Lower bound methods have had little application in shell design. The paper presents optimum lower bound solutions for a circular cylindrical tank unrestrained at the top, and either fixed or hinged around the base. Both the optimization method of Rozvany and of Marcal, Prager, and Shield give the same results. A numerical comparison of optimized lower bound design, elastic design, and uniform isotropic yield-line analysis is made. Savings in reinforcement volume of 20% to 25% can be obtained in certain cases. The effects of prescribed minimum amounts of reinforcing and of cracking below working load are analyzed.
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