This study conducts an in-depth investigation into the lateral resistance of multi-storey steel frames with sparse chevron bracing. By combining finite element analysis and theoretical derivation, the mechanical behaviour of structures with under-strengthened beams and its influence on lateral resistance are systematically examined. Through elastoplastic pushover analysis, the accuracy of the series-parallel theoretical model for dual lateral force-resisting systems is validated, and the variation of bracing internal forces with inter-story drift angle is revealed. Finite element results indicate that the stiffness and strength of beams significantly influence the development of tensile brace forces after buckling of the compressive brace. As a secondary lateral force-resisting system, the frame effectively compensates for the degradation in load-bearing capacity after brace buckling. In addition, the composite effect of the slab effective width and steel beam notably enhances the flexural stiffness of beam, thereby facilitating the development of tensile brace forces, and reducing the degradation of load-bearing capacity after compressive brace buckling. For rigid frame-chevron bracing structures with inadequately strengthened beams, under the combined action of lateral displacement and unbalanced forces, plastic hinges in the beam initially form at the beam end on the compressive brace side, followed by the mid-span of the beam. Based on this failure mode, formulas for calculating tensile brace forces and beam unbalanced forces are derived, demonstrating high accuracy. The study indicates that even when beams do not meet the sufficient strengthening requirements specified in Clause 8.2.6-2 of the Code for Seismic Design of Buildings, the overall load-bearing capacity does not deteriorate with increasing lateral displacement, provided that the frame contributes a relatively high proportion of lateral resistance. This ensures structural safety under seismic actions with an intensity of 7 degrees (0.1g). The proposed calculation method for beam unbalanced forces provides a new approach to optimizing chevron-braced frame design, avoiding the problem of excessively large beam depths in traditional design, and offering important theoretical support and practical guidance for engineering applications.