An attempt to classify horizontal and vertical space development

Introduction

Andrea Deplazes, Christoph Wieser

Fig. 1: Section after Palladio, 1570

Pantheon, Rome (I), 118-128 AD

Fig. 1: Section after Palladio, 1570

Pantheon, Rome (I), 118-128 AD

Fig. 2: Filigree loadbearlng structure based on a modular arrangement and standardised member length

Konrad Wachsmann: model of a three-dimensional (space) frame

The job of the architect is actually to demarcate a piece of infinite space and place it in an enclosure. The most elementary form of such an enclosure, the simple compartment (the nucleus of human shelter), is our starting point for the following deliberations. What principles apply when extending this single room in the horizontal and vertical directions to form complex room conglomerates? In doing so, how do we alter the structure of the resulting buildings?

We shall proceed from the space to the structure (and back again), both in the concrete and the abstract sense. The deliberately simplified hypothetical model we shall be using for this purpose shall serve to establish a provisional classification which will be enriched with practical examples and hence also placed in perspective. This is because the proposed development does not pretend to be universally applicable; more complex sequences and hybrid forms of all kinds can prevail in everyday situations.

Horizontal space development

For the sake of simplicity let us take this ancient compartment, so to speak, to be an abstract, early square hut measuring about four by four metres and with a height of two to three metres. Its effective size is primarily governed by its use and - in contrast to the snail's shell - is not directly derived from the size of the human body, even if this analogy does seem tempting. For there is no direct, ing capacities of the materials are reached, thus forcing a change to the construction system. Although the increase in volume results in the desired enlargement of the interior space (the living space for one family becomes the communal hall for a whole village), there is a conflict of interests from a structural viewpoint. To span large distances we need more material, which leads to an increase in weight and hence to complications in the loadbearing

Fig. 2: Filigree loadbearlng structure based on a modular arrangement and standardised member length

Konrad Wachsmann: model of a three-dimensional (space) frame

"genetic" link between architectural form and the physiology of the human body. However, the form does not "simply appear". Besides materials-related, structural, cultural and social factors, the radius of action of our arms and human strength, for example, are just as important for determining the final size of huts and tents as are the materials employed.

Starting with the model of a one-room house, horizontal space development can take place in two basic ways: a) by increasing the volume, and b) by multiplying the compartments, which are then linked together.

From chamber to hall

The desire to increase the size of the individual compartment has many causes. One of the earliest and most obvious may well be that a group needed to create a suitable place of assembly for festivities and other purposes. If the volume is enlarged, however, the dimensions of the structurally relevant parts also have to increase: the structural depth of the roof and the thickness of the walls. But this is possible only up to a certain degree - until the load-carry system, which in turn has an effect on the maximum span possible.

Depending on their properties, loadbearing structures can be designed with an "active cross-section"" or an "active form". What interests us here though is not an understanding of these different concepts from a structural engineering point of view but rather their function with respect to architectural structures. In constructions with an active cross-section the forces flow within an unspecified cross-section which is "oversized" and hence includes structurally inactive zones, or rather the relevant cross-section becomes the general cross-section. To save weight therefore it is often possible to use a lightweight material. For example, the Pantheon in Rome (118128 AD), whose circular dome consists of ever lighter concrete mixes as it approaches the crown. This is accompanied, however, by a decrease in the thickness of the shell, which makes the dome of the Pantheon a good example of an early, partly optimised loadbearing structure with an active form. For in such structural systems the flow of forces becomes a form-finding parameter and the structure is reduced until only the structurally relevant parts remain. Typical examples of this are frames of all kinds, be they simple trusses for spanning Roman basilicas, or the experiments of Konrad Wachsmann, who by means of an ingenious node design devises ever bolder space frames in steel. In contrast to loadbear-ing structures with an active cross-section, those with an active form demonstrate the "unadulterated" flow of forces. It is no surprise that this latter form was especially cultivated as an "honest" approach to form-finding during the Modern Movement.

