Controlled Rocking Steel Braced Frames (CRSBFs) are being developed as a high-performance seismic force resisting system to reduce structural damage and residual drifts. CRSBFs replace the braced bays in a typical steel structure with a braced frame that is intentionally allowed to uplift and rock during a large seismic event. As a CRSBF displaces laterally, the system stiffness is reduced due to uplift of the frame, rather than yielding, enabling the system to self-centre with minimal residual drifts. This rocking response is controlled using a combination of post-tensioning and supplemental energy dissipation. This design approach is in contrast to conventional codified steel systems, in which the earthquake forces are reduced by allowing certain steel members in the seismic force resisting system to yield, leading to structural damage and residual drifts that may render the structure economically unfeasible to repair. Extensive research has been conducted to show that CRSBFs can improve structural performance, but it is also important for designers to know if utilizing a CRSBF will provide increased, decreased, or similar non-structural component performance when comparing to more traditional yielding lateral force resisting systems. As such, the purpose of this paper is to investigate how the demands on acceleration-sensitive attached non-structural components in buildings with CRSBFs compare to those demands with a buckling-restrained braced frame (BRBF) for the lateral force resisting system. A three-story building is designed to meet the structural drift and collapse criteria for seismic design set out by ASCE 7, twice using a CRSBF with different levels of energy dissipation, and again using a BRBF as the seismic force resisting system. Both structures are modelled in OpenSees, and nonlinear time-history analyses are performed on the three lateral force resisting systems for a suite of ground motions. Using a cascading analysis approach, these floor responses are used to compute floor pseudo-acceleration spectra to examine the demands on acceleration-sensitive attached non-structural components. The results indicate that providing a nonlinear structural response only through rocking at the base, while producing the intended benefit of elastic response of structural members, also has an unintended consequence of relatively higher floor pseudo-acceleration spectra at short periods. These demands do not appear to be caused by impact of the CRSBF on its foundation, but rather by vibration of the CRSBF in its higher modes. They are not effectively reduced by supplemental energy dissipation at the base rocking joint, but could potentially be reduced by providing multiple mechanisms for nonlinear response.