This thesis investigates the effect of having brace strength eccentricity (slip load eccentricity) negative that of stiffness eccentricity on the performance of friction damped braced frames, in an effort to improve the efficiency of friction damped braced frames in single and multi-storey buildings.  Firstly, multi-storey models having stiffness ratio (brace stiffness to frame stiffness) of three and strength ratio (brace strength to frame strength) of unity are subjected to an ensemble of earthquakes over a wide range of stiffness eccentricity $\rm e\sb{s}$ such that $\rm0<e\sb{s}<1.2$ and a range of slip load $\rm e\sb{pb}$ such that $-$e$\rm\sb{s}<e\sb{pb}<e\sb{s}$. The results demonstrate that as the slip load eccentricity $\rm e\sb{pb}$ moves from the stiff side to the flexible side of the structure, maximum displacement and ductility demands are reduced and more storeys participate in dissipating energy. Maximum improvement is obtained when $\rm e\sb{pb}$ = $-$e$\rm\sb{s}$.  The inelastic behavior of single-storey model is studied using the history of base shear and torque. A single storey model with stiffness ratio of three and strength ratio of one is subjected to an earthquake over the range of slip load and stiffness eccentricity indicated above. The results show that as $\rm e\sb{pb}$ shifted to the flexible side of the structure the maximum base torque is decreased.  The energies imparted and dissipated by brace slippage and frame yield of the single storey model indicated above are studied. The results demonstrate that the energy dissipated by the braces increases as the slip load eccentricity moves to the flexible side of the structure.  The research demonstrates that the slip load eccentricity must be considered in the design of friction bracing