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.     

Finite strip elastic buckling solutions for thin-walled metal columns with perforation patterns

Approximate finite strip eigen-buckling solutions are introduced for local, distortional, flexural, and flexural-torsional elastic buckling of a thin-walled metal column with perforation patterns. These methods are developed to support a calculation-based strength prediction approach for steel pallet rack columns employing the American Iron and Steel Institute׳s Direct Strength Method, however they are generally posed and could also be useful in structural studies of thin-walled thermal or acoustical members made of steel, aluminum, or other metals. The critical elastic global buckling load including perforations is calculated by reducing the finite strip buckling load of the cross-section without perforations using the weighted average of the net and gross cross-sectional moment of inertia along the length of the member for flexural (Euler) buckling, and for flexural-torsional buckling, using the weighted average of both the torsional warping and St. Venant torsional constants. For local buckling, a Rayleigh–Ritz energy solution leads to a reduced thickness stiffened element equation that simulates the influence of decreased longitudinal and transverse plate bending stiffness caused by perforation patterns. The cross-section with these reduced thicknesses is input into a finite strip analysis program to calculate the critical elastic local buckling load. Local buckling at a perforation is also treated with a net section finite strip analysis. For distortional buckling, a reduced thickness equation is derived for the web of an open cross-section to simulate the reduction in its transverse bending stiffness caused by perforation patterns. The approximate elastic buckling methods are validated with a database of 1282 thin shell finite element eigen-buckling models considering five common pallet rack cross-sections featuring web perforations that include 36 perforation dimension combinations and twelve perforation spacing combinations.     

剖分T型钢压杆的弯扭屈曲试验研究

《钢结构设计规范》(GB50017—2003)提出对单轴对称截面钢压杆的弯扭屈曲需做单独验算。本文通过27根剖分T型钢压杆的试验,并借助有限元分析软件对剖分T型钢压杆的弯扭屈曲进行了几何非线性及材料非线性的有限元分析,分析时考虑了残余应力、几何缺陷的不利影响,在此基础上对规范(GB50017—2003)计算值、本文试验值、有限元计算值做了分析比较。研究结果表明规范(GB50017—2003)中单轴对称截面压杆的弯扭屈曲计算公式是安全可靠的。     

Interaction of local buckling and lateral torsional buckling of T-shaped cantilevering beams

The structural resistance of T-shaped cantilevering beams is governed by combined stability phenomena of lateral torsional buckling and local buckling. The aim of this paper is to show the applicability of the “general method” [1], to the prediction of the combined stability behaviour for single symmetric cross-sections. Since the approach is based on the modal shape and modal edge-moment distribution, it does not distinguish between local and lateral torsional buckling, but considers both phenomena in a single trail. A buckling curve for tapered T-shaped members is suggested and boundaries of applicability investigated.     

Compression tests of longitudinally stiffened plates undergoing distortional buckling

This paper describes a series of compression tests performed on longitudinally stiffened plates fabricated from a mild steel plate of thickness of 4.0 mm with nominal yield stress of 235.0 MPa. The stiffened plates with longitudinal stiffeners of a range of rigidities were tested to failure. The ultimate strengths and performances of the longitudinally stiffened plates in compression undergoing distortional buckling or interaction between local and distortional buckling were investigated experimentally and theoretically. The compression tests indicated that the critical buckling mode was dependent mainly on the rigidity of the longitudinal stiffeners and the width-to-thickness ratio of the sub-panels. A noticeable interaction between local and distortional buckling was also observed for some stiffened plates. A significant post-buckling strength reserve was shown for those sections with distortional buckling and for those sections showing interaction between local and distortional buckling. A limiting strength curve for distortional buckling of longitudinally stiffened plates was studied. Simple design strength formulas in the direct strength method are proposed to account for the distortional buckling and the interaction between local and distortional buckling of longitudinally stiffened plates. The strength curves were compared with the test and FE results conducted. The adequacy of the strength curve was confirmed. A set of conclusions on the buckling behavior of longitudinally stiffened plates was drawn from the experimental studies.     

