ballots.api.orgballots.api.org/.../ballots/docs/spring2019/650-1074_R0.docx · Web viewAPI 650’s requirements for tank components that resist wind loads (e.g., wind girder size

AGENDA ITEM 650-1074

TITLE ASCE 7 Wind UpdateDATE December 12, 2018CONTACT Randy Kissell

Trinity Consultantsphone 919-493-8952cell 919-636-0072

PURPOSE To update 650’s references to ASCE 7, Minimum Design Loads and Associated Criteria for Buildings and Other Structures for wind loads

SOURCE Bruce Roberts’ commentREVISION 0IMPACT This ballot presents API-650’s requirements for wind loads more clearly and

rationally, making the standard more user-friendly and cost-effective, and reduces the wind uplift on roofs in accordance with the latest ASCE 7 edition. The ballot also modifies the requirements for sizing wind girders, eliminating the conservatism in yield strength and the buckling check (shown to be unnecessary), and revises the shell contribution to top wind girders for consistency with 650’s treatment of other stiffeners.

RATIONALE API 650 references the ASCE 7 2005 and 2010 editions, but the current ASCE 7 edition is 2016, which treats wind loads differently than the earlier editions.

PROPOSAL Make the changes shown below.

DISCUSSION:

IntroductionAPI 650’s wind loads are based on ASCE 7, as of 2016 titled Minimum Design Loads and Associated Criteria for Buildings and Other Structures. In 2010, ASCE 7 wind speeds were revised upwards from a 100 year mean recurrence interval (MRI) to a 1700 year MRI for Category III structures, while the factor on wind loads for allowable strength design (that API 650 uses) was reduced from 1 to 0.6. The net effect of these changes on wind pressures was slight as long as both changes were recognized. ASCE 7-16, the current ASCE 7 edition, maintained this approach, made some revisions to the wind speed maps to reflect better data, and added provisions that better address wind loads on some API 650 tanks. This ballot revises API 650 to recognize these changes in ASCE 7.

API 650’s requirements for tank components that resist wind loads (e.g., wind girder size and unstiffened shell height) have the wind pressure embedded in them rather than showing the wind pressure explicitly. To reflect different wind loads at different sites, 650 factors its requirements by the design wind speed. Wind pressures are proportional to the wind speed squared. This ballot proposes to change 650’s factor to wind pressure to make the requirements more transparent.

API 650 has exempted supported cone roof tanks from wind uplift design because the uplift pressure from earlier ASCE 7 editions would sometimes require anchors and larger roof-to-shell joints than previous designs, which have largely been deemed adequate. Tank roof failures from wind uplift are rare, suggesting that current 650 wind uplift pressure is an overestimate. Based on ASCE 7-16, this ballot proposes to reduce the wind uplift pressure and eliminate the supported cone roof exemption, thereby making 650 more rational and consistent. No change to API 650’s current design wind

API 650-1074 Updating Storage Tank Wind Loads 1

pressures on tank shells is proposed. For ease of use, these pressures are approximated as uniform over projected areas, and don’t include variations in factors such as site exposure, topographic factor, site elevation, and tank height.

We can’t predict future developments in wind loads, but we put API in the best position to accommodate the inevitable changes by using transparent equations that explicitly identify the load (e.g., wind pressure), material properties (e.g., modulus of elasticity, yield strength), and safety factor. Furthermore, such an approach makes it much simpler to address different materials (e.g., carbon steel, stainless steel, aluminum), new alloys and material specifications, or different design conditions (e.g., elevated design temperatures). This ballot uses that approach.

Wind SpeedsLong ago, when wind speed maps weren’t available and wind speeds were measured by averaging over the time it took one mile of air to pass an observer (called the fastest mile wind speed), designers often just used a 100 mph wind speed for design. (Hey, it sounded good). When wind speed measurements changed to averaging over a 3 second time interval (called the 3 second gust wind speed), 100 mph became about 120 mph. (At 120 mph, the averaging time is the 30 seconds it takes air to travel a mile. The shorter the averaging period, the faster the average speed, so the wind speed measured by averaging over 3 seconds is greater - as it happens, about 20% greater – than the wind speed measured by averaging over 30 seconds). But 120 mph has no special significance. It’s retained in this ballot simply because it’s familiar to users.

The wind speed is a function of the mean recurrence interval (MRI): greater intervals have greater wind speeds. When ASCE 7 changed the MRI from 100 years to 1700 years, wind speeds increased. So what was a 120 mph site now became something like a 150 mph site. Not to worry, though, because at the same time ASCE 7 changed the factor on wind load from 1 to 0.6, which effectively offsets the increase in wind speed. Why the change in MRI? It’s technical and need not bother us here; suffice it to say that we can use the new ASCE 7 1700 year MRI wind speed maps with a 0.6 factor on wind load without increasing or decreasing the wind pressures on tanks.

API 650’s design requirements for wind loads are factored by the square of the ratio of the design wind speed for a given site to the reference wind speed. This factor is (V/120)2, for example, for shell wind pressure. In this case, the adjustment factor is 1 if the design wind speed is the same as the reference wind speed of 120 mph. As explained above, 120 mph is arbitrary, however, and API 650 could use any reference wind speed as long as the 650 requirements for components designed for wind are based on the wind pressure produced by that reference wind speed.

Wind PressuresAPI 650 Section 5.2.1(k) provides the horizontal wind pressure PWS on vertical projected areas of cylinders (tank shells) and the vertical wind pressure PWR on horizontal projected areas of conical and doubly curved surfaces (tank roofs). The wind pressures for the 120 mph reference wind speed are determined as shown below. A detailed explanation of the ASCE 7-16 variables used is given in Table 1.

Table 1 ASCE 7-16 Factors for Determining Wind Pressures on Tanksparameter symbol value ASCE 7-16 sectionwind exposure category

C: Open terrain with scattered obstructions that have heights generally < 30 ft. This includes flat, open country and grasslands.

Section 26.7.2


wind directionality factor

Kd 1.0 Table 26.6-1

load factor for wind 0.6 Section 2.4.1topographic factor Kzt 1.0 Section 26.8.2ground elevation factor

Ke 1.0 at sea level Section 26.9

velocity pressure exposure coefficient

Kz 2.01(z/900)2/9.5

for Exposure Category C, where z = height Section 26.10.1

gust-effect factor G 0.85 Section 26.11.1enclosure classification partially open or enclosed (see below) Section 26.12internal pressure coefficient

GCpi 0.18 Table 26.13-1

default risk category (used solely to determine the design wind speed V)

III: Buildings and other structures, the failure of which could pose a substantial risk to human life. Buildings and other structures not included in Risk Category IV (including, but not limited to, facilities that manufacture, process, handle, store, use or dispose of such substances as hazardous fuels).

Table 1.5-1

Enclosure classification addresses internal pressure from wind. For enclosure classification, there are two types of tanks: tanks with open vents (Annex H venting) and closed vent tanks. (The other tank type, open top tanks, have no internal pressure.) Table 2 shows that the ASCE 7 wind enclosure classification of open-vent tanks is partially open and the classification of closed-vent tanks is enclosed. Both of these classifications have an internal pressure coefficient GCpi of 0.18.

