Cross bracings in tapered systems: Semirigid ends

Several analytical and experimental studies have been recently conducted on the behavior of cross-bracing systems subjected to out-of-plane buckling. Semirigid connections, however, were not considered or modeled. This paper derives and solves for the exact expressions for evaluating the effective length factors of semirigidly connected cross bracings. Moreover, the expressions are derived for tapered systems where the bracings are connected at off-midspan locations. Parametric solutions for the end flexibility coefficient versus the buckling parameter are graphically displayed to clarify distinct behavior, and solutions for typical cases are provided. In the example cases, a double-wave mode versus a single-wave mode is exhibited for the compression and tension members respectively when the tensile and compressive forces are equal, and when the tensile force is zero, both members show a single-wave mode.