calculation api 650

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)

ROOF THICKNESS VERIFICATION AS PER API 620

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 :

Desig Code

Client's Specs

Fluid Sulphuric Acid

Material A36

Design Density of Contents = 1820

= 113.623

Density of water for hydrotest 1000

= 62.43

Specific Gravity Of Contents 1.82

Material Yield Strength = 248.21

= 36000

Design Temperature 100

Internal Pressure = 1.015

146.16

Extrenal Pressure = 0.0725

Liquid Level = 4200

= 13.78

API 620 10TH Ed. ADD.01

Design Liquid Level = 4200

= 14

Allowable Tensile Stress At Design Temperature = 110.32

16000

Corrosion Allowance

Shell 6.4

0.25197

Bottom 6.4

0.25197

Roof 6.4

0.25197

Inside Dia Of Tank D = 4000

13.12

Nominal Dia Of Tank Dn = 4010

13.16

Outside Dia of tank D0 = 4020

13.19

158.27

Height Of Shell = 4200

14

Weight Of Compression Ring IF applicable 450

Weight Of Accessories = 3000

Wind Velocity = 96.31

Yield Strength Of Steel Structure = 36000

Roof Angle = 11.3

Roof Design As Per API 620 B 5.10.2

Assumptions

Taking Thickness t = 14 mm

= 0.551 inch

Joint Efficiency E = 0.7

Radius Of Dome rr = 1 x D

= 13.12 ft

Height Of Cone Roof h = 1.31 ft

One Half The included apex angle a = 78.7

of the Conical roof or bottom

.

Radius Of Cone L = 6.69 ft

Angle b/w the normal to roof q = 11.30

and a vertical line at the roof to shell juncture

Roof Area At' = 20256

= 141

Roof Weight W (Uncorroded)= Density x t x Roof Area

3163

Roof Weight W (corroded) = 1719

Cross sectional Area At = 19478

at roof to shell junction = 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 = 6.562 ft

= 78.74 inch

Case I : Thickness At The Top Head Edge Against Internal Pressure

W/At = -0.162 psi

W/At' = -0.156 psi

(force acting in downward direction)

Now Calculating Meridional and Latitudinal Forces

T1 = {R3/(2Cosa)}*{P+W/At} Equation 8 of 5.10.2.5

= 171 lbf/in

T2 = {(P × R3)/(Cosa)} Equation 9 of 5.10.2.5

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

Case II : Thickness At The Top Head Center Against Internal Pressure

T1' = Rs/2(P+W/At')

= 0 lbf/in

T2' = Rs x (P+W/At') - T1

= 0 lbf/in

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

T = Max.(T1' and T2')

= 0 lbf/in


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

T = (tprov. - C.A) X Sts X E

= 3351 lbf/inNow putting this value of T in the equation of T2, where we find the

maximum calculated thickness

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

Provided Thickness is Ok

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

= -4985 lbf

W/At = -0.256 psi

W/At' = -0.246 psi

Now Calculating Meridional and Latitudinal Forces

T1 = {R3/(2Cosa)}*{P+W/At} Equation 8 of 5.10.2.5

= -66.0 lbf/in

T2 = {(P × R3)/(Cosa)} Equation 9 of 5.10.2.5

-29.1 lbf/in

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

Similarly,

R' = Infinity

R" = 78.74 inch

Now,t18 = Sqrt{(T'+0.8 X T") X R'}/1342 + C.A

= Infinity inch

t19 = SQRT{T'' x R''}/1000 + CA

0.300 inch

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 = Max(t18 , t19)

treq = 0.300 inch

tprovided = 0.551 inch

As per 5.5.4.3

Allowable Compressive Stress; Sca

Case IV : Thickness At The Top Head Center Against External Pressure

T1' = Rs/2(P+W/At' )

= 0.00 lbf/in

T2' = Rs(P+W/At' ) -T1'

= 0.00 lbf/in

Now As Per 5.10.3.5

T' = Max.{ABS(T1' ) , ABS(T2' )}

0.00 lbf/in

T" = Min.{ABS(T1' ) , ABS(T2' )}

0.00 lbf/in

SimilarlyR' = R2 0.00 inch

R" = R1 0.00 inch

Now,t18 = Sqrt{(T'-0.8 X T") X R'}/1342 + C.ASolving By Equation 18 of API 620

0.252

t19 = SQRT{T'' x R''}/1000 + CA Solving By Equation 19 of API 620

0.252


Step-2

t18 - C.A

R'

t19 - C.A

R''


treq = 0.252 inch

tprovided = 0.551 inch

Provided thickness is O.K

= #DIV/0! < .0067

= #DIV/0! < .0067

= 0.0006 < .0067

As per 5.5.4.3

Allowable Compressive Stress; Sca = 106 x (t - C.A)

R' Sca = #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'' = #DIV/0! lbs/in

T'' = -Rs/2(P+W/At' )

Pext = 2/Rs x T'' - W/At'

#DIV/0! Psi

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


Taking thickness of Ist Shell Course = 0.630 inch

Total weight of shell of different = 26004 lbs

thicknesses.

