A modal pushdown procedure for progressive collapse analysis of steel frame structures

A modal pushdown analysis procedure is developed for progressive collapse assessment of multi-storey steel frame buildings under sudden removal of a column due to catastrophic events. Since the first vertical bending mode generally dominates the behaviour of the structure after column removal, the global response is assumed entirely in this mode shape while no contribution is considered from other modes. Thus, the target displacement of the column-removed point is estimated from the nonlinear response–history analysis of a modal inelastic single degree-of-freedom (SDOF) system under a rectangular pulse force that simulates the abrupt column removal. The properties of this SDOF system are calculated from the nonlinear static (pushdown) analysis of the damaged structure using the modal properties of the first bending mode shape. A two-step pushdown analysis procedure is developed to estimate the inelastic response of the structure and the dynamic amplification factor (DIF) to use when conducting the nonlinear static analysis. The accuracy of the proposed procedure is estimated and compared to other formulations in the literature. For this reason, a series of three-dimensional steel frame buildings with varying number of spans and storeys have been considered in the analysis. Different loading levels and column removal scenarios are investigated. The study results show that the modal pushdown procedure gives accurate solution, accounting for both real plastic deformation demand and catenary stiffening action in steel beams.