Dear ASA,

You can take as reference "Introduction to Pipe Stress Analysis" by Sam Kannapan Chapter V - Expansion Loop and Expansion Joint. There is one very simple methode to have it there by using "Nomograph to determine loop size"

If we have Pipe OD (inches), expansion to be absorbed (inches) = L*e = L *alpha*delta Temp; note that L = distance anchor to anchor where the loop compensate the axial growth, we are able to generate bend length L2.