In passive controlled buildings, H-shaped beams connected to steel dampers are subjected to the cyclic axial force in addition to the flexural moment during earthquake, and then the plastic deformation capacity of H shaped beams may decrease because of compressive forces. The direction and magnitude of axial force from dampers changes with the flexural moment, so that the local buckling of the beams under the tensile axial force does not occur. This paper conducts the cyclic axial and shearing forces of H-shaped beams, and investigates the local buckling behavior. The plastic deformation capacity and hysteresis energy of the beams are clarified.