What you find is most likely the case. If you can follow the pipe movement and rotations you may be able to make the both side loads close to equal by rotating both trunnions (they shall have 180 degrees between)around the vertical pipe.
In case you do the same analysis by using two spring hangers with 180 degree angle in between you will get similar result, hangers will have different operating loads and/or may require different springs under the different loads unless they are rotated properly.
You either will accept the result and design/check the trunnions for the loads or rotate around the vertical pipe untill they have the same load.
You can only see this kind of behaviour from the support in case you model them or previously experienced with this problem. Most of the engineers I have met do ignore this effect or do not see it, however I do think they are lucky if anything does not happen.
Some cases the trunnion yields with the development of plastic hinge and equalize the load between the two if the yielding stops at the shared load somehow. Or one of the trunnion takes the load if oversized the other do not even touch the suppoirt structure. Most of the cases this may not be acceptable and may cause fructure depending on material and manufacture.
Our approach has to be seeing the problem area at front and do the design properly at the first place by complying with requirements. I suggest you rotate them properly and equalize the loads and make deflections same for both. Otherwise everyone in the chain will have some kind of difficulty to understand the difference and the result is not going to be the intended.
Kind regard,
Ibrahim Demir
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Peace at Home, Peace in the World.
M.K. Ataturk