You are right that the traditional arch construction made by stacking rocks without any binders only handle compression but not tension. Rocks in general do not handle tension very well and when you do not bind them together they do not handle any tension. So you can collapse an arch bridge by lifting it just slightly, there have been a number of accidents like this when the loading gauge have been exceeded.
However an arch does become stronger in tension once you start adding binders between the rocks or even rebar. This is fairly common in modern concrete bridges where they make the deck arched because just as rocks concrete also handles compression better then tension, but then add rebar to the bridge elements to handle tension loads as well.
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