Calculation API 650

ROOF THICKNESS VERIFICATION AS PER API 620 Contents: 1

Design Data

2

Roof Design

3

Shell Desin

4

Compression Area Design

5

Bottom Plate Design

6

Intermediate Wind Girder Calculations

7

Stabiltility Calculations Against Wind Load

8

Stabiltility Calculations Against Seismic Load 8.1

Resistance To Over Turning

8.2

Shell Compression For Unanchored Tanks

8.3

Maximum Allowable Shell Compression For Unanchored Tanks

8.4

Shell Compression For Anchored Tanks

8.5

Maximum Allowable Shell Compression For Anchored Tanks

9

Uplift Load Cases As Per API 650 Table 3-21a

10

Anchor Chair Calculations

11

Foundation Loading Data

12

Nozzle Reinforcement Calculations(LATER)

13

Nozzle Flexibility Analysis As Per Appendix P of API 650(LATER)

14

Venting Calculations As Per API 2000(LATER)

7.1)

Roof Thickness and Compression Area Verification As Per API 620 Nomenclature P

= =

Total pressure in lbs/ft2 acting at a given level of the tank under the particular condition of loading. P1 + Pg

P1

=

Pressure in lbs/ft2 resulting from the liquid head at the level under consideration in the tank.

Pg

=

Gas pressure in lbs/ft2 above the surface of the liquid. Thwe maximum gas pressure(not exceeding 15 lbs/ft2) is the nominal pressure rating of the tank. Pg is the positive except in computation used to investigate the ability of the tank to withstand a partial vacuum; in such computations its value is negative.

T1

=

Meridional unit force in lbs/inch of latitudinal arc, in the wall of the tank at the level of the tank under consideration. T1 is positive when in tension.

T2

=

Latitudinal unit force in lbs/in of maridional arc, in the wall of the tank under consideration. T2 is positive when in tension.(in cylinderical side walls the latitudinal unit forces are circumfrential unit forces)

R1

=

Radius of curvature of the tank side wall in inch in a meridional plane at the level under consideration. R1 is to be considered negative when it is on the side of the tank wall opposite from R2 except as provided in 5.10.2.6

R2

=

Length in inch of the normal to the tank wall at the level under consideration measured from the wall of the tank to the axis of the revolution. R2 is always positive except as provided in 5.10.2.6

W

=

Total weight in lbs of that portion of the tank and its contents(either above the level under consideration, as in figure 5-4 panel b, or below it, as in figure 5-4 panel a) that is treated as a free body on the computations for that level. Strictly speaking the total weight would

include the weight of all metal, gas and liquid in the portion of the tank treated as described; however the gas weight is negligible and the metal weight may be negligible compared with the liquid weight. W shall be given the same sign as P when it acts in the same direction as the pressure on the horizontal face of the free body; it shall be given the opposite sign when it acts in the opposite direction. At

=

Cross section area in in2 of the side walls, roof or bottom of the tank at the level under consideration.

t

=

Thickness in inch of the side walls, roof or bottom of the tank at the level under consideration.

c

=

Corrosion allowance in inch

E

=

Joint efficiency

Sts

=

Maximum allowable stress for simple tension in lbs/in2 as given in table 5-1

Sca

=

Allowable compresive stress in lbs/in2 established as prescribed in 5.5.4

Design Data : API 620 10TH Ed. ADD.01

Desig Code Client's Specs Fluid Material Design Density of Contents

= =

Density of water for hydrotest = Specific Gravity Of Contents Material Yield Strength Design Temperature Internal Pressure Extrenal Pressure Liquid Level

= = = = = =

Sulphuric Acid A36 1820 113.623 1000 62.43 1.82 248.21 36000 100 1.015 146.16 0.0725 4200 13.78

Design Liquid Level

= = =

Allowable Tensile Stress At Design Temperature

4200 14 110.32 16000

Corrosion Allowance Shell

6.4 0.25197 6.4 0.25197 6.4 0.25197

Bottom Roof

Inside Dia Of Tank

D

=

Height Of Shell

=

Weight Of Compression Ring IF applicable Weight Of Accessories Wind Velocity

= =

4000 13.12 4010 13.16 4020 13.19 158.27 4200 14 450 3000 96.31

Nominal Dia Of Tank

Dn

=

Outside Dia of tank

D0

=

Yield Strength Of Steel Structure Roof Angle

= =

36000 11.3

Roof Design

As Per API 620 B 5.10.2

Assumptions

Taking Thickness

t

Joint Efficiency

E

Radius Of Dome

rr

Height Of Cone Roof

One Half The included apex angle of the Conical roof or bottom . Radius Of Cone

= = = = =

14 mm 0.551 inch 0.7 1xD 13.12 ft

h

=

1.31 ft

a

=

78.7

L

=

6.69 ft

Angle b/w the normal to roof q and a vertical line at the roof to shell juncture

=

At'

