The text presented here is not precisely as published by OUP, but modifications are minor. Illustrations are another matter. Where images used in the original book were not my copyright, I have in most cases been able to substitute links to coloured images on the web. The sources are listed under Image Acknowledgements.

When this text was submitted as part of a PhD thesis in 1996, the Notes were greatly extended. Most readers may prefer to ignore them. They have been collected at the end of each chapter, with internal links leading to them and back to the text. They are a mixture of: simple page references; additional examples or quotations to justify generalisations; and some afterthoughts.

Introduction.

As we saw in the previous Chapter, it is a very common theme in the philosophy of structures that the imposed or internal forces should be transmitted 'directly', 'efficiently' or 'logically'. In this Chapter we shall discuss briefly the implications and difficulties inherent in this concept.

A major aim of this book has been to show that such prescriptions, if taken at face value, represent a great over-simplification of the problem. The word 'possible' does allow for the fact that functional necessities regarding free space may require that the forces take a circuitous path. However, even in the case of purely load-bearing structures, such as transmission line towers, the pressure of economic necessity, particularly with regard to fabrication, transport and erection, influence the form of the structure and hence the manner in which load is transmitted.

Nevertheless, such abstract principles are of some value in helping us to take our bearings when confronted by a problem and give us an idea of the localized influence of certain parameters, as long as we do not forget their inherent limitations.

Abstract principles of structural efficiency.

A common prescription, advanced most often by non-engineers, is that structural forms should be similar to those found in nature. The assumption here is that evolution has developed forms which must be highly efficient in order to survive, and therefore by copying these forms we shall achieve a similar degree of efficiency.

In its most simplified form this principle has been illustrated by comparing the structure of Nervi's Palace of Labour at Turin (Fig. 19.1) to that of a tree and commending the 'natural' way in which the radiating arms are used to gather the load in towards the columns which then, like the trunk of a tree, carry it down to the foundation.

Fig. 19.1. The cantilever columns and radial roof beams of Nervi's Palace of Labour at Turin (1961) are erroneously likened to trees. [Photo: Aloss. (See thumbnail 'Palazzo del Lavoro'.)]

Of course, this type of comparison completely ignores the fact that the immediate function of the structure of a tree is to support the leaves in such a way as to collect a maximum of sunlight while resisting wind forces. Rigidity is not a criterion nor is the nature of the internal space. In contrast the structure of the Palace of Labour must rigidly support a brittle envelope which will protect its occupants from the elements. The comparison also ignores the fact that trees construct themselves without the use of formwork or cranes; that their branches are not prefabricated; that the loads imposed on them are different; that the branches of adjacent trees are not connected together at their tops for mutual support; and that trees do not have to meet a strict construction schedule.

In its more intelligent form, the nature analogy simply proposes natural forms as a source of inspiration for the structural designer when he can recognize some correspondence between the purposes of a biological structure and his own aims in a particular project.

Another simple principle is that there is an hierarchy of efficiency of structural action with tension as the most efficient means of carrying load, compression as the next and bending as a poor last. At first sight the argument appears quite plausible. In bending the material near the neutral axis is understressed; in fact it is only the material at the extreme top and bottom of a beam that is being fully utilized. In simple compression or tension, all the material in the cross-section should operate at its full capacity. However, compression members are liable to buckle and this limits the extent to which the material can be so utilized. Therefore tension is the simplest and most efficient means of transmitting load, compression comes second, and bending last.

If one looks at actual usage however, the occurrence of these structural actions is in inverse ratio to their alleged attractiveness: bending is most common, followed by compression and a long way behind, tension. The reasons lie, of course, in the factors discussed in the previous chapters. From a functional point of view, people prefer to walk on flat floors rather than dished or domed ones. Less obviously, most people prefer vertical walls and rectangular rooms, thus limiting the appeal to the occupant of such structurally efficient forms as concrete or geodesic domes.

Also, to support a load over a gap by axial force generally requires a greater depth of construction than by bending action. This is often inconvenient for functional reasons and in multi-storey buildings it is axiomatic that floors should be as thin as possible consistent with the services layout, because any increase in the height of a building adds to the area of expensive external cladding, and the overturning effect of wind action.

While roofs and the floors of tanks and silos need not be flat, problems arise with the more complex structures because deflection due to load or thermal effects may give rise to difficulties with waterproofing, particularly where glass walls fit underneath domes.

Questions of fabrication and erection are also relevant. Concrete domes, for example, must normally be supported over their entire area by falsework or inflated membranes until they reach sufficient strength to support their own weight whereas column-and-beam structures can be erected piecemeal.

Considering the mechanics of the problem, few structures can consist purely of tension members unless they are strung from surrounding hill-tops or sunk into the ground. Generally, like suspension bridges, they require massive supporting columns. Furthermore, the inclined reactions developed by domes and cables must be resisted by compression or tension rings, ties or heavy foundations. In contrast it is easy to ensure that the reactions from a beam are purely vertical, and these are more easily resisted at foundation level.

Fig. 19.2. Although tension is a highly efficient means of resisting load, nearly all 'tension' structures depend on heavy compression members. Paper mill for SocietÀ Burgo, Mantua. (Engrs: P. L. Nervi, G. Covre.) [Photo: Aloss. (Thumbnail 'Cartiere Burgo'.)]

