Calculating the global buckling resistance of thin-walled steel members with uniform and non-uniform elevated temperatures under axial compression

This paper develops a method, based on the Direct Strength Method (DSM) global buckling curve, to calculate the global buckling ultimate strength of cold-formed thin-walled (CF-TW) steel members under uniform and non-uniform elevated temperatures. The assessment is carried out by checking the DSM curve-based results with numerical simulation results using the general finite element software ABAQUS. The numerical model has been validated against a series of ambient temperature and fire tests on panels made of two different lipped channel sections tested to their ultimate load carrying capacities at ambient temperature or to their fire resistance at different load levels. The validated numerical model has been used to generate a database of numerical results of load carry capacity of CF-TW members with different uniform and non-uniform temperature distributions in the cross-sections under different boundary and loading conditions and with different dimensions. It is concluded that the DSM global buckling column curve is directly applicable for uniform temperature but a simple modification is required for non-uniform temperature distributions.     

Elastic lateral buckling of cantilever Litesteel Beams under transverse loading

The LiteSteel Beam (LSB) is a new hollow flange channel section developed by OneSteel Australian Tube Mills using its patented dual electric resistance welding and automated continuous roll-forming technologies. The LSB has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. Its flexural strength for intermediate spans is governed by lateral distortional buckling characterised by simultaneous lateral deflection, twist and web distortion. Recent research on LSBs has mainly focussed on their lateral distortional buckling behaviour under uniform moment conditions. However, in practice, LSB flexural members are subjected to non-uniform moment distributions and load height effects as they are often under transverse loads applied above or below their shear centre. These loading conditions are known to have significant effects on the lateral buckling strength of beams. Many steel design codes have adopted equivalent uniform moment distribution and load height factors based on data for conventional hot-rolled, doubly symmetric I-beams subject to lateral torsional buckling. The non-uniform moment distribution and load height effects of transverse loading on cantilever LSBs, and the suitability of the current design modification factors to include such effects are not known. This paper presents a numerical study based on finite element analyses of the elastic lateral buckling strength of cantilever LSBs subject to transverse loading, and the results. The applicability of the design modification factors from various steel design codes was reviewed, and suitable recommendations are presented for cantilever LSBs subject to transverse loading.     

Flexural-torsional buckling of shallow arches with open thin-walled section under uniform radial loads

An arch with an open thin-walled section that is subjected to a radial load uniformly distributed around the arch axis may suddenly buckle out of its plane of loading and fail in a flexural-torsional buckling mode. The classical flexural-torsional buckling load for an arch with an open thin-walled section under a uniform radial load has been obtained by a number of researchers, based on the consideration that the uniform radial load produces a uniform axial compressive force without in-plane bending prior to the occurrence of flexural-torsional buckling. This assumption is correct for deep arches. However, the uniform radial load may produce substantial bending actions in shallow arches prior to flexural-torsional buckling, and so the classical buckling analysis based on the assumption of uniform axial compression may produce incorrect flexural-torsional buckling loads for shallow arches. This paper investigates the flexural-torsional buckling of shallow arches with an open thin-walled section that are subjected to a radial load uniformly distributed around the arch axis. It is found that shallow arches under a uniform radial load are subjected to combined in-plane compressive and bending actions prior to flexural-torsional buckling, and that using the classical buckling solution for circular arches under uniform compression produces incorrect buckling loads for shallow arches. A rational finite element model is developed for the flexural-torsional buckling and postbuckling analysis of shallow arches with an open thin-walled section, which allows the buckling loads to be obtained correctly.     

