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
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/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
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
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
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
= 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
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 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
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
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
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 = 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
Joint Efficiency E = 0.7
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
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
Transposed Course Width Wtr = #DIV/0!
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 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
Equation 9 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
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
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
-
-
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
Per API 620 Appendix. L.5.3
Per API 620 Appendix. L.5.2
Per API 620 Appendix. L.5.3
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]
0.025
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
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