Structures- Or Why Things Don't Fall Down

by J E Gordon

  Riveting may not be heaven, but, by contrast, welding was certainly hell. Welding is amusing enough for the first hour or two -as I dare say hell may very possibly be – but after this the task of watching a hissing, flickering arc and a wretched little pool of molten metal becomes intolerably dull, and the dullness is not much relieved by the sparks and blobs of molten metal which find their way down one’s neck and into one’s shoes. After a very few days a feeling of boredom and bloody-mindedness settles in and it becomes very difficult to concentrate upon making a satisfactory weld.

  Nowadays welds in tubing and in pressure vessels are made by automatic machines, which I suppose do not get bored, and so these welds are usually reliable. However, automatic welding is often impracticable in large structures like ships and bridges, where, in practice, the welding generally turns out to be very imperfect. Furthermore a welded joint provides little or no barrier to crack propagation, and this is one reason why so many large steel structures have failed catastrophically in recent years.

  Creep

  Homer knew that the first thing to do on getting your chariot out was to put the wheels on.

  John Chadwick, The Decipherment of Linear B (Cambridge University Press, 1968)

  The chariots of Mycenaean and archaic Greece had very light and flexible wheels, made from thin bent wood – willow or elm or cypress – usually with only four spokes (Figure 11). Such a construction was highly springy and resilient, and it seems to have enabled these vehicles to be galloped across the rough ground of the Greek hillsides, where a heavier and more rigid vehicle would have been useless. In fact, the rim of the wheel bent, rather like a bow, under the weight of the chariot, and, just as a bow must not be left strung for any length of time; so the weight must not be left on the wheels of a chariot. In the evening, therefore, one either tipped the vehicle vertically against a wall with the weight off the wheels, as Telemachus did in Book IV of the Odyssey, or else one took the wheels off altogether. Even on Mount Olympus the goddess Hebe had the morning chore of fitting the wheels to the chariot of grey-eyed Athene. With the much heavier wheels of later times such a procedure is less necessary and less practicable, although I understand that the wheels of the present Lord Mayor’s coach are distinctly eccentric, presumably because the weight has been left on them for long periods.*

  Figure 11. The Homeric chariot wheel was essentially flexible and made by bending quite thin wood. It could easily distort or’ creep’ under any prolonged load.

  The distortion of bows and chariot wheels under prolonged loading is due to what the engineer calls ‘creep’. In elementary Hookean elasticity we assume, for simplicity, that if a material will sustain a stress at all, it will sustain it indefinitely, and also that the strains in a solid do not change with time, so long as the stress remains constant. In real materials neither of these assumptions is strictly true; nearly every substance will continue to extend or creep under a constant load with the passage of time.

  The amount by which materials creep, however, varies a great deal. Among technological materials, wood and rope and concrete all creep very considerably and the effect has to be allowed for. Creep in textiles is one reason why our clothes go out of shape and the knees of trousers get baggy; it is, however much more pronounced in natural fibres, such as wool and cotton, than it is with the newer artificial fibres. This is why Terylene sails not only keep their shape but do not need to be carefully ‘stretched’ when new, as had to be done with cotton and flax sails.

  Figure 12. Typical time-creep curves for a material subjected to a series of constant stresses, sl, s2, s3... etc.

  Creep in metals is generally less pronounced than it is in non-metals, and, although steel creeps significantly at high stresses and when heated, the effect can often be neglected when one is dealing with light loads at ordinary temperatures.

  Creep in any material causes the stress to be redistributed in a manner which is often beneficial, since the more highly stressed parts creep the most. This is why old shoes are more comfortable than new ones. Thus the strength of a joint may improve with age if the stress concentrations are diminished. Naturally, if the load on the joint is reversed, creep may have the opposite effect and the joint may be weakened.

  The effect of the distortions caused by creep is particularly conspicuous in old wooden structures. In buildings the roof often sags in a picturesque way, and old wooden ships are generally ‘hogged’: the ends of the ship droop while the middle part rises. This is very noticeable in the gun-decks of H.M.S. Victory. With metals such as steel we generally notice the effects of creep when the springs of a car ‘sit down’ and have to be replaced.

  Although the amount of creep which is likely to occur varies greatly between different solids, the general pattern of behaviour is very much the same for nearly all materials. If we plot deformation or strain against the logarithm of time (which is a convenient way of contracting the time-scale) for the same material when subject to a series of constant stresses, s1 s2, s3 ... etc., we get a diagram very like Figure 12. It will be seen that there is a critical stress, s3 perhaps, below which the material will never break, however long it may be loaded. At stresses higher than s3 the material will not only distort with time but will also gradually progress to actual fracture and destruction, an effect we generally wish to avoid.

  Soils, too, creep under load like other materials, and thus, unless we build upon rock or very hard ground, we need to watch the ·settlement’ of foundations, which will usually need to be deeper for large buildings than for small. This is the reason for constructing large buildings on concrete ‘rafts’. Note the subsidence of the foundations of the arches of Clare bridge in Plate 7.

