Arches, or so I would guess, are the strongest designs. How are they tested?Good question. I'm sure that they are tested by subjecting them to carrying weights such as they would be expected to carry. Thereafter, they are rated as being able to carry that weight. Of course, this is just the largest weight that they are known to be able to carry; they can probably carry larger weights, but this is dangerous because it is not known where the point of failure will be.

The strongest materials are the Biphasic materials composed of something with great tensile strength (e.g. protein) and something with great compressional strength (e.g. a mineral) will make the strongest bridges, but so far only living organisms are able to build materials like that, and when they do they are sufficiently porous because they primary function in other ways than just to provide support (e.g. wood is used by trees to carry water through the plant, in addition to hold it up). As a result, something solid, but less structurally strong, makes for stronger bridges. Metals are a good choice,and I think that most modern bridges are made out of steel.

There goes a lot of planning into the design.

The bridges are not terribly often checked. It probably depends on the bridge.I'm sure some are never checked, except by the traffic moving over them.