Structures- Or Why Things Don't Fall Down

by J E Gordon

  It is impossible, in practice, to plan for a ‘safe’ life of exactly so many hours or years. We can only consider the problem in statistical terms and in the light of accumulated data and experience. We then build in whatever margin of safety seems reasonable. All the time Ave are working on a basis of probabilities and estimates. 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. As we shall see, there are many cases where more danger is incurred by extra weight than is avoided by the corresponding increase of strength. Because we are necessarily working on a statistical basis, when we design a practical structure for a realistic life we have to accept that there is always some finite risk, however small, of premature failure.

  As Sir Alfred Pugsley points out in his book The Safety of Structures,* it is just at this rather interesting stage that we may have to abandon a strictly logical approach to the problem. As Pugsley says, the human emotions are quite exceptionally sensitive to the fear of structural failure, and the layman clings with great tenacity to the idea that any structure or device with which he is personally associated should be ‘unbreakable’. This crops up in all sorts of connections; sometimes it does no harm, sometimes the effect is counter-productive. During the last war aircraft designers had the choice, to some extent, of trading off structural safety against other qualities in the aircraft. Now the losses of bomber aircraft by enemy action were very high, something like one out of twenty in each sortie.† Against this, the losses from structural failures were very few, much less than one aircraft in ten thousand. The structure of an aeroplane accounts for practically a third of its total weight, and it would have been rational to have slimmed the structural parts of the bombers in return for other advantages.

  If this had been done there would have been some small increase in the structural accident rate, but the weight that would have been saved could have been invested in more defensive guns or in thicker protective armour. In that case there would no doubt have been a significant reduction in the net, or overall, casualty rate. But the airmen would not hear of anything of the kind. They preferred the big risk of being shot down by the enemy to the smaller risk of the aircraft breaking up in the air for structural reasons.

  Pugsley suggests that the feeling that it is in some way outrageous for a structure to break may be inherited from our arboreal ancestors, who were frightened, above all things, that the trees in which they lived might break beneath them – when down would come baby and cradle and all. And besides, the ancestors and their babies would fall into the mouths of their enemies on the ground, such as sabre-toothed tigers or whatnot. Whether this is the real reason or no, engineers have to take these sort of feelings into account, even though the extra weight incurred may involve dangers of its own.

  The accuracy of strength calculations

  It is implicit in any rational approach to questions of strength and safety that the engineer should be able to predict, with sufficient accuracy, the strength of a proposed structure when it is new -even if he is in doubt about how long it may be expected to last. While this may be roughly the case for simple structures such as ropes and chains and straightforward beams and columns, as we saw in Chapter 4, it is just not true at all for the more elaborate and critical artefacts, things like aircraft and ships.

  Since there is available a great body of accumulated experience with various kinds of structures, since there also exists a vast and highly mathematical literature on the subject, and since academic elasticians, in their pride, deliver endless lectures about the theory of structures, that statement might be regarded as sticking one’s neck out. However, it is true.

  Consider, for instance, the statistics for the strength of aircraft. Since the saving of weight is important and since the consequences of failure are very horrible, a great deal of care and thought is naturally given to the structural design of aeroplanes, and every detail is meticulously checked. The drawings and calculations are made by highly skilled designers and stressmen and draughtsmen, using the most scientific methods. When these people have done their sums the strength calculations are checked, quite independently, by an entirely different set of experts. Thus the strength predictions which are finally arrived at are about as accurate and painstaking as is humanly possible. Finally, and to make quite certain, an actual full-scale airframe is tested to destruction.

  It is not possible to give really up-to-date results because so few different types of aeroplane have been ordered in recent years that the figures are not statistically significant. However, when aircraft were simpler and cheaper, a comparatively large number of designs reached at least the prototype stage. Between 1935 and 1955 something in the region of a hundred different kinds of aeroplane were built and tested to destruction in this country. Thus the results for this period form a fairly reliable guide with some sort of statistical basis.

  Naturally, the actual figures of the required strengths for these different aircraft varied a great deal, according to the size and type of aeroplane. However, each design team could be said to be aiming at that strength which is known in the jargon of the aircraft trade as ‘120 per cent fully factored load’.* If structural design were anything like an exact profession one would expect the various test results, when plotted on a curve or ‘histogram’, to cluster pretty closely around the value for 120 per cent fully factored load, give or take a very little. In other words the results should produce a narrow ‘normal’ or bell-shaped distribution curve, much like Figure 1.

  As is fairly well known, nothing of the sort happened. When the results are plotted the histogram looks more like Figure 2. The experimental strengths tend to be randomly distributed between about 50 per cent and 150 per cent of the required or fully factored load. That is to say, even the most eminent designers cannot be relied upon to predict the strength of an aeroplane within a range of three to one. Some of these aircraft were less than half as strong as they should have been; others were much too strong and therefore considerably heavier than they needed to be.

