were conducted. All tested specimens were cold-formed from Grade 1.4401 stainless steel and had an aspect ratio of approximately 1.5. The full moment-rotation responses of the specimens were recorded and have been presented herein. The tests were replicated numerically by means of non-linear finite element (FE) analysis and parametric studies were performed to investigate the influence of key parameters, such as the aspect ratio and the cross-section slenderness, on the flexural response. Based on both the experimental and numerical results, structural design recommendations for stainless steel OHS in bending in accordance with Eurocode 3: Part 1.4 have been made.