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)

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 in

2

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/in 2

as given in table 5-1

Sca = Allowable compresive stress in lbs/in

2 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 .

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

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 5.10.3.2

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

T = (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

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

= -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 Solving By Equation 18 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 Similarly R' = 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 Now; As per 5.10.3.5.b Step-2 t18 - C.A R' t19 - C.A R'' treq = Max(t18 , t19) treq = 0.252 inch tprovided = 0.551 inch

Provided thickness is O.K

= #DIV/0! < .0067

= #DIV/0! < .0067

As per 5.5.4.3

Allowable Compressive Stress; Sca = 10 6

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

Joint Efficiency E = 0.85

Taking thickness of Ist Shell Course = 0.630 inch

Total weight of shell of different = 26004 lbs thicknesses.

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

tcalc. = 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

T2 = Rc x P

Pmax.int = T2/Rc T2=T

= 65.28 psi

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 Now; As per 5.10.3.5.b Step-2 t18 - C.A R' t19 - C.A R'' treq = Max(t18 , t19) = 0.3087 inch As per 5.5.4.3

Allowable Compressive Stress; Sca = 10 6

x (t - C.A) R'

Sca = 0 Psi

Back calculating the external pressure limited by the actual provided thickness = 0.0007 < .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

Hydrotest T1 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.

External Pmax.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

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

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

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

Joint Efficiency E = 0.7

As per 5.9.4.2

tmin bottom = .25 + C.A

= 0.502 inch

tprov bottom = 10 mm

0.394 mm

tmin 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 inch

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

0.38 inch

C = 0.33 X td ext./tprov

= 0.12 Therefore,

Thickness required against vacuum

tvacuum = OD X ( C X Pext.eff/S X E)

0.5

= 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

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

Transposed Course Width Wtr = 5.47

3rd Shell Course

Thickness Of 3rd Shell Course t3 = 0.472

Transposed Course Width Wtr = 8.04

4th Shell Course

Thickness Of 4th Shell Course t4 = 0.394

Transposed Course Width Wtr = 5.41

5th Shell Course

Thickness Of 5th Shell Course t5 = 0.000

6th Shell Course

Thickness Of 6th Shell Course t6 = 0.000

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 V

2

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

= 1.2

C1 = 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

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

Where

Wt = 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

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 Tanks

Per 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 Tanks

Per API 620 Appendix. L.5.3

= 10994

= 0.39

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 and 16,426

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 and 18,145

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

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 - 8t

_h

) x D

2

x 4.08) - W

₁

₂₁₇

((P

_t

- 8t

_h

) x D

2

x4.08) - W

₁

5153

(4 x M

_w

/ D) - W

₂

-12192.06

(4 x Ms / D) - W

₂

_5043.39

((P - 8t

_h

) x D

2

x 4.08) + (4 x M

_w

6170

/ D) - W

₁

((P - 8t

_h

) x D

2

x 4.08) + (4 x Ms / D) - W

23405

₁

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 inch

2

Bolt Area Provided Aprov. 3.25 inch

2

(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

A

_r

= t

_b

/F

_all

(in

2

)

Reqd. Bolt

Area

0.00025

F

all

For Anchor Bolts

(PSI)

Design Pressure

15300

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*h

2

/Rt)+(4ah2)0.333}+{0.031/(Rt)0.5}] t2

Reduction Factor Z =

1/[{0.177am(m/t)

2

/(Rt)

0.5

}+1]

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 on roof

= 25 psf

Area Of Roof Ar = 20256 inch

2

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=W= o 36039 lbs/ft

2

operating condition

Uniform Load In Self Wt+Water=W= h 283,819 lbs/ft 2

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/ft

2

uniform Load Test Condition Wh 283,819 lbs/ft

2

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

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 psi O C 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 psi 0 ( 0.8D TO 1.2D) B

in2 ft2 lbf lbf in2 ft2

(force acting in downward direction)

Equation 8 of 5.10.2.5

Equation 8 of 5.10.2.5

Equation 9 of 5.10.2.5

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

Psi

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

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

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

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

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.

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

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

-[{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 V 2 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

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

Per API 620 Appendix. L.5.3

Per API 620 Appendix. L.5.2

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

F

all

For Anchor Bolts

(PSI)

t

b

= U / N

Load /

15300

Pe[{1.32*Z/(1.43*a*h2/Rt)+(4ah2)0.333}+{0.031/(Rt)0.5}]

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/At Rc/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