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

The lateral-torsional buckling of composite strip- and I-beams is considere d. The geometrically exact governing equations are simplified by consistent ly 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 refinem ents of previously published results, including the Vlasov effect, elastic coupling, the offset of the load from the centroid, and, of course, prebuck ling deflections. The analysis is thereby reduced to a single fourth-order differential equation and boundary conditions, all of which are derivable f rom a corresponding energy expression. From the form of matched asymptotic expansions of the buckling mode when small parameters are ignored altogethe r, a single comparison function is found which gives the correct buckling l oad to within 1% for a wide range of the warping rigidity. Using this compa rison function, a formula for the buckling load as a function of the small parameters of the problem is found and validated. With certain exceptions r egarding the load offset parameter, the formula provides results which agre e quite well with the numerical solution of the exact equations as long as all the small parameters remain small. However, the load offset parameter a lways appears in the governing equations as multiplied by a ratio of stiffn esses, which can become large, especially for composite I-beams. For this c ase, a special treatment is required. (C) 2001 Elsevier Science Ltd. All ri ghts reserved.