Uncertainties in Seismic Collapse Analysis of Framed Structures

Can small-displacement-based solution algorithms be used to predict large displacement responses, such as at collapse or near-collapse? Framed structures often experience large displacement with significant nonlinear response prior to collapse. To capture the nonlinearity in structural response, both geometric and material nonlinearities must be considered in the analysis. The implementation of geometric and material nonlinearities in solution algorithms among various software packages is not treated consistently, where different assumptions are made in the formulations without the users' knowledge. For example, large-displacement-based solution algorithms use finite element formulations that update geometry at every time step, which is significantly different from other structural analysis solution algorithms that use small displacement theory with constant geometric stiffness matrix. These different assumptions introduce levels of uncertainty in the structural response prediction, especially when one solution algorithm predicts structural collapse while another solution algorithm predicts that the structure remains standing. To quantify these uncertainties associated with different small-displacementbased solution algorithms, this research investigates the dynamic instability of framed structures by quantitatively comparing the responses predicted among the associated software packages with a large-displacement-based software package that is more capable of predicting large displacement responses. The focus is placed on how each software package implements geometric nonlinearity for analyzing steel framed structures. Comparing the simulated response history results shows that the mean percentage differences between small-displacement-based and large-displacement-based solution algorithms range from 10 % to 30 % at near-collapse based on the use of seven earthquake ground motions. The outcome of this research provides insights to questions that have often been raised in terms of the precision of small-displacement-based solution algorithms in predicting large displacement response and structural collapse.

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