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Rectangular tank sizing Calculation

Objectives

- To calculate the thickness of tank plates- To determine the size of stiffening frame for tank- To determine dry and test weights

Assumptions

- Specific gravity of liquid is 1

-

- - Minimum Distance between stiffeners = 1.05m

References

1. UL-142, Steel Aboveground Tanks for flammable and combustible liquids, Underwriters Laboratories Inc.

2Publishing Inc.

3 Corus Construction and IndustrialStructural Sections to BS 4: Part 1:1993 & BS EN 10056:1999

4 ASME Boiler and Pressure Vessel Code Section II subpart D5 Trauvay and Cauvin (2001), Piping Equipment6

7th ed., McGraw-Hill. 20027 ASME B31.10M - 2000: Welded and Seamless Wrought Steel Pipe8 ASME B.16.5 - 2009: Pipe Flanges and Flanged Fittings

Notes

1 A total of 10 Stiffeners were used based on a spacing of 1.05 m on the long sides (3 stiffeners on each longer side; and 2 stiffeners on each shorter side)

2 Sump Pump weight was not included in calculations3 Weights are calculated weights. Final weights to be advised by vendor

Weight calulation does not include weir.

Acceleration due to gravity is 9.81 m/s2

Density of steel is 7850 kg/m3

Eugene F. Megyesy, Pressure Vessels Handbook, Pressure Vessels

Young, W. C. & Budynas, R. G. (2002) Roark's Formulas for Stress and Strain

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Definition of Terms

- a Length of top plate

- b Width of top plate

- CA Corossion Allowance

- E Modulus of Elasticity

- g Gravitational acceleration

- H Height of tank

- Minimum Moment of inertia of top edge stiffening

- L Length of tank

- l Spacing between vertical stiffeners

- Spacing of bottom plate support

- R Reaction at top edge

- r Radius of contact of heaviest dead weight on top tank

- S Allowable stress of tank material

- t Required thickness

- Selected thickness

- w Load

- W Heaviest Dead weight on top plate

- Minimum Section Modulus of vertical stiffener

- α Factor Depending on ratio of Length to Width of top plate a/b

- β Factor Depending on ratio of Height to Length H/L

Density of tank material

ρ Density of liquid in tank

ν Poisson ratio of tank material

CSA Cross-Sectional Area

Imin

lb

ta

Zmin

ρp

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Equipment Tag No. ABH 8000 Project No. 1216 No. of equipments 1

1 DESIGN DATA

Tank Material SA-516 Gr. 60

Modulus of Elasticity E = 203.4E+09

Allowable Stress S = 117.9E+06

Density of tank material = 7850Tank Dimensions:Length L = 4.2 mWidth W = 3 mHeight H = 2.4 mType of Liquid WaterSpecific Gravity = 1

Density of liquid ρ = 1000

Acceleration due to gravity g 9.81No. of vertical stiffeners one side = 3Maximum Distance between Stiffners l = 1.05 mCorrosion Allowance CA = 3 mmHeight/length ratio (H/L) = 0.5714Factor for H/L β = 0.095 (See Appendix)

2 SIDE PLATE THICKNESS

Required Plate Thickness = 0.00457334 m

= 4.57 mm

Thickness + Corossion Allowance = 7.57 mm

Selected Plate thickness = 8 mm

3 LOAD= 28252.8 N/m

= 28.25 N/mm

4 VERTICAL STIFFENINGMinimum Section Modulus

= 77.538

An equal angle L-section of dimensions

150 x 150 x 15 (section modulus = 83.5frame is satisfactory for vertical stiffening

Total no. of vertical stiffeners = 10 (Note 1)

N/m2

N/m2

ρp kg/m3

kg/m3

m/s2

ts

cm3

cm3)

S

gHlt

2

2gHw

S

HlwZ

1284.0min

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5 TOP EDGE STIFFENING

Reaction at top edge = 8.48 N/mm

Minimum required moment of inertia for top edge stiffening:

= 22512126

= 2251.2

200 x 200 x 16 (moment of inertia = 2342frame is satisfactory for vertical stiffening

