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 + P g

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/ft 2) 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. R 1 is to be considered negative
when it is on the side of the tank wall opposite from R 2 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/in 2 as given in

table 5-1

Sca = Allowable compresive stress in lbs/in2 established as prescribed

in 5.5.4

Design Data :

Desig Code API 620 10TH Ed. ADD.01

Client's Specs

Fluid Sulphuric Acid

Material A36
Design Density of Contents = 0.8
= 0.050
Density of water for hydrotest 1000
= 62.43
Specific Gravity Of Contents 0.0008
Material Yield Strength = 248.21
= 36000
Design Temperature 100
Internal Pressure = 2.5
360
Extrenal Pressure = 0
Liquid Level = 1000
= 3.28
Design Liquid Level = 10000
= 33
Allowable Tensile Stress At Design Temperature = 110.32
16000
Corrosion Allowance
Shell 3
0.11811
Bottom 3
0.11811
Roof 0
0.00000

Inside Dia Of Tank D = 14500

47.57
Nominal Dia Of Tank Dn = 14510
47.60
Outside Dia of tank D0 = 14520
47.64
571.65
Height Of Shell = 10000
33
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 = 8 mm
= 0.315 inch
Joint Efficiency E = 0.7

Radius Of Dome rr = 1xD

= 47.57 ft

Height Of Cone Roof h = 4.75 ft

One Half The included apex angle a = 78.7
of the Conical roof or bottom
.
Radius Of Cone L = 24.26 ft
Angle b/w the normal to roof q = 11.30
and a vertical line at the roof to shell juncture

Roof Area At' = 266172

= 1848
Roof Weight W (Uncorroded)
= Density x t x Roof Area
23750
Roof Weight W (corroded)= 23775

Cross sectional Area At = 255952

at roof to shell junction = 1777

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 = 23.786 ft
= 285.43 inch

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

W/At = -0.093 psi

W/At' = -0.089 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

= 1753 lbf/in

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

3642 lbf/in
Now As Per 5.10.3.2
If T1 and T2 both are +ve, then

T = Max.(T1 and T2)

 3642 lbf/in

tcalc. = T/(Sts.E) + C.A

= 0.325 inch

Provided thickness is less than Required

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

0.000 inch

As these thicknesses are calculated based on the internal pressure of

= 2.5 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

= 3528 lbf/in
Now putting this value of T in the equation of T 2, 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. 3.125 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

= -65508 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

= -186.4 lbf/in

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

0.0 lbf/in
Now As Per 5.10.3.5

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

= 186.4 lbf/in

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

0.0 lbf/in
Similarly,
R' = Infinity
R" = 285.43 inch
Now,
t18 = Sqrt{(T'+0.8 X T") X R'}/1342 Solving By Equation 18 of API 620
= Infinity inch

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

0.000 inch
Now; As per 5.10.3.5.b
Step-2

t18 - C.A
= Infinity < .0067
R'

t19 - C.A
= 0.0000 < .0067
R''

treq = Max(t18 , t19)

treq = 0.000 inch
tprovided = 0.315 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' = 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 +Solving By Equation 18 of API 620
0.000
t19 = SQRT{T'' x R''}/1000 + CA Solving By Equation 19 of API 620
0.000
Now; As per 5.10.3.5.b
Step-2
 t18 - C.A
= #DIV/0! < .0067
R'

t19 - C.A
= #DIV/0! < .0067
R''

treq = Max(t18 , t19)

treq = 0.000 inch

tprovided = 0.315 inch

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 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 #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 = 0.6

Taking thickness of Ist Shell Course = 0.315 inch

Total weight of shell of different = 50430 lbs
thicknesses.
Total weight of roof = 23750 lbs
Total Weight; W (Roof Pl.+Shell)= 74180 lbs
W/At = 0.29 psi
Now Total Pressure
Internal Pressure + Pressure due to liquid head
= 2.51 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

= 400 lbs/inch

T2 = Rc x P equation 11 of 5.10.2.5
= 717 lbs/inch
Now As Per 5.10.3.2
If T1 and T2 both are +ve, then
T = Max.(T1 and T2)
= 717 lbs/inch

tcalc. = T/(Sts.E) + C.A

= 0.19 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
= 2.51 psi
Back calculating the internal pressure limited by the actual provided thickness
tprov. = T/(Sts.E) + C.A
 T = 3,024 lbs/inch

