Buckling resistance of the cylindrical shells with two secondary stiffening rings under external pressure

The common way to amplify strength and stiffness of the tank wall is to use the stiffening rings. These stiffening rings can be classified as the primary and secondary stiffening rings (PSRs and SSRs). PSR is placed around the top of the tank shell and it assists to avoid ovalization at the top when the open-top tank is exposed to the external pressure. PSR having small dimensions may be used for fixed roof tanks since the roof system attached to the top of the cylindrical shell provides a natural restraint at this location. On the other hand, one or more SSRs may be required to preclude local buckling in both fixed and open-top cylindrical steel tanks (CSTs) which are exposed to external pressure. The requirements of single secondary stiffening ring have been investigated in detail in previous studies. However, in same cases, a single SSR does not provide sufficient resistance to maintain stability over the entire shell height. Thus, buckling capacity of the CSTs with two identical secondary stiffening rings have been explored in this present work. Pursuant to this aim, the requirements for stiffness of the SSRs which are given in terms of minimum second moment of area (SMA) were evaluated by performing Linear Elastic Bifurcation Analysis (LBA) of CSTs under uniform external pressure. Analysis results show that minimum SMA expression proposed by Blackler underestimates critical buckling value for the tanks, having especially low height-to-diameter ratios and low radius-to-thickness ratios. Furthermore, to trace strength reduction in the tank due to geometrical imperfections, Geometrically Nonlinear Analysis including Imperfections (GNIA) was performed. Analysis findings affirm that thin-walled structures are very sensitive to geometrical imperfections