41914644 storage-tank-design-calculations-seismic-design-overturning-moment-by-abdel-halim-galala

DESIGN CALCULATIONS OF STORAGE TANKS
According to API 650 Code, Edition Sept. 2003 Page : 23 of 34
Designed by : Eng. Abdel Halim Galala, Design General Manager REV. : 0
Project : Design & procurement of storage tanks Date : 26.9.2008
Job Name : El-Gamil Plant Storage Facilities Location : Port Said
Service : Crude Oil Storage Tank Client : PETROBEL
Capacity : 5000 M3 Item : TK-01A
A. Cylindrical Tank, Fixed-Roof with Rafter & Column (cont.)
9. Seismic Design. [APPENDIX E, API 650]
9.1. Overturning Moment due to Seismic forces applied to bottom of tank shell,
M = Z I (C1 Ws Xs + C1 Wr Ht + C1 W1 X1 + C2 W2 X2) 10488643 Ft-lb Kg-M
where,
Z = Seismic force factor, depends on seismic zone [Table E-2] 0.15
Seismic zone of site 2A
I = Importance factor 1
C1 = Lateral earthquake force coefficient [Para. E.3.3.3] 0.6
C2 = Lateral earthquake force coefficient [Para. E.3.3.3]
= 0.75 S / T when T <= 4.5 0.203019
= 3.375 S / T2 when T > 4.5 0.164867
S = Site coefficient [Table E-3] 1.5
T = Natural period of the 1st sloshing mode = k (D0.5) 5.541355 Sec.
k = Factor depends on ratio D/H [Figure E-4] 0.625
D = Nominal tank dia. 78.60892 Ft 23.96 M
H = Max. design liquid level 40.28858 Ft 12.28 M
Ratio D/H 1.951147
Since T > 4.5 seconds, Use C2 0.164867
Ws = Total weight of tank shell 180760.5 lb 81.9917 Ton
Xs = Height from bottom of tank shell to shell's center of gravity 15.6939 Ft 4.7835 M
Wr = Total weight of tank roof (fixed or floating) + portion of the 106077.9 lb 48.1162 Ton
snow load, if any, specified by the purchaser
Ht = Total height of tank shell 40.28858 Ft 12.28 M
W1 & W2 = Weight of effective mass of tank contents that move
in unison with tank shell [Para. E.3.2.1 & Figure E-2]
D/H 1.951147
- Find ratio W1 / WT by knowing D/H [Figure E-2] 0.38
- Find ratio W2 / WT by knowing D/H [Figure E-2] 0.52
WT = Total weight of tank contents = Tank volume x specific gr. 12206584 lb 5536.82 Ton
(specific gravity of the product to be specified by the purchaser)
Tank volume 5.99E+12 Ft3 5536.82 M3
W1 = Ratio ( W1 / WT ) . WT 4638502 lb Kg
W2 = Ratio ( W2 / WT ) . WT 6347424 lb Kg

9. Seismic Design. (cont.) [APPENDIX E, API 650]
X1 = Height from bottom of tank shell to the centroid of lateral Ft
seismic force applied to W1 [E.3.3.2 & Figure E-3]
X2 = Height from bottom of tank shell to the centroid of lateral Ft
seismic force applied to W2 [E.3.3.2 & Figure E-3]
D/H 1.951147
- Find ratio X1 / H by knowing D/H [Figure E-3] 0.375
- Find ratio X2 / H by knowing D/H [Figure E-3] 0.56
X1 = Ratio ( X1 / H ) . H 15.10822 Ft 4.60498 M
X2 = Ratio ( X2 / H ) . H 22.5616 Ft 6.87678 M
9.2. Resistance to Overturning Moment at bottom of tank shell, WL [Para. E-4]
Resistance to the overturning moment at the bottom of the shell
may be provided by the weight of the tank shell and by the anchorage
of the tank shell,
or, for unanchored tanks, the weight of a portion of the tank contents
adjacent to the shell.
For unanchored tanks, the portion of the contents that may be
used to resist overturning depends on the width of the bottom
plate under the shell that lifts off the foundation and may be
determined as follows : wL = 7.9 tb ( Fby G H )0.5
lb/Ft
However, wL shall not exceed 1.25 G H D lb/Ft
Where, wL = max. weight of the tank contents that may be used
to resist the shell overturning moment,
wL1 = 7.9 tb ( Fby G H )0.5
5470.978 lb/Ft
wL2 = 1.25 G H D 3958.802 lb/Ft
Use wL = Min ( wL1 , wL2 ) 3958.802 lb/Ft
tb = Thickness of the bottom plate under the shell 0.629921 INCH MM
Fby = Min. specified yield strength of the bottom plate under the shell 30000 PSI
G = Design specific gravity of the liquid to be stored 1

