PSI - Issue 64

Edward Steeves et al. / Procedia Structural Integrity 64 (2024) 1975–1982 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

1977

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Although not properly distinguished from robustness, structural redundancy has been defined as the ability of the originally intact system to continue to carry load after first element failure (Miao and Ghosn 2016), and has been advocated as beneficial for structural robustness (Izzuddin et al. 2008). A similar definition describes redundancy as the capability of a bridge superstructure to continue carrying load after element-level damage (Ghosn and Moses 1998). A more recent interpretation defines redundancy as the availability of alternate load paths allowing a load to transfer from the point of application to the point(s) of resistance within the structure if the primary load path is compromised (Fiorillo and Ghosn 2022). More generic definitions suggest redundancy is generally attributed to redistribution of forces so that more load can be carried than that indicated by structural analysis (Galambos 1990), or simply the availability of warning before collapse (Hendawi and Frangopol 1994). Based on these findings, redundancy is a structural property that can be measured for both damaged and intact systems. It must account for the structure’s ability to carry additional load after element failure, redistribution of forces after local damage, and element-level ductility. Lastly, robustness and redundancy should be distinguished from resilience, which has been defined as the ability of a community built around a structure to recover from economic losses resulting from damage (Bhattacharya 2021). Resiliency has been presented as a function of redundancy and robustness (Argyroudis 2022) and has also been described as the structure’s ability to maintain a level of robustness in a damaged state and return to a desired level of performance in an expeditious timeframe (Minaie and Moon 2017). This paper is focused on advancing the current measures of structural robustness and structural redundancy as opposed to resilience, since the former are structural engineering concepts and research related to the latter must account for socio-economic aspects of structural collapse. Multiple structural robustness measures have been published in peer-reviewed journals and technical documents since the 1980’s. Not all the measures are referred to as “structural robustness” measures given that the definition of robustness has been evolving over time (Bhattacharya 2021). In general, robustness measures can be classified as either deterministic, probabilistic, or risk-based. Representative measures from each of these categories were selected and presented below to illustrate the advantages and disadvantages of each. Ultimately, a holistic structural robustness and structural redundancy index formulated by Steeves and Oudah (2024) are selected to use in the case study in the following section. Deterministic: residual redundant factor (Frangopol and Curley 1987): = (1) is the load carrying capacity of the damaged structure, and is the load carrying capacity of the intact structure (Frangopol and Curley 1987). Probabilistic: structural robustness index (Bhattacharya 2021): = (− − ′ ) (2) is the reliability index of the intact structure, and ′ is the reliability index conditioned on the loss of element (Bhattacharya 2021). 3. Structural robustness measures 3.1. Existing robustness measures