NATURE, DESIGN AND INNOVATION,
Light and spacious. Aspects of the design and construction of spacious light structures
1. The principle of light construction
The present position of construction is characterized by a high degree of specialization. The complexity of construction assignments compels a division of the work. Opposed to this is the idea that the art of construction is much more than the simple sum of individual pieces of work. Ove Arup, one of the great engineers of our day, has expressed it in these terms: «All the facts and possibilities that influence a project must have been understood and assimilated before the project is defined. The whole must be more important than any one of its parts.» There is thus one sole consequence: team work. This means that the group, like the master builder in the classical sense, is necessary to harmonize all the aspects of a building: the creation of the form and technical construction, whether it is a functional and economic proposition, the natural environment and aesthetic criteria. The art of building as «the perfect harmony of the means and the end» (Henry van der Velde).
If it is true that man has a genetically determined capacity for perception and sensation, and if it is true that «knowledge as a condition for the understanding of the architectonic formal world» (Curt Siegel) is indispensable, then aesthetics in architecture is no longer a formulation for aesthetes and pure artists but rather it must be included in the rational field of technical realities. The maxim of «yielding more with less», which sums up the latest ideas in architecture with light structures, here takes on a totally new and extensive dimension which converts it into the principle of light construction. A light object is one which weighs little and so has a small mass. The mass of an object is equivalent to the quantity of material enclosed in it.
Every object that has a material existence is exposed to internal or external forces and has the ability to accept such demands or to transmit them. Every object is, therefore, in the widest technical sense, a construction.
If a comparison is made of different objects in a situation where they transmit equal forces over equal distances, the one which does this work with the smallest mass is lighter than the other objects. Objects which can transmit forces with a smaller mass are called light constructions.
1.1. Light construction in nature
A living being which, with a smaller mass or less energy, supports larger loads or exerts greater forces, has an advantage over others.
Living objects in nature can have very different sizes and masses. They fulfil different functions and possess different possibilities of movement. Versatility and mobility with high structural performance are the criteria which characterize the principle of light construction in living nature (figs. 1 and 2).
Light construction in living nature has a structurally predetermined basic form, which is highly productive: the cell. From the individual cell to the complex systems of plants and animals, this is the structural element in all living beings. Cells can be soft, they can remain soft, but they can also adopt all the degrees of hardening.
A soft cell is a pneumatic structure: a structural system based on a flexible covering (membrane) subjected to traction and an inner fluid filling (protoplasm) which exerts internal pressure on the covering (fig. 3). All living objects in nature are or consist of pneumatic structures. The pneumatic structures adapt to other pneumatic structures; they wrap themselves up in pneumatic structures, receiving internal pressures and causing variable tensions, through the fillings (gaseous, liquid, granulated) and membranes. The diversity of forms and structures of living beings rests on this single system.
One of the most important «inventions» of live nature, or even of non-live nature, is the fibre. It is a drawn-out element, capable of submitting to requests for traction. Installed in cellular membranes or placed between cells, lined up or laid out as a net, they are, together with the substances which can be subjected to requests for pressure, the decisive building elements in living nature for shaping and for increasing performance in the sense of the principle of light construction.
Mountains, thrown up by folds in the Earth’s crust or as volcanic eruptions, can reach certain sizes and have certain forms which are not arbitrary. External influences such as erosion by water and wind or earthquakes give rise to changes in form. Stars form gigantic systems of equilibrium. The bigger a star becomes, the more spherical it must be. If it passes its size limit and its matter no longer resists the pressure of gravity, then it explodes and a black hole appears. Inside atoms there are powerful internal forces at work whose equilibrium can only be broken in exceptional cases or with violence. With their sparse mass, atoms constitute the lower limit of lightness.
Animals have technology too. They use materials from non-living nature and from dead nature, such as earth and wood. They produce materials and elements with their own structures, such as highly consistent glues and extremely resistant fibres. They form structures for capture (spiders’ webs) and dams (beavers’ dykes), houses (dens and nests) and cities (corals, termites, wasps, bees), whose structural and functional efficiency, in accordance with the principle of light construction, can attain the highest values and totally compete with the products of man.
1.2. Light construction in technology
Any well-developed construction has two components: lightness and economy. The most important criteria in industrialized countries are the use of materials and energy for production and transport, as well as wage costs. Optimization in the technical field is aimed, as a priority and in the short term, at the reduction of costs. Greater masses are often accepted if transport is cheaper or wage costs lower.