Roof Area Roof Weight

= = W (Uncorroded) =

Roof Weight

W (corroded) = At

Cross sectional Area at roof to shell junction

11.30

20256 141 Density x t x Roof Area 3163 1719

= =

19478 135

As per API 620 5.10.2.5.a

For Conical Seg.

R1

=

Infinity

ft

As per API 620 5.10.2.5.a

R3 = D/2

Case I :

= =

6.562 ft 78.74 inch

Thickness At The Top Head Edge Against Internal Pressure

W/At W/At'

= =

-0.162 psi -0.156 psi (force acting in downward direction)

Now Calculating Meridional and Latitudinal Forces T1

=

{R3/(2Cosa)}*{P+W/At}

= T2

=

Equation 8 of 5.10.2.5

171 lbf/in {(P × R3)/(Cosa)} 408 lbf/in

Now As Per 5.10.3.2 If T1 and T2 both are +ve, then T

=

Max.(T1 and T2) 408 lbf/in

tcalc.

= =

T/(Sts.E) + C.A 0.288 inch

Equation 9 of 5.10.2.5

Provided Thickness is Ok

Case II :

Thickness At The Top Head Center Against Internal Pressure

T1 '

T2 '

=

Rs/2(P+W/At')

=

0 lbf/in

= =

Rs x (P+W/At') - T1 0 lbf/in

Now As Per 5.10.3.2 If T1 and T2 both are +ve, then T

= =

Max.(T1' and T2') 0 lbf/in

tcalc.

=

T/(Sts.E) + C.A 0.252 inch

As these thicknesses are calculated based on the internal pressure of = 1.015 psi Therefore, Back calculating the internal pressure limited by the actual provided thickness

tprov.

=

T/(Sts.E) + C.A

(tprov. - C.A) X Sts X E = = 3351 lbf/in Now putting this value of T in the equation of T2, where we find the maximum calculated thickness T

T2

=

Rs x (P+W/At x cos a) - T1

T

=

Rs x (P+W/At x cos a) - Rs/2(P+W/At) T2 = T

P

= =

(2 X T/Rs) - W/At(2*cos a -1) #DIV/0! #DIV/0!

As Per 7.18.3.2, our roof will be safe against the hydro test pressure of 1.25 x internal pressure i.e. 1.26875 psi

Case II :

Thickness At The Top Head Edge Against External Pressure

W = - (Live Load + Dead Load) x Roof Area -ve sign id due to the downward direction of load -(25 + weight of roof in lbs/ft2) x roof area

=

W/At W/At'

=

-4985 lbf

= =

-0.256 psi -0.246 psi

Now Calculating Meridional and Latitudinal Forces T1

= =

{R3/(2Cosa)}*{P+W/At} -66.0 lbf/in

Equation 8 of 5.10.2.5

T2

=

{(P × R3)/(Cosa)} -29.1 lbf/in

Equation 9 of 5.10.2.5

Now As Per 5.10.3.5 T'

= =

Max.{ABS(T1) , ABS(T2)} 66.0 lbf/in

T"

=

Min.{ABS(T1) , ABS(T2)} 29.1 lbf/in

R' R"

= =

Infinity

t18

= =

Sqrt{(T'+0.8 X T") X R'}/1342 +Solving C.A By Equation 18 of API 620 Infinity inch

t19

=

SQRT{T'' x R''}/1000 + CA 0.300 inch

Similarly, 78.74 inch

Now,

Now; As per 5.10.3.5.b Step-2 t18 - C.A R'

=

Infinity

< .0067

Solving By Equation 19 of API 620

t19 - C.A R'' treq treq tprovided

=

0.0006

< .0067

Max(t18 , t19) 0.300 inch

= = =

0.551 inch

As per 5.5.4.3 Allowable Compressive Stress; Sca

Provided thickness is O.K

Case IV :

Thickness At The Top Head Center Against External Pressure

T1 '

Rs/2(P+W/At' )

= =

0.00 lbf/in

T2 '

