In the industry, pipe stress analysis on cryogenic application is not always performed for small diameter of pipes. (below 1 1/2")(instrument pipes). Is there a technical reason for that?
Small diameter piping is very flexible so unless it is a very unusual case (such as a short length between two large vessels) there is little chance for any significant stresses to be developed.
Another "unusual case" to consider is if there is a material difference involve, i.e. a joint between materials with grossly different thermal expansion coefficients.