Optimal Design of Vertical Cylindrical Storage Tanks by Eurocode for Seismic Loading

The methodology described in Eurocode 8, Part 4, for calculating seismic effects on vertical cylindrical rigid and fixed steel storage tanks is programmed in MATLAB®. The walls of the tanks are constructed of shell courses with varying thicknesses of sheet material. The strength conditions for the ultimate limit states of plasticity, elastic buckling, and elastoplastic buckling (“elephant foot”) are checked at many calculation points along the height of the storage tank. The thicknesses of the courses are determined to satisfy all strength conditions for different slenderness ratios of the tanks and for different volume capacities. Tanks with supported roofs and those with self-supporting roofs are considered, as well as open-top tanks. A mass per unit volume capacity is the criterion for optimization for different seismic loadings and steel grades. The criterion is not a smooth function because of the discrete thicknesses of the shell courses and their number. A smooth objective function is created for better parametric optimization analysis. The dependence of the optimal slenderness ratio on the volume capacity is determined, as well as the inverse dependence. The problem of the optimal number of storage tanks in a set of tanks with a given total volume capacity is also considered.