Exact lateral–torsional buckling solutions for cantilevered beams subjected to intermediate and end transverse point loads

This paper presents exact stability criteria for the lateral–torsional buckling of cantilever strip beams under intermediate and end point loads. The two-dimensional stability domain is given in closed-form solutions, in terms of Bessel functions. The limit of the convex stability domain tends towards Dunkerleyʹs line when the intermediate load approaches the tip of the cantilever. However, the Dunkerleyʹs line is no longer appropriate when the distance between both loads is sufficiently large. An approximate set of formulas is proposed for quick estimation of the buckling load.