Now putting this value of T in the equation of T 2, where we find the

maximum calculated thickness

T2 = Rc x P

Pmax.int = T2/Rc T2=T

= 10.59 psi

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

W = -(Weight Of Roof Plates + Weight Of shell + Live Load)

= -120390 lbs
Pext. = 0 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

-67 lbs/inch

T2 = Rc x P equation 11 of 5.10.2.5
0.00 lbs/inch
Now As Per 5.10.3.5

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

67 lbs/inch
T" = Min.{ABS(T1) , ABS(T2)}
- lbs/inch
similarly,
R' = Rc = 285.43 inch
R" = Rc = 285.43 inch
Now,

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

= 0.2213 inch
t19 = SQRT{T'' x R''}/1000 + CA Solving By Equation 19 of API 620
= 0.1181 inch
Now; As per 5.10.3.5.b
Step-2
t18 - C.A
= 0.0004 < .0067
R'

t19 - C.A
= - < .0067
R''

treq = Max(t18 , t19)

= 0.2213 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
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. = -0.48 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 Thickness Width Weights

Coures # mm inch mm inch Kgs
1 8 0.315 2000 78.74 5,716
2 6 0.236 2000 78.74 4,287
3 6 0.236 2000 78.74 4,287
4 6 0.236 2000 78.74 4,287
5 6 0.236 2000 78.74 4,287
 6 0 0.000 0 0.00 -
Total Weight Of Shell =

Table 2.

Weight of Weight of Total Weight Total Weight

Shell Coures W/At
Roof Shell W WHydrotest
#
lbs lbs lbs lbs Psi
1 23,750 50,430 74,180 74,180 0.29
2 23,750 37,821 61,571 61,571 0.24
3 23,750 28,364 52,114 52,114 0.20
4 23,750 18,907 42,657 42,657 0.17
5 23,750 9,450 33,200 33,200 0.13
6 23,750 - 23,750 23,750 0.09

Table 3.

Contents Water Total Total

Internal
Shell Coures Pressure Pressure Pressure Pressure
Pressure
# head Head PContents PHydrotest
Psi Psi Psi Psi Psi
1 2.5 0.01 14.22 2.51 17.35
2 2.5 0.01 11.38 2.51 14.50
3 2.5 0.01 8.53 2.51 11.66
4 2.5 0.00 5.69 2.50 8.81
5 2.5 0.00 2.84 2.50 5.97
6 2.5 0.00 0.00 2.50 3.13

As Per 7.18.3.2 Internal Presssure for Hydrotest is 1.25 * P int

Now Calculating Meridianal and Latitudinal Forces aginst pressure and

During Hydrotest Condition.

Pcon.+W/At Phydro+W/At
Shell Coures T1 T1hydro
internal Hydrotest
#
Psi Psi lbs/inch lbs/inch
1 2.80 17.64 399.78 2,517.41
2 2.75 14.75 392.42 2,104.37
3 2.71 11.86 386.82 1,693.08
4 2.67 8.98 381.23 1,281.80
 5 2.63 6.10 375.63 870.51
6 2.59 3.22 370.03 459.23

T{Max. T{Max.
Shell Coures T2 T2hydro
(T1,T2)} (T1hyd.,T2hyd.)}
#
lbs/inch lbs/inch lbs/inch lbs/inch
1 716.83 4,952.10 716.83 4,952.10
2 716.18 4,140.07 716.18 4,140.07
3 715.53 3,328.05 715.53 3,328.05
4 714.88 2,516.03 714.88 2,516.03
5 714.23 1,704.00 714.23 1,704.00
6 713.58 891.98 713.58 891.98

Now Calculating the required thickness as Per 5.10.3.2

Shell Coures tcalc. thydro tcalc<tprov. thydro<tprov.

# inch inch inch inch
1 0.19 0.63 OK Not OK
2 0.19 0.55 OK Not OK
3 0.19 0.46 OK Not OK
4 0.19 0.38 OK Not OK
5 0.18 0.27 OK Not OK
6 0.18 0.20 Not OK Not OK

Now Back Calculating the pressure limited by actual provided thicknesses.

Shell Coures T Pmax. internal Pmax.inter>Pint.

