The stability design of steel structures by second order inelastic analysis with strain limits is addressed in this thesis. In the proposed design approach, a geometrically and materially nonlinear analysis with imperfections (GMNIA) of members and frames is carried out and the ultimate strength of the structure is signified by reaching either the strain limit defined according to the Continuous Strength Method (simulating cross-section failure) or the peak load factor, whichever occurs first. The method has been established for the in-plane design of prismatic structural components. In the present thesis, its scope is extended to the in-plane design of members with three-flanged cross-sections (representing the haunch and apex regions of portal frames) and web-tapered members, subjected to combined loading conditions ranging from pure compression to pure uniform and non-uniform bending. Explicit formulae, which have been developed previously to predict the elastic local buckling stress of single I-sections, are first extended to cover the case of three-flanged cross-sections, subjected to combined loading conditions ranging from pure compression to pure major axis bending. The predictions are shown to be more accurate than the calculations performed on an element-by-element basis – the way in which the local buckling of cross-sections is typically treated in current structural steel design specifications.
Attention then turns to the development of the proposed design approach for scenarios in which out-of-plane stability effects, with a focus on lateral-torsional buckling, govern. First, equivalent imperfections for the out-of-stability design of steel and stainless steel members by second order inelastic analysis are established. Then, the existing strain limits for in-plane design are extended to allow for the influence of shear, torsion and warping, to enable their general applicability to three-dimensional buckling problems. It is shown that the proposed design method provides more accurate and consistent ultimate strength predictions than traditional design methods and also streamlines the design process by eliminating the need for cross-section classification and individual member design checks.