Categorization of seismically-induced stresses for civil and mechanical engineering

Both civil and mechanical engineers come across loads of the force-controlled type (qualified as “primary”) or of the displacement-controlled type (qualified as “secondary”). For decades, different authors with either civil or mechanical backgrounds have been debating whether a particular seismic load should be classified as primary or secondary, but without apparent mutual understanding or mutual benefit so far. The purpose of this paper is to bring some clarity to the subject by considering a family of oscillators, which are characterized by their ductile capacity, μu, and their “effective stiffness factor”, τ. The considered range of τ values (0 < τ < 1) enables to cover all cases from the perfect damage to the perfect non-damage models. A structural index λ is also introduced, which is a mix of ductility and effective stiffness factor. It is concluded that a seismic input cannot be a priori regarded as primary or secondary. Both the λ value of the structure or component and the slope, p, of the input spectrum in the vicinity of its (dominant) natural frequency should be considered concurrently when making a decision about stress categorization. A margin index m is introduced, which controls seismic load/stress categorization. A formula is given that provides the primary part of a seismically-induced stress.