The seismic performance of steel frames equipped with a particular type of bending dissipative braces (BDBs) having U elements, which has recently been introduced and tested by the authors, is investigated. For this purpose, two structural systems, i.e., simple and dual steel building frames, both with diagonal BDBs and different number of stories, are considered. After providing a design method of this new BDB, the detailed structural models are developed in the OpenSees platform to perform nonlinear dynamic analyses. Seismic performance factors like ductility, overstrength, response modification and deflection amplification factors are calculated using incremental dynamic analysis (IDA). In addition, to assess the damage probability of the structural models, their seismic fragilities are developed. The results show high energy dissipation capacity of both structural systems while the number of U elements needed for the bracing system of each story in the moment frames are less than those in the corresponding non-moment (simple) frames. The average response modification and deflection amplification factors for both structural schemes are obtained about 8.6 and 5.4, respectively, which are slightly larger than the corresponding recommended values of ASCE for the typical buckling-restrained braces (BRBs).