AGENDA ITEM 650-1074

TITLE ASCE 7 Wind Update

DATE December 12, 2018
CONTACT Randy Kissell
Trinity Consultants
phone 919-493-8952
cell 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’ comment
REVISION 0
IMPACT 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:

Introduction
API 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 Speeds
Long 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 Pressures
API 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 Tanks

parameter symbo value ASCE 7-16 section
l
wind exposure C: Open terrain with scattered obstructions Section 26.7.2
category that have heights generally < 30 ft. This

API 650-1074 Updating Storage Tank Wind Loads 2

 includes flat, open country and grasslands.
wind directionality Kd 1.0 Table 26.6-1
factor
load factor for wind 0.6 Section 2.4.1
topographic factor Kzt 1.0 Section 26.8.2
ground elevation Ke 1.0 at sea level Section 26.9
factor
velocity pressure Kz 2.01(z/900)2/9.5 Section 26.10.1
exposure coefficient for Exposure Category C, where z = height
gust-effect factor G 0.85 Section 26.11.1
enclosure classification partially open or enclosed (see below) Section 26.12
internal pressure GCpi 0.18 Table 26.13-1
coefficient
default risk category III: Buildings and other structures, the failure Table 1.5-1
(used solely to of which could pose a substantial risk to
determine the design human life. Buildings and other structures
wind speed V) 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).

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 Tanks

tank 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/2
gross areas w/o
Ag Agi ft2 4273 15394 28981 46496 = πDH/2 + πD2/4
total area of
openings in wall Ao ft2 4.0 10.0 15.0 20.0 = 0.1D (= 0.2D/2)
total area of Ao
openings g 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 is Ao > 1.1 Aoi and Ao > min(0.01Ag, 4) and
enclosed?     NO NO NO NO Aoi/Agi < 0.2?
if not enclosed or partially enclosed, partially
partially open?     YES YES YES YES open

API 650-1074 Updating Storage Tank Wind Loads 3

Closed Vent Tanks
gross area of wall
for Ao Ag ft2 3016 7540 11310 15080 = πDH/2
gross areas w/o
Ag Agi ft2 4273 15394 28981 46496 = πDH/2 + πD2/4
total area of
openings in wall Ao ft2 0.0 0.0 0.0 0.0 = 0
total area of Ao
openings g 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 is Ao > 1.1 Aoi and Ao > min(0.01Ag, 4) and
enclosed?     NO NO NO NO Aoi/Agi < 0.2?
if not enclosed or partially enclosed, partially
partially open?     NO NO NO NO open

Shell Pressure
For the shell, the velocity pressure is
qz = 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/qz0.5 = 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

API 650-1074 Updating Storage Tank Wind Loads 4

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.

Tank Shell Wind Pressure Coefficent Cp vs angle to wind

2

1.5
Pressure Coeficient Cp

0.5

0
0 20 40 60 80 100 120 140 160 180
-0.5

-1 Closed

-1.5
Angle to Wind Direction

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 15 o 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

API 650-1074 Updating Storage Tank Wind Loads 5

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
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.

Shell Wind Pressure Coefficients Cp

open top tanks closed top tanks
1
35 36 2 3
34 4
33 5
32 6
31 7
30 8
29 9
28 10
27 11
26 12
25 13
24 14
23 15
22 16
21 20 17
19 18

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

Roof Pressure
This 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

API 650-1074 Updating Storage Tank Wind Loads 6

 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 Roofs

f/D CpA CpB CpC
0.05 0 < H/D < 1.0, 0 < H/D < 0.5, 0 < H/D < 0.5,
supported cone roofs, CpA = -0.16 – 1.56H/D CpB = -0.22 – 0.56H/D CpC = -H/D
1:10 roof slope; H/D > 1.0, H/D > 0.5, H/D > 0.5,
say down to 1:16 roof slope CpA = -1.4 CpB = -0.5 CpC = -0.5
0.15 0 < H/D < 0.25, 0 < H/D < 0.5, 0 < H/D < 0.5,
self-supporting cone roofs, CpA = 0.3 – 4.8H/D CpB = -0.45 – 0.9H/D CpC = -H/D
dome and umbrella roofs, 0.25 < H/D < 1.0,
aluminum dome roofs CpA = -0.67 – 0.93H/D
H/D > 1.0, H/D > 0.5, H/D > 0.5,
CpA = -1.6 CpB = -0.9 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/ft 2) for other roofs,
and
KR2 = 4.7 N/m3 (0.03 lb/ft3)