9.3. Shell Compression . [Para. E-5]
9.3.a. Unanchored Tanks [Para. E.5.1]
Value of M / [ D2 (wt + wL)]
where,
b = max. longitudinal compressive force at the bottom of the shell lb/Ft
(lb/Ft of shell circumference)
wt = weight of tank shell and the portion of the fixed roof 731.9506 lb/Ft
supported by the shell (lb/Ft of shell circumference) = wt / 3.14 D
I. When M / [ D2 (wt + wL )] <= 0.785 0.361854
b = wt + 1.273 M / D2
2892.698 lb/Ft
II. When 0.785 < M / [ D2 (wt + wL )] <= 1.5 0.361854
b may be computed from the value of (b + wL )/ (wt + wL )
obtained from Figure E-5.
Value obtained from Figure E-5 2
b = ( wt + wL ) . Value from Figure E-5 - wL 5422.703 lb/Ft
III. When 1.5 < M / [ D2 (wt + wL )] <= 1.57 0.361854
6415.053 lb/Ft
b
w w
w t L
M
D w w
t L
VI. For M / [ D2 (wt + wL )] > 1.57 0.361854
or when b / 12 t > Fa
Value b / 12 t 478.3498 PSI < Fa
Value Fa 6410.684 PSI OK
In case b/12 t > Fa, the tank is structurally unstable.
It is necessary to take one of the following measures :
a. Increase the thickness of the bottom plate under the shell,
tb, to increase wL without exceeding the limitations of
E.4.1 and E.4.2.
b. Increase the shell thickness, t (see Item 9.5 for shell courses).
c. Change the proportions of the tank to increase the dia.
and reduce the height.
d. Anchor the tank in accordance with E.6.
L
=
+
−
+

 

 
−
1490
1
0 637
2
0 5
. ( )
.
( )
.

9.3.b. Anchored Tanks [Para. E.5.2]
For anchored tanks, the max. longitudinal compressive force at
the bottom of shell, b = wt + 1.273 M / D2
2892.698 lb/Ft
9.4. Max. Allowable Shell Compression [Para. E.5.3]
The max. longitudinal compressive stress in the shell, b / 12 t,
shall not exceed the max. allowable stress, Fa determined by
the following formulas for Fa, which take into account the effect
of internal pressure due to the liquid contents.
G H D2 / t2 980331.9 > 106
- When G H D2 / t2 >= 106, Fa = 106 t / D 6410.684 PSI
- When G H D2 / t2 < 106, Fa = 106 t / 2.5 D + 600 (G H )0.5 6372.671 PSI
However, Fa shall not be greater than 0.5 Fty
0.5 Fty 15000 PSI OK
where, t = thickness of the bottom shell course, excl. any corr. allow. 0.503937 INCH
Fa = Max. allowable longit. compressive stress in the shell 6410.684 PSI
Fty = Min. specified yield strength of the bottom shell course 30000 PSI
9.5. Upper Shell Course [Para. E.5.4]
If the thickness of the lower shell course calculated to resist the
seismic overturning moment is greater than the thickness required
for hydrostatic pressure, both excluding any corrosion allowance,
then the calculated thickness of each upper shell course for
hydrostatic pressure shall be increased in the same proportion,
unless a special analysis is made to determine the seismic overturning
moment and corresponding stresses at the bottom of each upper
shell course.
9.6. Anchorage of Tanks [Para. E.6]
When anchorage is provided, it shall be designed to provide the
following min. anchorage resistance in lb/Ft of shell circumference :
Min. anchorage resistance = 1.273 M / D2 - wt 1428.797 lb/Ft

