Imperfection Sensitivity and Reliability Using Simple Bar-spring Models for Stability

The objective of this paper is to demonstrate how simple bar-spring models can illustrate elementary and advanced structural behavior, including stability, imperfection sensitivity, and plastic collapse. In addition, the same bar-spring models also provide a ready means for assessing structural reliability. Bar-spring models for a column (both post-buckling stable and unstable), a frame, and a plate are all developed. For each model the influence of geometric imperfections are explicitly introduced and the ultimate strength considering plastic collapse of the supporting springs derived. The developed expressions are compared to material and geometric nonlinear finite element analysis models of analogous continuous systems, using yield surface based plastic hinge beam elements (in MASTAN) for the column and frame and shell elements (in ABAQUS) for the plate. The results show excellent qualitative agreement, and surprisingly good quantitative agreement. The developed bar-spring models are used in Monte Carlo simulations and in the development of first order Taylor Series approximations to provide the statistics of the ultimate strength as used in structural reliability calculations. Good agreement between conventional first order second moment assumptions and the Monte Carlo simulations of the bar-spring models is demonstrated. It is intended that the developed models provide a useful illustration of basic concepts central to structural stability and structural reliability.