Table 2 ASCE 7 Wind Enclosure Classification for Tankstank diameter D ft 40 100 150 200 tank height H ft 48 48 48 48 Open Vent Tanks gross area of wall for Ao Ag ft2 3016 7540 11310 15080 = πDH/2gross areas w/o Ag Agi ft2 4273 15394 28981 46496 = πDH/2 + πD2/4total area of openings in wall Ao ft2 4.0 10.0 15.0 20.0 = 0.1D (= 0.2D/2)total area of openings

Aog ft2 8.4 20.4 30.4 40.4 = 0.2D + 0.35 (see API 650 H.5.2.2)

area of openings w/o Ao Aoi ft2 4.4 10.4 15.4 20.4 = Aog - Ao

enclosed? NO NO NO NO is Ao < min(0.01Ag, 4) and Aoi/Agi < 0.2?partially enclosed? NO NO NO NO

is Ao > 1.1 Aoi and Ao > min(0.01Ag, 4) and Aoi/Agi < 0.2?

partially open? YES YES YES YES if not enclosed or partially enclosed, partially open

Closed Vent Tanks


gross area of wall for Ao Ag ft2 3016 7540 11310 15080 = πDH/2gross areas w/o Ag Agi ft2 4273 15394 28981 46496 = πDH/2 + πD2/4total area of openings in wall Ao ft2 0.0 0.0 0.0 0.0 = 0total area of openings

Aog ft2 0.0 0.0 0.0 0.0 = 0

area of openings w/o Ao Aoi ft2 0.0 0.0 0.0 0.0 = Aog - Ao

enclosed? YES YES YES YES is Ao < min(0.01Ag, 4) and Aoi/Agi < 0.2?partially enclosed? NO NO NO NO

is Ao > 1.1 Aoi and Ao > min(0.01Ag, 4) and Aoi/Agi < 0.2?

partially open? NO NO NO NO if not enclosed or partially enclosed, partially open

Shell PressureFor the shell, the velocity pressure isqz = 0.00256Kz Kzt Kd Ke V 2 = 34.5 lbf/ft2

Applying the gust effect factor G of 0.85, the force coefficient on tank walls given in Section 29.4.2.1 Cf of 0.63 for tanks spaced center to center at least 2D, and the ASCE wind load factor for allowable strength design (ASD) of 0.6 gives the shell wind pressure

PWS = qz G Cf (0.6) = (34.5 lbf/ft2)(0.85)(0.63)(0.6) = 11 lbf/ft2

Although this wind pressure appears to be a reduction from 650’s current shell wind pressure of 18 psf for a 120 mph wind speed, it’s not. That’s because the ASCE mapped wind speeds have increased, offsetting the reduction in this pressure. For example, for a tank in Houston:

In ASCE 7-05, the wind speed is 110 mph, and the current API 650 wind shell pressure = 18 (110/120)2 = 15 psf

In ASCE 7-16, the wind speed is 140 mph, and the proposed API 650 wind shell pressure = 11(140/120)2 = 15 psf

ASCE 7 Section 29.4.2 is limited to tanks with diameters less than or equal to 120 ft. ASCE 7 Figure 29.4-1 provides a force coefficient Cf of 0.5 for round tanks with moderately smooth surfaces, D/qz

0.5 = 5.1 for the smallest tank diameter of 30 ft > 2.5, and H/D = 1. Since typical API 650 tanks meet all of these criteria, for tanks larger than 120 ft in diameter, Cf could be taken as 0.5, making the shell pressure

PWS = qz G Cf (0.6) = (34.5 lbf/ft2)(0.85)(0.5)(0.6) = 8.8 lbf/ft2

ASCE 7-16 Section 29.4.2 tank wind pressures are based on wind tunnel tests by MacDonald et al. (1988), shown in Figure 1 below for H/D = 0.5, which is about average for API 650 tanks. In Figure 1, positive Cp is inward pressure on the shell, and negative Cp is outward pressure on the shell. The pressure coefficients in Figure 1 are the maximum pressures over the height of the shell, and occur within 60 to 90% of the shell height. MacDonald’s study shows that the average pressure coefficient over the shell height is approximately 0.86 of the maximum pressure coefficient.


0 20 40 60 80 100 120 140 160 180

-1.5

-1

-0.5

0

0.5

1

1.5

2

Tank Shell Wind Pressure Coefficent Cp vs angle to wind

Angle to Wind Direction

Pres

sure

Coe

ficie

nt C

p

Open top tank

Figure 1 Maximum Tank Shell Wind Pressure Coefficient Cp for Open and Closed Top Tanks

Figure 1 shows:

a) For open top tanks, the maximum pressure coefficient varies approximately from 1.75 inward on the windward side, to 0.2 outward 90o to the wind direction, to 0.4 inward on the leeward third, with an average of 0.54 inward. Integrating the pressure in the wind’s direction over the shell’s circumference and height gives a drag coefficient Cf of 0.65, which compares well with the 0.5 and 0.63 coefficients given by the two approaches above from ASCE 7. When these pressure coefficients are averaged over the shell height (which is used to determine the loaded area of the shell for buckling pressure due to wind) and over the tank shell buckling length (about 15o of the circumference for common tank diameters), the maximum pressure coefficient for open top tanks is 1.5.

b) For closed top tanks, the maximum pressure coefficient varies approximately from 1.0 inward on the windward side, to 1.0 outward 90o to the wind, to 0.4 outward on the leeward third, with an average of 0.26 outward. Integrating the pressure in the wind’s direction over the shell’s circumference and height gives a drag coefficient Cf of 0.62, which compares well with the 0.5 and 0.63 coefficients given by the two approaches above from ASCE 7. Averaging these pressures over the shell height (which is used to determine the loaded area of the shell for buckling pressure due to wind) and over the tank shell buckling length (about 15o of the circumference for common tank diameters), the maximum pressure coefficient for closed top tanks is 0.8.

MacDonald’s pressure distributions are shown in plan view in Figure 2. For checking tank uplift, the average pressure is needed. For checking the strength of tank components such as the top wind girder or the shell, the maximum wind pressure on the tributary area of the component is required. The wind girder of open top tanks, as will be shown below, does not fail by buckling, but rather by flexural yielding, and therefore the portion of the circumference that influences the wind girder bending moment differs from the buckling length. Because the wind girder bending moment is derived from a


Closed

uniform horizontal pressure on the tank’s projected area, the average pressure is suitable for determining the wind girder size. The maximum pressure coefficient on the tank shell for open top tanks (1.5) and closed top tanks (0.8) is greater than the average pressure coefficient (0.63). However, the tributary area of the shell for buckling is arguably greater than the buckling length, since the shell buckling strength is derived from a uniform external pressure over the entire shell circumference. Since API 650 tanks have not often experienced shell failures due to wind, the average pressure coefficient seems suitable for shell checks also.

1 2 34

56

789

10

1112

1314

1516

171819202122

2324

2526

27

28

2930

3132

3334

35 36

Shell Wind Pressure Coefficients Cp

open top tanks closed top tanks

Figure 2 Tank Shell Wind Pressure Coefficient Cp for Open and Closed Top Tanks: Plan View

Roof PressureThis ballot proposes to reduce the wind roof pressure based on ASCE 7-16. The velocity pressure for the roof is

qh = 0.00256Kz Kzt Kd Ke V 2 = 40.5 lbf/ft2

The roof pressure is

PWR = qh (GCp – GCpi)(0.6) = (40.5 lbf/ft2)[(0.85)Cp + 0.18)(0.6)

The external pressure coefficient Cp depends on several factors:

a) Location on the roof (windward, leeward, or in between). For simplicity, this ballot uses a weighted average of these coefficients so a uniform roof pressure can be used.

b) Roof rise/tank diameter ratio f/D. For supported cone roofs, this ratio is typically 1/16/2 = 0.031; for all other roof types (self-supporting cone roofs (5.10.5), self-supporting dome and umbrella roofs (5.10.6), and aluminum dome roofs (Annex G), the average rise/tank diameter ratio is about 0.15.


c) Tank height/tank diameter ratio. Because tank heights are often about 48 ft, this ratio decreases as tank diameter increases from about 0.4 for D = 120 ft to 0.15 for D = 330 ft.

