Structures- Or Why Things Don't Fall Down

by J E Gordon

  Both the public and the experts were horrified, and the papers were full of letters prophesying that the bridge would never stand. To keep the correspondence and the publicity going, and perhaps to gratify his sense of humour, Brunei delayed removing the wooden centering or false-work on which the arches had been erected. Naturally, it was said that he was frightened to do so. When, after about a year, the centering was destroyed in a storm, the arches stood perfectly well. Brunei then revealed that the centering had, in fact, been eased to a clearance of a few inches soon after the brickwork was in place and had been doing nothing at all for many months. The bridge is still there today, carrying trains about ten times as heavy as Brunei ever intended.

  When we flatten the shape of an arch, so as to reduce the rise in proportion to the span, the compressive thrust between the voussoirs of the arch-ring is considerably increased, as we should expect. However, the compressive stresses are still, as a rule, well below the crushing strength of the masonry, and the voussoirs of the arch are seldom in any danger of being broken, although the deflections which occur when the arch settles after the centering is removed may be quite large and often amount to several inches.

  Any real damage to a ‘flat’ arch, however, is most likely to be a consequence of the greater thrust which must come upon the abutments. If the foundations are of a solid material, such as rock, all will be well, but if they are upon soft ground there may be serious trouble if they yield too much. Unfortunately, the need for a long, flat arch is most likely to occur when we are bridging rivers which flow across a level and boggy couiitry.

  It is for these reasons that bridges are often built with many small arches; in fact nearly all long medieval bridges are multi-arch bridges. The objection to this way of doing things is that the cost of building the supporting piers – usually under water and often on soft ground – is high, and, furthermore, the numerous piers and narrow arches obstruct the channel and may cause floods and danger to navigation.

  Cast-iron bridges

  Some of the objections to arched bridges can be got over by making them from less traditional materials. By the 1770s people like John Wilkinson (1728-1808) – who had greatly cheapened the manufacture of cast iron by improvements to blast-furnaces – began to cast voussoirs from iron. Cast iron is a totally different kind of material from wrought iron and steel because, unlike these substances, it is very brittle. It resembles stone in being strong in compression but weak and unreliable in tension, and so, in building construction, it has to be treated rather like masonry.

  An advantage of cast iron is that it is possible to cast architectural members, such as voussoirs, in the form of an open, trellis-like framework, so that there can be an enormous reduction in weight, as compared with traditional masonry. Furthermore, it is generally cheaper to cast iron than to carve stone, and, before taste degenerated around the time of the first Reform Bill, these iron castings were often of very attractive shape.

  The benefit of cast iron to bridge-building was two fold. In the first place, there was a saving in labour and transport costs; but more significantly the reduction in the weight of arches diminished the magnitude of the thrust upon the abutments and thus enabled engineers to build flatter arches with cheaper foundations.

  Curiously, one of the first people to take advantage of this technique was the American Thomas Paine (1737-1809), who is famous in the history books as the author of The Rights of Man. Paine planned to build a great cast-iron bridge, which he had designed himself, across the Schuylkill river, near Philadelphia. He came to England to order the castings, and while they were being made he decided, as a supporter of the French Revolution, to pay a visit to his Jacobin friends in Paris. These gentlemen put him in prison and very nearly guillotined him. He was just saved by the fall of Robespierre.

  As a result of the delay, Paine’s finances collapsed and the castings were sold off to build a bridge over the Wear at Sunder-land. The arch, which was finished in 1796, had a clear span of 236 feet with a rise of only 34 feet. The reason why Brunei did not use cast iron for the Maidenhead bridge forty years later was probably that he was afraid that the vibrations of the trains would crack the brittle cast iron. In any case, his brick arches worked very well.

  During the nineteenth century a great many cast-iron arch bridges were built. Although nearly all of them were successful, the method is scarcely ever used today, chiefly because there are now cheaper ways of doing the same job. Unfortunately, a very flat cast-iron arch looks, superficially, rather like a beam (see Chapter 11). Structurally the two are quite different, since the arch is, or should be, entirely in compression, whereas the underside of a beam is in tension. T/’the material can be relied upon to carry tensile stresses, then a beam is often lighter and cheaper than an arch, for a comparable service.

  Some of the early engineers, notably Robert Stephenson (1803-59), were tempted by this prospect of economy to venture into using cast-iron beams. Because of Robert Stephenson’s outstanding professional reputation the railway companies were persuaded to build several hundred cast-iron beam bridges. However, as we have said, cast-iron is weak and treacherous in tension, and these bridges turned out to be very dangerous indeed. In the end, every one of them had to be replaced and the expense to the companies was naturally severe.

  The arch bridge with suspended roadway

  A modern tendency in building large arch bridges is to use a suspended roadway. If we split the arch-ring into two parallel elements, which are made from steel or reinforced concrete, then we can hang the roadway from the arches, at any level we like, in much the same way as is done in suspension bridges (Figure 1). There is then, of course, no restriction on the rise of the arch.

  Figure 1. Arch with suspended roadway.