Total weight of roof = 3163 lbs

Total Weight; W (Roof Pl.+Shell).= 29167 lbs

W/At = 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 equation 11 of 5.10.2.5

= 1,915 lbs/inch

Now As Per 5.10.3.2

If T1 and T2 both are +ve, then

T = Max.(T1 and T2)

= 1,915 lbs/inch


= 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

T2 = Rc x P

Pmax.int = T2/Rc T2=T

= 65.28 psi

Case II : Thickness of 1st shell course Against External Pressure

W = -(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

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

69 lbs/inch

T" = Min.{ABS(T1) , ABS(T2)}

6 lbs/inch

similarly,

R' = Rc = 78.74 inch

R" = Rc = 78.74 inch

Now,

t18 = Sqrt{(T'+0.8 X T") X R'}/1342 + C.A Solving By Equation 18 of API 620

= 0.3087 inch

t19 = SQRT{T'' x R''}/1000 + CA Solving By Equation 19 of API 620

= 0.2732 inch


Step-2

t18 - C.A

R'

t19 - C.A

R''


= 0.3087 inch

As per 5.5.4.3

Allowable Compressive Stress; Sca = 106 x (t - C.A)

R'

Sca = 0 Psi

Back calculating the external pressure limited by the actual provided thickness

= 0.0007 < .0067

= 0.0003 < .0067

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 = Sqrt{(T'+0.8 X T") X R'}/1342 + C.A

{1342 x (tprov.-C.A)}2/R' = T'-0.8 X T"

{1342 x (tprov.-C.A)}2/R' = -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. Internal Pressure With Full of Liquid

Table 1.

Shell

Coures # mm inch mm inch Kgs

1 16 0.630 2450 96.46 3,863

2 14 0.551 2450 96.46 3,380

3 12 0.472 2450 96.46 2,897

4 10 0.394 1650 64.96 1,626

5 0 0.000 0 0.00 -

6 0 0.000 0 0.00 -

Total Weight Of Shell =

Table 2.

Weight of

Roof

Weight of

Shell

Total Weight

W

Total Weight

WHydrotest

W/At

lbs lbs lbs lbs Psi

1 3,163 26,004 29,167 29,167 1.50

2 3,163 17,467 20,630 20,630 1.06

3 3,163 9,997 13,160 13,160 0.68

4 3,163 3,594 6,756 6,756 0.35

5 3,163 - 3,163 3,163 0.16

6 3,163 - 3,163 3,163 0.16

Weights

Shell Coures

#

Thickness Width

Table 3.

Internal

Pressure

Contents

Pressure

head

Water

Pressure

Head

Total

Pressure

PContents

Total

Pressure

PHydrotest

Psi Psi Psi Psi Psi

1 1.015 23.30 12.80 24.31 14.07

2 1.015 16.96 9.32 17.97 10.59

3 1.015 10.61 5.83 11.63 7.10

4 1.015 4.27 2.35 5.29 3.62

5 1.015 0.00 0.00 1.02 1.27

6 1.015 0.00 0.00 1.02 1.27

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.

Pcon.+W/At

internal

Phydro+W/At

HydrotestT1 T1hydro

Psi Psi lbs/inch lbs/inch

1 25.81 15.57 1,016.22 612.92

2 19.03 11.64 749.25 458.46

3 12.30 7.78 484.44 306.16

4 5.63 3.96 221.79 156.01

5 1.18 1.43 46.35 56.34

6 1.18 1.43 46.35 56.34

T2 T2hydro

T{Max.(T1,T2)

}

T{Max.(T1hyd.,

T2hyd.)}

lbs/inch lbs/inch lbs/inch lbs/inch

1 1,914.53 1,107.93 1,914.53 1,107.93

2 1,415.11 833.52 1,415.11 833.52

3 915.69 559.11 915.69 559.11

4 416.27 284.71 416.27 284.71

5 79.92 99.90 79.92 99.90

6 79.92 99.90 79.92 99.90

Now Calculating the required thickness as Per 5.10.3.2

tcalc. thydro tcalc<tprov. thydro<tprov.

