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 simplified by consistently regarding certain configuration 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 refinements of previously published results, including the Vlasov effect, elastic coupling, the offset of the load from the centroid, and, of course, prebuckling deflections. The analysis is thereby reduced to a single fourth-order differential 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 offset 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 offset parameter always appears in the governing equations as multiplied by a ratio of stiffnesses, which can become large, especially for composite I-beams. For this case, a special treatment is required.