Experimental and Numerical Study on Buckling Behavior of a Rigidly Stiffened Plate with Tee Ribs

In the bridge structures, stiffened plates are usually designed as rigidly stiffened when the orthotropic steel box girder is used as the main load-bearing structure. Therefore, the buckling mode of stiffened plates is plate buckling which occurs in subpanel supported by stiffeners. The orthotropic steel box girder is used as the main girder for Egongyan Rail Special Bridge, which is a self-anchored suspension bridge. Plates of the steel girder are rigidly stiffened with unequal spacing open ribs, and the most slender stiffened plate is the mid web stiffened with Tee ribs. In order to ensure the safety of the bridge, the buckling behavior of the web and orthotropic steel box girder under axial compression, including ultimate strength, post-buckling behavior and failure modes, should be clearly investigated by experimental and numerical methods. The design, loading and testing methods of the 1:4 scale model of the orthotropic steel box girder are introduced in detail firstly. The orthotropic steel box girder and the stiffened web finite element (FE) models are validated by the test results, and the effects of residual stress and the magnitude of geometric imperfections are discussed roughly. Based on the validated web FE model, a detailed parametric study is performed to systematically investigate the effects of residual stress and geometric imperfections on buckling behavior of the web. The effect of shapes of geometric imperfections discussed is highlighted. Through tracing stress states, the failure modes of stiffened plate are in agreement with the experimental phenomenon to some extent. Results show that shapes of geometric imperfections have significantly influenced post-buckling behavior and failure modes of the web, but slightly affected the ultimate strength. It is advised that residual stress and geometric imperfections should be controlled to make full use of excellent performance of steel materials.     

具有缺陷和应力限值的预应力钢支撑柱屈曲性能

通过预应力支撑加固的钢柱,一般增加了轴向抗压强度。过去,十分强调获得更高的临界屈曲荷载,然而,后屈曲性能是结构安全性和功能的重要保证。对具有几何缺陷和与可能的材料失效相关的应力极限的支撑柱的屈曲性能进行检验。考虑有几何缺陷支撑柱的屈曲性能,采用Rayleigh-Ritz方法对几何非线性模型公式化,并通过有限元方法进行验证。研究显示：对于承受最高临界荷载的预应力状态,系统对有几何缺陷的柱更为敏感。对某一给定形状结构,实际的最大荷载似乎随着预应力的增加而增加。研究建议：最佳的预应力取值应该大于基于传统方法的线性分析的结果。     

Buckling behaviour of a liquid storage tank

The buckling behaviour of a liquid storage tank built up of circular cylindrical shell-sections with different thicknesses is investigated. In any partially filled state the critical vacuum for bifurcation is determined taking into account the weight of the structure. For a storage tank with small geometrical imperfections the behaviour is analysed asymptotically using Koiter's general post-buckling theory. The initial post-buckling analysis based on the assumption of linear pre-buckling behaviour indicates that the storage tank is imperfection-sensitive in any partially filled state. Finally, bifurcation analyses accounting for nonlinear pre-buckling show that the assumption of linear pre-buckling is a good approximation even at high liquid levels.     

Behaviour of thin steel plate shear walls regarding frame members

Steel plate shear walls in buildings are known to be an effective and strong means for resisting lateral forces. The view of some structural designers is to use heavy stiffeners to reinforce and increase the buckling capacity of shear walls; whereas, if the walls are left unstiffened and allowed to buckle, their energy absorption will increase significantly due to the post-buckling capacity. On the other hand, the optimal design of thin steel plate shear walls (TSPSWs), which are categorized as thin-walled structures, involves the proper prediction of their buckling strength. In turn, this prediction is a function of the status of their assumed boundary conditions. Many design rules conservatively suggest simply supported boundary conditions for elastic member restraints. In this paper, the effects of surrounding members (i.e. beams and columns) on the overall behaviour of TSPSWs are studied. The results show that, unlike the present view, the flexural stiffness of surrounding members has no significant effects, either on elastic shear buckling or on the post-buckling behaviour of shear walls. The torsional rigidity has a significant effect only on the elastic buckling load, and the extensional stiffness slightly affects the post-buckling capacity.     

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.     

Buckling behaviour of prestressed steel stayed columns with imperfections and stress limitation

A steel column that is reinforced by prestressed stays, generally has an increased strength in axial compression. In the past, greater emphasis was placed on obtaining a higher critical buckling load. However, detailed knowledge of the post-buckling behaviour is important to ensure the safety and efficiency of the structure. The current work examines the buckling behaviour of a stayed column with geometrical imperfections, and stress limitation relating to possible material failure. A geometrically nonlinear model accounting for imperfect buckling behaviour of a stayed column was formulated using the Rayleigh–Ritz method, and then validated, using the finite element method. It is shown from these studies that the system tends to be most sensitive to imperfections at a prestress level that yields the highest critical load, and that the real maximum load capacity seems to increase as the prestress increases with a given configuration. The findings suggest that the optimal prestress should be greater than that found from using the previous convention that was based on linear analysis.     

