Arches in Religious Buildings - Part Two
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The method of supporting a roof by splitting the supports to spread the load is rather like the left hand picture, where the plant makes a roof of flowers. The umbelliferous plants are not the favourites of many people, and are seldom used by gardeners. They are not even coloured in most cases. Yet they are very interesting indeed. In the first picture we see four of the stems that have branched out from a bigger stem, and each of these fans out into many smaller ones. Each smaller one branches again into many tiny stems, each bearing one flower. The end product is a wide and highly visible mass of white or whitish flowers, often forming an almost continuous flat sheet like a roof or parasol. But the many stems here are not struts, as in a roof, but cantilevers.
A single flower of the same area might be much heavier. Furthermore, its pollen and nectar would probably be in the centre, requiring visiting insects to aim at the right place. Indeed, many flowers have guide lines, sometimes visible only in the ultra-violet, to help the insects. On an umbelliferous plant, an insect can find something almost immediately, a great advantage given its exposure to predators while feeding. In fact, numerous insects can feed at the same time. If an insect is interrupted shortly after landing, the plant still has a good chance of being pollinated.
These buttresses outside the south aisle at Gloucester oppose the the thrust of the roof of the aisle. Though not as spectacular as the flying buttresses of Chartres or Notre Dame de Paris, they do the job. The little spires on the buttresses may be for decoration, or they be for extra weight to direct the thrust more steeply. Even if they are for decoration, they may have been copied from an example where they were functional in steering the thrust.
These sturdy buttresses are seen on the north side of the cloister garden in Gloucester cathedral. In the second picture, eroded stone is being replaced. The right hand buttress has had its little spire removed. This hasn't had any effect on the structure, so the spire must be there for decoration rather than weight. The left one had already been replaced when the picture was taken.
The tower of Gloucester cathedral is furnished with buttresses, one of which is visible here, going westward from the SW corner. Others are built into interior walls, like the one shown in the next picture, cutting through the arched openings in the walls. After looking around this building, you might think that it is a bit of a mess in terms of engineering. Remember, though, the proximity of the River Severn, and the depth of the alluvial soil in the flood plain, waterlogged to within a short distance of the surface.
Here are two views of the buttress that runs south from the SE corner of the tower. On the east side of the south transept you can see a similar buttress from the outside. Not surprisingly, the south wall of this transept leans outwards, having pushed by the buttress for several hundred years. You can find several other supporting features around the cathedral. Since the foundations are in ground that is below the water table, being near the river Severn, and not very elevated, problems are to be expected.
Note the great contrast between the upper and lower parts of the buttress. The upper part is a beam, supported by narrow pillars, both above and below, but the lower part spans the entrance to a small chapel, and requires an arch to support the beam which actually takes the thrust. Many details in such a building reveal existence of problems, and the thoughts that went into solving them.
The beautiful tower of Cirencester church has buttresses which go right down into the ground in the west wall. Because of difficulties with the ground, threatening the tower, this wall had to be taken down on the south side in order to add the buttresses. The NW and SW corners of the tower are also well buttressed. Should you climb the helical stairway to the top to see the splendid view of the town and country, you can be quite sure that the tower will stay upright. More pictures are shown below.
There is actually something peculiar about these buttresses - they are straight. If you look at the page about the funicular you will see that the buttresses should logically curve towards the ground. These, however, are almost entirely supported by the west wall, and so function as struts. In the case of Cirencester we can imagine that the builders wanted to anchor the buttresses as far from the tower as possible, in the hope of finding better ground.
Perhaps appearance entered into the design, since a window was required, and curving the buttress around the window would have looked rather strange. On the other hand, the builders might not have understood the flow of the forces at all, as everything seems to have been done empirically in the middle ages. In the first picture, we see that the buttress actually reaches the ground perilously near the corner of the building, but in fact there probably isn't much thrust left in it by that point.
Just for a change, here are two structures that are not buttresses. They are outside the big west window of Gloucester Cathedral. If you go inside, you will see that they don't push against an opposing force. The builders may have felt unhappy with this huge area of glass, facing the prevailing wind, and held by a few narrow pillars, and so they added these supports, which build the structure into the third dimension. If you look at the huge east window, you will see a similar thing. But the east window is different: it isn't flat - it is slightly bowed, and it is even slightly wider than the building, because the walls of the last bay are turned slightly outwards.
