Structures- Or Why Things Don't Fall Down
Page 17
Plate 9
Chapter 9
Skeletons of (a) gibbon and (b) gorilla (to scale). The ‘square-cube’ law applies more to beams than to columns. Thus as animals get larger, their ribs and limb bones tend to become thicker in proportion to their vertebrae.
Plate 10
Chapter 10
Brunei’s Maidenhead bridge (1837) has the longest and flattest brick arches in the world. Many people predicted that the arches would not stand, but they are still there today carrying trains ten times heavier than Brunei’s.
Plate 11
Chapter 10
Telford’s Menai suspension bridge (1819). The span of 550 feet (166 metres) is approaching the limit for wrought-iron suspension chains.
Plate 12
Chapter 10
The Severn suspension bridge. High tensile steel cables with. ten times tne tensile strength of wrought iron enable bridges nearly ten times as long as Telford’s Menai bridge to be constructed.
Plate 13
Chapter 11
Where there are no side aisles, as in King’s College Chapel, Cambridge, the buttresses can be carried straight up without further complication.
Plate 14
Chapter 11
H.M.S. Victory. Her masts form a superb example of a trussed cantilever structure of very large dimensions.
Plate 15
Chapter 11
The American railways could be built quickly and cheaply because wooden trestle bridges were used very extensively to save the cost of earthworks (c. 1875).
Plate 16
Chapters 11 and 13
Stephenson’s Britannia railway bridge (1850) used wrought-iron box beams. The trains ran inside the beams. Much trouble was experienced in preventing the thin iron plating from buckling. In front of the bridge are grouped a number of contemporary engineers; Robert Stephenson is seated in the left centre and I. K. Brunei is seated on the extreme right.
Plate 17
Chapter 12
The bias cut, invented by Mile Vionnet, exploits the low shear modulus and high Poisson’s ratio of certain square-weave fabrics in the 45° direction. This is one of the earliest Vionnet bias-cut dresses (a.d. 1926).
Plate 18
Chapter 12
Contemporary square-cut dress (also Vionnet). Note low Poisson’s ratio and lack of clinging effect. The vertical creases are caused by the existence of a Wagner tension field.
Plate 19
Chapter 12
Wagner tension field in the fuselage skin of a Fairey Rotadyne.
Plate 20
Chapter 15
The Tacoma Narrows bridge is a classic example of a suspension bridge built with inadequate torsional stiffness. Known as ‘Galloping Gertie’ it displayed serious oscillation when exposed to quite moderate winds, and very soon wriggled and buckled itself into failure in a wind of only 42m.p.h.
Plate 21
Chapter 16
The first real mass-production machinery to come into use was the block-making equipment at Portsmouth Dockyard. Both the machinery and the blocks themselves may be regarded as handsome, perhaps as beautiful.
Plate 22
Chapter 16
The classical form of steam yacht developed by George Lennox Watson is one of the most beautiful of all ship conventions. But it is largely non-functional. The ends and especially the bowsprit represent sailing-ship practice. That is to say they are “skiamorphs.” (S.Y. Nahlin. )
Plate 23
Chapters 9 and 16
No single photograph can do justice to the Parthenon, but this picture of part of the south-west corner may give some slight impression. (Note that the left-hand lintel is cracked; for this reason the architraves are in triplicate. Note also numerous skiamorphs or vestiges of wooden construction, e.g., triglyphs, mutuies, etc.)
Plate 24
Chapter 16
Unlike the classical Greeks one thousand years later, the Mycenaean Greeks (c. 1,500 B.C.) designed their buildings to take account of the low tensile strength of stone. The lintel of the Lion Gate at Mycenae is provided with a triangular block of stone to relieve the tensile loads. The architrave is a single block and carries very little stress. The distance between the centres of the chariot ruts corresponds accurately to the “standard” gauge of modern railways.
