This paper introduces a new aid to the design of economical plane structures, based on the twin concepts of structural task, which is an invariant for a given load system and given constraints on where material may be placed, and (absolute) pertinacity, which is the product of force and member length. An optimum (Michell) structure has task equal to pertinacity for every element of every member. The ratio u of task to pertinacity is unity everywhere in an optimum structure, and constitutes a utility factor: u may be negative for a member, that is, it is possible for a member to increase the task to be borne by the rest of the structure. A parallel is drawn with First and Second Law analysis in thermodynamics.

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