archtwoc

An Unusual Arch at Ross-on-Wye – Wilton Bridge

This bridge over the river Wye at Ross-on-Wye is built of red sandstone. It has a very unusual feature. Instead of the voussoirs having the normal slightly tapered trapezium shape, every one of them has a zig-zag shape on both sides. One of them has been outlined in white to show this more clearly, as the photograph is poor, because of the flat lighting.

An enlargement is inset at the lower left of the picture. It is as if the designer thought that there could be shear between each voussoir and its neighbours. This should not, of course, happen in a well designed arch.

Here is another picture taken with more favourable lighting, showing the erosion of the old red sandstone. Lighting can be very important if you want to reveal features of a structure.

Here is a picture of one arch. Note the flood relief arches in the distance, under the Ross-on-Wye bypass A40. The river Wye and the river Severn are very prone to flooding, which has caused great damage in several recent years.

Perhaps the designer had experienced a problem with a previous construction, and was trying to make sure that nothing could go wrong. If these shapes are to achieve anything, the stone must experience both shear and tension. What structures can exist which experience no shear and no tension? This bridge has very large cutwaters, perhaps because the Wye in spate has a very fast flow. A refuge for pedestrians is provided over each cutwater.

Here are two more pictures of the Wilton bridge at Ross-on-Wye. The piers are very wide, and the bridge presents a significant obstacle to the flow.

Ribblehead Viaduct

The magnificent Ribblehead viaduct seen (just about) from near the summit of Ingleborough. This how not to do it – on a very dull, very windy day, without a filter, without a tripod, from too far away. This viaduct is a fitting construction for the locality. If you look up the height of Ingleborough you will probably not be impressed. Don’t be fooled, it can be a very wild place. The wind from the Atlantic Ocean can whip across the summit plateau so fast that you cannot walk against it: in those conditions, to go upwind, you have to crawl. These pictures were taken from the edge of the plateau.

Newcastle arch under construction This link is to a photograph showing how an arch can be constructed in two halves, each held back by cables. This avoids expensive falsework and keeps the navigation channel open during construction.

Gothic Arches

The points of Gothic arches, like the pointed tops of Sydney opera house, do not seem to correspond to anything in the loading. Like the pointed arches found in many other beautiful buildings, they remind us that functionality includes the function of pleasing the eye and the mind.

What is the correct shape of an arch? The Romans always used semicircles, but this cannot be the correct shape for a bare arch of voussoirs, because at the two ends the curve is vertical, providing no provision for containing the outward thrust of the arch.

The theoretical shape for a set of uniform voussoirs would be a catenary, the same shape as a hanging cable. But when masonry or other loads are added above the voussoirs, the weight distribution and the added stiffness can allow many different shapes. In fact the masonry spreads the load, so the effect of any live load will probably not move the thrust line as much as if it were applied direct to one voussoir.

The pointed arch was used in a great number of medieval bridges as well as buildings.

So the shapes of arches vary considerably. Brunel built two very flat elliptical brick arches at Maidenhead, for the Great Western Railway. They are still in use. The illustrated bridge carries a road.

Three Hinged Arch

As mentioned earlier, arches may include up to three hinges. If an arch departs from the optimal shape it will require some form of stiffening to transmit the bending moments. The arch shown here is a three-hinged reinforced concrete arch over the M6 at New Hall in Lancashire. Effectively the ground and the two halves of the bridge form a triangle, which is a stable shape. A fourth hinge would render the structure unstable.

The span of this reinforced concrete arch is about 150 feet/46 m. Arches can be built with three hinges, two hinges, one hinge, or none at all, as in traditional masonry arches.

What about bridges like this? Are they too far from the usual arch shapes to merit the name? This is a three-pinned footbridge with helical ramps.

These ramps are a visually interesting solution to the difficult problem of integrating ramps with footbridges. In a town there would not often be room, and straight or zig-zag ramps would be used.

Here are departures from the funicular in the opposite direction.

A Devil’s Bridge

Several bridges in Britain are called "Devil’s Bridge". This one is at Kirby Lonsdale. It is hardly surprising that people could be astonished by the building of a bridge like this, and, as a result, attribute its construction to a supernatural being. If you don’t know about centring it certainly looks difficult. This is a splendid structure; two ribbed arches cross the fast flowing river Lune at a place where it is quite narrow. Ribbed arches were not uncommon in medieval bridges. Ribs reduce the weight, and improve the appearance. The outline of the walls is distinctive without being overdone.

