Structural Stability Theory and Practice

5Frames

5.1 Introduction

So far we have considered the stability of members, i.e. columns, beams, and beam columns as individual members that have ideal boundary conditions, e.g. pinned, fixed, or free. In actual engineering systems these members exist as part of a larger framework, and their ends are elastically restrained by other members to which they are joined. It is usually assumed that, in a frame, members are connected by rigid joints, meaning all members connected at a joint rotate in the same direction by an equal amount. Under these conditions the member end restraints not only depend on the stiffness of members joining directly at a joint, but end restraints depend on the stiffness of all other members in the system. Therefore, we need to examine the stability of the whole frame. Another problem is that a member of a frame does not exactly behave like a column with spring supports at both ends, because the spring stiffness varies with the load. There can be different cases of loading in a frame. If the member of a frame are geometrically perfect and there is no primary moments present in the members, then there is no bending deformation and moment in the member until the critical load P_cr is reached. In this case, the problem can be solved as an eigenvalue problem as in the case of an individual column. On the other hand, if the members are geometrically imperfect or primary moments are present in the members due to eccentric loading or lateral loads, the frame ...