ROOF THICKNESS VERIFICATION AS PER API 620 Contents: 1
Design Data
2
Roof Design
3
Shell Desin
4
Compression Area Design
5
Bottom Plate Design
6
Intermediate Wind Girder Calculations
7
Stabiltility Calculations Against Wind Load
8
Stabiltility Calculations Against Seismic Load 8.1
Resistance To Over Turning
8.2
Shell Compression For Unanchored Tanks
8.3
Maximum Allowable Shell Compression For Unanchored Tanks
8.4
Shell Compression For Anchored Tanks
8.5
Maximum Allowable Shell Compression For Anchored Tanks
9
Uplift Load Cases As Per API 650 Table 3-21a
10
Anchor Chair Calculations
11
Foundation Loading Data
12
Nozzle Reinforcement Calculations(LATER)
13
Nozzle Flexibility Analysis As Per Appendix P of API 650(LATER)
14
Venting Calculations As Per API 2000(LATER)
7.1)
Roof Thickness and Compression Area Verification As Per API 620 Nomenclature P
= =
Total pressure in lbs/ft2 acting at a given level of the tank under the particular condition of loading. P1 + Pg
P1
=
Pressure in lbs/ft2 resulting from the liquid head at the level under consideration in the tank.
Pg
=
Gas pressure in lbs/ft2 above the surface of the liquid. Thwe maximum gas pressure(not exceeding 15 lbs/ft2) is the nominal pressure rating of the tank. Pg is the positive except in computation used to investigate the ability of the tank to withstand a partial vacuum; in such computations its value is negative.
T1
=
Meridional unit force in lbs/inch of latitudinal arc, in the wall of the tank at the level of the tank under consideration. T1 is positive when in tension.
T2
=
Latitudinal unit force in lbs/in of maridional arc, in the wall of the tank under consideration. T2 is positive when in tension.(in cylinderical side walls the latitudinal unit forces are circumfrential unit forces)
R1
=
Radius of curvature of the tank side wall in inch in a meridional plane at the level under consideration. R1 is to be considered negative when it is on the side of the tank wall opposite from R2 except as provided in 5.10.2.6
R2
=
Length in inch of the normal to the tank wall at the level under consideration measured from the wall of the tank to the axis of the revolution. R2 is always positive except as provided in 5.10.2.6
W
=
Total weight in lbs of that portion of the tank and its contents(either above the level under consideration, as in figure 5-4 panel b, or below it, as in figure 5-4 panel a) that is treated as a free body on the computations for that level. Strictly speaking the total weight would
include the weight of all metal, gas and liquid in the portion of the tank treated as described; however the gas weight is negligible and the metal weight may be negligible compared with the liquid weight. W shall be given the same sign as P when it acts in the same direction as the pressure on the horizontal face of the free body; it shall be given the opposite sign when it acts in the opposite direction. At
=
Cross section area in in2 of the side walls, roof or bottom of the tank at the level under consideration.
t
=
Thickness in inch of the side walls, roof or bottom of the tank at the level under consideration.
c
=
Corrosion allowance in inch
E
=
Joint efficiency
Sts
=
Maximum allowable stress for simple tension in lbs/in2 as given in table 5-1
Sca
=
Allowable compresive stress in lbs/in2 established as prescribed in 5.5.4
Design Data : API 620 10TH Ed. ADD.01
Desig Code Client's Specs Fluid Material Design Density of Contents
= =
Density of water for hydrotest = Specific Gravity Of Contents Material Yield Strength Design Temperature Internal Pressure Extrenal Pressure Liquid Level
= = = = = =
Sulphuric Acid A36 1820 113.623 1000 62.43 1.82 248.21 36000 100 1.015 146.16 0.0725 4200 13.78
Design Liquid Level
= = =
Allowable Tensile Stress At Design Temperature
4200 14 110.32 16000
Corrosion Allowance Shell
6.4 0.25197 6.4 0.25197 6.4 0.25197
Bottom Roof
Inside Dia Of Tank
D
=
Height Of Shell
=
Weight Of Compression Ring IF applicable Weight Of Accessories Wind Velocity
= =
4000 13.12 4010 13.16 4020 13.19 158.27 4200 14 450 3000 96.31
Nominal Dia Of Tank
Dn
=
Outside Dia of tank
D0
=
Yield Strength Of Steel Structure Roof Angle
= =
36000 11.3
Roof Design
As Per API 620 B 5.10.2
Assumptions
Taking Thickness
t
Joint Efficiency
E
Radius Of Dome
rr
Height Of Cone Roof
One Half The included apex angle of the Conical roof or bottom . Radius Of Cone
= = = = =
14 mm 0.551 inch 0.7 1xD 13.12 ft
h
=
1.31 ft
a
=
78.7
L
=
6.69 ft
Angle b/w the normal to roof q and a vertical line at the roof to shell juncture
=
At'
Roof Area Roof Weight
= = W (Uncorroded) =
Roof Weight
W (corroded) = At
Cross sectional Area at roof to shell junction
11.30
20256 141 Density x t x Roof Area 3163 1719
= =
19478 135
As per API 620 5.10.2.5.a
For Conical Seg.
