Florence in Early May

We thought we’d be avoiding the bulk of the tourists in early May. Perhaps we did, but there were still plenty to rub up against in Florence. The larger problem of limited time kept us from visiting the interior of the Duomo,[i] the Cathedral of Florence. The line stretched the whole length of the cathedral; it was hot, and we were running short of time and hungry, so we sat on the piazza beside of one of the world’s most famous places, ordered pizza, white wine and people-watched. They’ll probably revoke my architectural degrees for admitting this, and Dr. Cooledge is crying to hear me admit it. In our defense, we’d been given only three hours ‘to do Florence’ and climb back on the bus else swim to the next port of call. I know, such a first world problem.

To console herself, D found a busy jewelry shop at the Piazza di Sanra Croce a few blocks away where a sharp dressed Italian flattered her saying she had such a beautifully designed engagement ring and began showing her interesting gold necklaces. You do have to watch out for charming Italians. So instead of stunning interior photos of the Duomo, D has an interesting, multifaceted Italian necklace and I have this blog. It’s damnable embarrassing.

Lemme call you back. There’s a pile of Carrara marble here.

Lemme call you back. There’s a pile of Carrara marble here.

This many centuries later, it seems quaint to comment on the Florentines’ boastful claims of how they would out-build the neighboring cities, Pisa and Sienna. For the human ego, time doesn’t seem to change the nature of the beast. Could just as well be Dallas competing with Houston. Pisa, well, it’s Pisa. Sienna has a renowned cathedral of its own that I’ve always liked from the pictures. But Florence has the greater claim on history, because without Florence, Michelangelo would have been lost to the world. But I am getting a few years ahead of myself.

A hundred years after breaking ground on their ‘new’ cathedral, it was nearly complete, though missing the dome. Took another forty or so years before the dome was finally completed in 1438. In the 15th Century, there was this difficult engineering obstacle no one seemed to be able to overcome, mainly the shear size of the basilica’s crossing made constructing its dome a daunting challenge. [ii] No one had tried a dome of this size. Did the architect, ‎Arnolfo di Cambio by name, envision the problem? Had he been boasting too much drinking white wine while chatting his patrons up?

In Italy In those days, architects weren’t sued for their mistakes.

Churches emerging from the ruins of the Western Roman Empire had evolved through the Medieval period to take the shape of the Latin Cross (whereas eastern Byzantine churches continued in the shape of the Greek Cross coming from the Roman).

The Greek Cross is the purer symmetry.

Gothic churches were formed along a central nave (long axis) with side aisles built mainly to brace the nave’s vaults, which wanted to blow out sideways if not braced by sufficient gravity. This is called in the construction industry as learning by example. In turn, church naves were intersected by the transept forming the cross. So in their earliest Romanesque conception, the intersection of vaults running at ninety degrees to each other introduced structural problems for the builders. The vaults were round arched (thus Romanesque) though nothing in scale to the original Roman due to the loss of Roman building knowledge.

Romanesque architecture is impressively gloomy, built mostly for mass and not finesse.

In the evolution to gothic the transept for the most part occurred preceding the choir and ending at an apse. The principal alter is either located back in the apse, or placed in the crossing itself in the larger ones. The crossing became, because of the tricky vault geometries, what one could call the church’s centroid and best ‘design opportunity.’ Because of the intersecting stone massing at the crossing’s four corners, it was also was the best opportunity to go vertical. What burned (sadly enough) at Notre Dame in Paris was the wooden spire rising from the crossing.

One reason architectural students are instructed in the history of architecture (other than to impress their bored dates at dinner parties) is the relatively simple lessons it can teach about structure. Architects are in truth technicians in the building sciences who like to wear bow ties. I kid the profession. But the bit about lessons in structure is true enough.

General load types in building construction are defined as lateral and vertical to make it easy on the freshman engineering students. When a book drops on your foot, the pain comes from a vertical load falling; likewise if your roof were to come down on you. When someone runs a red light, it’s the lateral load of the vehicle ramming your newly leased Mercedes that does the damage. In a cartoon, when the pig’s house is leaning sideways from the wolf’s blowing, that’s a lateral load the cartoonist wants you to laugh at. Close to the subject at hand, high winds in a hurricane create the lateral loads people living on the Outer Banks fear.

