Reduced order modelling of steel beams and columns for analysis against accidental actions

The majority of relevant accidental scenarios on building structures are initiated at the ground level by a column suffering damage, mainly due to a localized explosion or a vehicle impact. The transmitted vertical forces from the column to the structure as well as the residual resistance of the column are decisive to understand the response of the building and are the subject of analysis of this work. Using the same principles of energy equivalence common to existing reduced order models (ROM), a generalized methodology for the model reduction of beam elements is derived, which overcomes the limitations of existing methods by explicitly considering in its analytical formulation: a) the coupled bending-membrane resisting behavior of the beam, b) arbitrary rotational boundary conditions, c) arbitrary longitudinal boundary conditions, d) arbitrary inertial boundary conditions (i. e. the presence of a head mass), and e) arbitrary loading states in transverse and longitudinal directions. An analytical and a numerical solution methodology are proposed to calculate the ROM in explosive and impact loading scenarios. Due to the explicit inclusion of geometric nonlinear effects in the formulation of the model, an analytical solution for the determination of the residual strength of a damaged column undergoing an arbitrary residual deformation is possible. This result is of great importance for the assessment of the robustness of the structure in its damaged state. A small-scale experimental weight drop set-up has been constructed and used to impact small beam elements under variation of mechanical and inertial boundary conditions. The performed experimental campaign is used to validate the theoretical and numerical results of this work.