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Structural Mechanisms and Geometry

At some point in every class on structural analysis, the students will be confronted with a diagram like the one above, showing something that looks like a potato with cartesian axes penetrating it. The fancier potatoes have straight and curved arrows for applied forces and moments drawn in as well. There are important points to be made with such diagrams, but there is a limit on their applicability: structures, in general, are not potatoes.

I’ve been talking about “structural mechanisms” for three days without attempting to give a general definition or general examples. I’m not a theorist, so my definition is a little rough, but I’d say that a mechanism is a simple (possibly irreducibly simple) structural action consisting of a a load, a member resisting the load, and a load path. Examples will probably make that more clear.

The word “column” has a lot of baggage attached to it so I’m going to use the name “strut” for a structural member that does nothing but carry compression along its length. The last three words are important, because the structural action depends on the geometry. If I want to be formal, I’d say that a strut is a linear member (idealized as a one-dimensional line) that carries one force: compression parallel to and concentric with its axis. Pin-connected compression members in trusses are struts (if we hand-wave away all the imperfections in modeling reality), as are interior columns in building with exterior bearing walls that carry both vertical and lateral loads. There’s an obvious counterpart mechanism of a tension tie, which is the same thing except with the direction of the load reversed.

One-dimensional members carrying one-dimensional loads are sort of boring (although not really because buckling still enters into the analysis) so let’s look at a “beam”: idealized as a straight one-dimensional member carrying loads at right angles to its axis. So it’s modeled as a 1D member (sort of) but with 2D structural action. For that to work, the 1D member has to have strength and stiffness at right angles to its axis, so it’s not really 1D, but that kind of fiction lies at the base of all structural analysis. Of course, the strut had to have cross-sectional area so it’s not really 1D either. Why is the load at right angles to the axis and not in an arbitrary direction? Because an arbitrary-direction load can be broken down into vector components parallel to and perpendicular to the axis, and turned into a combination of the strut mechanism and the beam mechanism. (This is why I’m playing around with the idea of “irreducibly simple.”)

You can go a long way identifying mechanisms in this manner. An arch is a linear member with a single direction of curvature loaded in the plane of curvature and on the convex side. A catenary (in the broad sense) is a linear member with a single direction of curvature loaded in the plane of curvature and on the concave side. A dome is a curved plane with a single direction of curvature loaded on the convex side. A potato…

Note what’s not here: complex assemblies. Trusses are not, nor are frames. In short, most trusses are beams as mechanisms. The example of the wood trusses at the Wagner Institute could be looked at as beams or as arches. The frame of a tall building can be looked at as a cantilever beam, sticking out of the ground…as a matter of fact, the portal method that was used to analyze the frames of most early skyscrapers is based on that assumption.