Shell Coures

#

Shell Coures

#

Shell Coures

#

Shell Coures

#

inch inch inch inch

1 0.39 0.33 OK OK

2 0.36 0.31 OK OK

3 0.32 0.29 OK OK

4 0.28 0.27 OK OK

5 0.26 0.26 Not OK Not OK

6 0.26 0.26 Not OK Not OK

Now Back Calculating the pressure limited by actual provided thicknesses.

T Pmax. internal Pmax.inter>Pint.

lbs/inch Psi inch

1 5,140 65.28 OK

2 4,069 51.68 OK

3 2,998 38.08 OK

4 1,928 24.48 OK

5 (2,822) (35.84) Not OK

6 (2,822) (35.84) Not OK

CASE 2. External Pressure In Empty Condition

External

Pressure

Weight of

Roof

Weight of

Shell Live Load

Total Weight

W

Psi lbs lbs lbs lbs

1 -0.0725 3,163 26,004 3516.60 -32683.74

2 -0.0725 3,163 17,467 3516.60 -24146.34

3 -0.0725 3,163 9,997 3516.60 -16676.11

4 -0.0725 3,163 3,594 3516.60 -10273.06

5 -0.0725 3,163 - 3516.60 -6679.51

6 -0.0725 3,163 - 3516.60 -6679.51

W/At P+W/At T1 T2

Psi Psi lbs/inch lbs/inch

1 -1.678 -1.750 -69 -5.709

2 -1.240 -1.312 -52 -5.709

3 -0.856 -0.929 -37 -5.709

4 -0.527 -0.600 -24 -5.709

5 -0.343 -0.415 -16 -5.70866142

Shell Coures

#

Shell Coures

#

Shell Coures

#

Shell Coures

#

6 -0.343 -0.415 -16 -5.70866142

T' T'' R' R''

lbs/inch lbs/inch inch inch

1 69 6 79 79

2 52 6 79 79

3 37 6 79 79

4 24 6 79 79

5 16 6 79 79

6 16 6 79 79

t18 t19

t18-

C.A/R'<.0067

t19-

C.A/R'<.0067

inch inch inch inch

1 0.3087 0.2732 0.0007 0.0003

2 0.3016 0.2732 0.0006 0.0003

3 0.2944 0.2732 0.0005 0.0003

4 0.2871 0.2732 0.0004 0.0003

5 0.2822 0.2732 0.0004 0.0003

6 0.2822 0.2732 0.0004 0.0003

tcalc. tcalc<tprov.

inch inch

1 0.3087 OK

2 0.3016 OK

3 0.2944 OK

4 0.2871 OK

5 0.2822 Not OK (3,200)

6 0.2822 Not OK (3,200)

Now Back Calculating the pressure limited by actual provided thicknesses.

Pmax.

ExternalPmax.ext.>Pext.

Psi inch

1 -31.27 OK

2 -19.53 OK

3 -10.53 OK

4 -4.29 OK

5 -14.05 OK

Shell Coures

#

Shell Coures

#

Shell Coures

#

Shell Coures

#

6 -14.05 OK

Compression Area Design As Per API 620

As Per 5.12.4.2

Wh = Width in inch of roof consider to participate in resisting the

circumfrential forces acting on the compression ring region.

Wc = Corresponding Width in inch of shell to be participating.

th = Thickness in inch of roof at and near the juncture of the

roof including corrosion allowance.

tc = Corresponding thickness in inch of shell at and near the

juncture of the roof and shell.

R2 = Length in inch of the normal to the roof at the juncture b/w

the roof and the shell measured from the roof to the tank

vertical axis of of revolution.

Rc = Horizontal radius in inch of the cylinderical shell at its

juncture with the roof of the tank.

T2s = Circumfrential unit force in the shell side wall of the tank

at its juncture with the roof in lbf/in measured along an

element of the cylinder.

a = Angle b/w the direction of T1 and a vertical line .

Q = Total circumfrential force in lbs acting in a vertical cross

section through the corresponding ring region.

AC = Net Area in Inch2 of the vertical cross section of metal

required in the compression ring region exclusive of

of all corrosion allowances.

Now,

Calculating the Wh and Wc based on the acual provided thickess of the

roof and shell.

Wh = 0.6 x {R2 x (th-C.A)}0.5

= 2.91 inch

Wc = 0.6 x {Rc x (tc-C.A)}0.5

= 2.91 inch

Now,

As per 5.12.4.3

Q = T2 X Wh + T2s x Wc - T1 X Rc x Sin a equation 26

Therefore,

T2s = P X R3

79.92125984 lbs/inch

Q = -11807

So, As per 5.12.4.3

AC = Q/15000 equation 27

= 0.79 inch2 507.84 mm2

Aprovided = 2.01 inch2 1295 mm2

Providing the compression Area As per Figure 5-6 of API 620 Detail f

Provided Thickened Plate t 36 mm

Provided thickness and the compression area is sufficient compared with values, achieved, based on API 620.

