Improved frame stability analysis with effective lengths

Approximate methods for determination of effective lengths of compression members in frame systems are normally based on rotational restraints defined through so-called joint stiffness ratios or G-factors. These approaches allow the member to be considered in isolation from the rest of the frame. However, they are known to be inaccurate in many cases. A method is proposed that involves postprocessing of effective lengths from isolated column analyses to arrive at improved, weighted mean values. The approach, termed the method of means, satisfies general system instability principles, is attractively simple, and yields in general effective length predictions in excellent agreement with exact results for a wide variation of parameters. The errors are normally within a few percent of exact solutions. The method is applicable to braced and to a range of unbraced frames. It is particularly suitable for cases where drastic changes of beam or column stiffness occur, such as in the top or bottom stories of a frame, or where column stiffness, axial force level, and story height change at certain floor levels.