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

The Rayleigh damping model, which is pervasive in nonlinear response history analysis (RHA) of buildings, is shown to develop spurious' damping forces and lead to inaccurate response results. We prove that a viscous damping matrix constructed by superposition of modal damping matricesirrespective of the number of modes included or values assigned to modal damping ratioscompletely eliminates the spurious' damping forces. This is the damping model recommended for nonlinear RHA. Replacing the stiffness-proportional part of Rayleigh damping by the tangent stiffness matrix is shown to improve response results. However, this model is not recommended because it lacks a physical basis and has conceptual implications that are troubling: hysteresis in damping force-velocity relationship and negative damping at large displacements. Furthermore, the model conflicts with the constant-damping model that has been the basis for fundamental concepts and accumulated experience about the inelastic response of structures. With a distributed plasticity model, the structural response is not sensitive to the damping model; even the Rayleigh damping model leads to acceptable results. This perspective on damping provides yet another reason to employ the superior distributed plasticity models in nonlinear RHA. OpenSees software has been extended to include a damping matrix defined as the superposition of modal damping matrices. Although this model leads to a full populated damping matrix, the additional computational demands are demonstrated to be minimal. Copyright (c) 2015 John Wiley & Sons, Ltd.