ASCE 7 Section 29.4.2.2 (Table 29.4-5) can be applied to tanks up to 120 ft in diameter and gives an average roof external pressure coefficient of 0.65 (the average of 0.8 and 0.5). For larger tanks, ASCE 7 Figure 27.3-2, External Pressure Coefficients for Domes with Circular Base, allows interpolation to determine Cp at three locations (A windward, B middle, C leeward) on the roof. The interpolations, reduced to equations from Figure 27.3-2, are:

Table 3 External Pressure Coefficients Cp for Tank Roofsf/D CpA CpB CpC

0.05supported cone roofs,1:10 roof slope;say down to 1:16 roof slope

0 < H/D < 1.0,CpA = -0.16 – 1.56H/DH/D > 1.0,CpA = -1.4

0 < H/D < 0.5,CpB = -0.22 – 0.56H/DH/D > 0.5,CpB = -0.5

0 < H/D < 0.5,CpC = -H/DH/D > 0.5,CpC = -0.5

0.15self-supporting cone roofs, dome and umbrella roofs, aluminum dome roofs

0 < H/D < 0.25,CpA = 0.3 – 4.8H/D0.25 < H/D < 1.0,CpA = -0.67 – 0.93H/DH/D > 1.0,CpA = -1.6

0 < H/D < 0.5,CpB = -0.45 – 0.9H/D

H/D > 0.5,CpB = -0.9

0 < H/D < 0.5,CpC = -H/D

H/D > 0.5,CpC = -0.5

Wind pressures on API 650 tanks using the factors given above are shown in Table 4 for roofs with a slope of 1:10 or less and Table 5 for all other roofs. Because the roof wind pressure varies by tank diameter, this ballot proposes an equation dependent on tank diameter to determine the roof wind pressures:

For roofs with a slope of 1:10 or less,

PWR = 18 psf – (0.03 lb/ft3)D

For all other roofs,

PWR = 24 psf – (0.03 lb/ft3)D

Where D = tank diameter. The equations can be expressed for both SI and USC units more simply as

PWR = KR1 – KR2D

Where KR1 = 0.86 kPa (18 lbf/ft2) for roof slopes of 1:10 or less and 1.15 kPa (24 lbf/ft2) for other roofs, and

KR2 = 4.7 N/m3 (0.03 lb/ft3)


Table 4 ASCE Wind Pressures for Tanks with Roof Slope 1:10 or less for V = 120 mph

D H H/DKz for shell

Kz for roof

qz

for shell

qz

for roof Cp PWS PWRC PWR

ft ft - - - lb/ft2 lb/ft2 - lb/ft2 lb/ft2 lb/ft2

30 30 1.00 0.849 0.989 31.3 36.4 -0.67 10.1 16.5 17.140 40 1.00 0.902 1.050 33.2 38.7 -0.67 10.7 17.5 16.860 48 0.80 0.937 1.093 34.5 40.3 -0.66 11.1 17.9 16.580 48 0.60 0.937 1.096 34.5 40.4 -0.55 11.1 15.8 15.6

100 48 0.48 0.937 1.099 34.5 40.5 -0.51 11.1 14.8 15.0120 48 0.40 0.937 1.102 34.5 40.6 -0.44 11.1 13.5 14.4140 48 0.34 0.937 1.105 34.5 40.7 -0.39 11.1 12.5 13.8160 48 0.30 0.937 1.107 34.5 40.8 -0.37 11.1 12.1 13.5180 48 0.27 0.937 1.110 34.5 40.9 -0.33 11.1 11.2 12.6200 48 0.24 0.937 1.113 34.5 41.0 -0.30 11.1 10.8 12.0250 48 0.19 0.937 1.119 34.5 41.3 -0.26 11.1 10.0 10.5300 48 0.16 0.937 1.126 34.5 41.5 -0.24 11.1 9.5 9.0330 48 0.15 0.937 1.130 34.5 41.6 -0.22 11.1 9.3 8.1

Table 5 ASCE Wind Pressures for Tanks with Roof Slope > 1:10 for V = 120 mph

D H H/DKz for shell

Kz for roof

qz

for shell

qz

for roof Cp PWS PWRC PWR

ft ft - - - lb/ft2 lb/ft2 - lb/ft2 lb/ft2 lb/ft2

30 30 1.00 0.849 0.989 31.3 36.4 -0.96 10.1 21.7 23.140 40 1.00 0.902 1.050 33.2 38.7 -0.96 10.7 23.1 22.860 48 0.80 0.937 1.093 34.5 40.3 -0.95 11.1 23.8 22.580 48 0.60 0.937 1.096 34.5 40.4 -0.88 11.1 22.6 21.6

100 48 0.48 0.937 1.099 34.5 40.5 -0.85 11.1 21.9 21.0120 48 0.40 0.937 1.102 34.5 40.6 -0.77 11.1 20.4 20.4140 48 0.34 0.937 1.105 34.5 40.7 -0.72 11.1 19.4 19.8160 48 0.30 0.937 1.107 34.5 40.8 -0.70 11.1 19.0 19.5180 48 0.27 0.937 1.110 34.5 40.9 -0.65 11.1 18.0 18.6200 48 0.24 0.937 1.113 34.5 41.0 -0.62 11.1 17.4 18.0250 48 0.19 0.937 1.119 34.5 41.3 -0.54 11.1 15.8 16.5300 48 0.16 0.937 1.126 34.5 41.5 -0.48 11.1 14.7 15.0330 48 0.15 0.937 1.130 34.5 41.6 -0.46 11.1 14.3 14.1


Figure 3 Wind on a Tank – Elevation View

H

D

PWS

PWR

ASCE 7 Section 29.7 requires that the design wind pressure > 16 psf; with the 0.6 wind load factor, this would be a minimum design wind pressure of 9.6 psf = (16 psf)/0.6. This minimum is not proposed in the ballot, however, since it’s arbitrary, and not reflective of actual wind pressures.

Compressive Strength of the ShellThe 6th edition of the Guide to Stability Design Criteria for Metal Structures published by the Structural Stability Research Council (SSRC) provides the strength of cylinders with and without circumferential (ring) stiffeners. Section 14.3.5, Cylindrical Shells Subjected to Uniform External Pressure, provides a criterion for determining whether such cylinders buckle elastically and their elastic buckling strength. Table 4 below provides the buckling parameters for API 650 tanks.

The SSRC provides two equations for the buckling strength of unstiffened cylinders subjected to uniform external pressure – one for hydrostatic pressure, which includes the effect of longitudinal stress due to pressure on the cylinder ends, and one for lateral pressure, which does not include pressure on the cylinder ends. API 650 tanks are cylinders filled with liquid and occasionally with a small internal pressure, and thus are subjected to lateral pressure rather than hydrostatic pressure. However, for typical API 650 tanks, the hydrostatic (PH) and lateral pressure (PL) buckling strengths are nearly the same, as shown in Table 4.

