Hencky bar-chain model for buckling analysis of non-uniform columns

The Hencky bar-chain model is developed for the buckling analysis of non-uniform columns. While the end rotational spring stiffnesses of the Hencky bar-chain are uniquely calibrated by the finite difference column model, the internal rotational spring stiffnesses may be defined in various ways for non-uniform columns. This paper studies three different ways in specifying the internal rotational spring stiffnesses and examine their effects on the buckling loads for various shapes of non-uniform columns. The developed Hencky bar-chain model facilitates buckling analysis and optimization of non-uniform columns as well as providing a physical interpretation to the numerical finite difference method.