Practical Calculation Method for Overall Stability of Bent Frames and Frame Structures Based on Critical Force Redistribution

The effective length factor method cannot account for variations in axial forces between columns and the mutual assistance among columns, resulting in overestimation of the critical load of columns that receive assistance and underestimation of that of columns that provide assistance. Moreover, this method is not readily applicable to bent frames and frame structures with multi-story tie beams. The phenomenon of critical load redistribution among columns under non-uniform loading conditions is revealed in this paper, and its underlying mechanical mechanism is elucidated. Based on this, a two-stage loading procedure for critical load redistribution analysis is proposed, in which the instability process of irregular structures is divided into two stages: independent loading of individual columns and combined loading of the assembly. By superimposing the critical load of columns in regular structures with the remaining load capacity, a formula for evaluating the overall stability critical capacity of bent and frame structures is established. The proposed method effectively accounts for the restraint provided by tie beams between columns, eliminating the need for iterative solutions of transcendental equations or the construction of complex total potential energy equations, thereby significantly simplifying the computational process. Comparative analyses of numerical examples demonstrate that the proposed method achieves high accuracy and enables quantitative assessment of mutual assistance between columns. It provides a conceptually clear, computationally efficient, and reliable practical tool for the stability design of bent and frame structures under complex loading conditions.