If you enjoy doing the mathematics, then the Von Mises-Hencky equation for triaxial state of compression is dependent upon the internal bore pressure and physical pipeline cross sectional geometry.
Of interest is the fact that wall material stress is a linear correlation to both these factors, something frequently overlooked in the literature. The Von Mises-Hencky equation is a natural extension of Thick Wall Pressure Vessel Theory of which a pipeline is treated infinitely long. You could get fancy and model longitudinal stress as thermal expansion/contraction, but this would presuppose that those steel properties were well understood.
Of course the easy way to do it is open a basic textbook on Mechanics of Materials, go to the appendix and look for Pressure Vessel Theory.
Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada