Rectangular Tank Sizing

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 Acceleration due to gravity is 9.81 m/s2 Density of steel is 7850 kg/m3 Minimum Distance between stiffeners = 1.05m

References 1. UL-142, Steel Aboveground Tanks for flammable and combustible liquids, Underwriters Laboratories Inc. 2 Eugene F. Megyesy, Pressure Vessels Handbook, Pressure Vessels Publishing 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 D 5 Trauvay and Cauvin (2001), Piping Equipment 6 Young, W. C. & Budynas, R. G. (2002) Roark's Formulas for Stress and Strain 7th ed., McGraw-Hill. 2002 7 ASME B31.10M - 2000: Welded and Seamless Wrought Steel Pipe 8 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 calculations 3 Weights are calculated weights. Final weights to be advised by vendor Weight calulation does not include weir.

Page 1 of 8

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

- Imin

Minimum Moment of inertia of top edge stiffening

-L

Length of tank

- l

Spacing between vertical stiffeners

- lb

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

- ta

Selected thickness

-w

Load

-W

Heaviest Dead weight on top plate

- Zmin

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

ρp

Density of tank material

ρ

Density of liquid in tank

ν

Poisson ratio of tank material

CSA

Cross-Sectional Area

Page 2 of 8

Equipment Tag No. 1

ABH 8000

Project No.

1216

DESIGN DATA Tank Material Modulus of Elasticity Allowable Stress Density of tank material Tank Dimensions: Length Width Height Type of Liquid Specific Gravity Density of liquid Acceleration due to gravity No. of vertical stiffeners one side Maximum Distance between Stiffners Corrosion Allowance Height/length ratio (H/L) Factor for H/L

2

No. of equipments

E S ρp

= = =

L W H

= = =

ρ g l CA β

t  l

 gH S

= = = = = = =

m m m

kg/m3 m/s2 m mm (See Appendix)

=

0.0045733 m

=

4.57

mm

=

7.57

mm

ts

=

8

mm

gH 2

=

28252.8

N/m

=

28.25

N/mm

0.1284 Hlw = S

77.538

cm3

Thickness + Corossion Allowance Selected Plate thickness

LOAD

w

4

4.2 3 2.4 Water 1 1000 9.81 3 1.05 3 0.5714 0.095

SIDE PLATE THICKNESS Required Plate Thickness

3

SA-516 Gr. 60 2 203.4E+09 N/m 2 117.9E+06 N/m kg/m3 7850

2

VERTICAL STIFFENING Minimum Section Modulus Z min 

An equal angle L-section of dimensions 150 x 150 x 15 (section modulus = frame is satisfactory for vertical stiffening

83.5

cm3)

Total no. of vertical stiffeners

=

10

Page 3 of 8

(Note 1)

1

5

TOP EDGE STIFFENING Reaction at top edge

R  0.3w

=

8.48

N/mm

Minimum required moment of inertia for top edge stiffening:

I min 

RL 4 192 Et

=

4 22512126 mm

a

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

= 2251.2 3 2342 cm )

cm4

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:

lb  1.254t

6

S

gH

=

0.406

m

TOP PLATE THICKNESS Dimensions of top plate Length a = Width b = Constant based on length to width ratio a/b a/b = α = Poisson's ration Total dead weight on tank top plate

= = Sum of Radii of load contacts with top plate r =

4.4 3.2

m m

1.375 -0.000125 (See Appendix) 0.3 325.69 3195.0 1475

kg N

(Note 2)

mm

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



3W  1   ln 2b    2  2t  r 

=

30608563 N/m2

2 This Stress value is < S ( 117.9E+06 N/m ) therefore required thickness for side plates is adequate

Selected thickness

=

Page 4 of 8

8

mm

7

WEIGHT CALCULATIONS a

Weight of Tank Plates (Surface area of tank * tank thickness * Density of tank material) i- Side plates 2170.368  2t p ( LH  WH ) = ii- Bottom Plate kg = 791.28  LWt s  p iii- Top Plate  abts  p = 884.224 Total weight of tank plates

b

=

3845.872

Weight of Stiffeners Weight of one vertical stiffener (CSA*Length*density of stiffener) Total Weight of vertical Stiffeners

= =

84.78 847.8

kg kg

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

=

723.456

kg

=

1571.256 kg

Total weight of stiffeners c

d

e.

f.

Weights of nozzles 7 Nos. 2" nozzles @ 2 Nos. 4" nozzles @ 2 Nos. 24" Manways @

3.63 kg/Nozzle 9.53 kg/Nozzle 140.6 kg/MW

= = =

25.41 19.06 281.22

kg kg kg

Total weight of nozzles

=

325.69

kg

Total Empty weight of tank (Weights of tank plates+Stiffners+nozzles)

=

Weight of water to fill tank (Volume of tank * density of water)

=

5742.818 kg

30240

kg

Operating Weight (Empty weight of tank + Weight of water at NLL) NLL = Weight of water at NLL = Total Operating Weight =

1.06 m kg/m3 13356 19098.818

Weight of tank filled with water (Empty weight of tank + Weight of water)

35982.818 kg

=

Page 5 of 8

TANK SKETCH

Top Plate

2.4m

150mm 15mm 150mm Vertical Stiffener Cross-Section

200mm

16mm 200mm Top-Edge stiffening Cross-Section

Page 6 of 8

Summary of Results

-- Tank material

SA-516 Gr. 60

-- Thickness of plates Sides Bottom Top

= = =

8 mm 8 mm 8 mm

-- Number of vertical stiffeners

=

10

-- Stiffener configuration Stiffener Cross-section Dimensions

Equal leg (L section)

Vertical

=

150mm x 150mm x 15mm

Top edge

=

200mm x 200mm x 16mm

-- Dry weight of tank

=

5742.818 kg

-- Operating weight of tank

=

19098.82 kg

-- Weight of tank filled with water

=

35982.82 kg

Page 7 of 8

APPENDIX Values for factors used 1 Ratio Constant

6

7

8

9

10

11

12

13

0.4

0.5 0.667

1

1.5

2

2.5

3

3.5

4

0.024 0.031 0.041 0.056

0.08 0.116

H/L or H/l β

2

3

4

0.25 0.286 0.333

5

0.16 0.26 0.34

0.38 0.43 0.47 0.49

Table 1: Values of β Table from Ref. 3

Ratio Constant

a/b α

1

2

3

4

5

6

1

1.2

1.4

1.6

1.8

2

∞

-0.238 -0.08 0.011 0.053 0.068 0.067 0.067

Table 2: Values of β Table from Ref. 8

Interpolation for β Col. No. 5 6

H/L or H/l 0.5 0.667 0.5714

Interpolation for α β 0.08 0.116 0.095

Page 8 of 8

Col. No. 2 3

H/L or H/l 1.2 1.4 1.375

β -0.078 0.011 -0.000125