Viscous Damping in Inelastic Structural Response

A practical method for proper modeling of structural damping in inelastic plane structural systems

“…Solutions to this problem have been proposed by Bernal [3], Hall [5], and Charney [8]. Bernal [3] proposed a solution in which Caughey-type damping should be used and the damping matrix should be assembled by restricting the exponents of the Caughey series (l terms in Eq.…”

“…As shown by Bernal [3], Medina and Krawinkler [4], and Hall [5], when Rayleigh-type damping based on the initial stiffness matrix is used, unrealistic damping forces are generated at joints in which structural elements undergo abrupt changes in stiffness. This is due to the tendency of degrees of freedom with small inertias to undergo abrupt changes in velocity once the stiffness of the element changes during the inelastic response [3]. Thus, unrealistic damping forces develop at these degrees of freedom resulting in an underestimation of the peak displacement demands in the structure and an overestimation of internal forces for elements in the system that do not undergo changes in stiffness [4].…”

Effect of record scaling on the behavior of reinforced concrete core-wall buildings subjected to near-fault and far-fault earthquakes

“…Inappropriate choices may not simulate the real responses of a structure and are primarily the result of numerical errors [35]. Bernal [36] showed that Rayleigh damping may lead to excessive damping forces. Chopra [37] believed that Rayleigh damping cannot be used unless similar damping mechanisms are provided throughout the structure.…”

Modelling of elastic damping in nonlinear time-history analyses of cantilever RC walls

“…In the work of several researchers (Chrisp 1980;Hall 2005;Charney 2008) the unforeseen consequences by the use of Rayleigh damping are illustrated through a number of examples. Specifically, Chrisp (1980) concluded that the use of Rayleigh damping without ensuring that the higher modes are sub-critically damped is responsible for excessive damping forces accompanied by loss of equilibrium locally in the structure, while Bernal (1994) reported the appearance of spurious damping forces. Similarly, Hall (2005) showed that when significant yielding takes place, the Rayleigh damping model may produce "a damping force that is relatively high in relation to the strength of the building" that cannot be physically justified, implying non conservative analysis results.…”

“…Thus, it becomes apparent that this modelling choice will alter the relative contribution of each mode, raising doubts about the final reliability of the analyses results. Finally, Bernal (1994) draws the attention to the application of Rayleigh damping when there are degrees of freedom without mass, a case not examined in this work since the case-study walls, presented in following section, were modelled as stick elements (Giberson 1967) with discrete mass at each floor level that corresponds to one degree of freedom.…”