Press Coverage

22 Spring 2019 cylindrical shape. This is the same formula documented by Raymund McGrath in a paper given at the 1963 midyear API Refi ning meeting, which has been used successfully for API storage tanks for many years. The compressive strength of tank shells, thus, has been well understood. Wind girders The design of circumferential stiffeners for the shell, called wind girders, on the other hand, has not been as well understood by tank designers. Wind girders are used at the top of the shell on all open top tanks and near the mid-height of both open and closed top tanks if the shell thickness is insuffi cient to resist the wind pressure. The former are called top wind girders and the latter intermediate wind girders. Because labour costs have increased more rapidly than material costs, intermediate wind girders are becoming less frequent, and it is often more cost-effective to thicken the shell than to provide an intermediate wind girder. Wind girder design is critical to open top tanks, which require a top wind girder regardless of shell thickness. While the wind-induced bending moment in wind girders has been known, the strength of the wind girder has been debated. API 650 has included the paradoxical provision that the top wind girder's size be a function of the tank diameter squared for diameters up to 200 ft, while over 200 ft no increase in wind girder size was required. (To further confuse, intermediate wind girders had no such exemption for diameters over 200 ft.) Just as the shell strength is given in the SSRC Guide, wind girder strength can also be established using the Guide. For a ring-stiffened cylinder, the SSRC Section 14.4.2 gives the uniform external pressure P over the circumference of the shell causing elastic buckling as: P = 2E D/t λ 4 (n 2 +(λ/2) 2 -1)(n 2 +λ 2 ) 2 + EI(n 2 -1) HD 3 Where I = the moment of inertia of the ring stiffener, and λ = πD/(2H). The fi rst term is the contribution to the buckling strength from the shell, and the second term is the contribution to the buckling strength from the stiffener. The second term is also called the Levy formula for buckling of a circular ring under uniform external pressure. The number of buckle waves, n, is determined by minimising the buckling strength. Very conservative approaches to wind girder buckling were recently incorporated in API 650 Section 5.9.6.2, neglecting the shell stiffness, assuming the number of buckling lobes n = 2, and neglecting the shape and load factors for wind pressure on the shell. Table 1 provides the accurate buckling strength, and shows that the wind girder size determined by API 650 for yield strength in Section 5.9.6.1 is much greater than that required for buckling. For example, for an open top 50 ft dia. tank, the buckling pressure is 792 psf, over 70 times greater than the wind shell pressure of 11 psf for a design wind speed of 120 mph. For a 300 ft dia. tank, the buckling pressure is 1320 psf, or 120 times the wind shell pressure. Therefore, a wind girder buckling check is unnecessary – only the API wind girder yield check is needed. The required wind girder section modulus can thus be written as: S = 0.00877P WS HD 2 Ω/F y Where Ω is the safety factor (1.6 in API 650) and F y is the yield strength of the wind girder. Summary Revisions to wind roof pressures are being proposed for API 650. The proposed uplift pressures decrease as the tank diameter increases. For all diameters, they are less than API 650's current uplift pressures for roofs with rise to span ratios less than 0.05, and they are less than API 650's current pressures for higher profi le roofs for diameters over approximately 190 ft. Changes to the wind girder requirements are also being considered to eliminate the unnecessary buckling check and generalise the expression for tanks of any diameter and material strength. Table 1. Buckling strength of ring-stiffened cylindrical shells subjected to uniform external pressure Tank diameter D ft 50 100 150 200 300 Shell height H ft 48 48 48 48 48 Minimum shell thickness t min in. 0.250 0.250 0.312 0.312 0.375 Shell thickness assumed t in. 0.250 0.250 0.312 0.312 0.375 Number of buckles n - 7 8 10 11 14 Distance from shell to wind girder centroid c in. 4 9 16 20 20 API 650 wind girder section modulus S in. 3 12 48 108 192 192 Wind girder moment of inertia = Sc I in. 4 48 432 1728 3840 3840 Shell pressure resistance p s lb/ft 2 189 523 492 525 389 Shell portion of pressure resistance p s /P - 0.24 0.36 0.22 0.21 0.29 Ring pressure resistance p r lb/ft 2 602 914 1701 1,933 931 Ring portion of pressure resistance p r /P - 0.76 0.64 0.78 0.79 0.71 Total pressure resistance P lb/ft 2 792 1437 2193 2458 1320

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