Buckling and strength characteristics of some CFRP stiffened curved panels

This paper describes the initial and post-buckling behaviour of CFRP stringer-stiffened curved panels. The panels are of 500-mm radius, 2-mm thickness and have either three or four blade stringers. Initial buckling loads were calculated using the finite strip code VIPASA within the design optimisation program PASCO. An unstiffened, externally supported panel is also considered.Stringer stiffening gave higher buckling loads than external supports. The initial buckling behaviour was influenced by geometric imperfections, and methods of modelling these with PASCO are discussed. The imperfections caused scatter in buckling load, but there was minimal scatter in failure load, despite the presence of impact damage in some cases. The failure loads were about 50% higher than the buckling loads.     

Buckling and cyclic inelastic analysis of steel tubular beam-columns

An numerical procedure combining the Finite Segment Method (FSM) with the Influence Coefficient Method (ICM) is presented for estimating the inelastic behaviour of steel tubular beam-columns under post-buckling and cyclic loading conditions. This combination takes the advantages of FSM and ICM, overcoming the difficulties encountered in numerical analysis at the stages of buckling and post-buckling. The effects of initial imperfections, residual stresses, and end-restraints are taken into account. Generalized stress-strain relationships are used in the analysis. Complete results obtained for a pin-ended beam-column are discussed and compared with available theoretical results.     

Buckling and post-buckling behaviour of rectangular plates under linearly varying compression and shear: part 1 — Theoretical analysis

The buckling and post-buckling behaviour of thin, rectangular, simply supported flat plates subjected to end compression which varies linearly in the direction of loading and simultaneously loaded in shear is the subject of this paper. Part 1 presents a theoretical analysis of the problem. In this analysis the Rayleigh-Ritz energy method is utilised, and numerical minimisation of the total potential energy is applied to obtain the magnitude of the parameters of the assumed deflection functions. These are then used to define and describe other post-buckling characteristics of the plate. A simplified imperfection analysis is used to examine certain cases. The wide range of results presented covers many aspects of plate post-buckling behaviour.     

Plastic buckling of complete toroidal shells of elliptical cross-section subjected to internal pressure

The plastic bifurcation buckling pressures of 60 internally-pressurised, perfect, complete toroidal shells of elliptical cross-section are given in the present paper, assuming elastic, perfectly plastic, material behaviour. The shell buckling programs employed in the computations were BOSOR 5 and INCA. Denoting the major-to-minor axis ratio by k, the numerical results show that the plastic buckling pressures are considerably lower than their elastic counterparts in the range 1.25≤k≤1.5 and are approximately equal to them for k=2.5. A limited study of the effects of non-axisymmetric initial geometric imperfections on the buckling pressures of the shells was also carried out using the INCA code. For the four cases studied the post-buckling behaviour was stable. This means that designers can use the buckling pressures given herein for perfect shells as a basis for their initial designs.     

冷弯薄壁卷边槽钢轴压构件畸变与局部相关屈曲试验研究

对卷边尺寸不同的两类腹板中间设置加劲卷边槽形截面,共18个冷弯薄壁型钢固支轴压试件进行畸变屈曲与局部屈曲相关作用的静力试验研究。得到试件的屈曲模式、相关屈曲行为、破坏模式以及极限荷载。试验结果表明：畸变屈曲与局部屈曲的耦合相关对试件的变形和极限荷载有不利作用;畸变屈曲与局部屈曲的耦合相关作用存有较大的屈曲后承载力;畸变屈曲与局部屈曲的耦合相关顺序,即畸变屈曲 局部屈曲耦合相关、局部屈曲 畸变屈曲耦合相关,对试件的变形、非线性平衡路径、破坏模式以及极限荷载的影响有所不同。采用ABAQUS有限元软件对试件进行模拟分析,计算结果与试验结果吻合良好。     

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.     

Effects of localized imperfections on compressive strength of long rectangular plates

Results are presented of a numerical study of the buckling and post-buckling behaviour of long rectangular plates under uniaxial longitudinal compression. Consideration is given to various forms of imperfection with particular reference to the influence of localized initial deformation on plate stiffness and strength.     

