Beams, cables, arches and trusses are all two dimensional structural forms. They are useful because when engineers develop mathematical models of real structures we treat them as a series of repeated two dimensional structures joined together to form a three-dimensional structure. This makes them easier to analyse and easier to build. None the less, there are times when a structure is truly three dimensional – a load is dispersed along load paths which exist in all three dimensions. We will look briefly at some of these.
Slabs and Plates
When a beam is extended into the third dimension it becomes a slab, or a plate. These bend in two directions at the same time.
Nets or Membranes
When a cable is extended into three dimensions a net is created if the cables are kept discrete. If the cables merge together to from a continuum, a membrane is created. Nets and membranes form some of the worlds most unusual but exciting structures. Because of the efficiency of the structure (carrying the load in pure tension), these structures can cover very large areas with very light structures.
Shells and Domes
When an arch is extended into three dimensions a shell or dome is created. Like all three-dimensional structures, shells and domes provide many alternative load paths for any applied load, and by dispersing the load paths through the structure, thinner and more elegant structures are possible with three dimensional compared to two dimensional structures.
Space Frames
When a truss is extended into three dimensions a space truss or space frame is created. These can span large distances because the load is dispersed through many load paths.
Folded Plates
A folded plate is an uncommon three dimensional structure, but it illustrates well the importance of shape in determining the strength and stiffness of a structural form. A flat sheet of paper is useless as a beam, but when folded into a series of peaks and valleys it becomes very much stiffer and stronger. This principle has been used to create long span concrete roofs.
