Keywords: progressive, collapse, disproportionate, robustness, structural, assessment, modelling.

Progressive collapses typically give rise to disproportionate collapse where the overall damage is not in keeping with the cause of the initial failure. The Ronan Point collapse was the most important disproportionate collapse because of the influence it has had on the current design codes. More recently, the attacks on the World Trade Centre and the Oklahoma bombing have highlighted the potential risks of terrorist attacks designed to cause progressive collapse. As a result, the behaviour of buildings following local collapse is receiving renewed attention. The objective of limiting such collapses is being tackled on a number of fronts.

This paper describes an algorithm for modelling the progressive collapse of buildings. The algorithm presented in this paper models how collapse progresses through a structure when one member fails as a result of an extreme local load, the loss of a column due to vehicular impact or an explosion, for example. The program considers the dynamic effects of the falling loads and considers the dynamic response of the structure due to impact and due to both material and geometric (P-Delta) non-linearity.

A flow-diagram for the algorithm is presented and the paper highlights and explains some of the key components of the algorithm detailing: how plastic hinges should be modelled, how mechanisms should be identified; the importance of considering the connection details to assess the maximum axial forces and rotations that can be developed before failure; and appropriate means of modelling the redistribution of applied loads, including falling loads.

Such algorithms can be used for a number of purposes. By modelling the behaviour of a structure following local damage they can be used to assess the vulnerability of structures to progressive collapse. By systematically removing members and modelling the resulting behaviour the algorithm can be used to identify critically vulnerable members. The algorithm can also be used to assess the effectiveness of strategies such as "shear fuses" in limiting collapse progression, or the algorithm can be coupled with an optimisation algorithm to develop efficient structures designed to limit progressive collapse.

Disproportionate collapse usually involves progressive collapse but defining disproportionate collapse or quantifying robustness are outside the scope of this paper, and perhaps of limited use.

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