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

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.