Structures- Or Why Things Don't Fall Down

by J E Gordon

  Thus in choosing a material for a tension member we are commonly faced with incompatible requirements. To reduce the weight of the middle or parallel part of a tie-bar we should like to use a material of high tensile strength. For the end fittings we generally want a tough material – which is only too likely to imply the acceptance of a low tensile strength. Like many difficulties, this one must be solved by a compromise, which in this case depends chiefly on the length of the member. For very long members, such as the wire cables of a modern suspension bridge, it will generally pay to choose a high tensile steel, even if we have to accept extra weight and complication in connection with the end fittings at the anchorages of the cables. After all, there are only two of these, one at each end of the bridge, while there is perhaps a mile of wire in between. Thus the saving of weight over the middle part will more than compensate for any losses at the ends.

  But when we come to things like chains with shortish links, the situation is totally different. In each short link the weight of the end fittings may well be greater than that of the middle part and must be carefully considered. This is the case with the supporting chains of the older suspension bridges. Such things were generally made from a tough and ductile wrought iron of quite low tensile strength. As we said in Chapter 10, the tensile stress in the plate links of Telford’s Menai bridge chains is less than a tenth of that in the wires of a modern suspension bridge – for this excellent reason. Very similar arguments apply to shell structures such as ships and tanks and boilers and girders which are fabricated from comparatively small plates of iron or steel. It also applies to riveted aluminium structures, such as conventional aircraft. All these may be considered more or less as two-dimensional chains with rather small links. In such cases it pays to use a weaker but more ductile material; otherwise the weight of the joints would be prohibitive (see Chapter 5, Figure 13, p. 106).

  The multiplication of ropes and wires in ships and biplanes and tents generally results in a saving, rather than an increase, of weight.* Naturally, all this cat’s-cradle business incurs the penalty of high wind resistance, high maintenance costs and general complication. This is the price we may have to pay for low structure weight. A similar principle can be seen in animals, where Nature does not hesitate to multiply tension members such as muscles and tendons. Indeed she adopts the same device as the Elizabethan seamen to reduce the weight of end attachments. The ends of many tendons are splayed out into a fan-shaped contrivance which Sir Francis Drake would have called a ‘crowsfoot’. Each branch of the tendon has a separate little joint to the bone. Thus the weight (and perhaps the metabolic cost) is minimized.

  The relative weights of tension and compression structures

  As we saw in the last chapter, the breaking stresses in tension and in compression for a given solid are often different, but for many common materials, such as steel, the difference is not very great, and so the weights of short tension and compression members are likely to be fairly similar. In fact, because a compression member may not need to have heavy end fittings – whereas a tension member does – a short compression strut may well be lighter, for comparable conditions, than a tension bar.

  However, as a strut gets longer, Dr Euler begins to make himself felt. It will be remembered that the buckling load of a long column varies as l/L2 (where L is the length) and this implies that, for a rod of constant cross-section, the compressive strength diminishes very rapidly with increase of length. Thus, to support any given load, a long strut has to be made very much thicker, and therefore heavier, than a short one. As we said in the last section, the same consideration does not apply to tension members.

  It is revealing to study the problem of carrying one ton (1,000 kg or 10,000 Newtons) over a distance of 10 metres (33 feet) first in tension and then in compression.

  IN TENSION. For a steel rod or a cable we might allow a working stress of, say, 330 MN/m2 or 50,000 p.s.i. in tension. Taking into account the end fittings, the total weight comes out at about 3-5 kg or about 8 lb.