API 650-1074 Updating Storage Tank Wind Loads 7

Table 4 ASCE Wind Pressures for Tanks with Roof Slope 1:10 or less for V = 120 mph
qz qz
Kz for Kz for for for
D H H/D shell roof shell roof Cp PWS PWRC PWR
2 2 2 2
ft ft - - - lb/ft lb/ft - lb/ft lb/ft lb/ft2
30 30 1.00 0.849 0.989 31.3 36.4 -0.67 10.1 16.5 17.1
40 40 1.00 0.902 1.050 33.2 38.7 -0.67 10.7 17.5 16.8
60 48 0.80 0.937 1.093 34.5 40.3 -0.66 11.1 17.9 16.5
80 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 15.0
120 48 0.40 0.937 1.102 34.5 40.6 -0.44 11.1 13.5 14.4
140 48 0.34 0.937 1.105 34.5 40.7 -0.39 11.1 12.5 13.8
160 48 0.30 0.937 1.107 34.5 40.8 -0.37 11.1 12.1 13.5
180 48 0.27 0.937 1.110 34.5 40.9 -0.33 11.1 11.2 12.6
200 48 0.24 0.937 1.113 34.5 41.0 -0.30 11.1 10.8 12.0
250 48 0.19 0.937 1.119 34.5 41.3 -0.26 11.1 10.0 10.5
300 48 0.16 0.937 1.126 34.5 41.5 -0.24 11.1 9.5 9.0
330 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
qz qz
Kz for Kz for for for
D H H/D shell roof shell roof Cp PWS PWRC PWR
2 2 2
ft ft - - - lb/ft lb/ft - lb/ft lb/ft2 lb/ft2
30 30 1.00 0.849 0.989 31.3 36.4 -0.96 10.1 21.7 23.1
40 40 1.00 0.902 1.050 33.2 38.7 -0.96 10.7 23.1 22.8
60 48 0.80 0.937 1.093 34.5 40.3 -0.95 11.1 23.8 22.5
80 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 21.0
120 48 0.40 0.937 1.102 34.5 40.6 -0.77 11.1 20.4 20.4
140 48 0.34 0.937 1.105 34.5 40.7 -0.72 11.1 19.4 19.8
160 48 0.30 0.937 1.107 34.5 40.8 -0.70 11.1 19.0 19.5
180 48 0.27 0.937 1.110 34.5 40.9 -0.65 11.1 18.0 18.6
200 48 0.24 0.937 1.113 34.5 41.0 -0.62 11.1 17.4 18.0
250 48 0.19 0.937 1.119 34.5 41.3 -0.54 11.1 15.8 16.5
300 48 0.16 0.937 1.126 34.5 41.5 -0.48 11.1 14.7 15.0
330 48 0.15 0.937 1.130 34.5 41.6 -0.46 11.1 14.3 14.1

API 650-1074 Updating Storage Tank Wind Loads 8

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 Shell

The 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

API 650-1074 Updating Storage Tank Wind Loads 9

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.

buckle

Wind

Uniform External Pressure Wind Pressure

Figure 4 Pressure Distributions on a Tank Cross Section

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

 
2E (t / D)  (t / D)2  2 2 2 4 
2  
    2
   2
n 2n 1

n  ( / 2)  1  3(1   )  
 n    
2 2 2 2

PHP = 
where
n = 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

API 650-1074 Updating Storage Tank Wind Loads 10

 2.6E

PHA = 
H / D  D / t 
2.5

H D
1.818
since the parameter θ = D t 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:

 H   Fy 
0.75
D
    
K=    D  E 
t

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 30 100 150 200 300
tank height H ft 48 48 48 48 48
API 650 minimum shell thickness tmin in. 0.188 0.25 0.312 0.312 0.375
shell thickness assumed t in. 0.188 0.250 0.312 0.500 0.500
buckling mode factor K - 12.9 14.1 13.2 10.0 11.0
is buckling elastic or inelastic? elastic elastic elastic elastic elastic
λ = πD/(2H) λ - 0.98 3.27 4.91 6.54 9.82
D/t - 1915 4800 5769 4800 7200
.5
θ = 1.818H/D(D/t) θ - 127.3 60.5 44.2 30.2 24.7
no. of buckles (hydrostatic pressure) n - 9 21 24 31 39
buckling lobe length Lbw ft 10.5 15.0 19.6 20.3 24.2
approx hydrostatic buckling pressure PHA lb/ft2 42.3 14.2 13.4 28.3 15.4
2
hydrostatic buckling pressure PHP lb/ft 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

API 650-1074 Updating Storage Tank Wind Loads 11

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

(0.8)2.6E 2.1E

P= 
H / D  D / t   H / D  D / t 
2.5 2.5

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

Wind Girders
Shell 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

2E 4 EI  n2  1 

D / t  n2  ( / 2)2  1   n2  2  2 HD 3
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 50 100 150 200 300
shell height H ft 48 48 48 48 48
minimum shell thickness tmin 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. 4.0 9.0 16.0 20.0 20.0

API 650-1074 Updating Storage Tank Wind Loads 12

API 650 wind girder section modulus S in3 12 48 108 192 192
4
wind girder moment of inertia = Sc I in 48 432 1728 3840 3840
2
shell pressure resistance ps lb/ft 189 523 492 525 389
shell 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 1,933 931
ring 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

API 650-1074 Updating Storage Tank Wind Loads 13

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,
E
0.56  
F 
which is approximately  y  , 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.