The bridge is very narrow, and it now carries pedestrians only: a rather undistinguished – though not unpleasant – concrete bridge carries the road nearby.

The legend of the devil’s bridge has occurred in several European countries. Click also here.

Not so Fast

We are used to the idea of bridges as a means of getting people and goods across an obstacle as quickly as possible, often avoiding a long detour. But many of us need sometimes to go slowly. Parks and gardens are found in many countries for this purpose. Streams and lakes, sometimes artificial, may need to be crossed by paths, and so the most naturalistic garden may include an engineering construction.

Many Japanese gardens look very natural, but like many other gardens, result from careful planning and continual maintenance. Some consist only of gravel with a few rocks. Others abound with plants and water. All exhibit the ability to make the planned object look unaffected and accidental. The bridge here is in Korakuen in Tokyo, near a huge amusement park. The old Korakuen is an amusement park from a different age, when people would stroll through a garden, stopping at strategic places to contemplate the view. A bridge might be more than a crossing point: it would probably be one of the viewing places.

Use of Local materials

Using the local stone makes it more likely that a bridge, or indeed any structure, will fit in well with the landscape. In Derbyshire, Lancashire and Yorkshire, and of course many other places, there are many old bridges that achieve this. A good design may be a personal creation, or it may be a team creation, but it will have character, whether it be in stone, pre-stressed concrete or steel. If the design is right, the material used need not be a bar to integrating structure into a site. This is not to be confused with adding decoration or unnecessary features to an uninspired piece of work.

Some good examples of well-attuned bridges have already been shown.

Here are some other bridges, built in local stone, which work well in their surroundings.

Note, in the third picture, the cutwater on dry land. In fact the upper Thames floods quite frequently, so they may have some function. In any case they fit in with the general design of the bridge, and prevent it ending tamely at the abutment.

A bridge doesn’t have to be the biggest to be successful. It doesn’t have to have a feature that nobody else has used. All it needs is to be a good answer to the problem in hand, and to be inoffensive to the people who have to see it.

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Although a fine bridge in local stone is a pleasant sight, the ability to transport materials and to subject them to processes which change their appearance or characteristics, as in brick making, has been of great importance in the progress of technology. As far back in time as the building of parts of Stonehenge, some people thought it was worth moving large stones long distances.

Some of the examples have shown that the distinction between bridges and buildings is not clear-cut. The Ponte Vecchio in Florence and the Pulteney Bridge in Bath have shops on them. This was not uncommon in older times. An early London Bridge had houses along its entire length.

As many bridges were built on the boundaries of counties or other areas, they sometimes include gate-houses, as in the Monnow bridge at Monmouth.

And of course many buildings include arched doorways, windows and gateways.

See also Arches in architecture

Destroying arches

Arches are surprisingly resilient. In many parts of England you can see arched ruins left from the dissolution of the monasteries. Here are some arches left after bombing during the 20th century.

The vault of the banqueting hall at Ctesiphon, Iraq, looks fairly close to a catenary. The walls are thickened towards the ground, to make sure that the funicular remains inside them. This is shown clearly in Figure 20 of "The Story of Architecture" by Patrick Nuttgens, Phaidon, ISBN 0-7148-3616-8. Click here for a picture which does not show the side walls quite so well. Built in about 550 AD, this building survived until 1987, when most of it was destroyed by a flood. ……………………………

Developing the Arch

Since the semi-circular Roman arch has served so well, some examples still standing after nearly 2000 years, it must have some strong points. Let’s see what we can do by messing around with the semicircle.

If we reflect it about a diameter we have a ring. Add some spokes and we have a wheel, such as a bicycle wheel. We can learn a lot from the bicycle. The Wright brothers did, and of course they were brilliant and patient reseachers.

A bicycle wheel is very light, but very strong. It is rather like a bowstring arch in which the straight part has been squashed to a point, and the curved part wrapped right round it. Although the rim and the spokes are not very rigid, the assembly is very rigid indeed.

Since the spokes cannot take compression without bending, the weight of the bike must be transmitted from the hubs to the top of the wheel through the upper spokes.

Other spokes hold the rim in shape as the force is taken down and around the rim. At the bottom of the wheel, the weight is tending to push the rim towards the hub. The vertical spokes cannot resist this action, but for one part of the rim to move inward, another part must move outward. So the spokes as a whole are keeping the wheel in shape.

The spokes in a bicycle wheel are not along radii, because they have to transmit rotational torque from hub to rim. So they are tangential to the hub. The hub is wider than the rim in an axial direction to keep the hub rigidly in the mid-plane of the rim.

