1. The force exerted as a result of thermal expansion in a rigid system is going to be E*A*alpha*delta T regardless of the distances involved. You should know that. It's the zeroth theorem of pipe stress analysis; until you have absorbed this you are in over your head; it's what we are fighting against continually.
2. Try calculating the stiffness of the structure for your support and entering that. Even if it's very stiff, it's not likely to be anywhere near the magnitude of the stiffness term E*A in the above equation. for instance, if you have a couple of rod hangers you can figure the spring constant for the rods (remember to use the root area if they're all-thread). Or if its a cantilever beam, you can handle that I hope.
3. Most spiral wound gasket vendors will tell you that E for their gasket is less than about 450,000 psi. You can put a 1/8" thick gasket element into your model and calculate an axial stiffness for it based on this E, a 1/8" thickness, and the contact area (from Sect VIII Div 1 Appx 2). Warning - flaunting this knowledge in the face of an uninformed supervisor can get you into a world of trouble.
4. Modeling the gasket compression as a gap is pure fiction - gasket compression is caused by the bolts holding the flange to the valve, and the gap is essentially closed before the system is started up. Normal bolt loads flatten the spiral element until there is some contact with the retaining ring. Usually, operating pressures will cause the bolts to stretch and the flange to cup so that a gap is created (that's why there are two load cases to calculate in Sect. VII Div 1 Appx 2). You probably can argue that this gap creates some "give" in a flanged joint (but not with the uninformed supervisor of (3.) above), but I recommend 2. as a first pass at solving your problem. (Numerous other people have also recommended (2.) to posts here as a first pass at dealing with minute lift-off of rigid supports at risers in a rack, but somehow this advice keeps flying by the readers.) USE THE SEARCH FUNCTION, GUYS AND GALS!!!!
5. I'm glad to hear that your employer understands that outside training is appropriate where no capable supervision is available. If more employers had this mindset, there would be a lot fewer posts to this board, and a lot more good pipe stress analysts around.
_________________________
CraigB