With planes, light construction is a necessity for functional reasons. As for cars or trams, the situation is similar. Here functional motives no longer have such significance for a reduction in materials; rather they take a step backwards when faced with the desire for a reduction in production costs. This also affects naval and craft construction. The effort to achieve light construction entails keeping as low as possible the weight of a construction with an unchanged or increased carriage capacity, by means of an extensive use of all the creative, static and structural possibilities as well as those that depend on the material.
Light construction is a requirement for great sizes and heights. However, constructing in a really light way is a virtue which is still relatively little cultivated in building. This is perhaps because there is a lack of conditions which oblige either functionally or structurally. Although perhaps the crux of the matter resides only in the absence of simple understanding: the only thing that is «good» and «substantial» is what is built heavily or massively (or at least appears to be). The awareness of always having to build for centuries or, at least, for successive generations is still too deeply ingrained. With our gaze fixed on the longest possible period of use or —what almost always has even worse consequences— on high and rapid profits, our environment continues to be constructed without scruples or misgivings.
Neither is light construction the panacea. But it could be a means of help on the arduous path that leads to improvement and change. This does not involve tendencies such as, for example, the area of conventional construction in steel or building with prefabricated sections. In both of these the primary object is the reduction in the use of materials for economic reasons. Neither does it involve so-called disposable architecture, «use it and throw it away. In view of the dangerously rapid reduction in the world’s natural reserves, we can in no way permit such senseless economic extravagance.
Behind everything that is built by man for man is the desire for architecture to create an environment that is worthy of man and to destroy as little of nature as possible. The following demands are made with ever-growing insistence: flexibility of adaptation, mobility, building within a fixed time, versatility, possibility of recycling —to name just a few of the more important. None of these demands is new, but conventional construction methods offer few starting points towards satisfying them. With light constructions the possibilities are substantially better. One way among many other possible ways. A genuine alternative to conventional construction with a wealth of new building possibilities and an infinitely wide variety of forms.
Every object is a construction. It has form, it can receive forces and it consists of material. Its form is made up of the external figure and the internal structure; in many cases it is hardly possible to measure it geometrically. Its ability to receive forces is noted by experiments or through calculations. Its material has a mass which on earth is equal to its own weight; this can be determined in most cases with scales.
With this general concept of construction it no longer matters if an object belongs to living nature or non-living nature, or if it proceeds from human technology and if it incorporates a constructive or weight-supporting «mission».
An object arises with all its components by a process that is either self-forming or occurs through the human creative will, depending on physical, chemical or —when it is a living being— genetic laws. Therefore, a construction is not only a naked object but also one which displays at the same time a process and its result. Both things must be considered together.
This is especially valid when an object is composed of similar or different elements in an arbitrary mixture with arbitrary proportions. In such an object the sum of its parts is not easy. Each work of construction —and even more each living being— is a complex unit. The process of formation and the formal aspect constitute one unit. In a scientific analysis this unit is of necessity broken down for simplification and sometimes certain aspects are neglected in order to find at least a way of access. The important thing is the next step; joining together all the knowledge acquired in one synthesis.
In the same generalizing way in which the concept of construction is understood, there can also be a division in the different types of construction. Immediately afterwards, the division of how we perceive objects: hard or soft; then how we see them, that is, according to their form: one-dimensional, two-dimensional, three-dimensional or perhaps lineal, superficial or corporeal; next and lastly in what ways the objects are subjected to forces: dragged, pressed, curved, displaced or twisted or even subjected to traction, pressure, inflection, push or torsion (fig. 4).
Forces can act on a construction from outside (persons, vehicles, snow, wind) and from within (own weight, temperature, humidity) and can be transmitted by the construction itself. What these loads cause is wear on the construction, usually externalized through tensions in the material. Materials can be solid, liquid or gaseous bodies, in different combinations and densities. Among them there are sometimes intermediaries that are difficult to define, such as, for example, magnetic forces, centrifugal forces, gravitation and irradiation of energy.
The number of possible forms is infinite, the operating forces are normally known; the materials available are limited in their quantity. If now there is a desire to raise the carrying capacity of a construction or reduce the costs of materials —for a specific construction mission and for given forces— it is essential to know the relationships between the form and the mass of the construction and its capacity for transmitting forces. Form, force and mass are in direct interdependence with each other and together determine the productivity or efficiency of the construction.