  * * *

  *Note that, if an ‘undrawn’ nylon thread be cast into a block of ‘rigid’ plastic, the thread can always be drawn out of the plastic by pulling on it, however long the thread may be. This is a good way of making long and complicated holes, for instance in wind-tunnel models, for pressure measurements.

  *This is also true for the adhesion between metals and paint or enamel, including ‘vitreous enamel’, i.e. glass. Before the days of modern extenso-meters, engineers used to judge the ‘yield-point’ of hot-rolled steel by the load at which the ‘mill-scale’, or black oxide film, cracked off the surface.

  * This sort of thing is at the root of most of the stories about V.I.P.s being seasick when riding in state-coaches.

  Chapter 8 Soft materials and living structures

  -or how to design a worm

  ‘I’m very glad,’ said Pooh happily, ‘ that I thought of giving you a Useful Pot to put things in.’

  ‘I’m very glad,’ said Piglet happily,’ that I thought of giving you Something to put in a Useful Pot.’

  A. A. Milne, Winnie-the-Pooh

  When Nature invented Something called ‘life’ she may have looked around, a little anxiously, for a Useful Pot to put it in, for life would not have prospered for long naked and unconfined. At the time this planet presumably afforded rocks and sand, water and an atmosphere of sorts, but it must have been rather short of suitable materials for containers. Hard shells could be made from minerals, but the advantages of a soft skin, particularly in the earlier stages of evolution, seem to be overwhelming.

  Physiologically, cell walls and other living membranes may need to have a rather closely controlled permeability to certain molecules but not to others. Mechanically, the function of these membranes is often that of a rather flexible bag. They generally need to be able to resist tension forces and to be able to stretch very considerably without bursting or tearing. Also in most cases skins and membranes have to be able to recover their original lengths of their own accord when the force which has been extending them is removed.* The strains to which present-day living membranes can be extended safely and repeatedly varies a good deal but may typically lie between 50 and 100 per cent. The safe strain under working conditions for ordinary engineering materials is generally less than 0-1 per cen
t, and so we might say that biological tissues need to work elastically at strains which are about a thousand times higher than those which ordinary technological solids can put up with.

  Not only does this enormous increase in the range of strain upset a number of the conventional engineer’s preconceived ideas about elasticity and structures; it is also clear that strains of this magnitude cannot be furnished by solids of the crystalline or glassy type based on minerals or metals or other hard substances. It is therefore tempting, at least to the materials scientist, to suppose that living cells might have begun as droplets enclosed by the forces of surface tension. We must be quite clear, however, that it is very far from certain that this is what actually happened; what really did occur may have been something quite different – or at any rate considerably more complicated. What is certain is that some features of the elasticity of animal soft tissues resemble the behaviour of liquid surfaces and thus may possibly derive from them.

  Surface tension

  If we extend the surface of a liquid, so that it presents a larger area than before, we shall have to increase the number of molecules present at the surface. These extra molecules can only come from within the interior of the liquid and they will have to be dragged from the inside of the liquid to its surface against the forces which tend to keep them in the interior, which can be shown to be quite large. For this reason the creation of a new surface requires energy, and the surface also contains a tension which is a perfectly real force.* This is most easily seen in a drop of water or mercury, where the tension in the surface pulls the drop into a more or less spherical shape against the force of gravity.

  When a drop hangs from the mouth of a tap, the weight of the water in the drop is being sustained by the tension in its surface. This phenomenon is the subject of a simple school experiment where one measures the surface tension of water and other liquids by counting the drops and weighing them.

  Although the tension in a liquid surface is just as real as the tension in a piece of string, or any other solid, it differs from an elastic or Hookean tension in at least three important respects:

  The tension force does not depend upon the strain or extension but is constant however far the surface is stretched.

  Unlike a solid, the surface of a liquid can be extended, virtually indefinitely and to as large a strain as one cares to call for, without breaking.

  The tension force does not depend upon the cross-sectional area but only upon the width of the surface. The surface tension is just the same in a deep or ‘thick’ liquid as it is in a shallow or ‘thin’ one.

  Drops of liquid in air are of little use for biological purposes, because they soon fall to the ground; but droplets of one liquid floating within another liquid can continue to exist indefinitely and are of great importance both in biology and in technology. Systems of this kind are called ‘emulsions’ and are familiar in milk, in lubricants and in many kinds of paint.

  Droplets are generally spherical and the volume of a sphere is as the cube of its radius, whereas the surface area of a sphere is as the square of the radius. Thus, if two similar droplets were to join up so as to make one droplet of twice the volume, there would be a considerable net reduction in surface area and so in surface energy. So there is an energy incentive for the drops in an emulsion to coalesce and for the system to segregate into two continuous liquids.

