You say the deadweight movement is small. I would disregard.
Some situations (e.g. very flexible pipe, very high load variation) will produce larger displacement here.
I know of a few users who will attempt to select a shorter range spring based on this reduced deflection. If that's your intent, you can use parts of your CAESAR II output to size your own spring and then specify the spring rate and theoretical cold load as model input.
We also have a Configuration switch that will allow you to include the proposed spring stiffness in the operating case which collects the proposed hanger's deflection - "Include Spring Hanger Stiffness in Hanger OPE Travel Cases".
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Dave Diehl