Analytical Floor Response Spectra for Performance-Based Seismic Design of Non-structural Elements in Reinforced Concrete Frame Buildings

Damage to non-structural elements significantly impacts the seismic performance of buildings in terms of economic and functionality losses. Consequently, performance-based seismic design of non-structural elements has become a key pillar of a comprehensive building-seismic resilience strategy, for instance, through loss-targeted earthquake design. An essential aspect in the seismic design of non-structural elements is the definition of seismic demands in terms of absolute acceleration and relative displacement floor response spectra. However, most existing methods for estimating floor response spectra require detailed information about the dynamic properties of the supporting structure, as well as time-consuming numerical analyses. This hinders the seamless integration of performance-based seismic design of non-structural elements into risk-targeted seismic design frameworks for buildings, where multiple structural solutions are evaluated to identify the optimal, loss-minimising design. Building on an existing refined methodology, this paper presents an analytical approach to estimate floor response spectra in regular reinforced concrete frame supporting structures, eliminating the need for preliminary numerical structural analyses. In particular, the simplifications include: estimating the force-displacement curve of the supporting structure using available equilibrium-based formulations, estimating the fundamental period of the supporting structure directly from such curve and estimating the fundamental mode shape using a closed-form equation. The ranges of higher mode periods and the higher mode shapes are estimated using a consolidated reduced-order model formulation. The proposed procedure is benchmarked against the results from non-linear time history analyses of four archetype reinforced concrete frames representative of modern building typologies typical of high-seismicity regions for a wide range of structural performances. For most case studies, the proposed methodology provides mean relative errors below 20% and close to 10%. The proposed methodology provides higher errors close to the yield point of the supporting structure, although these estimates are generally conservative.