An equivalent stiffness approach for modelling the behaviour of compression members according to Eurocode 3

The development of design procedures based on inelastic advanced analysis is a key consideration for future steel design codes. In advanced analysis the effect of imperfections has to be modelled in such a way that the incremental analysis fully captures this effect in the process of moment redistribution. In modelling the influence of imperfections on the behaviour of individual members of real structures, different approaches have been used to globally represent this effect in the overall analysis of structural systems. They are referred to as the initial bow imperfection approach or as the equivalent transverse load approach. When using the abovementioned approaches in analysis of multiple member structural systems, the designer is required to arrange the directions of bow imperfections or equivalent transverse loads in such a way that the imperfection arrangement leads to the least constrained solution, i.e. the lowest ultimate load predicted from all possible sets of member initial imperfection arrangements. Since there is still ongoing research on the development of simple application rules ensuring that the designer obtains a unique solution when choosing a certain set of member initial imperfections, there is at the same time interest in the development of alternative approaches to modelling the influence of member imperfections on the behaviour of structural systems. This paper provides the necessary background information as well as describes the formulation and modelling techniques used in the development of a new approach to modelling the influence of imperfections on the stability behaviour of structural components and systems. This new approach, called hereafter an equivalent stiffness approach, has an advantage over the previously described approaches since an imperfect member is treated as a hypothetically straight element, flexural and axial stiffnesses of which at each load level are predicted in a continuous fashion dependent upon the actual force and deformation states. This type of modelling does not require any explicit modelling of equivalent geometric imperfections or equivalent forces and their directions in advanced analysis; therefore also it does not require any buckling mode assessment. Moreover, the effects of strain hardening and section class may conveniently be included in modelling. Finally, European buckling curves are used to estimate the values of parameters of the developed model that can be immediately used in advanced analysis conducted according to Eurocode 3.     

Direct Strength Method for calculating distortional buckling capacity of cold-formed thin-walled steel columns with uniform and non-uniform elevated temperatures

This paper assesses the applicability of the Direct Strength Method (DSM) to calculating the distortional buckling strength of cold-formed thin-walled (CF-TW) steel members with uniform and non-uniform elevated temperature distributions in the cross-section. The assessment was carried out by checking the DSM calculation results with numerical simulation results using the general finite element software ABAQUS which was further validated against ambient and uniform elevated temperature tests on short lipped channel sections, in addition to the author's previous validation studies for thin-walled steel columns with non-uniform temperature distributions. The validated numerical model has been used to generate an extensive database (453) of numerical results of load carrying capacity of CF-TW members with different uniform and non-uniform temperature distributions in the cross-sections, under different boundary and loading conditions and with different dimensions and lengths. It is concluded that the existing DSM distortional buckling curve for ambient temperature application is also applicable for columns with uniform temperature distributions in the cross-section, but is un-conservative for columns with non-uniform temperature distributions in the cross-section. This paper proposes a modification to the distortional buckling curve to enable DSM to deal with distortional buckling in columns with non-uniform temperature distributions.     

Dynamic analysis methodology for progressive failure of truss structures considering inelastic postbuckling cyclic member behavior

Over the years, several catastrophic collapses of truss structures have been reported. Sudden failure or reduction in member capacity of a single member in a truss structure gives rise to dynamic force redistribution in the remaining members and may lead to progressive collapse of the entire structure. During failure, truss members can undergo inelastic cyclic behavior (including postbuckling in compression and yielding in tension) that may not have existed in the intact structure. This paper presents a methodology to incorporate the inelastic cyclic member force-deformation behavior in the dynamic analysis of truss structures and at the same time incorporates the possible dynamic effects arising from the sudden change in load carrying capacity of a member due to failure or buckling/postbuckling. The method tracks and generates the force-deformation characteristics of every member of the truss at each incremental time step. The continuous change in the load-carrying capacity and the stiffness of members during the nonlinear force-deformation history has been incorporated in the analysis scheme using the Pseudo-force approach. The solution methodology for obtaining the dynamic response of the structure is based on the finite element technique and considers elasto-plastic material and large deformation geometric nonlinearities. The methodology is applied to a two-dimensional three-member toggle redundant truss subjected to external static, quasi-static, and dynamic (sinusoidal and ramp) loads. Results delineating the effects of the inelastic cyclic axial force-deformation relation of each member and the time variation of joint displacements and member forces are presented for each loading condition. The results show that there exist cases where modeling a compression member with its actual postbuckling behavior, which although has some reserve load carrying capacity, are more critical than the case where the same member is considered to suddenly lose its full load carrying capacity at its buckling load.     

