This study proposes an innovative hybrid lateral load-resisting system, termed the ring-cable-cylinder bracing system, aimed at improving the energy dissipation capacity and ductility of the previously introduced cable-cylinder bracing (which offers relatively the same level of seismic energy dissipation and ductility as the original bare steel frame), and minimizing the damage to the beam-to-column connections via utilizing quarter-ring curved yielding devices. First, the proposed bracing system and its working mechanism are introduced. A mathematical procedure based on the theorem of the least work and the method of virtual work is then presented to derive highly-accurate, practical, and easy-to-use equations for calculating the thickness of the utilized quarter-ring yielding devices. The design requirements for these curved devices, based on the characteristics of the frame in which they are utilized, are also discussed exhaustively. In the next step, the presented formulae’s accuracy and usability are comprehensively investigated by conducting a finite element parametric study. The results show that the proposed system can provide an extra source of energy dissipation and ductility. It was also observed that the new system leads to an increase in both initial stiffness and ultimate strength and limits the pinching phenomena in the hysteretic cycles.