Some engineering concepts are easy to explain. For example, the idea that stress and strain are related can also be expressed, crudely, as objects squash when you push on them. Everyone understands that on an intuitive level. Other concepts, like strain compatibility, are a little more difficult.
The short version of strain compatibility, if I attempt to define it without math, is that objects – structures – have an uninterrupted physical presence. If the steel frame of a building is not broken (which can be a big if), and is loaded and therefore has deformed, we can assume that the geometry of the deformation of each beam and each column is such that they match up where they connect. If a specific column at the second floor has deformed 0.4 inches east, 0.2 inches north, and has shorted by 0.05 inches, then the ends of the beams that are connected to that column have to have moved the exact same amounts. “Strain” in engineering means movement, so “strain compatibility” means that the movements of different pieces of structure have to match. The big exception, as I mentioned above, is if things break.
The picture above shows, obviously, a crack in a brick wall. The crack is caused by failure of some adjacent structure, so that the part of the wall to the right of the crack is moving to the right. That’s not the interesting part of the picture. The interesting part is the top, where the big crack turns into several small cracks. I’m not sure why that change takes place but it’s necessary that it does. The big crack is roughly the same width top to bottom, indicating that the movement is horizontal, rather than tilting. So if the crack were to simply end, we would have a strain incompatibility, which is something that should not exist. There are a few ways that the crack could end: at an intersecting horizontal crack, at a group of smaller cracks, or if the material present could support a large tensile stress directly above the crack end. The last option isn’t true for brick, and there’s no horizontal crack. So we have several smaller cracks whose cumulative width is about the same as the big crack.
This may seem like nit-picking, but when this logic is worked in reverse, it’s quite powerful. It can be difficult to distinguish between a gap in a wall from poor workmanship and a crack in the wall. The gaps will simply end, as they do not represent movement under load; the cracks will always terminate in another crack, or at a window opening, or something similar. Cracks show the effect, in negative, of strain compatibility; gaps do not.
