When a structure is excited by an earthquake ground motion the input energy may be reduced by inelastic action or by supplemental damping devices. If the seismic energy dissipation can be achieved by means of separate non-load bearing supplementary damping systems, the structure itself can remain elastic providing a continuing serviceability following the design level earthquake. This paper illustrates the advantages of using added, or supplemental, damping in structures. The control system consists of passive friction dampers installed in the ground floor of the structure using tendons to transmit the damper forces to the other parts of the structure. The damping forces generated by the dampers are transferred to the structure by the tendons and horizontal links that oppose the inertial loads applied to the structure by the earthquake excitation. The dampers are ring spring friction devices consisting of inner and outer ring elements assembled to a form a spring interface. A four storey-two bay steel frame was used in the study.