If we go back in time to the Normans, we see a complete contrast to the last picture. The pictures at left, on the south side of Gloucester cathedral, show a very thick wall, almost a metre thick, which the builders have built with small holes for windows. Not only did the Normans build small windows, in this case they tapered the holes toward the outside, so that the aperture there is actually considerably smaller than the windows. Because the Cotswold stone is pale, the recesses would have reflected some light into the windows: painting them white would have helped. We are used to seeing bare stone in most cathedrals and churches, but in medieval times they were often painted inside. Traces of the painting can still be seen in Cirencester church.
If you go a few miles up the A38 to Tewkesbury, you can see the magnificent abbey, begun, like Gloucester cathedral, by the Normans. These photographs show the amazing west end. Do you think that some of the thrust of the arch spreads out into the flanking walls?
Not far from the abbey is a modern church. It, too, has a tall west arch, the effect of which is diluted by the small porch at the bottom. On the other hand, the purpose of the building is not the intimidation of the worshippers, so a small entrance is probably more suitable.
Here is a fine stone barn in the Cotswolds. The roof is heavy, being made of Cotswold limestone, which cannot be split into thin sheets. So the outward thrust of the roof, which behaves like a three pinned arch resting on the walls, is resisted by massive buttresses. Looking at the shape of the buttresses, you can see that the builders' insights were sound, and that the outline imitates the funicular quite well. A nice piece of work.
These buttresses receive thrust from the south aisle of a church at Wotton in Gloucester, and indirectly from the nave as well. Note that a buttress cannot eliminate the horizontal component of thrust. All it can do is increase the vertical component, thus making the line of thrust steeper. This is why extra masonry or a statue was often added to the pier of a flying buttress, as well as above the outer half of the arch. The outward component of the thrust can only be resisted by an inward force, which is only counteracted finally when the buttress reaches the ground. The inward push of the ground on the buttress is cancelled by the diffuse tensile force in the ground under the building. In a sense, all forces in static objects comprise closed loops of tension and compression. This is not true of rockets and gas turbine engines, in which the momentum of the ejected gas creates a pressure on the engine.
The famous tower at Pisa never received the buttress treatment, whether for stylistic reasons or for structural reasons. It is one thing to buttress at a corner: another to push into a cylinder. In such a case there would probably have to be strong floors at the level of the buttress to spread the load. Digging to make foundations for a buttress would have weakened the ground on the side which could least afford it.
The exciting Wildwalk at Bristol includes a tropical area with a tented roof and trussed ends. Here we see at the bottom right how the support leans inwards, because the funicular can never become vertical. Next to Wildwalk is Explore At Bristol, which is a magnificent exploratory of engineering and science. Unfortunately, the road was too wide for the camera lens, and the camera was tilted, leading to converging verticals in the image.
The flying buttresses at the lower left of this photograph are a part of the cathedral of Seville. Flying buttresses are not always outside the building; in the south aisle of Gloucester cathedral you can see examples cutting across the arches of the aisle.
Flying buttresses demonstrate clearly the difference between a buttress and a gravity dam. In a buttress the force is applied mainly near the top: in a dam the force increases towards the bottom, and is purely horizontal. Any vertical component on a buttress is the easy bit: it's the sideways push that's the problem.
This picture is of a part of Liverpool cathedral. The conical roof reaches almost to the ground, and the thrust is continued right to the foundations by the struts which hold up the roof. Exactly like the walls in a medieval cathedral, the walls of this cathedral play no part in taking the thrust of the roof. The structure is not a dome: the straight sloping beams are just that - beams. They experience bending moments, and are therefore quite thick. Unlike a horizontal beam, however, they experience thrust, and could in a sense also be called piers. They are giant roof rafters.
France has many beautiful Gothic cathedrals. These pictures of the cathedral at Chartres, from the south-east, show flying buttresses at the east end and on the south side. The first picture file is very large. Some of the buttresses are buttressed in their turn. The cathedral of Notre Dame in Paris has many buttresses also.
Here is another look at Assisi. Down in the plain, inside a huge basilica, you can find a little chapel that St Francis used. He isn't there, of course, but his spirit can still be sensed in the town on the hillside.
