## Agenda item: 650-472 Load Combinations 8th Ballot
Dead Load: API 650 currently requires there to be no stress at the shell-to-bottom joint when wind loads act on the tank. This is inconsistent with API 650’s approach for seismic loads, and too conservative when wind loads are applied in accordance with accepted codes. The dead load of a tank includes the portion of the tank bottom and liquid contents (if any) that is able to act with the shell against overturning before the bottom yields. API 650 E.4.1 recognizes this and gives the width of this portion. Therefore, this weight is included in the wind overturning check. This approach is also consistent with the new approach to frangibility that the frangibility task force is proposing.
The weight of the tank contents that can be used to resist uplift is based on E.4.1 with G = 0.7 and height as 0.5H, which is:
Wind Loads for Tanks
API 650’s 10 ^{th} edition, section 3.11.1 specifies overall wind loads of 18 psf on projected areas of cylindrical surfaces and 15 psf on projected areas of conical and double-curved surfaces, and footnote a of 3.9.7.1 indicates that the local load considered for wind girder design is 31 psf. These are based on a design wind speed of 100 mph (fastest mile speed). These wind loads are compared to ASCE 7, Minimum Design Loads for Buildings and Other Structures, below.
The design wind speed is determined from ASCE 7 Figure 6-1, which is based on 3-second gust speeds (discussed further below). The ASCE 7 design wind pressure is: p = q_{z} G = 0.00256K_{z} K_{zt} K_{d} V^{ 2} I G
Assume the exposure category for all tanks is conservatively taken as category C, open terrain with scattered obstructions with heights generally less than 30 ft. This includes flat open country and grasslands. Virtually all locations are exposure category B (urban or suburban areas, wooded areas, or other terrain with numerous closely spaced obstructions having the size of single-family dwellings or larger) or exposure C. The wind load in exposure B is about 70% of that in C, so using exposure C for all cases doesn’t introduce a large conservatism, and as will be seen below, gives design wind pressures consistent with those currently used in 650. The velocity pressure exposure coefficient K_{z} for exposure C at a height of 40 ft is 1.04, and less at lower heights (Table 6-3). A height of 40 ft is proposed since the mid-height of most tanks is less than 40 ft. The topographic factor K_{zt} is 1.0 for all structures except those on isolated hills or escarpments (6.5.7.1). The directionality factor K_{d} is 0.95 for round tanks (Table 6-4). The importance factor I is taken as 1.0 for ASCE 7 Category II structures (Table 6-1). The gust factor G is 0.85 for exposure C (6.5.8.1).
Since the adoption of API 650's existing provisions regarding wind load, the US National Weather Service has changed the way wind speeds are measured and recorded from fastest mile (the maximum speed of a one mile long column of air passing a reference point) to 3-second gust (the maximum speed associated with an averaging time of 3 seconds). The speed V given in ASCE 7 Figure 6-1 is the 3-second gust speed, which ranges from 85 to 150 mph in the US, depending on location. Converting a 100 mph fastest mile wind speed to a 3 second gust wind speed per ASCE 7-98 Figure C6-1 gives a 117 mph non-hurricane wind speed and a 121 mph hurricane wind speed, so a 3-second gust wind speed of 120 mph is used here in order to compare to existing practice in API 650. The conversion factor of 1.2 given to adjust fastest mile wind speed to 3 sec gust wind speed has an error typically less than 2% for the range of wind speeds likely to be considered.
The design wind pressure is then: p = q_{z}G = 0.00256K_{z} K_{zt} K_{d}V^{ 2} I G = 0.00256(1.04)(1.0)(0.95)(120)^{2 }(1.0)(G) = 36.4 G
p = (36.4)(0.85) = 31.0 psf
This wind pressure matches the 31 psf in API 650 section 3.9.7.1 footnote (a) before a 5 psf internal vacuum is applied. As explained in footnote (b) of 3.9.7.1, the 36 psf pressure is assumed to apply uniformly over a local area of the tank shell (equal to the theoretical buckling mode), and a shape factor is not applied. This is consistent with the distribution of wind pressure shown in the diagram below, where the maximum inward pressure is shown to occur on the windward side of the tank, at a pressure equal to 1 p. The assumption of a 120 mph 3-second gust design wind speed is thus shown to provide an equivalent wind pressure (i.e., 31 psf) to that presently assumed for the design of wind girders.
