|Abstract: ||Compression members, made from slender metallic plate elements, are prone to a wide range of different elastic instability phenomena. A thin-walled I-section strut, made from a linear elastic material, can suffer from the nonlinear interaction between a global (Euler) buckling mode, and a local flange plate buckling mode. The interactive buckling behaviour is usually much more unstable than when the modes are triggered individually and hence significantly reduces the load-carrying capacity of real struts. The current work focuses on such a problem using an analytical approach, the methodology of which has been well established in previous works on sandwich struts and I-section beams.
An analytical model that describes the interactive buckling of a thin-walled I-section strut under pure compression based on variational principles is presented. Analytical formulations combining the Rayleigh–Ritz method and continuous displacement functions are presented to derive a series of systems that comprise differential and integral equilibrium equations for the structural component. Solving the systems of equations with numerical continuation reveals progressive cellular buckling (or snaking) arising from the nonlinear interaction between the weakly stable global buckling mode and the strongly stable local buckling mode. The resulting behaviour is highly unstable and when the model is extended to include geometric imperfections it compares excellently with some recently published experiments. Imperfection sensitivity studies reveal high sensitivity to both global and local imperfection types. The worst forms of local imperfection are identified in terms of the initial wavelength, amplitude and degree of localization. The effect of the varying rigidity of the joint of the section web and flanges is also studied and a rapid erosion of the cellular buckling response is revealed with increasing rigidity of the flange–web joint. A shell-based nonlinear finite element model is presented, primarily for validation purposes. The results from the analytical and finite element models show a good comparison, particularly for higher rigidities of the flange–web joint.
A parametric study is conducted for two limiting cases, where the flange–web joint is assumed to be fully pinned or fully rigid. For a chosen set of geometries, the most undesirable interactive region is identified for both global and local slendernesses, in terms of the strut length and the flange width respectively. Practical implications are discussed in terms of the idealized buckling design curve. An analytical framework for the structural analysis of the thin-walled I-section struts that exhibit the nonlinear interaction of a global and a local buckling mode, including cellular buckling, has therefore been established.|