Design of imperfect cross-bracings

In recent years, several analytical studies have been conducted on the behavior of cross-bracing members subjected to out-of-plane buckling. Most of these studies do not consider boundary conditions such as the relative stiffness of the end connections and adjoining members and eccentricity in loading. In this paper closed-form relationships are obtained for the direct evaluation of the critical loads of cross-bracings with semirigid ends for any value of relative stiffness of the end connections and any ratio of the dimensionless parameters of tension and compression members. The criteria are formulated for the general case, i.e., tension and compression braces have different section properties, lengths, and axial loading. Parametric solutions are graphically displayed to clarify distinct behavior including the boundary separating symmetrical and antisymmetrical modes of buckling. Analytical expressions for eccentrically loaded cross bracings with simple end connections are further derived and studied to yield a result that the tensile force does not contribute substantially to the load-carrying capacity of the bracing system.