2. Large light structures: forms and constructions
Light structures of a large size have become, in the last two decades, an important component of contemporary architecture all over the world.
However, light constructions have remained till now rather like exotic objects in the construction landscape. They do not even belong in the repertory of architects and engineers. There is also an impression that they are only remembered when something special is being looked for: an attraction to improve an image and generate prestige; something to attract attention for publicity purposes, which will induce people to buy; a weakness in architecture.
On the other hand, every year hundreds of light constructions are built all over the world, from a small garden shed to a huge awning for a stadium. But this should not conceal the fact that most of what is built is a copy, more or less deficient, of far better models. Truly original and successful works of construction are few and far between.
The different types of construction of light structures offer an unlimited variety of forms. They can be built in the most diverse sizes and for a wide variety of purposes and uses. Today only some of the multiple possibilities for use are taken advantage of.
The present state of technology in the field of light structures can be summarized in a few words.
The basic problems of determining the form, the section, the calculations and behaviour of the structure have been solved. The essential questions concerning the construction process, raw materials and building materials, production and assembly have been answered. We know how we have to construct them, but we also know that we can still improve them in many aspects. We know their formal and structural properties, their advantages and their weaknesses.
With such a range of possibilities there is also the great danger of considering that «everything can be built». Architecture is more than technical potential. The simple log cabin is an ideal construction, because it offers its inhabitant what is his primary need: protection from the weather, security, a place to sleep —the man who has built it is in harmony with nature, not her opponent. If architecture ot light structures could contribute in some way to this effect, it would have achieved a great objective.
2.1. Forms and constructions
A load-bearing structure is a construction of one or more surfaces and their respective supports.
These surfaces can be curved in the shape of a saddle or perhaps dome-shaped or they can also be flat. In relation to their size their height is always limited. They can be closed surfaces or built with an open mesh structure.
Depending on the type of construction, the load-bearing surface maintains its form by tension, rigidity of the material or by weight. When it is loaded with weight, it is then only subjected to traction or, mainly, pressure and flection.
The supports can be straight or curved, based on a point (for example, a post) or in the form of a line (for example, beams, arches, cables) and can be situated on the edge or perhaps inside the load-bearing surface. When they are loaded, they are subjected to traction, pressure or flection.
A structure is light because it has little weight of its own in relation to its size and weight-bearing capacity. That is to say, it is a construction which has a small mass and requires little material.
A structure is light when, taking its own weight as a specific magnitude of the material used per unit of surface, it permits the following relationship: the greater the size of a construction, the smaller should be its own weight.
For purposes of general clarification it would seem sensible at this point to explain briefly the elements and characteristics of the distinct types of construction of light structures.
2.2. Tents and nets
Prestressed membranes are tents and tent-like constructions. A membrane or fine film, usually curved in the form of a saddle, is stabilized by means of mechanical tensing. The membrane is only subjected to traction —between all the external loads. These membranes almost always have the typical shape of the pointed tent (fig. 5). But they can also be supported by arches (fig. 6) or have a curved form like a sphere. There also exist other types which consist of flat membranes (circus awnings, tents and traveling stalls in which the prestressed aspect of the membrane plays a less important role).
Pretensed nets of cables or ropes. In general, nets of homogeneous mesh, are chequered (fig, 7) and normally have, because of their constructional assembly, a heavier weight than membranes and are especially suitable for large areas or also for larger building works such as roofs of sports pavilions.
Spatial nets are also stabilized by tensors, although it is also possible for them to be hanging structures or to be stabilized by their own weight. The cords of the net form flat or partially curved surfaces which describe different bodies such as, for example, pyramids, dice, rectangular prisms and other polyhedra —depending in each case on the shape of the mesh. They have been applied in children’s parks.
Hanging structures (figs. 8 and 9) are constructions which consist of ropes and other traction elements such as chains or ribs and are stabilized thanks to their own weight, to loads or to rigid complementary elements.
2.3. Rope nets and tents
Tents figure among the most primitive constructions of man. In all epochs of history the tent was used as a dwelling in the most diverse shapes and sizes.
The circular tent, resting on wooden poles, is one of the oldest types of tent. Other types of tent are the simple awning, the bell tent and, as variations, the parasol and the umbrella. The North American Indian hut, the circular Persian, Turkish and central European tents of the twelfth to the eighteenth centuries, the tents of the Arabian, North African (fig. 10) and Asiatic nomads are all examples of perfection of forms and structures —of their elements and of the equipment of the tents, which have lasted for centuries.
