Evaluating the Most Common Modeling Methods of Rayleigh Damping and the Critical Damping Ratio Limitation Approach

Tunc Deniz Uludag, University of Nebraska-Lincoln

Document Type Article

A THESIS Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Master of Science, Major: Architectural Engineering, Under the Supervision of Professor Jay A. Puckett. Lincoln, Nebraska: December 2020

Copyright 2020 Tunc Deniz Uludag

Abstract

Performance-based design such as FEMA P-695 and ASCE 7 prescribe/limit damping ratios associated with dynamic nonlinear seismic analysis; however, the method for computing inherent damping is not prescriptive. The analyst in conjunction with the peer-review panel (FEMA P-695) or authority having jurisdiction (ASCE 7) must determine how damping is modeled. Depending upon the method, e.g., Rayleigh, simulations can result in significantly different responses even with the same assumed damping ratio. Note that over estimating damping will underestimate energy absorption by inelastic displacement, a non-conservative outcome.

FEMA P-695 non-linear time history analysis of 44 earthquakes was used for several Rayleigh methods to model four- and nine-story archetypes. The collapse margin ratios were obtained to assess the effect on collapse prediction. The results varied significantly depending upon the Rayleigh approach.

A new framework is proposed by limiting the energy dissipated by inherent damping, not using a damping ratio directly. This approach helps to ensure that the procedure (described by FEMA P-695, or ASCE 7) is prescriptive enough to prevent the unintended and non-conservative consequences and promote consistency of results. The approach is functional for time histories and are critical for determining the collapse margin ratio.

The new method provides similar collapse margin ratios invariant with the particularities of the Rayleigh method. This approach may provide code writing committees, and authorities having jurisdiction, a definitivemethod for consistently prescribing/limiting inherent damping energy as a percent of seismic energy input, thereby forcing the reminder of the energy dissipation into planned inelastic deformations. Although, the present work is limited to buckling restrained braced frames, the framework should work across various structural systems. The percentage associated with inherent damping will depend upon the structural system and is not addressed in the present work is left to experts in particulars for each system.

Advisor: Jay A. Puckett