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Yes, see below for more on that...
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Indeed, that's where I was confused before...I had misunderstood and thought this U was the full-length beam replacement and were trying to figure out how to get it in place on one end. I couldn't figure out how, since the main load was, as you say being carried by the columns one needed anything anyways near that stout as the intermediate beam between them. That it's a gusset plate I can go with at the dimensions.
But, that leaves me w/ the problem of not understanding what's the issue in the installation I think.
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No, I don't think that would work; what I was envisioning was a full length side plate of (say) 1/2" x 10" bolted thru the existing beam to handle the longer span w/ the upstairs load handled by the columns.
I thought your original proposal was to replace the existing beam in its entirety and my suggestion was to leave it in place and rather than put something underneath it over the existing column to trim the joists and rehang them leaving the vertical primary support on the column.
I think there's still some talking past each other owing to each having a vision but not a common set of drawings/concepts...
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Always is when get an engineer involved... ;)
Altho I commend you for getting somebody to actually look at the situation given the nontrivial nature of the loading distributions and particularly that discontinuous beam that complicates things.
Good luck; knowing the guy didn't try to fit in a full-length U to bridge the gap and claim it had a stress problem makes me feel much better about his doings...I believe it for the 1/4"T short section to hold the end moments; I wasn't so sure when presumed it was much heavier material and full length.
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