Nonlinear stability analysis of non-prismatic simple steel frames with flexible supports and semi-rigid connection

In this paper, various methods of linear and nonlinear stability analysis of simple steel frames are introduced. In the following, based on moderately large rotations and small strains, nonlinear stability analysis of a non-prismatic simple steel frame with semi-rigid connection and flexible supports is performed, which is subjected to a concentrated vertical load eccentrically at its joint. Accordingly, firstly, the accuracy and capability of suggested formulations will be verified by comparing with the results of other researchers. Then, the effects of eccentric axial load factor, shape factor of non-prismatic column, rotational stiffness of elastic support, translational stiffness of lateral support, rotational stiffness of beam-column connection and slenderness ratio of members on the pre-bucking and post-buckling behavior of a steel frame will be investigated. The results show each of these factors has a significant effect on the equilibrium path and buckling load of the structure. In other words, by increasing the slenderness ratio of members, shape factor and stiffness of connections, increases the nonlinear buckling load of the structure. Accordingly, the translational stiffness of lateral support and slenderness ratio of members have the maximum and minimum effect on this increase, respectively. Moreover, by utilizing the non-linear stability analysis, the buckling load of the simple steel frame reduces with respect to linear stability analysis.