Buckling of Columns With Nonmovable Boundaries

The global buckling problem of slender tubulaj columns subject to distributed load is studied. The load consists of the column weight, tension/compression exerted at the top of the column, and internal and external variable static pressure forces due to fluids in gravity field. Nonmovable supports at the upper and lower columns ends define the boundary conditions. The resulting nondimensionalized eigenvalue problem is general, and applicable to columns, tubes, pipelines, marine drilling and production risers, mining risers and legs of tension leg platforms. The eigenvalue problem consists of a linear, fourth order differential equation with variable coefficients and four homogeneous boundary conditions. The exact solution is derived in terms of Airy functions of the first and second kind. A power series solution is presented as well. Both methods are numerically implemented and become unstable only for high values of the loading variables. The combined results of the two methods cover the entire domain of practical interest. The critical curves are plotted in the space of the two loading variables for the first six modes. Their asymptotic behavior and its dependence on the boundary conditions is revealed.