This paper presents a new analytical framework for determining the exact critical in-plane buckling load of multi-story, multi-compartment elastic frames with rigid and semi-rigid joints. In contrast to the existing analytical methods, which are typically based on second-order theory and often neglect shear deformability, the proposed approach is based on the findings of Keller, who demonstrated that the critical points of a nonlinear system of equations coincide with the critical points of a linearized system of equations. While this methodology has previously been demonstrated for isolated columns, its extension to frame structures is introduced here for the first time. The accuracy of the framework is verified through comparison with published results obtained by alternative methods. The results indicate that neglecting the shear deformability of frame members is justified for slender frames, as it has been previously demonstrated for isolated columns. Its practical value is further illustrated through parametric studies, which highlight the advantages of the approach and clarify the influence of key parameters such as imperfection sensitivity, crossbar-to-column stiffness ratios, the stiffness of lateral and base supports, and the rigidity of frame joints on the exact critical load.
Kočman et al. (Tue,) studied this question.