  In many applications of Structural Engineering the following question arises:
given a set of forces $\mathbf{f}_1,\mathbf{f}_2,\dots,\mathbf{f}_N$ applied at
prescribed points $\mathbf{x}_1,\mathbf{x}_2,\dots,\mathbf{x}_N$, under what
constraints on the forces does there exist a truss structure (or wire web) with
all elements under tension that supports these forces? Here we provide answer
to such a question for any configuration of the terminal points
$\mathbf{x}_1,\mathbf{x}_2,\dots,\mathbf{x}_N$ in the two- and
three-dimensional case. Specifically, the existence of a web is guaranteed by a
necessary and sufficient condition on the loading which corresponds to a finite
dimensional linear programming problem. In two-dimensions we show that any such
web can be replaced by one in which there are at most $P$ elementary loops,
where elementary means the loop cannot be subdivided into subloops, and where
$P$ is the number of forces $\mathbf{f}_1,\mathbf{f}_2,\dots,\mathbf{f}_N$
applied at points strictly within the convex hull of
$\mathbf{x}_1,\mathbf{x}_2,\dots,\mathbf{x}_N$. In three-dimensions we show
that, by slightly perturbing $\mathbf{f}_1,\mathbf{f}_2,\dots,\mathbf{f}_N$,
there exists a uniloadable web supporting this loading. Uniloadable means it
supports this loading and all positive multiples of it, but not any other
loading. Uniloadable webs provide a mechanism for distributing stress in
desired ways.
