Calibration of a new metric for computing structural robustness

Structural robustness has emerged as a fundamental property in the design of structures in modern days, reflecting the need for system-level design approach against unforeseen and accidental actions. In fact, traditional design approaches based on member-level checks, mainly for strength and stability, have proven to be not sufficient in some occurrences, in particular in case of local damages. Despite its recognized importance, structural engineers and the research world around it are still struggling in assessing robustness in a quantitative way. This thesis aims thus to try filling that gap, by calibrating and developing a new quantitative metric based on connectivity for assessing robustness of frame structures, starting from the Resilience Index proposed by Chiaia et Al. (2019). The metric evaluates the response of a frame structure to a local damage, by analysing its kinematic matrixes for every possible damage scenario, defined by the removal of elements and degree of constraints. The work so begins with a wide theoretical framework. First the evolution of the concept of robustness is analysed, along with its history and definitions, showing also its integration in some of the major international standards (Eurocode, U.S. and Canadian codes). Subsequently, the mathematical formulation of the metric is discussed, together with its original MATLAB implementation. Such program automatically constructs kinematic matrixes from structural data (only topology and constraints setup) for the frame itself and for every analysed damaged condition, computing finally a scalar robustness index which quantifies the system’s ability to avoid disproportionate collapse after a local damage. It follows an accurate calibration phase, in which are defined the constants that govern the metric, ensuring physical meaningfulness and that the contributions of different damage typologies are equally balanced. The metric is then tested against a series of operative properties, each reflecting a precise expectation for a general robustness metric, as to assess its consistency with intuitive structural behaviour. Finally, future possible developments are highlighted, with special focus on the introduction of a genetic algorithm, to identify efficiently critical scenarios and avoid calculating every possible one, preventing computational burden, which otherwise arises as a main limitation across the whole thesis work. The concluding chapter then summarises obtained results, discussing the potential of the proposed approach as a way how to give a scalar value to such a complex structural aspect.