Plastic Design of Metal Thin-Walled Cross-Sections of Any Shape Under Any Combination of Internal Forces

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 W-pl,W-y,W-nB and W-pl,W-z,W-nB for bimoment not considered as a constraint; W-pl,W-y, W-pl,W-z, and W-pl,W-w for bimoment considered as a restraint; and maximum values W-pl,W-y,W-max, W-pl,W-z,W-max, and W-pl,W-w,W-max. The values of cross-section plastic resistances N-pl, M-pl,M-y,M-Rd, M-pl,M-z,M-Rd, and B-pl 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.