An insight into the behaviour of two-dimensional and three-

As referenced in the introductory part, grid-shells and grid systems present a very particular and unique dynamical behaviour. In order to understand further the mechanism behind their formal organisation, we may take into consideration a very familiar example, that of a metal strainer. Even though very small in scale, it represents, in fact, the behaviour of grids acting in space. The metal strainer consists of metal stripes combined in a diagonal configuration. If those metal stripes were used in one direction only, surely it would be very easy for the shape to be deformed, as every single stripe acts solely to retain the overall strainer shape. This indeed looks impossible and

falls into a paradox. On the contrary, the system of this example (strainer) is an interconnected system of several elements combined together. Therefore, when applying a pinch at a random point on its surface, it feels rather stiff and seems initially to be rather hard to deform and change the shape. It is only after a certain amount of pressure that you may be able to observe in fact any deformation in the curvature. This indeed demonstrates how grid structures can act as a collaborating system. Every loading metal stripe in the strainer is partly supported by all the others and the applied load is clearly distributed more evenly and better through the diagonal net below (Figure 48), increasing at the same time the overall strength.

Figure 48: Metal Strainer, the curvature obtained by an interconnected grid system of metal stripes.

Similar effects and behaviour in load distribution can be observed in larger in scale examples, in architecture and engineering.

Figure 49: The load transportation of a beam and a truss network respectively. (Chilton J., 2000, p.13)

For instance, a load applied to a one-way beam or plane truss⁷⁶ is distributing the load to its supports. However, if this shape was formed as an interpretation of interconnected beams or trusses, the load instead will be transmitted to all the other elements in this grid and in turn to all the supports (^{Figure 49}). This configuration, thus, requires no longer heavy or large beams, but utilises elements, smaller in diameter and much lighter, having also numerous advantages regarding their ability to span.

There are numerous space configurations of intersecting grid systems in the bibliography, which in turn behave variant structurally depending the applied load. A configuration, for instance, of an intersecting beam system, is referred to as a single-layered grid and can be also displayed in some case as grid-shell or two-dimensional

76 “In engineering, a truss is a structure that "consists of two-force members only, where the members are organized so that the assemblage as a whole behaves as a single object". A "two- force member" is a structural component where force is applied to only two points.”

(Link: https://en.wikipedia.org/wiki/Truss )

Figure 50: Deflection in the case of a one-way system (left) and two-way system (right), demonstrating the behavior and the load transition respectively (Chilton J., 2000, p.13).

grid (Figure 50). Even though it exhibits stability, mainly inherited by the combination of the intersecting (subdividing) method, it can be the least effective in terms of structural performance. A span of the structure (one-layered grid) that exceeds a certain amount of length becomes uneconomical and is subject to structural failures with the need of reinforcing it with extra structural extensions, such as Vierendeel girders ⁷⁷ . However, in the case of more complex configurations, we may observe grid systems that exhibit resilience and present better structural performance. This case is the example of an intersecting network of trusses that articulates a primary three- dimensional grid network, also referred to as ‘double-layered grid’ or

‘space truss’ (Chilton J., 2000). Although this multi-layer grid is generated more for load bearing enhancement purposes, it is also considered to be lightweight and significantly structurally efficient, due to this complex articulated grid system. It can be offered with a variety of configurations with interesting also geometrical results, mainly distinguished by different structural actions.

1. Double-layer grids with inclined members

2. Double-layer grids with no inclined members, but with horizontal and vertical chords.

77 ‘The Vierendeel truss/girder is characterized by having only vertical members between the top and bottom chords and is a statically indeterminate structure. Hence, bending, shear and axial capacity of these members contribute to the resistance to external loads. The use of this girder enables the footbridge to span larger distances and present an attractive outlook. However, it suffers from the drawback that the distribution of stresses is more complicated than normal truss structures.’

(Link: http://www.engineeringcivil.com/what-are-the-characteristics-of-vierendeel-girder.html, Accessed: 16/11/ 2017)

These actions include, for the first instance, of a structural system where loads are concentrated in the nodes, whilst the members are subjected to either axial tension or compression forces.

Bending actions are present but are introduced depending on the rigidity of the connection between the bar members. In the case of the later instance, the structural system, mainly prefabricated constructed, has the bar members subjected to a combination of bending, shear and axial tension and compression forces.

6.2. Rigidity of grid systems and the act of resilience