  Figure 1. Expected statistical distribution of experimental aircraft strengths (schematic diagram).

  Figure 2. Actual distribution of strengths of airframes broken in test-frame, 193S-5S (very approximate schematic diagram).

  When it comes to ships, there are really no data on which one can base this sort of judgement – for the reason that ships are almost never tested to destruction under laboratory conditions. It is therefore impossible to tell how good or bad naval architects are at their job – at least as far as strength predictions are concerned. However, as we said in Chapter 5, the number of structural accidents to ships is considerable, and it seems very possible that the number of accidents per ton-mile is increasing at the present time.

  With regard to bridges, the problem of strength calculation is in some respects easier than with ships and aircraft, since the loading conditions are less varied. Nevertheless, the number of failures in modem bridges is quite significant.

  Designing by experiment

  Now, in building of chaises, I tell you what,

  There is always somewhere a weakest spot -

  In hub, tire, felloe, or spring or thill,

  In panel, or crossbar, or floor, or sill,

  In screw, bolt, thoroughbrace – lurking still,

  Find it somewhere you must and will.

  Oliver Wendell Holmes, The One-Hoss Shay

  The fallibility of the theoretical design process is, of course, the reason for the insistence on the experimental strength testing of all aircraft. However, the benefits of an experimental approach extend still further. We have assumed that it ought to be the designer’s aim for a structure to fail, the first time it is tested, exactly at the required load. But even the most scientifically designe
d structure is very unlikely to be of consistent strength throughout all its parts – like the legendary shay, where and so on for many components and many lines of verse.

  ...the wheels were Just as strong as the thills,

  And the floor was just as strong as the sills,

  And the panels were just as strong as the floor -

  On the test-frame the structure breaks at the weakest place; all the rest of the structure is therefore of greater strength. If an air-frame fails initially at just the required 120 per cent it follows that much the greater part of the structure is too strong for its purpose, and this extra strength is completely wasted. But we have no means of knowing where and how to lighten the structure. Repeated tests on large structures are expensive and time-consuming, but, where time and money allow, it is better to arrange, if possible, for the initial failure to occur at a load comfortably below the official 120 per cent. The weak place thus indicated can then be strengthened and the whole structure retested – and so on.

  The war-time Mosquito bomber, which was one of the most successful aircraft in history, failed initially at 88 per cent of the factored load – in the rear wing-spar. The aeroplane was then progressively strengthened up to a figure of 118 per cent. It was owing, partly, to the exceptionally light and strong airframe that the performance of this aircraft was outstanding.

  This is, roughly speaking, the Darwinian method, which Nature seems to rely on to develop her own structures – though she seems to be in less of a hurry and less mindful of the value of life than are most civilized human engineers. It is also, to a notable extent, the method employed by the makers of cars and other cheap, mass-produced goods. These people tend to make their products deliberately too weak for their purpose and to rely upon customers’ complaints to detect the significant faults.

  Thus a great deal of the strength-predicting element of design boils down to a sort of game in which we try to spot the weakest link in a load-bearing system. The more complicated the structure, the more difficult and unreliable this becomes. Fortunately, the design of a great many structures, from furniture and buildings to aeroplanes, is rescued from becoming a completely ridiculous process by the fact that the stiffness requirements may be more exacting than the strength requirements. Thus, if the structure is made stiff enough for its purpose, it may then very well be sufficiently strong. Since the deflections in a structure depend upon its general character rather than upon the existence of a ‘weakest link’, stiffness predictions are much easier to make, and more reliable, than strength predictions. This is what we really mean when we talk about designing a thing ‘by eye’.

  How long will it last?

  This also said Phocylides:

  A tiny rock-built citadel

  Is finer far, if ordered well,

  Than all your frantic Ninevehs.

  Phocylides (translated by Sir Maurice Bowra)

  In discussing the strength and stability of the masonry cathedrals Professor Jacques Heyman has laid down the principle that ‘If a structure will stand for five minutes, it will stand for five hundred years.’ For masonry structures built upon rock this is, broadly speaking, true. However, many cathedrals and other buildings have been founded upon soft ground. If this soft soil creeps (Chapter 7) – which happens quite often – curious things will happen, such as the Leaning Tower of Pisa. Such movements take time and can often be predicted, but they are very expensive to put right, and a certain number of buildings, both ancient and modern, fall down or have to be demolished for this reason.

  In most types of structure, rot and rust are very active agents of decay. It is partly the fear of rot which has turned engineers and architects in Britain against timber. However, the poor benighted foreigners in America and Canada and Scandinavia and Switzerland, who build between them about 1,500,000 wooden houses each year, do not seem to be troubled with rot to the same extent, and it might be a good idea to see how they manage these things. The use of wood is greatly on the increase in these countries.