1.417 inch

Wh = 0.6 x {R2 x (t-C.A)}0.5

= 0.00 inch

Wc = 0.6 x {Rc x (t-C.A)}0.5

= 5.75 inch

Therefore,

Aprov. = Wh x (t-C.A) + Wc x (t-C.A)

= 6.7 inch2

As Aprov.>Areq. Compresssion Ring Is OK

As the required area for compression ring region is extra ordinary high

Therfore we will provide the Curved Knuckle region in order to avoid the

requirement of compression ring region.

Tori Spherical Head Knuckle Calculation (Per ASME Section VIII Division 1 Sec.4)

L = Inside Dish Radius 0 inch

P = Internal Design Pressure 1.015 psi

E = Joint Efficiency 0.7

t = Provided Thickness 0.551 inch

r = Knuckle Radius(12% of diameter 100.8 inch

of shell as per 5.12.3.1)

s = Material Allowable Design Stress 16000 psi

M = 0.25 X {3 + (L/r)0.5}

= 0.75

tcalc = [{P X L X M}/{2 X S x E - 0.2 X P}] + C.A

= 0.252 inch

Now back calculting the internal pressure limited by actual provided thickness.

Pmax. Int = {2 x S x E x (tprov.-C.A)}/{L x M + 0.2 x (tprov.-C.A)}

= 112000.00 psi

5) Bottom Plate Design

Bottom Plate Area = p/4(Bottom OD-2 X Annular Ring Width)2

= 7140 inch2

Annular Plate Area = p/4(Bottom OD)2 - Bottom Plate Area

= 13540 inch2


As per 5.9.4.2

tmin bottom = .25 + C.A

= 0.502 inchtprov bottom = 10 mm

0.394 mmtmin annular = .25 + C.A

0.502 inch

tprov.annular 10 mm

0.3937 inch

Total Weight = Density x (tprov.x Bottom Area + tprov x Annular Area)

= 2307 lbs

= 830 lbs (Corroded)

Vacuum Calculations as Per ASME Section VIII Div.1

Weight of bottom plate resisting = 0.2833 x tprov.bottom.corr.

external vacuum Pbottom = 0.0402 psi

Effective External Pext.eff = Pext + Pbottom

Pressure = -0.0323 psi

As the weigt of bottom plate is greater than the vacuum.

So there is no need to calculate the thickness agianst vacuum.

td ext for 1st shell course = (tcalc. - C.A)

= 0.14 inchtprov ext for 1st shell course = (tprov. - C.A)

0.38 inch

C = 0.33 X td ext./tprov

= 0.12

Therefore,

Thickness required against vacuumtvacuum = OD X ( C X Pext.eff/S X E)0.5 + C.A

= 0.318 inch

tcalc. = Max.(tcalc.,tvac.)

= 0.502 inch

tprov. = 0.394 inch

Now back calculating the maximum external pressure limited by bottom plate

Pmax.ext. = -[{tprov. - C.A}/OD}2 X {S X E/C} + Pbottom]

= -0.1132 psi

6) Design Of Intermediate Wind Girder As Per 5.10.6

H1 = 6 x (100 x t) x (100xt/D)3/2

Where,H1 = Vertical Distance b/w the intermediate wind girder and the top

of the shell or in the case of the formad head the vertical distance

b/w the intermediate wind girder and the head bend line plus

one third the depth of the formed head.

t = The thickness of the top shell course as ordered condition

unless otherwise specified in inch.

D = Nominal tank diameter in ft.

H1 = 1928.97 ft

Now, As per 5.10.6.1.a

Dynamic Pressure Against the wind velocity @ 100mph = 31

Dynamic Pressure due to internal vacuum = 5

Total Dynamic Pressure @ 100mph = 36

Now, As per 5.10.6.1.d

Dynamic Pressure due to vacuum = 10.44

Actual Dynamic Pressure = 41.44

Therefore H1 shell be decreased by the factor = 0.87

Now,

H1 = 1675.7 ft (after multiplying with load factor)

Transformed Shell Thicknesses As Per 5.10.6.2

Wtr = W X (tuniform/ttop)2.5

Where,

tuniform = Thickness Of Top Shell Course as ordered condition in inch.

ttop = Thickness Of Shell Course for which transposed width is

being calculated as ordered condition in inch.

