Marie’s post on cracks and stability attracted a fair bit of notice, so I want to continue the discussion by talking about the intersection of the field investigation of cracks and analysis methods. More specifically, I want to talk about using the esoteric-to-nonengineers concept of “strain compatibility” to decide whether a crack is dangerous or not.
“Strain” is the deformation of a structural element under load. In short, push or pull on something and it moves. Strain compatibility is the idea that structural elements (nearly all of which are solids and I’m assuming solids for this discussion) move smoothly: they bend without kinking, they remain whole without cracking or disintegrating, and their volume remains roughly constant. These are simplifying assumptions that obviously are not always true: brittle structural elements can crack or chip, ductile elements can kink.
Strain compatibility is a helpful idea when used properly. The basic equations that are used to analyze simple beams, for example, assume that the deformation of the beam is negligible compared to its length. This method works fine for such a basic structure, but can’t be used for complicated frames because there isn’t enough information to solve the equations that describe the frame. The FEM computer programs that are used to analyze frames take deformation into account, and the combination of analyzing deformation and assuming that the frame members remain connected at their joints is enough to make the analysis workable.
But let’s look at a much simpler example, a small crack:
Very small. The crack is in the horizontal mortar joint to the left of the stone with the lighter-colored patch, and extends down the left side of the vertical hint below. This picture is a buttress projecting from a stone wall.
Common sense tells us that a crack this small is unlikely to mean anything, but [cue the laugh track] engineers aren’t hired for common sense. We’re hired for analysis. So how can I prove that this crack is unimportant? The fastest way is strain compatibility. A crack is dangerous when it allows structural movement that should not be taking place. In this case, the crack is quite short along its (vertical) length and dies into undamaged masonry. Stone is quite stiff, and there is nothing here capable of exerting enough force to significantly bend the stone; both stone and mortar are brittle and crack if they are forced to move. So if that crack represented something bad larger than itself, where does the movement go? In other words, if the left and right sides of the buttress were moving apart (which is one possible form of failure) and that’s what caused this crack, what happens to the movement at the ends of the crack? The stone is too stiff to bend around the crack if the crack were moving while the stone above and below does not, and the mortar would crack otherwise.
When we look at masonry, we see a lot of short cracks that go nowhere at their ends. Strain compatibility tells us that they can’t represent structural movement or they would be longer, intersect with other cracks at their ends, or end in spalls or other gross damage. In most cases, as is true in the picture, they represent poor adhesion of the mortar to the masonry, or poor quality mortar.
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