Buckling-restrained braces (BRBs) represent a significant improvement compared to conventional braces in terms of cyclic inelastic deformation capacity. However, buckling restrained braced frames may undergo large inelastic storey drifts without the ability to distribute the ductility demand over the height in multi-storey structures, due to possible localizations of inelastic deformations. This critical aspect deserves particular attention due to the bracing system characteristics, i.e., statically determinate structural configuration and limited BRB hardening, especially in steel frames with beams connected to columns by means of pinned joints as often happens in Europe. As a result, the frame global ductility is strongly dependent on the distribution of BRB strength and stiffness at each storey level. Methods for the definition of optimal distributions of column stiffness and of BRB stiffness in multi-storey bracings systems are important tools for structural engineers. Such methods can be defined and/or validated based on response sensitivity analysis, as essential tool in gradient-based optimization. This work focuses on a procedure for response sensitivity analysis of steel frame structures equipped with BRBs within a displacement-based finite element formulation. Realistic steel frames equipped with buckling-restrained V-bracings systems are used as benchmark problems for response and response sensitivity analysis. Selected sensitivity analysis results are shown for quantifying the effect and relative importance of BRB design parameters in regards to the nonlinear dynamic response under seismic ground motions of the benchmark structures.