W = Actual course width in ft

Wtr = Transposed course width in ft

1st Shell Course

Thickness Of First Shell Course t1 = 0.630

Transposed Course Width Wtr = 3.92

2nd Shell Course

Thickness Of 2nd Shell Course t2 = 0.551


3rd Shell Course

Thickness Of 3rd Shell Course t3 = 0.472


4th Shell Course

Thickness Of 4th Shell Course t4 = 0.394


5th Shell Course


Transposed Course Width Wtr = #DIV/0!

6th Shell Course


Transposed Course Width Wtr = #DIV/0!

Now,

Transformrd height of shell Htr = 22.83

7) Stability Calculations Against Wind Load Per ASCE-02

Wind Velocity V = 0.0

Height Of Tank including Roof Height Ht = 15.1

= 4.6

Effective Wind Gust Factor qf = 0.85

Force Coefficient Cf = 0.7

Wind Directionality Factor Kd = 0.95

Velocity Pressure Exposure Co-eff Kz = 0.95

Topo Graphic Factor Kzt = 1

Importance Factor I = 1.25

V = 38.89

Design Wind Pressure qz = 0.6013 x Kz x Kzt x Kd x V2 X I/1000

= 1.046

Design Wind Load P1 = qz x D0 x qf x Cf x Ht

= 11.51

Overturning Wind Moment

Mw = P1 X Ht

2

As Htr<H1Intermediate Wind Girder In Not Required

= 26

19530

Resisting Moment

Mr 2 x (Ws' + Wr' - Uplift Due to Internal Pressure)

3 2

Ws' = Total Weight Of Tank Shell 13426 lbs

Wr' = Total Weight Of Tank Roof 1719 lbs

Mr 8555 lbs-ft

Uplift is graeter than shell and roof weight

8) Stability Calculations Against Seismic Load Per API 620 Appendix. L

Ms = Over Turning Moment Due To Siesmic Forces

Ms = Z x I x {C1 x WS x XS + C1 x Wr x Ht + C1 x W1 x X1 + C2 x W2 x X2}

Therefore,

Z = Seismic Zone Factor From Table L-2

= 0.075 For Seismic Zone One

I = Importance Factor

= 1.25

S = Site Amplification Factor From Table L-3

= 1.2C1 = Lateral Earthquake Force Coefficient

= 0.6 As Per L.3.3.1

C2 = Lateral Earthquake Force Coefficient

= 0.75 X S As Per L.3.3.2

Where T

T = Natural Period Of First Sloshing ModeAs Per L.3.3.2

= k x OD0.5

And

k = Factor For D/H Obtained From Figure L-4

So,

D/H = 0.957

Now,

k = 0.607 From Figure L-4

As Mw>Mr Anchorage is Required

T = 2.204

C2 = 0.4083

Now,

From Figures L-2 and L-3

X1/H = 0.375 From Figure L-3

X2/H = 0.585 From Figure L-3

W1/Wt = 0.543 From Figure L-2

W2/Wt = 0.461 From Figure L-2

WhereWt = Weight of tank Contents @ Maximum Liquid Level

= 211,777 lbs

So,X1 = 5.17

X2 = 8.06

W1 = 114,994.96

W2 = 97,629.24

Xs = Height From The Bottom Of Tank Shell To The Shell Centre Of Gravity

= 6.89 ft

Now,

C1 x WS x XS = 107498

C1 x Wr x Ht = 26,150

C1 x W1 x X1 = 356,530

C2 x W2 x X2 = 321,305.66

Ms = 76,077 lbs-ft

8.1) Resistance To Over Turning Per API 620 Appendix. L.4

Assuming No Anchors are provided

WL = 7.9 x tb x (Fby x G x H)0.5

= 2837.1 lbs/ft

Now,

1.25 x G x H x D = 413.5 lbs/ft

AS WL>1.25GHD Therefore WL=1.25GHD

WL = 413.5 lbs/ft

8.2) Shell Compression For Unanchored Tanks Per API 620 Appendix. L.5.1

Ms= 0.39

D2(Wt+WL)

Where,Wt = {Weight of Roof + Weight Of Shell}/p x D

= 704 lbs/ft

As Ms/{D2*(Wt+WL)<0.785 Use b=Wt+ 1.273*Ms/D2

The Maximum Longitudinal Compressive Force at The Bottom Of The Shell

So,

b = Wt + 1.273 x Ms

D2

= 1,260.68 lbs/ft

8.3) Maximum Allowable Shell Compression For Unanchored TanksPer API 620 Appendix. L.5.3

b/12t = Maximum Longitudinal Compressive Stress

= 166.78 psi

Now,

GHD2

t2

So,

GHD2

t2

As GHD2/t2<1000000 Use Fa=(1000000*t/2.5*D)+600*sqrt(GH)

