We've covered cables...so now we're talking about how arches work. Arches are the opposite of cables. So, just as cables work in tension, arches work in compression.

A cable pulls in from its supports, so an arch pushes outwards. That's how they both span.

Now, you can see the force in a cable represented by the shape of a cable itself. But an arch is rigid so we can't "see" the force in it. What we can do is take the shape of a cable for certain loads and reverse it. That's the direction of compression force in an arch and we can call it a "thrustline".

A cable can fail in only one way: breaking. An arch can fail in two ways. It can fail equivalent to a cable i.e. a material crushing failure. Or, it can also buckle. In many ways, tension is stable while compression can be unstable.

We see this if we apply an offcenter load to an arch. We place that offcenter load on a cable, reverse its shape, and we see that the thrustline now leaves the material of the arch itself. The physical result of that is its easy to buckle the arch with the force applied offcenter.

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