The modern conception of the tent has set out from these traditions and rests on the same bases and formal and structural details. It was therefore natural and necessary to activate the development of tent construction through research into traditional methods and the historical materials of the craftsman, to prevent ancient practices from falling into oblivion and to make them useful for present-day construction praxis. The structures of rope nets consist of two basic elements, the load-hearing surface, responsible for traction, and the post —subjected to pressure demands— as a support. The compactly woven material has been transferred in larger dimensions to the mesh net, not very dense and knotted with ropes.
Together with the large roofs of rope mesh there are numerous examples in technology of nets well-known throughout the world, from all kinds of fishing and protective nets to wire netting and the tennis racket.
Fabrics and nets cannot be supported directly on one point, owing to their material structure and because of the distribution of tension in the load-bearing structure. The points of tension can be resolved by one or more rope knots, by grooves and groins reinforced with rope, by steel rings, by convex devices and supports branching out like a tree. The edges of the load-bearing surface must also be gripped with ropes, to receive the tensions of the membrane and to divide them between the post and the fastening.
Rope nets and tents can have different degrees of transparency. The fabrics of natural and synthetic fibres can be with colour or can be painted. The nets can be covered with these or with glass, with synthetic materials, with wood or with boards, and also in combination with other measures and devices for containing heat and sound.
Every year 200 to 300 million square metres of the Earth’s surface are covered with fabrics or nets of the most diverse types: stationary or temporary, long-lasting or short-lived, fixed, movable or transformable.
Their functions and uses range from exhibition halls, industrial premises and warehouses, greenhouses, schools, university institutes, department stores, commercial zones and roofing for leisure activities and sports to complete camps and towns, dwellings for protection against catastrophes and autarchic one-family homes (figs. 11-14). If the concept of «tent» no longer fits in so often with the original idea, nevertheless these constructions rest fundamentally on the principles of form and structure of tents and nets of rope.
2.4. Membranes or pneumatic structures
A fine membrane, almost always with a dome-shaped curve, is stabilized by the pressure or depression of a medium which causes tension in the membrane. The membrane is only subjected to traction, among all the external forces. The medium is, in most cases, air, although it can be other gases or water and all kinds of liquids, even products in bulk. The structures of pneumatic membranes generally have the typical bubble (fig. 15) or cylindrical shapes, which can vary and combine in multiple ways.
Pneumatic membrane structures are, without doubt, the lightest constructions and can withstand extreme sizes. In hydraulic constructions especially, pneumatic structures are used as retaining receptacles and as dykes.
Pneumatic structures are among man’s most ancient constructions. Wineskins made of animal hide and swimming lifebelts are still common examples today. The dream of flying was first realized with a paper balloon. Without the invention of the rubber tyre filled with air the car would be unthinkable today. From the chewing gum bubble to the football bladder, from the pneumatic can to the aerostatic publicity balloon, from the camping water bag to the sandbag for catastrophes, from the plastic bag for goldfish to the shopping net filled with oranges: pneumatic structures are everywhere in every-day life. You can eat them and play with them, they can swim and fly —there is always an external cover tensed by some internal filling.
The development of pneumatic structures as constructions has been conditioned by the technical capacity for making hermetic textile fabrics with adhesives of rubber and synthetic materials.
In pneumatic structures in construction on land a membrane covers a closed space in which, by means of ventilators, there is a pressure only fractionally higher than the pressure of normal air so that it is scarcely perceptible (fig. 16). The inside of the construction is accessible to persons and goods by means of airlocks.
When great areas are covered without any support, with large coverings which are at the same time not only a protection against atmospheric agents but also climatic covers, the membrane must be reinforced with nets of loose mesh rope. There are also certain special forms of pneumatic structures which are cushions filled with air and tubes (fig. 17) and these, either in isolation or as complements, can serve as walls or roofs for buildings.
Because of their extremely low mass and a simple mooring system, pneumatic structures are especially suitable for transportable and mobile buildings. This also means that pneumatic structures like durable constructions whose demand disappears after a certain period of use can be eliminated at a comparatively low expense and without leaving large amounts of residues. They can probably even be recycled.
Pneumatic constructions do no necessarily have to be fixed, but can also be transformed. The change in the form of construction is controlled by means of injection or escape of air. Or perhaps one membrane is placed over another and stabilized by internal pressure.