  The Hell Gate bridge in New York (1915), which is 1,000 feet (300 metres) span, and the Sydney Harbour bridge (1930), which has a span of 1,650 feet or 500 metres, are steel bridges of this type. In such bridges the main loads are carried entirely in compression in the arches, and the hanging roadway is free from longitudinal stresses. In big bridges the thrust upon the abutments is therefore considerable, and very reliable foundations are needed. Both the Hell Gate and the Sydney Harbour bridges are founded on solid rock.

  Suspension bridges

  Masonry arches have a number of advantages. As we have seen in the last chapter, they are comparatively easy to design, since one can generally scale up from previous experience quite safely. In fact, as Professor Heyman remarks, it is very difficult to design an arch which will actually fall down. This feat was, in fact, achieved by a certain William Edwards at Pontypridd in 1751, but I do not think there is any record of its happening since. Again, arches are not unduly sensitive to a reasonable amount of movement in the foundations. However, foundations of some sort there must be; and on soft ground they have a way of being both troublesome and expensive.

  Furthermore, although the maintenance cost of masonry is usually low, the first cost has always been high, and this is particularly the case with large bridges, which need elaborate centering during erection. For these reasons there has always been a demand for something cheap and cheerful in the bridge line. In primitive countries suspension bridges of various sorts were fairly common; these were made from rope or other kinds of vegetable fibre. Rope suspension bridges were also used by military engineers for temporary bridging, notably by Wellington’s sappers during the Peninsular War.

  However, although rope is a strong and reliable material for carrying tension when it is new, ropes made from plant fibres deteriorate fairly quickly in the open and become undependable -as the more interesting personalities in the neighbourhood of the bridge of San Luis Rey discovered.* For a permanent suspension bridge, cables of iron or steel are necessary. Cast iron was far too brittle and steel was not commercially available until relatively recently, but wrought iron is fairly strong and very tough; also it is exceptionally resistant to corrosion.

  Although a footbridge 70 fee
t (20 metres) long, made with iron chains, was erected over the Tees in 1741, wrought iron was generally too expensive to be used at all widely in bridge-building until the puddling process† was introduced about 1790. After this, wrought-iron chains became comparatively cheap. In the Tees bridge the flooring was attached directly to the chains in the primitive manner, so that the bridge was impassable to vehicles and must have been both steep and alarming for pedestrians. The modern system of supporting the cables from high towers and hanging the roadway below the cables (Figure 2) was invented by James Finlay, of Pennsylvania, who began to build bridges of this kind around 1796.

  Figure 2. The modern form of suspension bridge, with a level roadway hung from the cables, was invented by James Finlay about 1796.

  The combination of a suspended, level roadway with the availability of wrought-iron chains at a reasonable price made the suspension bridge an attractive proposition for carrying wheeled traffic over wide rivers. For many situations these bridges were much cheaper and more practical than large masonry bridges. The idea was taken up very actively in many countries, and especially by Thomas Telford, whose bridge across the Menai Straits (Plate 11) was finished in 1825; it has a centre span of 550 feet (166 metres), by far the longest then in existence.

  Telford’s chains, like all the suspension chains used in bridges at that time, were made from flat plates or links, joined by bolts or pins, very much like the links of a modern bicycle chain. The concentration of stress at the pin joints calls for a tough and ductile material, such as wrought iron, and indeed chains of this type have been very successful and have seldom given any trouble. Although wrought iron is reliable in tension it is not especially strong, and Telford wisely kept the highest nominal stress in his chains down to about 8,000 p.s.i. (55 MN/m2), which is less than a third of the breaking stress.

  In these circumstances a great deal of the strength of the chains was devoted to supporting their own weight, and Telford was of the opinion that the Menai bridge represented about the maximum safe span for a suspension bridge, using the materials of the day. Although Brunei eventually showed that Telford was being rather cautious – Brunei’s Clifton bridge has a span of 630 feet or 190 metres – yet for many years the span of the Menai bridge remained a record; and, in any case, the limitations of wrought-iron chains were clearly within sight.

  The recent fashion for road suspension bridges of great length is made possible by the availability of high tensile steel wire. This material is very much stronger than wrought iron or mild steel and can therefore support a much greater length of its own weight. High tensile steel is more brittle than wrought iron, but this can be accepted, since the cable is continuous and does not have to have links with pinned joints, which are particularly vulnerable to cracking. Again, instead of having only three or four plate links in parallel with each other in each element of a chain cable, the wire cables are woven from many hundred separate wires, so that the failure of any individual wire is not likely to be dangerous (Plate 12).

  As an example of the sort of thing one can do nowadays, the new Humber motorway bridge has a clear span of 4,626 feet (1,388 metres), which is over eight times the length that Telford thought practicable. This is made possible by the fact that the suspension wires operate, quite safely, at a working stress of 85,000 p.s.i. or 580 MN/m2, which is more than ten times the stress in Telford’s wrought-irdn chains.