API 650-1074 Updating Storage Tank Wind Loads 14

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 0.78 2 = 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 Girders

API 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:

2E 4 EI  n2  1 

D / t  n2  ( / 2)2  1   n2  2  2 HD 3
P=

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

LD 3  2E 
 P 
I=
8E (n  1) 
2
D / t 

where
L = distance between stiffeners (for one intermediate wind girder at the midheight of the tank, L
is approximately H/2)
4
n  ( / 2)2  1  n2   2 
2 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

API 650-1074 Updating Storage Tank Wind Loads 15

 LD3 P
I = 8E (n  1)
2

0.814
H4 t
where n = D D

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.2
FRSy = least of the minimum yield strengths of the materials in the shell-roof joint
Θ = slope of the roof
WR = 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

API 650-1074 Updating Storage Tank Wind Loads 16

(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 Appendices
Appendix 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.

References
1. 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 Structures
ASCE Standard 7-10, Minimum Design Loads for Buildings and Other Structures
ASCE 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.

API 650-1074 Updating Storage Tank Wind Loads 17

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 speed
D = 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); or

b) 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; or
c) 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

where
Kz 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;

API 650-1074 Updating Storage Tank Wind Loads 18

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

where
G is the gust factor = 0.85
Cf 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

where
Kz 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)

where
G is the gust factor = 0.85
Cp 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 less
PWR = 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:

API 650-1074 Updating Storage Tank Wind Loads 19

In SI Units:
❑
(❑❑ ❑❑) ( ❑ )
❑
❑❑
0.00877PWS HD2
Fy
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 = 1.6
D 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

API 650-1074 Updating Storage Tank Wind Loads 20

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

where
I is the required minimum moment of inertia (cm 4);
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

where
I 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 Girders

5.9.7.1 The maximum height Hmax of the unstiffened shell shall be calculated determined as follows:
In SI units:

API 650-1074 Updating Storage Tank Wind Loads 21

 3 2
2.1Et 2.5  t   190 
9.47t    
P D
H1max = WS
1.5
D  V 

where
H1 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 = 1.6
D 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:

3 2
 t   120 
600, 000t    
H1 = D  V 

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

2.5
 t  D
2.1E    
p= D H

a) The velocity pressure is:

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

API 650-1074 Updating Storage Tank Wind Loads 22

where
Kz 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/ft 2).

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:
❑
(❑❑ ❑❑) ( ❑ )
❑
❑❑
0.00877PWS h1D2
Fy
ZS=

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 = 1.6
h1 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.

API 650-1074 Updating Storage Tank Wind Loads 23

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 Joint

The 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 5.2.2
DLR = dead load of the roof plates and any structural members attached to the roof plates
PWR = wind roof pressure given in 5.2.1(k)
FySR = least of the minimum yield strengths of the materials in the roof-to-shell joint
Θ = 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 Girders

The section modulus of wind girders shall equal or exceed:

API 650-1074 Updating Storage Tank Wind Loads 24

 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 Girders

The height of the unstiffened shell shall not exceed:

3
 1200t   EMDT 
2400t    
 D   E40 
H1 =

where
H1 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 Pressures

Figure 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 Pressure

The 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
8 AFy tan  4DLR
 2
P= D2 D

API 650-1074 Updating Storage Tank Wind Loads 25

 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 = 1.6
Fy 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:
0.962 AFy tan  0.245DLR

P= D2 D2
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 inches 2
Fy is the lowest minimum specified yield strength (modified for design temperature) of the
materials in the roof-to-shell junction, in lb/inch 2;
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:
 0.00127DLR   2 4DLR 
200D2  Pi     PD  
 D2    
Fy tan  8Fy tan 
A=

where
A 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 = 1.6
DLR is the nominal weight of the roof plates plus any attached structural members attached to
the roof plates, in N.

API 650-1074 Updating Storage Tank Wind Loads 26

In USC units:

 0.245DLR 
D2  Pi  
 D2 
0.962Fy tan 
A=

where
A is the total required compression area at the roof-to-shell junction, in inches 2;
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 Roofs

Figure 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 Sheet

9. 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 Temperatures

M.6 Wind Girders
In 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 Tanks

X.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).

API 650-1074 Updating Storage Tank Wind Loads 27

Annex V Design of Storage Tanks for External Pressure

V.3.1 Nomenclature
W 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/ft 2). 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

where
V 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:

 D 
0.75
 H   Fy    D   HTS   Fy  
0.5 0.75 0.5

   TS  E  
 t s min   D      t s min   D   E  
> 0.00675

In USC units:

 D 
0.75
 H   Fy    D   HTS   Fy  
0.5 0.75 0.5

   TS  E  
 t s min   D      t s min   D   E  
> 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:

 D 
0.75
 H   Fy    D   HTS
0.5 0.75 0.5
 TS   Fy 
   E   
 t s min   D      t s min   D  E


  > 0.006750.19

 75 
0.75
 43.54   36 0.5  0.5
 75   43.54   36  
0.75

          
 0.3125   75  30,000    0.3125   75  30,000   = 1.231.61 > 0.19, thus
buckling will be elastic.

API 650-1074 Updating Storage Tank Wind Loads 28