Modeling Viscous Damping in Nonlinear Response History Analysis of Steel Moment-Frame Buildings: Design-Plus Ground Motions, Revision 1.0
Authors: Qian Xin , Chopra Anil , McKenna Frank 
Published: July 2022

This report investigates the question: can seismic demands on steel moment-frame buildings due to Maximum Considered Earthquake (MCER) design-level ground motions [2% probability of exceedance (PE) in 50 years] be estimated satisfactorily using linear viscous damping models or is a nonlinear model, such as capped damping, necessary? This investigation employs two models of a 20-story steel moment-frame building: a simple model and an enhanced model with several complex features. Considered are two linear viscous damping models: Rayleigh damping and constant modal damping; and one nonlinear model where damping forces are not allowed to exceed a pre-defined bound. Presented are seismic demands on the building due to two sets of ground motions (GMs): MCER design-level GMs (2% PE in 50 years) and rarer excitations (1% PE in 50 years); and even more intense GMs. Based on these results, we do not recommend Rayleigh damping for use in nonlinear response history analysis (RHA) of buildings. Recommended instead is constant modal damping, which also is available in commercial computer codes. Although satisfactory for estimating seismic demands for MCER design-level motions and even more intense GMs, this damping model may not be appropriate for extreme motions that deform the structure close to collapse. Updated October 5, 2020: Revision 1 was issued September 2020, with the following information provided by the authors. Two sections—Introduction and Conclusions—of the report, first issued in June 2020, were expanded in September 2020. These revisions were prompted by comments on a paper submitted to the journal Earthquake Engineering and Structural Dynamics. These comments came from two anonymous reviewers and Michael Constantinou, the editor. The conclusions now emphasize several results of interest to the profession: First, linear viscous damping models are adequate for estimating seismic demands on buildings—designed to satisfy current story drift and plastic rotation limits—due to MCER design-level ground motions (GMs). Second, between the two linear damping models—Rayleigh damping and constant modal damping—the latter is preferable for nonlinear RHA of buildings because it leads to modestly larger demands. This is a prudent choice in the absence of a benchmark or “exact” result. Third, we do not recommend the Rayleigh damping model in nonlinear RHA of buildings because it leads to smaller demands and, hence, could lead to the conclusion that design or evaluation criteria have been satisfied, when other linear damping models lead to the opposite conclusion. Furthermore, various problems and deficiencies have been identified with Rayleigh damping depending on how the yielding elements in the building are modeled. Fourth, if the goal is to arrive at conclusions valid for professional practice, research investigations on modeling damping in nonlinear RHA of buildings should be based on realistic, state-of-the-practice models of buildings subjected to an ensemble of GMs that correspond to the MCER and have been selected by modern methods. In contrast, earlier studies have questioned the validity of linear models, but they typically used simplistic models of buildings and/or extremely intense GMs.