Developing  the  Beam

Both shapes match the curve of bending moment for a uniform weight distribution, which is roughly what they have, so these are good forms.

Beam Sections

Besides the truss or bowstring arch, there is another approach to getting material into the right place. This is to use an I beam or a tube. Stephenson’s Menai bridge has already been mentioned. A rectangular tube is suitable when the forces are always vertical, but if they may be in any direction, as with a mast or a reed in the wind, a circular cross-section is better. In the Menai bridge the horizontal parts were not simple plates, but cellular, so Stephenson had produced an early example of box construction.

A box girder need not have a rectangular cross-section – the sides may slope in order to improve the appearance or the  structural behaviour, or a footpath or a part of the road may be cantilevered out or supported on brackets. Anything that can reduce the apparent bulk may be worth doing. The diagrams below show some possible cross-sections for beams.

These two pictures show curved beams carrying the M5 motorway along the side of a valley south west of Bristol. The two carriageways are at different levels, to keep the piers to reasonable heights.

Beam Railway Bridges

Let’s spare a thought for the humble railway bridge. Many British towns have one, even if the railway has long been disused. Some are brick arches, occasionally of the skew variety which always create interest. Others are beams, often comprising two vertical plate girders with flanges top and bottom. Sometimes these flanges are thicker towards the middle. This is achieved by riveting a series of plates of several different lengths to the main plate. There are often vertical flanges at intervals along the span.

Spanning the gap between the two main plate girders there will often be a series of I-beams. And across the spaces between these the older bridges often had a series of small arches, supporting the floor of the bridge. Later bridges may have some kind of slabs, a construction which is often used when a beam bridge carries a motorway.

In older times, people would not have been able to calculate the stresses at every point in such a bridge. For short spans they would have used the knowledge gained from earlier experience.

A Footbridge Over the Seine

This footbridge spans the river Seine in Paris. This is a very long narrow beam indeed.

A Small Beam Over the Thames

The designer of this bridge, with a span of about five metres, only about four miles from the source of the river Thames, was taking no chance with the force of the river when he designed the cutwater. Definitely over the top, as the water is only a few inches deep, and unlikely to flow very fast, even when flooded, and the fall from the source is very slight.

An elegant Beam

This bridge is built on a skew with the road, but is in fact symmetrical.  Note the shape of the end walls, reducing the tunnel effect, the twin beams, and the large overhang of the deck at each side. A tidy design.

The diagrams above represent a simple beam bridge, which has been affected by subsidence (exaggerated). One response is for the beam  to remain so straight that it is only supported in two places, leading to a bigger effective span. Another is for it to bend. A third would be to break, if either of the first two conditions were unsustainable by the structure.

In practice the designers might include jacks at the base of the piers, to allow for adjustment.

What happens as a result of the movement is that the beam suffers stresses which were not in the design. In fact the problem exists from the start.

The four support points can never be perfectly aligned, but the alignment is of course made so small that the beam can adjust its shape without absorbing too much energy.

The penalty for a through beam, is the over-determined status. The benefit is the spreading and controlling of loads and stresses.

The diagram above represents the response of a simple cantilever bridge to subsidence. In this case the joints allow stress-free movement, so nothing is distorted.

Jacking might still be provided. In a very slender foot-bridge, the slightest error could be noticeable, and so some adjustment may be needed.

After a bridge has been completed, jacks may be concreted over, or they may be left as usable adjusters. The Eiffel tower is a good example of the jacking requirement. The stresses, and therefore the strains, at the base, changed markedly during construction. Jacking enabled the builders to compensate.  This subject is developed further in Indeterminacy.

In a multi-span beam bridge, the deflection between the supports can be reduced by joining the spans, as mentioned earlier. Better still, by pre-stressing the spans, the deflection can be made even smaller. Robert Stephenson did something like this in the Britannia bridge across the Menai Strait.

The diagrams below suggest crudely how this works. At the bottom is a set of separate spans. At the top is a set that have been joined. The middle diagram is the result when the temporary supports are removed.

A Multi-span Beam

The A417/A419 from the M4 to the M5 provides a dual carriageway for most of the route. A tremendous effort has been made throughout in order to create an attractive route. Some farm land had to be purchased, and some old Cotswold walls had to come down. Some were already old and crumbling. In return, the road builders have preserved a well-known wind break near Duntisbourne, they have planted large numbers of saplings, and they have built miles of new Cotswold walls.

The designs of the new bridges are as attractive as possible, given the technical requirements, and the whole route is a good example of modern construction.

Near Baunton in Gloucestershire, an interesting beam bridge crosses the valley of the river Churn, north of Cirencester, carrying the A417(T).  This part of the route is a bypass of Cirencester, which relieved that town of through traffic, and took as much as fifteen minutes off typical journeys. The pictures below show this bridge from below. The line of the road is slightly curved in both dimensions, and the bridge is a continuous beam.

