Prediction of elastic-plastic displacements of tubular joints under combined loading using an energy-based approach

A series of 24 geometrically and materially non-linear finite element analyses of a simply supported YT tubular joint, with axial loads on the T- and Y-brace ends, was carried out to collapse, using solid three-dimensional element models. The analyses all have proportional and monotonic loading histories (i.e. radial load paths) and each analysis has a different T-brace to Y-brace load ratio so that the series ranges over all four quadrants of the two-dimensional load space. The results of the analyses are processed and combined by means of an energy approach, specifically a generalization of Castigliano's theorem on displacements using the concept of complementary work. A prediction method is thus developed to determine the non-linear, elastic-plastic, force-displacement responses of the joint for arbitrary (in-plane) radial load paths in the two-dimensional load space of the structure. One immediate application envisaged is the development of an elastic-plastic 'joint finite element' for use in the collapse prediction of tubular structures. The method is potentially applicable to a range of structures and loading scenarios, including other tubular joint types, both uniplanar and multiplanar, with bending moments and/or torques as well as transverse and axial loads.