Will an unreinf. conc. dome stand?

Few 1800-year-olds look so good. From within the rotunda of the Pantheon, you could be excused for thinking that the church was constructed just recently. Among all the remaining Roman sites of the Mediterranean, the basilica is probably the most well preserved. Two features contributed greatly to the preservation: its constant use as a place of worship and the incredible concrete enclosure that protects the interior from the elements.

Constructed in 126 A.D., the Pantheon very likely represents the height of Roman structural engineering achievement. In fact, the 142 ft. diameter cupola is still the largest unreinforced concrete dome in the world. That record is in no jeopardy of being broken, as no modern building code would permit such a structure without the use of at least a minimum of steel reinforcing. And yet the Pantheon stands today without any significant reinforcing to alter the original engineers' design intent.

Ancient engineers and architects found a synergy in form that provides a visual experience while enabling the structure to function. Weight was judiciously removed from the roof structure by including a 30 ft. diameter oculus and coffered interior surface. The oculus is simply a large hole in the ceiling that admits the only natural light into the space. Some might also interpret the opening as a spiritual window to the world of the gods. The coffered sides of the dome provide a waffle-shaped pattern that draws attention upward. These two elements give the only outwardly apparent visual clues to the means of structural support.

Several recent investigations have been undertaken to answer the mystery of the structure. The most frequent citation found on online accounts of the Pantheon follows: Mark, R.; Hutchinson, P. (1986), "On the structure of the Pantheon", Art Bulletin 68: 24–34. A nice online summary of those findings is presented by David Moore, P.E. at RomanConcrete.com. Some of the grandstanding is a bit unwarranted, but it is definitely easy to get carries away when describing the achievement of the Roman Engineers.

To start with, the original designers were accustomed to super-sized structures. And for all the delicacy portrayed within the Pantheon interior, the first rule of the construction is to build it big. The strip foundation on which the curved building rests is about 34 ft. wide. The wall which supports the dome is about 20 ft. thick. However, perhaps to reduce weight or provide behind the scenes storage space, 8 large niches were created within the otherwise solid wall. As usual, arches are used to great effect to relieve distribute load to piers, thus permitting the openings. This great mass of wall was necessary to provide adequate resistance to the inevitable outward thrust of the dome. No buttresses or perpendicular supporting structures were employed, as was common in later medieval structures.

The dome itself is nearly 20 ft. thick at its base and tapers to just 5 ft. thick at the oculus. A number of techniques were used to achieve the full span. First, a series of seven concentric rings of decreasing size were constructed one on top of the other, like stacking incrementally smaller metal washers. Other authors have suggested that this form is likely borrowed from the very early structural development of the corbeled arch - where a series of stones are stacked, with each cantilevering slightly past the previous. Using this technique, it's possible that the first stages of the dome were constructed without shoring down to the floor.

Beyond the stepped region, the shell becomes a smooth continuous surface. This part of the dome, in addition to the visible interior coffers, was likely cast on formwork supported from below. At the ring of the oculus, the building materials change again. Here a combination of tile and metal plates provide the compression ring that resolves all of the forces acting at the apex of the dome.
The Roman engineers impressively used the materials and methods available to them for maximum structural efficiency. They even created special light-weight concrete to reduce the overall weight of the dome. The 85 lb/ft3 (PCF) mix used at the top of the dome is approximately 40% lighter than today's normal weight concrete. It's even lighter than most conventionally available lightweight concrete. Despite the selection of lightweight aggregates, the engineers still achieved a compressive strength near 3000 lb/in2 (PSI), very near modern expectations for standard strength concrete. It's also important to point out that the Pozzolan binder used by the Romans differs quite a bit from the Portland Cement we use today (which requires a very high energy industrial process).

Despite their best efforts, cracks have been witnessed in the dome. The papers I reference above go into detail about their possible origins. They tend to equate the problem as one of excessive tensile hoop stresses near the base of the dome. Like a simple arch, domes also convert vertical forces into horizontal pressure. I prefer to think of the cracking in terms of the small displacement probably occurring at the top of the supporting wall. Stone and concrete, we all know is not a flexible material.

The obvious solution to the problem would be to wrap the base of the dome with some form of tension ring, essentially preventing it from spreading further. However, experts again disagree about when the cracks first appeared. It's possible that they formed immediately after construction, and the dome has stood for over 18 centuries since. It's even possible that the ancient designers were aware of this phenomenon but anticipated it and compensated in the early construction phases.