As the example of the Pantheon - whose dome diameter of 43.3 metres was not equalled and exceeded until the 20th century - shows, even high-performance loadbearing structures for spanning a space without intervening supports reach the limit of the technical feasibility of their age at some point. And they are often totally

Fig. 3: Cross-section through basilica with double aisles

Earlier building on site of St Peters, Rome (I), 4th century AD

Fig. 4: Plan of small thermae

Hadrian's villa, Tlvoll (I), 118-134 AD

Fig. 3: Cross-section through basilica with double aisles

Earlier building on site of St Peters, Rome (I), 4th century AD

Fig. 4: Plan of small thermae

Hadrian's villa, Tlvoll (I), 118-134 AD

inadvisable for reasons of proportions. Therefore, the basilica was an early form of one-room building whose multi-bay arrangement cleverly distributes the loads: the horizontal component of the thrust which ensues from spanning the nave is resisted by the aisles. This measure produces not only a large, coherent interior space, but the distribution of the loads enables a construction with more slender members - the loadbearing walls were essentially resolved into colonnades, as in Gothic churches. The spectacular interiors flooded with light are paid for with a row of flying buttresses which, placed on the outside, guarantee the necessary equilibrium of forces and return the external form to earthly reality.

From the compartment to the conglomerate

The addition of further compartments produces a conglomerate whose parts can be composed to form a complex whole. Everyday needs trigger this type of horizontal development: the selection of spaces available has to be expanded. At the same time, there is the option of differentiating the individual spaces, e.g. to suit various functions, because the additional compartments need not have the same form nor the same dimensions. It is therefore conceivable that a ring of ancillary spaces could be arranged around one central, main space. If this latter space is open to the sky we create a courtyard house, a type of building design that had already been fully explored

by 2000 BC. Or the individual spaces of a conglomerate can be grouped in a tight sequence of varying proportions, dimensions and types, e.g. Hadrian's villa in Tivoli (118134 AD), where this principle is artistically and enthusiastically celebrated, particularly in the small thermae.

Characteristic of such conglomerates is their tendency to be flexible with regard to further extensions, which Hadrian's villa demonstrates in exemplary fashion. The Roman Emperor Hadrian built a huge country retreat on a raised piece of ground covering about 300 hectares. The villa comprises four complexes with four different axes. As the external form of such a complex built in phases is not determined by restrictive conventions such as symmetry, in principle every new addition can change the configuration of the building completely.

The situation is of course much different in an urban context, where the perimeter practically prescribes, or at least severely influences, the external form. In this case the development will not be additive but rather divisive: starting with our external form the building is divided into individual spaces depending on the respective wishes and utilisation requirements. Incidentally, this method is even found in ancient one-room houses whose volume has been subdivided into separate rooms; sometimes, though, the walls do not extend up to the underside of the roof but instead are merely partitions reaching a certain height. This observation brings to light a structural phenomenon: buildings conceived with a divided interior are frequently built with solid external walls but an internal structure which owes its origins to f iligree construction. This was the case with the castles of the Middle Ages, whose defensive walls were supplemented internally by relatively lightweight timber constructions. These days for

reasons of fire protection party walls still make use of solid construction, while the inner construction is less strictly regulated.

In structural terms the linking of individual compartments is interesting because there is a direct relation-

Fig. 5: Ludwig Mies van der Rohe: brick country house project (1923-24)

Fig. 5: Ludwig Mies van der Rohe: brick country house project (1923-24)

reasons of fire protection party walls still make use of solid construction, while the inner construction is less strictly regulated.

In structural terms the linking of individual compartments is interesting because there is a direct relation-

ship between the openness principle and the construction system. In solid constructions the openness of the rooms with respect to each other, but also to the outside world, is severely restricted, although techniques have been developed here that allow the walls to be reduced to loadbearing columns. The solid walls are the dominating element and openings have to be - figuratively speaking - punched through these subsequently. By contrast, in f iligree construction openings and connections of any size are possible anywhere, provided they do not break the logic of the loadbearing "skeleton". We could say, somewhat exaggeratedly, that in filigree construction the spaces do not need to be connected with each other, but instead individual spaces must first be created by means of separating elements because the structure provides merely a three-dimensional framework.

The example of additive interior space development is based on the assumption that individual compartments, independent in terms of layout and structural factors, are joined to form a conglomerate. However, this results in a doubling of the walls, which in reality does not take place of course because this would represent an uneconomic use of resources. Consequently, the extensions, in structural terms consist "solely" of wall segments of all shapes and sizes. Only in conjunction with the existing space(s) do they produce additional spaces and achieve the equilibrium of forces necessary for load-carrying purposes.

