Epistemic Uncertainty in Solution Algorithms for Analyzing the Geometric Nonlinearity of Framed Structures

One important aspect of performance-based earthquake engineering is developing structural models that can accurately capture key characteristics of dynamic responses up to structural collapse. This in turn requires the solution algorithm to be capable of capturing large displacement responses through appropriate use of geometric nonlinearity. Small-displacement-based solution algorithms possess this capability in the analysis with high computational efficiency and relatively good accuracy; while large-displacement-based finite element analysis algorithms address geometric nonlinearity through satisfying equilibrium in the deformed position which capture large displacement accurately but with poor computational efficiency. The objective of this research is to investigate the impact of epistemic uncertainty in small-displacement-based algorithms for capturing large displacement responses. Consistent models of steel moment frames are developed for analysis using various solution algorithms based on different geometric nonlinearity formulations. Response history analysis is performed under the same input ground motions. Analysis results show that some formulations address the geometric nonlinearity more appropriately with less uncertainty than others.