Evaluation of equivalent modal and uniform damping ratios in hybrid structures

In hybrids, the different damping ratios of two parts of these structures make earthquake design of such structures troublesome procedure. Many design engineers end up using an overall conservative damping ratio equal to 2% in order to be on the safe side. In this paper, the MDOF structure is transformed to a 2-DOF oscillator; in the first step, an equivalent modal damping ratio is proposed. The new 2-DOF equivalent structure with equivalent modal damping ratios has been real appreciated eigen-values. Next step is introducing an equivalent uniform damping ratio that is obtained by semi-empirical error minimization and can be used in available commercial software. The results in models indicate that the use of these damping ratios with acceptable accuracy (in most cases errors are below 5%) and also the response of approximate structure obtained by these damping ratios is much closer to actual one when compared to the usual approach that adopts the overall conservative damping equal to 2%.