Reliability assessment of steel braces in seismically retrofitted buildings: A case study using a novel integral extrapolation scheme

The probabilistic assessment of structural reliability under extreme seismic loading is a critical challenge, compounded by the path-dependent nature of damage ('structural memory') and the numerical instability associated with extrapolating from limited, complex datasets. This paper introduces and formalizes a novel Logarithmic Integral Extrapolation Scheme designed to address these challenges. The methodology circumvents the direct fitting of complex distributions by first transforming the empirical failure probability data into a regularized integral domain, which is inherently more amenable to stable extrapolation. The utility and performance of the scheme are demonstrated through its application to a complex dataset of peak axial force demands generated from nonlinear time-history analyses of a six-story reinforced concrete building retrofitted with eccentric steel chevron braces and ductile shear links. The predictive capabilities of the proposed scheme are benchmarked against a conventional 4-parameter Weibull parametric fit. The results demonstrate that the logarithmic integration approach not only provides enhanced numerical stability but also yields a more conservative prediction for the design-level force demands. This enhanced conservatism provides a greater margin of safety for capacity-protected elements, establishing the proposed methodology as a robust and valuable tool for the reliability-based design and assessment of high-performance structural systems.