In construction, vertical loads are taken in compression, given that it’s the cheapest (and oldest) method. Lateral loads, on the other hand, complicate the picture. It’s the lateral loads that introduce stresses in traditional building materials that are wickedly difficult to resist without steel. And a good part of why gothic cathedrals look as they do.

To use another classic example, the lean of the Tower of Pisa has mainly to do with poor soils settling under too many tons of stone. Presently at Pisa, what’s endangering the structure are the lateral loads that the lean has induced, gravity wanting to pull the stones further landward. Had the 14th Century stone masons known to build a steel armature for their stone cathedral, Pisa would never had had its iconic ‘is it gonna fall while we’re here?’ tourists’ economy.

Think of a stack of books at a serious lean. The lesson for serious bibliophiles with limited shelf space is to stack your books perfectly vertical, or they may crush an unsuspecting big toe. See this if you’re still shaking your head: tension vs compression or just skip to the end.

Stone masonry is supremely capable of carrying compression loads. The Roman aqueducts are a great example still seen today. Granite has massive compressive strength of 20,000 psi (pounds per square inch). You can crush granite, but it takes some doing (20,000 psi give or take a few p’s). Please don’t plan to use it for a diving board however; it has very poor tensile strength (resistance to bending).

Think of that stack of books, one’s pages pressing down on the next. As long as no one pushes against them laterally, you can go pretty tall with your books. Books, like the dead weight of stones, don’t have great strength against lateral loads. Push against the stack and ‘Ah man, my books again!’

Before the process for modern steel was invented in the late 19th Century, wood remained the best that builders had to span wide building spaces. Wood is good in compression, and has way better tensile strength than stone.. Wood was cheaper than iron ore until the forests of Europe were denuded, which was a main attraction for shipping lumberjacks off to North America. Leaving trusses aside, wood remains limited by the size of the trees carpenters can find.

Back in Roman days, builders learned (one might argue engineered) perfectly round stone and brick arches to span over distances they couldn’t make in wood. What makes the arch so special? Round verses pointed arches–isn’t that an interior decorator’s trope thingy?

In structural engineering courses, one learned that the roof loads pressing stone against its neighbor is also trying to blow out sideways. But in an arch the weight of the stone, by friction with its neighbor, helps lock them in place, provided you get the angle of the arch correct. Stone arches work by translating the lateral forces into vertical loads onto the foundation walls via friction between the stones. The true master masons of the stone arch were the Romans. The round arch geometry did the best job to that day of not introducing large lateral loads that might blow out the supporting walls of a building. The only arch better than a round arch at transferring the loads vertically to the ground would come later: the catenary arch.

Arches receive (resist) the vertical roof loads across the width of a space, sending them to the side walls.

But since medieval builders had lost the mason’s art of round Roman arches (that more completely transfer the loads to the supporting walls, their pointed arches produced super high lateral loads they could only resist by gravity, i.e. by propping heavy stone side aisles against the nave with very limited windows and flying buttresses to resist the lateral load by their weight alone. [iii]

Brunelleschi’s Dome

The Romans had built their Pantheon to an impressive scale, but what Roman engineers had learned was lost with the collapse of their empire. Moreover, the Florentines were aiming to outdo everybody with their cathedral. The overall scale of what the Florentines’ crazy architect was hoping to build was twice that of their Roman ancestor’s best known work.

The Pantheon’s rotunda is perfectly round in plan and section, standing as one more example of Roman engineering.

Photo by Roberta Dragan, 10 September 2006

Photo by Roberta Dragan, 10 September 2006

A rectangular vestibule links the porch to the rotunda, which is under a coffered concrete dome, with a central opening (oculus) to the sky. Almost two thousand years after it was built, the Pantheon’s dome is still the world’s largest unreinforced concrete dome. The height to the oculus and the diameter of the interior circle are the same, 43 metres (142 ft.).
— https://en.wikipedia.org/wiki/Pantheon,_Rome
Pantheon’s Rotunda with oculus. Photo by  Mohammad Reza Domiri Ganji , 19 October 2017

Pantheon’s Rotunda with oculus. Photo by Mohammad Reza Domiri Ganji, 19 October 2017

The Romans had built the Pantheon’s dome using cast-in-place concrete, without reinforcement.[iv] They were the earliest to employ what is today a standard engineering method. The best present day example of a structural vault with coffered interior can be found in the early D.C. Metro stations, which were built of reinforced cast-in-place concrete. Harry Weese, the Metro architect, had studied the Romans.

