Elastic stability of non-uniform columns

Abstract A simple and efficient method is proposed to investigate the elastic stability of three different tapered columns subjected to uniformly distributed follower forces. The influences of the boundary conditions and taper ratio on critical buckling loads are investigated. The critical buckling loads of columns of rectangular cross section with constant depth and linearly varied width ( T 1 ), constant width and linearly varied depth ( T 2 ) and double taper ( T 3 ) are investigated. Among the three different non-uniform columns considered, taper ratio has the greatest influence on the critical buckling load of column T 3 and the lowest influence on that of column T 1 . The types of instability mechanisms for hinged-hinged and cantilever non-uniform columns are divergence and flutter respectively. However, for clamped-hinged and clamped-clamped non-uniform columns, the type of instability mechanism for column T 1 is divergence, while that for columns T 2 and T 3 is divergence only when the taper ratio of the columns is greater than certain critical values and flutter for the rest value of taper ratio. When the type of instability mechanism changes from divergence to flutter, there is a finite jump for the critical buckling load. The influence of taper ratio on the elastic stability of cantilever column T 3 is very sensitive for small values of the taper ratio and there also exist some discontinieties in the critical buckling loads of flutter instability. For a hinged-hinged non-uniform column ( T 2 or T 3 ) with a rotational spring at the left end of the column, when the taper ratio is less than the critical value the instability mechanism changes from divergence to flutter as the rotational spring constant is increased. For a clamped-elastically supported non-uniform column, when the taper ratio is greater than the critical value the instability mechanism changes from flutter to divergence as the translational spring constant is increased.