The ASCE 7 wind pressure distribution on a tank shell is not the uniform external pressure shown on the left side of Figure 3, but rather is given as an average pressure on the vertical projected area. The actual wind pressure is more like the distribution shown on the right side, which is based on MacDonald (1988), for an open top tank with H/D = 0.5, which is about average for API 650 tanks, as shown in Table


Figure 4 Pressure Distributions on a Tank Cross Section

Wind PressureUniform External Pressure

buckle

Wind

5. However, over a buckle wavelength, the actual pressure distribution is nearly uniform so the buckling strength of a cylinder subjected to uniform external pressure is used for the buckling strength of the shell subjected to wind pressure. The actual peak wind pressure exceeds the average wind pressure, but this is neglected.

The uniform hydrostatic external pressure PHP over the circumference of the shell causing elastic buckling is

PHP = wheren = the number of buckling lobes; the correct value of n is that which minimizes PHP. (An approximate value for n is given in API 650 Annex V.8.2.2.1)λ = πD/(2H)

As shown in Table 4, for API 650 tanks, this formula is approximated fairly accurately by


PHA =

since the parameter θ = is between 10 and D/t. This is a very happy outcome, since this approximate strength is independent of the number of buckling lobes n. This is also the equation in API 650 for shell buckling due to wind (5.9.7.1) or external pressure (V.8.1.2) and used by McGrath, who called it the modified Model Basin formula because it was based on work done in 1934 by Windenburg and Trilling at the US Navy’s Experimental Model Basin.

The K factor indicates if the buckling is elastic or inelastic:

K =

If K > 1.2, buckling is elastic. (This equation is also given in API 650 Section V.8.1.1, although it has a typo there that is being corrected in Addendum 3). Table 4 shows that buckling is elastic for API 650 tank shells, as Annex V also concludes.

Table 4 Strength of Unstiffened Cylindrical Shells Subjected to Uniform External Pressure Poisson’s ratio = ν = 0.3, modulus of elasticity = E = 29,000 k/in2

tank diameter D ft 30 100 150 200 300tank height H ft 48 48 48 48 48API 650 minimum shell thickness tmin in. 0.188 0.25 0.312 0.312 0.375shell thickness assumed t in. 0.188 0.250 0.312 0.500 0.500buckling mode factor K - 12.9 14.1 13.2 10.0 11.0is buckling elastic or inelastic? elastic elastic elastic elastic elasticλ = πD/(2H) λ - 0.98 3.27 4.91 6.54 9.82

D/t - 1915 4800 5769 4800 7200θ = 1.818H/D(D/t).5 θ - 127.3 60.5 44.2 30.2 24.7no. of buckles (hydrostatic pressure) n - 9 21 24 31 39buckling lobe length Lbw ft 10.5 15.0 19.6 20.3 24.2approx hydrostatic buckling pressure PHA lb/ft2 42.3 14.2 13.4 28.3 15.4

hydrostatic buckling pressure PHP lb/ft2 43.0 14.8 13.7 31.6 16.3

no. of buckles (lateral pressure) n - 9 19 25 27 36

shell lateral buckling pressure PL lb/ft2 43.2 14.6 13.9 30.0 16.6

maximum allowable eccentricity e in. 0.75 1.11 1.46 1.63 1.95

eccentricity/half the buckle length 2e/Lbw - 0.012 0.012 0.012 0.013 0.013

Imperfections in the cylinder shape decrease the buckling strength. To account for this, Windenburg developed an empirical expression for the maximum eccentricity e over a circumferential arc with a


length of ½ the buckle length such that the collapse pressure is at least 80% of a perfect cylinder:

e = 0.018D/n + 0.015nt

For typical API tanks, this limit on out-of-roundness divided by one-half the buckle length is approximately 0.012, as shown in Table 4. API 650 Section 7.5.4 limits local deviations in the shell to ½ in. over 3 ft, which is a ratio of 0.014, reasonably consistent with the Windenburg limit. Therefore, the buckling strength for API 650 tanks is approximately 80% of the perfect elastic buckling strength, giving the buckling strength of API 650 tank shells as

P =

The 0.8 imperfection factor is the same factor used in Annex V.8.1.

Wind GirdersShell stiffeners are required at the top of the shell for all open top tanks, and for fixed roof and open top tanks around the mid-height of the shell when the buckling strength of the unstiffened shell is less than the wind pressure on the shell. The former are called top wind girders, and the latter intermediate wind girders.

To call each a “wind girder” is perhaps misleading, because the function of a top wind girder is to act like a bulkhead on the cylinder that is the tank, whereas an intermediate wind girder serves only to stiffen the shell sufficiently to prevent the shell from buckling.

For a ring-stiffened cylinder, the SSRC Guide Section 14.4.2 gives the uniform external pressure P over the circumference of the shell causing elastic buckling as

P = where I = the moment of inertia of the ring stiffener

The first 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 the Levy formula for buckling of a circular ring under uniform external pressure.

Table 5 Buckling Strength of Ring-Stiffened Cylindrical Shells Subjected to Uniform External Pressure tank diameter D ft 50 100 150 200 300shell height H ft 48 48 48 48 48minimum shell thickness tmin in. 0.250 0.250 0.312 0.312 0.375shell thickness assumed t in. 0.250 0.250 0.312 0.312 0.375number of buckles n - 7 8 10 11 14distance from shell to wind girder centroid c in. 4.0 9.0 16.0 20.0 20.0


API 650 wind girder section modulus S in3 12 48 108 192 192

wind girder moment of inertia = Sc I in4 48 432 1728 3840 3840

shell pressure resistance ps lb/ft2 189 523 492 525 389shell portion of pressure resistance ps/P - 0.24 0.36 0.22 0.21 0.29

ring pressure resistance pr lb/ft2 602 914 1,701 1,933 931ring portion of pressure resistance pr/P - 0.76 0.64 0.78 0.79 0.71

total pressure resistance P lb/ft2 792 1,437 2,193 2,458 1,320 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 5 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 diameter 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 diameter 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 650 wind girder yield check was recently addressed in agenda item 650-1063 which determined the moment in the wind girder due to a uniform horizontal pressure distributed load w over the tank diameter as

M = 0.14wR2

This moment is determined by combining two Roark cases for loads on a ring, case 8 for a uniform lateral pressure, and case 20 for a tangential shear:

This estimate of the moment in the wind girder is approximate because the wind pressure is not uniform, nor is the resisting shear in the shell.

Presumably this moment could be positive or negative: that is, it could cause compression at the outside of the wind girder in some places around the top of the tank, and in other places it could cause tension at the outside of the wind girder. Assuming that wind pressure PWS acting on the top ¼ of the shell height H is resisted by the wind girder, and the wind pressure on the bottom ¾ of the shell height is


resisted by the tank bottom, w = PWSH/4, the tank radius R = D/2, and the moment acting on the wind girder is

M = 0.14wR2 = 0.14(PWS H/4)(D/2)2 = 0.00877PWSHD2

This is the requirement used in API 650 Section 5.9.6.1 and in this ballot.

The strength of flexural members like wind girders is the least of the strengths for lateral-torsional buckling (LTB), yielding, and local buckling. Because the shell is assumed to provide a continuous lateral brace to the wind girder, LTB needs no further consideration. API 650 currently sets the flexural strength M of the wind girder as Smin Fy, where Smin is the minimum elastic modulus of the wind girder about its vertical neutral axis and Fy is the yield stress. The AISC Specification for Structural Steel Buildings Section F12 prescribes this approach for the yield strength of unsymmetric shapes other than angles but notes this “can be overly conservative”.

