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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 atprescribed points $\mathbf{x}_1,\mathbf{x}_2,\dots,\mathbf{x}_N$, under whatconstraints on the forces does there exist a truss structure (or wire web) withall elements under tension that supports these forces? Here we provide answerto such a question for any configuration of the terminal points$\mathbf{x}_1,\mathbf{x}_2,\dots,\mathbf{x}_N$ in the two- andthree-dimensional case. Specifically, the existence of a web is guaranteed by anecessary and sufficient condition on the loading which corresponds to a finitedimensional linear programming problem. In two-dimensions we show that any suchweb 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 showthat, by slightly perturbing $\mathbf{f}_1,\mathbf{f}_2,\dots,\mathbf{f}_N$,there exists a uniloadable web supporting this loading. Uniloadable means itsupports this loading and all positive multiples of it, but not any otherloading. Uniloadable webs provide a mechanism for distributing stress indesired ways.

On the forces that cable webs under tension can support and how to design cable webs to channel stresses