Structures- Or Why Things Don't Fall Down

by J E Gordon

  Indeed it is the relative importance of the need for strength and for stiffness which really lies at the root of the question of the cost and efficiency of structures. Where the need is chiefly for rigidity rather than strength, the whole problem becomes very much easier and cheaper. This is nearly always the case with furniture and floors and staircases and buildings generally, and also with cookers and refrigerators and with many tools and heavy machinery and with some of the parts of motor cars. These things do not very often break, but, if we made the material much thinner, the deflections and bendiness and general wobbliness would soon become unacceptable. Thus, to be rigid enough, the various parts generally have to be so thick that the stresses in them are very low, often, from the engineer’s point of view, absurdly so.

  It follows that, in structures of this kind, even if the material is riddled with defects and stress concentrations, it probably does not matter Very much, and, what is more, the strength of the joints is unlikely to be critical; in many cases, a few nails may be perfectly adequate. This sort of thing is, of course, the basis of most people’s instinctive approach to design. Millions of people who have never heard of Hooke’s law or Young’s modulus can guess the stiffness of a table or a chicken-coop quite nearly enough by experience and common-sense, and, if such things are made stiff enough, they are very unlikely to break under their ordinary, everyday loads.

  Furthermore, a little bit of ‘give’ in some of the joints may be no disadvantage, and this is more likely to be available in a traditional joint than in a sophisticated one. For one thing a certain amount of flexibility may enable the loads to be evened out in a beneficial way. Although it is true that furniture does not very often get broken, quite a good way of attempting to do so is to sit on a chair, three of whose legs are on the carpet while the fourth rests, hopefully, on the bare floor. With traditional furniture the load may be spread over all the four legs by the distortion of the tenoned joints; in modern factory-made chairs with ‘efficient’ glued joints, these joints may just break, after which the chair is difficult to repair in any satisfactory way.

  Another reason for encouraging a certain amount of flexibility in joints is that wood, and sometimes other materials, change their dimensions with the weather. Wood shrinks and swells in the cross-grain direction by up to 5 or even 10 per cent. Traditional joinery allows for this by means of ‘inefficient’ slotted joints. In Churchill College we had a fine new High Table made from the best and most expensive wood, which had been scientifically glued together with strong, rigid joints. After a few months in the scientifically heated Hall, this table shrank and split down the middle. The result was not an unobtrusive little crack but a crevasse many yards long and quite capable of providing sheltered accommodation for large numbers of peas of normal or standard diameter.

  Strong joints and frail people

  Many deflection-controlled peasant structures are wholly excellent in their proper places but when we come to demand weight-saving and strength and mobility we may get into all sorts of difficulties, especially in relation to the reliability of the joints between the various parts. Historically, this has always been the most serious problem in ship construction and in windmills and water-mills. The great skill of the old shipwrights and millwrights lay in somehow combining sufficient strength for safety with the modicum of flexibility needed to allow for the ‘working’ of timber. The older shipwrights erred on the side of flexibility, and, though their ships were often excessively leaky, they seldom actually broke at sea. It required the administrative abilities of modern war-time governments to produce wooden ships which really did fall to pieces.

  Troubles with joints in ships and aircraft were a fairly prominent feature of both the World Wars. During the first war the Americans built a large number of wooden ships, both steam and sail, frequently by unorthodox methods; and many of these ships broke up. In the second war they produced even greater numbers of welded steel steamers, of which an even higher proportion broke, either at sea or in harbour. In England, in both wars, we manufactured very large quantities of wooden aircraft, which always seemed to be having joint troubles of one kind or another.

  As far as aircraft are concerned this was not wholly surprising, for I remember being shown, right inside vital glued joints in the main structure, on various separate occasions:

  A pair of scissors.

  A first-aid manual (pocket-size),

  No glue at all.

  On the whole I do not think that most of these accidents were caused by sub-normal or abnormal people; I am afraid the guilt generally lay with very ordinary people, and that was just the trouble. Naturally, people get tired or bored, but I think the root of the matter was much deeper than that. Very few of those who made, or failed to make, these joints had any personal experience of a situation in which the failure of a joint could cause a fatal accident, though collectively they had a great deal of experience of things like cupboards and garden sheds, where the strength of the joints really mattered very little. All our efforts to persuade them that a badly made joint was morally equivalent to manslaughter foundered on a deeply-held folk tradition that it was silly to fuss about such things and that strength is a boring subject anyway. All this would not have mattered so much if it had not been practically impossible to inspect the joints properly after they were made.

  In more recent years very efficient metal-to-metal adhesives have been developed which have a number of solid technical advantages, always provided that the joints are really conscientiously made. Unfortunately, their use in modern aircraft has been handicapped by the fact that it has proved necessary to provide a separate inspector to watch each worker throughout the gluing operation – also inspectors to inspect the inspectors. Rather naturally, these arrangements have proved expensive. In spite of all this, I am told that the use of glue in modern metal aircraft is increasing.