Therefore,

Fa = 1000000 x t + 600 (GH)0.5

2.5 x D

= 22109.2 psi

As b/12t<Fa Shell is Safe In Compression

8.4) Shell Compression For Anchored Tanks Per API 620 Appendix. L.5.2

The Maximum Longitudinal Compressive Force at The Bottom Of The Shell

So,

b = Wt + 1.273 x Ms

D2

= 1,260.68 lbs/ft

8.5) Maximum Allowable Shell Compression For Anchored TanksPer API 620 Appendix. L.5.3

= 10994

= 0.39

< 1.00E+06

b/12t = Maximum Longitudinal Compressive Stress

= 166.78 psi

Now,

GHD2

t2

So,

GHD2

t2

As GHD2/t2<1000000 Use Fa=(1000000*t/2.5*D)+600*sqrt(GH)

Therefore,

Fa = 1000000 x t + 600 (GH)0.5

2.5 x D

= 22109.2 psi

As b/12t<Fa Shell is Safe In Compression

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

P = Design Pressure in inch of water Column 28.0952

Pt = Test Pressure in inch of water column 35.119

th = Roof Plate thickness in inches 0.551

Mw = Wind Moment in ft-lbs 19530

Ms = Seismic Moment in ft-lbs 76,077

W1 = Dead Load Of shell minus any corrosion allowance and16,426

any dead load other than roof plate acting on the shell

minus any corrosion allowance in lbs

W2 = Dead Load Of shell minus any corrosion allowance and18,145

any dead load including roof plate acting on the shell

minus any corrosion allowance in lbs

W3 = Dead Load Of shell using as built thicknesses and29004

any dead load other than roof plate acting on the shell

< 1.00E+06

= 11486

using as built thicknesses in lbs

Note = The Allowable Tension Stresses are Taken From Table 5-7

of API 620

Material = A36

Fy = 36000 psi From Table 1 of B55-E01

UPLIFT LOAD CASES NET UPLIFT FORMULA, U

(lbf)

((P - 8th) x D2 x 4.08) - W1 217

((Pt - 8th) x D2 x4.08) - W1 5153

(4 x Mw / D) - W2 -12192.06

(4 x Ms / D) - W2 5043.39

((P - 8th) x D2 x 4.08) + (4 x Mw / D) - W1 6170

((P - 8th) x D2 x 4.08) + (4 x Ms / D) - W1 23405

UPLIFT LOAD CASES

Design Pressure 0.16

2.92

-4.88

2.02

3.49

13.25

No Of Anchor Bolt Provided N 56

Max. Required Bolt Area Areq. 0.02054 inch2

Bolt Area Provided Aprov. 3.25 inch2(Providing 2.25" anchor bolt area by considering

the corrosion allowance of 1/4"on the dia)

Dia Of Anchor Bolt d 2.5 inch

Bolt Circle Dia 20240 mm

Bolt Spacing 1135 mm

Value of Area is obtained from Table II of B55-E01

As Aprov.>Areq. Anchor Bolt Is Safe.

Design Pressure + Seismic 0.02054

Wind Load -0.00756

Seismic Load 0.00313

Design Pressure + Wind 0.00541

Test Pressure 0.00452

Wind Load 28800

Seismic Load 28800

Design Pressure + Wind 20349

Design Pressure + Seismic 20349

Reqd. Bolt Area

Ar = tb/Fall (in2)

Reqd. Bolt

Area

0.00025

Fall For Anchor Bolts

(PSI)

Design Pressure 15300

Test Pressure 20349

10) Anchor Chair Calculations

As Per AISI E-1, Volume II Part VII

Top Plate Thickness C = [P(0.375g-0.22d)/Sf]0.5

Critical Stress b/w the hole and S = 21 ksi

and the free edge of plate

Distance from outside of the f = 2.67 inch

top plate to edge of the hole

Distance b/w gussett plates g = 3.93 inch

Anchor Bolt Diameter d = 2.5 inch

Design Load Or Maximum P = 1 kips

Allowable load or 1.5 times the

actual bolt load whichever is lesser

So,

Top Plate Thickness C = 0.10 inch

2.58 mm

Actual Used Plate Thickness C = 30 mm

Anchor Chair Height Calculations

Sinduced = Pe[{1.32*Z/(1.43*a*h2/Rt)+(4ah

2)

0.333}+{0.031/(Rt)

0.5}]

t2

Reduction Factor Z = 1/[{0.177am(m/t)2/(Rt)

0.5}+1]