Application of the Direct Strength Method to local buckling resistance of thin-walled steel members with non-uniform elevated temperatures under axial compression

This paper assesses the applicability of the Direct Strength Method (DSM) to calculating the local buckling ultimate strength of cold-formed thin-walled (CF-TW) steel members with non-uniform elevated temperature distributions in the cross-section. The assessment was carried out by checking the DSM calculation results with numerical simulation results using the general finite element software ABAQUS which was validated against ambient and uniform elevated temperature tests on short lipped channel sections. The validated numerical model was used to generate an extensive database (372 models) of numerical results of load carry capacity of CF-TW members with different uniform and non-uniform temperature distributions in the cross-sections, under different boundary and loading conditions and with different dimensions and lengths. It was concluded that the DSM local buckling curve was directly applicable for columns with uniform temperature distributions in the cross-section. For columns with non-uniform temperature distributions, a modification to the local buckling curve was necessary and this paper has proposed a new curve.     

Application of the Direct Strength Method to local buckling resistance of thin-walled steel members with non-uniform elevated temperatures under axial compression

This paper assesses the applicability of the Direct Strength Method (DSM) to calculating the local buckling ultimate strength of cold-formed thin-walled (CF-TW) steel members with non-uniform elevated temperature distributions in the cross-section. The assessment was carried out by checking the DSM calculation results with numerical simulation results using the general finite element software ABAQUS which was validated against ambient and uniform elevated temperature tests on short lipped channel sections. The validated numerical model was used to generate an extensive database (372 models) of numerical results of load carry capacity of CF-TW members with different uniform and non-uniform temperature distributions in the cross-sections, under different boundary and loading conditions and with different dimensions and lengths. It was concluded that the DSM local buckling curve was directly applicable for columns with uniform temperature distributions in the cross-section. For columns with non-uniform temperature distributions, a modification to the local buckling curve was necessary and this paper has proposed a new curve.     

单角钢轴压杆件弹性和非弹性稳定承载力

热轧角钢有等边和不等边两种类型。由于截面对称性方面的差异,两类角钢在承受轴压力时,性能有明显差别。针对等边角钢在非弹性范围的受压承载力由弱轴弯曲屈曲控制还是强轴弯扭屈曲控制这一问题进行了分析,结果表明：在非弹性范围和弹性范围一样,杆件失效时呈弯曲屈曲,对于宽厚比较大的高强度角钢,需要计及局部屈曲效应。不等边角钢压杆失效时总是呈弯扭屈曲,其临界力计算比较复杂。通过计算分析,得出了把问题转化为按弯曲屈曲分析的等效长细比的方法。此法既适用于弹性范围,也适用于非弹性范围。和现有试验资料对比表明,文中的等边和不等边角钢轴压杆件的计算方法,都可用于设计工作。     

Design of tapered member portal frames

Non-uniform steel frames, incorporating tapered or haunched members, have proved to be economical solutions for warehouses and factory buildings over a wide range of spans. Design rules, however, deal only with uniform member frames and therefore attempts have been made to convert the non-uniform frame into an equivalent uniform frame. One such method appears in the AISC Specification for the Design of Steel Buildings^(l) but it is relatively complex and of limited application.A simpler and more general procedure, based on a parametric study and using a limit state interaction equation, is presented. In the study, elastic instability computer programs were used and changes were made to the values of the principal variables. The results were subjected to an analysis of variance and equations of best fit were obtained for the conversion to an equivalent uniform frame. At this stage of the research program only completely symmetrical taper member frames have been investigated. The proposed conversion enables the designer to use all the currently available design aids dealing with the effective length factors of uniform members. The method is illustrated by two numerical examples.     

