turning a corner

During last fall’s research trip to Chicago, SOM’s Bill Baker and I got into a conversation about the intractable problem, in architectural detailing, of turning a corner.  You’d think this was an easy thing, but any wall with a thickness makes a 90° turn (or, really, any turn) something of an issue, especially in so-called ‘re-entrant,’ or inside corners.  Especially if you’re anything of a structural rationalist and want to emphasize the importance of your structural grid, because as the layers of the wall sprout out from the column line, the edge line of your elevation and the grid line of your plan start to diverge, with consequences that you can’t fully understand in two-dimensional drawing.

That’s something of a moot point these days, with the ease of digitally modeling in 3-d, but historically it’s been a point of some debate.  If the edge line of the building (the “demise line,” in the more theatrical British term) doesn’t coincide with the structural line, then what do you emphasize?  Do you make the corner lightweight, trying to make it disappear?  This was an established International Style approach–pioneered by Walter Gropius but absolutely employed by SOM in their classic glass skyscrapers.  Inland Steel took a particularly brave stance, making external corners of its floor plates and re-entrant corners of its cladding system.

By the end of the evening, we’d pointed out to ourselves that this wasn’t just a skyscraper problem, and that the corner had produced headaches and inspiration for a few hundred years.  And in the last couple of weeks that conversation has fueled a few detours to find examples of Renaissance architects struggling with this problem–how to express a one-dimensional grid line that gets manifested in three dimensional material.  Or, in Alberti’s words, how the lineaments of a design, which exist only as mathematical entities, get expressed in the matter of design, the actual stuff that buildings get made of.

Here’s the crux of the problem: Brunelleschi’s cloister at Santa Croce (1453):


You can see what he’s done–the column lines supporting the two arcades both hit on one single point, where the corner column is located.  This is correct in plan, correct in elevation…and totally wrong in perspective, because our eyeballs correctly read that the thrusts of those two arches (which, admittedly, aren’t that much physically because of the nature of the wall, but are still visually how we read the arcades) as trying to topple the column back into the cloister behind it.  It’s a visually weak detail–the column doesn’t have the whoomph (technical term) to resist the visual pressure being put on it.  (Also, the arches collide with one another in a detail that’s visually awkward and undoubtedly cost a few extra florins, as the stonecutters had to figure out the tough three-dimensional geometry of intersecting arcs).

But it wasn’t just arcades that gave Brunelleschi fits.  In the Old Sacristy of San Lorenzo, you can see that he knows there’s a ‘column’ at the internal corner of the main space, but the wall folds it in two, leaving it kind of stuck.  Its counterpart in the background is also clearly not happy:


Alberti faced the arcade problem in the Rucellai Palace (also 1451)–not open to the public, but you can see this in the Strozzi Palace, designed in the 1480s and clearly patterned on Alberti’s work:


It’s odd that Alberti would have struggled with this, since his re-invention of the pier and engaged pilaster actually provided a reasonable solution to the problem.  By giving the arches and the architrave above separate vertical elements, his successors discovered that you could have the arches land on their supports, turn the corner on the ‘column’ that now found itself buried in the depths of the pier, and then start fresh around the corner.  Here’s Bramante figuring this out in the cloister of Santa Maria della Pace in Rome:

bramante 1


There’s still the problem of the trapped column, though, right?  It turns out that if you adhere so strictly to the fairly simple rules that Vitruvius and Alberti codified, there’s no good way to turn this corner–either you end up with a weak corner or you trap a column inside a pier.

The trick turned out to be offsetting the grid by a column’s width and tripling up on columns in the corner, creating a dense area of detail while making the corner structurally and geometrically sound.  Michelangelo figured this out in his redesign of the Farnese Palace’s courtyard:

You can see that the first column in each wall is actually offset from the actual grid, like this (or, you can think of it as Michelangelo shortening the inner bays of the grid to ‘dig out’ the otherwise trapped column):

Asset 1-80

This trick shows up all over the place for the next five hundred years–in Schinckel, in Mies, in almost anything designed by an architect obsessed both with order and with the visual effects of expressing that order.  What I like best about this story is that the apparently ‘perfect’ rules of antiquity contained within them inherent contradictions between what the building order ‘wanted’ to be, and what our eyeballs want to see.  And it took some futzing around on the part of Bramante and Michelangelo to figure out how to get our senses and our minds to both be happy with what they’re seeing, even if it required a bit of fiction and chopping out a thin layer of building to get back to the grid we’re expecting.  It’s a classic case of “the lie that tells the truth,” to paraphrase a colleague of mine.  Or, as Vignola put it, right around the time Michelangelo was working on the Farnese,

“Should someone judge this a vain effort by saying that one cannot lay down a fixed rule, since, according to the opinion of all and especially of Vitruvius, it is often necessary to enlarge or to diminish the proportions of ornamental members in order to remedy with art where our vision has been deceived by some occurrence, to him I reply that concerning this matter it is necessary to know how much should appear to the eye…and then proceed in this by certain good rules of perspective, whose practice is fundamental both here and in painting…”

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