AbstractDuring earthquakes, I‐shaped beams installed in a braced structure are subjected to a bending moment and compressive and tensile axial forces transmitted from the braces. The buckling behavior of a beam under the impact of an earthquake is thereby more complex than that under no axial force or constant compressive axial forces considered in previous studies. In this paper, cyclic loading tests and numerical analyses are presented with emphasis on cyclic buckling behavior and moment and deformation capacity of the beams subjected to synchronized flexural and axial loading. As a result, it is confirmed that the I‐shaped beams originate local buckling under compressive axial force, whereas the strength is regained up to the full plastic bending moment under tensile force. Based on the results obtained, this paper presents evaluation formulae for estimating the ultimate strength, plastic deformation capacity, and cumulative plastic deformation capacity. Finally, an empirical formula to convert cumulative plastic deformation capacity into hysteretic energy dissipation is proposed.