Chapter 27 Estimating Effective Viscous Damping and Restoring Force in Reinforced Concrete Buildings P. Hesam, A. Irfanoglu, and T.J. Hacker Abstract In seismic design, buildings are designed to respond to strong earthquake ground motions inelastically. The engineering norm followed in design and analysis is to use constant modal viscous damping ratios to account for all energy dissipation aside from that arising from material nonlinearity. In general, equivalent linear models, which aim to capture primarily the peak response with typically 2–5 % of critical damping are employed. In this paper, we show that the effective viscous damping ratio can be estimated from the dynamic response of actual building structural systems without linearization of the load-deformation characteristics. The empirical method we present, which estimates the effective viscous damping ratios of buildings, has been applied to several laboratory specimens and actual buildings. We show that the effective viscous damping ratio in a low to mid-rise reinforced concrete (RC) building responding at its dominant mode (equivalent of fundamental mode in linear elastic systems) varies linearly with the effective period of its dominant mode. The practical use of the method is demonstrated using acceleration records obtained in two 9-story small-scale RC laboratory test specimens during a series of strong base motions. Fundamental mode envelopes of hysteretic responses, that is, the backbone curves for both structures are estimated by excluding higher mode effects from the measured responses. Keywords Effective viscous damping ratio • Viscous damping coefficient • Reinforced concrete buildings 27.1 Introduction The response of buildings to earthquake ground shaking is a complex process. During strong shaking, the structural system of the building may be forced to behave inelastically. In addition to the hysteretic energy dissipation due to inelastic behavior, the structure will dissipate energy through means currently not well understood. In the simplest of approaches, linear viscous damped models with constant modal damping ratios are used. More elaborate models may use Rayleigh damping or Caughey damping [1] but not necessarily always with justification [2]. Compared with assuming a constant value for the viscous damping ratios, say, 2 % or 5 % of the critical damping, using effective damping ratios estimated from the dynamic response of actual building structural systems would be more realistic. Such an empirical approach may also help identify the structural system and response parameters that are well-correlated with the damping ratio. An empirical method based on the procedure proposed by Dowgala [3] is presented here. The method is applied to two 9-story reinforced concrete laboratory specimens tested on a shaketable at the University of Illinois at Urbana-Champaign. 27.2 Background Based on tests by Eberhard [4] and Schultz [5], Algan [6] observed that the peak inelastic displacement of a reinforced concrete (RC) structure subjected to a strong ground motion (GM) correlates with its elastic fundamental period. Different methods have been proposed to estimate the maximum inelastic deformation using equivalent periods and damping ratios (for example, Lepage [7] or displacement modification factors Newmark [8] and Miranda [9]). The key parameters P. Hesam( ) • A. Irfanoglu Lyles School of Civil Engineering, Purdue University, West Lafayette, IN 47907, USA e-mail: pedramhesam@purdue.edu; ayhan@purdue.edu T.J. Hacker Department of Computer and Information Technology, Purdue University, West Lafayette, IN 47907, USA e-mail: tjhacker@purdue.edu © The Society for Experimental Mechanics, Inc. 2016 S. Pakzad, C. Juan (eds.), Dynamics of Civil Structures, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-29751-4_27 265
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