Many applications require roofs or covers that are flat, or nearly flat. Spatial structure provide efficient solutions for these requirements. The most common Spatial Structure geometries are called "offset rectangular grids", "square on square spatial structures", or simply "square grids".
But square grids have a couple of characteristics that may limit their use for the longest spans:
With the Geometrica system, it is possible to overcome each of these disadvantages, and thus use square grids for longer spans by modifying the conventional square grid as follows:
Increased chord density: In order to build a square grid that can transfer loads diagonally, we can take advantage of the Geometrica joint's capacity to resist bending moments. Square grids in each layer of chords can be reinforced with diagonal elements that are not directly connected to the webs. This stiffens the grid against twist, increases the density of the bending-resisting elements, and allows for longer spans.
Varying depth: The top chord of spatial Structures may be sloped to provide a deeper section at the middle of the span as well as positive drainage.
Double depth: The depth of the frame layer of webs and chords. The additional depth increases the second moment of area of the spatial structure, increasing the possible span substantially. Chords in the middle of the double depth frame may be removed because the Geometrica joint can resist bending. And because web members in the Geometrica system may be very light and slender, the increased web count does not result in significant additional weight.
Camber: The "flat" spatial structure may be manufactured with a slight deformation in the direction contrary to the expected deflection under service loads. This eliminates any possible unsightly sag of the structure, particularly for the longer spans. Camber may be applied to either or both chord layers of a spatial structure.
Another spatial structure geometry commonly used is the triangular grid. Because of their triangular pattern, these grids can resist in-plane twist. But as in square grids, their depth is limited and, for a large portion of their extent, they often contain more web members than are necessary to carry the load. In order to overcome these disadvantages, triangular grids may also benefit from the modifications available to square grids. See section on domes for some of the variations in triangular grids.