R1
=
Infinity
ft
As per API 620 5.10.2.5.a
R3 = D/2
Case I :
= =
6.562 ft 78.74 inch
Thickness At The Top Head Edge Against Internal Pressure
W/At W/At'
= =
-0.162 psi -0.156 psi (force acting in downward direction)
Now Calculating Meridional and Latitudinal Forces T1
=
{R3/(2Cosa)}*{P+W/At}
= T2
=
Equation 8 of 5.10.2.5
171 lbf/in {(P × R3)/(Cosa)} 408 lbf/in
Now As Per 5.10.3.2 If T1 and T2 both are +ve, then T
=
Max.(T1 and T2) 408 lbf/in
tcalc.
= =
T/(Sts.E) + C.A 0.288 inch
Equation 9 of 5.10.2.5
Provided Thickness is Ok
Case II :
Thickness At The Top Head Center Against Internal Pressure
T1 '
T2 '
=
Rs/2(P+W/At')
=
0 lbf/in
= =
Rs x (P+W/At') - T1 0 lbf/in
Now As Per 5.10.3.2 If T1 and T2 both are +ve, then T
= =
Max.(T1' and T2') 0 lbf/in
tcalc.
=
T/(Sts.E) + C.A 0.252 inch
As these thicknesses are calculated based on the internal pressure of = 1.015 psi Therefore, Back calculating the internal pressure limited by the actual provided thickness
tprov.
=
T/(Sts.E) + C.A
(tprov. - C.A) X Sts X E = = 3351 lbf/in Now putting this value of T in the equation of T2, where we find the maximum calculated thickness T
T2
=
Rs x (P+W/At x cos a) - T1
T
=
Rs x (P+W/At x cos a) - Rs/2(P+W/At) T2 = T
P
= =
(2 X T/Rs) - W/At(2*cos a -1) #DIV/0! #DIV/0!
As Per 7.18.3.2, our roof will be safe against the hydro test pressure of 1.25 x internal pressure i.e. 1.26875 psi
Case II :
Thickness At The Top Head Edge Against External Pressure
W = - (Live Load + Dead Load) x Roof Area -ve sign id due to the downward direction of load -(25 + weight of roof in lbs/ft2) x roof area
=
W/At W/At'
=
-4985 lbf
= =
-0.256 psi -0.246 psi
Now Calculating Meridional and Latitudinal Forces T1
= =
{R3/(2Cosa)}*{P+W/At} -66.0 lbf/in
Equation 8 of 5.10.2.5
T2
=
{(P × R3)/(Cosa)} -29.1 lbf/in
Equation 9 of 5.10.2.5
Now As Per 5.10.3.5 T'
= =
Max.{ABS(T1) , ABS(T2)} 66.0 lbf/in
T"
=
Min.{ABS(T1) , ABS(T2)} 29.1 lbf/in
R' R"
= =
Infinity
t18
= =
Sqrt{(T'+0.8 X T") X R'}/1342 +Solving C.A By Equation 18 of API 620 Infinity inch
t19
=
SQRT{T'' x R''}/1000 + CA 0.300 inch
Similarly, 78.74 inch
Now,
Now; As per 5.10.3.5.b Step-2 t18 - C.A R'
=
Infinity
< .0067
Solving By Equation 19 of API 620
t19 - C.A R'' treq treq tprovided
=
0.0006
< .0067
Max(t18 , t19) 0.300 inch
= = =
0.551 inch
As per 5.5.4.3 Allowable Compressive Stress; Sca
Provided thickness is O.K
Case IV :
Thickness At The Top Head Center Against External Pressure
T1 '
Rs/2(P+W/At' )
= =
0.00 lbf/in
T2 '
= = Now As Per 5.10.3.5
Rs(P+W/At' ) -T1' 0.00 lbf/in
T'
=
T"
=
Max.{ABS(T1' ) , ABS(T2' )} 0.00 lbf/in Min.{ABS(T1' ) , ABS(T2' )} 0.00 lbf/in
Similarly R' = R2 R" = R1
0.00 inch 0.00 inch
Now, t18
=
t19
=
Now; As per 5.10.3.5.b Step-2 t18 - C.A R' t19 - C.A R'' treq
=
treq
= =
tprovided
Sqrt{(T'-0.8 X T") X R'}/1342 + Solving C.A By Equation 18 of API 620 0.252 SQRT{T'' x R''}/1000 + CA Solving By Equation 19 of API 620 0.252
=
#DIV/0!
