System Safety Performance Metrics for Skeletal Structures

Abstract

A system safety performance metric is a tool to quantify the degree of safety of a structural system for a given performance objective. Classically, safety of skeletal structure as a complete system, designed by member-based structural codes, was evaluated by checking for system stability. Reliability oriented research has focused on ultimate strength and probability of failure as system safety performance objectives, whereas earthquake engineering evaluations have considered displacement as the performance objective. This paper explores and clarifies the connection between system safety and structural redundancy concepts, provides alternative interpretation of structural system redundancy, and proposes two nondimensional system safety performance metrics for skeletal structures with stability as the performance objective. The proposed structural system safety performance metrics conveniently range from 0 to 1, and use algebraic properties of stiffness matrix to (1) measure the minimum distance of stiffness matrix from a set of singular matrices; and (2) quantify the degree of linear dependency of column vectors of the stiffness matrix, respectively. Also, approaches for identifying critical structural member and quantifying failure path importance are addressed.