The flexibility or force method of analysis of structural frames is complicated by the choice of appropriate unknowns. A mixed approach is presented in which member-end moments and sway deflections are adopted as unknowns, thereby providing uniformity of approach for computer analysis. The corresponding rotation-compatibility and sway-equilibrium equations are described in an example of linear frame analysis. The theory is amplified to include the influence of axial force on member flexibility and P-A effects. Results of examples of elastic instability are compared-with established solutions. A simple transition to plastic analysis is made by replacing plastic end-moments by hinge rotations as unknowns. The method is extended to represent more general material non-linearity and combined elastic-plastic instability analysis. This formulation represents a consistent and relatively simple solution to linear and non-linear analysis of frames based on a mixed flexibility and sway-deflection method.
Recent proposals to avoid snap-through failure of practical pitched-roof steel frames incorporate the elastic snap-through buckling load of such frames. In this study it is shown that the elastic snap-through buckling load used in these proposals is far higher than the snap-through buckling load obtained from a more rigorous elastic analysis. The background details and the results of such rigorous snap-through analysis are presented and compared with experimental results as well as with the results incorporated into BS 5950. The significance of the findings in relation to practical pitched-roof steel frames is discussed briefly. The aspects of lateral torsional member buckling, frame buckling in a sway mode and local member buckling (web and flange) are excluded from this study.