Grid configurations

Regular shaped grids are considered to be more economical but there are only three regular polygons that can be used to fill a plane (the equilateral triangle, square and hexagon).

There are many possible ways of dividing up a flat plane by a grid of lines connecting points in a regular or irregular pattern but this may produce considerable variation in the length of lines and the angles between them. However, in modular structural systems such as single or double-layer grids it is advantageous if, in any structure, the number of different member lengths can be limited and connection angles at the joints standardised. Therefore, regular shaped grids are usually adopted for both the top and bottom layers of space grids but there are only three regular polygons, the equilateral triangle, square and hexagon, that can be used exclusively to completely fill a plane.

In square grids the grid lines can be parallel to the edges of the grid or set on the diagonal, usually at 45° to the edges. Both of these are two-way grids having members orientated in two directions, however, plane grids of triangles and hexagons produce three-way grids with members orientated in three directions.

More complex grid geometries may be produced by combining the regular polygons or by using them in combination with other polygonal shapes (e.g. triangles and squares, triangles and hexagons, squares and octagons).

Regular tessellations of a plane (a) squares, (b) diagonal squares, (c) equilateral triangles and (d) hexagons (Drawing: John Chilton).

In space grid structures, where two plane grids are separated by web members to form a double-layer grid, the top and bottom grids do not necessarily have to have the same pattern or orientation but in practice, for reasons of cost and the required connection of web members, the number of common configurations is limited.

The common forms of double-layer grids are:

• Square-on-square - where the top grid is directly above the bottom grid and the web members connect the layers in the plane of the grid lines.
• Square-on-square offset - where the bottom grid is offset by half a grid square relative to the upper grid with web members connecting the intersection points on the top and bottom grids.
• Square-on-diagonal square - where the lower grid is both set at 45° to and is usually larger than the top grid and again with web members connecting the intersection points on the top and bottom grids. An alternative version of this grid is diagonal on square where the upper grid is at 45° to the lines of support and the lower grid is parallel to the supports.
• Triangle-on-triangle offset where both grids are triangular but the lower grid intersections occur below the centroids of alternate triangles in the upper grid with web members connecting the intersection points on the top and bottom grids.
• Triangle-on-hexagon - where the upper grid is triangular and the lower, more open, grid is hexagonal due to removal of some joints and web elements from grid type (d) below.

More open grid geometries are often possible in the lower layer of a double-layer grid because the members are generally in tension, i.e. not subject to buckling, and may, therefore, be longer than the upper compression members even though the forces in the lower chords may be greater. In modular systems it is often possible to omit complete modules in a regular pattern to produce a more open geometry and reduce the self-weight of the structure.

Square-on-square space grid (Drawing: John Chilton)

Choice of grid configuration and depth will affect the economy of the space grid as the node joints are usually the most expensive components, therefore, the more there are in a given plan area the higher the cost is likely to be.

Increasing the grid module size reduces the number of joints for a given plan area but there may be adverse consequences. The depth between the two grid layers may have to be increased to accommodate the web members at an appropriate angle and individual members will inevitably be longer. When the longer members are subject to compressive forces they will almost certainly be larger in cross section to avoid buckling and, consequently, heavier and more costly.

For multi-layer, three-dimensional grids the use of quasicrystal geometry has recently been explored.

Quasicrystals are formed from six rhombic faces of equal side that can be assembled to make both a "fat" and a "thin" version. These can then be combined to make "non-repeating", three-dimensional grids that have a constant member length and dodecahedral nodes that are all oriented in space in the same way. No full sized structures have yet been built although one was proposed for the Danish Technical University at Lyngby.

Instead a sculpture with quasicrystal geometry was assembled by artist, Tony Robbin, and students of the university and suspended in the atrium of the administration block.