BOTTOM PLATE SUPPORT SPACING

using a minimum plate thickness of 4.57 mm calculated for side plates above,the maximum spacing of bottom plate supports:

= 0.406 m

6 TOP PLATE THICKNESS

Dimensions of top plate

Length a = 4.4 m

Width b = 3.2 m

Constant based on length to width ratio a/b

a/b = 1.375

α = -0.000125 (See Appendix)

Poisson's ration 0.3

Total dead weight on tank top plate = 325.69 kg (Note 2)= 3195.0 N

Sum of Radii of load contacts with top plater = 1475 mm

Total Stress due to dead load on 4.57mm required plate thickness

= 30608563 N/m2

This Stress value is < S ( 117.9E+06therefore required thickness for side plates is adequate

Selected thickness = 8 mm

mm4

cm4

cm3)

N/m2)

gH

Stlb

254.1

r

b

t

W 2ln1

2

32

wR 3.0

aEt

RLI

192

4

min

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7 WEIGHT CALCULATIONS

a Weight of Tank Plates (Surface area of tank * tank thickness * Density of tank material)

i- Side plates= 2170.368

ii- Bottom Plate kg= 791.28

iii- Top Plate= 884.224

Total weight of tank plates = 3845.872

b Weight of StiffenersWeight of one vertical stiffener(CSA*Length*density of stiffener) = 84.78 kgTotal Weight of vertical Stiffeners = 847.8 kg

Weight of top edge stiffening(CSA*Length*density of stiffener) = 723.456 kg

Total weight of stiffeners = 1571.256 kg

c Weights of nozzles7 Nos. 2" nozzles @ 3.63 kg/Nozzle = 25.41 kg2 Nos. 4" nozzles @ 9.53 kg/Nozzle = 19.06 kg2 Nos. 24" Manways @ 140.61 kg/MW = 281.22 kg

Total weight of nozzles = 325.69 kg

d Total Empty weight of tank(Weights of tank plates+Stiffners+nozzles) = 5742.818 kg

Weight of water to fill tank(Volume of tank * density of water) = 30240 kg

e. Operating Weight(Empty weight of tank + Weight of water at NLL)

NLL = 1.06 m

Weight of water at NLL = 13356Total Operating Weight = 19098.818

f. Weight of tank filled with water(Empty weight of tank + Weight of water) = 35982.818 kg

kg/m3

)(2 WHLHt p

psLWt

psabt

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TANK SKETCH

Vertical Stiffener Cross-Section

150mm

150mm

15mm

200mm

200mm

16mm

1.05m

2.4m

1m

4.2m

3m

Top Plate4.4m x 3.2m

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Top-Edge stiffening Cross-Section

200mm

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Summary of Results

-- Tank material SA-516 Gr. 60

-- Thickness of platesSides = 8 mmBottom = 8 mm

Top = 8 mm

-- Number of vertical stiffeners = 10

-- Stiffener configuration Equal leg (L section)

Stiffener Cross-section Dimensions

Vertical = 150mm x 150mm x 15mm

Top edge = 200mm x 200mm x 16mm

-- Dry weight of tank = 5742.818 kg

-- Operating weight of tank = 19098.818 kg

-- Weight of tank filled with water = 35982.818 kg

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APPENDIX

Values for factors used

1 2 3 4 5 6 7 8 9 10 11 12 13

Ratio 0.25 0.286 0.333 0.4 0.5 0.667 1 1.5 2 2.5 3 3.5 4

Constant β 0.024 0.031 0.041 0.056 0.08 0.116 0.16 0.26 0.34 0.38 0.43 0.47 0.49

Table 1: Values of βTable from Ref. 3

1 2 3 4 5 6

Ratio a/b 1 1.2 1.4 1.6 1.8 2 ∞

Constant α -0.238 -0.078 0.011 0.053 0.068 0.067 0.067

Table 2: Values of βTable from Ref. 8

Interpolation for β Interpolation for α

Col. No. β Col. No. β5 0.5 0.08 2 1.2 -0.0786 0.667 0.116 3 1.4 0.011

0.5714 0.095 1.375 -0.000125

H/L or H/l

H/L or H/l H/L or H/l

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