= = Now As Per 5.10.3.5

Rs(P+W/At' ) -T1' 0.00 lbf/in

T'

=

T"

=

Max.{ABS(T1' ) , ABS(T2' )} 0.00 lbf/in Min.{ABS(T1' ) , ABS(T2' )} 0.00 lbf/in

Similarly R' = R2 R" = R1

0.00 inch 0.00 inch

Now, t18

=

t19

=

Now; As per 5.10.3.5.b Step-2 t18 - C.A R' t19 - C.A R'' treq

=

treq

= =

tprovided

Sqrt{(T'-0.8 X T") X R'}/1342 + Solving C.A By Equation 18 of API 620 0.252 SQRT{T'' x R''}/1000 + CA Solving By Equation 19 of API 620 0.252

=

#DIV/0!

< .0067

=

#DIV/0!

< .0067

Max(t18 , t19) 0.252 inch 0.551 inch

As per 5.5.4.3 Allowable Compressive Stress; Sca Sca

=

= 106 x (t - C.A) R' #DIV/0!

As these thicknesses are calculated based on the external pressure of P = 0.0725 psi Therefore, Back calculating the external pressure limited by the actual provided thickness

Now; As per 5.10.3.5.a t19

=

SQRT{T'' x R''}/1000 + CA

tprovided

=

SQRT{T'' x R''}/1000 + CA

T''

=

[(tprovided-C.A) x 1000 ]2 / R''

T''

=

T''

=

-Rs/2(P+W/At' )

Pext

=

2/Rs x T'' - W/At' #DIV/0! Psi

#DIV/0!

lbs/in

NOTE:

As Per 32-SAMSS-006 Para 5.4.k, roof live loads shall not be less than concentrated load of 225 Kgs over 0.4 meter square area. for this purpose, by considering the roof segment of 700mm diamter which is equivelant to 0.4 meter squre area is to be analysed against these loading conditions #DIV/0! For result and methodolgy see ANNEXURE 1

3)

Shell Design Shell calculations are based on different assumed thicknesses, here we will perform the specimen calculations for 1st shell course and the others are given in the tabulated form which are mentioned below.

Case I :

Thickness of 1st shell course Against Internal Pressure

Joint Efficiency

E

Taking thickness of Ist Shell Course Total weight of shell of different

=

0.85

= =

0.630 inch 26004 lbs

=

3163 lbs

thicknesses. Total weight of roof

Total Weight; W W/At

(Roof Pl.+Shell).= =

29167 lbs 1.50 psi

Now Total Pressure Internal Pressure + Pressure due to liquid head

=

24.31 psi

Now calculating the latitudinal and maridianal forces As Per 5.10.2.5.c

T1

= =

Rc/2(P+W/At) equation 10 of 5.10.2.5 1,016 lbs/inch

T2

= =

Rc x P

Now As Per 5.10.3.2 If T1 and T2 both are +ve, then T = = tcalc.

= =

equation 11 of 5.10.2.5 1,915 lbs/inch

Max.(T1 and T2) 1,915

lbs/inch

T/(Sts.E) + C.A 0.39

inch

The same procedure is adopted while confirming the thickness during hydrotest

As this thickness is calculated based on the internal pressure of P = Internal Pressure + Pressure due to liquid head = 24.31 psi Back calculating the internal pressure limited by the actual provided thickness tprov. T/(Sts.E) + C.A = T

=

5,140 lbs/inch

Now putting this value of T in the equation of T2, where we find the maximum calculated thickness

Case II :

T2

=

Rc x P

Pmax.int

= =

T2/Rc

T2=T 65.28 psi

Thickness of 1st shell course Against External Pressure

= -(Weight Of Roof Plates + Weight Of shell + Live Load) = -32684 lbs Pext. = -0.0725 psi -ve sign id due to the downward direction of load W

Now calculating the latitudinal and maridianal forces As Per 5.10.2.5.c

T1

=

Rc/2(P+W/At) equation 10 of 5.10.2.5 -69 lbs/inch

T2

=

Rc x P

equation 11 of 5.10.2.5 -5.71 lbs/inch

Now As Per 5.10.3.5 T' T"

