Plastic Interaction Relations for Elliptical and Semi-Elliptical Hollow Sections

The advancement of the structural steel manufacturing industry has led to the recent emergence of steel members with Elliptical Hollow Sections (EHS) and Semi Elliptical Hollow Sections (SEHS). Although these sections are gaining popularity among architects, the lack of design guidelines specifically tailored towards these sections inhibits their efficient structural use. Within this context, this thesis provides several steps towards the development of such guidelines. A review of the manufacturing process of hot-rolled steel sections is conducted with emphasis on hollow structural sections. The main factors affecting the formation of residual stresses during cooling of the sections are discussed. Lower bound plastic interaction relations for EHS subjected to combinations of axial force, bi-axial bending moments and torsion are then derived. The formulation is based on the lower bound theorem of plasticity and the maximum distortional energy density yield criterion. Its applicability for conducting the cross-sectional interaction check in structural steel design problems is illustrated through a practical example. A simplified and conservative interaction equation is then proposed based on curve fitting of the results of the lower bound solution. Upper bound interaction relations are next developed for EHS subjected to combinations of axial force, bi-axial bending moments, torsion and bimoments. The formulation is based on kinematically admissible strain fields within the context of the upper bound theorem of plasticity. The interaction relations derived successfully capture the effect of confining radial strains present at welded end sections, as well as sections that are free to deform in the radial direction away from end welded sections. An iterative solution technique is developed to solve the resulting highly non-linear system of interaction relations. The effects of residual stresses and initial imperfections on axial compressive resistance of hot-rolled EHS are then incorporated into the lower bound interaction relations. Towards that goal, the thermo-mechanical properties of steel were extracted from the literature. A thermo-mechanical finite element model was developed for prediction of residual stresses in rolled sections. The validity of the model was assessed by comparison against residual stress measurements available in the literature. The model is then applied to predict the residual stresses in hot-rolled EHS. A series of geometric and material nonlinear finite element analyses is conducted on columns of EHS sections. The analyses include predicted residual stresses and initial out-of-straightness imperfections in order to determine the inelastic buckling capacity of EHS members and generate column curves for EHS sections. The column curves are subsequently compared to those based on Canadian, American and European design codes. Two column curve equations are proposed in a format similar to that of the Canadian Standards for buckling about major and minor axes. The column curves were subsequently combined with the interaction relations developed to provide design rules for EHS members under combined loads. The last contribution of the thesis provides a formulation of lower bound interaction relations for SEHS subject to combinations of axial force, bi-axial bending moments and torsion. An iterative scheme for solving the parametric form of the interaction relations is developed and a grid of admissible stress resultant combinations is generated. A series of trial functions are fitted to the grid of internal force combinations and two simplified and conservative interaction equations are proposed.

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