Application of Linear Programming to the Limit Analysis of Conical-Shaped Steel Water Tanks

In the past two decades, accidental failure of conical-shaped steel water tanks under hydrostatic pressure has been reported. For safety analysis, the limit analysis of such structures is formulated as a linear programming problem. Comparing with experimental and numerical results available in the literature, the accuracy of the linear programming approach is found to be high, with respect to the limit loads and failure modes of the conical shell structures. In the process of formulation, the equilibrium conditions of the problem, not the constitutive equations, are directly involved. Thus, overestimation of the stiffness for thin plates or shells resulting from inadequate constitutive equations—a phenomenon often encountered in the nonlinear finite-element analysis for thin-walled panels or shells—does not exist. Based on the internal forces at collapse, some important mechanical aspects as related to the failure mechanism and failure modes, as well as some structural characteristics, are also discussed.