#
lbs/inch Psi inch
1 3,024 10.59 Not OK
2 2,268 7.94 Not OK
3 2,268 7.94 Not OK
4 2,268 7.94 Not OK
5 2,646 9.27 OK
6 - - Not OK

CASE 2. External Pressure In Empty Condition

 External Weight of Weight of Total Weight
Shell Coures Pressure Roof Shell W
# Live Load
Psi lbs lbs lbs lbs
1 0 23,750 50,430 46210.34 -120390.12
2 0 23,750 37,821 46210.34 -107781.06
3 0 23,750 28,364 46210.34 -98324.26
4 0 23,750 18,907 46210.34 -88867.47
5 0 23,750 9,450 46210.34 -79410.67
6 0 23,750 - 46210.34 -69960.40

Shell Coures W/At P+W/At T1 T2

# Psi Psi lbs/inch lbs/inch
1 -0.470 -0.470 -67 0.000
2 -0.421 -0.421 -60 0.000
3 -0.384 -0.384 -55 0.000
4 -0.347 -0.347 -50 0.000
5 -0.310 -0.310 -44 0
6 -0.273 -0.273 -39 0

Shell Coures T' T'' R' R''

# lbs/inch lbs/inch inch inch
1 67 - 285 285
2 60 - 285 285
3 55 - 285 285
4 50 - 285 285
5 44 - 285 285
6 39 - 285 285

t18-C.A/ t19-C.A/
Shell Coures t18 t19
R'<.0067 R'<.0067
#
inch inch inch inch
1 0.2213 0.1181 0.0004 -
2 0.2157 0.1181 0.0003 -
3 0.2113 0.1181 0.0003 -
4 0.2067 0.1181 0.0003 -
5 0.2019 0.1181 0.0003 -
6 0.1967 0.1181 0.0003 -
Shell Coures tcalc. tcalc<tprov.
# inch inch
1 0.2213 OK
2 0.2157 OK
3 0.2113 OK
4 0.2067 OK
5 0.2019 OK 414
6 0.1967 Not OK (414)

Now Back Calculating the pressure limited by actual provided thicknesses.

Pmax.
Shell Coures Pmax.ext.>Pext.
External
#
Psi inch
1 -0.48 OK
2 -0.08 NOT OK
3 -0.09 NOT OK
4 -0.10 NOT OK
5 -0.12 NOT OK
6 -0.13 NOT 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

= 7.52 inch

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

= 6.67 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
713.5826772 lbs/inch

Q = -458581

So, As per 5.12.4.3

AC = Q/15000 equation 27
= 30.57 inch2 19723.89 mm2
 Aprovided = 2.01 inch2 1295 mm2
Provided thickness and the compression area is sufficient compared with values, achieved, based on API 620.

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

= 11.55 inch

Therefore,

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

= 15.0 inch2

As Aprov.<Areq. Compression Ring Is Not 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 2.5 psi

E = Joint Efficiency 0.7

t = Provided Thickness 0.315 inch

r = Knuckle Radius(12% of diamet 100.8 inch

of shell as per 5.12.3.1)
s = Material Allowable Design St 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

= 0.000 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

= 203269 inch2

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

= 56994 inch2
Joint Efficiency E = 0.7
As per 5.9.4.2
tmin bottom = .25 + C.A
= 0.368 inch
tprov bottom = 10 mm
0.394 mm
tmin annular = .25 + C.A
 0.368 inch
tprov.annular 10 mm
0.3937 inch
Total Weight = Density x (tprov.x Bottom Area + tprov x Annular Area)
= 29029 lbs
= 20320 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 = 0.0781 psi

Effective External Pext.eff = Pext + Pbottom

Pressure = 0.0781 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)

= 0.07 inch
tprov ext for 1st shell course = (tprov. - C.A)
0.20 inch
C = 0.33 X td ext./tprov
= 0.13
Therefore,
Thickness required against vacuum
tvacuum = OD X ( C X Pext.eff/S X E)0.5 + C.A
= 0.492 inch

tcalc. = Max.(tcalc.,tvac.)
= 0.492 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]

= -0.0989 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 = 49.54 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 = 0

Actual Dynamic Pressure = 31

Therefore H1 shell be decreased by the factor = 1.16

Now,
H1 = 57.5 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 = 0.315

Transposed Course Width Wtr = 3.20

2nd Shell Course

Thickness Of 2nd Shell Course t2 = 0.236

Transposed Course Width Wtr = 6.56

3rd Shell Course

Thickness Of 3rd Shell Course t3 = 0.236

Transposed Course Width Wtr = 6.56

4th Shell Course

Thickness Of 4th Shell Course t4 = 0.236

Transposed Course Width Wtr = 6.56

5th Shell Course

Thickness Of 5th Shell Course t5 = 0.236

Transposed Course Width Wtr = 0.00

6th Shell Course

Thickness Of 6th Shell Course t6 = 0.000

Transposed Course Width Wtr = #DIV/0!

