Higher-order non-linear analysis of steel structures.Part I : elastic second-order formulation

This paper presents a higher-order beam-column formulation that can capture the geometrically non-linear behaviour of steel framed structures which contain a multiplicity of slender members. Despite advances in computational structural frame software, analyses of large frames can still be problematic from a numerical standpoint, with efficacious and reliable convergence not always being ensured. To this end, the intent of this paper is to fulfil a need for versatile, reliable and efficient non-linear analysis of general steel framed structures with a large number of members suitable for engineering practice. Following a comprehensive review of numerical frame analysis techniques, a fourth-order element is derived, in which the crucial member bowing effect involved in the equilibrium equation is captured, and implemented in an updated Lagrangian formulation. Because of this, it is able to predict flexural buckling, snap-through buckling and the large displacement post-buckling behaviour of typical structures whose responses have been reported by independent researchers. The present approach with its efficacious and reliable convergence is shown in comparison studies to be applicable to selected applications which are prone to several forms of geometric non-linearity.