< .0067
=
#DIV/0!
< .0067
Max(t18 , t19) 0.252 inch 0.551 inch
As per 5.5.4.3 Allowable Compressive Stress; Sca Sca
=
= 106 x (t - C.A) R' #DIV/0!
As these thicknesses are calculated based on the external pressure of P = 0.0725 psi Therefore, Back calculating the external pressure limited by the actual provided thickness
Now; As per 5.10.3.5.a t19
=
SQRT{T'' x R''}/1000 + CA
tprovided
=
SQRT{T'' x R''}/1000 + CA
T''
=
[(tprovided-C.A) x 1000 ]2 / R''
T''
=
T''
=
-Rs/2(P+W/At' )
Pext
=
2/Rs x T'' - W/At' #DIV/0! Psi
#DIV/0!
lbs/in
NOTE:
As Per 32-SAMSS-006 Para 5.4.k, roof live loads shall not be less than concentrated load of 225 Kgs over 0.4 meter square area. for this purpose, by considering the roof segment of 700mm diamter which is equivelant to 0.4 meter squre area is to be analysed against these loading conditions #DIV/0! For result and methodolgy see ANNEXURE 1
3)
Shell Design Shell calculations are based on different assumed thicknesses, here we will perform the specimen calculations for 1st shell course and the others are given in the tabulated form which are mentioned below.
Case I :
Thickness of 1st shell course Against Internal Pressure
Joint Efficiency
E
Taking thickness of Ist Shell Course Total weight of shell of different
=
0.85
= =
0.630 inch 26004 lbs
=
3163 lbs
thicknesses. Total weight of roof
Total Weight; W W/At
(Roof Pl.+Shell).= =
29167 lbs 1.50 psi
Now Total Pressure Internal Pressure + Pressure due to liquid head
=
24.31 psi
Now calculating the latitudinal and maridianal forces As Per 5.10.2.5.c
T1
= =
Rc/2(P+W/At) equation 10 of 5.10.2.5 1,016 lbs/inch
T2
= =
Rc x P
Now As Per 5.10.3.2 If T1 and T2 both are +ve, then T = = tcalc.
= =
equation 11 of 5.10.2.5 1,915 lbs/inch
Max.(T1 and T2) 1,915
lbs/inch
T/(Sts.E) + C.A 0.39
inch
The same procedure is adopted while confirming the thickness during hydrotest
As this thickness is calculated based on the internal pressure of P = Internal Pressure + Pressure due to liquid head = 24.31 psi Back calculating the internal pressure limited by the actual provided thickness tprov. T/(Sts.E) + C.A = T
=
5,140 lbs/inch
Now putting this value of T in the equation of T2, where we find the maximum calculated thickness
Case II :
T2
=
Rc x P
Pmax.int
= =
T2/Rc
T2=T 65.28 psi
Thickness of 1st shell course Against External Pressure
= -(Weight Of Roof Plates + Weight Of shell + Live Load) = -32684 lbs Pext. = -0.0725 psi -ve sign id due to the downward direction of load W
Now calculating the latitudinal and maridianal forces As Per 5.10.2.5.c
T1
=
Rc/2(P+W/At) equation 10 of 5.10.2.5 -69 lbs/inch
T2
=
Rc x P
equation 11 of 5.10.2.5 -5.71 lbs/inch
Now As Per 5.10.3.5 T' T"
=
Max.{ABS(T1) , ABS(T2)}
=
69 lbs/inch Min.{ABS(T1) , ABS(T2)} 6 lbs/inch
similarly,
R' = Rc R" = Rc Now,
= =
78.74 inch 78.74 inch
t18
= = t19 = = Now; As per 5.10.3.5.b Step-2 t18 - C.A R' t19 - C.A R'' treq
= =
Sqrt{(T'+0.8 X T") X R'}/1342 + C.A 0.3087 inch SQRT{T'' x R''}/1000 + CA 0.2732 inch
=
0.0007
< .0067
=
0.0003
< .0067
Solving By Equation 18 of API 620 Solving By Equation 19 of API 620
Max(t18 , t19) 0.3087 inch
As per 5.5.4.3 Allowable Compressive Stress; Sca Sca
=
= 106 x (t - C.A) R' 0
Psi
Back calculating the external pressure limited by the actual provided thickness
Now; As per 5.10.3.5.a as the maximum thickness is obtained by equation 18, therefore back calculating the external pressure limited by tprov.
t18
=
{1342 x (tprov.-C.A)}2/R'
=
{1342 x (tprov.-C.A)}2/R'
=
Sqrt{(T'+0.8 X T") X R'}/1342 + C.A T'-0.8 X T" -Rc/2(P+W/At)- 0.8 x (Rc x P)
Now Putting the values in the above equation
Pmax.ext.
