A new generation of DCR by introducing reliability-survivability safety measure

The traditional approach to assessing structural safety, using the Demand-Capacity Ratio (DCR), evaluates the adequacy of a structure by comparing its demand (applied loads) to its capacity (ability to resist loads). However, this method, which expresses the DCR as a deterministic value, is limited by its failure to acknowledge the probabilistic nature of structural demand and capacity, its lack of a direct correlation with the system's overall reliability, and its disregard for the effects of structural stability or survivability on failure patterns. Addressing these limitations, this study introduces a novel DCR framework that integrates a reliability-survivability metric to enhance the representation of structural safety. The proposed framework presents a vector-based DCR that encapsulates the randomness inherent in structural demand and capacity. It introduces a 'survivability index' to rank structural components based on stability considerations. It offers a more efficient alternative to existing robustness or progressive collapse metrics due to its reduced computational demands and ability to account for the simultaneous reduction in resistance across elements following a disruptive event. In addition, the study leverages graph theory to establish a system reliability matrix, from which the system reliability index is calculated using eigenvectors and Jacobian transformations. This leads to an innovative reliability-survivability safety measure derived from the product of the system's reliability and survivability indices. This measure compares the ideal structure with perfectly designed elements (representing demand) to the actual structural design condition (representing capacity), culminating in a new-generation DCR that embodies the Reliability-Survivability Safety Measure (RSSM). To illustrate the application and benefits of the RSSM, this paper presents a detailed procedure through case studies of various structural archetypes and frames, highlighting the advantages of this advanced method in structural safety assessment.