Quote History Quoted:
Your summary is correct.
Water leaves the bridge as the boats go onto it. You could fill it with boats, there would be less water, but the water that left would equal the weight of the boats that were sitting there.
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Technically, adding boats will raise the height of the water in both the lakes and the bridge and thereby increase the load, although the amount is pretty much insignificant for the case of the bridge, unless its surface area makes up a significant percentage of the area of the combined bridge plus lakes. Also, the location of the boats being in either lake or "on" the bridge has no effect on the total. The effective load on the bridge of any boat anywhere on the body of water would be (displaced weight of boat) * (surface area of the bridge) / (Total surface area of bridge and lakes).
You will also get some transient changes in the load carried by the bridge due to movement - wakes, wind-blown waves and other water movement will affect how much water is actually being held up by the bridge at any given instant, but will also (most likely) be very minor compared to the total static load.
Mike