Stress resultants for wind girders in open-top cylindrical steel tanks

Abstract

Empty open-top cylindrical steel tanks are susceptible to buckling when subjected to external pressure due to wind or partial vacuum due to blocked vents. A "wind girder" is commonly used at the top of the tank wall to increase its strength against external pressure instability. The wind pressure varies around the circumference of the tank, but is relatively constant up its height. A series of cosine functions is typically used to describe the variation of wind pressure around the circumference. Expressions for stress resultants, that form the basis of widely used design specifications such as API 650 and SH 3046, are based on simple mechanical models that adopt simplified pressure distributions and ignore interactions between the wind girder and the tank shell. Furthermore, in classical treatments a tributary height is postulated for wind loading on the girder, and this height is taken as independent of the properties of the girder and the shell. The purpose of this study is to develop a rational procedure to determine the stress resultants in a wind girder. Pursuant to this goal, Vlasov's curved beam theory is used to derive the stress resultants and displacements for an isolated wind girder under a pressure distribution defined in terms of cosine functions. A parametric study employing finite element analysis is conducted to investigate the interaction of the wind girder with the tank shell. The stress resultants and the tributary height are found to be closely related to a shell-girder stiffness ratio that is devised in this study. This stiffness ratio was developed by considering the relative radial stiffness of the cylindrical shell and that of the wind girder. The changes in response quantities are expressed as functions of the shell-girder stiffness ratio. The developed expressions are presented in a form that is immediately useful for adoption into design standards.