Abstract
Minimum‐weight designs of statically indeterminate elastic beams subject to given loading are provided. Constraints are prescribed on flexural and shear stresses, and on the maximum deflection. The resulting mathematical optimization problems are solved by using concepts from Differential Game Theory and Variational Calculus. The game problem under stress constraints is reduced to a minimax one. The solution procedure is illustrated by several examples of statically indeterminate beams. The optimal designs are compared with prismatic and linearly tapered beams. Suggestions are made as to the extension of the procedure to other indeterminate structures, such as beamcolumns.
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