The ultimate in windowed buildings is the glasshouse. The one in the first picture has buttresses which with the roof make much better approximations to funiculars than the walls and roof can provide. They may have been added as an afterthought. The second picture shows wooden buttresses holding a wall after an adjoining building has been removed. The third picture shows steel buttresses in the form of I-beams.
The next diagram hints at a type of construction that in principle allows four walls of a rectangular area to be completely glazed. In principle, the glazing could hang from the roof, though some form of stiffening would be required, as it was in medieval cathedrals and churches. The roof and the the buttresses are integrated into a single shell. In addition, no internal supports are needed.
This utilitarian design would bear little resemblance to a medieval cathedral. With so much glass, there would be no contrast between the glowing windows and the dusky interior. On the other hand, the design allows for much more glass than any medieval cathedral, offering the possibility of including far more narrative pictures, and other designs carrying spiritual messages. The symmetry and simplicity of this building would lend itself badly to enlargement and modification, and the inclusion of the numerous small chapels that are often found in an old cathedral.
How Buttresses Work
An orang utan hangs from a rope, distorting the smooth curve. The natural curve of the forces in an object is called the funicular, and a freely hanging flexible object follows it. An applied force, as here, makes a discontinuity in the slope of the curve. The animal could also make a kink by standing underneath and pushing upwards. Turning the curve upside down forms the funicular of an arch, as in the Gateway Arch, St Louis.
The funicular is not necessarily a "mathematical" curve - it differs for each stucture. But building something that does not follow the funicular leads to the need for extra stiffness to resist bending moments.
Not many buildings follow the funicular, the main reason being that we generally prefer vertical walls for rooms in which to live and work. But large enclosures such as hangars have often been built with curved walls and roofs. A huge example is the airdock at Akron.
The diagram below represents a cross section through an imaginary building, with a section drawn thick, to represent, roughly, the vault of a cathedral.
An actual cathedral usually has vertical walls, as we see below. Just as the downward weight of the gibbon kinks the tensile funicular upwards, the upward force from the wall kinks the compressive funicular upwards also. In fact, the funicular becomes horizontal, because the wall takes all the weight of the vault. Where it goes after that depends on the distribution of mass in the supporting structure.
On the left is a solid buttress. We see immediately why the builders needed to make their vaults as light as possible, not for artistic reasons, but to reduce the effort required of the buttresses. On the right is a flying buttress. Real buttresses sometimes have another arch further down to supply rigidity.
To make the flying buttress narrower at the base, we could make the funicular dip more steeply. If the wall pushing up kinks it upwards, adding weight at the top kinks it downwards, as we see below. We can also see that adding mass above can reduce the necessary mass by a larger amount down below. The great medieval builders discovered all this without mathematics, and even succeeded in reaching the limits of the technology. Sometimes they went beyond the limits, and some cathedrals collapsed, suddenly, and apparently without warning. It is unlikely that there were no precursor movements, but the congregations would not have been looking for them. The cracks and crumblings might well have been high up out of sight.
The foot of the buttress is narrower than before, and the line of thrust lies within it, not at the edge. The funicular as drawn, is still at the edges near the top. But this whole scheme is highly idealised. Vaults do not necessarily connect to the walls at narrow points, and the walls do have a certain amount of rigidity. This can be seen on the south side of the nave of Salisbury cathedral, where buttresses are provided only at alternate bays. So don't take these diagrams literally. But the system works, and has worked for hundreds of years.
More peculiarly, on the north side of Tewkesbury Abbey, there is only one buttress, albeit a massive one. It is hard to believe that the wall, however thick, provides lateral beam action over such a long distance. Perhaps the builders felt nervous about some feature of the building or the ground at that point, though there is nothing to see, either inside or outside. But wait - look at the next picture, which is a squashed version of the one above.
It looks as though the wall is bulging outwards below the line of the buttress. You can see this in both sides of the window and in the line of the drain-pipe. Perhaps the builders tapered the wall. There is also a hint of the buttress pushing its pier outwards - compare it with the drain-pipe behind. A return visit is needed, to look at the wall inside. When looking at the structure of a building, don't turn away until you have made sure that you have seen every detail. Now look again at the original picture.
