Rome, the Eternal City. It is beautiful, full of history and life. I had a 5 day trip to Rome in the Fall of 2013, but 5 days is barely enough to check-off the major tourist attractions: the Colesseum, Vatican, Pantheon, and so on. Rome is so full of things to see that I didn't make a list of things-to-do, except one: I wanted to see the Pantheon.

 Pantheon Oculus

Pantheon Oculus

At the end, I visited it twice, and it was everything I expected to be: it feels wonderfully serene because of the single, large space, and the quality of light from the oculus. The receding geometrical shapes of the coffered dome give it a sense of vast scale, and its not hard to think of the celestial sphere when contemplating the concrete one. It feels monumental without making one feel insignificant (unlike, say, St. Peter's).

Pantheon is about 1,900 years old, and still an engineering marvel. The concrete dome is 43.4m in diameter, the same as the height of the oculus, the circular opening. Thus, you could fit a full sphere of the same diameter in the interior. It is still the largest unreinforced concrete dome in the world. Despite some cracking, it has stood up to the test of time. How?

The basic idea of a dome is simple. It is an arch rotated around a vertical axis. Thus, just like an arch, it transmits the force of gravity downwards and sideways to the foundation (or to the walls, as in Pantheon).

It is this sideways component that causes problems in structural engineering of roofs of any sort, first because it needs to be balanced, second because it can lead to tensile forces as opposed to the compressive forces of simple gravitational loading and typical building materials like stone and unreinforced concrete are a lot weaker in tension than in compression. In a dome, the lower part experiences 'hoop tension', that is tension stess along the horizontal 'rings'.

Roman engineers used several devices to ensure that their work would last. First, they made sure that the foundations of the building was sound despite weak, boggy soil. They simply threw more material at the problem when the original foundation ring cracked because of differential settlement. They built a second, larger foundation ring outside the original one.

Second, they built nice, thick walls to carry the lip of the dome. You can still see the brickwork with relieving arches on the outside.

They lightened the dome by making it thinner and by using lighter stones in the aggrage, and even inserting empty terracotta vessels towards the top. The coffer decorations reduce the volume of concrete without significaly weakening the dome structure. They also took out a lot of weight from the very top by using an oculus, which technically functions as a compression ring.

The weakest part of a dome is the lip, because its there the hoop tension is largest. Even though they didn't fully understand the cause, Romans were aware of the tendency of domes to crack along the lip and they made sure that there are a lot of reinforcement in that area. For comparison, despite Michealangelo's design to try and avoid this danger, the lip of the dome of St. Peter's had to be reinforced with iron chains in the 17th century after cracks formed.

I hope to revisit Rome some day, but for now, I have the photos from this visit in this gallery.