N. Boissonnade

New interaction formulae for beam-columns in Eurocode 3: The French–Belgian approach

Abstract This paper presents one of the two new proposals for beam-column interaction formulae, which will be made available in the forthcoming EN version of Eurocode 3. It is based on second-order in-plane elasticity, and has been derived in order to exhibit an understandable physical background, as well as accuracy and consistency with the other resistance and stability formulae of the code. The formulae ensure all the required continuities: between the cross-section classes, from plasticity to elasticity when slenderness and axial force are increasing, and continuity between all the individual stability member checks and cross-section verifications. The paper shows how the basic format may be extended to cover a wider range of cases, i.e. spatial elastic–plastic behaviour with possible lateral–torsional buckling. Through an extensive comparison with the results of FEM numerical simulations of about 15 000 beam-columns, the proposal is found to be safe and accurate.

Stability, failure and design of I-section steel beams subjected to tension

This paper reports the results of an analytical, numerical and experimental investigation dealing with I-section steel members acted by a combination of major-axis bending and axial (“beams subjected to tension”), which is relatively rare in practice and, therefore, has received little attention in the past. In particular, there are no guidelines for the design against buckling ultimate limit states of such members (only their cross-section resistance is checked). This means that the axial tension favorable effect on lateral-torsional buckling/failure is neglected, leading to over-conservative designs − indeed, a beam subjected to axial tension is currently designed against lateral-torsional failure as a “pure beam”. In order acquire scientific knowledge and provide design guidance on this topic, the lateral-torsional stability, failure and design of hot-rolled steel I-beams with fork-type end supports and acted by simple transverse loadings (mostly applied end moments) and various axial tension values are addressed in this work. After developing and validating an analytical expression to calculate critical buckling moments of beams under uniform bending and axial tension, beam finite element buckling results are presented for the non-uniform bending cases. Then, two full-scale tests involving a narrow and a wide flange beam under eccentric tension are described and their results are used to develop finite element models, subsequently employed to perform a parametric study aimed at gathering a fairly extensive ultimate strength/moment data bank. Finally, this data bank is used to assess the merits of a design approach proposed here for beams subjected to tension and collapsing in lateral-torsional modes − this design approach, which consists of slightly modifying the current procedure prescribed in Eurocode 3 to design beams against lateral-torsional failures, is shown to provide ultimate moment estimates that correlate very well with the values obtained from the numerical simulations.

A proposal for beam-column interaction formulae

In order to improve Eurocode 3 beam-column formulae, a research was led by a so-called “ECCS TC8 – ad-hoc working group”, and, as a result, a new proposal dealing with plane and spatial behaviour has been suggested. It was derived according to the following requirements: theoretical background, strong physical meaning, consistency with the other formulae of the code, and accuracy. It should also cover all types of continuities: between the cross-section classes, from plasticity to elasticity as slenderness and axial force increase, and continuity between individual stability checks and cross-section verifications. In this paper, the theoretical basis are first established and then the proposal is detailed for in-plane behaviour. Extension to spatial behaviour is next tackled, without accounting for lateral torsional buckling. Finally, in order to check the accuracy of the proposal, the results of comparisons based on a large number of numerical simulations are presented. It shows that the proposal gives satisfactory results.

Local and interactive post-buckling of RHS thin-walled members - Comparing a new special beam finite element with shell FE models

This paper presents a special thin-walled plane beam finite element that accounts for the in-plane cross-section local deformation. The element is based on the superposition of a classical beam displacement field and of an additional field describing local effects, with an approximation on the local second-order membrane stress field. The theoretical formulation is summarized and an application of the resulting numerical tool to the post-buckling analysis of RHS thin-walled members with moderate local and global slenderness susceptible to both global and local buckling is then performed. Different types of analyses are presented (computation of critical bifurcation loads, geometrically non-linear analysis, geometrically and materially non-linear analysis). The results obtained with the proposed beam finite element are compared to values provided by shell FE models.

A non-linear 3D beam finite element for the study of steel frames with tapered members

In recently build structures, instability problems have become of prime importance, mainly because of the general tendency to increase the structural and members slenderness, coupled with the development of high strength steels. In that way, tapered I-members become more and more usual since they allow significant material savings and a consistent design. Indeed, because such members are built-up from several plates, designers get the possibility to spread out the material in the most efficient way over the cross-section and over the beam length, thus leading to a rather economical distribution of the material. Such members are particularly efficient in steel portal frames of medium and long span with no in-plane bracing system, where the increase in the fabrication cost is more than compensated by the decrease in weight when compared to rolled sections.

Interactive buckling of thin-walled rectangular hollow sections - a comparison between beam models and shell finite elements.

In nowadays steel construction, thin-walled members have become very common through the use of both welded and cold-formed profiles. This implies that phenomena such as local buckling of the walls or distortional buckling of the section require a due attention.