Seismic Energy Dissipation in Inelastic Frames: Understanding State-of-the-Practice Damping Models

Abstract

During seismic action, energy dissipation in structures occurs in structural and non-structural components, as well as in the substructure. Several of these dissipative mechanisms are modelled explicitly in nonlinear dynamic analyses, notably through relatively sophisticated hysteretic finite elements. Nevertheless, in most practical applications, it is not possible to simulate all the physical contributions to energy dissipation.Structural engineers are thus constrained to overcome this limitation by a mathematical artifice, in the form of equivalent linear viscous damping, which accounts for the remaining ‘un-modelled’ energy dissipation. The state-of-the-practice damping models that are currently available to practitioners and researchers are basically the following: mass-proportional, initial stiffness-proportional, tangent stiffness-proportional and Rayleigh damping. The first goal of this paper is to revise the motivation behind their introduction in nonlinear dynamic analyses as well as to recall their general theoretical background and known problems.The second objective is to critically examine the abovementioned alternatives, using, for illustrative purposes, a cantilevered reinforced concrete column with a mass on its top. This simple specimen was tested in a shaking table; hence, the additional complexity originating from non-structural and sub-structural energy dissipation is of no concern. Although a few qualitative remarks are made by comparing the experimental and numerical displacement time-histories, fundamental assessment is carried out on the basis of only the numerical behaviour of the distinct damping models and undamped response, interpreted from a yet unreported viewpoint. Namely, the evolution with time of several force quantities unveils unexpected features of the damping models as well as surprising differences between them. Furthermore, complex interaction phenomena, typical of nonlinear analyses, between the horizontal, rotational and vertical vibrations are also interpreted. Finally, some conclusions and practical recommendations regarding the use of damping models are presented, which may eventually be extended to other structural types in future validation studies.