  IN COMPRESSION. To try to carry such a load in compression over such a distance by means of a solid steel rod would be silly, because if a solid rod were thick enough to avoid buckling it would need to be very heavy indeed. In practice we might well use a steel tube, which would have to be about 16 cm (6 inches) in diameter with a wall-thickness of, say, 5 mm (0-2 inch). Such a tube would weigh 200 kg or about 450 lb. In other words it would weigh between fifty and sixty times as much as the tension rod. The cost might well be in the same proportion. Furthermore, if we should want to subdivide a compression structure the situation gets not better but much worse. If we wanted to support a load of one ton, not by a single strut, but by some table-like arrangement of four struts, each 10 metres long, then the total weight of the struts would be twice as great: that is to say, 400 kg or 900 lb. The weight goes on increasing the more the structure is subdivided – in fact as √n̄ where n is the number of columns. (See Appendix 4.)

  On the other hand, if we increase the load, keeping the distance the same, then the weight of a compression structure becomes relatively better. For instance, if we increase the load a hundredfold, that is, from one ton to 100 tons, then, though the weight of a tension member has gone up at least in proportion from 3-5 kg to 350 kg, yet the weight of a single strut to carry this load over 10 metres increases only tenfold, that is, from about 200 kg to about 2,000 kg. So, in compression, it is proportionately very much more economical to support a heavy load than a light one (Figure 1). All these considerations operate in the same sort of way for panels and shells and plates and membranes as for simple struts and poles and columns (Appendix 4).

  Figure 1. Diagram illustrating the relative weight-cost of carrying a given load over a distance L.

  Considerations of this kind provide the rationale of things like tents and sailing ships. With such devices it pays, hands down, to collect the compression loads into a small number of masts or poles, contrived to be as short as possible. At the same time the tension loads, as we have said, are better diffused into as many strings and membranes as may be. Thus a bell-tent, which has a single pole but many guy-ropes, is likely to be the lightest ‘building’ which can be made in proportion to its volume. However, almost any tent will generally be lighter and cheaper than a solid building made from timber or masonry. In the same way, a cutter or a sloop, which has a single mast, is a lighter and more efficient rig than a ketch or a schooner or any other more complicated arrangement with several masts. This is also the reason why the A-shaped or tripod masts used by the ancient Egyptians and by the designers of Victorian ironclads (Chapter 11) were heavy and inefficient.

  Again, the typical vertebrate animal, such as man, is on the whole a good deal like a bell-tent or a sailing ship. There is a small number of compression members, that is, bones, more or less in the middle, and these are surrounded by a wilderness of muscles and tendons and membranes – even more complicated than the ropes and sails of a full-rigged ship – which carry the tensions. Furthermore, from the structural point of view two legs are better than four, and the centipede is perhaps only saved from total inadequacy by the fact that its legs are so short.

  Scale effects – or second thoughts on the ‘square-cube law’

  It will be remembered that, long ago, it occurred to Galileo that, whereas the weight of a structure increased as the cube of its dimensions, the cross-sectional area of its load-carrying members increased only as the square, and so the stress in the material of geometrically similar structures ought to increase in direct proportion to the dimensions. Thus a structure which is liable to fail by tensile fracture induced, directly or indirectly, by its own weight must be made of thicker and stockier proportions the larger it becomes. In fact, its members would have to be made disproportionately thicker and heavier than the simple rule would indicate, because there is a sort of ‘ compound interest’ effect. Thus the size of all structures might be expected to be quite strictly limited.

  This sq
uare-cube law has been bandied about by both biologists and engineers for a long time. Herbert Spencer and, later, D’Arcy Thompson said that it limited the size of animals, such as elephants, and engineers used to explain that it rendered impracticable the building of ships or aircraft appreciably larger than those already in existence. In spite of this, both ships and aircraft continued to get bigger and bigger.

  As a matter of fact the square-cube law seems to apply with full force only to the lintels of Greek temples (which are made from weak, heavy stone), icebergs and icefloes (which are made from weak, heavy ice) and things like jellies and blancmanges.

