On Gothic Cathedrals [yet again]

Flying Buttresses 

The flying buttress is synonymous with gothic cathedrals. It moves their structural skeleton out with the building envelope and exposes it to view. It is probably for this reason that it is readily identifiable as one of the defining features of gothic design.

The name flying buttress is also interesting, because if they were invented today we might simply have called them props. The term flying buttress is, I think, a reflection of the history and development of masonry structures.

As we have learned in prior blog posts, early barrel vaulted roofs required thick heavy walls to resist the lateral thrusts, which result from the vaults’ tendency to spread under the influence of their own weight. It was possible to obviate the need for heavy wall construction by concentrating these thrusts using ribbed vaults. This meant that the outer walls need only be reinforced with localised buttresses.

This was all well and good if the church had only a nave, however if there were aisles either side, or additional cloisters, then in order to avoid being in the way the buttresses had to be moved farther away from the nave. This led directly to a requirement for masonry props to ‘fly’ from the nave, over the aisles, and onto external buttresses. 

The flying buttress must resist three different types of loading. In the first instance it must resist its own self weight. It does this by forming a relatively flat arch, just like a segmental arched bridge. The vertical weight of the arch is supported on one side by the nave and on the other by the buttress. The lateral arch thrust is resisted by pushing back against the nave vaulting and against the external buttress. The thrust produced by the nave vaulting is much larger than that produced by the self-weight of the arch and therefore both the nave and the external buttresses can readily accept this load.

Of course, the thrust produced by the nave vaults is the second form of loading to be resisted. Unlike the curved load-path from the self-weight of the flying buttresses this load-path is essentially applied in a straight line, which is probably why the top surface of many flying buttresses is linear and not curved like their soffit.

There are two ways in which the nave thrusts may cause the external buttresses to fail. Firstly, they might rotate about their base due to the thrust being applied at their head. This would be an overturning or toppling failure. Providing there is sufficient mass in the buttress to provide a restoring force overturning will not occur. This is primarily a question of geometry.

The second potential mode of failure is a line of shear extending from the flying buttress to the outside face of the external buttress. In this scenario the top of the buttress is simply pushed laterally relative to the masonry below. To prevent this from happening most buttresses have a large pinnacle, whose weight squashes the shear surfaces together in order to prevent a crack plane from forming. It is in effect the application of a pre-stress, much like that which was encountered in a prior post about gothic window tracery.

The final type of loading to be resisted is wind load. Most cathedrals have a large wooden roof located above the masonry vaults. Without flying buttresses to transfer load from the base of the roof into the external buttresses the wind would generate an unacceptable thrust at the head of the nave walls. There is also a view that the weight of large timber roofs would be too great for timber ties to prevent them from spreading and consequently the flying buttresses must provide a load-path for restraint to roof spreading as well as a route for transferring wind load.

It is the requirement to provide restraint to the timber roof, which is responsible for the presence of high level flying buttresses located above those which prop the nave vaults. 

Something else which is interesting about flying buttresses is how load is actually transferred into them. This is not a trivial question. It is perhaps a statement of the obvious to say that flying buttresses are located outside the nave, while the vaults are located inside. What is perhaps less obvious is how load transfers from one into the other.

The flying buttresses are actually located just above the level at which the vaults are sprung on the inside. This is done to help facilitate lateral load transfer.

The masonry walls and piers in a cathedral are not normally solid, as you might suppose, and neither are the vault conoids. They are generally formed of dressed stone either side of a rubble-mortar infill. Medieval masons did not trust the rubble infill to transfer the vault thrusts from the solid ribs and therefore they would include full depth ‘through-stones’ known as ‘tas de charge’ just above the level at which the vault ribs spring from the internal piers. This is reflected in the external level of the flying buttresses.

The tas de charge was generally located at the top of the pier capitals and below the point at which the transverse and diagonal ribs [assuming a quadripartite vault] run together. This section of masonry was formed from several courses of single stones. There are three advantages of using single stone courses.

The first advantage is that they are able to bind the piers together and stop the dressed facing stones separating from the mortar-rubble infill. Secondly, they enable the tas de charge to transfer load into the flying buttresses efficiently. Finally, these courses can be placed without formwork before the ribs are constructed.

From the necessity for pinnacles, to pre-compress the external buttresses, to the positioning of a tas de charge to ensure that vault thrusts are transferred effectively, it is clear that medieval masons understood exactly what the load paths were in a system of flying buttresses and that they had thought about the details carefully. It is also clear that though the concept of a flying buttress is relatively simple there is actually some relatively complex thinking required to execute that concept.