Look at the flying buttresses of the cathedral of Notre Dame. The daring of the arches is breathtaking - remember - the line of thrust must remain inside the stonework at all points.
Here are two buttresses on the south side of Salisbury cathedral. They are very different in style. The right hand one is a typical flying buttress, with a thick steep strut, supported by a thinner arch. This is all very funicular. But the left hand one looks very peculiar: there is no straight strut. Yes, there is an arch, but it supports a structure that curves the wrong way to be funicular. Furthermore, this buttress is not furnished with a heavy spire to move the funicular downwards. Why didn't the builders make them both the same? For the sake of appearance, they probably wouldn't bother, because a cathedral was built to the glory of god and to provide places of worship. Perhaps the interior details of the building would supply a reason for the difference. Perhaps the builders were simply experimenting.
The four piers of Salisbury cathedral (yellow arrow in picture) are highly stressed, because of the added spire, for which they were not designed. All four are visibly curved. This picture of the north side of the nave shows two buttresses (red arrows in picture) assisting in keeping the piers vertical and straight. Perhaps the most beautiful part of Salisbury cathedral is the octagonal chapter house. No picture is given here, because the presence of a copy of the Magna Carta means that photography is forbidden. Such a structure would be difficult to photograph in any case.
A roof has been added to our imaginary cathedral described above. This could be supported on wooden beams. As drawn, it would exert lateral force on the walls. By raising the roof, space would be created for ties to hold the beams together, making a simple truss.
In Beauvais cathedral, another trick was tried. Around the buttresses of the semicircular east end. tie-bars join all the buttresses. These act like the chains that often serve to take the tension in domes. They act like the metal tyre of a wagon wheel that is shrunk on after heating. You might ask - If the bars contain the thrust, why did they build buttresses at all? Why not just fix the bars around the walls?
Perhaps they were an afterthought - a belt and braces solution. The full story of Beauvais may provide another clue. Beauvais was intended to be the most stupendous cathedral ever built. Its choir is almost 160 feet high. But in 1284, 59 years after construction of the building began, it collapsed. During the next forty years it was rebuilt, more robustly. Over 200 years later, in 1569, Beauvais boasted a spire reaching 492 feet into the air. It lasted less than four years. When it crashed, it damaged the choir, which was then repaired for the second time: the nave was never started. No wonder if the builders took precautions with the rump of a building that was left.
It is easy to say that these people did not know what they were doing. To think that people of different times and of different places were necessarily inferior to ourselves is as absurd as to romanticise them or to place them on a pedestal. Strangely, some people have thought that the great pyramids required the help of creatures from another planet. You don't hear this about cathedrals, which are much more ingenious and much more daring. To have made a 492 foot spire that stayed up for well over three years was a tremendous achievement, and the structure was clearly only just outside the region of stability. We shouldn't necessarily blame the builders: it's possible that they were browbeaten by an ambitious bishop - who knows?
That the builders did not use our mathematics and science does not mean that they did not understand what they were doing. A cricketer does not understand the mechanics of a well-timed cover drive, but only a fool would say that he does not understand the game. An arch, a beam, a cathedral, you name it - it requires heart as well as head. Building is art as well as science. There are several pictures in these pages of structures that have too little art, as opposed to pointless decoration.
The biggest buttresses on earth are gravity dams that hold back the water in a reservoir. It is imperative that there is no tension at any point, as water seeping underneath exerts an upward pressure that reduces the effective weight of the dam, which of course increases the tendency to crack. Some gravity dams are made like a multi-span arch bridge lying on its side, with individual buttresses instead of piers. See Gravity dams.
Sometimes we use the idea of adding weight without thinking about flying buttresses. If we lean a ladder against a wall, the force at the ground has a vertical component, the total weight, and a horizontal component, the reaction of the wall on the ladder. The resultant acts at an angle to the vertical. If this angle is smaller than cot-1(CF), where CF is the coefficient of friction, the ladder will slide. By adding weight at the bottom of the ladder, a man, for example, we can make the angle steeper, because weight added there does not increase the horizontal force. This is the exact equivalent of adding pinnacles to a flying buttress.
