Agenda item: 650-472 Load Combinations 8th Ballot




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AGENDA ITEM: 650-472 Load Combinations 8th Ballot



HANDLED BY: Randy Kissell (SG Design)

PH: 919-644-8250 FX: 919-644-8252 tgbjrk@mindspring.com


SOURCE: API Fall Meeting 1998 SGD discussions.
PURPOSE: Using API 650's current level of risk of tank failure, provide a method for combining new loads, such as external pressure, with current loads, such as wind, and provide rules for combining currently considered loads (for example, snow and seismic).
IMPACT: Some designs would be more costly and some would be less costly than current designs. By making the risk of tank failure more uniform, however, the overall cost of owning and operating tanks will decrease.
PROPOSED CHANGE: This item was moved to publication at the Spring 2002 meeting with the editorial changes approved at the meeting. Publication of this item was withheld pending a reballot of the single issue contained in this ballot, which is the application of wind loads for the tank overturning stability check. The scope of this ballot is limited to this issue only. Changes from the last ballot are shown in red. The changes are those Larry Hiner requested to address his negative ballot and several other affirmative comments requesting clarifications. Briefly summarized, the changes are:


  1. Provide a default wind speed of 120 mph.

  2. Set the horizontal wind pressure as 18 psf rather than 16 psf.

  3. Limit design uplift to the strength of the shell-to-top joint.

  4. Make the load coefficient for internal pressure consistent with the rest of the load combination ballot when wind and pressure both act.

  5. Do not include the weight of the bottom in uplift resistance to be consistent with Appendix E.

  6. Set the specific gravity for the half full overturning check to 0.7.



3.2.1 (f) Wind (W): The design wind speed shall be 190 km/hr (120 mph), the 3 sec gust design wind speed shall be determined from ASCE 7 Figure 6-1, or unless the 3 sec gust design wind speed (that equals or exceeds the value based on a 2% annual probability of being exceeded (50 yr mean recurrence interval)) is specified by the purchaser (this specified wind speed shall be for a 3 second gust based on a 2% annual probability of being exceeded (50 yr mean recurrence interval). The design wind pressure shall be 0.77 0.86 kPa(V/190)2 , ((16 18 lbf/ft2)(V/120)2) on vertical projected areas of cylindrical surfaces and 1.44 kPa(V/190)2 , ((30 lbf/ft2)(V/120)2) uplift (2) on horizontal projected areas of conical or doubly curved surfaces, where V is the 3 sec gust wind speed. The 3 sec gust wind speed used shall be reported to the purchaser.

1) These design wind pressures are in accordance with ASCE 7 for wind exposure category C. As a alternative, pressures may be determined in accordance with ASCE 7 (exposure category and importance factor provided by Purchaser) or a national standard for the specific conditions for the tank being designed.



2) The design uplift pressure on the roof (wind plus internal pressure) need not exceed the design pressure P determined in F.4.1.

3) Windward and leeward horizontal wind loads on the roof are conservatively equal and opposite and therefore they are not included in the above pressures.


3.11.1 Wind Pressure Overturning stability shall be calculated using the wind pressures given in 3.2.1(f).

3.11.2 Unanchored Tanks

Unanchored tanks shall satisfy both of the following uplift criteria:


1) 0.6Mw + MPi < MDL /1.5

2) Mw + 0.4MPi < (MDL + MF)/2


where

MPi = moment about the shell-to-bottom joint from design internal pressure

Mw = overturning moment about the shell-to-bottom joint from horizontal plus vertical wind pressure

MDL = moment about the shell-to-bottom joint from the weight of the shell and roof supported by the shell and portion of the bottom that acts with the shell against uplift, roof, and shell

MF = moment about the shell-to-bottom joint from liquid; where weight of liquid is wL defined in E.4 using with the design a specific gravity G of 0.7 and a height of one half the design liquid height H, so

3.11.3 Anchored Tanks

When anchors are required, the design tension load per anchor shall be calculated as follows:



tB = 4Mw/dNW/N
where

tB = design tension load per anchor (N) (lbf)

d = diameter of the anchor circle (m) (ft)

N = number of anchors

W = weight of the shell plus roof supported by the shell less 0.4 times the uplift from internal pressure