Looking at the problem philosophically, the stability of a building is not different from the stability of a balance or a weighing machine such as a steelyard (Figure 17). The upsetting moments on both sides will be as the fourth power of the dimensions; if we scale up, everything remains in balance. Thus, if a small building stands, a scaled-up version of it can also be relied upon to do so, and the ‘mystery’ of the medieval builders consisted in reducing this experience to a series of rules and proportions. However, that they also used models – sometimes 60 feet (18 metres) long – made from masonry or plaster is well established. This mode of procedure generally worked even for structures of incredible complexity, such as Rheims Cathedral (Figure 18).
Figure 17. The stability of a building is like that of a balance; it is not affected by scaling up.
The Greeks of the classical period abandoned the arch for most of their serious architecture, preferring to use stone beams or lintels. In such beams the tensile stresses were relatively high and often too near the limit for safety. A considerable number of these architraves were cracked, even in ancient times. This is why iron reinforcement was used in the marble beams of the Propylaea, for instance. What saved the Doric temple from structural collapse was that the stone beams were short and deep and, as they cracked, they turned themselves into arches (Figure 19, Plates 8 and 23).
Figure 18. Rheims Cathedral: flying buttresses (after Viollet-le-Duc).
Greek trabeate* architecture required very large blocks of stone. When civilization decayed, the transportation of large masses became increasingly difficult, and this may have been one, strictly practical, reason why the medieval builders favoured Gothic arches and vaults, which can be made from quite small stones.
Figure 19. If a short stone lintel or architrave cracks on the tension face, it may turn itself into a three-hinge arch and continue to support the load.
As Sir John Soane pointed out nearly 200 years ago in his lectures on architecture, in spite of the limitations of stone beams, the size of ancient buildings was often greater than that of corresponding modern ones. The Parthenon, for instance, is considerably bigger than St Martin-in-the-Fields. Nevertheless, the Parthenon – about 230 by 100 feet (69 by 30 metres) – is small compared with Hadrian’s temple of the Olympian Zeus close by, which measures 359 by 173 feet (108 by 52 metres) and would fill most of Trafalgar Square (Plate 8). Yet Hadrian’s temple, in its turn, is dwarfed by the walls of the Acropolis, which tower high above it. Again, for sheer size, many of the Roman bridges and aqueducts are impressive by any standards.
These ancient constructions have more often been destroyed by men than by Nature and some of them are still in good condition today. However, in all these works the ancients were more or less following familiar examples; when they were unable to do so they were apt to come badly unstuck. Not only are ancient ships and vehicles almost pathetically small and fragile to our modern eyes, but new and unconventional buildings such as the Roman Insulae – which were tall blocks of flats – fell down with such depressing frequency that the Emperor Augustus was compelled to pass laws restricting their height to 60 feet (18 metres).
On backbones and skeletons
The backbones of people and animals consist of a series of short, drum-like vertebrae, made from hard bone. They are separated from each other by the ‘intervertebral discs’, which are made from comparatively soft material and thus allow a limited amount of movement between the vertebrae. As a rule, the spine is subject to an overall compression arising both from the weights it has to carry and also from the pull of the various muscles and tendons.
In young people the material of the discs is flexible and to
ugh, and it can withstand considerable tensile stresses if it has to. So much so that, if the spine is damaged by tensile forces, fracture is likely to occur in the bone rather than in the discs. After the age of about twenty, however, the disc material gets progressively less flexible and also considerably weaker in tension. As we get more venerable, therefore, we approach a situation in which our backbone is getting rather like a column in a church or a temple. The vertebrae represent the stone drums and the discs the weak mortar. Although the discs can still, at a pinch, take a certain amount of tension, this is, on the whole, a situation to be avoided.
Therefore, for middle-aged people, it is wise to keep the thrust line as near the middle of the backbone as possible. This is why there is a right and a wrong way of lifting a heavy weight. If we lift the weight in the wrong way, excessive tensile forces are set up in the joints and one of these may break. The result is likely to be a ‘slipped disc’ or one of the other manifold and rather mysterious back troubles which we include under the name of ‘lumbago’ – which is apt to be surprisingly painful.