The yield strength can be as great as ZFy, where Z is the plastic section modulus, since the flexural strength is reached when the full cross section has yielded rather than only the extreme fiber. For the wind girder shapes in API 650 Figure 5-24, Z/S ranges from 1.14 to 1.80. To avoid yielding at service loads, the strength increase above initial yield is usually limited to 1.5 or 1.6.

Local buckling strength is a function of the slenderness (b/t ratio) of the wind girder elements. API 650 only addresses local buckling of the shell (by limiting the shell’s contribution to the wind girder to 16t,

which is approximately , roughly in the middle of AISC’s non-compact range for I-shape beam flanges). The length of the shell that API 650 includes on each side of the wind girder is (in 5.9.7.6.2, adjusted for consistent units) 0.424(Dt).5 for intermediate wind girders, Annex V tank stiffeners for external pressure, and tank top compression rings for internal pressure, but 16t only for top wind girders for open top tanks. The SSRC Guide Section 14.4.2 gives the participating length of the shell as 0.55(Dt).5, since the parameter θ discussed above is greater than 2 for API 650 tanks. API 650 is inconsistent and conservative, especially on large diameter tanks, because the 16t rule neglects the effect of tank diameter. Therefore, this ballot proposes to change the shell contribution from 16t to 0.424(Dt)0.5.

API 650 does not address the local buckling strength of other elements of wind girders, which could be unconservative. Therefore, this ballot addresses local buckling by:

a) Limiting the slenderness of webs stiffened at both edges to 5.7(E/Fy)0.5, which is 163 for Fy = 36 ksi. This is the AISC Specification Table B4.1b case 19 limit on web slenderness for rectangular tubes, above which the strength of the section must be reduced below Fy S. It’s interesting that the largest web slenderness currently shown in API Table 5-24 detail e is 40”/0.25” = 160.

b) Limiting the slenderness of flanges stiffened on one edge to 1.0(E/Fy)0.5, which is 29 for Fy = 36 ksi. This is the AISC Specification Table B4.1b case 10 non-compact to slender limit on flanges of I-shapes, channels, and tees. A limit of 29t on the effective length of the shell acting with the stiffener is about twice the current 650 top wind girder limit of 16t.

c) Limiting the slenderness of webs stiffened on one edge to 1.52(E/Fy)0.5, which is 43t for Fy = 36 ksi. This is the AISC Specification Table B4.1b case 14 non-compact to slender limit on stems of tees in flexure.


For yielding with initial yield as the limit state, M/S = Fy/Ω, and S = MΩ/Fy, where Ω is the safety factor. Substituting for M,

S = 0.00877PWSHD2Ω/Fy

This formula gives the same results as the current formula when the safety factor Ω = 1.6 and VASCE7-05 = 0.78VASCE7-16. (The wind speed is squared to determine the wind pressure, and 0.782 = 0.6, the factor on wind load given by ASCE 7).

API 650 includes a significant conservatism in the wind girder formula by limiting the yield strength used to determine the wind girder size to 30 ksi, even though the wind girder’s yield strength is usually at least 36 ksi. This conservatism of 20%, and the extremely conservative wind girder buckling check, means that API 650 can currently require wind girders to be considerably larger than necessary.

API 650, though, does not require that the top wind girder for tanks larger than 200 ft in diameter be sized for the difference in the actual tank diameter and 200 ft. API 650 does require that the actual tank diameter be used to determine the size of intermediate wind girders for all tank diameters. This ballot makes these requirements consistent and more rational by using the actual yield strength of the wind girder and the actual tank diameter to determine each wind girder’s size.

Intermediate Wind GirdersAPI 650 currently requires that intermediate wind girders meet similar requirements as top wind girders – that is, resist wind pressure in bending rather than merely stiffen the tank shell to prevent the shell from buckling – while the top wind girder and tank bottom act as bulkheads. The intermediate wind girder size could instead be based on the moment of inertia I required to prevent shell buckling, included in the equation for shell buckling above:

P =

Solving for I, with a safety factor Ω for the buckling pressure P:

I =

whereL = distance between stiffeners (for one intermediate wind girder at the midheight of the tank, L

is approximately H/2)

β = For typical API 650 tanks, 2Eβ/(D/t) is small compared to ΩP, so the required stiffener moment of inertia can be approximated as


I =

where n =

This ballot proposes no change to the intermediate wind girder equation, however, since the current equation is conservative.

Roof-to-Shell Joint On tanks with fixed roofs, uplift on the roof causes compression in the roof-to-shell joint. API 650 requires that the roof-to-shell joint be checked for compression due to uplift caused by internal pressure (in Annex F), but not due to uplift caused by wind. A 3/16” fillet weld joining the roof plates to the top of the shell provides much greater resistance to uplift than wind pressure, and experience shows that the roof plates don’t tear off during wind storms and relieve wind pressure. This ballot therefore includes a check of the roof-to-shell joint for wind uplift.

API 650 F.4.1 defines the relationship between the strength of the roof-to-shell joint and the uplift pressure p as:

p = [8FRSy ARS tanθ + 4WR/π]/D2

where ARS = area of the roof-to-shell joint defined by Figure F.2FRSy = least of the minimum yield strengths of the materials in the shell-roof jointΘ = slope of the roofWR = weight of the roof plates and any structural members attached to the roof plates

Solving for the area of the roof-to-shell joint and applying a safety factor Ω to the uplift pressure p,

ARS = [Ω pD2 – 4WR/π]/(8FRSy tanθ)

where p is the greater of Pi + 0.6PWR and FpPi + PWR, (consistent with the tank uplift checks in 5.11) and Ω is 1.6, consistent with the safety factor for other tank stiffeners.

The roof-to-shell joint experiences no compression until the roof uplift pressure exceeds the weight of the roof plates, which, for 3/16” thick steel typically used in supported cone roofs, is approximately 8 psf. Thus, while wind pressures less than 8 psf have no effect on the joint, the joint is very sensitive to uplift pressures just greater than 8 psf. For example, increasing the wind uplift pressure from 10 to 12 psf doubles the stress in the joint, since (12 – 8)/(10 – 8) = 2. Therefore, it’s important to accurately determine the wind uplift pressure, which helps to justify using two equations for wind uplift on roofs.

This ballot also proposes to improve the accuracy of the roof-to-shell joint strength by dropping the arbitrary 12” limit on the width of the roof that contributes to the area of this joint. This ballot also addresses local buckling of any stiffeners by limiting the slenderness of elements stiffened on one edge


(such as the outstanding leg of stiffeners) to 0.56(E/Fy)0.5, which is 16 for Fy = 36 ksi. This is the AISC Specification Table B4.1a case 1 non-slender to slender limit on flanges of I-shapes, channels, and tees.

Shell and Wind Girder Requirements for Wind Loads in API 650 AppendicesAppendix AL (aluminum tanks), Appendix M (tanks at elevated temperatures), and Appendix X (stainless steel tanks) use the provisions in the body of API 650 unless the appendix states otherwise. The current requirements for shells and wind girders for wind loads in these appendices are unnecessary when the 650 equations are revised to be transparent and show the modulus of elasticity and yield strength. Accordingly, this ballot deletes those requirements. This not only avoids redundancy, it ensures that the requirements are consistent.