  As we have seen, in many sophisticated structures the weight of the compression members is likely to be many times greater than that of the tension parts. Since the compression members are likely to fail by buckling they will become more efficient the larger the load they are called upon to bear – that is to say, the larger the structure is made. For this reason, although there is a disproportionate increase of weight with increase of size, the penalty is very much smaller than is implied by the square-cube law. In practice this penalty may be more than offset by various ‘economies of scale’. For instance, in a ship or a fish, an aircraft or a bird, the resistance to motion will be nearly in the ratio of the surface area, and this area will diminish, proportionately to the weight, as the size increases. It was Brunei’s perception of this which impelled him to design the Great Eastern. Brunei’s perception was right, though his great ship was a failure, and this is why we build enormous ships, such as super-tankers, today. Furthermore, as we saw in Chapter 5 the size of large animals is more likely to be limited by considerations related to the ‘critical Griffith crack length’ in their bones than by the square-cube law.

  Space-frames versus monocoques

  Quite frequently the engineer is faced with a choice between a lattice structure built up, Meccano-fashion, from separate struts and tension rods – which is called a ‘space-frame’ – and a shell structure in which the load is carried in more or less continuous panels; this is called a ‘monocoque’. Sometimes the distinction between the two forms of construction is obscured by the fact that space-frames are covered over with some sort of continuous cladding which does not really carry much load. This is the case with traditional timbered cottages, with modern steel-framed sheds and barns (which are covered with corrugated iron) and, of course, with animals which are covered with shells or scales.

  Sometimes the decision about which form to use is dictated by requirements which are not strictly structural. Thus an electricity pylon offers least wind resistance and least area of steel to paint when it is in the form of an open trellis or lattice tower. Again it is generally more convenient to make a water-tank, for instance, from a shell of thickish steel plates than in the form of a trellis supporting a water-tight bag or membrane, even though the latter form may be lighter and is, in fact, the solution usually adopted by Nature for stomachs and bladders.

  Sometimes the difference in weight and cost between the two forms of construction is marginal and it may not matter very much which is used. In other cases the difference is very great. As we have seen, a tent is always much lighter and cheaper than any equivalent building made from continuous panels or concrete or masonry. In coachbuilding the old-fashioned ‘Weymann’ saloon car body, circa 1930, which consisted of a wooden space-frame covered with padded fabric, was very much lighter than any of the pressed metal shell bodies which have been used since. In these days of expensive petrol the Weymann body might well be revived.

  There is, however, an idea about that monocoque shells are somehow more ‘modern’ and more advanced than space-frames, which are sometimes considered to be primitive and rather Heath Robinson. Although a good many engineers who ought to know better subscribe to this view, there is in fact no objective structural justification for it. When it comes to carrying loads which are primarily compressive, the space-frame is always lighter and usually cheaper than the monocoque. The weight penalty for using a monocoque, however, is less severe when the loads are high in relation to the dimensions, and this, in conjunction with other considerations, may justify the use of shells in some instances. However, for large, lightly loaded structures, such as ‘rigid’ airships, the space-frame or trellis structure is the only practicable one. The alternative for lighter-than-air transport is not a vast monocoque airship made from an engineer’s dream of shiny aluminium plates, but a pressurized bag or ‘blimp’.

  The transition from the stick and string and fabric construction of the early aircraft to modern monocoques was not dictated by some sudden surge of fashion but was a strictly logical step in aircraft design once certain loads and speeds were reached. As we have said, regarded solely as a means of taking compression and bending, the monocoque is always heavier than the space-frame; but the extra weight required gets less in proportion as the load on the structure increases. On the other hand, regarded as a means of resisting shear and torsion, the monocoque is more efficient than the space-frame.* As aircraft speeds increase, so do the requirements for torsional strength and stiffness. There comes therefore a transition point, which was reached in the 1930s, when it pays, in terms of structure weight, to change over the construction of airframes from space-frame to monocoque. This is especially the case with monoplanes. Thus modern aircraft are usually built as continuous shells, using aluminium sheet, plywood or Fibreglass for the skin. We see an equally logical reversion to space-frame construction in modern hang-gliders, which are very light indeed.

