Equivalent Damping in Support of Direct Displacement-Based Design

The concept of equivalent linearization of nonlinear system response as applied to direct displacement-based design is evaluated. Until now, Jacobsen's equivalent damping approach combined with the secant stiffness method has been adopted for the linearization process in direct displacement-based design. Four types of hysteretic models and a catalog of 100 ground motion records were considered. The evaluation process revealed significant errors in approximating maximum inelastic displacements due to overestimation of the equivalent damping values in the intermediate to long period range. Conversely, underestimation of the equivalent damping led to overestimation of displacements in the short period range, in particular for effective periods less than 0.4 seconds. The scatter in the results ranged between 20% and 40% as a function of ductility. New equivalent damping relations for four structural systems, based upon nonlinear system ductility and maximum displacement, are proposed. The accuracy of the new equivalent damping relations is assessed, yielding a significant reduction of the error in predicting inelastic displacements. Minimal improvement in the scatter of the results was achieved, however. While many significant studies have been conducted on equivalent damping over the last 40 years, this study has the following specific aims: (1) identify the scatter associated with Jacobsen's equivalent damping combined with the secant stiffness as utilized in Direct Displacement-Based Design; and (2) improve the accuracy of the Direct Displacement-Based Design approach by providing alternative equivalent damping expressions.