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 Designed by : Eng. Abdel Halim Galala, Design General Manager

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Project Job Name Service Capacity

Date : 26.9.2008 Location : Port Said Client : PETROBEL Item : TK-01A

: Design & procurement of storage tanks : El-Gamil Plant Storage Facilities : Crude Oil Storage Tank : 5000 M3

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 where, Z = Seismic force factor, depends on seismic zone [Table E-2] Seismic zone of site I = Importance factor C1 = Lateral earthquake force coefficient C2 = Lateral earthquake force coefficient = 0.75 S / T when T <= 4.5 = 3.375 S / T2 when T > 4.5

[Para. E.3.3.3] [Para. E.3.3.3]

Kg-M

0.15 2A 1 0.6 0.203019 0.164867

S = Site coefficient [Table E-3] T = Natural period of the 1st sloshing mode = k (D0.5) k = Factor depends on ratio D/H [Figure E-4] D = Nominal tank dia. H = Max. design liquid level Ratio D/H Since T > 4.5 seconds, Use C2

1.5 5.541355 Sec. 0.625 78.60892 Ft 40.28858 Ft 1.951147 0.164867

Ws = Total weight of tank shell Xs = Height from bottom of tank shell to shell's center of gravity Wr = Total weight of tank roof (fixed or floating) + portion of the snow load, if any, specified by the purchaser Ht = Total height of tank shell

180760.5 lb 15.6939 Ft 106077.9 lb

81.9917 Ton 4.7835 M 48.1162 Ton

40.28858 Ft

12.28

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 - Find ratio W 1 / W T by knowing D/H [Figure E-2] - Find ratio W 2 / W T by knowing D/H

[Figure E-2]

W T = Total weight of tank contents = Tank volume x specific gr.

23.96 12.28

M M

M

1.951147 0.38 0.52

12206584 lb

5536.82 Ton

3 5.99E+12 Ft 4638502 lb

3 5536.82 M Kg

(specific gravity of the product to be specified by the purchaser)

Tank volume W 1 = Ratio ( W 1 / W T ) . W T W 2 = Ratio ( W 2 / W T ) . W T

6347424

lb

Kg


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9. Seismic Design. (cont.)

[APPENDIX E, API 650]

X1 = Height from bottom of tank shell to the centroid of lateral seismic force applied to W 1

Ft

[E.3.3.2 & Figure E-3]

X2 = Height from bottom of tank shell to the centroid of lateral seismic force applied to W 2

Ft

[E.3.3.2 & Figure E-3]

D/H - Find ratio X1 / H by knowing D/H

[Figure E-3]

1.951147 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

6.87678 M

9.2. Resistance to Overturning Moment at bottom of tank shell, WL

Ft

[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 wL2 = 1.25 G H D Use

wL = Min ( wL1 , wL2 )

5470.978 lb/Ft 3958.802 lb/Ft 3958.802 lb/Ft

tb = Thickness of the bottom plate under the shell

0.629921 INCH

Fby = Min. specified yield strength of the bottom plate under the shell G = Design specific gravity of the liquid to be stored

30000 1

PSI

MM


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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 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 II. When

2892.698 lb/Ft

0.785 < M / [ D2 (wt + wL )] <= 1.5

b may be computed from the value of (b + wL )/ (wt + wL ) obtained from Figure E-5. Value obtained from Figure E-5 b = ( wt + wL ) . Value from Figure E-5 - wL III. When

2

1.5 < M / [ D (wt + wL )] <= 1.57

b=

VI. For

1490 . (w t + wL )  0.637 M 1 − 2 D (w t + w L 

731.9506 lb/Ft

  )

0 .5

− wL

M / [ D2 (wt + wL )] > 1.57

or when b / 12 t > Fa Value b / 12 t Value Fa

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.

0.361854

2 5422.703 lb/Ft 0.361854

6415.053 lb/Ft

0.361854 478.3498 PSI 6410.684 PSI

< Fa OK


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9.3.b. Anchored Tanks

[Para. E.5.2]

For anchored tanks, the max. longitudinal compressive force at 2 the bottom of shell, b = wt + 1.273 M / D

9.4. Max. Allowable Shell Compression

2892.698 lb/Ft

[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 2 2 6 6 - When G H D / t >= 10 , Fa = 10 t / D 2 2 6 6 0.5 - When G H D / t < 10 , Fa = 10 t / 2.5 D + 600 (G H ) However, Fa shall not be greater than 0.5 Fty 0.5 Fty where, t = thickness of the bottom shell course, excl. any corr. allow. Fa = Max. allowable longit. compressive stress in the shell Fty = Min. specified yield strength of the bottom shell course

980331.9 > 106 6410.684 PSI 6372.671 PSI 15000

PSI

0.503937 INCH 6410.684 PSI 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

OK


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0


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A. Cylindrical Tank, Fixed-Roof with Rafter & Column (cont.) 10. Overturning Moment due to Wind, Mw. Mw1 = P (Ar Xr + As Xs) Where, P = Wind pressure Ar = Projected area over roof = 0.5 Do (Ht - H) Xr = Height from bottom of tank shell to center of gravity of roof = H + 0.3 (Ht - H) As = Projected area of shell = Do H Xs = Height from bottom of tank shell to shell's center of gravity = (H1+H2)/2 + (H2+H3)/2 + x where x (see next page) Do = D + 2 t1 ( Up- lift for wind ) = 4 Mw / 3.14 D2

549994.2 lb-ft PSI INCH2 Ft INCH2 Ft

113.3247 lb/ft

Total load, W (operating: full liq. p = 1+ wind) ( Dead Load ) = W / 3.14 D where W = weight of tank exc. weight of floating roof & bottom