  The need to resist large torsional loads is almost confined to artificial structures such as ships and aircraft. As we said in Chapter 12, Nature nearly always manages to avoid torsion, and thus, at least as far as large animals are concerned, monocoques or exo-skeletons are uncommon. Most sizeable animals are vertebrates and therefore highly sophisticated and successful space-frames, not very different in their structural philosophy from biplanes and sailing ships. The avoidance of severe torsional requirements is very noticeable in birds and bats and pterodactyls. It is this which enabled these animals to retain their light space-frame construction when they took to the air. Aircraft designers, please note.

  Blown-up structures

  It is sometimes interesting to speculate about the technological ‘ifs’ and ‘buts’ of history. If Isambard Kingdom Brunei had come upon the railway scene a very few years earlier than he did it is probable that most of the railways of the world would have standardized on a gauge of 7 feet instead of using his rival George Stephenson’s ‘coal wagon gauge’ of 4 feet 8£ inches, which derived from the Roman chariots. The Stephenson gauge has proved something of a handicap, as Brunei predicted it would. If they had a wider gauge today, the railways might perhaps be in a stronger position, technically, and economically, than they are. If so, the world might be slightly different.

  On the other hand, if an effective pneumatic tyre had been available around 1830, we might have gone direct to mechanical road transport without passing through the intervening stage of railways at all. In that case the present-day world would have been even more different. In fact the pneumatic tyre was invented about fifteen years too late. It was patented in 1845 by a young man called R. W. Thomson, then aged twenty-three. Thomson’s tyre was surprisingly successful technically, but by that time the railways were well established, and the rail interests combined with the horse interests to promote absurd and restrictive legislation, which had the effect of delaying the development of the motor car until the turn of the century.

  Since the bicycle was never thought to constitute a serious threat either to trains or to horses its development was legally permitted in Victorian times. The pneumatic tyre was revived with considerable success, for use on cycles, by J. B. Dunlop in 1888. Dunlop made a fortune out of it, but by that time Thomson was dead and his patent had expired. With solid tyres lorries are limited to something like 15 m.p.h., and cars cannot go very much faster. Thomson’s invention has not only made fast and cheap ro
ad transport practicable; it has also enabled aircraft to operate from dry land. Without pneumatic tyres we should probably have to use some form of seaplane.

  Tyres, of course, have the function of spreading and cushioning the load beneath the wheels of a vehicle, and in this they are extremely successful. However, tyres are really only one example of a whole class of blown-up structures. Quite apart from any cushioning effects, blown-up structures provide a very effective way of evading the serious penalties in weight and cost which are incurred when we try to carry light loads over a long distance in bending or in compression. What such a structure does is to carry the compression, not in a solid panel or column which is liable to buckle, but by compressing a fluid, such as air or water. Thus the solid parts have only to sustain tension forces, which, as we have seen, involve very much less weight and cost than compression.

  In technology the idea of using blown-up structures in an intelligent way is not new. Around 1,000 B.C., the up-river boatmen of the Tigris and the Euphrates were making boats and rafts from blown-up animal skins. These boats voyaged down-stream carrying, not only produce for sale in the cities of the plains, but also mules or donkeys. On arrival at their destination, the skins were deflated and returned to their home-ports, overland, on the backs of the pack-animals. Nowadays pneumatic boats are common and so are pneumatic tents and furniture. They are often packed up and carried around on cars.

  The air-supported roof was invented by the great engineer F. W. Lanchester in 1910. It consists simply of an inflatable membrane, attached at its edges to the ground. It is kept up by air at very low pressure provided by a simple fan arrangement. Although it has to be entered and left by means of an air-lock, this is not usually a very serious handicap in view of the other advantages. Lanchester’s roof allows large areas to be covered very easily and cheaply, but its use is at present confined to things like greenhouses and covered tennis courts; it is prevented from being used for factories or houses by rather grandmotherly building regulations.