I said yesterday that the change from empirical rule-of-thumb building structure to analytically-designed structure involved reductive thinking. To me, the best example is the way (a) most analysis is performed in two dimensions and (b) 2D analysis is used as the basis for structural form. In other words, it’s a self-reinforcing loop of epistemology.
The picture above shows a structural groin vault at the 1822 County Records Building in Charleston, South Carolina. (There are examples closer to home, but they don’t have such pretty HABS documentation.) The rare-for-the-US use of masonry vaulting for floors instead of wood joists both leads to and is explained by the building’s popular name, The Fireproof Building. Those vaults were not designed by an engineer, they were designed according to geometric rules for vaulting developed through centuries of trial and error. It should go without saying that they are two centuries old and working fine. More importantly for today’s topic, their presence required the buildings designer, Robert Mills, to think in three dimensions. Groin vaults produce thrust in two directions in plan, at right angles to one another (both north-south and east-west, for example) and require vertical support. This is perhaps not the most complicated 3D model I can imagine, but it is and has to be 3D. You have to have walls, piers, and neighboring vaults located to provide vertical support, and abutments or balancing thrusts. Not to get too far into anthropomorphizing the structure, you have to provide what the vault needs for stability.
The alternate in 1822 would be wood beams. At that time they’d also be sized empirically rather than analytically designed, but if we allow a moment of anachronism and assume the beams would be designed the way that they are today and have been for some time, that analysis is very much not 3D. A beam is a linear element loaded at right angles to its main axis. The force, moment, and deflection diagrams are all 2D. There is a taste of 3D thinking in that we have to worry about the beam being braced to percent lateral-torsional buckling, but in a wood-joist floor that can be addressed solely through nailing down the subfloor. (Using blocking or cross-bracing is better but not absolutely necessary.) Certainly the beam does not impose absolute requirements on its surroundings: it creates no thrust and can be supported vertically by walls, or other beams, or masonry arcades…
Another easy example is the exterior walls of a building. If you’re relying on a frame, the walls don’t have to have any relation to one another or to structure. (Decades ago, I saw a proposal at MoMA for a modernist house with a concrete frame and with curtain walls consisting of curtains. It was not meant for our climate.) If you’re relaying on the walls, then their geometry in plan, the amount of their area give to windows, and their connections to one another at corners are all structural issues. The relationship of one wall to another matters. It’s worth noting that, prior to the use of computers in structural analysis, large-building frames were designed as a series of 2D frames. The Empire State Building – tallest building in the world for 40 years – has a steel frame designed solely in 2D. The effects of the east-west and north-south frame analyses had to be combined when designing columns, but the analysis themselves remained separate.
If you’re analyzing a frame in 2D and ignoring the potential structural contributions of anything other than the frame, then your frame design will reflect that. You end up with the rigid structural geometry of the mid-1900s because anything else will require difficult analysis. The curves and blobs of our contemporary architecture depend in part on the development of 3D finite-element analysis software.