Another unique feature is membranes which are stabilized not by means of pressure from above but by depression (fig. 18) and which can be supported by convex or arched internal posts (they can also be high pressure pneumatic tubes).
Alongside these types of enclosed pneumatic structures there are also open pneumatic constructions. Typical examples are the sails of boats, parachutes and open-topped liquid deposits such as collapsible swimming pools.
One field of application which is becoming every day more important is that of pneumatic structures in water such as engineering constructions for the protection of water and coasts, for use in catastrophes and for the saving of energy (figs. 19 and 20). This field ranges from dykes, sluices and dams of all types, wave powered electricity stations, purifying plants, desalination of maritime waters and solar installations to the capture of algae and fishes.
Examples are water-filled membrane tubes of one or more units (width up to 5 metres and length more than 50), which are capable of floating, acting as emergency gates for cracks in dams and dykes (fig. 21); and breakwaters of water-filled membrane tubes (width approximately 2.5 metres and length approximately 40 metres) to regulate water levels, speed of flow and the amount of drainage in rivers. Other examples are movable gates of flexible water-filled tube for the maintenance of ship canals or for blocking off and emptying certain stretches; large containers for storing cereals or gravel set up on land or floating on water.
As constructions they have proved to be very economical, especially in relatively short term applications, as well as being extraordinarily advantageous as far as general energy expenditure is concerned both in their production and in their operation.
2.5. Mesh coverings
Mesh coverings are structures with curved ribs, inflexible and continuous, which form a flat grille with a chequered pattern and a constant distance between knots. They are subject mainly to demands of pressure and flection (fig. 22).
An important advantage of these types of constructions is that the range of possible technologies for their realization is enormously wide (figs. 23 and 24). They are, thus, constructions that can be effected with primitive means, little technical know-how and easily accessible tools.
Light coverings are structures which, owing to an extremely weak consistency in their walls, and/or to the use of special materials (for example, reinforced concrete or a synthetic material), have a weight that is considerably lower than other protective buildings (figs. 25 and 26).
Transformable load-bearing structures or, rather, transformable roofs are constructions which can be opened or closed, that is, whose shape can be changed according to necessity. Most are built with pretensed membranes (fig. 27), although some have also already been built with pneumatic membranes and also with every conceivable type of net and mesh. The construction consists, in general terms, of a load-bearing structure greater than what the roof itself can add to or take away from it. The action takes place by hand or by means of a motor. One special type of transformable roof construction is the umbrella. There also exist transformable roofs conventionally made of wood, steel, concrete and glass, where complete pieces of the construction work move on rails.
Transformable load-bearing structures serve as roofs for small or medium-sized building works, guaranteeing them independence from weather conditions, such as, for example, swimming pools, sports installations, theatres or public places of all types. As awnings over theatres and stadiums, this type of construction reached considerable sizes with the Romans.
Mixed load-bearing structures or hybrid structures are constructions that have arisen from the constructional combination of one or more of the types of constructions mentioned above, or of one of them with conventional construction elements. Here belong, for example, the tensed membranes between pneumatic high-pressure tubes (fig. 28); mesh coverings which, with rigid building elements, contribute to supporting the weight of a steel or concrete framework; hanging roofs with little pretension such as a rope net for certain loads; suspension bridges where the rigid support of the road surface contributes to support and solidity.
Ribbed reticulate structures
These consist of straight ribs, subjected to pressure or traction, which with a variety of spatial lay-outs and in different flat forms are assembled in a flat or spatially curved latticework. The final construction can also acquire a spherical form (fig. 29).
However, because of their special generation of forms and their load-bearing behaviour, they are basically a completely independent, and at the same time very extensive, speciality. As for their application they have been used for some time by architects and engineers for the most diverse functions.
Also belonging to the ribbed structures are the so-called Tensegrity constructions developed by Buckminster Fuller. They consist of continuous pretensed ropes subjected to traction by external loads, and of pressure ribs which tense the ropes in accordance with a specific system.
One of the basic themes in the history of construction is that of covering large spaces. This, together with the desire to build in a flexible way and at a minimum cost, has led us from the heavy roofs of antiquity to delicate roofs cushioned with concrete. Latticework as an element of construction is by no means new. The huts and houses of Africa and Asia, built with simple branches, with worked wooden ribs or bamboo, are examples that are thousands of years old, as are the folding latticework walls of the Asians. The Romans built little arbours with lattices of arch-shaped wood (fig. 30), the Turkish galleys had curved latticework in the form of buoys as buildings at the stern.
