Nonlinear SDOF Model for Dynamic Response of Structures under Progressive Collapse

Abstract

The transient dynamic response of the substructures above a removed column is the most direct and realistic to demonstrate the structural performance against progressive collapse. To efficiently obtain the transient dynamic response, a nonlinear single degree-of-freedom (SDOF) model is proposed with a tri-linear resistance function that is capable of describing various forms of structural resistance, including catenary action and softening resistance and a loading function consisting of a linear ascending part and an ensuing constant force that considers the effect of column removal time. Moreover, the model accounts for nonzero initial conditions, which are very likely to occur under blast loading. The closed-form analytical solutions of the model are derived with Laplace transform techniques and verified with dynamic experimental results of steel and reinforced concrete assemblies subjected to column removal scenarios. The verification indicates the generality and the accuracy of the SDOF model in predicting displacement responses of substructures. Then, the model is used for parametric studies. The results show that sudden column removal scenarios, which are used for progressive collapse design, provide an upper bound of structural deformation in cases that take a relatively long time to destroy a column but underestimates the structural deformation in cases that have upward displacement and nonzero velocity at the start of the progressive collapse stage.