The elastic stability of a thin cantilever beam under an articulated tip force—I: Statics analysis

Previous work on the buckling of thin elastic cantilever beams when subjected to tip forces applied by means of an articulated rod is here extended to cases when the axis of the rod is directed at any angle to the beam axis. The system is typical of engineering situations in which mechanical control circuits involve a bellcrank lever connected to an articulated rod, the remote end of which is loaded by a tube directionally guided in rollers. The function of the articulated rod is to permit geometric changes to take place in the mechanical system.A numerical solution is provided to the differential equation system by finite-difference approximations. The resulting equations are of a sufficiently simple form as to permit evaluation of buckling forces by desk calculation; alternatively a computer adaptation can be made.The results of the analysis are verified by an experimental investigation.