This paper presents a plastic design method of steel frames with a vibration control system with U-shaped steel dampers based on a quasi-linear motion mechanism. Firstly, a plastic collapse load of the damper system is evaluated using the upper bound theorem where the U-shaped dampers are assumed to have three plastic hinges. The accuracy of the evaluation is examined by comparing the cyclic loading test results. Secondly, the plastic design is discussed for steel frames considering some

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... e mechanisms. The shear stress in the beam web is also discussed for the beam attached with the U-shaped dampers. Finally, for the sake of introducing the proposed device into the practice, nonlinear finite element analyses are conducted for the three-story three-span steel moment frames with and without the damper system. Relationships between the story shear and story drift obtained from the static pushover analysis are examined. The Von-Mises stress distributions are also examined to reveal the influence of the proposed device on the steel moment frame.