Pressure Vessel Calculations for External Pressure: ASME vs. European Code Approaches

Thin cylindrical shells under external pressure – such as those found in vacuum vessels, underwater pipelines, and jackets – are vulnerable to elastic buckling. The safe design of such shells is addressed by two main regulatory traditions: the ASME Boiler and Pressure Vessel Code (Section VIII, Divisions 1 and 2) and the European codes (EN13445, PD5500 and AD2000). While they all aim to prevent collapse, their analytical methods and assumptions differ significantly, especially in how they treat buckling mode shapes, or lobes. In this article we will bring forth the main difference among the Codes and its affect in pressure vessel calculations.

ASME Division 1: Empirical & Conservative

ASME Section VIII, Division 1 uses a chart-based empirical method derived from mid-20th-century experimental testing. No explicit formula for buckling is used. Instead, engineers compute geometric ratios A and B and with these they enter external pressure charts (ASME II, Part D) and find the maximum allowable external pressure Pa based on assumed collapse modes. Notably, Division 1 does not account for the number of lobes (buckling ridges), and any stiffening rings are treated simply by reducing the effective length between supports. This method is highly conservative but simple to use, making it suitable for general-purpose static equipment where material efficiency is not critical.

ASME Division 2: Elastic Buckling + Knockdowns

ASME Division 2 provides a more analytical option, closer to European methods. It introduces an elastic critical pressure Pcr, which is then reduced by a factor for imperfections: Pa = f {Pcr, FS, K}, where FS is the Safety Factor and K is the imperfection factor. Division 2 formulas take into account the effect of plasticity, like Division 1, the equations still do not consider circumferential lobe formation explicitly. It assumes a conservative minimum critical mode shape.

European Codes (EN 13445, PD 5500, AD 2000): Theoretical + Mode-Based

European pressure vessel codes are based on classical shell buckling theory, first established by Richard von Mises in 1929. These methods use the following generalized formula for critical buckling pressure:

Pcr = {2 E / (1-v)² } * { t / D }² * f { t/D , L/D , n }

Where “n” is the number of lobes (buckling ridges), and f {n, t/D , L/D} is a function from elastic theory. This formula gives an accurate critical pressure, which is then reduced using empirically derived imperfection and safety factors. So Pa = f {Pcr} * x, where “x” is the reduction factor. The explicit inclusion of lobes makes the European method more responsive to geometry and loading, often allowing lighter designs without compromising safety.

The choice between ASME and European pressure vessel codes is more than a regulatory decision – it’s a matter of design philosophy. ASME Division 1 offers simplicity and high conservatism, ideal for standard applications where ease of use and proven safety margins are priorities. Division 2 brings greater analytical rigor, bridging toward more efficient designs, but still remains conservative by omitting explicit buckling mode shapes.

On the other hand, the European approach – grounded in von Mises’ shell buckling theory – models the actual physical behaviour of shells more accurately. By incorporating the number of lobes and capturing geometry-sensitive instabilities, it allows for material-efficient and geometry-optimized designs, especially in weight-critical or thin-walled applications