A short tribute to pioneers in the development of the plastic design of metal thin-walled cross-sections is presented. This large study investigates altogether fourteen steel and four extruded aluminum cross-sections in detail. Six groups of the cross-sections with various shapes consist of four I-shaped doubly symmetric sections with or without lips; three monosymmetric sections with an axis of symmetry z including T- and diamond sections; four monosymmetric channels with or without lips; two point-symmetric Z-sections; and four asymmetric sections. The four extruded aluminum cross-sections are an I 200a section, a diamond section, and closed oblique and irregular sections. For all 18 cross-sections, the plastic section moduli of three kinds were calculated, namely Wpl,y,nB and Wpl,z,nB for bimoment not considered as a constraint; Wpl,y, Wpl,z, and Wpl,w for bimoment considered as a restraint; and maximum values Wpl,y,max, Wpl,z,max, and Wpl,w,max. The values of cross-section plastic resistances Npl, Mpl,y,Rd, Mpl,z,Rd, and Bpl are calculated in numerical examples too. The values of cross-section properties are calculated in different ways to verify the correctness of the results. The following methods of calculation are used: the rules given in Eurocode EN 1993-1-1:2022; MathCad programs; and freeware. Recommendations for educational institutes and designers in practice are given, including simple formulae for all cross-sectional properties for doubly and monosymmetric I-shaped sections, channels, and Z-sections. The formulae are presented in three tables containing formulae in dimensionless form convenient for parametrical studies and formulae for direct design. The background of the Eurocode rules given in EN 1993-1-1:2022 is explained together with recommendations for how to avoid the problems with using them.

As part of the ongoing revision of the Eurocodes, design provisions in EN 1999-1-1 on the buckling of longitudinally welded aluminium compression members have been subjected to a critical review. The numerical investigations described in part 1 of the paper were conducted because a need for improvement was identified. In part 2 of the paper, the main observations are presented in qualitative terms. Those observations are: the influence of the allocation of the materials to buckling classes, the influence of the imperfections plus the cross-section geometry including the position and size of the HAZ within the cross-section. Part 3 will conclude this paper by discussing the proposed design approaches in detail.

As part of the ongoing revision of the Eurocodes, design provisions in EN 1999-1-1 on the buckling of longitudinally welded aluminium compression members have been subjected to a critical review. The numerical investigations described in part 1 of the paper were conducted because a need for improvement was identified. In part 2 the main observations were presented qualitatively. Part 3, the final part of the paper, presents the statistical evaluation of the numerical investigations and the determination of the buckling curves. Two different approaches are conceivable for these buckling curves: conventional buckling curves with explicitly specified imperfection factor and plateau length parameters, and a modified Ayrton-Perry approach with interpolated parameters. Both approaches are compared with the results of the numerical investigations and with test results.

As part of the ongoing revision of the Eurocodes, design provisions in EN 1999-1-1 on the buckling of longitudinally welded aluminium compression members have been subjected to a critical review. Numerical investigations were conducted because a need for improvement was identified. This part 1 of the paper describes the individual steps of the revision and the modifications discussed, which include the introduction of longitudinally welded members. Before going into the numerical investigations in more detail, previous observations are presented regarding buckling classes and plateau lengths. In part 1 of the paper, explanations of the numerical investigations are limited to presenting the modelling of the geometry, the mechanical properties and the imperfections as well as their respective variation in the context of the parametric studies. The results of the numerical investigations and the proposed design approaches will be presented in detail in parts 2 and 3.

Numerical investigations of compression members made of aluminium are presented and recommendations for reorganizing the buckling classes and curves are derived from these. Finally, the curves are compared with test results

As part of the ongoing revision of the Eurocodes, the regulations in EN 19991-1 on the buckling of aluminium compression members were also subjected to a critical review. This resulted in the need to revise the regulations for non-welded compression members and for longitudinally welded compression members. For the design provisions of longitudinally welded aluminium compression members, a more extensive revision was necessary. The design concept was completely revised. In the course of the revision, some quite complex design models were discussed with which the cross-section types, residual stress distributions as well as size and position of the heat-affected zone (HAZ) were to be taken into account. In order not to complicate the application of the standard too much (ease of use), a clearly simplified procedure was finally chosen. The following contribution will justify these simplifications.

As part of the ongoing revision of the Eurocodes, the regulations in EN 1999-1-1 on the buckling of aluminium compression members were also subjected to a critical review. This resulted in the need to revise the regulations for non-welded compression members and for longitudinally welded compression members. For the design provisions of longitudinally welded aluminium compression members, a more extensive revision was necessary. The design concept was completely revised. In the course of the revision, some quite complex design models were discussed with which the cross-section types, residual stress distributions as well as size and position of the heat-affected zone (HAZ) were to be taken into account. In order not to complicate the application of the standard too much (ease of use), a clearly simplified procedure was finally chosen. The following contribution will justify these simplifications.

Deflections at the serviceability limit state are often decisive in the design of aluminium structures due to the low elastic modulus. Where design is based on deflections, it may not be necessary to calculate the resistance exactly and simple conservative methods are sufficient. The proposed method may be used to generate a quick, approximate and safe solution, perhaps for the purpose of initial member sizing, with the opportunity to refine the calculation for final design. Another reason for the simple method is enhancing ease of use of Eurocode 9. The principal of the proposed method is to eliminate calculation of effective cross-sections by reducing the elastic resistance with the reduction factor for the most slender part of the cross-section or the factor for HAZ softening whichever is less. This means that you don't need to define the cross-section class. The disadvantage is that you don't utilize the plastic reserve for class 1 and 2 cross-sections, nor the redistribution of stresses in the post-buckling range of class 4 cross-sections or sections with HAZ. The procedure is similar to the method with permissible stresses familiar to most engineers.

The effective bearing length of trapezoidal sheeting on cold formed sections at inner supports is 10 mm according to EN 1999-1-4 (aluminium) and EN 1993-1-3 (steel). In the original design provisions the effective bearing length on Z-sections was the actual width of the loaded flange. In order to find out the appropriate effective bearing length, FEM calculations were made on simply supported beams with C-, Z- and Sigma-cross-section. Contact elements between the trough of the trapezoidal sheeting and the loaded flange of the beam made it possible to evaluate the contact area. This area and the stresses in the trapezoidal sheeting show that the effective bearing length is very small for C-sections. For Z-sections and for Sigma sections with large folds in the web the contact area is the flange width, unless the flange width versus profile height is large and the plate thickness is small.

The initial bow imperfection e(0) is required if structures are designed with the internal forces and moments from second-order analysis. The National Annex DIN EN 1999-1-1/NA/A1 as a NDP to 5.3.2(3) of DIN EN 1999-1-1 describes how e(0) may be calculated. Based on this, formulae are derived for calculating the relative initial bow imperfections e(0)/L for six very different types of cross sections which cover a very wide range. Linear as well as nonlinear M-N-interaction relations are used depending on the type of cross section. These formulae describe e(0)/L as product of functions of which the first depends on the cross section, the second on the proof strength f(o) and the third on relative slenderness, buckling class and interaction relation. The numerical evaluation of these formulae gives conservative limit values for e(0)/L. However, due to the wide range of the parameters these values will in general be that far on the safe side that the application of the formula with the relevant parameters is recommended. For members where fo due to the HAZ is variable over the cross section a linear and alternatively a nonlinear interaction relation may be used as safe approximation. This is demonstrated with a thin-walled circular tube.