The average wind pressure on a cylindrical tank given in ASCE 7 is the design wind force ( F/A_{f} = p C_{f} = p_{avg}
ASCE 7 Figure 6-19 gives a force coefficient ( C_{f }) of 0.5 for API tanks (round cross section tanks with moderately smooth surfaces, a height-to-diameter (h/D) ratio of 1, and for which > 2.5). Applied to the previously determined design wind pressure of 31 psf, this yields an average pressure on the tank shell of 15.5 psf. For h/D equal to 2 (rare for API tanks), C_{f} is 0.52 and the average wind pressure is 16.1 psf. This ballot leaves the current API 650 requirement of 18 psf (section 3.11.1) For cone roofs, ASCE 7-98 Figure 6-3 gives external pressure coefficients ( C_{p}), and Table 6-7 gives internal pressure coefficients (GC_{pi}) to be used to determine the design wind pressure p in the equation:
p = qGC_{p} – q_{i} (GC_{pi})
ASCE 7 qualifies a tank as an enclosed structure since the area of openings in the windward shell doesn’t exceed the sum of the area of openings in the leeward shell and roof. For roofs of enclosed structures, the design wind pressure p is:
p = q_{h}GC_{p} – q_{h} (GC_{pi}) = q_{h} (GC_{p} - GC_{pi})
ASCE 7 Figure 6-5 gives the internal pressure coefficient ( GC_{pi}) for an enclosed structure as +/-0.18.
Supported cone roofs typically have a roof slope of ¾ on 12, or 3.6 ^{o} (see API 650 3.10.4.1). This is a roof-height-to-tank-diameter ratio of (¾)/12/2 = 0.031. ASCE 7 does not specifically address cone roof wind loads, but they could be determined by approximating the cone roof as a dome roof or as a hip roof. ASCE 7 Figure 6-7 for dome roofs, however, indicates that hip roof pressures should be used for dome roofs if the roof-height-to-tank-diameter ratio is less than 0.05. Therefore, wind loads for cone roofs must be determined as for hip roofs by Figure 6-6. For both domes and cones, however, the ASCE 7 wind pressure coefficients are a function not only of the roof-height-to-tank-diameter ratio (f/D), but also the tank-height-to-tank-diameter ratio (h/D). API tank-height-to-tank-diameter ratios vary from about 0.2 (for a 40 ft tall tank 200 ft in diameter) to about 1.33 (for a 40 ft tall tank 30 ft in diameter) and average about 0.6.
Considering a cone as a hip roof and using ASCE 7 Figure 6-6 for a roof slope of 3.6 ^{o} (< 10 ^{o}) and a tank-height-to-tank-diameter ratio of 0.5 gives the following values for C_{p} and pressure.
For example: p = q_{h} (GC_{p} - GC_{pi})
p = 36.4 (-0.9(0.85) – 0.18) = 36.4 (-0.945) = 34.4 psf (uplift)
ASCE 7-02 provides wind pressures for dome roofs in Figure 6-10. Like cone roofs, dome pressures are a function of the tank-height-to-diameter ratio, distance from the windward edge, and roof profile. For typical profiles permitted by API 650 (for steel domes, see 3.10.6.1 and for aluminum domes, see G.6.2) on an 80’ diameter, 48’ tall tank, ASCE 7 Figure 6-10 gives an approximate average C_{p} = -0.97, so the design wind pressure is
p = q_{h} (GC_{p} - GC_{pi})
p = 36.4 (-0.97(0.85) – 0.18) = 36.4 (-0.94) = 36.6 psf (uplift)
A computation of ASCE 7-02 wind pressure on domes is shown for 3 tanks below, using a dome radius equal to the tank diameter ( D), a typical radius for API 650 tanks (see section 3.10.6 for steel domes and G.6.2 for aluminum domes), resulting in a dome-height-to-tank-diameter ratio of 0.13:
Dome Roof Wind Pressure Coefficients C_{p} for 3 Tank Sizes
In each case, the uplift on the windward side is about 3 times the uplift on the leeward side, producing a net horizontal force in a direction opposite to the wind direction. API 650 G.4.2.3.1 similarly specifies a higher outward pressure on the windward side than the leeward side. Therefore, the horizontal effect of the wind counteracts overturning and can be conservatively neglected. A 30 psf roof uplift pressure is selected as a reasonable average for all roofs based on the above. Cone roof tanks that have a frangible connection to the tank shell are exempted from the uplift pressure since the connection of these roofs to the shell is designed to fail in the event of significant uplift pressure acting on the roof. Also, these roofs are not connected to the rafters, so the light roof plates transfer part of the imparted energy from the wind into kinetic energy, moving in wavelike action and dissipating part of the wind force. Experience shows that the proposed roof uplift loading may be too conservative for overturning calculations. The proposed loading would cause significant damage to the roof to shell junction in many tank configurations, however, this damage is not realized in existing tanks. It therefore is reasonable to limit the uplift pressure to maximum allowed by roof to shell junction.
650-472 4/24/03 |