A pulley wheel is more like an arch with a distributed load.

The rim of a bicycle wheel is not very stiff, so the wheel is like a deck-stiffened bowstring arch, where the deck has become a point. But some motor-cycle wheels have stiff rims, with as few as three spokes. They are more like self-stiff arches.

Strangely enough, some wheels are the exact opposite: they have rims in tension around a compressed wheel. In such cases, a metal rim or tyre is heated, fitted to the wheel, and allowed to cool and contract on to the wheel.

Related to the bicycle wheel are the rackets for games like badminton, squash and tennis, shown diagrammatically below. These have an oval frame with a grid of taut strings. The array must be two-dimensional, because one parallel set of strings alone would easily distort the frame. Striking a ball would be ineffective, because the distortion would increase, reducing the ability of the tension to send the ball on its way.

If we think of the frame as two opposing arches, pulled together by parallel strings (the load), the other set of strings can be thought of as resisting the outward thrust, (the abutments of an arch). In effect, these rackets are like double tied arches.

If we rotate a ring about its centre we get a ball. Balls are ubiquitous. A ball flies straight if not spun, and it rolls straight and bounces true – hence its use in games. It can take the tension if inflated, and the light table-tennis ball can take surprising amounts of compression if applied uniformly. One make of gardeners’ barrow uses a ball instead of a wheel, to spread the load on soft ground.

Many balls, such as footballs, are under internal pressure, and so, although they look like domes, they are actually in tension. In fact, vessels to contain gases at high pressure have been made by winding steel wires around spheres or cylinders. Golf balls have been made by winding rubber threads around and around. Although the bands are in longitudinal tension, they are compressed laterally by the threads outside them.

Then, of course, there are eggs and skulls. Nature did it first, as usual. When a chick tries to break out of a shell, does it need a greater force than a predator trying to break in?

Here are some eggs, one of which has hatched. Egg-shells are sometimes used as a symbol of fragility, and certainly a small piece of a small egg is not very strong. But opening a complete egg is not quite as easy as cracking a flat sheet. The dispute between the big-endians and the little-endians in Gulliver’s Travels is well known as a symbol of factional behaviour. As an engineer, would you open an egg at the big end or the small end, or even halfway between? A sphere, an ellipsoid and a cylinder are all good shapes for withstanding pressure differences in either direction.

Eggs are well constructed to withstand forces which are typical for their environment, and they can be surprisingly strong when someone tries to open them. Some of the larger birds eggs are so strong that birds carry them into the air and drop them on hard ground. A domestic hen’s egg is no match for a sharp tap with a spoon or a swift hack with a knife, both of which impart great stress on a small area. The shells of snails are strong enough for everyday life, and in fact they are not easy for a small bird to open. The common thrush picks up a snail by gripping the rim, and then with sideways flicks of the neck and head, whacks the snail on to a hard rock or concrete. Sooner or later, the impact occurs at a place that the kinetic energy can crack.

The problem is that arches and domes, shells, bottles, cans, tubes and the like, are all designed to withstand a continuous stress all over, rather than a large force at one small place. No doubt if you immersed an egg in liquid in a closed container, and you then connected the container to a pressure pump, the egg would withstand a considerable pressure.

Obviously, the snails could evolve thicker shells, but this would require more energy and more material, and the snail would have to carry a greater weight, again, requiring more energy. Like everything else in nature, the shell is a compromise.

Stringed musical instruments are of two main types; those like the harp, the harpsichord, and the pianoforte, in which a strong frame surrounds the strings, and those like the violin family and the guitar family, in which the strings are stretched across a box, and spaced from it by a bridge. In all cases, the rigid part has to be strong. The total force on the frame of a large piano is enormous. There may be over eighty keys, many working two or even three strings.

The diagrams below represent the outline of a zither or cembalom. If the frame were made of the same material as the strings, we might expect that the cross-sectional area of the two compression legs need be no bigger than the total area of the strings. On this basis the frame on the left is too thick. In fact it is too thin. Why? The reason is that long before failing under compression, the frame will fail by buckling. Euler showed that a strut under compression will buckle in response to a tiny deflection, if its thickness is less than a critical value.

Because the top and bottom of the frame do not follow the funicular, they have to be very thick as well. In a sense, the frame contains both an arch and a suspension cable; this is discussed in beams. The shape is determined by musical, and not structural requirements: it has to suit the lengths of the strings that produce the right wavelengths and therefore the right frequencies. By arranging the strings in a different order and at varying angles, it might be possible to use a funicular frame, but the striking mechanism of a piano would be very complex if the strings were all at different angles, and the non-musical order of the notes would be most unhelpful to the player.