Now,
Transformrd height of shell Htr = 22.88

As Htr<H1Intermediate Wind Girder In Not Required

7) Stability Calculations Against Wind Load Per ASCE-02

Wind Velocity V = 0.0

Height Of Tank including Roof Height Ht = 37.6

= 11.5

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 = q z x D 0 x q f x Cf x H t

= 103.48

Overturning Wind Moment

Mw = P1 X H t
2

= 592

437021

Resisting Moment
Mr 2 x (Ws' + Wr' - Uplift Due to Internal Pressure)
3 2

Ws' = Total Weight Of Tank Shell 26776 lbs

Wr' = Total Weight Of Tank Roof 23775 lbs

 Mr -162742 lbs-ft
Uplift is graeter than shell and roof weight

As Mw>Mr Anchorage is Required

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 Slosh As Per L.3.3.2
= k x OD0.5
And
k = Factor For D/H Obtained From Figure L-4
So,
D/H = 1.452
Now,
k = 0.607 From Figure L-4

T = 4.190

C2 = 0.2148

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
= 291 lbs
So,
X1 = 12.30
X2 = 19.19
W1 = 158.15
W2 = 134.27
Xs = Height From The Bottom Of Tank Shell To The Shell Centre Of Gravity
= 16.40 ft
Now,

C1 x W S x XS = 496356
C1 x W r x H t = 467,521
C 1 x W 1 x X1 = 1,167
C 2 x W 2 x X2 = 553.58

Ms = 90,525 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

= 47.8 lbs/ft
Now,

1.25 x G x H x D = 1.6 lbs/ft

AS WL>1.25GHD Therefore WL=1.25GHD

WL = 1.6 lbs/ft

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

Ms
= 0.08
D (Wt+WL)
2

Where,
Wt = {Weight of Roof + Weight Of Shell}/p x D
= 496 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
= 546.44 lbs/ft

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

b/12t = Maximum Longitudinal Compressive Stress

= 144.58 psi

Now,
GHD2
< 1.00E+06
t2

So,
GHD2
= 600
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
= 2741.8 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
= 546.44 lbs/ft
8.5) Maximum Allowable Shell Compression For Anchored TaPer API 620 Appendix. L.5.3

b/12t = Maximum Longitudinal Compressive Stress

= 144.58 psi

Now,
GHD2
< 1.00E+06
t2

So,
GHD2
= 414
 = 414
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
= 2741.8 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 69.2

Pt = Test Pressure in inch of water column 86.5

th = Roof Plate thickness in inches 0.315

Mw = Wind Moment in ft-lbs 437021

Ms = Seismic Moment in ft-lbs 90,525

W1 = Dead Load Of shell minus any corrosion all 29,776

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 all 53,551

any dead load including roof plate acting on the shell
minus any corrosion allowance in lbs

W3 = Dead Load Of shell using as built thicknesse 53430

any dead load other than roof plate acting on the shell
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 F Fall For Anchor Bolts
(lbf) (PSI)
Design Pressure ((P - 8th) x D2 x 4.08) - W1 585917 15300
Test Pressure ((Pt - 8th) x D2 x4.08) - W1 745656 20349
Wind Load (4 x Mw / D) - W2 -16805.06 28800
Seismic Load (4 x Ms / D) - W2 -45939.42 28800
Design Pressure + Wind ((P - 8th) x D2 x 4.08) + (4 x M622663
w / D) - W1 20349
Design Pressure + Seismic ((P - 8th) x D2 x 4.08) + (4 x Ms
593528
/ D) - W1 20349

UPLIFT LOAD CASES Reqd. Bolt Area Reqd. Bolt

Ar = tb/Fall (in ) Area
2

Design Pressure 0.68384 441.19

Test Pressure 0.65435 422.16
Wind Load -0.01042 -6.72
Seismic Load -0.02848 -18.38
Design Pressure + Wind 0.54641 352.52
Design Pressure + Seismic 0.52085 336.03

No Of Anchor Bolt Provided N 56

Max. Required Bolt Area Areq. 0.68384 inch2

Bolt Area Provided Aprov. 3.25 inch2 (Providing 2.25" anchor bolt area by co
the corrosion allowance of 1/4"on the
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.

