Title: The set of forces that ideal trusses, or wire webs, under tension can support,
Abstract: The problem of determining those multiplets of forces, or sets of force
multiplets, acting at a set of points, such that there exists a truss
structure, or wire web, that can support these force multiplets with all the
elements of the truss or wire web being under tension, is considered. The
two-dimensional problem where the points are at the vertices of a convex
polygon is essentially solved: each multiplet of forces must be such that the
net anticlockwise torque around any vertex of the forces summed over any number
of consecutive points clockwise past the vertex must be non-negative; and one
can find a truss structure that supports under tension, and only supports,
those force multiplets in a convex polyhedron of force multiplets that is
generated by a finite number of force multiplets each satisfying the torque
condition. Progress is also made on the problem where only a subset of the
points are at the vertices of a convex polygon, and the other points are
inside. In particular, in the case where only one point is inside, an explicit
procedure is described for constructing a suitable truss, if one exists. An
alternative recipe to that provided by Guevara-Vasquez, Milton, and Onofrei
(2011), based on earlier work of Camar Eddine and Seppecher (2003), is given
for constructing a truss structure, with elements under either compression or
tension, that supports an arbitrary collection of balanced forces at the
vertices of a convex polygon. Finally some constraints are given on the forces
that a three-dimension truss, or wire web, under tension must satisfy.