Structures: Or Why Things Don't Fall Down

by J.E. Gordon

engineering. It is obvious that energy can be stored in a wound-up spring, but, as Hooke pointed out, official springs are only a special case of the behaviour of any solid when it is loaded. Thus every elastic material which is under stress contains strain energy, and it does not make much difference whether the stress is tensile or compressive.

In a vehicle with no springs there must be violent interchanges of potential and kinetic energy (energy of motion) every time a wheel passes over a bump. These energy changes are bad for the passengers and bad for the vehicle. Long ago some genius invented the spring, which is simply an energy reservoir which enables changes of potential energy to be stored temporarily as strain energy so as to smooth the ride and prevent the vehicle and its occupants from being racketed to bits.

It will be seen that the strain energy storage per unit weight is about twenty times higher for tendon than it is for modern spring steels.

Light aircraft, which have to be designed for bad landings on rough ground, often have their undercarriages sprung by means of rubber cords which have a strain energy capacity much better than that of steel springs, and are also better than tendon, though they are less durable.

With a bow or a palintonon, when the bowstring is first released, some of the stored strain energy is communicated directly to the missile as kinetic energy. More of the available energy, however, is being used to accelerate the arms of the bow or the catapult, where it is temporarily stored as kinetic energy, much as it is in the trebuchet. In this case, though, as the discharge mechanism proceeds, the moving arms are slowed down, not by a fixed stop, but by the bowstring itself as it straightens and tautens. This further increases the tension in the string, enabling it to push yet harder on the missile and so speed it on its way. Thus, much of the kinetic energy stored in the arms is recovered.

This quality of being able to store strain energy and deflect elastically under a load without breaking is called ‘resilience’, and it is a very valuable characteristic in a structure. Resilience may be defined as ‘the amount of strain energy which can be stored in a structure without causing permanent damage to it’.

Things like aeroplanes and buildings and tools and weapons have to be pretty rigid in order to do their job. In this respect most structures have to be a compromise between stiffness and strength and resilience, and the achievement of the best compromise is likely to tax the skill of a designer severely.

A simple but interesting example occurs in an ordinary spider’s web. The web is subject to impact loads arising from flies blundering into it, and the energy of these blows must be absorbed by the resilience of the threads. It turns out that the long radial threads, which form the main load-carrying part of the structure, are three times as stiff as the shorter circumferential threads which have the duty of actually catching the flies.

As we have said, it is quite possible to break a bow by ‘shooting’ it without an arrow. What happens is that the strain energy which was stored in the bow can no longer be disposed of safely as kinetic energy in the arrow, and so some of it is employed in producing cracks within the material of the bow itself. In other words the bow has used its own strain energy to destroy itself.

According to the modern view of the subject, when we break a structure by loading it in tension, we ought not to regard fracture as being caused directly by the action of the applied load pulling on the chemical bonds between the atoms in the material. That is to say, it is not the consequence of the simple action of a tensile stress as the classical text-books would have us believe.* The direct result of increasing the load on the structure is only to cause more strain energy to be stored within its material.

The quantity of energy required to break a given cross-section of a material defines its ‘toughness*, which is nowadays more often called its ‘fracture energy’ or ‘work of fracture*.

It is possible to get rather better combinations of strength and toughness by using ‘alloy steels’, that is, steels alloyed with elements other than carbon, but these are generally too expensive for large-scale construction.

It is well known that old people are particularly liable to break their bones, and this is generally attributed to a progressive em-brittlement of bone with age.

As far as I know, there are no reliable data on the change of work of fracture of bone with age, but, since the tensile strength is only reduced by about 22 per cent between the ages of twenty-five and seventy-five, it does not look as if there were a very dramatic reduction.

Professor J. P. Paul, of the University of Strathclyde, tells me that his researches seem to indicate that a more important cause of fracture in old people is the progressive loss of nervous control over the tensions in the muscles.

Muscle is a soft tissue which, when it receives an appropriate nerve signal, is able to shorten itself and so produce tensile forces by pulling in an active way.* However, although muscle is a more efficient device than any artificial engine for converting chemical energy into mechanical work, it is not very strong.

As far as our legs are concerned, muscle is not only bulky but heavy, and the object seems to be to arrange for the centre of gravity of our legs to be as high up in the body as possible. The reason for this is that, in normal walking, the leg operates as a pendulum swinging freely in its own natural period and therefore consuming as little energy as may be. It is because we have to force our legs to oscillate faster than their natural frequency that running is so tiring. The natural period of swing of our legs will be faster the nearer the centre of gravity of the limb is to the thigh-joint. This is why we have thick calves and thighs and, hopefully, small feet and ankles.

The frequency* of the note given out by a stretched string depends, not only on its length, but also upon the tensile stress in it. In stringed instruments the appropriate stresses are produced by stretching the strings – which are made of stiff material, such as steel wire or catgut – across a suitable framework, which may be the wooden body of a violin or the cast-iron frame of a piano.

Incidentally, the higher frequencies of the voices of women and children are caused, not by higher tensions in their vocal cords, but simply by the fact that the larynx is smaller and the vocal cords therefore shorter. There is a surprising difference in this respect between grown-up men and women, the relevant larynx measurements being about 36 millimetres for men against about 26 for women. However, the larynxes of both boys and girls are of very similar size up to the age of puberty. The ‘breaking’ of boys’ voices is due, not to any change of tension in the cords, but to a rather sudden enlargement of the larynx around the age of fourteen.