Crossing this valley, including the tiny river Churn, presented the problem of appearance. The actual construction tends to obscure the view of the valley from the road. Let’s look at this in some detail.

Firstly, the valley is barely visible from the road in most of the route, because of trees and hedgerows. That it is visible here may be partly due to the effects of construction work. Within a few years, trees will have grown up to hide the valley from the road. So it could be argued that the view doesn’t matter very much.

Secondly, what is the intention when building such a bridge? If we want to make the bridge as inconspicuous as possible, we can build it on very narrow piers. If this had been done in this case, replacing each pier by two narrow ones, making four at each position, there would have been a good view through the bridge, but the effect of all these piers would have been very untidy. Obtaining an ordered appearance from all directions is an almost insoluble problem with a two-dimensional array of piers. The other difficulty would have been the avoidance of a top-heavy appearance.

Another possible solution would have been to have one pier at each location, on the centre line of the road. The very wide beam would have had to be very stiff indeed to carry torsional forces to the abutments, increasing the cost of the structure. Alternatively, these single piers could have been splayed at the top to provide paths for the asymmetrical forces.

At the other extreme, solid walls would have produced a very heavy effect. The actual design balances the mass of the beam and the piers very well, and the hints of gothic curves echo those of the nearby Cirencester church and Gloucester cathedral. The view across the valley is more or less blocked, but was not especially inspiring in any case.  In a few years’ time, most of the bridge will probably be hidden by the growing hedge and trees.

The river Churn, which lies at the bottom of the valley, is only a few metres wide at this point. The pictures show it a few miles downstream as it reaches Cirencester. Fairly soon after Cirencester it is joined by the little river Thames. The names Churn and Cirencester probably echo the Roman Corinium, an important fortified town. The A417/A419, apart from the new bypasses of Cirencester and Latton, follows the old Roman road, later called Ermine Street, quite closely. Comparing a map of Roman roads with a modern map shows that the routes of many Roman roads can still be traced via modern roads, tracks and footpaths. The influence of the Romans on our language is also enormous. On the road we may come across words such as bus (omnibus), car, engine, entry, exit, logistics, traffic, trailer, transport, and vehicle, all derived from Latin. The Corinium museum in Cirencester offers an excellent insight to Roman life in Britain.

Just south east of this bridge, a minor road, the Whiteway, crosses the bypass. At this point, as on the other side of the Churn valley, the A417 is in a cutting, to reduce the gradient down to the Churn bridge, and to reduce the height of that bridge. The typical bridge in this situation would have been a simple concrete beam or cantilever type, but what we see is apparently a flat arch, faced attractively with Cotswold stone. But as we pass underneath, we see that the arch is only a facade, and that the bridge is a concrete beam. In fact, under the right hand side of the bridge, you can see a part of the sloping haunch.

Is it a fraud? Well, it looks a lot better in that location than a grey concrete bridge would have done. It avoids the concrete piers that would have blocked the view of the cutting, and it generates a lot less thrust than a real flat arch would have produced.

This picture, looking north from the small over bridge, shows the deck of the big beam in the distance. We can see the slight curvature of the bridge. On each side of the road, on both sides of the bridge, the Jurassic limestone is cut into steps, to improve the appearance of the cutting, and to provide footholds for the growth of vegetation, as the second picture shows. No doubt the fissures in the rocks will provide shelter for a wide range of invertebrate and vertebrate life. Kestrels are a common sight over verges, and the occasional buzzard is seen on a fence on days when thermals are not forthcoming.

These are just a few examples of the thinking that lies behind the A417/A419 link road.

In more mountainous areas of the world, road building is much more expensive, and roads may contain many bridges and tunnels per 100 km, because of the need to keep gradients low on fast routes. The picture shows an example of a type of beam bridge which is found, with numerous differences of detail, in many places. In landscapes which are on a huge scale, a structure which might be considered intrusive in a smaller location may even add to the grandeur of the scene.

Another  Beam  Bridge

This footbridge crosses the A34 at Chilton. Since we have seen that a beam requires only two hinges as supports, the extra two here can be used to control bending moments. This bridges exhibits the use of completely unadorned grey concrete to create a simple and elegant structure. But what if this treatment is applied to buildings, such as apartment blocks or universities (for example the university of Essex)?

The pictures below show some of the possibilities for bridges that look similar to this one, by making cuts in the beam. In each case, what are the advantages and the disadvantages of the design as compared with the actual one.

The original design

Two cuts create three arch-like spans with cantilever extensions.

Two cantilevers and a beam

Two cantilevers and two beams

 A Different Type of Bridge

How does this bridge over the M11 motorway differ significantly from the one we just looked at, even though looks rather similar?

