Structures consisting of concrete and steel parts, which are irregular in damping ratios are investigated. This investigation is a code-based seismic design of such structures. Several practical difficulties encountered, due to inherent differences in the nature of dynamic response of each part, and the different damping ratios of the two parts. These structures are irregular in damping ratios and have complex modes of vibration so that their analysis cannot be handled with the readily available commercial software. Therefore, this work aims to provide simple yet sufficiently accurate constant values of equivalent damping ratios applied to the whole structure for handling the damping irregularity of such structures. The results show that the equivalent damping ratio changes with the height of the building and the kind of the structural system, but it is constant for all accelerations values. Thus, available software SAP2000 applied for seismic analysis, design and the provisions of existing seismic codes. Finally, evaluation of different kinds of structural system used in this research to find the most energy dissipating one found by finding the best value of quality coefficient.