卷焊圆管、方管轴压杆的脆性屈曲

钢管截面构件受压时为脆性屈曲,可靠指标β与普通压杆理应有所不同,但目前国内有关设计规范(程)对此都没有反映。本文采用弹塑性梁柱理论、数值积分法计算了卷焊圆管、方管截面轴压杆完整的荷载-位移曲线,分析了纵向焊接残余应力、初弯曲、板件宽厚比(径厚比)对钢管压杆屈曲及屈曲后性能的影响,提出了圆管、方管截面轴压杆稳定承载力计算方法。     

A unified energy formulation for the stability analysis of open and closed thin-walled members in the framework of the generalized beam theory

Generalized beam theory—GBT—is among the most adequate tools for the analysis of thin-walled prismatic elements. It enables the analysis of the distortion of the element cross-section and local buckling of individual walls in a unified manner that incorporates the results from classical bending theory. The basis of this theory was developed in the 1960s by Schardt for first and second order elastic behaviour of thin-walled members.Open and closed thin-walled members present the distinctive difference of the unknown shear flow that characterizes the latter. More specifically, shear strains must follow an elasticity law, as opposed to the simplifying assumptions for open cross-sections.It is the purpose of the present paper to present a unified energy formulation for the non-linear analysis of both open and closed sections in the framework of GBT, able to deal with all modal interaction phenomena between local plate behaviour, distortional behaviour and the more classical global (flexural, torsional and flexural–torsional) response. Finally, an application to the stability analysis of a compressed thin-walled column is presented and discussed.     

基于压杆失稳的张拉整体结构极限承载力

张拉整体结构是连续的拉索和不连续的压杆所构成的自应力平衡体系,由一系列张力索和受压杆件组成,具有较少的赘余单元,是极其高效的结构形式.张拉整体结构的压杆是"张力海洋中的孤岛",显然,压杆是不可或缺的组成部分,起着十分重要的作用.压杆的失稳将导致结构的失效.本文根据非线性有限元理论研究讨论基于压杆失稳的张拉整体结构极限承载能力.文中结合平面尺寸为2m×2m的平板型张拉整体结构的模型试验,进行了理论计算与试验结果分析比较,为张拉整体结构应用于实际工程提供一定理论依据.     

Elastic distortional buckling of doubly symmetric steel I-section beams with slender webs

Doubly symmetric steel I-section members with thin webs and stocky flanges have a tendency to buckle in a so-called distortional buckling mode, involving distortion of the web of the I-section in the plane of its cross-section. As this mode is more complicated than the local or global buckling, analytical expressions take empirical forms and vary in between different proposals. This paper has two main objectives. The first objective is to propose a complex finite strip method for distortional buckling analysis of I-section beams with slender webs and check the suitability for such analysis by comparing its accuracy with other methods and the second objective is to propose a simple method for predicting the distortional buckling loads of I-beams. The latter objective is superior to current methods with respect to the weight of the sections.     

Elastic distortional buckling of continuously restrained I-section beam-columns

Doubly symmetric steel I-section members with thin webs and stocky flanges that have their tension flange restrained fully against translational and lateral rotational buckling deformations and elastically against twist rotation during buckling by the flexibility of a continuous restraint have been shown in previous studies to buckle in a so-called restrained distortional buckling (RDB) mode, involving distortion of the web of the I-section in the plane of its cross-section. These bifurcative buckling modes must necessarily occur in the negative moment region of composite T-beams and in half-through girder bridges. The present paper describes the elastic RDB analysis of a simply supported doubly symmetric I-section beam-column subjected to combined uniform axial force and moment gradient. The study adopts an energy method of analysis. The numerical solutions are used to develop a simple method of predicting the elastic RDB loads of beam-columns for use in design.     

