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12 ft. is a decent span. A 2x4 stud wall with a double top plate will likely hold more because the studs are in compression where the stress on the header would be along its "side". Just a guess, I am not a structural engineer.

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That depends on where it is placed. could be side stress or top.

If it's a header then it's on its side, sported at both ends while spanning the gap. Are you talking about a point load or uniform load?

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either or, thus it depends how its placed. The specific one Im thinking about if a tree falls is simply holding up a few ceiling joists.