Modified and improved hoop stress formulas

Offshore oil and gas pipelines are exposed to external pressure due to the hydrostatic head of the water column, which is not negligible, especially for pipelines installed in deep waters. The required pipe wall thickness (WT) to resist internal and external pressures is commonly determined using a hoop stress formula. Several hoop stress formulas have been used in the industry codes [1-4] but most of them do not correctly account for external pressure. There are two types of formulas available in calculating hoop stress; a thin wall pipe formula and a thick wall pipe formula. The thin wall pipe formula is simpler and easier to use, but it is not accurate for thick wall pipes and high external pressures. The thick wall pipe formula gives an accurate solution, but the formula is complicated and does not give the required WT directly, so it is not widely used. In this paper, a modified thin wall pipe formula (very simple but moderately accurate) and an improved hoop stress formula (less simple but very accurate) are introduced to improve the accuracy of the thin wall pipe formula and to reduce the complexity of the thick wall pipe formula. Eventually, the pipe WT may be governed by collapse, bending buckling, or installation restraints (such as reeling requirements), but it is true that the hoop stress formula is useful to initially check for the required pipe WT. The purpose of this paper is to draw special attention when using the thin wall pipe hoop stress formula with the (P_i-P_o) term. If the external pressure is to be considered, the proposed modified thin wall pipe formula (containing an extra-P_o term) or the improved hoop stress formula (containing another extra -0.4 (P_i-P_o) term) is recommended.