Local and distortional buckling of thin-walled short columns

This paper assesses the applicability of Eurocode 3 (EC3) to the prediction of the compression capacity of short fixed-ended columns with different cross-sections. This compression capacity is determined by combining the effective width of plane elements due to local buckling and the effective stiffener thickness due to distortional buckling. Numerical calculations have been carried out in order to compare alternative methods for determining the minimum elastic distortional buckling stress in compression. The method given in EC3 does not correlate as well as Lau and Hancock's method with the results given by Generalized Beam Theory (GBT). The end boundary conditions have a significant influence on the distortional buckling strength, and thus also on the compression capacity of short columns. Selected experimental results from compression tests on C-, Hat- and rack upright-sections are compared with the predictions given by EC3. The procedure in EC3 was modified by determining the distortional buckling stress using GBT, taking into account the actual column length and the end boundary conditions. This lead to better agreement between the experimental results and the theoretical predictions.     

Compression tests of high strength cold-formed steel channels with buckling interaction

This paper describes a series of compression tests conducted on cold-formed simple lipped channels and lipped channels with intermediate stiffeners in the flanges and web fabricated from high strength steel plate of thickness 0.6 and 0.8 mm with the nominal yield stress 560 MPa. A range of lengths of lipped channel sections were tested to failure with both ends of the column fixed with a special capping to prevent local failure of column ends and influence from the shift of centroid during testing. The high strength cold-formed steel channel sections of intermediate lengths generally displayed a significant interaction between local and distortional buckling. A noticeable interaction between local and overall buckling was also observed for the long columns. A significant post-buckling strength reserve was shown for those sections that showed interaction between local and distortional or overall buckling. Simple design strength formulas in the Direct Strength Method for the thin-walled cold-formed steel sections failing in the mixed mode of local and distortional buckling have been studied. The strengths predicted by the strength formulas proposed are compared with the test results for verification.     

高强度钢材工字形截面轴心受压短柱局部稳定试验研究

针对高强度钢材焊接工字形截面轴心受压短柱的局部稳定性能,对9个Q460C工字形截面短柱进行轴心受压试验,分析试件局部屈曲应力、极限应力随板件宽厚比的变化规律,研究翼缘、腹板嵌固系数的取值。此外,将屈曲应力、极限应力试验结果与我国、美国和欧洲钢结构设计规范的相应设计计算结果进行对比分析,研究相应规范对于高强度钢材的适用性。结果表明：翼缘的嵌固系数可取为定值1.0,腹板的嵌固系数不宜取为定值;GB 50017-2003《钢结构设计规范》中关于高强度钢材工字形截面短柱的局部屈曲应力的计算结果是不合理的;AISC 360-05规范的极限应力计算值误差较大,但偏于保守;Eurocode 3规范的极限应力计算值与试验值较为接近,但大部分计算结果较试验值偏大。为此,建议提出新的公式计算工字形截面短柱的局部屈曲应力,而对Eurocode 3规范关于工字形截面短柱的极限应力计算公式进行修正,使其能适用于Q460C高强度钢材。     

Local buckling of structural steel shapes

The objectives of this paper are to (1) provide analytical expressions for the elastic cross-section local buckling stresses, including element interaction, of hot-rolled steel structural shapes, and (2) compare these local buckling results to the assumptions inherent in the local slenderness limits of the US AISC structural steel specification. The cross-section local buckling stress is determined by finite strip analysis (FSA). Local stability of each cross-section in the AISC shapes database (excluding pipes) is considered in axial compression, as well as positive and negative bending about the major and minor geometric axes. Local buckling stresses are converted into plate buckling coefficients (k’s) and simplified expressions are provided for all observed k’s. The new k’s explicitly include elastic web-flange interaction amongst the elements comprising the cross-section. The k values from the FSA are compared to those inherently assumed in the AISC Specification, significant differences are observed.     

Local buckling restraint condition for core plates in buckling restrained braces

Buckling Restrained Braces (BRBs) are commonly used as bracing elements in seismic zones. A key limit state governing BRB design is to prevent flexural buckling. However, when the wall thickness of the steel tube restrainer is relatively small compared to the cross-section of the core plate, the restraint conditions against the local buckling of the core plate can be critical for the stability and strength of the BRB. In this study, cyclic loading tests and numerical analyses of BRBs were carried out using various tube restrainer configurations to investigate the influence of local buckling of the restrainer on BRB strength and ductility.     