  Stress distribution in joints

  Since the function of a joint is to transmit load from one element of a structure to its neighbour, stress has somehow got to get itself out of one piece of material and then get itself into the adjoining piece; such a process is only too likely to result in severe concentrations of stress and consequent weakness. All the same, in a few favourable circumstances it may be possible to arrange for the stress to pass uniformly across the joint from one component to the other with little or no concentration of stress; this is more or less the case with a glued scarf joint in timber (Figure 1) and a butt-weld in metal (Figure 2).

  Figure 1. Glued scarf joint in timber.

  Figure 2. Butt-weld in metal.

  However, it is by no means always practicable to use scarfed or butt-welded joints, and some form of lapped joint between two adjacent planks or plates is probably more common. This sort of geometry at once introduces stress concentrations, and as far as a ‘rigid’ lapped joint is concerned it does not make much difference whether the joint is glued, nailed, screwed, welded, bolted or riveted. In all cases most of the load is transferred at the two ends of the joint (Figure 3).

  Figure 3. Load transfer in a lapped joint.

  For this reason the strength of such joints depends largely upon their width and very little upon the length of the overlap between the parts. This is why the simplest and commonest forms of riveted and welded joints between two metal plates (Figures 4 and 5) are reasonably effective and not much improved by complicating them.

  Figure 4. Riveted lapped joint.

  Figure 5. Welded lapped joint.

  Very often we want to provide an end attachment for a tension bar or rod to some kind of socket or solid anchorage; again much the same considerations apply, except that in this case there is only one stress concentration, which usually occurs at the point where the rod enters its socket (Figure 6). If the rod is screwed into its anchorage, for instance, nearly all of the load is taken out by the first two or three threads, and any extra length of rod within the socket will do little or no good. Thus the difficulty which a thrush has in
pulling a worm out of a lawn does not depend on the length of the worm; a short worm is just as hard to extract as a long one.*

  Figure 6.

  The distribution of stress which is shown in Figure 6 applies when the two components of the joint have similar Young’s moduli, which is usually the case with metal-to-metal joints. It also applies when the rod or tension bar is less stiff than the material of its socket or anchorage – which appears to be the case with worms and lawns. If the rod or bar is substantially stiffer than the material into which one is trying to anchor it, however, the stress situation may be reversed and the stress concentration may exist mainly at the bottom or inner end of the rod or insert (Figure 7).

  In practice, of course, both situations are likely to weaken the joint about equally. There may exist, perhaps, a ratio between the modulus of the insert and that of its surroundings which would give an optimum distribution of stress in the joint; but, if there is such a ratio, it is very difficult to hit it off in real life.

  At one time I was concerned with making point attachments between a reinforced plastic wing and the metal fuselage of an aircraft. Although I should have known perfectly well about stress concentrations and worms in lawns and so on, I was foolish enough to begin by moulding strong wire cables, with frayed-out ends – like the roots of a tree – into the body of the plastic. When specimens of this ill-conceived construction were loaded in a testing machine, the wires pulled out of the plastic with a succession of cracking noises and at ridiculously low loads.

  Figure 7. Load transfer in embedded rods under tension.

  In the next experiment sword-like tapered steel blades or prongs were substituted for the cables and were moulded into the plastic Wing structure after being coated with a suitable adhesive (Figure 8). This time the test-specimen failed, not with a series of cracking noises, but with one loud bang, but still at just as low a load.

  Figure 8. The wrong shape for a steel insert. This arrangement is weak.

  After a pause for reflection and intelligent thought about worms, we tried out a series of wide spade-shaped steel inserts which were much shorter and looked something like Figure 9. All these failed at far higher loads which were, in each case, proportional to the breadth of the ‘spade’. By developing this design we were able to take out loads in the region of 40 to 50 tons from plastic structures by means of quite a small steel fitting.

  Figure 9. The right shape for a steel insert. This is much stronger.

  Such joints depend entirely upon the adhesion between the metal and the plastic and must therefore be moulded conscientiously and under suitable inspection. They must also be designed with care, because, in all such cases, adhesion between a metal and a non-metal will fail completely as soon as the metal reaches its yield-point and ceases to behave elastically.* Since the stresses in the metal are much higher than one might expect, it is generally necessary to make the insert from high tensile steel, carefully heat-treated. Furthermore the ‘trailing edge’ of the steel insert must be ground sharp, like a chisel.

  Riveted joints

  ‘I’ve got one-fraction of an inch of play, at any rate,’ said the garboard-strake, triumphantly. So he had, and all the bottom of the ship felt easier for it.