Capacity : 5000 M3 0 Item : TK-01A

10. Overturning Moment due to Wind, Mw.
Mw1 = P (Ar Xr + As Xs) 549994.2 lb-ft 76089.4 Kg-M
Where, P = Wind pressure PSI 50 Kg/M2
Ar = Projected area over roof = 0.5 Do (Ht - H) INCH2 8.994 M2
Xr = Height from bottom of tank shell to center of gravity Ft 12.5049 M
of roof = H + 0.3 (Ht - H)
As = Projected area of shell = Do H INCH2 294.621 M2
Xs = Height from bottom of tank shell to shell's center of gravity Ft 4.7835 M
= (H1+H2)/2 + (H2+H3)/2 + x
where x (see next page) -0.0165 M
Do = D + 2 t1 23.992 M
( Up- lift for wind ) = 4 Mw / 3.14 D2 113.3247 lb/ft 168.757 Kg/M
Total load, W (operating: full liq. p = 1+ wind) 116.672 Ton
( Dead Load ) = W / 3.14 D lb/ft 2098.53 Kg/M
where W = weight of tank exc. weight of floating roof & bottom 157.962 Ton
Ratio of Up-lift load / Dead load 0.080417 < 1
Since Up-lift (128 Kg/M) < Dead load (2838 Kg/M) Not necessary of Anchor Bolts.
11. Anchor Bolt Strength.
11.1. Wind Load, Pw = 0.7 x P x Do x H lb 10311.7 Kg
Where, P = Wind Pressure 50 Kg/M2
Do = Tank diameter 23.992 M
H = Tank Height 12.28 M
Wt = Total Tank Weight (excluding corrosion allowance) 151746 Kg
Wt' = Tank Weight except Bottom Plate (excl. corr. allow.) 126369 Kg
Design pressure atmospheric
11.2. Overturning Moment, Mw2 = Pw . Xs 356542.5 lb-ft 49326.2 Kg-M
Overturning moment, Mw = Max. (Mw1 , Mw2) 549994.2 lb-ft 76089.4 Kg-M
11.3. Anti-Overturning Moment, Rw = Wt' . D/2 10957504 lb-ft 1515925 Kg-M
Ratio of Mw / Rw 0.050193 < 1
Since Mw < Rw Anchor Bolts are not required.

To find tank shell's CG : Take Moment about CG :
W1 [(H1+H2)/2 + (H2+H3)/2 + x] + W2 [(H2+H3)/2 + x] + W3 [x]
= W4 [(H3+H4)/2 - x]
+ W5 [(H3+H4)/2 - x + (H4+H5)/2]
+ W6 [(H3+H4)/2 - x + (H4+H5)/2 + (H5+H6)/2]
+ W7 [(H3+H4)/2 - x + (H4+H5)/2 + (H5+H6)/2 + (H6+H7)/2]
+ W8 [(H3+H4)/2 - x + (H4+H5)/2 + (H5+H6)/2 + (H6+H7)/2 + (H7+H8)/2]
W1 [(H1+H2)/2 + (H2+H3)/2] + W1 x + W2 [(H2+H3)/2] + W2 x + W3 x
= W4 [(H3+H4)/2] - W4 x
+ W5 [(H3+H4)/2 + (H4+H5)/2] - W5 x
+ W6 [(H3+H4)/2 + (H4+H5)/2 + (H5+H6)/2] - W6 x
+ W7 [(H3+H4)/2 + (H4+H5)/2 + (H5+H6)/2 + (H6+H7)/2] - W7 x
+ W8 [(H3+H4)/2 + (H4+H5)/2 + (H5+H6)/2 + (H6+H7)/2 + (H7+H8)/2] - W8 x
x (W1 + W2 + W3) + W1 [(H1+H2)/2 + (H2+H3)/2]
= W4 [(H3+H4)/2]
+ W5 [(H3+H4)/2 + (H4+H5)/2]
+ W6 [(H3+H4)/2 + (H4+H5)/2 + (H5+H6)/2] Figure (13)
+ W7 [(H3+H4)/2 + (H4+H5)/2 + (H5+H6)/2 + (H6+H7)/2]
+ W8 [(H3+H4)/2 + (H4+H5)/2 + (H5+H6)/2 + (H6+H7)/2 + (H7+H8)/2]
- x (W4 + W5 + W6 + W7 + W8)
x (W1 + W2 + W3) + x (W4 + W5 + W6 + W7 + W8)
+ W1 [(H1+H2)/2 + (H2+H3)/2]
+ W2 [(H2+H3)/2]
= W4 [(H3+H4)/2]
+ W5 [(H3+H4)/2 + (H4+H5)/2]
+ W6 [(H3+H4)/2 + (H4+H5)/2 + (H5+H6)/2]
+ W7 [(H3+H4)/2 + (H4+H5)/2 + (H5+H6)/2 + (H6+H7)/2]
+ W8 [(H3+H4)/2 + (H4+H5)/2 + (H5+H6)/2 + (H6+H7)/2 + (H7+H8)/2]
x =[W4 [(H3+H4)/2] -0.054127 Ft -0.0165 M
+ W5 [(H3+H4)/2 + (H4+H5)/2]
+ W6 [(H3+H4)/2 + (H4+H5)/2 + (H5+H6)/2]
+ W7 [(H3+H4)/2 + (H4+H5)/2 + (H5+H6)/2 + (H6+H7)/2]
+ W8 [(H3+H4)/2 + (H4+H5)/2 + (H5+H6)/2 + (H6+H7)/2 + (H7+H8)/2]
- W1 [(H1+H2)/2 + (H2+H3)/2]
- W2 [(H2+H3)/2]]
/ (W1+W2+W3+W4+W5+W6+W7+W8)

