Effect of vortex shedding on a cylindrical column

In this investigation, the effect of vibratory forces, due to vortex shedding, acting transversely on a cylindrical column member is evaluated analytically. The primary application for this work is its effect on the design of cylindrical members of the underwater portion of fixed offshore platforms. The problem is considered as a lateral forced vibration of a beam, complicated by the presence of an axial compression load. The classical differential equation for a vibrating beam, modified to account for axial load, is solved to determine the frequencies and eigenfunctions of the beam-column. The mathematical description of the magnitude and frequency of the vortex-shedding lift forces are provided from a study of the literature. General deflection and moment expressions are then determined for the column under the forced vibration due to vortex shedding. Four such expressions are provided, accounting for both pinned and fixed end conditions as well as two different longitudinal distributions of the lift force. The quantitative effect of vortex shedding on offshore structural members is evaluated by substituting, for the variables of these expressions, a range of numerical values generally considered for offshore structures. The theoretical results are then applied to the AISC beam-column design formula and a modified formula is developed which accounts for the dynamic effect of the oscillating lift forces. Finally, a dimensionless grouping of the problem variables is developed which can be easily used to estimate the significance of vortex shedding on the design of underwater cylindrical-column members. The overall conclusion reached from this investigation is that the additional vortex-shedding lift forces will probably not affect the design of most cylindrical column members of offshore structures. The error resulting from neglecting the vortex-shedding effect is quite small except for extreme cases as are discussed.