Critical behavior of rectangular frames considering the influence of non-linear flexible connections and lateral bracing in the presence of primary bending moments.

In almost all investigations on stability of frames having flexible connections, it has been assumed that frames are loaded in such a manner that no bending moments are present when instability is initiated. Apparently, this condition is not fulfilled for many frame work systems that are designed in principle to undertake bending moment. The question arises as to how the combined influence of connection stiffness and primary bending moments affect the buckling strength of a structure and how to account for these factors. To answer this question a Fortran program is developed for the analysis of flexibly jointed symmetric one-story frames and two-story frames. The well known slope-deflection equations are utilized in the analysis. The exact moment-rotation attributes of several connections are used in the analysis. Iterative procedures are implemented to permit reducing the stiffnesses of the compression members according to the values of their axial forces and to find the connection rotations that correspond to the pertinent bending moments. The elastic critical load of the structure is found by tracing its load-deflection behavior throughout the entire range of loading up to the critical load. Further studies include the effect of lateral bracing on the critical behavior of framed structures. Both modes of buckling, symmetrical and anti-symmetrical, are considered. The critical load for the anti-symmetrical mode of buckling is found to be considerably lower than that corresponding to the symmetrical mode. When sufficient lateral bracing is provided, the frame buckles only in a symmetrical mode. Values for the minimum ratios of brace-to-frame stiffness required to prevent lateral instability are given for several cases. Diverse numerical applications are presented to show the impact of the presence of flexible connections and lateral bracing on the critical behavior of frames. The proposed analysis, utilizing the slope-deflection equations in a unique way and implementing the Newton-Raphson procedure to solve the related non-linear equations for multi-story frames, is found to be both simple and efficient