2 Space grid geometry – thinking in three dimensions
There is often a tendency for architects, and possibly more so engineers, to think in terms of planar structures such as beams, trusses and portal frames when considering methods of spanning space. However, in many cases there are advantages to be gained from thinking in three dimensions and adopting spatial structures for medium to long spans. This is particularly true where heavy point loads or moving loads are to be supported. Of course, all structures are three-dimensional in the sense that they have length, depth and thickness. However, planar beams and trusses are predominantly two-dimensional in their structural action, as they effectively resist loads applied only in one direction between their supports (usually in the vertical plane). Nevertheless, even for these simple structures it is unwise to neglect their stability in three-dimensions. For example, beams and trusses, in bending, are made deeper with increasing span and this, in turn, increases the tendency for the compression zone to buckle sideways, perpendicular to the vertical plane. To counteract this tendency, lateral bracing of the compression zone must be provided. With a system of multiple parallel beams with bracing systems at right angles to the span, it may become economical to take advantage of the benefits of three-dimensional structural action described below. Because of the planar nature of individual beams or trusses, they must be designed to resist the full magnitude of any point or moving load applied to them. However, with some modification of the lateral bracing system provided to maintain stability of typical beams and trusses, it may be employed to distribute loads between adjacent beams. This forms a three-dimensional structure where loads are rapidly distributed throughout the whole system. Every member usually contributes some resistance to the applied load unless the load is located at or very near a support.
Why two-way spanning structures? To demonstrate the principle and benefit of using a twoway spanning structure we can consider a familiar example in the home, the woven canvas webbing often used for seats of stools or to support chair cushions. If webbing strips are used only in one direction, a load applied 12
to one strip will cause it to sag and transfer load to only two sides of the supporting frame. However, if the webbing strips are interwoven in two orthogonal directions the loaded strip is partly supported by all of the others. This reduces the sag of the loaded strip and distributes the applied load more evenly to all sides of the frame. In the second case, each strip does not have to be capable of carrying the full applied load on its own and a lighter structure can be used for the supporting frame. Another advantage is that, if one of the webbing strips breaks, the seat as a whole will still support loads. Similar benefits may accrue from the use of two-way spanning structures in architecture and engineering. For example, a load applied to a simple one-way spanning beam or plane truss, must be transmitted through the structure directly to its supports (Figures 2.1(a) and 2.1(b)). If, however, a grid of connected intersecting beams or trusses is formed in the horizontal plane, a vertical load applied to any one beam or truss will be distributed, in part, to all the other elements in the grid and thus to all of the supports. Figure 2.1(c) shows this for a small grid of intersecting trusses. Although, in these cases, the structural action differs from that described above for the woven webbing (bending and shear for the beams, axial forces for the trusses and pure tension for the webbing), an analogous, more efficient, load-sharing system has been produced. A configuration of intersecting beams is usually described as a single-layer grid and a very common example of its use in buildings is the coffered reinforced concrete slab where the orthogonal ribs produced by the coffering effectively form a grid of intersecting beams supporting a thin floor slab. When the span of the structure exceeds about 10 m, the use of beam elements in a single layer grid becomes less economical and open web trusses or Vierendeel girders may be substituted for the solid beams. The structure then effectively consists of two parallel horizontal grids of ‘chord’ elements connected with a pattern of vertical and/or inclined ‘web’ elements between the two plane grids. This three-dimensional structure is generally described as a double-layer or space grid, and is also commonly known as a space frame or space truss depending on the type of bracing between the two layers and the method of connecting the members. Doublelayer grids are one of the most efficient and lightweight