Based on analysis of the test results of 50 RC specimens of circular columns failed in flexure, an expression for defining the hysteretic loop is proposed and a model for predicting the equivalent damping ratio is developed. The procedure for associating the equivalent damping ratio of a structure as a whole with those of its element is established by an example of double-column pier-bridge. It’s indicated that the expression of hysteretic loop proposed well defines the hysteretic loops of RC columns. Rational outcome can be expected when performing pushover analysis using the relationship of equivalent damping ratio of a bridge as a whole with those of its element. The target displacement predicted with the proposed model is different from those predicted with Rosenblueth’s model and Kowalsky’ model.