###### Abstract
The proposed methodology was applied to SDOF linear systems, and demand hazard curves of the relative displacement between adjacent buildings as a function of the 50-year probability of bounding were developed. Thereafter, [PERSON] and [PERSON] [14] recast the bounding issue as an inverse reliability problem and defined the separation distance at a target probability of bounding during the design lifetime of the structure. In 2016, [PERSON] et al. [13] assessed the structural bounding risk through demand hazard curves considering different IMs and regression models. For this purpose, a probabilistic seismic demand model (PSDM) in terms of the peak relative displacement between the adjacent structures was introduced. Finally, [PERSON] et al. [36] developed a probabilistic procedure to determine the critical separation distance. They assessed the bounding probability in 50 years in terms of the peak relative displacement between the adjacent structures. Different parameters, such as the adjacent structures' period ratio and the seismic hazard curve of the examined site, have been considered to evaluate their influence on the magnitude of the critical separation distance. [PERSON] et al. [37] evaluated the MAF of collapse, taking into account different separation gap distances and floor-to-floor bounding cases of nonlinear MDOF models. Recently, in 2023, the first decision model for the verification of structural performance due to bounding conditions was presented in the literature [38]. Linear and bilinear PSDMs were developed, different EDPs were involved, and performance objectives (POs) for structural bounding conditions were introduced. The above review of the literature indicates the following shortcomings: (a) the structural bounding risk is expressed only as the probability of exceedance of the peak relative displacement of the colliding structural systems, (b) the magnitude of the critical separation gap distance is estimated based only on this displacement demand parameter, and (c) none of the existing risk-targeted methods involve a decision concept that controls the seismic local or global demand hazard of a structure due to the structural bounding effect. So, the objective of this study is to overcome these limitations and provide a new risk-targeted method that defines (a) the optimal separation gap distance \(\left(\mathrm{d}_{\mathrm{g,min}}^{\mathrm{Pt}}\right)\) at a targeted value of bounding risk (probability per year) \(\mathrm{Pt}\) (Decision A) and (b) the minimum acceptable structural bounding risk \(\mathrm{p}_{\mathrm{min}}^{\mathrm{d}_{\mathrm{g,t}}}\) at a targeted value of separation gap distance \(\mathrm{d}_{\mathrm{g,t}}\) (Decision B). The method is based on two distinct acceptable performance objectives, the POs-\(\delta_{\mathrm{max}}\) and the POs-EDP, defined as a function of \(\mathrm{P}\) vs. \(\mathrm{d}_{\mathrm{g}}\). Each pair of \(\mathrm{P}_{1}\)-\(\mathrm{d}_{\mathrm{gi}}\) indicates the acceptable bounding risk (probability per year) at the capacity level of an EDP when the separation distance is equal to \(\mathrm{d}_{\mathrm{gi}}\). For the needs of this attempt, a seismic hazard curve compatible with Eurocode's 8 hazard zone is adopted, and the corresponding demand hazard curves of \(\delta_{\mathrm{max}}\) and EDP are developed. Thereafter, an eight-story RC structure with the potential top point of colliding being the fourth story is examined (floor-to-floor interaction type). IDAs are performed, and the demand hazard curves of \(\delta_{\mathrm{max}}\) and \(\mathrm{IDR}_{\mathrm{max}}\) are developed based on linear PSDMs and linear approximation of the site hazard curve. The bounding hazard of the structure is evaluated based on the proposed method taking into account different risk-targeted scenarios.