References1. Ziemian, Ron, ed. (2010), Guide to Stability Design Criteria for Metal Structures, 6th ed., John

Wiley and Sons, Hoboken, NJ.2. American Society of Civil Engineers (2017), ASCE/SEI 7-16, Minimum Design Loads and

Associated Criteria for Buildings and Other Structures, ASCE, Reston, VA.3. American Petroleum Institute (2013), API Standard 650, Welded Tanks for Oil Storage, 12th ed.,

Addendum 2, API, Washington, DC.4. American Institute for Steel Construction (2016), AISC 360-16, Specification for Structural Steel

Buildings, Chicago, IL. 5. MacDonald, P.A., et al (1988), Wind Loads on Circular Storage Bins, Silos and Tanks: I. Point

Pressure Measurements on Isolated Structures, Journal of Wind Engineering and Industrial Aerodynamics, Amsterdam.

Proposed Changes:Section 2 – Normative References

ASCE Standard 7-056, Minimum Design Loads for Buildings and Other StructuresASCE Standard 7-10, Minimum Design Loads for Buildings and Other StructuresASCE Standard 7-16, Minimum Design Loads and Associated Criteria for Buildings and Other Structures

5.2.1 Loads

k) Wind (W): The design wind speed (V) shall be either:the 3-sec gust design wind speed determined from ASCE 7-05 multiplied by √I, Figure 6-1; or

[1)] the 3-sec gust design wind speed determined from ASCE 7-10 Figure 26.5-1 for risk category III or the risk category specified by the Purchaser (Figure 26.5-1A, Figure 26.5-1B, or Figure 26.5-1C) multiplied by 0.78; or

[2)] [3)] the 3-sec gust design wind speed at 10 m (33 ft) above ground for ASCE 7 exposure category

C specified by the Purchaser, which shall be for a 3-sec gust based onwith a 2 3 % annual probability of being exceededexceedance in 50 years [50-year mean recurrence interval].

The 3-sec gust wind speed used shall be reported to the Purchaser.


1) Design wind pressure (PWS and PWR) using design wind speed (V): The design wind pressure on shell (PWS) shall be 0.860.53 kPa (V/190)2 , ([18 11 lbf/ft2][V/120]2) on vertical projected areas of cylindrical surfaces, and . Tthe design wind uplift pressure on roof (PWR) shall be 1.440.86 kPa (V/190)2, ([30 18 lbf/ft2][V/120]2) (see item 2)uplift on horizontal projected areas of conical or doubly curved surfaces; The design wind pressure acting on vertical projected areas of cylindrical surfaces shall be

PWS = PWSR (V/Vr)2

The design wind pressure acting upward on horizontal projected areas of roofs with a rise to span ratio of 0.05 or less shall be

PWR = (PWRC – KRD)(V/Vr)2

The design wind pressure acting on horizontal projected areas of roofs with a rise to span ratio greater than 0.05 shall be

PWR = (PWRO – KRD)(V/Vr)2

where PWSR = 0.53 kPa (11 lbf/ft2 )Vr = 190 km/hr (120 mph)PWRC = 0.86 kPa (18 lbf/ft2 )PWRO = 1.15 kPa (24 lbf/ft2 ) KR = 4.7 N/m3 (0.03 lbf/ft3 )V = design wind speedD = tank diameter

These design wind pressures are in accordance with ASCE 7-05 for wind exposure Category C. As alternativesAlternatively, pressures may shall be determined in accordance with ASCE 7 or :

a) ASCE 7-05 (exposure category and importance factor provided by Purchaser); orb) ASCE 7-10 (exposure category and risk category provided by Purchaser) with either velocity multiplied by 0.78 or the ASCE 7-10 pressure multiplied by 0.6; orc) a the national standardrequirements for the specific conditions for the tank being designedof the jurisdiction in which the tank is located.

2) The design uplift pressure on the roof (wind plus internal pressure) need not exceed 1.6 times the design pressure P determined in F.4.1.

NOTE: Design wind pressures are determined from ASCE 7 as follows: The velocity pressure on the shell is:

qz = 0.00256Kz Kzt Kd Ke V 2 = 34.5 lbf/ft2

whereKz is the velocity pressure exposure coefficient = 0.937 for exposure C at a height of 24 ft;Kzt is the topographic factor = 1.0 for all structures except those on isolated hills or escarpments;Kd is the directionality factor = 1.0 for round tanks;


Ke is the ground elevation factor = 1.0 at sea level;V is the reference design wind speed = 190 km/h (120 mph) at 10 m (33 ft) above ground with a 3 % probability exceedance in 50 years;

The shell design wind pressure is

PWS = qz G Cf (0.6) = (34.5 lbf/ft2 )(0.85)(0.63)(0.6) = 11 lbf/ft2

whereG is the gust factor = 0.85Cf is the force coefficient = 0.63 0.6 is the load factor for wind for allowable strength design

The velocity pressure on the roof is:

qh = 0.00256Kz Kzt Kd Ke V 2 = 40.5 lbf/ft2

whereKz is the velocity pressure exposure coefficient = 1.1 for exposure C at a height of 50 ft;

The roof design wind pressure is

PWR = qh (GCp – GCpi)(0.6) = (40.5 lbf/ft2 )[(0.85)Cp + 0.18)(0.6)

whereG is the gust factor = 0.85Cp is the external pressure coefficient, which is a function of the tank’s height to diameter ratio and the roof’s rise to span ratio. GCpi is the force coefficient = 0.18 (for open vent and closed vent tanks) 0.6 is the load factor for wind for allowable strength design

The resulting roof wind pressure is PWR = 18 lb/ft2 – (0.03 lb/ft3 )D for supported cone roofs with a rise to span ratio of 0.05 or lessPWR = 24 lb/ft2 – (0.03 lb/ft3 )D for all other roofs, based on an average rise to span ratio of 0.15.

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.

4) Fastest mile wind speed times 1.2 is approximately equal to 3-sec gust wind speed (V).

NOTE ASCE 7-10 wind velocities now have LRFD load factors and risk category (importance factors) built in, whereas API 650 uses the working stress. The 0.78 factor applied to the ASCE 7-10 wind speed provides a conversion to working stress levels.

5.9.6 Top Wind Girder 5.9.6.1 The required minimum section modulus S of the stiffening ringtop wind girder shall equal or exceed be determined by theas followsing equation:


In SI Units:

(❑❑❑❑) (❑❑ )❑

❑❑

S =

where Z is the required minimum section modulus, in cm3;PWS is the shell design wind pressure (see 5.2.1[k])Ω is the safety factor = 1.6D is the nominal tank diameter (for tanks in excess of 61 m) diameter, the diameter shall be

considered to be 61 m when determining the section modulus), in meters (m);H2 is the height of the tank, in meters, including any freeboard provided above the maximum

filling height as a guide for a floating roof;shell V is the design wind speed (3-sec gust), in km/h (see 5.2.1[k]);Fy is the least lesser of the minimum yield strength of the shell and stiffening ringwind girder at

the maximum operating design temperature, in MPa or 210, in MPa, whichever is less.

In USC units:

(❑❑❑❑) (❑❑ )❑

❑❑

where Z is the required minimum section modulus, in in.3;D is the nominal tank diameter (for tanks in excess of 200 ft diameter, the diameter shall be

considered to be 200 ft when determining the section modulus), in feet (ft);H2 is the height of the tank, in feet, including any freeboard provided above the maximum filling

height as a guide for a floating roof;V is the design wind speed (3-sec gust), in mph (see 5.2.1[k]);Fy is the least minimum yield strength of the shell and stiffening ring at maximum operating

temperature in psi or 30,000, in psi, whichever is less.

5.9.6.2 The width-to-thickness ratios of the elements of wind girders shall not exceed the following limits, where E is the modulus of elasticity of the element and Fy is the yield strength, each at the maximum design temperature.

