Lower Bounds to Column Buckling Loads

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Abstract
A lower bound theorem is adapted to columns with various boundary conditions and variable bending stiffness. The lower bound is expressed in terms of the Rayleigh and Timoshenko loads for the simply-supported columns. For other boundary conditions, a similar formulation is developed in terms of the moment function and its derivative so that continuity conditions for the lateral displacement and slope are not required. An iterative solution procedure involving finite elements is outlined. Numerical results are given for several columns that illustrate the procedure for representative combinations of boundary conditions and bending stiffness distributions.

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