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For fun, how would you analyze this joist?

I would let AI analyze it, since it looks like AI invented it. If anything screams "FEA", it is this. Looks like a hand-calc nightmare. The uphill side looks like a real conservative designed it while the downhill side looks a little LSD may have been involved.

Is that a single angle top chord? Is the bottom chord a single solid round? I think the wall panel reflection on the end joist makes it look like 2 thin bars with something intermittently welded between them.

I would bet it was tested for strength more than designed.
 
"OK BY INSPECTION"

Just kidding, but this does look like a fairly short span. My guess is this thing was designed/fabricated by an artist. If so, I'd have a hard time justifying any type of calcs for something that had no QA/QC involved in the fabrication.
 
Reminds me of the construction of the typical umbrella, which we know it NEVER buckles
 
I assume that you mean the circular part with three attached "legs". I don't think an analysis has to be very complicated but it depends on the loading and if the circular part is supported upwards.

There is something going upwards above the circle, can that be a support? If it is and the loading is the same in the three legs, and the circle has a reasonable stiffness, and the dome in the circle has no structural function. Then it shouldn't be to complicated.

But if the circle and the dome in the middle is working as a unit made of "thin" plate, that would be different.

I would use FEM to see how it performs when loaded.

Where did you find it :) ?
 
I assume that you mean the circular part with three attached "legs". I don't think an analysis has to be very complicated but it depends on the loading and if the circular part is supported upwards.

There is something going upwards above the circle, can that be a support? If it is and the loading is the same in the three legs, and the circle has a reasonable stiffness, and the dome in the circle has no structural function. Then it shouldn't be to complicated.
Now you have me lost. Where is there a circular part with 3 legs and a something going upwards?
 

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