  If we want the droplets to remain separate and not to coalesce, we have to arrange for them to repel each other. This is called ‘stabilizing the emulsion’ and is rather a complex process. One factor in stabilization is the provision of a suitable electrical charge on the surface of the drops – which is why emulsions are affected by electrolytes such as acids and alkalis. If stabilization has been done properly we have to do quite a lot of work to bring the droplets together – in spite of the saving in surface energy – which is why churning cream to make butter is hard work; Nature is rather good at stabilizing emulsions.

  Although it does have some serious disadvantages, yet, as long as an animal is content to be very small and round, there is a good deal to be said for surface tension as a skin or membrane or container. For one thing, such a skin is very extensible and it is also self-healing; for another, the problem of reproduction is greatly simplified, since, if a droplet swells, it can break into two and become two droplets.

  The behaviour of real soft tissues

  As far as I know, no present-day cell wall operates simply by a straightforward surface tension mechanism; but many of them do behave in a way which is mechanically rather similar. One of the difficulties about simple surface tension is that the tension force is constant and cannot be increased by making the skin thicker; this limits the size of any container made in this way.

  However, Nature is quite capable of producing a material which will have the characteristics of surface tension ‘right through its thickness’, so to speak. A slightly embarrassing example may be familiar to many people; when the dentist tells one to spit into his basin the resulting string or cord of saliva sometimes appears to be infinitely extensible and virtually unbreakable. What molecular mechanism is taking place is not at all clear, but the behaviour of such a material in terms of stress and strain is very much as in Figure 1.

  Figure 1. Stress-strain diagram for steel, bone and spit.

  Most animal tissues are not as extensible as spit, but a very high proportion of them do show rather similar characteristics up to strains of 50 per cent or more. The urinary bladder in young people will stretch, more or less in this fashion, to around 100 per cent strain and that of dogs to about 200 per cent. As we mentioned in Chapter 3, my colleague Dr Julian Vincent has recently shown that, whereas the soft cuticle of male locusts and of virgin female locusts is content with a strain of something under 100 per cent, that of the pregnant female will stretch to an incredible 1,200 per cent – and still recover completely.

  Although the stress-strain curve for most membranes and other soft tissues is not strictly horizontal, it is often very nearly so, at any rate up to the first 50 per cent or so of strain, and we may well consider what the consequences of this sort of elasticity are. In fact, any structure made from such a material must necessarily resemble one made from films of liquid under surface tension, and they are best observed by blowing soap bubbles next time you are in your bath.

  The basic principle involved is that a material or membrane of this sort is essentially a constant-stress device – that is to say, it has only one stress to offer, and that one stress will operate in all directions. The only shape of shell or vessel or pressure container which is compatible with this condition is either a sphere or else a part of a sphere. This can be seen pretty clearly with soap-suds and in the froth on beer. If one should want to make an elongated animal from membranes of this sort, then the best thing to do seems to be to make it of a ‘segmented’ construction, like Figure 2, and in fact this sort of thing is very common in worm-like creatures.

  Figure 2. A segmented animal. Stresses are equal in both directions in the surface.

  However successful this device may be for the cuticle of worms, it is of no use if what is wanted is a pipe or a tube, such as a bloodvessel. For pipes, as we saw in Chapter 6, the circumferential stress is ineluctably twice the axial stress, and this differential is just what a membrane of the sort we have been discussing cannot furnish. So it is necessary to have a material whose stress-strain curve slopes upwards after the fashion of Figure 3.

  Figure 3. To make the skin of a cylindrical container the stress-strain curve of the membrane must slope upwards so as to afford a circumferential stress which is twice the longitudinal stress.

  The most obvious kind of highly extensible solid which fulfils this condition is rubber, and there is nowadays a wide range of rubber-like materials available, both natural and artificial; some of these solids will extend to about 800 per cent strain. They are known to materials scientists as ‘elastomers’. We use rubber tubes for all sorts of technologica
l purposes, and one might suppose that the obvious thing for Nature to do would be to evolve a rubbery solid suitable for making veins and arteries. However, this is just what Nature has not done – and, as it turns out, for a very good reason.

  Materials of the rubbery kind have a stress-strain curve which has a very characteristic ‘sigmoid’ or’ S’ shape (Figure 4). According to my rather shaky mathematics, one can show that if we make a tube or a cylinder from such a material and then inflate it, by means of an internal pressure, so as to involve a circumferential strain of 50 per cent or more, then the inflation or swelling process will become unstable, and the tube will bulge out, like a snake which has eaten a football, into a spherical protrusion which a doctor would describe as an ‘aneurism*. Since one can easily produce this result experimentally by blowing up an ordinary child’s cylindrical rubber balloon (Plate 3), my mathematics are probably right.

  Figure 4. Stress-strain curve for typical rubber.

  Since veins and arteries do, in fact, generally operate at strains around 50 per cent, and since, as any doctor will tell you, one of the conditions it is most desirable to avoid in blood-vessels is the production of aneurisms, any sort of rubbery elasticity is quite unsuitable for most of our internal membranes; and in fact it is comparatively rare in animal tissues.