JUSTIFICATION:
Summary: API tanks have a successful history against tank overturning due to wind, but this is achieved by API 650 understating both wind loads and tank resistance to overturning. This ballot revises 650’s wind loads and resistance to overturning to make them consistent good practice while resulting in approximately the same anchorage requirements as the current edition of 650.
API 650 users have historically applied horizontal wind loads but ignored vertical wind loads, unlike building codes. ASCE 7 and other codes apply wind pressures normal to surfaces. For tank roofs with the ASCE 7 approach, the horizontal components largely offset one another, leaving the vertical component as the primary design consideration. Applying ASCE 7 has the effect of requiring about 30 psf uplift rather than 15 psf horizontal pressure as API 650 users have done.
Applying 30 psf uplift in combination with the most severe fluid load condition (i.e., an empty tank) results in most tanks not achieving the traditional 1.5 safety factor against overturning. This application is unduly conservative, though, because it combines the most severe effects of two different loads – the 50 year wind storm and an empty tank.
To address this situation in a manner consistent with the other proposed API load combinations, a load factor is applied to the wind when combined with the most severe fluid load (i.e., an empty tank). The proposed change is illustrated below:


Details: This discussion is divided into two parts:


  1. Wind overturning stability checks

  2. Wind loads for API tanks


Wind Overturning Stability Checks
Load Factors: Load combination theory requires that the design value of a given load be combined with the arbitrary-point-in-time (APT) value of other loads. For fluid loads and wind loads, there are two cases:
a) design fluid load (for overturning, this is an empty tank) and APT wind load

b) design wind load and APT fluid load


For case (a), the APT wind load is determined in the same manner as the other load combinations were determined in previous ballots by dividing the appropriate ASCE 7 load combination involving wind by 1.4:
[1.2D + 0.8W]/1.4 = 0.9D + 0.6W
The ratio of wind load to dead load is 0.6, so 60% of the wind load is combined with the dead load for an empty tank.
For case (b), the APT fluid load is reasonably estimated as ½ the full fluid load since the fluid load ranges from empty to full.
Safety factors: In addition to determining load factors for the load combinations, we must also establish safety factors. API 650 3.6.2.1 uses a safety factor of 2.5 against rupturing the shell due to the hydrostatic pressure of a full tank’s liquid contents. The safety factor used in API 650 3.11 for overturning of an empty tank subject to wind is 1.5. For tanks with liquid levels between empty and full, a sliding scale safety factor is proposed. For example, the safety factor required for a half-full tank would be the average of the safety factors for empty and full tanks, or (1.5 + 2.5)/2 = 2.0. (See table below.)
Safety Factor As a Function of Liquid Height

Liquid Height

Safety Factor

Full

2.50

Half Full

2.00

Empty

1.50


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 10th 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 = qz G = 0.00256Kz Kzt Kd 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 Kz 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 Kzt is 1.0 for all structures except those on isolated hills or escarpments (6.5.7.1). The directionality factor Kd 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 = qzG = 0.00256Kz Kzt KdV 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 1p. 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) averaged over the projected area normal to the wind (Af ):


F/Af = p Cf = pavg
ASCE 7 Figure 6-19 gives a force coefficient (Cf ) 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), Cf is 0.52 and the average wind pressure is 16.1 psf. This ballot proposes to change leaves the current API 650 requirement of 18 psf (section 3.11.1) to 16 psf.
For cone roofs, ASCE 7-98 Figure 6-3 gives external pressure coefficients (Cp), and Table 6-7 gives internal pressure coefficients (GCpi) to be used to determine the design wind pressure p in the equation:
p = qGCpqi (GCpi)
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 = qhGCpqh (GCpi) = qh (GCp - GCpi)
ASCE 7 Figure 6-5 gives the internal pressure coefficient (GCpi) for an enclosed structure as +/-0.18.
Supported cone roofs typically have a roof slope of ¾ on 12, or 3.6o (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 Cp and pressure.


location

Cp

pressure

windward half

- 0.9

34.4

leeward half

- 0.5

22.0

For example:



p = qh (GCp - GCpi)

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 Cp = -0.97, so the design wind pressure is
p = qh (GCp - GCpi)

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 Cp for 3 Tank Sizes




30’ x 40’h

80’ x 48’h

150’ x 48’h




5,000 bbl

43,000 bbl

151,000 bbl

h/D

1.3

0.6

0.32

Pt. A (windward edge)

-1.6

-1.4

-1.0

Pt. B (center)

-1.0

-1.0

-0.8

Pt. C (leeward edge)

-0.5

-0.5

-0.3

average coefficient

-1.02

-0.97

-0.72

average uplift (psf)

38.1

36.6

28.8

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




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