A semi-analytical method to study the post-buckling behaviour, imperfection-sensitivity and mode interaction in steel frames

A brief account of the main aspects involved in the formulation of a semi-analytical (asymptotic-numerical) method to investigate the geometrically non linear behaviour of elastic plane frames is first presented. The method (i) combines an analytical perturbation approach, due to Pignataro et al., with the FEM solution of the resulting sequence of differential equation systems, and (ii) is extended here to incorporate the effect of initial geometrical imperfections and primary bending moments. The paper illustrates the application of the method and the (analytical) results displayed and discussed concern single-bay pitched-roof and three-bay beam-to-column frames. Such results, which are compared with fully numerical values, consist of initial post-buckling slopes and curvatures and imperfect non linear equilibrium paths. Mode interaction phenomena involving two global buckling modes and a global and a local (member) buckling mode are also addressed.