Initial versus tangent stiffness‐based Rayleigh damping in inelastic time history seismic analyses

Abstract

SUMMARYIn the inelastic time history analyses of structures in seismic motion, part of the seismic energy that is imparted to the structure is absorbed by the inelastic structural model, and Rayleigh damping is commonly used in practice as an additional energy dissipation source. It has been acknowledged that Rayleigh damping models lack physical consistency and that, in turn, it must be carefully used to avoid encountering unintended consequences as the appearance of artificial damping. There are concerns raised by the mass proportional part of Rayleigh damping, but they are not considered in this paper. As far as the stiffness proportional part of Rayleigh damping is concerned, either the initial structural stiffness or the updated tangent stiffness can be used. The objective of this paper is to provide a comprehensive comparison of these two types of Rayleigh damping models so that a practitioner (i) can objectively choose the type of Rayleigh damping model that best fits her/his needs and (ii) is provided with useful analytical tools to design Rayleigh damping model with good control on the damping ratios throughout inelastic analysis. To that end, a review of the literature dedicated to Rayleigh damping within these last two decades is first presented; then, practical tools to control the modal damping ratios throughout the time history analysis are developed; a simple example is finally used to illustrate the differences resulting from the use of either initial or tangent stiffness‐based Rayleigh damping model. Copyright © 2013 John Wiley & Sons, Ltd.

Modeling viscous damping in nonlinear response history analysis of buildings for earthquake excitation

“…To reduce the unbalanced moments at joints arising from Rayleigh damping, several researchers have proposed to modify the stiffness‐proportional term by replacing the initial stiffness matrix by the tangent stiffness matrix, that is, …”

“…This remedy is not appealing because no objective basis exists for deciding on this bound. As mentioned earlier, to limit the damping forces after yielding of the structure, several researchers have proposed replacing initial stiffness by the tangent stiffness in Rayleigh damping [Equation ].…”

How Are the Equivalent Damping Ratios Modified by Nonlinear Engineering Demand Parameters?

“…hysteretic and viscous damping) can compromise the validity of a study and could require a reduction of the viscous damping in the nonlinear range [3]. In order to represent this dependency, several evolving Rayleigh-type viscous damping models have been proposed (see [6] for a study of such models), but experimental evidences on slender buildings tend to show that modal viscous damping can be thought to be an intermediate between constant viscous damping for all modes and stiffness-proportional damping [7,8]. Before performing such a fine analysis, simplified methodologies should be used in order to obtain a first design of a structure.…”

Seismic Performance Evaluation of Double‐Skin Semi‐Base‐Isolated Building Using Incremental Dynamic Analysis

“…A value of 5% Rayleigh damping, mass, and sti ness proportional damping, was used in the dynamic analysis [52,53]. e gravity load combinations for nonlinear analysis were di erent from design gravity load combinations, and e ective seismic weight for each oor was estimated using the load combination 1.05 DL + 0.25 LL [54,55] and was converted to lumped masses at beam-column joint in the story levels for dynamic analysis, where DL is the nominal and superimposed dead load of the structure, and LL is the nominal live load.…”