铝合金轴压构件屈曲荷载计算方法

铝合金轴压构件在建筑工程中有着广泛应用,但由于其材料弹性模量低,稳定问题比钢结构更加突出。文中对铝合金轴压构件进行屈曲分析,提出屈曲模式。采用解析法分析并结合现有轴压构件的各种屈曲理论,给出适合铝合金轴压构件的屈曲荷载计算公式,介绍有限样条法在构件屈曲分析中的应用,并用其验证所提出的各项屈曲荷载计算公式的正确性。     

RL型截面冷弯薄壁型钢的畸变屈曲荷载算式

为了对RL型截面冷弯薄壁型钢的畸变屈曲作进一步研究,以既有研究成果为基础,根据广义梁理论推导了两端简支和固支边界条件下RL型截面冷弯薄壁型钢的畸变屈曲荷载计算式。通过求解矩阵的广义特征值,利用推导的算式计算RL型截面型钢构件在轴压、绕弱轴和强轴弯曲下的畸变屈曲荷载和屈曲半波长,并与有限条软件CUFSM分析结果和既有理论公式的解相比,结果表明所得算式具有较高的精度。公式推导过程和结论可以为工程设计和进一步研究中计算畸变屈曲荷载提供参考。     

Development of a consistent buckling design procedure for tapered columns

EC3–EN 1993-1-1 provides several methodologies for the stability verification of members and frames. When dealing with the verification of non-uniform members in general, with tapered cross-section, irregular distribution of restraints, non-linear axis, castellated, etc., the code mentions the possibility of carrying out a verification based on 2nd order theory; however, several difficulties are noted when doing so, in particular when the benefit of plasticity should be taken into consideration.Other than this, there are yet no guidelines on how to apply standardized, easily reproducible rules as those contained in Section 6.3.1 to 6.3.3 of the code to non-uniform members. As a result, practical safety verifications for these members are often carried out using conservative assumptions, not accounting for the advantages non-uniform members provide. In this paper, firstly, available approaches for the stability verification of non-uniform members are discussed. An Ayrton–Perry formulation is then derived for the case of non-uniform columns. Finally, and followed by a numerical parametric study covering a range of slenderness, cross-sections and fabrication process, a design proposal is made for the relevant case of in-plane flexural buckling of linearly tapered columns subject to constant axial force. The proposal is consistent with current rules for uniform columns provided in EC3-1-1, i.e., clause 6.3.1.     

Buckling analysis of thin-walled members with closed cross sections

In this paper, an analytical procedure for the elastic buckling problems of thin-walled members with closed cross sections by the transfer matrix method is presented. The transfer matrix is obtained from the differential equations for a plate subjected to axial load, and the extended transfer matrix for closed cross sections is derived from that for branched panels. The analytical local and overall elastic buckling loads for thin-walled members with closed cross sections can be obtained simultaneously. Furthermore, a technique to estimate the buckling mode shapes of these members is also shown. To investigate the accuracy and efficiency of this method, some numerical examples are presented.     

Stability of multi-storey unbraced steel frames subjected to variable loading

Proposed in this paper is an approach of evaluating the elastic buckling loads for multi-storey unbraced steel frames subjected to variable loading or non-proportional loading. In the case of variable loading, the conventional assumption of proportional loading is abandoned, and different load patterns may cause the frame to buckle at different levels of critical loads. In light of the use of the storey-based buckling concept to characterize the lateral sway buckling of unbraced framed structures, the problems of determining the lower and upper bounds among all of the frame buckling loads associated with different load patterns are presented as a pair of minimization and maximization problems subjected to elastic stability constraints. The problems take into account the semi-rigid behaviour of beam-to-column connections and the lateral stiffness reduction of columns due to the presence of an axial compressive load. The minimization and maximization problems are then solved by a linear programming method; thus, the lower and upper bounds of the frame buckling loads subjected to variable loading are obtained. Parametrical studies on the influence of the connection rigidity to the lower and upper bounds of critical loads and the comparisons to the conventional proportional loading are also presented in this paper.     

Recent research advances on the ECBL approach. Part II: interactive buckling of perforated sections

Perforated cold-formed steel sections are often used in civil engineering as structural members for residential buildings and storage racks construction. In the case of buildings the perforations are provided to permit piping and bridging, while for rack systems they allow for simple connections between members. The load bearing capacity of these sections are influenced not only by the local buckling, global buckling and interaction between these two, but also by the reduction of cross-sectional properties due to perforations. Because of the wide variety in the size and configuration of perforations, it is impossible to provide a practical design procedure to calculate the ultimate strength of such a type of sections. The main objective of this paper is to calibrate an effective design width formula for the perforated sections and, using the ECBL approach, to evaluate an equivalent α imperfection factor for European buckling curves, in order to adapt them for sections with different perforation patterns.     