=
-31.27 Psi
-ve sign shows the vacuum condition. Assuming Thicknesses of Various Shell Courses and Calculate their Weights
Now following the above mentioned procedure for the calculation of remaining shell courses.
CASE 1. Table 1.
Internal Pressure With Full of Liquid
Shell
Thickness
Width
Weights
Coures #
mm
inch
mm
inch
1 2 3 4 5 6
16 14 12 10 0 0
0.630 0.551 0.472 0.394 0.000 0.000
2450 2450 2450 1650 0 0
96.46 96.46 96.46 64.96 0.00 0.00
Total Weight Of Shell
Kgs
3,863 3,380 2,897 1,626 =
Table 2.
Shell Coures #
1 2 3 4 5 6
Weight of Roof
Weight of Shell
lbs
lbs
3,163 3,163 3,163 3,163 3,163 3,163
26,004 17,467 9,997 3,594 -
Total Weight Total Weight WHydrotest W lbs
29,167 20,630 13,160 6,756 3,163 3,163
lbs
29,167 20,630 13,160 6,756 3,163 3,163
W/At Psi
1.50 1.06 0.68 0.35 0.16 0.16
Table 3.
Shell Coures #
1 2 3 4 5 6
Water Pressure Head Psi
Total Pressure PContents
Total Pressure PHydrotest
Psi
Contents Pressure head Psi
Psi
Psi
1.015 1.015 1.015 1.015 1.015 1.015
23.30 16.96 10.61 4.27 0.00 0.00
12.80 9.32 5.83 2.35 0.00 0.00
24.31 17.97 11.63 5.29 1.02 1.02
Internal Pressure
As Per 7.18.3.2 Internal Presssure for Hydrotest is 1.25 * Pint Now Calculating Meridianal and Latitudinal Forces aginst pressure and During Hydrotest Condition.
Shell Coures #
Pcon.+W/At internal Psi
Phydro+W/At Hydrotest Psi
T1
T1hydro
lbs/inch
lbs/inch
1 2 3 4
25.81 19.03 12.30 5.63
15.57 11.64 7.78 3.96
1,016.22 749.25 484.44 221.79
612.92 458.46 306.16 156.01
5 6
1.18 1.18
1.43 1.43
46.35 46.35
56.34 56.34
Shell Coures #
1 2 3 4 5 6
T2
T2hydro
lbs/inch
lbs/inch
1,914.53 1,415.11 915.69 416.27 79.92 79.92
1,107.93 833.52 559.11 284.71 99.90 99.90
T{Max.(T1,T2) T{Max.(T1hyd., T2hyd.)} } lbs/inch lbs/inch
1,914.53 1,415.11 915.69 416.27 79.92 79.92
1,107.93 833.52 559.11 284.71 99.90 99.90
Now Calculating the required thickness as Per 5.10.3.2 Shell Coures #
tcalc.
thydro
tcalc
thydro
14.07 10.59 7.10 3.62 1.27 1.27
Shell Coures #
inch
1 2 3 4 5 6
inch
0.39 0.36 0.32 0.28 0.26 0.26
0.33 0.31 0.29 0.27 0.26 0.26
inch
inch
OK
OK
OK
OK
OK
OK
OK
OK
Not OK
Not OK
Not OK
Not OK
Now Back Calculating the pressure limited by actual provided thicknesses.
Shell Coures #
1 2 3 4 5 6
T lbs/inch
5,140 4,069 2,998 1,928 (2,822) (2,822)
CASE 2.
