Without weight and if allowed to move freely, some very flexible systems will bow a great ammount in the vertical direction. If you allow CAESAR II to size springs all along these runs, you may see several contants selected. I am not saying this is your situation, but, if it is, try throwing in a rigid vertical support in the middle of these runs. You should see little thermal load on that rigid support and that may "calm down" your system.
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Dave Diehl