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But just to state the answer to this puzzle in real life where beams are not glued together under water:The devil is certainly in the details - and recalling that angels dancing on pinheads is a specialty of mine,
I have a wooden beam, circular cross-section. I install it into a concrete base inside a caisson (is that the big pipe they use for in-water projects?). The concrete sets and we allow water to fill in and completely cover the beam so that it is well below the surface of the water. I believe that the beam will shrink due to the pressure x area at the top and that if the water was high enough above the top of the beam, you could even get a measurable change in length.
And I guess if I believe the above then I also have to say that if the water is not above the top of the beam, then the beam will stay the same length as it was when it was vertical in dry air.
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