Revisiting Spherical Shell Knockdown Factors Used for Design Protection Against Collapse From Buckling

Abstract The buckling performance of shells is well-known to be sensitive to geometric imperfections. Previous research has shown that when critical buckling stress is calculated without consideration of such imperfections, the analytical and experimental results can differ substantially. ASME BPVC Section VIII Division 2 Part 5 offers two distinct methodologies (Method A and B) for protection against collapse from buckling of shells. Both methods require usage of Finite Element Analysis methodology for evaluations. Method A uses linear materials and eigenvalue solution to calculate the allowable compressive stress by employing a knockdown factor (capacity reduction factor) to account for the imperfections that may exist in the vessel without explicitly modeling the imperfection itself. Conversely, Method B requires the imperfection to be included in the model based on fabrication tolerances and the mode shape calculated from the eigenvalue solution instead of using a knockdown factor. In this study, the basis of the knockdown factor that is used for Method A is revisited for the spherical shells using case studies. A comprehensive parametric study utilizing finite element analysis is performed on various spherical shell radius to thickness ratios. The case studies used in this paper all have critical buckling stresses below 55% of the yield stress. This enables the calculations for allowable external pressure using either Method A or B in accordance with the code. The allowable external pressure is calculated using Method B for various shell radius to thickness ratios using initial imperfections that are based on fabrication tolerance and dominant eigenvalue mode shapes. The results of Method B are then utilized to calculate alternative knockdown factors for Method A that will yield the same allowable external pressure calculated using Method B. These results are presented to establish a lower bound analysis based knockdown factor for spherical shells.