On the design of Web-tapered,unequal-flanged structural steel columns

A study directed towards the development of an efficient and economical design for stability of structural steel members is described. A finite element method is presented for determining the lateral-torsional buckling load for linearly tapered I-section members with unequal flange areas. Solutions are obtained for different flange-area ratios and tapering ratios. Such solutions are used to develop an interaction relationship for tapered unequal-flanged steel structural colums subjected to both axial and bending stresses.The formulation is intended to provide a more rational approach to the design of tapered steel columns—a step towards an optimum stability design for structural steel members.     

Analysis of equal leg single-angle section beams subjected to biaxial bending and constant axial compressive force

Single-angle section beams are generally loaded parallel to their geometrical axes and their cross-sections are not symmetrical to their principal axes. Even equal leg angle beams have only one symmetrical axis. Many types of loading cause biaxial bending and axial forces in these members. Since single-angle section beams are slender members, they also need to be analyzed in terms of flexural buckling, lateral torsional buckling and local buckling effects. In this study, a calculation procedure is presented to analyze the nominal loads of equal leg angle section beams loaded vertically to the axis of the beam. It is assumed that the axial force is composed of a constant compressive force. The constant axial force is only taken into consideration for the uniform compressive stress and the second-degree effects caused in the cross-section. Thus only the biaxial bending moments remain. The first yield, full plastic and critical lateral torsional buckling moments for biaxial bending are calculated with respect to the slenderness of the beam and the axial force. The nominal design force on the cross-section is calculated according to the load and resistance factor design rules. The analysis proposed for the constant axial load can also be used for other axial forces, by using an iterative calculation procedure.     

Tangent moduli of hot-rolled I-shaped axial members considering various residual stress distributions

This paper presents an equation for the effective tangent moduli for steel axial members of hot-rolled I-shaped section subjected to various residual stress distributions. Because of the existence of residual stresses, the cross section yields gradually even when the member is subjected to uniform axial stresses. In the elasto-plastic stage, the structural response can be easily traced using rational tangent modulus of the member. In this study, the equations for rational tangent moduli for hot-rolled I-shaped steel members in the elasto-plastic stage were derived based on the general principle of force-equilibrium. For practical purpose, the equations for the tangent modulus were presented for conventional patterns of the residual stress distribution of hot-rolled I-shaped steel members. Through a series of material nonlinear analyses for steel axial members modeled by shell elements, the derived equations were numerically verified, and the presented equations were compared with the CRC tangent modulus equation, the most frequently used equation so far. The comparative study shows that the presented equations are extremely effective for accurately analyzing elasto-plastic behavior of the axially loaded members in a simple manner without using complex shell element models.     

轴心受压开口薄壁构件弹塑性屈曲荷载的统一计算方法

通过分析构件截面上应变与轴向力间的关系，以构件轴向应变为基本参数，提出了轴心受压开口薄壁构件的弹塑性屈曲荷载统一计算方法，给出了轴压构件的弯曲屈曲、扭转屈曲、弯扭屈曲等屈曲荷载的弦截法迭代格式，可应用于H形、T形、L形、十形截面等不同开口形式的轴压构件屈曲荷载计算，并可考虑具有残余应力的弹塑性本构关系。该方法以无残余应力的弹性屈曲荷载对应的轴向应变作为初始值，根据不同屈曲形式对应的非线性方程计算弦截区间点的函数值，进行弦截法迭代计算，得到弹塑性构件的临界轴向应变，进而获得屈曲荷载等信息。该方法采用的弦截法收敛速度快、计算量小、无需嵌套循环，可有效解决两端铰接轴心受压开口薄壁构件的弹塑性屈曲快速计算问题，便于工程应用。