  This paper investigates the use of the most fundamental elements; cables for
tension and bars for compression, in the search for the most efficient bridges.
Stable arrangements of these elements are called tensegrity structures. We show
herein the minimal mass arrangement of these basic elements to satisfy both
yielding and buckling constraints. We show that the minimal mass solution for a
simply-supported bridge subject to buckling constraints matches Michell's 1904
paper which treats the case of only yield constraints, even though our boundary
conditions differ. The necessary and sufficient condition is given for the
minimal mass bridge to lie totally above (or below) deck. Furthermore this
condition depends only on material properties. If one ignores joint mass, and
considers only bridges above deck level, the optimal complexity (number of
elements in the bridge) tends toward infinity (producing a material continuum).
If joint mass is considered then the optimal complexity is finite. The optimal
(minimal mass) bridge below deck has the smallest possible complexity (and
therefore cheaper to build), and under reasonable material choices, yields the
smallest mass bridge.
