Comparative analysis of the design rules of hemispherical, torispherical, and ellipsoidal heads under external pressure

The hemispherical, torispherical, and ellipsoidal heads are common parts of pressure vessels under external pressure. This paper compares the design rules in main standards including GB/T 150.3, GB/T 4732.3, ASME Ⅷ-1, ASME Ⅷ-2, ASME Code Case 2286-6 and EN 13445-3. The theoretical basis of design rules among these standards is presented while equations for calculating key parameters are compared. Torispherical and ellipsoidal heads are designed as hemispherical heads by equivalent methods. The buckling pressure difference between torispherical and ellipsoidal heads and corresponding equivalent hemispherical heads is compared by finite element eigenvalue buckling analysis. For most torispherical heads, the equivalent design method is conservative. For ellipsoidal heads, the equivalent design method adopted in EN 13445-3 is conservative. The Four-Center equivalent method is aggressive for thin heads but conservative for thick heads. Further, head thicknesses calculated according to different standards for six design cases are compared. The results indicate that EN 13445-3 is more economical for low design pressure, and GB/T 4732.3, ASME Ⅷ-2 and ASME Code Case 2286-6 are more economical for high design pressure. For moderate design pressure, the choice of the standard depends on the material, with GB/T 4732 being more economical for Q345R, GB/T 4732.3, ASME Ⅷ-2 and ASME Code Case 2286-6 for S30408 and ASME Ⅷ-2 for S22053. Meanwhile, the thicknesses calculated by ASME Ⅷ-1 are always the largest. This paper aims to comprehensively compare the design methods used by different standards and differences in their theoretical basis and to suggest the use of standards in engineering practice for designers.