Barring a catastrophic seismic event, raging fire or destructive conflict, the Roman Pantheon seems to be in shape to survive many more centuries. It is a credit to the initial work of the designers to plan such a robust and awe inspiring building that future generations would have such keen interest in maintenance and preservation. The structural elegance of the rotunda will be an inspiration to engineers for many generations to come.
Do you think that the Pantheon should be reinforced to withstand possible seismic events, or should the original design integrity be maintained? Are modern building codes overly prescriptive, effectively stifiling innovation like that used at the Pantheon? Should naturally occurring Pozzolan binders used more often in modern building construction. Add your comments below.

Will it stand as a "W"?

The opinion below was provided by Ken Maschke, editor of willitstand.com and structural engineer. He is NOT a member of the Walter Towers design team. Concept and images by BIG | Bjarke Ingels Group.


Will the Walter Towers stand? Sure. There are lots of leaning towers, employing a wide variety of materials and structural systems. Frequently, the most influential element of their construction is the foundation. Nevertheless, leaning towers like the famous one in Pisa stand to this day. A more compelling argument against the Walter Towers can be made on the basis of economics. But even here, smart engineering decisions can be made to lessen the cost impact.

The renderings of the development seem to show four adjacent leaning towers. It’s not clear if each is independent or conjoined where they brush by each other. In either case, the two end towers provide the greatest structural challenge, because they do not appear able to lean against anything. What prevents them from falling over?


In engineering circles, we prefer to call this overturning. All tall buildings must resist this force, but typically it’s caused by the wind. Let’s assume that the total force of the wind hits the building just above half the building’s height. The force multiplied by that distance is called overturning moment. Moment has a lot of physical meaning, but just assume for now that it provides a measurement for comparing overturning to the resistance. Then, take a portion of the building’s weight and multiply it by the distance between the extremes of the building’s lateral-force-resisting-system to compute the resistance to overturning. If the resistance is greater, you’re on your way to a stable building. If otherwise, you have three options: socket your foundations into bedrock, add weight to the building or spread apart the structural system. Each option negatively impacts the economics of the project.

Leaning towers are even more greatly influenced by overturning. That’s because the building’s weight now works against you – more lean, more overturning moment.

To resist the increased overturning, the building’s lateral force resisting system must be chosen carefully. However, most beams and columns are not engaged in the system and do not help resist overturning. That effort is typically left up to structural concrete walls and braced frames (X-braces, diagonals, chevrons, etc.). Buildings with a structural outer face, like the Hancock Tower in Chicago, are very stable in part because the lateral system is maximally spread out. However, this system typically introduces large outer braces or otherwise reduces the light entering through the façade. Most designers would prefer to locate this part of the structure within the building around windowless elevator and stair shafts.

The Walter Towers renderings seem to imply a very open façade, precluding the use of exterior braces. One way to extend the reach of the lateral system is to engage the outer columns through the use of outriggers. These are similar in concept to the outer pontoons that stabilize a trimaran sailboat. Every ten floor or so, a stiff truss connects the interior core with the exterior columns. Frequently this truss is hidden in areas intended for mechanical equipment or storage, so to minimally disrupt the programming of the building. Using a composite structural system with a central core linked to exterior outrigger columns maximizes the resistance to overturning moment while minimizing the aesthetic impact.

The extreme bend in the Walter Towers introduces complications toward providing stability in other ways too. Wind hitting the building on the face perpendicular to the lean will cause a twisting of the building. This can be countered by a strong central core, but the shape of the walls are important. To resist twisting, a closed square shape is better than an open C-shape. The extent of the tower’s bend will also influence the location of the core. Instead of placing the core in the center at the base, it should be located at a point where it can rise as high in the building as possible without itself leaning.

In order to further reduce the effect of the lean, lightweight building materials should be used in the upper half of the tower. Steel beams and columns can provide the freedom to frame the gradually changing floors at minimum weight. The need for mass and stiffness in the core, however, probably makes concrete a preferable alternative for that element.

Will the Walter Towers stand in Prague one day? I hope so. Within the design there are many opportunities to illustrate the potential of structural design practices.

What’s missing from this discussion? Are there any other design technologies that could be employed to make these buildings stand? How would you do it? Vote, comment below or contribute to the willitstand wiki.