RELIABILITY-ANALYSIS OF TRUSS STRUCTURES WITH MULTISTATE ELEMENTS .2.

Structural systems are typically redundant, and collapse usually occurs after a sequence of failures. This has led to failure-path approaches in which one identifies important sequences of element failures leading to collapse and estimates the probability of structural failure as the probability that one of these important sequences occurs. In this paper, failure-path approaches are extended from the two-state element representation (in which an element is either safe or failed) to a multistate representation in which the element has piecewise linear force-deformation characteristics. This allows realistic modeling of nonlinear element behavior including buckling, inelastic strain softening, strength degradation, etc. The basic event is the force/deformation in an element exceeding its limits and causing a change in the structure stiffness. An exact formulation of this event (and an approximate formulation for use in computations) is presented. The possibility of load decrements (e.g., due to buckling) and structure state changes during the decrements is included. The branch and bound search algorithm is used to identify important sequences of structure state changes leading to collapse and efficient first-order reliability methods are used for probability computations.