Elasto-plastic behavior of structural steel beam-columns subjected to repeated variable bending under a constant axial force are investigated, using the new unified method proposed in the authors' previous papers. According to Refs. 12)-14), the basic equations of a beam-column governing the relations between the magnitude of the domain of the variable external load, which is given as a randomly varying repeated curvature in the present study, and the extreme responses of the axial strain, the resisting moment and so on are derived. Several specific characteristics of the beam-column subjected to the repeated variable bending are indicated, which might be deduced from the derived basic equations and thus available for any beam-column. As an example, elasto-plastic and collapse behavior of a beam-column with the rectangular cross-section are formulated in the explicit expressions. Also, the incremental collapse limits, which are related to divergence phenomenon of the axial strain, are examined.