In principle, the flowing spatial concepts of De Stijl or Mies van der Rohe's design for a brick country house (1923-24) could be interpreted as a radical further development of this method. The self-contained structure of the intersecting wall segments has been resolved and walls not required for loadbearing purposes have been omit-

though in traditional building every compartment is often spanned individually for practical and economic reasons, the Modern Movement roof acts as a coherent l oadbear-ing structure which permits cantilevers to a certain extent (e.g. platforms of steel sections or flat reinforced concrete slabs).

Fundamental types of simple coverings over spaces

Back to the simple compartment. Its structural arrangement will now be investigated in somewhat more detail in relation to the system chosen for covering the space, and by means of a) vaulting, b) domes, and c) plane systems.

The choice of one or other type of roof over a hut in early times was governed by the materials available, and even to this day the material properties determine the

maximum span possible. The material also prescribes the constructional and the stylistic arrangement of the covering: heavyweight domes exhibit other properties to those of stressed skin structures or floors in timber and later in steel; yet further options became available in the 20th

ted; the plane, L-shaped and circular segments are freestanding and define the spaces in between only loosely. But the covering over the spaces is realised differently. Al-

century in the form of reinforced concrete slabs. Vaults and domes are usually associated with a solid form of construction. As ancient examples illustrate, these forms of loadbearing construction are also feasible in f iligree construction in terms of style (however, not in terms of their structural action).

a) Roofing over a compartment with vaulting results in a directional construction because the load of the vault is transferred to two of the four enclosing walls. Consequently, the structurally irrelevant end walls can be provided with large openings or even omitted completely, provided the transverse stability can be guaranteed in some other way. This simple shear wall principle can be further resolved by reducing the walls themselves to arches, then to columns.

b) A square single space with a dome as the r oof is often described as a "non-directional" construction, which, however, describes the actual situation rather imprecisely. It would be more correct to say "bi-directional" because the thrust from the dome is transferred equally

Fig. 6: View of the large hall transverse to the severely resolved wall structure consisting of columns and arches

Great Mosque, Cordoba (E), 785-961 AD

to all four walls. Providing a tension ring at the base of the dome enables the thrust to be neutralised, and hence the walls to be resolved as far as the load-carrying capacity of the arches and columns permit. Of course, a circular building following the same principles is also conceivable. Examples are provided by Greek and Roman temples in which the walls have been replaced by a ring of columns.

c) The third option for roofing over a compartment is the plane variety, using joists of timber or beams of steel which, in contrast to vaulting and domes, are subject to bending moments and not axial thrust. The enclosure of the space below can be in the form of solid construction - with walls - but also filigree construction - as a frame. In structural terms this version is related to the first one because the rooms are directional; the load-carrying roof members are supported on two of the four sides, on the walls or the frame. However, the reinforced concrete floor slabs so popular today exhibit a different behaviour; depending on how the reinforcement has been integrated, the direction of span can be chosen and manipulated. Thanks to the introduction of downstand beams this third variation enables the loadbearing walls or frames to be replaced by slender columns. However, once again it should not be forgotten that as the degree of resolution advances, so the stability in the longitudinal and transverse directions becomes ever more critical.

Fig. 6: View of the large hall transverse to the severely resolved wall structure consisting of columns and arches

Great Mosque, Cordoba (E), 785-961 AD

Fig. 7: Aerial view

Qarawiyin Mosque, Fez (Morocco), 857-1613

Fig. 7: Aerial view

Qarawiyin Mosque, Fez (Morocco), 857-1613

Qarawiyin Mosque, Fez (Morocco), 857-1613

Qarawiyin Mosque, Fez (Morocco), 857-1613

Roofing over complex layouts

We shall now transfer these three fundamental principles to geometrically "adjusted" conglomerates, i.e. more or less regular arrangements of interior spaces, to check the structural effects of the various roofing options.

a) A succession of spaces between loadbearing walls initially roofed over with vaults multiplies the effect of the already strongly directional structure exponentially. The orientation of the interior spaces runs parallel with the walls. And in this direction the individual spaces may also be extended ad infinitum, while in the transverse direction a complete, new "vaulted unit" must be added every time. Of course, the distances between individual walls could vary, but this would not change the primary direction of the plan layout. In architectural, but also in structural

terms, the connections between these elongated chambers perpendicular to the walls are interesting. For here we can offer the most diverse interpretations, stretching from minimal openings right up to resolution of the wall structure into minimal members.

