J. Randolph Kissell, Trinity Consultants, USA, solves a cold case, and outlines how to size wind girders for tanks of any diameter.
C
ylindrical aboveground storage tanks are very efficient at resisting hydrostatic pressure caused by the liquid they store, which puts the cylindrical shell in tension. Conversely, cylinders are less effective in resisting external pressure from wind, which places the shell in compression that can cause buckling. Tank design standards such as API 650 have long required that shell buckling strength be compared to these compressive stresses, and that stiffening rings (called wind girders) be provided when the shell would buckle without such stiffeners. Storage tanks without fixed roofs, called open top tanks, always require a wind girder near the top of the shell to resist buckling from the wind. Tanks with fixed roofs and open top tanks sometimes require a stiffening ring between the tank bottom and the tank top; such rings are called intermediate wind girders. The maximum distance between stiffened points (the tank bottom, a wind girder, or a fixed roof) was established by buckling theory for cylinders developed in the 1930s. McGrath adjusted the theory to address cylinders with varying thickness over their height and incorporated this into API 650 in the 1960s. The resulting 650 equation relating shell thickness (t), unstiffened shell height (H), tank diameter (D), and horizontal wind pressure (PWS) is well documented: Pws =
2.1 E ( H/D)( D/t) 2.5
(1)
Conversely, the origin of API 650’s wind girder size requirement is murky, based on an unpublished 1929 paper by Boardman, who proposed that the bending moment in the wind girder caused by wind on the tank shell is: M = 0.01PWSHD2
(2)
He noted that: “This formula has not been derived […] but at least its form has been shown to be logical”. Nonetheless, as far as estimates go, it was a fortunate one because it worked for tanks of that day. But as tank diameters
1 19 Summer 2021
