A new formulation for a code-based vertical design spectrum

Consideration of vertical seismic design loads is important for long-span structural systems, short-period structures, and for some nonstructural components in the buildings. To this end, seismic design codes utilize alternative approaches to define vertical design spectrum at different levels of complexity: either as a fraction of horizontal design spectrum or using a separate functional form having features different than the horizontal spectrum. In all cases, a consistency between the horizontal and vertical design spectral ordinates is sought. In this paper, we consider a set of modern seismic design codes, horizontal and vertical ground-motion datasets, as well as ground-motion predictive models (GMPMs) to assess the accuracy of code-based vertical design spectrum expressions. We compute horizontal and vertical spectra for different earthquake scenarios (magnitude-distance-soil condition combinations) from the selected horizontal and vertical GMPMs for comparisons with their code-based (idealized) counterparts. Besides that, we study the vertical spectrum behavior from observed ground-motion data. Our observations suggest that the vertical design spectrum formulations by current codes do not fully explain the actual vertical spectral acceleration trends. We discuss the possible reasons behind the misrepresentation of vertical spectrum by the current code approach and introduce our own expressions to compute horizontal spectrum consistent vertical design spectrum from a comprehensive simulated dataset of correlated vertical and horizontal spectral ordinates.