Shell Coures #
Pmax. internal Pmax.inter>Pint. Psi
65.28 51.68 38.08 24.48 (35.84) (35.84)
inch OK OK OK OK Not OK Not OK
External Pressure In Empty Condition
External Pressure
Weight of Roof
Weight of Shell
Live Load
Total Weight W
Psi
lbs
lbs
lbs
lbs
1 2 3 4 5 6
-0.0725 -0.0725 -0.0725 -0.0725 -0.0725 -0.0725
Shell Coures #
W/At
P+W/At
T1
T2
Psi
Psi
lbs/inch
lbs/inch
-1.750 -1.312 -0.929 -0.600 -0.415
-69 -52 -37 -24 -16
-5.709 -5.709 -5.709 -5.709 -5.70866142
1 2 3 4 5
-1.678 -1.240 -0.856 -0.527 -0.343
3,163 3,163 3,163 3,163 3,163 3,163
26,004 17,467 9,997 3,594 -
3516.60 3516.60 3516.60 3516.60 3516.60 3516.60
-32683.74 -24146.34 -16676.11 -10273.06 -6679.51 -6679.51
6
Shell Coures #
-0.343
T' lbs/inch
1 2 3 4 5 6
Shell Coures #
1 2 3 4 5 6
Shell Coures #
1 2 3 4 5 6
-0.415
-16
-5.70866142
T'' lbs/inch
R' inch
R'' inch
69 52 37 24 16 16
6 6 6 6 6 6
t18
t19
inch
inch
0.3087 0.3016 0.2944 0.2871 0.2822 0.2822
0.2732 0.2732 0.2732 0.2732 0.2732 0.2732
tcalc.
tcalc
inch
inch
0.3087 0.3016 0.2944 0.2871 0.2822 0.2822
79 79 79 79 79 79
79 79 79 79 79 79
t18t19C.A/R'<.0067 C.A/R'<.0067 inch
0.0007 0.0006 0.0005 0.0004 0.0004 0.0004
inch
0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
OK OK OK OK Not OK Not OK
(3,200) (3,200)
Now Back Calculating the pressure limited by actual provided thicknesses.
Shell Coures #
Pmax. External Psi
1 2 3 4 5
-31.27 -19.53 -10.53 -4.29 -14.05
Pmax.ext.>Pext. inch OK OK OK OK OK
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
=
Q
=
P X R3 79.92125984 lbs/inch -11807
So, As per 5.12.4.3 AC
Aprovided
= = =
Q/15000 2
0.79 inch
2.01 inch2
equation 27 507.84 mm2 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 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
P
=
Internal Design Pressure
E
=
Joint Efficiency
t
=
Provided Thickness
r
=
s
=
Knuckle Radius(12% of diameter 100.8 inch of shell as per 5.12.3.1) Material Allowable Design Stress 16000 psi
M
= =
tcalc
= =
0 inch 1.015 psi 0.7 0.551 inch
0.25 X {3 + (L/r)0.5} 0.75 [{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
5)
= =
{2 x S x E x (tprov.-C.A)}/{L x M + 0.2 x (tprov.-C.A)} 112000.00 psi
Bottom Plate Design = =
p/4(Bottom OD-2 X Annular Ring Width)2
= = =
p/4(Bottom OD)2 - Bottom Plate Area
tprov bottom
= = =
tmin annular
=
.25 + C.A 0.502 inch 10 mm 0.394 mm .25 + C.A 0.502 inch 10 mm 0.3937 inch Density x (tprov.x Bottom Area + tprov x Annular Area) 2307 lbs 830 lbs (Corroded)
Bottom Plate Area
Annular Plate Area Joint Efficiency E
7140 inch2
13540 inch2 0.7
As per 5.9.4.2
tmin bottom
tprov.annular Total Weight
= = =
Vacuum Calculations as Per ASME Section VIII Div.1
Weight of bottom plate resisting Pbottom external vacuum
= =
0.2833 x tprov.bottom.corr. 0.0402 psi
Pext.eff
= =
Pext + Pbottom -0.0323 psi
Effective External Pressure
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
tprov ext
for 1st shell course
C Therefore, Thickness required against vacuum tvacuum
= = = = =
=
(tcalc. - C.A) 0.14 inch (tprov. - C.A) 0.38 inch 0.33 X td ext./tprov 0.12
OD X ( C X Pext.eff/S X E)0.5 + C.A
tcalc. tprov.
=
0.318 inch
= = =
Max.(tcalc.,tvac.) 0.502 inch 0.394 inch
Now back calculating the maximum external pressure limited by bottom plate
Pmax.ext.