Model of local buckling in steel hollow structural elements subjected to biaxial bending

This paper presents a general formulation for the analysis of steel hollow structural beams subjected to biaxial bending. The model has been developed within the framework of lumped damage mechanics. In this approach, the models are based on methods of continuum damage mechanics and the concept of plastic hinge. The model was implemented in a commercial finite element program. In order to calibrate the model, a set of experimental tests were carried out in the Structural Mechanics Laboratory at the Lisandro Alvarado University. The model was evaluated by the numerical simulation of these tests finding a good agreement between the experimental tests and the numerical simulations.     

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.     

有平面外支撑的工形截面圆弧钢拱弹性稳定性能及支撑刚度设计

采用有限元特征值屈曲数值方法,对平面外支撑工形截面圆弧拱弹性屈曲荷载及其刚度取值进行研究。在考虑各种荷载条件与拱脚条件下,研究了支撑刚度,约束类型、数量以及作用位置对钢拱平面外屈曲性能的影响,对于设置等间距侧向支撑的情况,给出了侧向支撑弹性门槛刚度的拟合式,并提出了支撑点间拱段不发生平面外弹性失稳的条件。研究结果表明：平面外支撑越靠近拱顶,其防止平面外失稳的工作效率越高;设置侧向支撑的钢拱屈曲时,随着支撑刚度的增大其屈曲半波数逐渐增加,而仅在拱顶设置扭转约束时始终呈现1个半波失稳模式;从均匀受压圆弧拱的情况获得的等间距侧向支撑门槛刚度,应用在其他组合荷载作用下,同样可以获得足够的支承刚度;当工形截面钢拱的支撑点间拱段长度满足所提出的要求时,钢拱平面外失稳不先于平面内反对称整体失稳。     

Out-of-plane elastic buckling of I-section steel arches braced laterally and design of bracing stiffness

采用有限元特征值屈曲数值方法,对平面外支撑工形截面圆弧拱弹性屈曲荷载及其刚度取值进行研究。在考虑各种荷载条件与拱脚条件下,研究了支撑刚度,约束类型、数量以及作用位置对钢拱平面外屈曲性能的影响,对于设置等间距侧向支撑的情况,给出了侧向支撑弹性门槛刚度的拟合式,并提出了支撑点间拱段不发生平面外弹性失稳的条件。研究结果表明：平面外支撑越靠近拱顶,其防止平面外失稳的工作效率越高;设置侧向支撑的钢拱屈曲时,随着支撑刚度的增大其屈曲半波数逐渐增加,而仅在拱顶设置扭转约束时始终呈现1个半波失稳模式;从均匀受压圆弧拱的情况获得的等间距侧向支撑门槛刚度,应用在其他组合荷载作用下,同样可以获得足够的支承刚度;当工形截面钢拱的支撑点间拱段长度满足所提出的要求时,钢拱平面外失稳不先于平面内反对称整体失稳。     

Finite element modelling of cold-formed steel beams under local buckling or combined local/distortional buckling

The finite element (FE) method is capable of solving the complex interactive buckling of cold-formed steel beams allowing for all important governing features such as geometrical imperfections, material nonlinearity, postbuckling, etc.; this is unlikely to be achieved by analytical methods. In this paper, two series of finite element models for buckling behaviour of laterally-restrained cold-formed steel Z-section beams have been developed with special reference to material and geometrical nonlinearities: one to allow for the possibility of combined local/distortional buckling and the other to allow for local buckling only. Four-point bending tests carried out by previous researchers have been used to verify the FE models. A simplified configuration of the test setup has been modelled in ABAQUS. In the local buckling FE models, distortional buckling has been restricted in the member using translational springs applied to the lip/flange corner of the beam. Predictions of load carrying capacity and deformed shapes exhibit excellent agreement with both the results from the more extensive models and laboratory tests. Further papers will exploit the developed FE models to investigate the different forms of buckling that occur in laterally-restrained cold-formed steel beams i.e. local, distortional and combined local/distortional.