Thickness Provided Is OK

Top Plate Width a = 13.77 inch

Anchor Chair Height h = 22 inch

Nominal Shell Radius R = 79 inch

Shell Thickness Corroded t = 0.378 inch

Bottom Plate Thickness Corr. m = 0.142 inch

Anchor Bolt Accentricity e = 4.01 inch

Allowable Stress Sallowable = 25 ksi

So,

Z = 0.991

Sinduced = 0.17 ksi

Gussett Plate Thickness Calculations

Gussett Plate Thickness Jmin = 0.04(h-C)

= 0.83 inch

= 21.152 mm

Actual Gussett Plate Thickness J = 30

Gussett Plate Thickness Is Adequate

Now

J x K P/25 =

J = 1.181 in

Average Width of Gussett = K = 5.118 in

J x K = 6.045

P/25 = 0.0251

OK

11) Foundation Loading Data

The Self weight of roof and live load will be transferred to shell

Live load transferred to foundation

Live Load on roof = 25 psf

Area Of Roof Ar = 20256 inch2

Total Live Load = 3517 lbs

Circimference of tank C = 41 ft

Live Load Transferred LL = 85 lbs/ft

to foundation

Dead load transferred to foundation

Self Weight Of Shell Ws = 26004 lbs

Self Weight Of Shell Wr = 3163 lbs

Self Weight Of Bottom Wb = 2307 lbs

including annular plate

Weight of accessories Wa = 3000 lbs

Toatal Dead Load WD = 32167 lbs

Acting On Shell

Dead Load Transferred DL = 778 lbs/ft

to foundation

Operating & Hydrostatic Test Loads

Self weight of tank = 34474 lbs

Weight of contents in = 211777 lbs

operating condition

Weight Of Water = 249,345 lbs

in hydrotest condition

Uniform Load In Self Wt + Fluid=Wo= 36039 lbs/ft2

operating condition

Uniform Load In Self Wt+Water=Wh= 283,819 lbs/ft2

test condition

Wind Load Transferred to Foundation

Base Shear Due to Fw = 2588 lbs

wind load

Reaction Due To Rw = 36 lbs/ft

Wind Load

Moment Due to Mw = 19530 lbs-ft

wind load

Seismic Load Transferred to Foundation

Base Shear Due to Fs = 10083 lbs

Seismic load

Reaction Due To Rs = 140 lbs/ft

Seismic Load

Moment Due to Ms = 76,077 lbs-ft

Seismic load

Summary of Foundation Loading Data

Dead Load DL 778 lbs/ft

Live Load LL 85 lbs/ft

Uniform Load Operating Condition WO 36039 lbs/ft2

uniform Load Test Condition Wh 283,819 lbs/ft2

Base Shear Due TO wind Load Fw 2588 lbs

Reaction Due To Wind Load Rw 36 lbs/ft

Moment Due To Wind Load Mw 19530 lbs-ft

Base Shear Due TO Seismic Load Fs 10083 lbs

Reaction Due To Seismic Load Rs 140 lbs/ft

Moment Due To Seismic Load Ms 76,077 lbs-ft

Total pressure in lbs/ft2 acting at a given level of the tank under the

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

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

Meridional unit force in lbs/inch of latitudinal arc, in the wall of the tank

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)

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

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

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

Cross section area in in2 of the side walls, roof or bottom of the tank

Thickness in inch of the side walls, roof or bottom of the tank

Maximum allowable stress for simple tension in lbs/in2 as given in

Allowable compresive stress in lbs/in2 established as prescribed

Kg/m3

lbs/ft3

Kg/m3

lbs/ft3

Mpa

psiOC

psi

psf

psi

mm

ft

API 620 10TH Ed. ADD.01

mm

ft

Mpa

psi

mm

inch

mm

inch

mm

inch

mm

ft

mm

ft

mm

ft

inch

mm

ft

lbs

lbs

mph

psi0

( 0.8D TO 1.2D)

B

in2

ft2

lbf

lbf

in2

ft2

(force acting in downward direction)

Equation 8 of 5.10.2.5


Psi



Psi

#DIV/0!

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

for this purpose, by considering the roof segment of 700mm diamter which is equivelant to 0.4 meter squre

Internal Pressure + Pressure due to liquid head

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

lbs Kgs

8,537 2,318

7,470 1,835

6,403 1,352

3,594 585

- -

- -

26,004 corroded weight

Weight of

Contents

lbs

453,808

330,271

206,735

83,198

-

-

Weights Weights corroded

211,777

Total Weight

WHydrotest

lbs

278,512

202,098

126,750

52,470

3,163

3,163

T1

lbs/inch

1,933.49

1,416.82

902.31

389.96

-

-

T{Max.(T1,T2)

}

lbs/inch

1,933.49

1,416.82

915.69

416.27

-

-

by using eq.18

[1342(tprov-C.A)]2/Rc

3267

2048

1112

459

1452

1452

Width in inch of roof consider to participate in resisting the

circumfrential forces acting on the compression ring region.