6)
-[{tprov. - C.A}/OD}2 X {S X E/C} + Pbottom] -0.1132 psi
= =
Design Of Intermediate Wind Girder
As Per 5.10.6
H1
=
6 x (100 x t) x (100xt/D)3/2
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
=
Where,
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
Dynamic Pressure due to vacuum
=
10.44
Actual Dynamic Pressure
=
41.44
Therefore H1 shell be decreased by the factor
=
0.87
Now, As per 5.10.6.1.d
Now,
H1
=
1675.7 ft
Transformed Shell Thicknesses
(after multiplying with load factor)
As Per 5.10.6.2
Wtr
=
W X (tuniform/ttop)2.5
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
Where,
1st Shell Course Thickness Of First Shell Course
t1
=
0.630
Transposed Course Width
Wtr
=
3.92
Thickness Of 2nd Shell Course
t2
=
0.551
Transposed Course Width
Wtr
=
5.47
Thickness Of 3rd Shell Course
t3
=
0.472
Transposed Course Width
Wtr
=
8.04
Thickness Of 4th Shell Course
t4
=
0.394
Transposed Course Width
Wtr
=
5.41
Thickness Of 5th Shell Course
t5
=
0.000
Transposed Course Width
Wtr
=
2nd Shell Course
3rd Shell Course
4th Shell Course
5th Shell Course
#DIV/0!
6th Shell Course Thickness Of 6th Shell Course
t6
=
Transposed Course Width
Wtr
=
Now, Transformrd height of shell
Htr
=
0.000 #DIV/0!
22.83
As Htr
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
qz
=
Design Wind Pressure
= Design Wind Load
P1
= =
0.6013 x Kz x Kzt x Kd x V2 X I/1000 1.046 qz x D0 x qf x Cf x Ht 11.51
Overturning Wind Moment
Mw
=
P1 X Ht 2
=
26 19530
Resisting Moment
Mr
2 x (Ws' + Wr' - Uplift Due to Internal Pressure)
2
3
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
As Mw>Mr Anchorage is Required
8)
Stability Calculations Against Seismic Load
Per API 620 Appendix. L
Ms Ms
= =
Over Turning Moment Due To Siesmic Forces Z x I x {C1 x WS x XS + C1 x Wr x Ht + C1 x W1 x X1 + C2 x W2 x X2}
Z
= = = = = = = = = =
Therefore,
T
= =
Seismic Zone Factor From Table L-2 0.075 For Seismic Zone One Importance Factor 1.25 Site Amplification Factor From Table L-3 1.2 Lateral Earthquake Force Coefficient 0.6 As Per L.3.3.1 Lateral Earthquake Force Coefficient 0.75 X S As Per L.3.3.2 T Natural Period Of First Sloshing AsMode Per L.3.3.2 0.5 k x OD
k
=
Factor For D/H Obtained From Figure L-4
D/H
=
0.957
k
=
0.607
I S C1 C2 Where
And So, Now, From Figure L-4
T
=
2.204
C2
=
0.4083
Now, From Figures L-2 and L-3 X1/H X2/H W1/Wt W2/Wt
= = = =
Wt
= =
X1 X2 W1 W2 Xs
= = = = = =
0.375 0.585 0.543 0.461
From Figure L-3 From Figure L-3 From Figure L-2 From Figure L-2
Where Weight of tank Contents @ Maximum Liquid Level 211,777 lbs
So, 5.17 8.06 114,994.96 97,629.24 Height From The Bottom Of Tank Shell To The Shell Centre Of Gravity 6.89 ft
Now, C1 x WS x XS C1 x Wr x Ht C1 x W1 x X1 C2 x W2 x X2
= = = = Ms
8.1)
107498 26,150 356,530 321,305.66
=
76,077 lbs-ft
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
=
413.5 lbs/ft
Now, 1.25 x G x H x D
AS WL>1.25GHD Therefore WL=1.25GHD
WL
8.2)
=
413.5 lbs/ft
Shell Compression For Unanchored Tanks Ms
=
0.39
Per API 620 Appendix. L.5.1
D2(Wt+WL)
=
0.39
Where, Wt
{Weight of Roof + Weight Of Shell}/p x D 704 lbs/ft
= =
As Ms/{D2*(Wt+WL)<0.785 Use b=Wt+ 1.273*Ms/D2
The Maximum Longitudinal Compressive Force at The Bottom Of The Shell So, Wt + 1.273 x Ms b = 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
<
1.00E+06
GHD2 t2
=
10994
So,
As GHD2/t2<1000000 Use Fa=(1000000*t/2.5*D)+600*sqrt(GH)
Therefore, Fa
= =
0.5 1000000 x t + 600 (GH)
2.5 x D 22109.2 psi
As b/12t
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, Wt + 1.273 x Ms b = D2 = 1,260.68 lbs/ft
8.5)
Maximum Allowable Shell Compression For Anchored Tanks Per API 620 Appendix. L.5.3
