If you watch the video above, and you are patient, you can watch the Manhattan Bridge deck flex as subway trains pass over. The bridge is too big to visibly* move from the weight of individual cars driving but a subway train weighs some 850,000 pounds** which is enough to cause visible deformation of the deck and its stiffening trusses.
The short version of structural reality is that any freestanding structure (as opposed to one, say, buried in the ground) will move when loaded. The example I like to use because, specifically because it’s unexpected, is that the pyramids at Giza bend when the wind blows. They don’t bend very much, of course, as they are incredibly massive and stiff relative to the load that the wind places on them. But the bending is there even if it is too small for us to see, even if it is too small to measure. When you load a free-standing structure, it moves.
There is a common statement about structural action that shows up in the comments for that video (although I don’t generally recommend reading YouTube comments) that needs to be addressed. It doesn’t need to be addressed because the world will end if it isn’t, but rather because it drives me crazy. It is “the bridge would break if it didn’t flex.” No, that makes no sense. Resistance against breaking is strength, resistance against movement is stiffness. They are related but they are not the same thing. For simply-supported beams of uniform cross-section such as wood joist or a steel wide-flange – much, much simpler structures than the Manhattan Bridge – stiffness is E x I, the elastic modulus (a property of the material the beam is made from) times the moment of inertia (a geometric property of the beam cross-section). Strength is*** Fb x S, the allowable bending stress (a property of the material that is not directly related to E, although materials with higher Es usually have higher Fbs) times the section modulus (a geometric property of the beam section that is derived from I and the beam depth). In short, you can have stiff and strong beams, stiff but weak beams, limber and strong beams, and limber and weak beams. The fact that the bridge visibly flexes under load does not make it stronger than if it did not.
This may seem nit-picky, and maybe it is. But it’s not just random YouTube comments on an obscure video. Let me put that incorrect statement in a form you hear all the time: Bend so you don’t break. Or, the tree that bends doesn’t break.
It doesn’t work that way.
* See the next paragraph down.
** Empty. Passengers can easily add another 150,000 pounds or more.
*** This is one way of calculating strength. There are others. That doesn’t change the point being discussed.