In fact, by varying the thickness and tension of the strings, the musical requirements can be adapted to fairly simple shapes of frames. Since the time of Stradivari and Guarneri, violins have been dismantled and rebuilt with the fingerboard at a different angle, to allow for the greater tensions demanded by modern music and modern methods of playing in large halls as opposed to the small rooms for which chamber music was intended.

The strings of a racket, like the string of an archery bow, must impart maximum energy and momentum to the projectile, and retain as little vibrational energy as possible. A piano string, on the contrary, must absorb most of the hammer’s energy, while bouncing it quickly away, so that it cannot damp the vibrations. The mechanism of a piano is very ingenious: the parts have to be very light, yet they must be rigid enough to transmit the force of the finger exactly. The piano frame has to transmit the vibration of the string to the air, like the diaphragm of a loudspeaker. In this, the instrument is the opposite of a bridge, which is not supposed to oscillate, either wholly or in part.

The frame or body of a musical instrument must transmit vibration well, yet have no strong narrow resonances. It must give tone, but not colour the sound unduly. In electric guitars and electric violins, the body has no sonic function, and is purely a mechanical platform.

The archery bow differs in that the string is purely a means of transmitting the strain energy of the bow to the arrow. If a bow is shot without an arrow, where does the energy go? Don’t try it.

When lightness is paramount, as in the masts of yachts and other small craft, and in communications masts, the structure is thin, and is braced externally by wires. It is effectively divided into sections which are individually rigid.

From 1937 to 1940, Henry Moore made a number of sculptures which included strings or wires, but he stated that these were derived from organic forms, and indeed they do not convey a strong impression of tension against compression. Barbara Hepworth and Naum Gabo also made sculptures which included wires. One example by Gabo is shown here. Do you know of any works of art which really convey the ideas of structural forces?

This discussion could as well have been included in the pages about beams, cable-stayed bridges or suspension bridges, because many structures, including some bridges, cannot be assigned into a simple category.

Half a ball, or an arch rotated about its apex, makes a dome, again a strong shape, whether a human skull or the dome of St Paul’s cathedral. Distort a ball in the right way, and you have a rugby ball, an American football, or an egg. An egg is very strong, unless you poke it with something fairly sharp. In the same way, the curved case of a shell-fish is strong, until, for example, the sharp bill of an oystercatcher stabs it or prises it open.

If we rotate the ring about a line that is outside it, we get a torus, for example the inner tube of a tyre that fits the wheel already mentioned.

If we rotate a narrow arch about one of its abutments we get a circular shape, well seen in the beautiful chapter house of Salisbury cathedral. This building has a vault supported on a circular wall and a narrow central pillar.

Extended arches, intersecting in various ways, form the vaults of medieval cathedrals.

If we translate a ring we get a tube, described in another page of this web-site. (Tubes) The tube is of course a ubiquitous device in both the animate world and the inanimate world.

If we turn the tube on to its end we have the shape of a factory chimney or a lighthouse. An early example was the Eddystone lighthouse by Smeaton.

Some buildings, such as oast-houses or pottery kilns, have been made in conical shapes, with curved or straight sides.

Finally, if we turn an arch on its side, we have the shape of an arch dam. Of course the arch needs to be thicker at the bottom than at the top, to withstand the greater pressure. In fact the shape of a dam has to be such that it is stable for all levels of the water.

Some dams (cupola dams) are even curved in both directions, like a section of a dome. They can be quite thin, and even overhanging, near the top. Unlike a bridge, a dam does not experience rapidly changing live loads. The only change is in the water level, principally while the reservoir fills for the first time.

The cathode ray tube of a television set has a thick curved faceplate, and in fact the entire surface of the CRT is curved. This makes it possible to withstand the pressure of the atmosphere, with no pressure from inside the evacuated tube. It is analogous to a cupola dam, except that the pressure is the same all over.

The ideal shape for a pressure vessel is a sphere, a shape is often used for deep sea exploration. But a sphere would be impractical for a domestic device, and so some compromises have to be made . The faceplate must be thick enough to make sure that the surface of thrust lies entirely within the glass. Large CRTs are therefore very heavy.

What do you think is a typical total force on the front of a TV tube?

These pictures show a small part of a long reservoir that is held by an arch dam at the left. The pressure at any point on a dam is dependent on the depth and the density of water. The width and length of the reservoir have absolutely no effect on the pressure.