The topography of Japan, and its division into islands, has led to the building of many spectacular bridges, including some of the longest in the world, in order to achieve speedy travel between all regions of the country by rail and road.

But the first bridge depicted here typifies an earlier purpose, when a bridge in a garden would be designed to make sure that people stopped to view the garden at certain points. This one, in the Manyo Botanical Garden in Nara, has different levels, as well as a zig-zag.

The second picture shows a simple beam bridge in the same garden.

More Japanese Bridges

Many old Chinese and Japanese beams are curved quite strongly, but have supports that show them to be beams and not arches.

The Japanese Garden – Islands of Serenity     Photographs by Haruzo Ohashi –

    Graphic-Sha – ISBN 0-87040-731-7

Creating Japanese Gardens –  Phlip Cave – Aurum – ISBN 1-85410-423-3

A Helical Staircase

Each step of this elegant helical stair is a simple beam. Simplicity so often goes with good design.  This is in an old farm building in Tuscany that has been converted into a holiday apartment.

The helical stair has been a popular way of getting steps into a small space since medieval times. If you climb the tower of an old cathedral or church you will almost always find yourself inside a narrow cylinder of stone, with stone beams bridging the space between a centre pillar and the wall. These beams keep the pillar straight, in spite of its height, and the pillar supports the beams in the vertical direction.

Bridges, and other structures too, are made by army ants, using their own bodies, to allow colleagues to cross a gap. When the Herald of Free Enterprise rolled over near Zeebrugge, a very brave and altruistic passenger lay across a gap to allow others to escape. A fictitious living bridge is described in "Dr Doolittle’s Post Office", by Hugh Lofting. In this episode, the good doctor is privileged to see the "bridge of monkeys", which is rarely seen by people. This bridge was actually a suspension bridge, rather than a beam.

Definition of a Beam

After looking at this page, what do you think a beam is? This web-site is not intended as a text-book, and is not arranged in the logical fashion of a text-book. Although structures can be classified broadly into different basic types, in practice, few structures are pure examples.

Let’s look at beams.  How’s this for a description of a "pure" beam? 

A beam is a structure that is able to resist bending, without imposing bending moments or longitudinal forces on its supports. In other words, it can create within itself all the forces it needs, apart from those provided by the supports, to hold it up. Many larger beams are constructed in the form of trusses, which have their own page.

Many real structures are far from being "pure", but the ideas like "arch", "beam" and "truss" are useful in learning to understand. Conversely, many elegant structures have been made by combining features of different types.  Look at some structures and work out what is going on in them.

Conclusion

Often comprising an apparently simple series of rectangles, the beam, as we have seen, conceals many subtleties, its lines of force even simulating both arch and suspension  bridge, or lenticular truss, as Brunel revealed in his Royal Albert bridge. And we barely looked at the effects of live loads.

This multiplicity of ideas, and the complexity of the forces, is not an uncommon occurrence. Many ideas in science are in themselves very neat and simple, but not the consequences and the working out. Examples are Newton’s law of gravity, Darwin’s theory of natural selection Einstein’s relativity theory, and Dirac’s electron theory. But even today, there is no way of calculating exactly the orbits of three gravitating bodies – only approximations are possible.

The truss looks far more complex, but with narrow members the paths and magnitudes of all the forces are fairly simple to work out. The penalty is the multitude of attachments, where the forces have to change direction very sharply, as undesirable here as hairpin bends on a road.

You could say, fancifully, that inside a beam there are other types of bridges waiting to be released, just people sometimes think of a sculptor releasing a statue from a block of stone. Whether we use these other types is a matter of economics. In a small bridge it just isn’t worth designing all those parts and connections and then joining them all together. But on a very large scale, we are forced into the more complicated design by sheer weight: as Galileo rightly said, simple scaling does not work.

Since the living world was here before the works of people, we could finish on that note. Because of the growth of plants from seed, into the air and into the soil, most plants are like cantilevers, but in the animal world the beam comes into its own. The backbone of almost any quadruped is rather like a beam, perhaps a pre-stressed one, from which much else is suspended. But when you see the wonderfully elegant economy of the trotting rhinoceros, or the alternate storage and release of energy in the dashing cheetah, you see a glimpse of an incredibly complex system, for which the term beam is utterly inadequate. 

The information processing, chemistry, engineering and physics that are needed are all beautifully integrated into creatures that are good compromises between the conflicting requirements of its life and surroundings. But if these surroundings change faster than evolution or migration can cope with, there will eventually be one last member of the species who will find itself in the position of the last glass bead game player. And if the world changes more slowly, each species will vanish as it evolves into others. Can any species last for ever?

If you got this far, try a superb game about bridge building – http://firingsquad.gamers.com/games/pontifex/default.asp .