Another practical example occurs when hill walking or climbing. If you are on very steep grass, which can be dangerous with unsuitable footwear, especially when wet, you can slightly affect your chances of sliding by the way you stand. If you lean towards the slope, you are more likely to slide, by the argument given for the ladder. If you are climbing on a steep rock face, leaning towards it will not improve your resistance to slipping, not to mention making it harder to see the holds. Better to take an upright stance. On the other hand, when chimneying, you need an angle to get the required friction.
To avoid the use of buttresses, you can take the roof all the way to the ground, as in this elegant building by Foster and Arup. It houses a superb collection of US aircraft in the imperial War Museum at Duxford. The building had to be big enough to house a B52 and many other aircraft, with space for a viewing gallery and other facilities. It had to provide enough light for easy viewing And of course it had to provide easy access to get the aircraft in. The concrete shell allowed the provision of a huge south-facing window. Around the base of the shell a slot provides illumination for the viewing gallery, the shell being supported by struts. The building is beautifully adapted for its purpose (as are the aircraft for theirs), yet it does not obtrude into the consciousness of the visitor.
Here are two of the vaults on the centre line of Gloucester cathedral. These could almost be regarded as stone trusses with all the parts held in compression by their weight. The third picture was downloaded with kind permission from Welcome to Isfahan, and shows a very different style of vaulting - much more symmetrical, and probably based on geometry rather than rule of thumb.
The 14th century choir at Gloucester shows how much the technology had changed. In the "wool churches" of Gloucestershire, for example in Cirencester, Fairford, Lechlade and Northleach, you can see other fine examples of the lighter and more airy styles of building that replaced the Romanesque.
And of course in many Islamic buildings we see elegance and lightness of touch taken to great heights, in arches, vaults, piers and decoration. See Welcome to Isfahan.
A fundamental part of any mosque is the mihrab, which indicates the direction of Mecca. This sometimes has an arch shaped opening.
In the Sikh Golden Temple also, we see domes and arches.
Almost 1000 years after the bringing of the Romanesque arch to England by the Normans, the magnificent Shri Swaminarayan Mandir at Neasden brought Hindu stone architecture with arches and domes.
The buildings are, of course, only the most visible manifestation of both the indigent and the incoming cultures. The English language has been enriched again and again by people from other lands - the Romans, the Vikings, the Normans being just three of the groups who came to England. And not just language - literature, mathematics, medicine, music, and science have all been given new life by imported ideas.
Some cultures, notably the nomadic ones, have left no legacy in stone, or even on paper, but their ability to create and express ideas in music and poetry has nevertheless influenced what we hear. (See Bartok and Kodaly, for example.) Technology enables us to hear music from all over the world without travelling, and even though we cannot understand its history and meaning, we can appreciate its structure and ornamentation, and enjoy the sound it makes.
No doubt, in future times, people will realise that the 20th century was another great period of enrichment of English culture by ideas and practices from overseas. At the same time, cultural memory can be long, and even today there are people who can say - "My ancestors came over with the Normans."
Buildings for religious worship often express most clearly what we see in many other buildings, namely that they are far more than just boxes to keep the weather out while people perform some activity. A building can be an expression of the ideas and ideals of the designers and builders, and of the users. In some trading estates you can actually see constructions which are indeed little more than large boxes.
But we can also find examples that are both elegant and functional. The medium is not the message: whether we build in brick, stone, wood, steel or concrete, we can create works ranging from the superb to the downright ugly.
Many pictures in this web-site are of houses and other small buildings, because these, as much as large and famous ones, express peoples' tastes and aspirations. modified, of course, by the limitations set by their income. Like the larger buildings, even the smallest houses bear the imprint of their inhabitants' personality.
One of the pleasures of architecture is the huge variety of solutions to the technical problems posed by the users' requirements and the limitations of the laws of physics and the properties of materials. Many buildings appear to transcend these so well that we can easily forget that they weigh thousands of tons.
The great weakness of stone and brick as structural materials is their inability to take much tension, and their availability in only small pieces. The arch, the dome, and the vault, are the brilliant responses of people who were not willing to be imprisoned by these limitations. Not all cultures have made use of these structures. The "ancient Egyptians" and the "ancient Greeks", though possessing considerable mathematics, seem to have generally ignored the arch.
Looking at temples and shrines much further east, in Japan, one sees mainly beams and cantilevers. Many arched bridges there have intermediate supports which mean that these are beams and not arches. Some stone bridges were, however, built in gardens, often with steep gradients.
