Inelastic and stability analysis of flexibly connected steel frames by springs-in-series model

A beam-column element with springs connected in series is presented for efficient and effective geometric and material nonlinear analysis of steel frames with semirigid connections. When incorporated into a computer program for nonlinear analysis of steel framed structures, the effects of semirigid connections and material yielding can be accounted for in a simple and direct manner. Proposed mathematical models for various joint types and assumed patterns for material yielding can also be simulated independently, while the combined effect can be included in the analysis automatically. The obvious and direct method of adding the connection and plastic springs to the element matrix and to condense out the internal or dummy degrees of freedom for the final element matrix is also discussed in this paper and noted to be computationally infeasible due to the finite accuracy in computer analysis and the odd values of very large and small stiffness encountered during an ultimate analysis. This paper proposes an efficient and simple method to trace the equilibrium path of steel frames, allowing for geometrical, material, and joint stiffness nonlinearities up to the ultimate load. The benchmarked problem (Vogel's six-story frame) is analyzed and extended to include the effects of semirigid connections, which is new and is recommended to be used for validation of computer programs for this type of analysis.