Post-tensioned rocking frames have been proposed as damage-free seismic-resistant structures. However, currently available load resisting systems for rocking frames rely on sacrificial yielding components that accumulate damage during strong dynamic action. To address this shortcoming, this study proposes a novel thoroughly damage-avoidance solution by means of bracing elements with carefully controlled buckling behaviour. To this end, a proof-of-concept study is presented, whereby the elastic buckling response of buckling-enabled composite bracing (BECB) elements with circular-arc shaped cross-section is numerically investigated. Varying geometric properties are considered and validated against analytical approximations. Besides, a finite element study of a single-storey steel post-tensioned frame under static and dynamic actions is performed. The case study incorporates BECB elements made from glass-fibre reinforced polymer (GFRP). It is demonstrated that BECB enhances the non-linear static and dynamic response of rocking frames by providing stability and significantly reducing storey drifts and accelerations without accumulating damage.