Length in inch of the normal to the roof at the juncture b/w

Provided thickness and the compression area is sufficient compared with values, achieved, based on API 620.

Density x (tprov.x Bottom Area + tprov x Annular Area)

OD X ( C X Pext.eff/S X E)0.5 + C.A

-[{tprov. - C.A}/OD}2 X {S X E/C} + Pbottom]

Vertical Distance b/w the intermediate wind girder and the top

of the shell or in the case of the formad head the vertical distance

b/w the intermediate wind girder and the head bend line plus

The thickness of the top shell course as ordered condition

psf

psf

psf

psf

psf

(after multiplying with load factor)

Thickness Of Top Shell Course as ordered condition in inch.

Thickness Of Shell Course for which transposed width is

being calculated as ordered condition in inch.

inch

ft

inch

ft

inch

ft

inch

ft

inch

ft

inch

ft

ft

km/hr

ft

m

m/sec

0.6013 x Kz x Kzt x Kd x V2 X I/1000

KN/m2

qz x D0 x qf x Cf x Ht

KN-m

lbs-ft

2 x (Ws' + Wr' - Uplift Due to Internal Pressure)

(Corroded)

(Corroded)

Uplift is graeter than shell and roof weight

Z x I x {C1 x WS x XS + C1 x Wr x Ht + C1 x W1 x X1 + C2 x W2 x X2}

Height From The Bottom Of Tank Shell To The Shell Centre Of Gravity

Per API 620 Appendix. L.5.1

inch of H2O

inch of H2O

inch

ft-lbs

ft-lbs

lbs

lbs

lbs

3.88

92.01

-217.72

90.06

110.18

417.95

(Providing 2.25" anchor bolt area by considering

the corrosion allowance of 1/4"on the dia)

28800

28800

20349

20349

Fall For Anchor Bolts

(PSI)

tb = U / N

Load /

15300

20349

Pe[{1.32*Z/(1.43*a*h2/Rt)+(4ah

2)

0.333}+{0.031/(Rt)

0.5}]

1/[{0.177am(m/t)2/(Rt)

0.5}+1]

11 KN/m

1 KN/m

1726 KN/m2

13,589 KN/m2

12 KN

1 KN/m

26 KN-m

45 KN

2 KN/m

103 KN-m

lbs

5,110

4,045

2,981

1,290

-

-

13,426

Weight of

Water

Total Weight

W

lbs lbs

249,345 482,975 705896.6275

181,468 350,901

113,591 219,894

45,713 89,955

- 3,163

- 3,163

Weights corroded

W/At W/Athydro

Pcon.+W/At

internal

Phydro+W/At

Hydrotest

Psi Psi Psi Psi

24.80 14.30 49.11 28.37

18.02 10.38 35.99 20.96

11.29 6.51 22.92 13.61

4.62 2.69 9.90 6.31

0.16 0.16 1.18 1.43

0.16 0.16 1.18 1.43

T1hydro T2 T2hydro

lbs/inch lbs/inch lbs/inch

1,116.91 1,914.53 1,107.93

825.25 1,415.11 833.52

535.75 915.69 559.11

248.41 416.27 284.71

- - -

- - -

T{Max.(T1hyd.,

T2hyd.)}tcalc. thydro tcalc<tprov. thydro<tprov.

lbs/inch inch inch inch inch

1,116.91 0.17 0.35 OK OK

833.52 0.13 0.33 OK OK

559.11 0.08 0.30 OK OK

284.71 0.04 0.28 OK OK

- - 0.25 Not OK Not OK

- - 0.25 Not OK Not OK

by using eq.18

[1342(tprov-C.A)]2/Rc-Rc/2+W/AtRc/2+W/At Rc/2 0.8*Rc (Rc/2+0.8*Rc) P

3201.20 66.1 -39.3700787 -62.992126 -102.362205 -31.27

1998.90 48.8 -39.3700787 -62.992126 -102.362205 -19.53

1078.07 33.7 -39.3700787 -62.992126 -102.362205 -10.53

438.69 20.8 -39.3700787 -62.992126 -102.362205 -4.29

1438.61 13.5 -39.3700787 -62.992126 -102.362205 -14.05

1438.61 13.5 -39.3700787 -62.992126 -102.362205 -14.05

calculation api 650

Documents

tank wall

given level

level underconsideration

liquid weight

gas weight

total weight

total pressure

tankunder consideration