Siv
What you are asking for is unlikely to exist. In general, if you decide to go to the extreme of attempting to calculate the temperature profile of a Zick-type saddle support for a horizontal vessel, you are going to a lot of effort for precious little return. Many factor enter in to that calculation, and I would be horribly surprised to find that anybody had gone to the trouble of creating a "standard" that provides a quick solution for all possible problems.
What, precisely, are you hoping to learn from this exercise, or are you just seeking help for a grad school homework assignment?
Normal practice, at least in our office, is to assume that the vessel expands vertically from the lowest point on the saddle. This isn't quite correct; it overstates the thermal growth slightly since this assumption leads to the vessel being supported only at one point on each saddle. Obviously, the vessel would deform; as indeed it does.
But the effect you appear to be concerned about is going to add to the vertical thermal displacement of any tank nozzle. In fact, it may well overcompensate for the error. I would expect, for most of the saddles in my experience, that the effective error would be in the order of magnitude of 1mm. Most piping systems are not terribly sensitive to imposed displacements of that scale, and most of the rest are, IMHO, poorly designed. Perhaps your system is one of the few remaining. If so, it is not suitable for a professional to comment on it given the lack of detail that you have provided.
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CraigB