Elastic instability of cantilever struts under combined axial and transverse forces at the free end

摘要

This investigation considers the elastic instability of cantilever struts under applied axial and transverse forces at the free end. Fig.1 shows the general case of such a strut.First the strut of uniform depth and without sweep is studied. This is shown in Fig. 2. A derivation is given for the governing differential equation and boundary conditions. These are then solved for the minim coupled eigenvalues, which correspond to the critical load combinations. Fig. 10 is a plot of these calculated critical loadings.Next an experimental investigation, whose main purpose was to provide a check on the above theoretical calculations, is presented. Various difficulties are discussed in addition to the techniques finally adopted. Experimental values are shown to check theory within several per cent. See Fig. 16. Also Southwell’s experimental procedure for determining instability loading is shown to apply to this case of coupled loading.The theory is then extended to include the problem of the tapered strut. Equations and boundary conditions are given for the arbitrary taper case and a solution presented for the limiting strut having complete taper. These results are given in Fig. 24.In the concluding Part some of the more important unsolved problems are discussed in detail. These include the strut with arbitrary taper, the swept strut, and the strut which buckles inelastically.The Appendix derives the differential equation for the non-tapered strut by variational procedure.