AbstractThe development and applications of a semi‐active friction damping system with amplifying braces is studied. A system of dampers and braces, defined as the friction damping system with amplifying braces (FDSAB) is considered. Active control theory with velocity and acceleration feedback is used to obtain the control forces in the proposed system. The system can be used efficiently to enhance the damping of a structure and improving its response. The efficiency of the proposed system is demonstrated by the numerical simulation of a seven storey building subjected to earthquakes. The simulation shows that the behaviour of the damped structure with the FDSAB is significantly improved. The required control forces are much less compared with a control system with semi‐active friction dampers connected either to chevron or diagonal braces. Copyright © 2001 John Wiley & Sons, Ltd.