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 = 20 kips

Allowable load or 1.5 times the
actual bolt load whichever is lesser

So,
Top Plate Thickness C = 0.57 inch
14.57 mm
Actual Used Plate Thickness C = 30 mm

Thickness Provided Is OK

Anchor Chair Height Calculations

Sinduced = Pe[{1.32*Z/(1.43*a*h2/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 = 286 inch

Shell Thickness Corroded t = 0.197 inch

Bottom Plate Thickness Corr. m = 0.276 inch

Anchor Bolt Accentricity e = 4.01 inch

Allowable Stress Sallowable = 25 ksi

So,
Z = 0.851

Sinduced = 20.19 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
JxK ³ P/25 =
J = 1.181 in
Average Width of Gussett = K = 5.118 in

JxK = 6.045
P/25 = 0.7989
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 = 266172 inch2

 Total Live Load = 46210 lbs

Circimference of tank C = 150 ft

Live Load Transferred LL = 309 lbs/ft

to foundation

Dead load transferred to foundation

Self Weight Of Shell Ws = 50430 lbs

Self Weight Of Shell Wr = 23750 lbs

Self Weight Of Bottom Wb = 29029 lbs

including annular plate

Weight of accessories Wa = 3000 lbs

Toatal Dead Load WD = 77180 lbs

Acting On Shell

Dead Load Transferred DL = 516 lbs/ft

to foundation

Operating & Hydrostatic Test Loads

Self weight of tank = 106208 lbs

Weight of contents in = 291 lbs

operating condition

Weight Of Water = 3,640,611 lbs

in hydrotest condition

Uniform Load In Self Wt + Fluid=W

= o 106208 lbs/ft2
operating condition

Uniform Load In Self Wt+Water=W

= h 3,746,820 lbs/ft2
test condition

Wind Load Transferred to Foundation

 Base Shear Due to Fw = 23270 lbs
wind load

Reaction Due To Rw = 61 lbs/ft

Wind Load

Moment Due to Mw = 437021 lbs-ft

wind load

Seismic Load Transferred to Foundation

Base Shear Due to Fs = 4820 lbs

Seismic load

Reaction Due To Rs = 13 lbs/ft

Seismic Load

Moment Due to Ms = 90,525 lbs-ft

Seismic load

Summary of Foundation Loading Data

Dead Load DL 516 lbs/ft

Live Load LL 309 lbs/ft
Uniform Load Operating Condition WO 106208 lbs/ft2
uniform Load Test Condition Wh 3,746,820 lbs/ft2
Base Shear Due TO wind Load Fw 23270 lbs
Reaction Due To Wind Load Rw 61 lbs/ft
Moment Due To Wind Load Mw 437021 lbs-ft
Base Shear Due TO Seismic Load Fs 4820 lbs
Reaction Due To Seismic Load Rs 13 lbs/ft
Moment Due To Seismic Load Ms 90,525 lbs-ft
of the tank under the

d at the level under

e liquid. Thwe maximum

ominal pressure rating
tation used to investigate
cuum; in such

arc, in the wall of the tank

c, in the wall of the tank

nsion.(in cylinderical
frential unit forces)

h in a meridional plane
nsidered negative
from R 2 except

t the level under

ank to the axis of the
ided in 5.10.2.6

and its contents(either

re 5-4 panel b, or
d as a free body on the
he total weight would
n the portion of the
eight is negligible and
with the liquid weight.
ts in the same
e of the free body;
in the opposite

or bottom of the tank

om of the tank

n lbs/in 2 as given in

hed as prescribed

10TH Ed. ADD.01

phuric Acid

Kg/m3
lbs/ft3
Kg/m3
lbs/ft3

Mpa
psi
O
C
psi
psf
 psi
mm
ft
mm
ft
Mpa
psi

mm
inch
mm
inch
mm
inch

mm
ft
mm
ft
mm
ft
inch
mm
ft
lbs
lbs
mph
B
psi
0

( 0.8D TO 1.2D)
 in2
ft2

lbf
lbf

in2
ft2

ownward direction)

uation 8 of 5.10.2.5

uation 9 of 5.10.2.5
 x roof area

uation 8 of 5.10.2.5

uation 9 of 5.10.2.5

ving By Equation 18 of API 620

olving By Equation 19 of API 620

 Psi

ving By Equation 18 of API 620

ving By Equation 19 of API 620

 Psi

#DIV/0!

entrated load of 225 Kgs over 0.4

is equivelant to 0.4 meter squre

e to liquid head
ving By Equation 18 of API 620

ving By Equation 19 of API 620

ning shell courses.

