The theory of homogeneity of nonlinear structural systems -- A general basis for structural safety assessment

TL;DR

This paper introduces a new theoretical framework for assessing the safety of nonlinear structural systems by characterizing their nonlinearity and establishing bounds for reliability indices, aiding in safety code calibration.

Contribution

It develops a general methodology linking partial safety factors with reliability theory for nonlinear systems, introducing the degree of homogeneity as a key measure.

Findings

Reliability index is bounded by nonlinearity-invariant limits.

Critical safety factors can be determined to ensure target reliability.

Homogeneity analysis helps identify over-safe or under-safe safety cases.

Abstract

The paper develops a novel and general methodology to characterize the nonlinearity of structural systems and to provide a mathematically proven basis for applying partial safety factors to nonlinear structural systems. It establishes, for the first time since the development of limit-state theory, the necessary key relationship between the partial safety factor concept and the reliability theory of nonlinear structural systems. The degree of homogeneity has been introduced as a nonlinearity measure at the design point, allowing an efficient mathematical decoupling of the reliability index into nonlinearity-invariant partial reliability indexes. With this formulation, critical safety situations in extreme cases of nonlinearities have been identified in complex nonlinear structural systems. The theory resulted in two main outcomes based on the asymptotic behaviour of the reliability index. First, the reliability index of any nonlinear structural system remains always bounded between an upper and lower bound, which can be determined by the concept of nonlinearity-invariant partial reliability indexes. The second is nonlinearity-invariant critical partial safety factors, a concept that assures a reliability index greater than the target reliability index in any nonlinear structural system. Homogeneity analysis has been suggested to assess the safety of complex nonlinear structural systems. While it can be coupled with advanced computational methods available in structural mechanics, it is not specifically designed for engineering practice. The proposed theory is designed primarily to provide code writers with the necessary procedure for calibrating partial safety factors for nonlinear structural systems, and to identify the over-safe or under-safe cases in the codes of practice.