Engineering Rome

Evolution of the Roman Dome

jplehmer jplehmer Sep 16, 2013

This article highlights the evolution of the dome through engineering advancements by the ancient Roman civilization and summarizes their progress through several case studies. The influence the perfection of this structure had on the design of St. Peter’s Basilica Dome in Vatican City is then investigated.

Cover Figure: Interior of the Pantheon Dome (photo by author)

Roman Dome Development

As one of the most advanced ancient civilizations, the engineering accomplishments of the ancient Romans are typically recognized as extremely practical and purpose based. The engineers were always searching for structural solutions that would provide more open and usable spaces or more successful means of accomplishing their vision for a design. The concrete dome in particular is one of the most important structures that the Romans perfected through logical engineering and advancements and has had a profound impact on many large scale western civilization structures since.

Practicality of the Dome

The reason that the Romans began constructing domes is because they recognized the benefit of large spaces uninterrupted by columns, walls or any other roof supporting structure. However, with their technology of unreinforced concrete, masonry, flat roofs and columns, this vision was not possible because the unreinforced concrete or masonry roof could not span large distances without cracking and failure. Masonry and concrete both perform incredibly well in compression but poorly in tension. The difficulty in spanning long distances with flat forms of such materials is that the form will undergo bending which creates compression stresses on the top and tensile stresses on the bottom of the form as seen below in Figure 1. These bending stresses cause cracking on the tension side and the masonry or concrete form will collapse if the crack progresses through the cross section.

Figure 1: flat form bending and stresses (“Bending Stress”, n.d.)

Perhaps the Romans had attempted such designs and seen that they needed to develop a more suitable method of obtaining large open rooms. For a civilization that had extensive knowledge of arches, the dome seems like a logical progression as it is merely an arch spun 360 degrees to create a hemispherical three dimensional form. The engineers of the Roman time had already realized the potential of the concrete or masonry arch in spanning large distances under heavy loads by compression forces, so it is likely they realized that a well-engineered dome would be similarly effective for large spans when applied to a three dimensional space.

Influence from Other Civilizations

When considering the beginning of dome usage in Rome, it is reasonable to think the engineers developed the idea of a dome on their own. However, evidence of dome structures dated prior to the Roman Empire have been found throughout the middle east and surrounding regions, though many of these are corbelled domes and not true domes. A corbel dome is unlike a true dome in that it does not rely purely on the compressive forces between the masonry or concrete components to maintain it’s shape and structural integrity and therefore has a very limited span (Chant & Goodman, 1999). Some archaeological investigations have revealed other ancient civilizations that were building true domes and several have been uncovered in the ruins of the Sumerian city state of Ur (Chant et al., 1999). Chant and Goodman (1999) report that true domes and evidence of their wooden centering have been found in the royal [[#|cemeteries]] of ancient Ur and dated to 2500 BC. This would place knowledge of the masonry true dome long before the rise of the Roman Empire. Also, although not true domes, evidence of timber domes has been found in the ancient Etruscan area of Italy that date back to the beginning of [[#|the rise of Rome]] (Keinbauer, 1971). Since Rome began with heavy Etruscan influence it is easy to see how the timber dome would naturally become a part of the early engineering ideas in the city and it is likely many were constructed that we have no evidence of. As the city of Rome grew in power and began to expand, it is unknown whether or not masonry domes were encountered in nearby regions because no conclusive evidence for such structures has been found in these areas. It seems equally as likely that the domes of ancient Ur were known to the Romans through expeditions or that the Romans developed the technology on their own from progression of the arch. Either way, the dome was not a Roman invention but they were the first civilization to overcome the challenges associated with it and perfect the form.

Formwork Development

One of the greatest difficulties associated with building a large self supporting curved shape out of masonry or concrete is the formwork necessary to support it during construction. This difficulty is increased by the double curvature of a dome because it requires more support and smaller pieces of wood in order to approximate the rounded shape. For arches and domes this formwork is termed “centering” and enabled the Romans to construct the desired shape without danger of the unfinished structure collapsing in on itself before compressive forces are established by inserting the keystone and achieving equilibrium. Early in their history, the Romans developed a method of centering for arches that was accurate, stable and provided a firm support to build the arch on as seen in Figure 2 below.

Figure 2: Roman arch centering (Lancaster, 2005)

When concrete dome construction began, the centering system used for arches was a good two dimensional starting point but the engineers needed to develop a new system for double curvature. The error and progression of their method can be seen in the earlier Roman domes. Two different ways were developed to construct the dome centering, radial and horizontal formwork as seen in Figure 3 below (Lancaster, 2005). With horizontal formwork, the planks had to be relatively short in order to approximate a smooth curvature. The ends of each plank typically would line up with a single meridional line running vertically so that they could all be supported with evenly spaced radial frames. In a radial formwork system, the planks could be longer and each plank would typically end on a common circumferential line running horizontally. This method allowed less radial frames to be used but it required the circumferential line framing to be supported in a curved shape which was difficult. It is difficult to tell which system the Romans used more often because many of the domes constructed did not leave evidence of formwork on the interior (Lancaster, 2005).

Figure 3: Horizontal and Radial formwork for centering of Roman domes (Lancaster, 2005)

The way that the arches and domes of the Roman civilization were designed often provided ledges at the base of the curvature to place the centering in order to minimize the amount of ground support that was needed. For arches, often times long timber columns could be avoided through these designs and completely self supported centering was achieved (Lancaster, 2005). This avoided the problem of flimsy and unstable wood columns under heavy loads during construction that would deflect and result in a sagging arch. For domes, some columns were typically still required for support of the centering because the three dimensional shape and large spans made it difficult to achieve the same stability without added support from the ground. However, like arch centering, the Romans also had the technology to build self supporting centering for double curvature shapes but this system typically required support until all radial arches were in place and equilibrium was achieve (Lancaster, 2005). It took the engineers some time before designing a reliable method of centering for large domes that yielded a highly accurate completed shape but by the second century AD they had succeeded.

