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 e
ccentricity in loading. In this paper closed-form relationships are ob
tained for the direct evaluation of the critical loads of cross-bracin
gs with semirigid ends for any value of relative stiffness of the end
connections and any ratio of the dimensionless parameters of tension a
nd compression members. The criteria are formulated for the general ca
se, i.e., tension and compression braces have different section proper
ties, lengths, and axial loading. Parametric solutions are graphically
displayed to clarify distinct behavior including the boundary separat
ing symmetrical and antisymmetrical modes of buckling. Analytical expr
essions for eccentrically loaded cross bracings with simple end connec
tions are further derived and studied to yield a result that the tensi
le force does not contribute substantially to the load-carrying capaci
ty of the bracing system.