Given the preponderance of flat horizontal beams in the architecture, the number of arched beams is perhaps a little surprising, especially in garden bridges over little streams and ponds. But in a bridge which is a part of a carefully planned path around a garden, speed and economy were not the main determinants. By making an arch, especially a steep one, the designers gave the bridges a centre, encouraging people to stop and look at the view. The placement of the bridge was often chosen precisely for this reason.
In bridges that were actually built flat, corners or steps were often provided to slow people down, and hint at the places to stop and admire the view.
If you are not restricted to stone, you are freed from the tyranny of the arch, because you can employ tension. The chapel shown here has a roof based on wooden beams. From an engineering point of view, "tyranny" may be a suitable word, but from an aesthetic point of view, possibly not. And if you employ tension, there must be extra compression elsewhere, in addition to the compression already implied by the funicular. Even in the few examples in this web-page, we can see a wide range of styles and techniques within the category of arches and domes.
Often it is the very restriction in possibilities which forces the creation of ideas and techniques. In music and poetry, the necessity of adhering to the logic of the piece, for example in key, metre, rhyme-scheme and so on, may cause problems which lead to innovative solutions. Without a structure, anything goes, and where do you even start? And how do you know when you've finished.
With the huge range of strong materials now available, designers on the smaller scales are freed from the coupling of form and function. Many kinds of domestic equipments, from radios to food mixers, and of course cars, are designed for appearance. And why not - people have to live with them. Few people would want to live with things looking like tiny Pompidou centres.
At the larger scales, however, it is hard to escape from the necessities of engineering. The original design for Sydney opera house used roof sections that looked rather like gothic arches. But the pointed shapes did not correspond with the distribution of forces, and considerable ingenuity was needed in order to create something that resembled the original design, and was reasonably practicable. "Ingenuity", of course, comes from the same root as "engineer". And "reasonably", of course, normally includes cost. The question of cost is not quite straightforward. Maillart won contracts on price: had his designs been rather more expensive, would they have been built? But if we always build the cheapest of everything, what would our world look like? What do you think about this question?
The problems in engineering are generally of a different kind, but they also can lead to innovation. And the result will very often have aesthetic quality. Art and technology are not necessarily as different as might be thought. C P Snow's "Two Cultures" created a myth which was very persistent. Looking at some types of art, one might even think that some types of science and engineering have more beauty than those. But then, art does not have to be beautiful - it only has to express what is true for the artist.
To look at the details of large buildings, both internal and external, low-power binoculars are very useful.
These pages are entirely about the large and heavy artefacts that people have made to assist in living and travelling. But people who travel all the time, if they have dwellings at all, need ones that can be quickly built and taken down, and easily carried if re-used. Click A, B, C, and D for web-pages including a picture of a Kirghiz or Mongolian tent.
The walls of a Kirghiz tent are made using a large number of sloping strips of wood, with some horizontal hoops to help with rigidity. The roof is a dome, also braced with wood. The diagram below shows roughly how the walls are built. The diagram is made with straight lines for simplicity of programming, but the real thing uses smooth helices, with a few horizontal hoops to aid rigidity.
Such people do not leave grandiose ruins for future historians and tourists: their culture comes to us, if at all, in their influences on music and literature. We can hear this in music of eastern Europe, for example Bulgaria, Romania and Hungary, where the "east" has met the "west". These people may also express themselves in costumes, in the use of their animals, and of course in the type of social interactions they develop, which may be too subtle for the casual visitor to detect.
And even if, wherever we live, we have never seen a single foreign building, we have the benefit of ideas from all over the world. Even now, western scientists are re-discovering specialist medicinal techniques that have been used by many different cultures.
To find out more about the funicular that is the basis of buttresses, click here.
Links to other sites
A series of guides to British cathedrals is published by Pitkin.
See also -
The Horizon Book of Great Cathedrals - Edited by J Jacobs, Hamish Hamilton
The Cultural Atlas of Islam - I R al Faruqi and L L al Faruqi, Macmillan,
The mosque - M Frishman and H-U Khan, Thames and Hudson, ISBN 0-500-28345-1
The Cathedrals of Britain - David L Edwards, Pitkin Pictorials, ISBN 0 85372 451 2
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