PointedArches

This page could be read in conjunction with the pages about arches, funicular, and arches in religious buildings.

Arches are generally of two types, rounded at the crown, and pointed at the crown. The same could be said of domes. Modern arch bridges are generally round, though some concrete ones are segmented. Pointed arch bridges are mainly medieval. The shapes of domes also vary considerably, and in fact much more extremely, if we count a spire as an extreme case of a pointed dome. Many domes have a lantern or other structure at the top, which obscures the shape. Inside a spire we may see a clue to the construction of all these structures – it may contain many wooden struts, because a straight cone does not follow a funicular.

Pointed arches are found in the architecture of many cultures, particularly in buildings with a religious purpose. The shells of Sydney opera house are modern versions of the same idea.

Before looking into these arches, we can look at these two pictures, showing necklaces, one with, and one without, a pendant. Both follow funicular curves. We see that the discontinuity in the slope of the chain is associated with a point load. Inverting the chain, we see that a pointed arch should correspond to a large load at the top. In fact, the reverse is usually true – precisely because of the shape, there is less material above a pointed arch than above a round one which follows roughly the same line, apart from the point.

Some bridges do have segmental arches, because the load is applied to them at a few discrete points by columns or walls. The segments are often straight, as the main mass is in the thick deck which stiffens the whole structure. The force down each wall is large compared with the weight of the arch, and of course the thrust in the arch is even bigger, because of its slope. Thus the force in a segment is far greater than its weight, and it is more or less like a strut in a truss.

The diagrams below show the crown of an arch, and then a separation to show the forces which each half exerts on the other.

Diagram B above shows that the horizontal forces at the crown cannot go far before they reach the outer edge of the arch. Then what? Forces cannot just disappear. In C this has been emphasised by adding a pin at the top. Diagram D is similar, but with the pin at the bottom. In C, the pin pushes the half arch horizontally. But almost immediately the line of that force hits the edge of the stone. How can it be deflected downwards? There is hardly any weight above this point that can add a downward force. The answer is, the arch has to provide the force itself. The only way an object can create a force is by deforming. The point of the arch is highly stressed, and it might even break. The pin position D is much kinder. Removing the pin allows the faces of the arch halves to meet. If they are perfectly flat and vertical, they will in principal touch at all points. In view of the results already seen, how do you think the pressure will vary, if at all, over the interface?

So the pointed arch cannot behave as a pure arch, that is, one in which the forces are entirely parallel to the material at every place.

In the next diagram, the pointed arch is a part of a wall or a bridge, which the the normal habitat of this type of arch. If we now think about the horizontal force at the crown, it is entirely believable that the thrust goes outside the voussoirs into the masonry. This is probably true at some points in any arch that is part of a masonry structure.