Minimum weight design and the theory of plastic collapse

Abstract

This paper examines the problem of assigning economical sections to the members of a structure whose geometrical form is given. The criterion of failure is taken to be that of the plastic theory of collapse, and the criterion of minimum weight is employed to determine the best design. A geometrical analogue of the equations involved is used to clarify their significance, and such proofs as there are in the text, are cast into geometrical terms. A method of solution is suggested at the end of the paper, but the primary concerns of the paper are the general features of the problem.