On Gothic Cathedrals

How tracery works

When it comes to gothic cathedrals most people tend to think of flying buttresses. There is of course no doubt that flying buttresses were a tremendous invention and are indeed an important part of gothic architecture.

Nevertheless, while flying buttresses are rather clever devices that provide a clear load-path, the thing that always leaves me astonished is how gothic tracery works. Even when you know its secret the slenderness of gothic tracery still appears to defy the laws of physics. Perhaps, one of the best examples is to be found at Gloucester Cathedral.

The stained glass window at the end of the Chancel is reported to be the size of a tennis court, and it fills almost the entire gable. The stonework seems impossibly thin, how on earth do the mullions manage to span from floor to roof? 

Before we answer that question we are first going to take a diversion into my childhood. Every year, after Christmas, one of the things that we liked to do as a family was settle down in from of the television to watch the World’s Strongest Man competition, which back then was televised on the BBC. We would cheer on Geoff Capes, who won the competition on several occasions, and was always in with a chance.

One of the delights of the competition, which has been lost in its modern incarnation, was the nature of the games in which the competitors were required to compete. While truck pulling and car lifting has been retained, but back then there was arm wrestling, bending iron bars behind the neck, balancing weights on your head and other such fun. Another of the lost games was brick lifting. If you have never seen brick lifting before its not as straightforward as it sounds. The bricks are laid out horizontally on table and are lifted by stretching out the arms and grabbing the stack at either end. It is self evident that simply holding the two end bricks and lifting would not work. There is nothing joining the bricks together and therefore gravity will keep them firmly planted on the table. To lift the bricks it is first necessary to apply axial pressure to the stack in order to generate friction between the bricks. The magnitude of the frictional force must exceed the force of gravity in order that the strongman can lift the stack without the bricks falling out. 

It is also important to maintain the axial force directly through the centre of the bricks to prevent an unstable hinge from forming. This is harder to do than it might seem because while the arms are clamping they are also required to be lifting. You can see in the image below Geoff Capes’ right arm has moved slightly forward and a hinge has already started to form. It will not be long before the bricks experience a rapid increase in their entropy!

 This may have seemed like an odd digression from gothic cathedrals, however it is nonetheless a relevant digression, because it illustrates the principle of prestress that is at work in window tracery. In the case of brick lifting the prestress, which is applied to the bricks before they can be lifted, is provided by the strongman. It is a far greater test of his strength than the actual weight of the bricks themselves. For as long as he maintains compressive force in the stack of bricks it will continue to bridge between his two hands. Since the dominant behaviour is compression the load-path he has created is actually that of a flat arch.

We can apply the same principle to window tracery by turning the problem on its side. But before we do this let us considered the case without prestress. If we imagine the stone mullions as a tall stacks of bricks spanning between the floor and roof it would be rather easy for the wind to simple blow them over. The reason for this is because masonry can resist compression, but not tension. When the wind blows on the window load is transferred from the glass into the stone. The stone begins to bend causing it to take up a curved profile. The windward side of the curve is squashed and is therefore in compression, while the leeward side is stretched and is in tension. Of course masonry cannot resist tension and therefore the masonry fails. 

It follows that the purpose of compressive prestress in window tracery is to overcome the tensile forces that wish to cause bending in the stonework. Providing the compressive stress in the mullions exceed the tensile stresses generated by the wind they will remain stable and can arch from top to bottom. The obvious next question is where the prestress comes from? 

The answer is both simple and clever. Medieval masons simply built some rather heavy masonry above tracery windows demonstrating that they understood exactly what the load-path was. In the example above at Gloucester Cathedral the head of the primary mullions have cleverly been bent to the form of pointed arches and are actually supporting part of the roof, as well as masonry above.

This load path does of course have an important implication that is not necessarily evident straight away. Arches produce lateral thrusts, which must be resisted or they will collapse.

In the example above there is one large arch, which spans the chancel and two subordinate arches that fall within the larger arch. It is also possible to divide the larger arch into three parts; a central arch bridging the two internal mullions with buttresses either side, which transfer load into the two outer mullions. In reality the complete load-path is a combination of the two descriptions and it ensures that there is sufficient compressive load in each mullion.

If we begin with the two subordinate arches it is clear that the thrusts, which push towards the middle of the window are balanced against each other. It is no accident that the heaviest transom in the window extends from the base of each arch and joins them together.

It is also not an accident that the outward thrust from the large arch and the subordinate arches occur in the same place, though the method of resistance is not obvious from inside the chancel.

The key is of course the use of heavy buttresses on the outside of the chancel and that brings us back nicely to where we started, the humble buttress and its more elaborate cousin the flying buttress, which we will tackle in a different post.

Notwithstanding all of the above the ability of gothic tracery to resist all that nature can throw at it still amazes me!