11.4. Sliding.
Sliding force by wind, Ps = 0.7 x P x D x H lb 10311.7 Kg
Frictional Resistance Force by wind, Rs = 0.3 Wt lb 45523.9 Kg
Ratio Ps / Rs 0.226512 < 1
Since Ps < Rs Anchor bolts are not required.
11.5. Anchor Bolts Provided.
Number of anchor bolts, n 12
Size of anchor bolts (UNC) 0.75 INCH MM
Anchor bolt sectional area, A 2.36 CM2
Allowable load (for 3/4" bolt) :
- Tensile, fat 4299.009 lb 1950 Kg
- Shearing, fas 2976.237 lb 1350 Kg
11.6. Anchor Bolt Load.
Tensile load per each bolt, ft = (4 Mw / n D) - Wt' / n -9845.45 Kg/Bolt
Since ft < fat The anchor bolt is sufficient
Shearing load per each bolt, fs = (Ps - Rs)/n -2934.35 Kg/Bolt
Since fs < fas The anchor bolt is sufficient
12. Fixed-Roof Inspection Hatches. [API-650, Appendix H.65.3]
Inspection hatches shall be located on tank fixed roof to permit
visual inspection of the seal region.
- Max. spacing of inspection hatches per code 75 Ft 22.86 M
- Min. spacing of inspection hatches per code 4 Ft 1.2192 M
Circle dia. of inspection hatches = D - 6, Ft 72.60892 Ft 22.1312 M
Calculated No. of inspection hatches = 3.14(D-6)/75 3.041435
Assume actual No. of inspection hatches 6
Actual spacing of inspection hatches 38.01794 Ft 11.5879 M
< 75 Ft OK
> 4 Ft OK

13. Total Weight of Tank.
a. Weight of Shell
1st Course, W1 = 3.14 D t H p 22.6902 Ton
2nd Course, W2 19.8539 Ton
3rd Course, W3 15.5995 Ton
4th Course, W4 12.7632 Ton
7th Course, W7 0 Ton
8th Course, W8 0 Ton
Sub-Total (a) 180760.5 lb 81.9917 Ton
b. Weight of Bottom Plate, R1 = D/2 - Annular width, Rw 11.366 M
L1 = 2 R1 Sin (O/2) 1.82917 M
h1 = L1 / 2 R1 Tan (O/2) 11.3291 M
Total Bottom plate Area, A = 0.5 L1 . h1 . n 404.096 M2
Total bottom Plate Weight, W = A. ta . p Sub-Total (b) 69933.98 lb 31.7216 Ton
Figure (14)
c. Weight of Annular Bottom Plate 9593.336 lb 4.35147 Ton
d. Weight of Roof Plate = Roof area * t p 62546.89 lb 28.3708 Ton
Roof conical area = 3.14 * (D/2) * sq. root ((D/2)2 + h2) 451.765 M2
'where, h = Ht - H = Cone height = Rafter Slope * Do/2 0.74975 M
Rafter slope = 1/16 [see Figure (2)] 01:30

e. Weight of Rafters 13.3577 Ton
Total length of rafters (H beam 250x125x6/9) 467.22 M
Weight of one meter of beam 28.5897 Kg
f. Weight of Column, Pipe 20" NPS, Sch. 40 4.46457 Ton
g. Weight of Top Wind Girder 3.07263 Ton
Circumferential length of 2 angles 6x4x3/8" (160x100x10mm) 150.545 M
Weight of one meter of angle 20.41 Kg
Total area of top wind girder, A 60.7712 M2
Weight of top wind girder, W = A * P * t 3.02929 Ton
h. Weight of Intermediate Wind Girder 5 Ton
Wind Girder ID M
Wind Girder OD M
i. Weight of Manholes, Cleanout Doors & Nozzles 6 Ton
j. Weight of Ladders & Platforms 5 Ton
k. Weight of brackets (cooling system supports) 3.32338 Ton
No. of brackets per level = 3.14 D / 4000 20 Support
Total brackets for two levels of cooling system + level for foam 84 Support
Bracket dimensions 400x850x100x8 600x850x8
Weight of one bracket 39.564 Kg
l. Weight of Inspection Hatches. Ton
No. of inspection hatches, Nih 6
Weight of nozzle
Weight of flange (or loose cover)
m. Weight of Manways (for fixed-roof tanks). Ton
At least one manhole, min 24" ID shall be provided for access to
the tank interior. [API-650, Appendix H.6.5.1]
No. of manholes located at fixed roof, 24" NPS 2
Weight of nozzle
Weight of flange
Total Tank Weight 189.683 Ton

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