In so far as a backbone behaves like a wall or a masonry column and departure from the ‘middle third rule’ represents some sort of limiting condition, then the same kind of rules apply to scaling up an animal as we have seen apply to scaling up a building. Thus if we start with a small animal and progressively increase its size, the necessary thickness of the vertebrae will remain in due proportion. Most of the other bones, however, such as the ribs and the bones of the limbs, are subjected chiefly to bending – rather like the lintels of a temple – and the loads upon them are likely to be proportionate to the mass of the animal. It follows, therefore, that such bones have to be made disproportionately thicker.
If we look in a museum at the skeletons of a series of similar animals of increasing size, such as monkeys, it does appear that, whereas the dimensions of the vertebrae of little monkeys and middle-sized monkeys and gorillas and men are roughly in proportion to the height of the animal, the.limb bones and, especially, the ribs become very much thicker and heavier, for the size of the animal, as the scale increases (Plate 9).
In this respect Nature seems to be cleverer than the Roman architects, who, as they increased the size of their temples, abandoned the rather stocky Doric proportions and built, as a rule, in the florid Imperial Corinthian style, with slender architraves which frequently broke.
* * *
* Note that Genesis 11 specifically says *let us make bricks and bake them hard*. There was no question of using cheap mud bricks as the Egyptians did. This seems to be an early example of the Concorde syndrome.
* Of the abbey church of Saint Denis, in France, during the twelfth century, we read ‘. .. such a force of contrary gales hurled itself against the aforesaid arches, not supported by scaffolding nor resting on any props, that they threatened baneful ruin at any moment, miserably trembling and, as it were, swaying hither and thither.’ (I am indebted to Prof. Hey man for this reference.)
* Davy remained at the Royal Institution and prospered. He became Sir Humphry and President of the Royal Society. He is said to have been offered a bishopric if he would take Holy Orders. As a great man who had risen from humble beginnings he behaved rather badly to a coalminer called George Stephenson but rather well to a blacksmith’s son called Michael Faraday.
* That this is so can be checked by applying the parallelogram of forces (whose acquaintance can be renewed in the pages of elementary text-books on mechanics) at each level in the wall. The parallelogram of forces is supposed to have been invented by Simon Stevin in 1586. The absence of the concept of the resolution of forces is one reason why it is impossible that either ancient or medieval architects could have designed their buildings in the modern way.
* There are really several thrust lines, and all of them need to be kept inside the surface of the wall.
The passive thrust line. This is the thrust line which results from the weight of the wall itself and of all the things which are permanently attached to it, such as floors and roofs.
The active thrust lines. These are the thrust lines which result, not only from the permanent parts of the building, but also from all the transient loads which might be applied to it by wind pressure or the weight of things like water, coal, snow, machinery, vehicles, people and so on. The shapes of the various active thrust lines define the ways in which a masonry structure can safely be loaded.
† This is one of the reasons for the modern fashion of not plastering the insides of buildings.
* The true arch seems to be an old-world development. The indigenous civilizations of Mexico and Peru built their large buildings using only the corbelled arch.
* This is the rationale of mining or sapping under fortress walls during siege warfare. When the end of the tunnel was beneath the foundations of the wall its roof was supported by wooden props. At an appropriate moment a fire was lit so as to burn through the props, when it was hoped that the wall would collapse. The function of both wet and dry moats was chiefly to prevent sapping.
* The famous Bristol Channel pilot cutters (c. 1900) were ballasted with concrete which was run into the bilges. The concrete amidships, which needed to be heavy, was made up with scrap-iron and boiler-punchings. The concrete in the ends of the ship, which had to be light, was filled with empty beer bottles. For the plinths of statues and urns in my garden I generally use a mixture of old chicken-wire, empty wine bottles and concrete; it seems to work very well.
