Performant design tools based on random vibrations and first-passage principals for resistant NcD structures under stochastic earthquakes

Response Spectrum (RS) tools, commonly used in aseismic-design codes, exhibit a significant limitation due to their inability to address non-classically damped (NcD) systems. This research tackles this challenge with original design-oriented RS tools, specifically tailored to NcD systems, unveiling a new concept: the non-classical response spectrum (NcRS). For the first time, the non-classical damping (NcDing) effect is presented as a disturbance in the conventional RS, depending on a phase shift angle serving as a modal NcDing indicator. Then, a practical NcRS model, based on white noise (WN), is proposed allowing the generation of modified response spectra through effortless calibration of conventional ones. Further contribution involves introducing single-termed non-classical cross-correlation (Nc-Cc) coefficients, unique in their independence from structural properties. Afterwards, a random-vibrations-based exact non-classical response spectrum method (ENcRSM) is developed. The ENcRSM's novelty lies in its applicability to arbitrary frequency distributions inputs. Another contribution is the practical NcRSM, derived from the original WN-based Nc-Cc and NcRS tools, aligning with aseismic regulations. Validation of the NcRS models through artificial simulations involving stochastic seismic motions, demonstrates their excellent performance. Numerical implementations showcase the superior effectiveness of Nc-Cc coefficients, particularly in high NcDing scenarios. Applying these design tools to a benchmark equipment-structure system illustrates their outperformance over classical methods, revealing instances where the latter may lead to unsafe designs.