In modern buildings, the high percentage of costs for the framework means more than 50% of the total cost, so it is understandable that there is a preference for conventional surfaces such as cylinders, conoids or hyperbolic paraboloids.
Mesh coverings have arisen as the result of a search for a simple and economical means of construction for protected coverings. A mesh covering consists of a few simple building elements. The ribs of the lattice are straight and have the same transversal section. All the knots are the same. The edge is formed with various ribs placed alongside each other, or perhaps it is a special construction piece. Every piece can be prefabricated and transported, packed up, folded in sections or as a whole unit. The technological border runs from great branches or bamboo canes as ribs, with knots tied simply on sawn wooden ribs, or profiles of normal everyday steel with screws for assembly, to finished pieces which make up the ribs of the mesh, with pieces of metal or plastics as knots.
Mesh coverings can be erected speedily and at a low cost, since the lattice is assembled and the knots are rotarory. It is erected by hand or with a simple lifting device, with which the originally square meshes change their angles into a scissor-type lattice and the ribs are arched. No framework or special shell is necessary. After fixing the edge and tightening the knots, the model is fixed and the lattice shell can now support loads.
Lattice shells can be used in all climatic conditions and offer great flexibility. They are suitable for any purpose, where small or great spaces have to be covered, from a kiosk to a house, from a simple storage bay to a large multipurpose covering, from a temporary emergency dwelling-place to a definitive work (figs. 31 and 32). Mesh coverings need no foundations, they can be erected on almost any type of building land and are not affected by movements of the soil or by earthquakes, because they have little mass and are very elastic.
2.6. Branched supports
Branched supports are flat or spatial structural systems which consist of separate branches, each one of which forks out at a specific point (knot) into at least two other branches. Such structures can be subjected to tension, to compression, to flection and to torsion. External loads normally act only on the ends of the ribs. There are no loads on the knots. Branched columns are normally used as supports for any type of enveloping structure or roof (figs. 33 and 34).
Branched columns are not a new development or a modern invention. There are numerous historical antecedents of the same or similar style. To date, however, their geometric and structural bases have hardly been investigated. Most seem simply to have been built for spiritual or ornamental reasons.
The architectural aspect and economic efficiency depend decisively on form, in accordance with geometric parameters such as the type of knots, the length of the branches, the angle of the fork, etc. Every improvement on a design, directed towards a lower cost of material, must begin with form. Structural details, materials and the type of primary structure are also important, but have a second place. The structural analysis and the constructional working-out do not normally present great difficulties and can be carried out in most cases with every-day conventional methods. Although the basic rules, the laws of the form and the ideal construction of branched structures have not been totally investigated, they are already known in their essential lines or are, at least, recognizable.
It seems, however, that the architectural quality and aesthetic attraction of branched structures have been rediscovered in principle, without first acquiring a greater knowledge of the geometric and structural properties of the arboreal ramifications and initiating a profound study of an unknown but promising field for architecture.
Drawings of technical trees: from the simple column to a tree structure with nine generations. Given parameters: a constant relationship between length and diameter (area) of the ribs in each generation and a constant sum of diameters (areas) of the ribs in all the generations (fig. 35).
Computer drawings of a tree support with the same vertical loads at each point of support: displacements, moments of curvature, crossed forces (transversal), normal forces (from top left to bottom right) (figs. 36 and 37).
Model of a pretensed membrane structure (tent) resting on tree columns (fig. 38).
Model of a hexagonal dome of ribs «in reverse», sustained by various branch supports (fig. 39).
3. Design and determination of the form
Light and large weight-bearing structures are not designed in the normal way. Their forms and constructions undergo a planning process which is different from conventional construction work. Its essential part is the determination of the form. In this case, the subjective choice of an architectural form is replaced by an objective determination of the form.
The determination of the form is an empirical operation that rests on simple physical laws and —depending on the type of construction— is determined by the laws of generation of form. This operation can be carried out experimentally with models or with mathematical computer programs.
«Liberty of projecting» is no longer found in any modelled form but in the choice and transformation of the advantages and conditions for determining an ideal form. To every type of light structure construction there corresponds one or more methods of determining the form, which contain all the essential features and properties of this type of construction. The decision to adopt one specific type of construction signifies in principle the establishment of a method of determining the form and vice versa.
