Lateral–torsional buckling of cantilevered elastically coupled composite strip- and I-beams

The lateral±torsional buckling of composite strip- and I-beams is considered. The geometrically exact governing equations are simpli®ed by consistently regarding certain con®guration parameters as small. The assumption that these parameters are indeed small is equivalent to the assumption that the square of the maximum prebuckling cross-sectional rotation due to bending is small compared to unity. The analysis takes into account various re®nements of previously published results, including the Vlasov e€ect, elastic coupling, the o€set of the load from the centroid, and, of course, prebuckling de¯ections. The analysis is thereby reduced to a single fourth-order di€erential equation and boundary conditions, all of which are derivable from a corresponding energy expression. From the form of matched asymptotic expansions of the buckling mode when small parameters are ignored altogether, a single comparison function is found which gives the correct buckling load to within 1% for a wide range of the warping rigidity. Using this comparison function, a formula for the buckling load as a function of the small parameters of the problem is found and validated. With certain exceptions regarding the load o€set parameter, the formula provides results which agree quite well with the numerical solution of the exact equations as long as all the small parameters remain small. However, the load o€set parameter always appears in the governing equations as multiplied by a ratio of sti€nesses, which can become large, especially for composite I-beams. For this case,