FEM-based prediction of elastic critical loads in steel frames with nonlinear semi-rigid connections

Due to the manufacturing constraints, steel frames are often divided into components and assembled together through connections. Studies have shown that the joints between components in steel frames are often semi-rigid. In addition, steel frames typically consist of slender members, so the frame tends to undergo large displacements, making the influence of the P-Delta effect on the steel frame more pronounced. These issues significantly affect the global stability behavior of the frame and must be taken into account. This paper presents a new elastic stability analysis method for steel frames with semi-rigid connections based on the finite element method. The method utilizes a novel stiffness matrix formulation and an equivalent nodal load vector, combined with a load-increment strategy to solve the nonlinear equilibrium equations. The relationship between displacement and load is investigated, the critical load is determined. An algorithm flowchart is provided, and verification examples are conducted. Comments on the instability process of frames with different types of connections are also presented. This paper is applicable to the study and analysis of the elastic stability of steel frames with nonlinear semi-rigid connections in particular, and rigid or semi-rigid connections in general, taking into account the influence of the P-Delta effect.