Buckling mode interaction in fixed-end column with central brace

The postbuckling behavior of an elastic fixed-end column with an elastic br ace at the center is investigated. Attention is focused on those of brace s tiffness near its threshold value at which, under axial load, the column be comes critical with respect to two buckling modes simultaneously. We show t hat, for the brace stiffness greater than the threshold value, there are pr ecisely two secondary bifurcation points on each primary postbuckling path bifurcating from one of the least two classical buckling loads, and the cor responding secondary postbuckling paths connect all of these secondary bifu rcation points in a loop. For the brace stiffness less than the threshold v alue, no secondary bifurcation occurs. The asymptotic expansions of the pri mary and secondary postbuckling paths are constructed. The stability analys is indicates that, when the brace stiffness goes beyond its threshold value , the primary postbuckling path with a node in the center becomes unstable from stable by means of the secondary bifurcation (i.e., secondary buckling occurs).