=

Max.{ABS(T1) , ABS(T2)}

=

69 lbs/inch Min.{ABS(T1) , ABS(T2)} 6 lbs/inch

similarly,

R' = Rc R" = Rc Now,

= =

78.74 inch 78.74 inch

t18

= = t19 = = Now; As per 5.10.3.5.b Step-2 t18 - C.A R' t19 - C.A R'' treq

= =

Sqrt{(T'+0.8 X T") X R'}/1342 + C.A 0.3087 inch SQRT{T'' x R''}/1000 + CA 0.2732 inch

=

0.0007

< .0067

=

0.0003

< .0067

Solving By Equation 18 of API 620 Solving By Equation 19 of API 620

Max(t18 , t19) 0.3087 inch

As per 5.5.4.3 Allowable Compressive Stress; Sca Sca

=

= 106 x (t - C.A) R' 0

Psi

Back calculating the external pressure limited by the actual provided thickness

Now; As per 5.10.3.5.a as the maximum thickness is obtained by equation 18, therefore back calculating the external pressure limited by tprov.

t18

=

{1342 x (tprov.-C.A)}2/R'

=

{1342 x (tprov.-C.A)}2/R'

=

Sqrt{(T'+0.8 X T") X R'}/1342 + C.A T'-0.8 X T" -Rc/2(P+W/At)- 0.8 x (Rc x P)

Now Putting the values in the above equation

Pmax.ext.

=

-31.27 Psi

-ve sign shows the vacuum condition. Assuming Thicknesses of Various Shell Courses and Calculate their Weights

Now following the above mentioned procedure for the calculation of remaining shell courses.

CASE 1. Table 1.

Internal Pressure With Full of Liquid

Shell

Thickness

Width

Weights

Coures #

mm

inch

mm

inch

1 2 3 4 5 6

16 14 12 10 0 0

0.630 0.551 0.472 0.394 0.000 0.000

2450 2450 2450 1650 0 0

96.46 96.46 96.46 64.96 0.00 0.00

Total Weight Of Shell

Kgs

3,863 3,380 2,897 1,626 =

Table 2.

Shell Coures #

1 2 3 4 5 6

Weight of Roof

Weight of Shell

lbs

lbs

3,163 3,163 3,163 3,163 3,163 3,163

26,004 17,467 9,997 3,594 -

Total Weight Total Weight WHydrotest W lbs

29,167 20,630 13,160 6,756 3,163 3,163

lbs

29,167 20,630 13,160 6,756 3,163 3,163

W/At Psi

1.50 1.06 0.68 0.35 0.16 0.16

Table 3.

Shell Coures #

1 2 3 4 5 6

Water Pressure Head Psi

Total Pressure PContents

Total Pressure PHydrotest

Psi

Contents Pressure head Psi

Psi

Psi

1.015 1.015 1.015 1.015 1.015 1.015

23.30 16.96 10.61 4.27 0.00 0.00

12.80 9.32 5.83 2.35 0.00 0.00

24.31 17.97 11.63 5.29 1.02 1.02

Internal Pressure

As Per 7.18.3.2 Internal Presssure for Hydrotest is 1.25 * Pint Now Calculating Meridianal and Latitudinal Forces aginst pressure and During Hydrotest Condition.

Shell Coures #

Pcon.+W/At internal Psi

Phydro+W/At Hydrotest Psi

T1

T1hydro

lbs/inch

lbs/inch

1 2 3 4

25.81 19.03 12.30 5.63

15.57 11.64 7.78 3.96

1,016.22 749.25 484.44 221.79

612.92 458.46 306.16 156.01

5 6

1.18 1.18

1.43 1.43

46.35 46.35

56.34 56.34

Shell Coures #

1 2 3 4 5 6

T2

T2hydro

lbs/inch

lbs/inch

1,914.53 1,415.11 915.69 416.27 79.92 79.92

1,107.93 833.52 559.11 284.71 99.90 99.90

T{Max.(T1,T2) T{Max.(T1hyd., T2hyd.)} } lbs/inch lbs/inch

1,914.53 1,415.11 915.69 416.27 79.92 79.92

1,107.93 833.52 559.11 284.71 99.90 99.90

Now Calculating the required thickness as Per 5.10.3.2 Shell Coures #

tcalc.

thydro

tcalc1.25GHD Therefore WL=1.25GHD

WL

8.2)

=

413.5 lbs/ft

Shell Compression For Unanchored Tanks Ms

=

0.39

Per API 620 Appendix. L.5.1

D2(Wt+WL)

=

0.39

Where, Wt

{Weight of Roof + Weight Of Shell}/p x D 704 lbs/ft

= =

As Ms/{D2*(Wt+WL)