  ‘Then we’re no good,’ sobbed the bottom rivets.’ We were ordered- we were ordered – never to give; and we’ve given, and the sea will come in, and we’ll all go to the bottom together! First we’re blamed for everything unpleasant, and now we haven’t the consolation of having done our work. ’

  ‘Don’t say I told you,’ whispered the Steam, consolingly;’ but, between you and me and the last cloud I came from, it was bound to happen sooner or later. You had to give a fraction, and you’ve given without knowing it. Now hold on, as before. ’

  Rudyard Kipling, The Ship that Found Herself

  Riveted joints in steel structures are rather out of fashion, chiefly because they are expensive but partly because they tend to be heavier than welded joints. This is a pity, because riveted joints have several advantages. A riveted joint is reliable and easy to inspect, and in a large structure it acts to some extent as a crack-stopper: that is to say, if a really large and healthy Griffith crack gets under way, it may quite often, though not infallibly, be stopped or delayed by the moat or discontinuity of a riveted joint.

  Even more importantly, riveted joints can slip a little and so redistribute the load, thus evading the consequences of the stress concentrations which are the bane of all joints. The process has been described for all time in The Ship that Found Herself, and indeed Kipling’s feeling for the problems of stress concentrations and cracks in structures, many years before Inglis and Griffith, is very remarkable; some of his stories about structures might well be required reading for engineering students.

  Because each individual rivet can slip very slightly, the worst effects of stress concentrations may be reduced, and so it may be worth while to make lap joints having several rivets in series, since the end rivets may be able to slip enough to enable those in the middle to do some work. 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.

  Figure 10. Three of the ways in which a riveted joint may fail.

  (a) Failure by shearing the rivets.

  (b) Failure by tearing the rivets out of the plate (i.e. by ‘bearing’ or elongation of the holes).

  (c) Failure by tearing the plates.

  When rivet holes are made in large steel structures, such as ships and boilers, it is usual to punch them. Although this is a quick and cheap way of making holes in steel it is not entirely satisfactory, since the metal at the edge of the hole is left in a brittle condition and also often contains small cracks. Since there will certainly be stress concentrations in this region, this is not a good state of affairs. For this reason, in high-class work, it is usual to punch the holes under-size and then ream them. Although this adds to the expense, it also adds materially to the strength and reliability of the joint.

  Both riveted and bolted joints can be made in all sorts of different shapes and sizes but, broadly speaking, all such joints have a choice of three different ways of failing (Figure 10): (a) by shearing or breaking off the rivets themselves; (b) by tearing the rivets out of the plate (i.e. by ‘bearing’ or elongation of the holes); or (c) by breaking the material of one of the plates in tension between the rivets, like tearing off a postage stamp.

  It is generally necessary to check the possibilities of failure by each of these three mechanisms by doing a suitable calculation. However, ‘rules’ for the design of riveted joints are laid down by organizations like Lloyds and the Board of Trade, and these are to be found in nearly all the engineering handbooks.

  Welded joints

  Welded joints of all kinds are very widely used in steelwork today, mainly because welding is generally cheaper than riveting and also because there is some increase in strength and saving in weight. In ships, too, the absence of rivet heads below the water-line reduces the resistance by a small amount.

  Most sophisticated welding is electric arc welding. In this process the welder holds a metal rod, the welding rod, in his right hand by means of an insulated clamp. With his left hand he generally holds a mask or screen, furnished with very dark glass, through which he can safely watch the arc, which he ‘strikes’ and holds between the tip of the rod and the seam which he is making. At the usual 30-50 volts the arc is perhaps a quarter of an inch (7 mm) long and results in the transference of metal from the end of the welding rod to a little pool of molten steel which the welder coaxes along the joint. The result is, or should be, a con
tinuous run or ‘leg’ of weld metal, about a quarter of an inch (7 mm) wide, which solidifies and bridges the joint. If a greater thickness of weld is needed, then the run must be repeated as many times as may be necessary.

  If the weld has been properly made it is generally very strong and satisfactory, but any lack of skill or attention on the part of the welder is likely to result in defects, such as slag inclusions, which weaken the joint and are not readily seen by an inspector. It is also easy for a clumsy welder to overheat enough of the surrounding metal to cause serious distortions. This is especially the case where the work to be welded is heavy and thick; the welded engine-seatings in the pocket battleship Graf Spee, for instance, gave serious trouble from this cause.

  In theory a welded joint in a tank or a ship should be completely watertight without further treatment, but this is seldom the case; in practice welded construction is likely to give more trouble than riveted work in this respect. A riveted lap joint is easily caulked by spreading the edges of the plates by means of a pneumatic chisel or caulking tool. This cannot be done with a welded joint, and the best way of dealing with the situation is to inject some kind of liquid sealing compound under pressure into the space between the two welds of a lap joint. All the same, I remember seeing much trouble in connection with the water-testing of compartments in welded warships.

  Once upon a time I had the privilege of working for a few weeks as a riveter and also as a welder in one of the Royal Dockyards, and during this time I learnt various things which I do not think are in the text-books. Although closing a two-inch rivet in an armoured deck with a pneumatic hammer is both hard and noisy work, it is also curiously interesting, and most forms of riveting seemed to me to have at least some of the attraction of golf with the advantage of being more useful. A further sporting element was added by the operation of the inspection process; in those days we were paid at the rate of so much for every rivet closed, but five times so much was deducted for every rivet which was condemned by the inspector and had to be drilled out and replaced.