* From the Latin trabs, a beam.
Chapter 10 Something about bridges
-or Saint Benezet and Saint Isambard
London Bridge is falling down,
Falling down, falling down;
London Bridge is falling down;
My fair lady.
Build it up with brick and stone,
Brick and stone, brick and stone;
Build it up with brick and stone;
My fair lady.
Set a man to watch all night,
Watch all night, watch all night;
Set a man to watch all night;
My fair lady.
The more we think about this familiar nursery rhyme, the more eerie it appears to be. Though it cannot be traced with certainty much before the seventeenth century, it is undoubtedly very much older, and the Oxford Dictionary of Nursery Rhymes devotes several rather gruesome pages to it. All over the world bridge-building used to be associated with children’s dances – on y danse, on y danse9 sur le pont d’Avignon – and with human sacrifices which are not just legends. At least one child’s skeleton has been discovered immured in the foundations of a bridge.* Perhaps for this reason, special orders of bridge-building friars -Fratres Pontifices – were founded during the Middle Ages in various parts of Europe. They produced a saint, St Bénezèt, who is supposed to have designed the pont d’Avignon. Like Telford, in a later age, he had been a shepherd boy, and it is rather a nice thought that, dispensing with the sacrifices, he kept the children’s dances and the tune to which French children dance to this day. The French branch of the order of bridge-building friars had a monastery, near Paris, with the charming name of Saint Jacques-de-Haut-Pas.
In practical terms, the purpose of a bridge is to enable heavy objects, such as vehicles, to cross over some kind of gap or chasm. Provided that the weight is supported in a safe manner it usually does not matter very much by what technical means this is done. As it turns out, there is a very considerable variety of structural principles which can be employed.
The method which is actually chosen in any given case depends not only upon the physical and economic conditions but also upon the fashion of the day and the whim of the engineer. Almost every conceivable way in which a bridge could possibly be made has actually been tried, at one time or another, for making real bridges. One might have supposed that one approach to the problem would have turned out to be the ‘best’ one and would have come to be generally accepted, but this is not the case; and the number of struc
tural systems which are in common use seems to increase as time goes on.
In civilized countries bridges are littered about the landscape in generous numbers and in a rich variety; they provide a very interesting display of different structural principles. With most other artefacts the vital structure is hidden away behind panelling or insulation or wiring or gadgets of one kind or another and is not easily seen or inferred. One virtue of bridges is that both the structure and the way in which it works are clear for all to see.
Arch bridges
Arch bridges have always been popular and, in various forms, they are still very much in fashion. A simple masonry arch can quite safely be built with a span of well over 200 feet (60 metres). For most sites, if there are objections they are likely to be associated with the cost or with the rise of the arch and with the load on the abutments or foundations.
If we are concerned with the plain, semi-circular masonry arch which was widely used in Roman and medieval times, then one of the facts of life is that the rise of the arch must be about half its span. Thus a 100 foot span will call for a rise of at least 50 feet – in practice rather more. This is all very well if the bridge is spanning a ravine which is more than 50 feet deep, because the arch can then be sunk so that its crown is level with the roadway on either side. However, if the bridge is to be built on flat ground, then we have the alternatives, on the one hand, of a hump-backed bridge, which is inconvenient and dangerous, or, on the other, of having to build long and expensive sloping approaches.
The problem became particularly important with the coming of railways, because trains don’t like hump-backed bridges – or indeed gradients of any kind – and the expense of earth-moving to make embankments for a flat approach is a serious matter. One way of getting round the difficulty, at least to a certain extent, is to build a rather flat arch with considerably less rise. In 1837, faced with the problem of getting the Great Western Railway across the Thames at Maidenhead, Isambard Kingdom Brunei built a bridge of two brick arches, each with, a span of 128 feet and a rise of only 24 feet (Plate 10).