Fascinating here are the prayer halls of colonnade mosques, as in the Great Mosque in Cordoba (785-961), which was extended in various stages to create an overwhelming interior space with 600 columns. Or the prayer hall of the Qarawiyin Mosque in Fez (857-1613). Like the majority of colonnade mosques, these two examples also include flat timber ceilings between the walls. The roof construction consists of timber trusses and the pitched roofs emulate the wall structure below.

An early example of a barrel-vaulted building is the bathing house of the palace of Qusayr Amra (711 AD), which today stands in the middle of the Jordanian desert. The entrance hall is roofed over by three parallel barrel vaults supported on walls resolved almost completely into arches, creating a large, transverse room. Nevertheless, the longitudinal orientation of the barrel vaults determines the layout.

A modern variation of an extremely resolved wall structure was built by Louis I. Kahn at Fort Worth in Texas (1972). Here at the Kimbell Art Museum Kahn plays consciously with the dominance of the longitudinal vault form by placing the main direction of movement of visitors at 90 degrees to this. Arriving at the main entrance in the centre of the longitudinal racade, visitors are first channelled transverse to the structure and only then in the longitudinal direction of the exhibition areas. These latter are arranged with their principal dimensions transverse to the walls so that, once again, visitors have to move mainly across the structure.

b) Spaces beneath domes can also be assembled in modular form to produce complex internal layouts. If the intervening walls are resolved into columns, we achieve one or more large interior spaces. One characteristic feature of such interior spaces is the fact that the importance of the individual compartment is still apparent, or at least implied, because the dome has a strong centralising effect. Aldo von Eyck used this property in an ingenious way in his children's home in Amsterdam (1955-60). Taking as his model an African souk (bazaar), he designed a honeycomb-like configuration whose compartments are

Fig. 11: Barrel-vaulted wall structure

Louis I. Kahn, Kimbell Art Museum, Fort Worth (Texas, USA), 1972

Fig. 11: Barrel-vaulted wall structure

Louis I. Kahn, Kimbell Art Museum, Fort Worth (Texas, USA), 1972

Louis I. Kahn, Klmbell Art Museum Fort Worth (Texas, USA), 1972

Louis I. Kahn, Klmbell Art Museum Fort Worth (Texas, USA), 1972

Fig. 13: Honeycomb-like, dome-vaulted structure

Aldo von Eyck: children's home, Amsterdam (NL) 1960

Fig. 13: Honeycomb-like, dome-vaulted structure

Aldo von Eyck: children's home, Amsterdam (NL) 1960

spanned by domes. To distinguish special spaces he used larger dimensions, but also individual or ring-shaped roof-lights. In addition, he exploited the flexibility of the additive method to expand the plan layout to meet the respective requirements exactly.

Henri Labrouste employed the same vaulting method for his reading room at the Bibliothèque Nationale in Paris (1854-75), but in this case to create a quasi-ideal, geometrically "neutral" place of contemplation. The nine domes forming the roof over this square room are supported on 16 cast iron columns which themselves tend to divide the floor area into nine squares. Each of the nine domes has a glazed crown to ensure even illumination of the reading room below.

c) Different configurations are possible with a flat roof of timber, steel or reinforced concrete over a multi-compartment, enclosed building, especially in terms of the resolution of the compartments into larger units. Owing to their relatively limited span, conventional timber j oist floors without glued laminated timber beams are suitable for room conglomerates with essentially enclosed compartments, but immediately restrict the extent of the plan dimensions. To improve the transverse stiffness, it is advisable to turn the joists through 90 degrees from room to room. On the other hand, plane constructions of steel enable extensive resolution of the structure because these can be designed to span over more than one compartment. And finally, the invention of the structure with flared column heads by Robert Maillart - which led to the r einforced concrete flat slab - enables the loadbearing elements to be reduced from walls and beams to a grid of columns.

