1837. Reducing the Weight of Trusses by Changeing Member Types
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Paper
Abstract
This paper defines two types of members which can occur in trusses: (1) members which resist only tension forces or only compression forces, called one-force members, and (2) members which resist both tension forces and compression forces, called two-force members. It then defines a very large set of trusses, called E2 trusses. That set includes many common trusses and many trusses with large numbers of joints. The paper then shows, by means of a geometrical theorem, that for any E2 truss the minimum number of two-force members which can make its joints stable and the the minimum number of one-force members which can make its joints stable have a difference of only one, a surprising difference for trusses with large numbers of joints. The theorem shows that for very many trusses replacing their customary two-force members with one-force members can produce certain desirable combinations of member changes, changes which often make possible large reductions in their weight. for example, the theorem indicates that for any E2 truss replacing a set of two-force members which makes its joints stable with the set of one-force members which produces the same result permits both: (a) a very large decrease in its number of members which resist compression forces, the members which most adversely affect its weight, and (b) a very small increase in its total number of members, at most an increase of one. This paper also identifies numerous other trusses which permit the same combination of changes, and it illustrates a routine by which such trusses can be designed.