But concrete requires formwork (scaffolding), built to carry the wet concrete until it can cure (harden), and the Florentines knew the amount of formwork required would exceed anything manageable. If you do the math, the height Cambio was planning (aka dreaming) his dome would attain was 375 feet, or approximately 37 stories in a modern high rise. Requiring that height of scaffolding done in wood was crazy. The Florentines may have been egoists, but they weren’t crazy, even if their architect was.

In those days an architect couldn’t be sued though might be executed by a Medici prince.

Arnoflo di Cambio, the original architect for the Florence Cathedral surely must have known the dome was beyond him. To make matters worse, he’d ordered the crossing built as a hexagon in plan, with the loads concentrated at the eight intersections. The Florentines evidently came to the same realization. What to do, what to do?

Hire Brunelleschi as your architect!

Brunelleschi was another Renaissance man. He’d studied the problem and proposed a unique solution. Instead of using cast-in-place concrete requiring scaffolding, Brunelleschi would use inner and outer layers to span the dome, the first a structural brick shell laid up in a herringbone pattern to be self-supporting as masons worked toward the center, and a second outer layer to be the weather barrier, carried on the first. Brunelleschi employed something closer to what became later known as the catenary arch, not round, but more vertical to further reduce the lateral thrust at the hexagon’s corners. Brunelleschi used scale models and intuition, since the engineering science was yet to be developed.

That’s the short story. Fifty years or so after the first crazy architect dreamed about his glorious dome and having no means to build it, Brunelleschi came through.

Still standing.  Giotto's Campanile  stands in the foreground.

Still standing. Giotto's Campanile stands in the foreground.

As a side note, Antoni Gaudi’s Sagrada Família (Church of the Holy Family) in Barcelona is the best known church employing catenary arches replacing the pointed gothic ones, geometry being something of a passion for Gaudi. Gaudi demonstrated how a catenary arch distributes loads equally over its entire shape. He did this by using a cord hung at equal distances apart, approximating a catenary curve, only upside down. [v] Gaudi was an early architect-hero for me. One day, I’ll make it to Barcelona.

Gaudi’s La Sagrada Família was largely unbuilt when Gaudi was killed by a passing tram, but he’d left drawings that brought this fantasy into existence.   SBA73  from Sabadell, Catalunya, 21 February 2011

Gaudi’s La Sagrada Família was largely unbuilt when Gaudi was killed by a passing tram, but he’d left drawings that brought this fantasy into existence.

SBA73 from Sabadell, Catalunya, 21 February 2011

This photo is of the crossing and dome of the Sagrada Família basilica, Barcelona, Catalonia. The basilica is a Barcelona icon. In 2011 the interior was completed in 2011. Work started in 1882, but the entire structure won’t be completed until the mid 2020s.

[i] From OED: duomo house, house of God, “chiefe Church or Cathedrall Church in a citie” (Florio). 

[ii] From Wikipedia:  The building area comprises of 8,300 square meters () with a length of 153 m (502 ft.), nave width 38 m (124.7 ft.), width at the crossing 90 m (295.3 ft.). The arch height is 23 m (75.5 ft.) while the height of the dome is 114.5 m (375.7 ft.)  

[iii] The oldest example of lateral loads influencing design can be seen in the Bent Pyramid in Egypt.  Dr. Cooledge taught that the Egyptians had been going for the steepest angle they could build, got about two-thirds to the top before the lack of friction resisting the lateral loads collapsed the stones.  So rather than tearing the whole thing down, they lessened the angle from there. 

[iv] An interesting side note: https: Reason-why-pantheon-hasn’t-crumbled 

[v] And a website on Gaudi’s uses of geometry: The_Geometry_of_Antoni_Gaudi