b/12t
= =
Maximum Longitudinal Compressive Stress 166.78 psi
Now, GHD2 t2
<
1.00E+06
GHD2 t2
=
11486
So,
As GHD2/t2<1000000 Use Fa=(1000000*t/2.5*D)+600*sqrt(GH)
Therefore, Fa
= =
0.5 1000000 x t + 600 (GH)
2.5 x D 22109.2 psi
As b/12t
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
W1
=
Dead Load Of shell minus any corrosion allowance 16,426 and 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 18,145 and 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
76,077
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
Design Pressure
Fall For NET UPLIFT FORMULA, U Anchor Bolts (lbf) (PSI) 2 ((P - 8th) x D x 4.08) - W1 217 15300
Test Pressure
((Pt - 8th) x D2 x4.08) - W1
Wind Load Seismic Load
UPLIFT LOAD CASES
Design Pressure + Wind Design Pressure + Seismic
5153
20349
(4 x Mw / D) - W2
-12192.06
28800
(4 x Ms / D) - W2
5043.39
28800
2
((P - 8th) x D x 4.08) + (4 x Mw6170 / D) - W1 2
((P - 8th) x D x 4.08) + (4 x Ms23405 / D) - W1
UPLIFT LOAD CASES
Reqd. Bolt Area Ar = tb/Fall (in2) 0.00025 0.00452 -0.00756 0.00313 0.00541 0.02054
Design Pressure Test Pressure Wind Load Seismic Load Design Pressure + Wind Design Pressure + Seismic
No Of Anchor Bolt Provided
N
Max. Required Bolt Area
Areq.
Bolt Area Provided
Aprov.
Dia Of Anchor Bolt
d
Bolt Circle Dia Bolt Spacing
20349 20349
Reqd. Bolt Area 0.16 2.92 -4.88 2.02 3.49 13.25
56 2 0.02054 inch 2 3.25 inch
(Providing 2.25" anchor bolt area by the corrosion allowance of 1/4"on th
2.5 inch 20240 mm 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
[P(0.375g-0.22d)/Sf]0.5
Top Plate Thickness
C
=
Critical Stress b/w the hole and and the free edge of plate Distance from outside of the top plate to edge of the hole
S
=
21 ksi
f
=
2.67 inch
Distance b/w gussett plates
g
=
3.93 inch
Anchor Bolt Diameter
d
=
2.5 inch
Design Load Or Maximum Allowable load or 1.5 times the actual bolt load whichever is lesser
P
=
1 kips
So, Top Plate Thickness
C
=
Actual Used Plate Thickness
C
=
0.10 inch 2.58 mm 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
=
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
Z
=
0.991
Sinduced
=
0.17
So,
ksi
Gussett Plate Thickness Calculations Gussett Plate Thickness
Actual Gussett Plate Thickness
Jmin
=
J
= = =
0.04(h-C) 0.83 inch 21.152 mm 30
Gussett Plate Thickness Is Adequate Now
Average Width of Gussett =
11)
JxK J K
= =
JxK P/25
= = OK
P/25 1.181 5.118 6.045 0.0251
Foundation Loading Data The Self weight of roof and live load will be transferred to shell
Live load transferred to foundation
= in in
=
Live Load on roof Area Of Roof
Ar
Total Live Load
=
25 psf 2 20256 inch
=
3517 lbs
Circimference of tank
C
=
41 ft
Live Load Transferred to foundation
LL
=
85 lbs/ft
Dead load transferred to foundation Self Weight Of Shell
Ws
=
26004 lbs
Self Weight Of Shell
Wr
=
3163 lbs
Self Weight Of Bottom including annular plate
Wb
=
2307 lbs
Weight of accessories
Wa
=
3000 lbs
Toatal Dead Load Acting On Shell
WD
=
32167 lbs
Dead Load Transferred to foundation
DL
=
778 lbs/ft
Operating & Hydrostatic Test Loads Self weight of tank
=
34474 lbs
Weight of contents in operating condition
=
211777 lbs
Weight Of Water in hydrotest condition
=
249,345 lbs
Uniform Load In operating condition
Self Wt + Fluid=W = o
2 36039 lbs/ft
Uniform Load In test condition
Self Wt+Water=W = h
2 283,819 lbs/ft
Wind Load Transferred to Foundation Base Shear Due to wind load
Fw
=
Reaction Due To Wind Load
Rw
=
36 lbs/ft
Moment Due to wind load
Mw
=
19530 lbs-ft
10083 lbs
2588 lbs
Seismic Load Transferred to Foundation Base Shear Due to Seismic load
Fs
=
Reaction Due To Seismic Load