For elements in flexure (webs) stiffened at both edges, 5.70(E/Fy)0.5

For elements in flexure (webs) stiffened at one edge, 1.52(E/Fy)0.5

For elements in compression (flanges), 1.0(E/Fy)0.5


For tanks larger than 61 m (200 ft) in diameter, an additional check for the minimum required moment of inertia for the top-stiffening ring shall be performed. The required minimum moment of inertia of the stiffening ring shall be determined by the following equations:

In SI units:

I = 3583 H2 D3 (V/190)2 /E

whereI is the required minimum moment of inertia (cm4);D is the nominal diameter of the tank, in meters (m);H2 is the height of the tank shell (m), including any freeboard provided above the maximum filling height as a guide for a floating roof;E is the modulus of elasticity (MPa) at maximum design temperature;V is the design wind speed (3-sec gust) (km/h) (see 5.2.1[k]).

In USC units:

I = 108 H2 D3 (V/120)2 /E

whereI is the required minimum moment of inertia (in.4);D is the nominal diameter of the tank, in meters (ft);H2 is the height of the tank shell (ft), including any freeboard provided above the maximum filling height as a guide for a floating roof,E is the modulus of elasticity (psi) at maximum design temperature;V is the design wind speed (3-sec gust) (mph) (see 5.2.1[k]).

5.9.6.3 The section modulus of the wind girder shall include the stiffening ring and a portion of the tank shell within a distance of 0.424(Dt)0.5 from the point of attachment of the stiffening ring to the shell, where t is the as-built shell thickness (see Figure 5.24).The section modulus of the stiffening ring shall be based on the properties of the applied members and may include a portion of the tank shell for a distance of 16t below and, if applicable, above the shell-ring attachment where t is the as-built shell thickness, unless otherwise specified. When curb angles are attached to the top edge of the shell ring by butt-welding, this distance shall be reduced by the width of the vertical leg of the angle (see Figure 5.24 and Table 5.20a and Table 5.20b).

Table 5.20a—Section Moduli (cm3) of Stiffening-Ring Sections on Tank Shells (SI)

Table 5.20b—Section Moduli (in.3) of Stiffening-Ring Sections on Tank Shells (USC)

5.9.7 Intermediate Wind Girders5.9.7.1 The maximum height Hmax of the unstiffened shell shall be calculated determined as follows:In SI units:


H1max =

whereH1 is the maximum height of the unstiffened shell, in meters;E is the modulus of elasticity of the shell at the maximum design temperature (see Tables P.1a and P.1b)t is the nominal thickness, unless otherwise specified, of the thinnest shell course, in millimeters (see Note 1);PWS is the shell design wind pressure (see 5.2.1[k])Ω is the safety factor = 1.6D is the nominal tank diameter, in meters;V is the design wind speed (3-sec gust), in km/h (see 5.2.1[k]).

In USC units:

H1 =

where

H1 is the maximum height of the unstiffened shell, in feet;t is the nominal thickness, unless otherwise specified, of the thinnest shell course, in inches (see Note 1);D is the nominal tank diameter, in feet;V is the design wind speed (3-sec gust), in mph (see 5.2.1[k]).

NOTE 1 The structural stability check of wind girder stiffened shells in accordance withrequirements of 5.9.6 and 5.9.7, shall be based upon nominal dimensions of the shell course and the wind girders irrespective of specified corrosion allowances whenever if the “No” option is selected for “Check Buckling in Corroded Cond.?” on the Data Sheet, Line 9. Whenever If the “Yes” option is selected, the check must shall be based upon the nominal dimensions minus the specified corrosion allowance.

NOTE 2 This formula is intended to coverfor tanks with either open tops or closed tops and is based on the following factors (for the background for the factors given in this note, see ASCE 7 and R. V. McGrath’s “Stability of API Standard 650 Tank Shells” for the buckling strength of the shell.): 21 with a 0.8 factor to account for tank out-of-roundness. The uniform external buckling pressure is

p =

a) The velocity pressure is:

p = 0.00256Kz Kzt Kd V 2 I G = 1.48 kPa (31 lbf/ft2)


whereKz equals the velocity pressure exposure coefficient = 1.04 for exposure C at a height of 40 ft;Kzt is 1.0 for all structures except those on isolated hills or escarpments;Kd is the directionality factor = 0.95 for round tanks;V equals 3-second gust design wind speed = 190 km/h (120 mph) at 10 m (33 ft) above ground (see 5.2.1[k]);I equals the importance factor = 1.0 for Category II structures;G equals the gust factor = 0.85 for exposure C.

A 0.24 kPa (5 lbf/ft2) internal vacuum is added for inward drag on open-top tanks or for external pressure on closed top tanks for a total of 1.72 kPa (36 lbf/ft2).

b) The wind pressure is uniform over the theoretical buckling mode of the tank shell, which eliminates the need for a shape factor for the wind loading.

c) The modified U.S. Model Basin formula for the critical uniform external pressure on thin-wall tubes free from end loadings, subject to the total pressure specified in Item a.

d) When other factors are specified by the Purchaser that are greater than the factors in Items a, b, and c, the total load on the shell shall be modified accordingly, and H1 shall be decreased by the ratio of 1.72 kPa (36 lbf/ft2) to the modified total pressure.

5.9.7.6 The required minimum section modulus S of an intermediate wind girder shall be determinedequal or exceed by as the following equation:

In SI units:

(❑❑❑❑) (❑❑ )❑

❑❑

Z S =

where Z is the required minimum section modulus, in cm3;D is the nominal tank diameter, in meters (m);PWS is the shell design wind pressure (see 5.2.1[k])Ω is the safety factor = 1.6h1 is the vertical distance, in meters, between the intermediate wind girder and the top angle of

the shell or the top wind girder of an open-top tank;V is the design wind speed (3-sec gust), in km/h (see 5.2.1[k]);Fy is the least lesser of the minimum yield strength of the shell and the intermediate wind girder

at the maximum operating design temperature, in MPa or 210, in MPa, whichever is less.

The width-to-thickness ratio of the elements of the wind girder shall not exceed the limits given in 5.9.6.2. The participating portion of the shell shall include a length 0.424(Dt)0.5 above and below the point of attachment of the wind girder to the shell.


In USC units:

(❑❑❑❑) (❑❑ )❑

❑❑

where Z is the required minimum section modulus, in in.3;D is the nominal tank diameter, in feet;h1 is the vertical distance, in feet, between the intermediate wind girder and the top angle of the

shell or the top wind girder of an open-top tank;V is the design wind speed (3-sec gust), in mph (see 5.2.1[k]);Fy is the least minimum yield strength of the shell and intermediate wind girder at maximum

operating temperature in psi or 30,000, in psi, whichever is less.NOTE A description of the loads on the tank shell that are included in the design wind speed can be found in Item a of the note to 5.9.7.1.

5.10.2.10 Roof-to-Shell JointThe cross sectional area ASR of the roof-to-shell joint defined in Figure F.2 shall equal or exceed:

ASR = [ΩpD2 – 4DLR/π]/(8FySR tanθ)

where p = the greater of Pi + 0.6PWR and FpPi + PWR Ω = 1.6 Pi = design internal pressure Fp = internal pressure combination factor given in 5.2.2DLR = dead load of the roof plates and any structural members attached to the roof platesPWR = wind roof pressure given in 5.2.1(k)FySR = least of the minimum yield strengths of the materials in the roof-to-shell jointΘ = slope of the roof at the shell

The width-to-thickness ratio of elements of the joint shall not exceed the following limits, where E is the modulus of elasticity of the element and Fy is the yield strength, each at the maximum design temperature.

