A “Second Law” for Structures: An Insightful Approach to the Design of Plane Frames

Abstract

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.