Weights Weights corroded

lbs Kgs
12,609 3,572
9,457 2,143
9,457 2,143
9,457 2,143
9,450 2,143
 - -
50,430 corroded weig

Weight of
Contents

lbs
2,912
2,330
1,747
1,165
582
-

291

Total Weight
WHydrotest

lbs
3,714,791
2,974,060
2,236,481
1,498,902
761,323
23,750

T1
lbs/inch
401.40
393.72

387.80
381.88
-
-
T{Max.
(T1,T2)}
lbs/inch
716.83
716.18
715.53

714.88
-
-
 by using eq.18
[1342(tprov-C.A)]2/Rc
244
88
88
88
88
88

resisting the
n ring region.

juncture b/w
to the tank
ieved, based on API 620.
 tprov x Annular Area)

X E)0.5 + C.A

OD}2 X {S X E/C} + Pbottom]

mediate wind girder and the top

 formad head the vertical distance
er and the head bend line plus

urse as ordered condition

psf

psf

psf

psf

psf

fter multiplying with load factor)

s ordered condition in inch.

hich transposed width is

dition in inch.
inch

ft

inch

ft

inch

ft

inch

ft

inch

ft

inch

ft

ft
 km/hr

ft
m

m/sec

6013 x Kz x Kzt x Kd x V2 X I/1000

KN/m2

x D 0 x q f x C f x Ht

KN-m

lbs-ft

plift Due to Internal Pressure)

(Corroded)

(Corroded)
than shell and roof weight

+ C2 x W2 x X2}
Shell Centre Of Gravity

endix. L.5.1
r API 620 Appendix. L.5.3

endix. L.5.2

r API 620 Appendix. L.5.3

inch of H2O

inch of H2O

inch

ft-lbs

ft-lbs

lbs

lbs

lbs
all For Anchor Bolts tb = U / N
(PSI) Load /
Anchor
15300 10462.80
20349 13315.29
28800 -300.09
28800 -820.35
20349 11118.98
20349 10598.72

oviding 2.25" anchor bolt area by considering

e corrosion allowance of 1/4"on the dia)
a*h2/Rt)+(4ah2)0.333}+{0.031/(Rt)0.5}]

t)2/(Rt)0.5}+1]
0.799
 8 KN/m
5 KN/m
5085 KN/m2
179,399 KN/m2
104 KN
1 KN/m
593 KN-m
21 KN
0 KN/m
123 KN-m
Weights corroded
lbs
7,875
4,725
4,725
4,725
4,725
 -
26,776

Weight of Total Weight

Water W

lbs lbs
3,640,611 77,092 4077.328734
2,912,489 63,901
2,184,367 53,861
1,456,245 43,822
728,122 33,783
- 23,750

Pcon.+W/At Phydro+W/At
W/At W/Athydro
internal Hydrotest

Psi Psi Psi Psi

0.30 14.51 2.81 31.86
0.25 11.62 2.76 26.12
0.21 8.74 2.72 20.40
0.17 5.86 2.68 14.67
0.13 2.97 2.63 8.94
0.09 0.09 2.59 3.22

T1hydro T2 T2hydro
lbs/inch lbs/inch lbs/inch
4,547.38 716.83 4,952.10
3,728.35 716.18 4,140.07

2,911.07 715.53 3,328.05

2,093.79 714.88 2,516.03
- - -
- - -
 T{Max.
tcalc. thydro tcalc<tprov. thydro<tprov.
(T1hyd.,T2hyd.)}
lbs/inch inch inch inch inch
4,952.10 0.06 0.56 OK Not OK
4,140.07 0.06 0.49 OK Not OK
3,328.05 0.06 0.42 OK Not OK

2,516.03 0.06 0.34 OK Not OK

- - 0.12 OK OK
- - 0.12 Not OK Not OK
using eq.18
[1342(tprov-C.A)]
Rc/2+W/At
2
/Rc-Rc/2+W/At
Rc/2 0.8*Rc (Rc/2+0.8*Rc) P
177.37 67.1 -142.7165354 -228.3464567 -371.0629921 -0.48
27.92 60.1 -142.7165354 -228.3464567 -371.0629921 -0.08
33.19 54.8 -142.7165354 -228.3464567 -371.0629921 -0.09
38.47 49.6 -142.7165354 -228.3464567 -371.0629921 -0.10
43.74 44.3 -142.7165354 -228.3464567 -371.0629921 -0.12
49.01 39.0 -142.7165354 -228.3464567 -371.0629921 -0.13