A re‐evaluation of equivalent linear models for simple yielding systems

Abstract

Commonly used equivalent linear models for simple yielding systems subjected to harmonic and earthquake excitations are re‐evaluated. It is shown that with respect to damping, these models contain the same basic information. Reported differences in the literature are simply due to scaling: since the product of the equivalent stiffness and equivalent damping is a constant, smaller damping values would be obtained by the use of the small amplitude equivalent stiffnesses. It is argued that for harmonic excitation, the secant stiffness is an appropriate representation of equivalent stiffness, leading to large equivalent damping values that increase with ductility. For earthquake excitation the Iwan proposal is shown to be the preferred model leading to larger damping values than previously reported. A comparison of the models for harmonic and earthquake excitations shows that, in general, and at comparable ductilities, damping values due to harmonic excitation are about five times those due to earthquake excitation, and the period changes due to harmonic excitation are about twice those due to earthquake excitation.

Effect of damping model on pre-yielding earthquake response of structures

“…However, this time a certain pattern can be observed -for very short natural periods of the systems (i.e., when values of T m /T 0 and, subsequently, of the equivalent damping ratio are high) the linear system has lower maximum displacements and higher values of the dissipated energy than the corresponding hysteretic system; this is opposite for long natural periods of the systems (see Figs. [5][6][7][8][9][10]. This indicates that the values of the ratio T m /T 0 used in Eq.…”

“…[5][6][7][8][9][10]. This is easily explained -choice of a particular value of the loss factor, ξ , of a hysteretic system in accordance to the damping ratio, ζ e , of a linear system (or vice versa) may provide a good agreement between the system responses to harmonic loading with a certain frequency but the frequency content of an earthquake load is random.…”

“…There have been a number of studies on the performance of the different analytical methods for the linearization of nonlinear systems subjected to earthquake loading. However, these comparative studies were limited to the case of nonlinearity associated with yielding so that a nonlinear system was usually presented by a simple bilinear model (e.g., [5,8,9]). Thus, no data are currently available which could give a clear indication which of the analytical linearization methods is the most suitable for the purpose of the present study.…”

“…In this case modeling damping as viscous (i.e., rate-dependent) may be a cause of error in the prediction of structural response. It should be noted that there have been a number of proposals to model the energy dissipation due to plastic deformations by using the equivalent viscous damping model (e.g., [5][6][7][8][9]) but this problem is out of the scope of the present paper.…”

Effective linear damping and stiffness coefficients of nonlinear systems for design spectrum based analysis

“…This was done vis-à-vis numerical results obtained by integrating the nonlinear equations of motion for an ensemble of 12 recorded accelerograms. Similarly, Hadjian [21] compared the formulae for defining equivalent linear properties resulting from several linearization techniques for elasto-plastic SDOF hysteretic systems. All the linearization techniques considered in these early studies define deterministically the ELSs without considering the statistical attributes of the seismic hazard explicitly.…”