Design Recommendations of Steel Compressed Columns of Variable Cross Sections

Abstract

AbstractSteel columns of hollow cross‐sections being the body of revolution and simply supported at their ends are considered in the paper. Columns of such shapes are recently very frequently proposed by architects of public facilities such as airports, entertainment halls and other objects encountered in engineering practice. The provisions of the EN 1993 standard do not provide for direct procedures that can be used when designing such columns. In this paper authors present the comparatively simple procedure which can be used by designers of steel columns of such shapes. The value of critical force required in the procedure was derived for columns of variable cross section by means of Mathematica™ system. The closed formulae were obtained for a rod with a certain, predefined geometry being the surface of revolution. To this end the Rayleigh quotient in the first form resulting from the energy criterion of stability was used and the half‐wave sine function was adopted to describe the buckling form. Critical forces obtained by means of derived formulae were compared with numerical solutions. To assess the compression resistance of considered rods the general Ayrton‐Perry approach was applied and bow imperfection with assumed amplitude was used in the analysis. Amplitudes of these initial imperfections can be chosen in correspondence to fabrication quality assumed in advance. An example inserted in the paper confirms the effectiveness of the proposed procedure. Formulas for allowable compressive force derived by the authors and presented in the paper can be treated as a measure of compressive resistance and used by engineers designing columns of the considered shape.