Abstraction At Different Scales

The picture above shows part of the exposed structure of the Oculus at the World Trade Center, as seen from an escalator heading up to the Dey Street underground passage between the Oculus and the Fulton Transit Center. Those are not very strange shadows on top of the curved structural members, rather that’s dirt collecting in hard-to-reach locations. One of the problems with a unique building design is that you may not foresee all of the issues that the geometry creates.

On to the real issue, which is related but less grimy. As I’ve said before, structural engineers do not analyze actual structures, we analyze simplified models. That’s true in any era, with any type of structure. Some models are more theoretically complex than others and some are complex simply because they represent complicated buildings. Regardless of the promises of first 3D CAD and later BIM software, there comes a point where accurate representation of actual buildings stops and models become idealized. If not, we would run the risk of making a Borges story come to life. Again, repeating old posts here, even something as simple as a single beam is abstracted in analysis. The analysis of a beam compares demand (the effect of loading) to capacity. If we temporarily ignore the capacity end of things, as being too thoroughly embedded in messy reality, we still have a lot of simplifying abstraction. The beam used (among engineers) as an expression of simplicity is the “simply-supported, uniformly loaded” beam, which has a bending moment of M=WL²/8 and an end reaction of R=WL/2. There are two simplifying assumptions in quotes above: simply-supported means that the ends of the beam are free to rotate as the beam bends under load, and uniformly loaded approximates whatever real-life loading the beam may have as a single value in pounds per foot, identical along the length of the beam. The easy equations I have above are derived from mechanics and have other assumptions embedded in them: plane sections remain plane (the beam bends in a uniform manner), quasi-static landing (the load is applied slowly enough that there are no dynamic effects), no second-order effects (the beam’s deflection under load is all enough relative to the other geometry that it can be neglected), no gross changes in geometry form temperature changes, and so on. We don’t give a second’s thought to these assumptions in most design work because they are so common.

At a smaller scale, there are abstractions in the beam’s connections at each end. For example, for steel beams we simplify the way that the bolts or welds (or, in the past, rivets) interact with the beam itself, we simplify how connecting elements (usually plates and angles) bend under load. We also simplify stresses with the beam itself, for the most part ignoring the locked-in stresses from the rolling process that created the beam. At a larger scale, we generally ignore the beam’s deflection under load and any possible torsional twist from pattern loading when looking at its ability to carry axial load as part of an overall frame, only performing that kind of second-order analysis when there are external oddities.

In the usually sequence of design, we analyze the demand on the beam for gravity load, come up with a preliminary design for capacity, analyze the overall frame and modify the preliminary design as required, and then design the connections. We use a different set of simplifying assumptions at each of those four steps. (Each step may be iterated several times along the way, but each iteration of a given step would use the same assumptions.) There are four different abstractions for the same piece of structural design. And yet things generally work, because the abstractions have been developed to be more conservative (in the engineering sense) than reality.

More on this to follow…

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