Thus, while the tension-compression-bending rule has its own logic and is worth keeping in mind it is by no means of general applicability.

Another common axiom is that the shape of a component or structure should reflect the 'natural' flow of forces. Examples given include the variation in cross-section of beams in accordance with the bending moment diagram, the thickening of columns at mid-height to increase their resistance to buckling, the flow of forces down Nervi's rafters and columns in the Palace of Labour and the ribbing of his floor slabs both there (Fig. 19.3) and in the Gatti Wool Factory.

Fig. 19.3. The ribs of the mezzanine floor slab at the Palace of Labour follow the trajectories of principal bending moments in a plane slab. Is this 'natural'?

The problem here is that forces do not flow, either 'naturally' or otherwise, until a solid object is interposed between the force and the foundation. When it is, the forces will certainly distribute themselves within it according to the law of minimum potential energy, but this distribution will be entirely dependent on the initial form chosen for the member. Thus the ribs of Nervi's floor slabs follow the 'isostatic lines' or directions of principal moments in a flat slab. As soon as the form of the floor is altered by insertion of the ribs, the distribution of forces is altered too.

It is not sufficient therefore to say that the forces should 'flow naturally'. Another criterion must be introduced. Common formulations are: that all material should be utilized close to its capacity; that minimum weight should be achieved; or that the structural action should be evident to the layman.

Hence while the isostatic lines relevant to an arbitrary body provide inspiration for attractive forms and possibly point the way to a more efficient arrangement of material, there is nothing inherently 'natural' about them.

Now let us consider the idea that the forces should be conducted to the ground by the most direct route possible. The weakness of this principle can be demonstrated by applying it to the design of a 'structure' required, say, to support a roadway across a valley. The most direct route for the forces would be directly downwards. Consequently the 'logical' solution would be to fill the valley beneath the road surface with a material of low cost and low strength leaving a suitable opening for the river (Fig. 19.4). Something stiffer than polystyrene foam would do: perhaps soil!

Fig. 19.4. (a) To carry load from a roadway to a valley floor by the 'most direct route' implies a continuous low-strength medium filling the gap. (b) In contrast the most economical solution is often to gather the forces into discrete elements of high-strength material.

The fact that in so many cases this solution is not adopted indicates that even where it is not necessary to envelop space as in habitable buildings, there are other factors at work besides a desire for the most direct transmission of forces. It is usually more economical to 'gather the forces together' and conduct them along discrete members of high strength and stiffness.

The 'direct flow' principle may also be criticized on purely mechanical grounds in that as normally expounded it focuses on transmission of forces axially and ignores the possible use of bending action and counter-weight as a means of responding to spatial constraints.

Another common theme is that 'materials should be used in accordance with their natural properties'. In its more extreme version the idea is that correct form is the inevitable outcome of the properties of the material when it is so used.

This is only true if the term 'properties' is assumed to include the cost, appearance, thermal and acoustic properties and workability of the material and if one assumes that aesthetics is an outcome of perfection of function. Many proponents of this theory do advance the latter view, but they tend to concentrate on the mechanical properties of the material in explaining traditional forms.

The most obvious and often-quoted example of this is masonry. The fact that masonry is weak in tension but strong in compression does explain a great deal about the form of churches and bridges built in this material, but it explains nothing about the great contrast between Gothic ecclesiastical and civil architecture (Fig. 19.5), the continued use of brickwork for cladding and partitions in modern multi-storey buildings, and its persistence in single storey houses where its strength is hardly utilized at all.

Another drawback is that the rule about using materials in accordance with their 'fundamental' nature could be interpreted in such a way as to inhibit new developments such as in this case, reinforced masonry by substituting 'traditional' for 'fundamental'. Nervi himself wrote that his development of 'ferrocement' and precasting techniques was inspired by the desire to "free reinforced concrete" from "the economic slavery of wooden forms".

These problems disappear only if terms such as 'properties' and 'essential nature' are given their widest and most truly fundamental meanings.

Proponents of this principle are much less specific about the 'fundamental' properties of steel and concrete apart from pointing out that, unlike masonry, they are capable of resisting pure tension and bending moment. The 'mouldability' of concrete and its suitability for surface structures such as floors and silos are usually mentioned and steel is described as a basically skeletal material.

However the cost of forming concrete with anything other than flat planes, and the fact that in box girder bridges it is economic to employ steel plates, proves that the final arbiter in all these matters is not the mechanical properties or even the fabrication characteristics, but the relative cost of employing each material in a given problem situation (tempered of course by considerations of aesthetics, durability and so on).

It must also be remembered that in buildings the cost of the structure may represent only 25% of the total cost and hence structural efficiency may need to be 'traded off' against advantages relating to HVAC, etc.

Therefore one cannot really separate out 'efficient force transmission' from all the other relevant factors even when no space-enclosing functions are involved.

Fig. 19.5. The great difference between Gothic civil and religious architecture proves that the form of church structure was not determined solely by technical imperatives; c.f. Fig. 10.4. (Drawing: Viollet-le-Duc.)

Image Acknowledgements. Linked images, Chapter 19.

Grateful thanks to the following for making it possible to provide links to full colour photographs and descriptions of buildings for this chapter.
Yoshito Isono, Dept of Architecture and Civil Engineering, Fukui University. Link.

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