Experiments and maths.
You need to break stuff to know what they can handle but we talk about smaller parts like putting a concrete sample in a hydraulic press and check what pressure it can handle. Reinforced concrete can made into a beam and you check what force is require fo it to crack. The same for metal or other material that is stretched, compressed, bent etc to see how much it can handle. This include joints between diffrent parts. Destructive testing like this is important to build up a understanding of material. But you do not need a complete bridge, we can separate individual parts.
You can then with maths calculate all the forces on a bridge to determine how much load it can hold.
That is a bit idealized because experience from previous bridged are included the mathematical model used determine the strength.
The methods have improved over time. There was no math models in the past just expedience what worked. at the same time there was no heavy vehicles and bridges spans was not very long. But it have change with out understanding of engineering.
It has been said that “Any idiot can build a bridge that stands, but it takes an engineer to build a bridge that barely stands.” The point is it is not had to make a bright that do not have to lon a span stong enough just use a lot of material. Arch bridge have been build since antiquity and some have remain to this day. The problem is the huge amount of material and work that need to be done and limits in bridge spans. Today we make bridges that can hold more for a lot less because we know what is just enough
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