Second-Order Elastic and Stability Analysis of Plane Steel Frames with Semirigid Connections

The beam-to-column connections in steel frames are assumed to be either pinned or rigid. Using pinned or rigid connections simplify the analysis, but they can not present the real behavior of the structure. Because, the experiments have shown that the connections under the loads will have some flexibility. Therefore, it is recommended that the flexibility of the connection should be included in the frame analysis. In this paper, the elastic secant stiffness matrix of a beam-column element with semi rigid connections under axial force, end moments and transverse distributed loads are derived. Second-order elastic and stability analysis of two-dimensional steel frames are carried out, afterward. The proposed stiffness matrix is very general and can be applied to a frame member with any type of connection. Furthermore, it is more accurate and efficient than the corresponding matrices obtained by other authors. In addition, this method uses only one element for each member and presents a single formulation for both tensile and compressive members in the analysis. Load-deflection curve and numerical values obtained by the suggested technique are compared with those found by other investigators. The effect of the connection flexibility on the equilibrium path and the stability load are also discussed.