Inelastic velocity ratio George D. Hatzigeorgiou 1, * ,† and George A. Papagiannopoulos 2 1 Department of Environmental Engineering, Democritus University of Thrace, GR-67100 Xanthi, Greece 2 Department of Civil Engineering, University of Patras, GR-26500 Patras, Greece SUMMARY Knowledge of maximum velocity is essential for the design of structures and especially those with supple- mentary dampers. Although the nonlinear time history analysis leads to reliable estimation of actual veloc- ities, it seems to be complicated for the everyday engineering practice due to the increased computational cost. This paper proposes an alternative for single-degree-of-freedom (SDOF) systems to estimate the actual velocity in a straightforward and effective manner. More specifically, this study examines the inelastic velocity ratio (IVR), i.e., the ratio of the maximum inelastic to the maximum elastic velocity of an SDOF system, the knowledge of which allows the computation of maximum inelastic velocity directly from the corresponding elastic counterpart. The proposed method is general and can be applied to both conventional structures and structures with supplementary dampers. Extensive parametric studies are conducted to obtain expressions for IVR in terms of the period of vibration, viscous damping ratio, force reduction factor, and soil class. Copyright © 2012 John Wiley & Sons, Ltd. Received 20 June 2011; Revised 18 January 2012; Accepted 25 January 2012 KEY WORDS: inelastic velocity ratio; viscous dampers; performance based seismic design 1. INTRODUCTION Conventional seismic design aims to prevent structures from collapse by permitting structural members to dissipate the input seismic energy through inelastic deformations. In this case, energy dissipation takes place in specially detailed sections of the structural members, i.e., in plastic hinges. However, this design philosophy allows a confident level of structural damage that frequently requires costly rehabilitation procedures. On the other hand, a different option to the aforementioned conventional seismic design is the installation of passive energy dissipation devices (PEDD). The role of adopting these devices is to provide supplemental damping and convert a part of the input seismic energy to heat [1]. In this case, the structural response due to earthquake motions is reduced by the dissipation of the major part of earthquake input energy. For the current practice and recent developments on these systems, the reader can consult the paper of Symans et al. [1]. Typical examples of PEDD are the viscous fluid dampers, which have been extensively used in military and aerospace industry and have recently been applied to civil structures. These devices are the most commonly used type of dampers today and consist of a piston filled with viscous fluid where its movement causes energy dissipation [2]. It should be noted that the output force of viscous damper is directly related to velocity and usually possesses only viscosity. Generally, the use of PEDD leads to reduced displacement structural response. Nevertheless, nonlinear time history analysis is also required for the majority of passively damped civil structures, since their earthquake vibration induces inelastic deformations in one or more structural elements [3, 4]. *Correspondence to: George Hatzigeorgiou, Environmental Engineering Department, Democritus University of Thrace, GR-67100 Xanthi, Greece. † E-mail: gchatzig@env.duth.gr Copyright © 2012 John Wiley & Sons, Ltd. EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS Earthquake Engng Struct. Dyn. 2012; 41:2025–2041 Published online 27 February 2012 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/eqe.2172