Timber Steel Reinforced concrete

Timber Steel Reinforced concrete

The different structural and material-related "degrees of perforation" of such room conglomerates suggest different applications. For example, many plan layouts with several essentially enclosed spaces in succession are ideal for museums because in this way many wall developments are created which can then be used for displays. The illumination of these individual chambers is commonly by way of rooflights. And rooflights also guarantee even illumination in large interior areas created by resolving the walls into columns. Production buildings and exhibition halls are examples of this.

Fig. 14: Drawing of reading room (right)

Plan, section and details (above)

Henri Labrouste, reading room of Bibliothèque

Nationale, Paris (F), 1854-75

Fig. 14: Drawing of reading room (right)

Plan, section and details (above)

Henri Labrouste, reading room of Bibliothèque

Nationale, Paris (F), 1854-75

Entrance

Fig. 15: The pockets for the ends of the scaffold beams are readily visible on the rear of the building.

Town Hall, Siena (I), 1288-1309, with the Torre della Mangia, 1338-48

Fig. 15: The pockets for the ends of the scaffold beams are readily visible on the rear of the building.

Town Hall, Siena (I), 1288-1309, with the Torre della Mangia, 1338-48

Fig. 16: External view of two-storey ghorfas

Ksar Ferich, fortified storehouse (Tunisia)

Fig. 16: External view of two-storey ghorfas

Ksar Ferich, fortified storehouse (Tunisia)

Fig. 17: Cross-section

Ksar Ferich, fortified storehouse (Tunisia)

Fig. 17: Cross-section

Ksar Ferich, fortified storehouse (Tunisia)

Vertical space development

Our starting point for presenting the development of vertical space is again our imaginary ancient compartment. If it is to be increased in height, the walls are simply raised. Mind you, this is easier said than done, for as we know such a measure leads - sooner or later - to constructional problems - strength, stability, material load-carrying capacities. In short, gravity makes its presence felt more and more the higher we build, and our efforts to overcome this determine our method of building. These conditions can be seen in simple buildings where the walls become thicker as they approach the base. Furthermore, above a certain height we shall require a scaffold. This could be called an independent, ephemeral structure because it is usually removed once the building is completed. However, a scaffold can leave behind tell-tale marks, as on the town hall in Siena (1288-1309), where on the rear of the building and on the tower (1338-48) the pockets for the ends of the scaffold members are still visible as an irregular pattern of holes in the surface of the brick walls.

Beyond a certain dimension increasing the height of the simple compartment opens up the option of adding a second floor. A multiple of our original height assumption of two to three metres is the module we shall use to divide the vertical space into horizontal units. In comparison to horizontal space development it would seem that the basic options in the vertical direction are more limited. It's all about stacking spaces, but in different ways: additive or divisive, exploiting the terrain or free-standing, as a repetitive layering or complex interlacing of the spaces.

The plan form as a projection of the storeys above

The simplest option for stacking spaces has proved to be the vertical layering of spaces with the same plan area. Expressed simply, in this method the plan shape of the ground floor is multiplied, with the loadbearing walls or columns continuing through all storeys. So in both the compartmentation principle and when using walls or columns the upper storeys are mapped on the ground floor. Whether the individual storeys are spanned by vaulting or plane elements is irrelevant for the stacking - the principle remains the same.

One example of a two-storey form of construction with vaulting is the Ksar Ferich fortified storehouse and

"additive" "divisive1

market in Tunisia, which consists of a succession of barrel-vaulted ghorfas (Arabic: space), each of which belongs to one family. The floors to the upper storey are not flat because the rounding of the underlying vaulting is not fully compensated for. A cross-section reveals the - from a modern viewpoint - elaborate form of construction. It is therefore not surprising that, when the situation and resources allow, flat floors are preferred, and are inserted between the loadbearing walls. In contrast to additive stacking this method could be described as divisive, with the joist floors providing stability as the walls are built. For starting from a certain height of wall the individual storeys, depending on utilisation requirements, are placed in the I oadbearing structure. Continuous loadbearing walls over the full height of the building enable the interior spaces, even within a storey, to be arranged with different heights. In other words: in a vertical building with walls, the walls are the primary element and the floors the secondary element.