76089.4 50 8.994 12.5049

2 294.621 M 4.7835 M

-0.0165 M 23.992 M 168.757 Kg/M 116.672 Ton

lb/ft

2098.53 Kg/M 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 Where, P = Wind Pressure Do = Tank diameter H = Tank Height Wt = Total Tank Weight (excluding corrosion allowance) Wt' = Tank Weight except Bottom Plate (excl. corr. allow.) Design pressure

Kg-M 2 Kg/M 2 M M

lb

10311.7 50 23.992 12.28 151746 126369

Kg Kg/M2 M M Kg Kg

atmospheric

11.2. Overturning Moment, Mw2 = Pw . Xs Overturning moment, Mw = Max. (Mw1 , Mw2)

356542.5 lb-ft 549994.2 lb-ft

49326.2 Kg-M 76089.4 Kg-M

11.3. Anti-Overturning Moment,

10957504 lb-ft

1515925 Kg-M

Rw = Wt' . D/2

Ratio of Mw / Rw Since Mw < Rw

0.050193 < 1 Anchor Bolts are not required.


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A. Cylindrical Tank, Fixed-Roof with Rafter & Column (cont.) 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] + 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)

Figure (13)

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] + 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)

-0.054127 Ft

-0.0165

M


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A. Cylindrical Tank, Fixed-Roof with Rafter & Column (cont.) 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 Since Ps < Rs

11.5. Anchor Bolts Provided. Number of anchor bolts, n Size of anchor bolts (UNC) Anchor bolt sectional area, A Allowable load (for 3/4" bolt) : - Tensile, fat - Shearing, fas

0.226512 < 1 Anchor bolts are not required.

12 0.75

INCH

4299.009 lb 2976.237 lb

2.36

MM CM2

1950 1350

Kg Kg

11.6. Anchor Bolt Load. Tensile load per each bolt, ft = (4 Mw / n D) - Wt' / n Since ft < fat

-9845.45 Kg/Bolt The anchor bolt is sufficient

Shearing load per each bolt, fs = (Ps - Rs)/n Since fs < fas

-2934.35 Kg/Bolt 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 - Min. spacing of inspection hatches per code

75 4

Ft Ft

Circle dia. of inspection hatches = D - 6, Ft Calculated No. of inspection hatches = 3.14(D-6)/75

72.60892 Ft 3.041435

Assume actual No. of inspection hatches Actual spacing of inspection hatches

6 38.01794 Ft < 75 Ft OK > 4 Ft OK

22.86 1.2192

M M

22.1312 M

11.5879 M


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A. Cylindrical Tank, Fixed-Roof with Rafter & Column (cont.) 13. Total Weight of Tank. a. Weight of Shell

180760.5 lb

22.6902 19.8539 15.5995 12.7632 9.92695 1.15797 0 0 81.9917

Ton Ton Ton Ton Ton Ton Ton Ton Ton

69933.98 lb

11.366 1.82917 11.3291 404.096 31.7216

M M M M2 Ton

c. Weight of Annular Bottom Plate

9593.336 lb

4.35147 Ton

d. Weight of Roof Plate = Roof area * t p Roof conical area = 3.14 * (D/2) * sq. root ((D/2)2 + h2) 'where, h = Ht - H = Cone height = Rafter Slope * Do/2 Rafter slope = 1/16 [see Figure (2)]

62546.89 lb

28.3708 Ton 2 451.765 M 0.74975 M

1st Course, W1 = 3.14 D t H p 2nd Course, W2 3rd Course, W3 4th Course, W4 5th Course, W5 6th Course, W6 7th Course, W7 8th Course, W8

Sub-Total (a) b. Weight of Bottom Plate, R1 = D/2 - Annular width, Rw L1 = 2 R1 Sin (O/2) h1 = L1 / 2 R1 Tan (O/2) Total Bottom plate Area, A = 0.5 L1 . h1 . n Total bottom Plate Weight, W = A. ta . p Sub-Total (b)

Figure (14)

01:30


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A. Cylindrical Tank, Fixed-Roof with Rafter & Column (cont.) e. Weight of Rafters Total length of rafters (H beam 250x125x6/9) Weight of one meter of beam

13.3577 Ton 467.22 M 28.5897 Kg

f. Weight of Column, Pipe 20" NPS, Sch. 40

4.46457 Ton

g. Weight of Top Wind Girder Circumferential length of 2 angles 6x4x3/8" (160x100x10mm) Weight of one meter of angle Total area of top wind girder, A Weight of top wind girder, W = A * P * t

3.07263 150.545 20.41 60.7712 3.02929

Ton M Kg M2 Ton

h. Weight of Intermediate Wind Girder Wind Girder ID Wind Girder OD

5

Ton M M

i. Weight of Manholes, Cleanout Doors & Nozzles

6

Ton

j. Weight of Ladders & Platforms

5

Ton

k. Weight of brackets (cooling system supports) No. of brackets per level = 3.14 D / 4000 Total brackets for two levels of cooling system + level for foam Bracket dimensions 400x850x100x8 Weight of one bracket

3.32338 Ton 20 Support 84 Support 600x850x8 39.564 Kg

l. Weight of Inspection Hatches. No. of inspection hatches, Nih Weight of nozzle Weight of flange (or loose cover) m. Weight of Manways (for fixed-roof tanks). 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 Weight of nozzle Weight of flange

Total Tank Weight

Ton 6

Ton

2

189.683 Ton

Storage Tank Design Calculations - Seismic Design & Overturning Moment - By Abdel Halim Galala

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