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Here's a zoomed piece of this image from Wikipedia

bridge tower close-up

That's a close-up of a tower holding a railroad bridge. A and B are two of the four columns in the tower's corners. I assume that they are placed symmetrically, so arrow B points onto the typical "outerwards" surface and arrow A points onto typical "inwards" surface.

Note that where arrow B points the surface is solid and where arrow A points there's a lattice instead. Note the numerous rivets alongside each beam - the beams look like they are box girders assembled such that each of them has three solid surfaces and one lattice surface.

What would be the reasoning for having a lattice on one of the surfaces only?

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I can see a few reasons why three of the sides would be solid and one side open. They are listed in roughly order of decreasing importance.

  1. Because of how the tower legs (columns) slope, the laced (lattice) side is the least exposed to the weather. Providing a solid surface on the three other sides limits the amount of rain and snow that will travel down the legs. This will help protect the steel and rivets from corrosion.

  2. The laced side prevents the entire leg from being closed and allows any moisture to dry without pooling.

  3. Another minor reason may be that keeping one side mostly open allows for easier access to actually construct the legs. Riveting take a lot of manual work, so being able to place hands and tools inside the member eases construction.

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