  Thrust lines in arches and suspension bridges

  The cables of a suspension bridge take up the best shape automatically, because a flexible rope has no choice but to comply with the resultant of all the loads which are pulling on it. We can therefore determine the shape of the cables for a suspension bridge either by loading a model of it, as Telford did, or else by means of a fairly simple exercise with a thing called the ‘funicular polygon’ on the drawing board. This is useful in designing suspension bridges – for instance we need to know the right lengths for the hangers for the roadway – but it is also useful in designing arches.

  If we look at a suspension bridge and then at an arch, it does not need much imagination to see that the suspension bridge is really an arch turned upside down – or vice versa. In other words, if we change the sign of all the stresses in an arch, that is, if we turn all the compressions into tensions, then these tensions could be carried by a single curved rope, which may be regarded as defining a ‘thrust line’ in tension. By doing this we can arrive, comparatively painlessly, at the compressive thrust line for an arched bridge or a vaulted roof.

  When we do so we may get various shapes of thrust line which will vary a bit according to the details of the loading, for instance the presence or absence of traffic on the bridge. Any of these thrust lines will be safe, provided that it lies wholly within the intended shape of the arch-ring; if not, not. It is sometimes said, by slightly superior people, that the thrust line of an arch obtained in this way has the shape of a catenary, and that a round arch is therefore ‘wrong’. This is by no means always the case, and in many instances the thrust line is quite near enough to an arc of a circle to justify the Romans in their highly durable semi-circular arches. However, if one wants to make a really thin arch – as is the custom with modern reinforced concrete bridges – then one had better get the shape just right, for there is very little room for the thrust line to wander about.

  The development of the bowstring girder

  Although the suspension bridge got off to a flying start at the beginning of the nineteenth century, its development was interrupted for about a hundred years by the coming of the railways. Most of the 25,000 major bridges which were built in England during the Victorian era were railway bridges. The suspension bridge is a highly flexible structure, and it is liable to deform dangerously under large concentrated loads. This characteristic does not matter very much for road bridges,* but trains are generally about a hundred times as heavy as carts or lorries, and so the deflections they cause are likely to be a hundred times as great and therefore unacceptable. The few railway suspension bridges which were built in England were conspicuous failures. The Americans, who had wider rivers, and at that time less money and more faith, persisted with them for a while but had to give most of them up in the end.

  There was therefore a need for bridges which were not only light and cheap but also rigid and suitable for large spans. This led to the development of what is called the ‘tied arch’ or ‘bowstring girder’ (Figure 3). An arch, of course, is pretty rigid, but it thrusts outward on its abutments with a very considerable force. This may not matter if these abutments consist of nice firm rock, but it is awkward in many of the situations which may arise in railway construction. It is particularly inconvenient if it is required to perch an arch, or a series of arches, on top of tall and slender piers which may be in no position to resist large lateral loads.

  Figure 3. The bowstring girder, or tied arch, relieves the abutments of lateral thrust. It was popular with Victorian railway engineers.

  However, this is just what the Victorian engineers so often wanted to do, for they frequently carried their railways boldly across deep valleys, sometimes at a height of 100 feet or more. One way of solving the problem is to tie the two ends of the arch together by means of a tension member. This can be done by using a suspended roadway, which in this case is made to work for its living: the roadway itself is put into tension.

  The bowstring girder looks superficially like an ordinary arch with a suspended roadway, but its manner of working is quite different. Now there is no sideways push or pull upon the foundations, which have only to support the vertical downward load arising from the actual weight of the girder and any vehicles which may be on it. In fact the whole affair can be mounted on rollers instead of on rigid foundations, and this is often done, mainly to allow for thermal expansions and contractions in the metal. Since such girders produce no lengthwise thrust, they can be mounted on top of relatively narrow masonry columns.

  The fact that a bowstring girder can be treated
as an integral, self-contained unit may greatly facilitate the construction of a large bridge, because it is possible to assemble the girders at ground level, on some site away from the bridge itself. They can then be floated out to the piers on rafts and raised into position by means of jacks. This is just what Brunei did with the spans of the Saltash bridge. As we shall see in the next chapter, the tied arch is really yet another member of the prolific family of ‘trusses’ or lattice girders with which structural engineering is so thickly populated.

  * * *

  * At the Roman fort at Lowbury Hill, in Berkshire, a mile or so from where I am writing this chapter, the body of a woman was discovered concreted into the foundations. The practice has lasted into modern times. In 1865 it was alleged that in Ragusa Christian children were being kidnapped by Mohammedans in order to immure them in the foundations of fortifications. Even in England, as late as 1871, a certain Lord Leigh was seriously suspected of having built an ‘obnoxious person’ into the foundations of a bridge at Stoneleigh in Warwickshire.

  * The Bridge of San Luis Rey, Thornton Wilder (1927).

  † The New Science of Strong Materials, Chapter 10.

  *All Telford’s bridges were road or canal bridges. The Americans made fairly extensive use of suspension bridges for canal aqueducts; the water channel was carried in a suspended wooden flume. Naturally there was no change of net load – and therefore no change of deflection – when a barge passed over the bridge.