Dome Stiffening

Once the problem of formwork was solved, the stiffness of these large domes came into question. If a dome is too flexible, when the centering is removed the dome apex may sag down significantly and this deflection could result in extensive cracking at certain areas. This may have been discovered through observed deflections and failed designs or perhaps it was something that the Roman engineers intuitively knew would happen. They developed different methods of building domes with stiffening elements placed throughout the curved shape in order to avoid such large deflections. One method developed used ribs that were visible on the interior of the structure as those on the vault in Figure 4 below. The Romans used this same technique in many of the domes that they constructed. These ribs not only served to strengthen the structure but also provided a strong visual texture to the otherwise plain interior of the curved shape through indentations called coffers. The structure would not have been stable with a uniform thickness of only that at the deepest point of the coffer but it was also excessive to use a uniform thickness matching that of the ribs. By employing this ribbed technique, the dome was able to be stiffened and decorated through one method and, although increasing the difficulty of formwork, was used extensively. Another system of stiffening that is evident in domes is placed within the dome shell and is not visible from the interior or exterior. This system began being used during the fourth century AD and is characterized by a type of brick lattice that is then filled in with concrete to create a closed dome as in Figure 5 below (Lancaster, 2005). The vertical lines of bricks essentially form a series of arches that are connected at the top of the dome by a common keystone. These arches would transfer loads through pure axial forces down to the base of the dome and in many domes it can be seen that the Romans placed these brick lattices so that they landed on a main support (Lancaster, 2005). In this manner, they could avoid placing unnecessary stresses on openings and thinner areas of supporting walls.

Figure 4: Vault in Roman Forum with interior coffers forming stiffening ribs (photo by author) Figure 5: Brick lattice ribbing at the Baths of Agrippa (Lancaster, 2005)

Additional purposes have been proposed for the use of the brick lattices in domes and they were likely also intended by the Roman engineers. During construction of a dome, the lattices likely served to divide the dome up into manageable sections of construction that could be completed in a day and also to aid in placing formwork for the general shape of the dome. Many domes have horizontal courses of bipedalis bricks at vertical intervals between the brick lattices and these could have been stood on by carpenters so they could place the formwork just ahead of the concrete pouring. In this way the formwork for the entire dome would not have to be built before any concrete placement began (Lancaster, 2005). The lattices would also keep the dome stiff while curing of the concrete took place (Lancaster, 2005). With the weight of the concrete, the wooden frames used to hold the formwork during curing would have slightly deflected and the brick lattices could help mitigate this problem and increase quality control.

Lightweight Concrete

Another construction technique the Roman engineers realized would enable larger and more stable domes is strategic variation of concrete weight in different areas of the dome by changing thickness and aggregate. Domes have complex stresses because of their double curvature and under a constant distributed gravity load over their entire surface they develop stress patterns as seen in Figures 6 and 7 below (Mehrotra et al, 2013). For our purposes the value of the numbers on the colored bar are not relevant but the sign and magnitude are. Negative numbers represent compressive stresses and positive numbers represent tensile stresses. It can be seen that the meridional stresses, which run vertically, are all compressive while the hoop stresses, which run horizontally, are a mix of compressive and tensile. What makes dome behavior difficult for engineering, especially with unreinforced concrete, is the band of tensile hoop stresses towards the bottom of the dome. In an unreinforced concrete dome these stresses are typically large enough to cause the concrete to crack into a series of arches connected by a common keystone and slump down as seen in Figure 8 below. The magnitude of the tensile hoop stresses is strongly dependent on the self weight of the dome and, therefore, it would be beneficial to decrease the weight of the dome where possible. The Romans recognized these characteristics of dome behavior and knew that towards the bottom of the dome the concrete needs to be thicker and use stronger aggregates in order to carry the weight of the top portion of the dome and to provide as much resistance as possible to the tensile hoop stresses. In contrast, towards the top of the dome there are much lower stresses and they are all compressive so the engineers knew the dome could be thinner and use lighter weight aggregates. The practice of varying the concrete weight began in the first century BC by using different lightweight aggregates such as tufo giallo della via Tiberina, Vesuvian scoria, and pumice which are all weaker than the heavier tuff and brick commonly used in Roman concrete (Lancaster, 2005). By the first century AD, this practice became standard in the larger domes that were being constructed and the thickness of the concrete also began to be varied according to the stress distribution (Lancaster, 2005).

Figure 6: Meridional stresses in a hemispherical dome due to constant distributed gravity loading (Mehrotra et al, 2013) Figure 7: Hoop stresses in a hemispherical dome due to constant distributed gravity loading (Mehrotra et al, 2013)

Figure 8: Dome cracking and slump due to tensile hoop stresses (Lancaster, 2005)

Once the Romans had developed these three major advances, the technology to design and build large scale concrete domes was complete. However, these advances only resulted by constructing domes and making improvements over time and the earlier domes attest to this progression.

Roman Dome Progression Case Studies

The development of the Roman dome can be seen through unique aspects in their design of the structure as the civilization’s history progressed. The Temple of Mercury at Baiae and Temple of Minerva Medica at Rome (see Figure 9 and 10 below for location) will be studied as each either resulted in or displayed major improvements that allowed Roman engineers to perfect their dome design.