Rs
=
140 lbs/ft
Moment Due to Seismic load
Ms
=
76,077 lbs-ft
Summary of Foundation Loading Data Dead Load Live Load Uniform Load Operating Condition uniform Load Test Condition Base Shear Due TO wind Load Reaction Due To Wind Load Moment Due To Wind Load Base Shear Due TO Seismic Load Reaction Due To Seismic Load Moment Due To Seismic Load
DL LL WO Wh Fw Rw Mw Fs Rs Ms
778 85 36039 283,819 2588 36 19530 10083 140 76,077
lbs/ft lbs/ft lbs/ft2 lbs/ft2 lbs lbs/ft lbs-ft lbs lbs/ft lbs-ft
of the tank under the
d at the level under
liquid. Thwe maximum minal pressure rating ation used to investigate cuum; in such
rc, in the wall of the tank
, in the wall of the tank sion.(in cylinderical frential unit forces)
h in a meridional plane nsidered negative from R2 except
the level under ank to the axis of the ded in 5.10.2.6
nd its contents(either e 5-4 panel b, or d as a free body on the he total weight would
n the portion of the ight is negligible and with the liquid weight. s in the same e of the free body; n the opposite
or bottom of the tank
om of the tank
n lbs/in2 as given in
hed as prescribed
10TH Ed. ADD.01
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
0
Bpsi
( 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
uation 8 of 5.10.2.5
uation 9 of 5.10.2.5
ving By Equation 18 of API 620
ving By Equation 19 of API 620
Psi
lving By Equation 18 of API 620
lving By Equation 19 of API 620
Psi
ntrated load of 225 Kgs over 0.4
s equivelant to 0.4 meter squre
#DIV/0!
e to liquid head
lving By Equation 18 of API 620
lving By Equation 19 of API 620
ing shell courses.
Weights
Weights corroded lbs
8,537 7,470 6,403 3,594 26,004
Kgs
2,318 1,835 1,352 585 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
resisting the n ring region.
juncture b/w
1452
ieved, based on API 620.
tprov x Annular Area)
S 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
ter 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 D0 x qf x Cf x Ht
KN-m lbs-ft
plift Due to Internal Pressure)
(Corroded) (Corroded)
han 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
Fall For Anchor Bolts (PSI) 15300
tb = U / N Load / 3.88
20349
92.01
28800
-217.72
28800
90.06
20349
110.18
20349
417.95
oviding 2.25" anchor bolt area by considering e corrosion allowance of 1/4"on the dia)
*h2/Rt)+(4ah2)0.333}+{0.031/(Rt)0.5}]
t)2/(Rt)0.5}+1]
0.025
11 1 1726 13,589 12 1 26 45 2 103
KN/m KN/m KN/m2 KN/m2 KN KN/m KN-m KN KN/m KN-m
Weights corroded lbs
5,110 4,045 2,981 1,290 13,426
Weight of Water
Total Weight W
lbs
lbs
249,345 181,468 113,591 45,713 -
482,975 705896.6275 350,901 219,894 89,955 3,163 3,163
W/At
W/Athydro
Pcon.+W/At internal
Phydro+W/At Hydrotest
Psi
Psi
Psi
Psi
24.80 18.02 11.29 4.62 0.16 0.16
14.30 10.38 6.51 2.69 0.16 0.16
49.11 35.99 22.92 9.90 1.18 1.18
T1hydro
T2
T2hydro
lbs/inch
lbs/inch
lbs/inch
1,116.91 825.25
1,914.53 1,415.11
1,107.93 833.52
535.75 248.41 -
915.69 416.27 -
559.11 284.71 -
T{Max.(T1hyd., T2hyd.)} lbs/inch
28.37 20.96 13.61 6.31 1.43 1.43
tcalc.
thydro
tcalc
thydro
inch
inch
inch
inch
OK
OK
OK
OK
OK
OK
1,116.91 833.52 559.11
0.17 0.13 0.08
0.35 0.33 0.30
284.71 -
0.04 -
0.28 0.25 0.25
OK
OK
Not OK
Not OK
Not OK
Not OK
using eq.18 2 [1342(tprov-C.A)] /Rc-Rc/2+W/At Rc/2+W/At Rc/2 0.8*Rc 3201.20 66.1 -39.3700787 -62.992126 1998.90 48.8 -39.3700787 -62.992126 1078.07 33.7 -39.3700787 -62.992126 438.69 20.8 -39.3700787 -62.992126 1438.61 13.5 -39.3700787 -62.992126
(Rc/2+0.8*Rc) P -102.362205 -102.362205 -102.362205 -102.362205 -102.362205
-31.27 -19.53 -10.53 -4.29 -14.05
1438.61
13.5 -39.3700787
-62.992126 -102.362205
-14.05