Form and construction condition each other reciprocally and form an inseparable unit. Every change in form has immediate consequences for the construction and its weight-bearing behaviour. Every demand related to the weight-bearing capacity and stability has a direct influence on the form.
Every formal or contructional decision implies possibilities of production and assembly.
The determination of the form is an integral process of progressive improvement. The criteria are architectural and static quality of the form and the construction, as well as the function and use of the work and its integration in a built up and natural environment. In each phase of a process of form determination, all the aspects of the construction to be projected must be included with perfect harmony if this possible. This means that in the planning process architects and engineers, experts and builders must co-operate «elbow to elbow» from the very beginning and in all its phases.
3.1. Determination of the form with models
The significance of the model in a process of form determination surpasses in a different way the importance that corresponds to it, as a rule, in a «normal» project process.
In the latter, the model is a complementary medium for the presentation of the architecture: it is a reproduction of the structure, whose form and construction were decided in another way. Here the model is the object of the planning: it is the same work on a lesser scale and therefore necessarily simplified and reduced to its essentials, although retaining all its basic features and properties of form and construction. In the model that determines the form, the state of the planning of a light structure is visible and tangible in each phase and at each moment.
In the process of deciding the form various models of different types and quality are normally necessary. These depend not only on the type of construction chosen, on the size of the structure and the complexity of its form but also on the quantity of information that we wish to transmit and the precision we desire (for example, preliminary model and measurement model) and on the proposed application of the respective model (for example, determination of the geometry, the section, the forces or the deformations). The types of model differ especially in the material and building technique. Moreover, there are substantial differences in the methods of evaluation and measuring.
It is often possible to make a model serve for various demands and purposes, for example, by means of a well-calculated improvement in the form, a variation in the details, the solidification of the surface, the incorporation of measuring instruments or the application of different methods of measurement; and with this model —gradually modified— it is possible to run through various phases of the process of determining the form.
One can differentiate three types of models: premodels, measurement models and special models. The order of succession corresponds, in principle, to the way we proceed in the process of form determination.
The premodels are simple models, almost always small and sometimes still quite generic, with which we can develop and present, relatively quickly and without great expense, the first idea of forms and structures: for example, stretched stocking fabric for tents and rope nets (fig. 40), inflated balloons for pneumatic structures, curved wire netting for mesh coverings (fig. 41), films and soap bubbles for tents and pneumatic structures. These models serve as an approach to a desired form and to its constructional possibilities, and provide a broad initial basis for the selection and later development of the definitive form and structure.
The real models for deciding on the form are the measuring models, since the determination of the form signifies the register and fixing of geometric values and —to the extent that the model is suitable for these— static values. An exact knowledge of the form in lengths, breadths and heights, in coordinates, angles, curvatures and contours, in developments and sections is the basis for all the subsequent project steps until the structure is realized, especially for static calculation and for the measurement of the construction elements. Examples of measuring models are, among others, films of soap and fabrics for tents and rope nets; soap bubbles and rubber film formed of plaster for pneumatic structures, and suspended chain nets for mesh coverings.
Confirming, by means of a model, static values such as loads, pretensing, forces and tensions, deformation and expansion is only possible when it is similar in its geometrical and static-elastic aspects to the planned work (for example, a model of metallic net pretensed for a construction of rope net). With a basis of the laws of the statics of models, these values can be transferred directly from the model to the construction. We thus have at our disposal all the data necessary for the calculation, measurement and realization of a load-bearing structure with a light and extensible surface.
The special models are, for example, section models of certain parts of a form examined in greater detail on a larger scale (high or low points, surface sections, among others); moving models of transformable load-bearing structures in which we can study driving procedures, retraction, folding and the motor mechanism in different stages; demonstration models which serve for presenting special problems: integration in the environment, interaction between internal and external space, the light aspect or the projection of the shadow in different positions of the sun, possibilities of disassembly or future enlargement (fig. 42); aerodynamic tunnel models (fig. 43).
3.2. Films and soap bubbles
Models of films of soap are the fundamental method of determining the form for tents and cable nets. Models of soap bubbles have the same elementary significance for deciding on the form of pneumatic structures.
The form of the film on a liquid, which extends between any two edges which are spatially closed, is a minimum surface. It results from the surface tension of the liquid caused by intermolecular forces and is so extremely thin that any variation in its form through its own weight is imperceptibly small. In order to obtain great surface tension, and with this long static periods and sufficient size, the films are mainly produced by using solutions of soap and detergents.
