…you know, the usual itinerary for an 80 minute class.
The default ‘textbook’ for “Big and Tall” is Bill Addis’ Building: 3000 Years of Design, Engineering, and Architecture. Bill’s 2007 book was epically deflating–it’s the brilliant, all-inclusive history of construction that many of us wish we’d written, and while it’s left a bit of room for a history of architecture and engineering, it’s the must-read general history of the subject. And it’s about 95% right on.
“…in a dome made from a homogeneous material, tensions stresses, called hoop stresses by analogy with the metal hoops used in wooden barrels, are able to develop. The magnitude of these hoop stresses depends on the total weight of material above, and can be reduced by making the dome as light as possible.
“In the Pantheon the weight of the dome is reduced in several ways…”
All correct, except that the Pantheon’s dome doesn’t have a chance to develop those hoop stresses, since it’s famously cracked along its meridians. These have been plastered over so as not to offend the delicate sensibilities of tourists, but they’re there–and said to be wide enough to fit a hand through.
To Robert Mark, these cracks show that the Pantheon works less like a dome that can develop compressive stresses along longitudinal lines and tension stresses along latitudinal ones and more like a series of radially-splayed arches that are statically independent of one another and that rely entirely on the buttressing of the thick, heavy wall below–and the dead weight of the roof’s stepped rings–to resist splaying (Robert Mark and Paul Hutchinson, “On the Structure of the Roman Pantheon,” The Art Bulletin, Vol. 68, No. 1 (Mar., 1986), pp. 24-34.) Mark further hints that Roman builders wouldn’t have had any idea whatsoever that concrete might be able to take tensile forces, since no other building material they’d worked with would have suggested this. All Apollodorus, or whomever was the Pantheon’s lead builder, would have had to base the dome’s design upon would have been the barrel vaults that had become common for structures such as the Colosseum or the Theater of Marcellus. The Pantheon simply blew this principle up several times, rotated it, and like many Roman buildings simply used brute force–or, in this case, weight–to ensure stability.
In Mark’s classic 1990 book Light, Wind, and Structure, he took this idea further, pointing out that the sections of the Hagia Sophia and the Pantheon are analogous in that they both support the thrusts of a relatively thin dome with massive buttressing–though in the case of the Hagia Sophia this buttressing takes the form of transverse shear walls and (gorgeous) semi-domes instead of a massive circular wall. But more interestingly, he suggests that the windows at the base of the Hagia Sophia’s dome occur at roughly 50° from horizontal–about where stresses in a dome begin to create bursting. This is about where the Pantheon’s cracks begin, and Mark proposes that the windows are both a way to stave off disturbing (though ultimately just aesthetic) cracking. They may, of course, also represented Isidorus and Anthemius’ understanding of the “dome” as a series of independent, radially-arranged arches.
Part of “Big and Tall” is trying to understand not just how historic buildings work, but how their designers and builders thought they would work. So this is a paradigm example–instead of analysis showing how the Hagia Sophia’s dome stands up, it’s important to think about what it’s designers knew, what they didn’t know, and what they assumed. The “audacious” windows that to modern eyes look like they occur right where the hoop stresses in the Hagia Sophia’s dome would be greatest are actually perfectly placed if all you know about masonry domes is that they can only stand if you treat them like arches. And, as a result, you would possibly think of replacing the Pantheon’s cracks with openings that let light in in the most dramatic position possible, leading observers to remark on its “terrifying” stability and to assume that it was held up only by “a golden strand from heaven.” Which, I can’t help but think, is a pretty great spec.