This study explores the effectiveness of shape-memory-alloy (SMA)-based self-centring energy-dissipation bays (SCEDBs) for enhancing the seismic performance of high-strength-steel (HSS) frames. The work commences with the development of an ensemble of prototype HSS frames equipped with SCEDBs, known as HSSF-SCEDB structures. The prototype systems are examined using cyclic-pushover and nonlinear-response-history analyses (NL-RHAs). According to the analysis database, it is found that the cyclic-pushover responses generally show a typical flag shape over a wide deformation range and that the post-earthquake residual deformations are below 0.5%, even following maximum interstorey drifts beyond the codified deformation threshold (i.e. 2%). To offer a practical tool to engineers for damage-control behaviour evaluation and seismic demand estimation, we develop a multimodal nonlinear static procedure based on a modified energy-balance concept. Conventional procedures relating to the fundamental vibration mode are also revisited. The results indicate that a medium-rise HSSF-SCEDB may be appreciably influenced by higher vibration modes. The difference between the average maximum interstorey drifts calculated by NL-RHAs and those obtained using the proposed procedure for an ensemble of earthquake motions is generally below 5%, and the adequacy of the proposed method is confirmed.