Method, apparatus, and systems are disclosed for damping the movements of structures undergoing dynamic forces. The disclosed dampers are a new type of steel plate dampers, intended to reduce the cost and improve the performance of structures subject to severe seismic loading. While in these dampers the metal plates undergo plastic deformation as a method of absorbing and dissipating energy, the disclosed designs do not allow the stress and strain in the metal plates to go above a predetermined design value and; therefore, the new dampers have long lives and do not need repair or replacement after a big earthquake or similar events. These dampers may be used for building and non-building structures. In such applications the required damping capacities are relatively high and different scales of sliding force and stroke are required.