  Timbers vary a great deal in their natural resistance to decay, and Lloyd’s Register allocates a fixed number of years of life to each of the different timbers which are used in shipbuilding. However, with modern knowledge and methods of treatment, it should be possible to get a practically indefinite life from almost any kind of wood.

  Most metals corrode in service. Modern mild steel rusts very much worse than Victorian wrought iron or cast iron, and so rust is, to some extent, a modern problem. Because the cost of labour is high, the cost of the painting and maintenance of steelwork is high. This is one good reason for using reinforced concrete, since steel embedded in concrete does not rust. In fact large modern ships, such as tankers, are constructed for a life of about fifteen years; on the whole it is cheaper to scrap than to paint. The life of cars is even shorter, usually for the same reason. It is true that for some structures one could use stainless steel but it is by no means always proof against corrosion, and stainless steels are expensive and awkward to fabricate. Besides this, the ‘ fatigue properties’ of stainless steels are usually bad.

  These are some of the reasons for choosing aluminium alloys; but, apart from the extra cost, there are a number of cases where the stiffness of aluminium has proved inadequate. The difficulty of welding aluminium is also a handicap. Some Communist countries see a great future for aluminium and have invested largely in aluminium plants. The London stock-markets were considerably shaken by the Tube Investments-British Aluminium take-over bid in 1961. However, the market for aluminium has not expanded to anything like the extent which was anticipated by the businessmen concerned in this transaction. In any case it requires more energy to make aluminium than to make steel.

  Even if the material of a structure does not deteriorate, its life may be subject to statistical effects which are sometimes calculable – and sometimes not. Many structures are likely to be broken only in rather exceptional circumstances, and it may be a long time before these circumstances arise. Freakishly high waves, in the case of a ship, and exceptionally severe upward gusts with aircraft are cases in point. Some structures are likely to be broken only by unusual combinations of events. For a bridge this might be the coincidence of very high winds with exceptional traffic loads. Although such eventualities ought to be provided for, it may be many years before they actually happen. So an essentially unsafe structure may stand for a long time, simply because it has never been fully tried.

  Responsible engineers do, of course, try to predict things of this sort and to make structural provision for them, but in many cases such peak loads shade off into what the insurance companies call ‘acts of God’.* If a ship runs into a large bridge, destroying both the bridge and the ship, as happened recently in Tasmania, it is very difficult to see what either the naval architect or the bridge designer could have been expected to do about it from the structural point of view. The problem is one not for the structural engineer but for the local Pilotage Association. Again, aircraft cannot be designed to be flown into mountains. We do, to a certain extent, design cars to be driven into brick walls without killing the passengers, but then we do not expect the car to be of much use afterwards.

  Metal fatigue, Mr Honey and all that

  One of the most insidious causes of loss of strength in a structure is ‘fatigue’: that is to say, the cumulative effect of fluctuating loads. The dramatic possibilities of fatigue in metals were first exploited in popular literature in 1895 in Kipling’s account of what happened when the propellor of the Grotkau dropped off somewhere in the Bay of Biscay because of a fatigue crack in the tailshaft.† Kipling went out of fashion, but public interest in fatigue was revived in 1948 by Nevil Shute’s No Highway. The success of this story, both as a book and as a film, was no doubt partly due to the character of Mr Honey, the archetypal boffin, but perhaps still more to the three Comet disasters, which occurred not very long afterwards. As Whistler remarked some time ago, Nature keeps creeping up on Art. The circumstances of the Comet ac
cidents were not very different from those imagined in No Highway, except that many more lives were lost and a great deal of damage was done to the British aircraft industry.

  As a matter of fact, engineers* knowledge of fatigue effects in metals goes back rather over a hundred years. Indeed it was not long after the Industrial Revolution that it began to be noticed that the moving parts of machinery would sometimes break at loads and stresses which would have been perfectly safe in a stationary component. This was especially dangerous in railway trains, whose axles would sometimes break off suddenly and for no apparent reason after they had been in service for a time. The effect soon came to be known as ‘fatigue’, and the classical researches on the subject were carried out during the middle years of the nineteenth century by a German railway official called Wöhler (1819-1914). From his photograph Herr Wöhler looks exactly what one would expect a German nineteenth-century railway official to look like; but he did a very useful job.

  As we said in Chapter 5, even though there may be a high local stress at the tip of a notch or a crack, the crack will not extend – so long as it is shorter than the ‘critical Griffith length’ – because making it spread requires work to be done against the ‘work of fracture’ of the material. However, when the stress in the material is a fluctuating one, slow changes take place within the crystalline structure of the metal, and this is particularly likely to happen in the region of a stress concentration. These changes have the effect of reducing the work of fracture of the metal in such a manner that the crack is able to extend, very slowly, even though it may be much shorter than the ‘critical length’.