Le plan libre

The reverse is true with the "column-and-slab system", our second option for stacking several storeys, and the one which has been the most frequently used since the appearance of reinforced concrete floor slabs at the beginning of the 20th century. Dominant here are the horizontal floor slabs, while the spaces between the loadbearing columns can be arranged in practically any form. In conventional applications the regular column grid continues through the entire building and, together with a stiffening core or suitably positioned shear walls, ensures sufficient stability. As the number of storeys increases, so the loadbearing columns become more massive towards the base, something which is particularly noticeable in a high-rise building.

Le Corbusier's "Dom-Ino" system (1914) is based on a combination of columns and slabs and was elaborated in his famous book Five Points of Architecture (1927); he developed this into a comprehensive programme for characterising his opinion of modern architecture. He was especially interested in the architectural freedom that this revolutionary "engineered" form of construction opened up: the "plan libre" and the "façade libre".

In the late 1980s Rem Koolhaas developed an updated variation of a spatially complex, layered building based on

Fig. 18: Sketch of principle of column-and-slab system

Le Corbusier: "Dom-Ino" construction system, 1914

Fig. 18: Sketch of principle of column-and-slab system

Le Corbusier: "Dom-Ino" construction system, 1914

Fig. 19: Cross-section through competition project

OMA, Rem Kolhaas: ferry terminal, Zeebrugge (B), 1989

Fig. 19: Cross-section through competition project

OMA, Rem Kolhaas: ferry terminal, Zeebrugge (B), 1989

the principle of separating structure (tectonics) and the formation of space, e.g. his competition designs for the Centre for Art and Media Technology in Karlsruhe (1989) and the ferry terminal at Zeebrugge (1989).

The spatial plan

The third variation for vertical space development is also the most complex because in this case the spaces and storeys are no longer simply stacked one upon the other, but are interlaced vertically and horizontally. Adolf Loos is well-known for favouring the spatial plan. In contrast to the "Five Points" of Le Corbusier, however, the spatial plan is not a set of instructions which can be carried out and ticked off one by one, but instead the realisation of a space-oriented, complex design conception which must be re-appraised from project to project.

The aim of the spatial plan is to organise spaces with different plan sizes and different heights (split levels) - which can be treated as individual volumes - in such a way that they form a dense configuration of spaces. In the sense of a three-dimensional undertaking, the spatial plan is therefore certainly an economic approach, but in contrast to the idea of a "home for a minimal existence" it strives to achieve not the minimum necessary but rather the maximum possible in that the luxury of taller living spaces is balanced by lower ancillary spaces. This is also possible with multistorey walled structures. However, taken to the extreme the spatial plan has no loadbearing walls or columns that pass through all storeys. A continuous access core, which in all other variations provides a sort of "automatic" zoning, is also lacking here. In structural terms every compartment is an autonomous link within a complex chain which creates plenty of freedom but many more mutual dependencies. Consequently, the formation of structure and space is (apparently) artificial. To optimise the fabric, the I oadbearing structure can be simplified by designing some parts as non-loadbearing.

Müller House in (1930) by Adolf Loos is, in spatial terms, the most versatile implementation of his notion of the spatial plan. Despite its spatial complexity, the construction system is nevertheless astoundingly simple: the external brick walls are loadbearing; internally, there are no loadbearing walls, merely four reinforced concrete columns and downstand beams on which the j oist floors are supported. In this way the columns subdivide the plan shape of the building into several rectangular zones. Therefore, the floors and roofs can be arranged at the necessary levels, corresponding to the requirements of the interior. These spaces, treated as autonomous volumes, are formed by cladding the framework - like infill panels - and are interconnected via precisely located openings. Thus Loos established an extremely flexible but also inexpensive construction system with which he could realise his idea of the spatial plan in an optimum and surprisingly complex fashion.

Loos worked with a pragmatic hybrid construction in which the structure- and space-forming part are separated from each other - just like with the column-and-slab system. If the walls and slabs, however, are used systematically as coherent, loadbearing elements, which is now possible thanks to slab and plate designs in r einforced concrete (e.g. by Jurg Conzett), this leads to a merging of the two systems - and a return to the principle of solid construction.

Concepts

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