Disproportionate Collapse: The Futility of Using Nonlinear Analysis

Collapse analysis can be used to assess the performance of a structure following the sudden destruction or removal of one or more columns or wall segments. The sudden removal usually takes place in a few milliseconds, with high local strain rates. This phase is not considered here. As forces are redistributed within the structure, it deflects dynamically, reaching a maximum deflection after roughly one second, with strain rates similar to those during an earthquake. This is the phase that is considered in this paper. The concern for design of the building is whether a substantial part of the structure is likely to collapse. This is commonly termed "progressive" or "disproportionate" collapse. The term "disproportionate" is used here. One way to assess the potential for disproportionate collapse is to use nonlinear structural analysis to simulate the dynamic behavior of the structure. This paper uses simple energy balance to explain the essential nonlinear behavior of a frame structure following sudden removal of a column. Based on this explanation, the paper argues that for most structures it is a futile exercise to use nonlinear analysis to assess the potential for disproportionate collapse. Instead, linear analysis can, and should, be used.