The effects of local buckling and material yielding on the axial stiffness and failure of uniformly compressed I-section and box-section struts

The behaviour of thin-walled compression members is known to be significantly influenced by the effects of local buckling. Thin-walled sections lose axial compressive stiffness and the compressive carrying capability of the members can be considerably reduced as a result of the effects of local buckling. Finite element simulation is employed in this paper to examine the post-buckled response of thin-walled I-section and box-section struts, giving due consideration to the influence of geometric imperfections and to elasto-plastic material behaviour. A detailed account of the growth and redistribution of stresses after local buckling as well as the initiation of yielding and yield propagation throughout loading is given in the paper. The influence of different in-plane displacement boundary conditions imposed in the simulations at the section plate junctions is also detailed in the paper as well as the effect of yielding on the post-buckled stiffness and failure of the sections. It is shown that the effects of geometrical imperfections are most prominent for strut designs with near simultaneous buckling and yielding and that the ultimate failure and unloading of strut designs, in general, is synonymous with the development of yielding at the section junctions along the full length of the struts and through to the middle surface of the section walls.     

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.     

Strength of biaxially loaded orthotropic plates

An approximate and simple method for rectangular orthotropic plates, loaded biaxially along two mutually perpendicular directions is presented. The theory is based on the energy method and it is free from difficult calculations such as those encountered when large deflection theory is used. Effects of initial imperfections are taken into account. The number and lengths of half-waves are assumed to be the same in the post-buckling stage as at incipient buckling. The finite buckled shape in the post-buckling stage is taken to be the same as that during incipient buckling. The Von Mises yield criterion is employed to determine the upper bound solution of the plate. Interaction curves for square plates subjected to longitudinal and transverse stresses, applicable to three different boundary conditions, four edges simply supported or four edges clamped or two opposite edges clamped with the other two edges simply supported, are presented in a non-dimensional form. Results for plates having different values of plate slenderness (b/t) and flexural rigidity ratios, D₂/D₁ are given.     

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.     

铝合金工形截面短柱轴压局部稳定试验研究

为研究铝合金工形截面轴压构件的局部稳定性能,对15根工程中常用大截面铝合金6061-T6和6063-T5轴压短柱试件进行试验研究,并对12组48个材性试样进行拉伸试验。研究了材料的力学性能、试件的局部几何初始缺陷、变形性能、局部屈曲荷载、轴压承载力等,并将试验结果与各国规范中设计方法计算结果进行对比。试验结果表明：铝合金6061-T6强度与普通钢材相当,但延性较差;铝合金挤压型材的局部几何初始缺陷很小,远小于规范中给定数值;板件宽厚比越大,局部屈曲发生越早,破坏时材料的强度越得不到充分发挥,但是局部屈曲后材料强度仍有较大的提高;翼缘和腹板之间存在相互作用;中国规范、欧洲规范、美国规范和澳大利亚/新西兰规范均低估了试件的轴压承载力,其中美国规范计算结果与试验结果最接近。因此,对于板件宽厚比大的试件,应充分利用其屈曲后强度,各国规范得到的承载力计算结果均较保守。     

Nonlinear buckling of microfabricated thin annular plates

Annular plate structures are commonly used in MEMS devices, particularly in pumps and valves. In MEMS applications, large nonlinear deflections are routinely achieved. In this paper, the nonlinear buckling of a thin elastic annular plate under a compressive radial force acting in the plane of the plate is considered. Although the critical loads at which buckling starts can be determined by solving a linear eigenvalue problem, the large deflection behavior of a buckled plate beyond the critical loads can be described by the nonlinear theory proposed by von Kármán. The buckling loads of the annular plate for various boundary conditions are calculated and the post-buckling behaviors are examined. Interestingly, the buckling of an annular plate exhibits a supercritical pitchfork bifurcation. Thus, the post-buckling behavior is stable and will not collapse catastrophically. Several design implications for microfabricated structures, in particular microvalves, are also given.     

A finite strip method for the elastic—plastic large dlisplacement analysis of thin-walled and cold-formed steel sections

A large deflection elastic—plastic analysis has been developed using the finite strip method of structural analysis to determine the non-linear local buckling behaviour of thin-walled and cold-formed sections in compression. The analysis accounts for plate geometric imperfections, the variation of yield stress around a section, the stress—strain characteristics of the material forming the section and complex patterns of residual stress produced by the cold-forming process.

The analysis is verified against reliable solutions for the non-linear buckling behaviour of plates and plate assemblies in axial compression and the non-linear overall buckling behaviour of a strut. The analysis is further compared with the results of plates with a rounded stress—strain curve typical of cold-formed steel and aluminium.