When a hawk kills a bird in the air it does not usually do so by wounding it with its beak or talons – which would probably not penetrate the feathers. It kills by striking the bird in the back with its outstretched feet so as to impart a violent acceleration to the bird as a whole which has the effect of breaking its neck – very much as happens in judicial hanging.

When a newly made riveted joint between steel or iron plates has settled itself into a reasonable distribution of load, then rust may have a chance to play its beneficent part. The products of corrosion, iron oxides and hydroxides, expand and so lock the joint and prevent it from sliding backwards and forwards when the load is reversed. Furthermore, the rust transmits some of the shearing forces between the plates, rather like a glue, and therefore the strength of a riveted lap joint generally increases with age.

The distortion of bows and chariot wheels under prolonged loading is due to what the engineer calls ‘creep’

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.

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.

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 cent, 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.

Egg membranes are rather exceptional, in that they exist in order to be broken after they have served their purpose of conserving the moisture in the egg and keeping out infection; as we have said, they possess a special sort of elasticity, very possibly for this reason.

If we are tempted to indulge in the fashionable activity of turning a modern attic into an extra bedroom, the most serious problem is likely to be the stiffness of the floor. Although the roof-truss is unlikely to break, the deflections caused by the extra weight of people and furniture may well cause serious and expensive damage to the house.

Although most of the buoyancy of a ship is provided by the middle part of the hull and comparatively little by the tapering ends, nothing will ever prevent people from putting heavy weights into the ends of a ship.

If tension is about pulling and compression is about pushing, then shear is about sliding.

Shear strain = angle through which material is distorted as a result of shear stress N = g, which is an angle - usually in radians.

In hard solids like metal or concrete or bone, the elastic shearing strain is likely to be less than 1° (1/57 radian). Beyond this shearing strain, materials of this kind will generally either break or else flow in a plastic and irrecoverable way, like butter. However, with materials like rubber or textiles or biological soft tissues, recoverable or elastic shear strains may be much higher than this – perhaps 30° to 40°.

With liquids and squidgy things like treacle or custard or plasticine, the shear strain is unlimited; but then it is not recoverable.

Some rockets are driven by combinations of liquid fuels such as kerosene and liquid oxygen, but these systems involve elaborate plumbing which is liable to go wrong. Thus it may be better to use a ‘solid’ fuel such as that known as ‘plastic propellant\

Like modern car enthusiasts, they were generally more interested in their noisy and unreliable engines than they were in the supporting structure, about which they knew little and often cared less.

The pre-war vintage cars were sometimes magnificent objects, but, like vintage aircraft, they suffered from having had more attention paid to the engine and the transmission than to the structure of the frame or chassis.

Like the noisy exhaust, this kind of thing was no doubt impressive to the girl passenger, but it did not really do very much to keep the car on the road.

It is not surprising, therefore, that she seems to avoid torsion like poison. In fact she nearly always manages to dodge out of any serious requirement for the provision of torsional strength or stiffness. As long as they are not subjected to ‘unnatural’ loads, most animals can afford to be weak in torsion.

However, when we attach long levers called skis to our feet and then proceed to ski rather badly, it is only too easy to apply large twisting forces to our legs. Because this is the commonest cause of broken legs in ski-ing, it has led to the development of the modern safety binding, which releases automatically in torsion.

This must have been one of the relatively few occasions in history when a group of aircraft engineers have been seriously tempted to throw their collective arms around the neck of a circus proprietor and kiss him.

The ‘design’ of plants and animals and of the traditional artefacts did not just happen. As a rule both the shape and the materials of any structure which has evolved over a long period of time in a competitive world represent an optimization with regard to the loads which it has to carry and to the financial or the metabolic cost.

The entire physical world is most properly regarded as a great energy system: an enormous market-place in which one form of energy is for ever being traded for another form according to set rules and values.

Sooner or later the weight will fall to the ground and the strain energy will be released; but it is the business of a structure to delay such events for a season, for a lifetime or for thousands of years. All structures will be broken or destroyed in the end -just as all people will die in the end. It is the purpose of medicine and engineering to postpone these occurrences for a decent interval.

If we make the structure too weak we may save weight and money, but then the chance of the thing breaking too soon will become unacceptably high. Contrariwise, if we make a structure so strong that, in human terms, it is likely to last ‘for ever’ – which is what the public would like – then it will probably be too heavy and expensive.

In nearly all accidents we need to distinguish two different levels of causation. The first is the immediate technical or mechanical reason for the accident; the second is the underlying human reason.

It is quite true that design is not a very precise business, that unexpected things happen, that genuine mistakes are made and so forth; but much more often the ‘real’ reason for an accident is preventable human error.

Of course I do not mean the more gilded and juicy sins like deliberate murder, large-scale fraud or Sex. It is squalid sins like carelessness, idleness, won’t-learn-and-don’t-need-to-ask, you-can’t-tell-me-anything-about-my-job, pride, jealousy and greed that kill people.

I very much doubt if the remedy lies in the imposition of yet more regulations. It seems to me that what is wanted is the creation of more public awareness and a climate of opinion which regards such ‘mistakes’ as morally culpable.

It is at least arguable that the countryside is more attractive than the town not because the country is more ‘natural’ but because town and country were made, by and large, by very different kinds of people. But the first thing is to see ugliness for what it is rather than accepting it as part of the natural order of things.

I believe that very few artefacts are intrinsically ugly or beautiful simply because of their function*; they are rather mirrors to an age, to a set of values.