Abstract Structures consisting of two parts, a lower part made of concrete and an upper part made of steel are investigated. In code-based seismic design of such structures several practical difficulties are encountered, due to inherent differences in the nature of dynamic response of each part. The specific issue addressed here is the analysis complications due to the different damping ratios of the two parts. Such structures are irregularly damped and have complex modes of vibration, so that their analysis cannot be handled with readily available commercial software. This work aims at providing a simple yet sufficiently accurate methodology for handling the damping irregularity of such structures, by proposing an overall equivalent damping ratio that can be applied to the complete structure for obtaining its dynamic response. This is achieved by first transforming MDOF irregular structures into equivalent 2-DOF oscillators, using the first mode characteristics of each part, and then using equivalent uniform damping ratios that are derived by means of a semi-empirical error minimization procedure. Thus, available commercial software can be applied for seismic analysis and design and the provisions of existing seismic codes can be adhered to.