The minimum surface of a soap film is a self-forming form. A model whose edges consist of fine threads is submerged in the solution. As it is taken our, the soapy film emerges by itself without any outside influence. A soap bubble is also self-forming, dependent only on the pre-established environment and internal pressure. If these experiments are carried out in an air-conditioned chamber free of dust and with a high degree of humity and a low temperature, the models will last for up to an hour and a half. The geometric measurement of the form takes place by means of photographs of the model on a reticulated piece of matt glass (fig. 44).
The minimum surface of a soap film fulfils two conditions. Firstly, the curvatures are equally counterpoised on each point of the surface. Secondly, the surface tension at each point is equal in all directions, and the only tensions that are involved are those of traction.
The second condition is also fulfilled in a soap bubble filled with air, that is, a bubble that has been formed pneumatically and stabilized. In the strictest sense, however, this is not a minimum surface because it presents a curvature in the shape of a dome. Nevertheless, the soap bubble is called a minimum surface because —independently of the magnitude of the internal pressure— it always covers the biggest possible volume on the smallest surface (fig. 45).
The form of the minimum film is the most advantageous form, constructively speaking, for the state of tension of a tent or a net of pretensed rope or for a pneumatic structure under constant internal pressure, and it requires very low costs for materials. This is not necessarily applicable to other cases of loads with external demands, such as the wind or the snow, which are normally unequally spread and appear from various directions and with varying intensity.
The determination of form with a soap film or with a bubble, therefore, can often be only a first step: the minimum surface provides an initial form which must go on developing up to the definitive construction form with other ways of determination of form. This means, specifically, that in many cases it will be necessary, for reasons of load and weight-bearing behaviour, to vary the form of the minimum surface for the actual execution of a construction, for example, by means of well-calculated changes in the surface curvatures, or by incorporating membrane reinforcement and complementary ropes, all of which not only changes the geometry of the form but also conditions the distribution of tensions in the form.
3.3. Fabrics and laminas
Models of fabrics and laminas are the two most important methods of form determination for the working-out and development of form and construction in tents and tope nets, as well as in pneumatic structures.
A fabric must be elastic (equal in the two directions of the mesh, if possible) or permit a sliding of angles between both directions of the threads to make spatial forms possible. Or it must already have an approximate form which is improved in the model. In general, the form of a tent or a rope net determined by a fabric model will always differ, to a greater or lesser extent, from the minimum surface.
Industrially produced light fabrics are used and lattice fabrics of all kinds of wool, silk, polyester, polyamides and others (fig. 46). For rope nets hand-made nets of thread or wire are also used.
A lamina can only be transformed, as a result of its elasticity, into an independent form that is curved and free from creases. When it is formed for a tent or for a rope net by means of external pretensing, it behaves in a similar way to the minimum surface.
These types of models can be used to calculate tensions and forces which act upon structures.
3.4. Suspended nets
These are a basic method for determining the form of mesh coverings, which can be characterized with three key terms: suspended form, inversion and shell form.
The suspended form is a self-forming figure in which only forces of traction intervene. The inversion of this gives the flection-resistant support surface of the mesh shell, in which only forces of pressure intervene, under their own weight, and there is not a single moment of flection.
A suspended form is not a minimum surface. The curvatures are dome-shaped. The forces in each knot of the net are of different dimensions and are not distributed regularly —except in symetrical forms.
The production of a suspended net of chains or hooks and rings is relatively expensive.
A model of suspended net is a measurement model. It provides all the geometric values that can be required about the form of a lattice shell and the shape of the lattice and the edges.
The determination of the form of a suspended net gives as a result the form for the definitive construction, when insignificant geometric differences between the polygonal lines of the net and the curved ribs of the lattice are ignored.
Basically, the method for the determination of the form with suspended nets is suitable for all types of coverings with a closed surface, as well as for ribbed coverings with reticles of modules of four or more sides.
3.5. Threads in water
This method serves to determine the form of supports and branched structures. A model of wool or silk threads of a given length is immersed in water. When the model is taken out of the water, the threads unite with each other because of the surface tension of the water and build tip a branched system (figs. 47 and 48).
Nevertheless, there has certainly been developed special know-how for calculations on models and their transfer to the design by computer, which will allow them to be developed on another more specific occasion.
W. HENNICKE JÜRGEN
Engineer. Professor of Soft Structures at the University of Stuttgart.
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