To see this, imagine a vertical plate in the dam. It has the same pressure on both sides, otherwise it would move. If it is enlarged to divide the dam into two parts, we could imagine filling one part with earth, without changing the pressure in the other part.

Here are pictures of the beautiful Slap Savica in the Triglav National Park, Slovenija. The dam has only slight curvature, and probably acts mainly as a gravity dam.

Because the arch dam and cupola dam rely on the rock to sustain the thrust, the quality of the rock is of the utmost importance. Grouting of the rock around the dam, both laterally and below, is usual. The water also exerts great pressure on the rock, which may create significant stresses. The lubricating and uplifting effects of water that has been forced into cracks may have serious consequences, as in the case of the Vajont dam. This was a magnificent feat of engineering, but in 1963 a fall of rock into the reservoir displaced a gigantic mass of water over the dam, killing about 2000 people.

Although arch dams can be quite thin, their weight can be used to aid stability if they are made thick. The dam is then a gravity-arch dam. See Gravity dams and Top Ten dam sites.

The arch dam is commonly seen in the form of the paired gates of dry docks and locks, which in effect form three-hinged arches. You might wonder why very large lock gates, such as those in the Panama canal, are not made as sections of cylinders. Perhaps the extra expense is not worthwhile, and also there would be some awkward forces at the hinges. Even the deepest lock doesn’t compare with the highest dams. Here is an idealised plan view of a pair of lock gates.

These pictures show a dry dock and its gates. When the dock is to be filled, it is not possible to open the gates against the pressure of the water: instead the dock is filled by opening valves in pipes that connect the main basin with the dry dock. …………………………………

Continuing the arch dam to make a complete free-standing circle, We get a cylindrical caisson or cofferdam, which keeps water out while a bridge pier is built. Turning the cylinder on its side, making it long, and adding end caps, we have a submarine. Some changes in shape are required to obtain minimum drag and to accommodate the necessary equipment. For a submersible which does not need to go fast, a simple cylinder with hemispherical end caps is adequate. In fact, some early submersibles were spherical.

Robert Maillart

The name of Swiss engineer Robert Maillart will always be associated with arch bridges, but he was in fact a brilliant and versatile creator, contributing to the development of efficient and elegant reinforced concrete buildings as well. It has been said by an aircraft designer – "If it looks right, it is right." That just about sums up the work of Maillart.

No building was too humble to benefit from Maillart’s best efforts. He was a true innovator, looking at problems and finding good solutions, looking at requirements, assessing known designs, and finding economic answers.

In his reinforced concrete buildings, he used columns which spread at the top, merging into the deck above. This looked good, better than the right-angle that we so often see. And it allowed the forces to flow from the deck into the column, at the same time reducing the spans between the columns, with a consequent saving of material by reducing the thickness of the deck. In fact, in these buildings, there is more than a hint of the medieval fan vault.

Nature seldom joins things together in a crude manner. Look at the way that a tree grows its branches – if you cut through the wood, you see the lines of force well inside the main branch, showing where the subsidiary branch grew out. The first two pictures below show how palm leaves grow.

The other pictures show pieces of wood cut from a place where two branches grew out, together with a computer simulation. If you look at an old fallen tree you can often see clearly the flow of the stresses to which its growth was a response. Given the enormous time-scale of evolution, we can assume that natural structures represent good compromises between all the requirements for survival and reproduction.

Definition of an Arch

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

Let’s look at arches. How’s this for a description of a "pure" arch?

An arch is a structure in compression, which follows the funicular, and is only thick enough to contain the live loads at all times. It will usually include extra members to support a more or less horizontal deck, though some older Chinese and Japanese bridges used the arch itself as a deck, sometimes with steps. It cannot exist without abutments that can react against the horizontal thrust, except in the case of a tied arch, which could be regarded as a beam in which the tension and compression have been separated. The stresses in an arch are purely compressive, and the horizontal component is constant throughout, but the vertical component varies, because each part has to support the higher parts, but not the lower parts.

In practice, arches often deviate from the funicular, sometimes to obtain clearance over a greater width, or for structural reasons. If an arch deviates too far from the funicular, it will require stiffness, and so it will to some extent have to behave like a beam.

Some arches are in the form of trusses, so that page should be looked at for further information. Masonry arches are often solid, and the the distribution of the weight of course affects the shape of the funicular, and hence enables arches of many different shapes to be built. The ancient Romans did not seem to know this, or if they did, they did not care. Their designs were very conservative by today’s standards.

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.

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