Buckling of columns of variable flexural rigidity

The stability of columns with continuous flexural rigidity monotonically changing along the length of the beam is considered. A new analytical solution for the buckling load is developed in terms of Airy functions for pin-ended columns. Buckling loads for different modes and upper bounds are given when the flexural rigidity at any cross section multiplied by a linear function of position stays constant along the beam. The buckling load for any mode is less than the critical load corresponding to a column of the same length and of constant flexural rigidity whose value is the minimum along the beam of variable flexural rigidity studied. The solution has applications to tapered pin-ended columns with variable modulus of elasticity.