For elements stiffened on both edges, 1.40(E/Fy)0.5

For elements stiffened on one edge, 0.56(E/Fy)0.5

The cross sectional area of the joint shall include any stiffening ring, the tank shell within a distance of 0.424(Dt)0.5 from the top of the shell, and the roof within a distance of 0.3(R2 th)1/2 from the shell.

Annex AL Aluminum Storage Tanks

AL.5.5.1 Wind GirdersThe section modulus of wind girders shall equal or exceed:


Z = pHwD3/(12Ec)

where

p equals (1.48 kPa) [V/(190 km/hr)]2;p equals (31 lb/ft2) [V/(120 mph)]2;V is the 3-sec gust design wind speed [see 5.2.1(k)];Hw is for top wind girders on tanks with no intermediate wind girder, the tank height; for tanks with intermediate wind girders, the vertical distance between the intermediate wind girder and the top angle of the shell or the top wind girder of an open-top tank;c is the lesser of the distances from the neutral axis to the extreme fibers of the wind girder.

AL.5.5.2 Intermediate Wind GirdersThe height of the unstiffened shell shall not exceed:

H1 =

whereH1 is the vertical distance between the intermediate wind girder and the top angle of the shell or the top wind girder of an open-top tank;t is the nominal thickness, unless otherwise specified, of the top shell course;EMDT is the modulus of elasticity at the maximum design temperature;E40 is the modulus of elasticity at 40 °C (100 °F).

Annex F Design of Tanks for Small Internal PressuresFigure F.2 wh = maximum width of participating roof = 0.3(R2 th)1/2 or 300 mm (12 in.) whichever is less.

NOTE 3: The unstiffened length of the angle or bar, Le, shall be limited to 0.56t(E/Fy)1/2 250t/(Fy)1/2 mm [3000t/(Fy)1/2 in.] where Fy is the minimum specified yield strength, MPa (lbf/in.2) and t = ta or tb, as applicable.

F.4 Maximum Design Pressure and Test Procedure

F.4.1 Maximum Design PressureThe maximum design pressure, Pi, for a tank that has been constructed or that has had its design details established mayshall be calculated from the following equation (subject to the limitations of Pmax in F.4.2 and F.4.3):

In SI units: Pi = lesser of P – 0.6PWR and (P – PWR)/Fp

where

P =


P is the internal design pressure, in kPaPWR is the roof design wind pressure; Fp is the internal pressure combination factor;

A is the area resisting the compressive forceof the roof-to-shell joint, as illustrated in Figure F.2, in mm2

Ω is the safety factor = 1.6Fy is the loweast minimum specified yield strength (modified forat the design temperature) of

the materials in the roof-to-shell junctionjoint, in MPa;Θ is the angle between the roof and a horizontal plane at the roof-to-shell junction, in degrees;tan θ is the slope of the roof, expressed as a decimal quantity;DLR is the nominal weight of the roof plates plus any structural members attached to the roof

plates, in N.

In USC units:

P = where P is the internal design pressure, in inches of water; A is the area resisting the compressive force, as illustrated in Figure F.2, in inches2

Fy is the lowest minimum specified yield strength (modified for design temperature) of the materials in the roof-to-shell junction, in lb/inch2; Θ is the angle between the roof and a horizontal plane at the roof-to-shell junction, in degrees; tan θ is the slope of the roof, expressed as a decimal quantity; DLR is the nominal weight of roof plate plus any structural members attached to the roof plate, in lbf.

F.5 Required Compression Area at the Roof-to-Shell Junction

F.5.1 Required Area for Compression Where the maximum design pressure has already been established (not higher than that permitted by F.4.2 or F.4.3, whenever applicable), the total required compression area at of the roof-to-shell junction shall be calculated from the following equation:

In SI units:

A =

whereA is the total required compression area at the roof-to-shell junction, in mm2;Pi is the design internal pressuregreater of Pi + 0.6PWR and FpPi + PWR, in kPa;Fy is the least minimum specified yield strength (at the design temperature) of the materials in

the roof-to-shell joint; Θ is the angle between the roof and a horizontal plane at the roof-to-shell junction;

Ω is the safety factor = 1.6DLR is the nominal weight of the roof plates plus any attached structural members attached to

the roof plates, in N.


In USC units:

A =

whereA is the total required compression area at the roof-to-shell junction, in inches2;Pi is the design internal pressure, in inches of water;DLR is the nominal weight of roof plate plus any attached structural, in lbf;

A is based on the nominal material thicknesses less any corrosion allowance.

F.5.2 Required Area for Tension For self-supporting roofs, the compression area of the roof-to-shell joint shall not be less than the cross-sectional area calculated inrequired by 5.10.5 and or 5.10.6.

Annex G Structurally-Supported Aluminum Dome RoofsFigure G.1 – Data Sheet for a Structurally Supported Aluminum Dome Added to an Existing Tank

10. Design Wind Speed: (Select One)190 km/h (120 mph)Purchaser Specified Wind Speed (50-YHR Min. 3-Sec Gust) ____Km/h (mph)3-Sec Gust from ASCE 7, Figure 6-1 _____ Km/h (mph)Importance Factor (If Other Than 1.0) _______Exposure Category per ASCE 7 _____________ Km/h (mph)

Annex L API Std 650 Storage Tank Data Sheet9. Wind Velocity for non-U.S. sites, 50-yr wind speed (3-sec Gust) with a 3 % probability exceedance*

Annex M Requirements for Tanks Operating at Elevated TemperaturesM.6 Wind GirdersIn the equation for the maximum height of unstiffened shell in 5.9.7.1, the maximum height (H1) shall be reduced by the ratio of the material’s modulus of elasticity at the maximum design temperature to 199,000 MPa (28,800,000 lbf/in.2) when the ratio is less than 1.0 (see Table M.2a and Table M.2b for modulus of elasticity values).

Annex X Duplex Stainless Steel Storage TanksX.3.7.5 In M.6 (the equation for the maximum height of unstiffened shell in 5.9.7.1), the maximum height shall be multiplied by the ratio of the material modulus of elasticity at the design temperature to the material modulus of elasticity at 40 °C (100 °F).


Annex V Design of Storage Tanks for External Pressure

V.3.1 NomenclatureW is the maximum design wind pressure on the shell PWS determined in Section 5.2.1(k). consistent with the specified design wind velocity, in kPa (lb/ft2). The maximum wind pressure shall be calculated as follows (see 5.9.7.1, Note 2):

In SI units: W = 1.48(V/190)2

In USC units: W = 31(V/120)2

whereV is the specified design wind velocity (3-sec gust), in kph (mph);

V.8.1.1 (note: this has been corrected by Addendum 3)In SI units:

> 0.00675

In USC units:

> 0.19

V.10.1 Data Design wind velocity (3-sec gust) = 120 mph (Maximum wind pressure, W = 31 lb/ft2)

V.10.2 External Pressure Calculations

3) Check that buckling will occur elastically in the unstiffened cylindrical shell:From V.8.1.1, elastic buckling will occur if the following equation is satisfied:

> 0.006750.19

= 1.231.61 > 0.19, thus buckling will be elastic.


Documents

ballots.api.orgballots.api.org/.../ballots/docs/spring2019/650-1074_R0.docx · Web viewAPI 650’s requirements for tank components that resist wind loads (e.g., wind girder size