950 m3 (TYPE-3) TANK CALCULATIONS A) SYSTEM AND DESIGN DATA Design pressure
Atmospheric
Tank inner diameter (m):
Di  11.5
Tank height (m):
H  11
Freeboard (m):
fb  0.5
Liquid level (m):
Hliq  H  fb
Discharge pipe level (m):
Hd  0
Tank usefull volume:
V 
Stored material:
Su
Density of stored material:
  1000
Hliq  10.5
m
m 2
  Di 4
3
 ( Hliq  Hd)
V  1.091  10
m
kg m
3

Specific gravity:
G 
Wind Velocity:
Vwm  36
G1
1000 m
Vw  Vwm  3.6
s
Vw  129.6
km h
Tank is outside the building. Design temperature:
Td  30
Snow load (kg/m2):
Sn  100
C kg m
Live Load on Roof (kg/m2):
2
Lr  250
kg m
Seismic Zone : (Turkis h Earthquake Code)
1
Corrosion allowance:
CA  6
Material:
ST37-2
Height of courses (m):
h0  1.5
Minimum Yield Strenght (MPa):
Sy  235
Minimum Tensile Strenght (MPa):
Sut  485
2
mm
The Maximum Allowable Product Design Stress (MPa): Sd1 
2 3
 Sy
Sd1  156.667
1
MPa
3
Sd2 
Sd 
 Sd1     Sd2 
2 5
 Sut
Sd2  194
Sd  min ( Sd)
MPa
Sd  156.667
Mpa
The Maximum Allowable Hydrostatic Test Stress (MPa): St1 
St2 
St 
 St1     St2 
3 4 3 7
 Sy
St1  176.25
MPa
 Sut
St2  207.857
MPa
St  min ( St)
Reference Standard:
St  176.25
Mpa
API Standard 650 12th Edition, 2013
B) SHELL DESIGN 1) 1 FOOT METHOD: Di  11.5 m
API 650 Section 5.6.3
60 m

1 Foot method can be used
Design shell thickness ( mm):
td 
Hydrostatic test shell thickness ( mm):
tt 
4.9  Di  ( Hliq  0.3)  G Sd
 CA
4.9  Di  ( Hliq  0.3) St
td  9.669
mm
tt  3.261
mm
2) VARIABLE DESIGN POINT METHOD: L 
( 500  Di  td)
L  235.787
mm API 650 Section 5.6.4
L Hliq
 22.456

1000
Variable Design Point Method can be used.
6
a) The bottom course thickness (t1): Design shell thickness (mm):
 
t1d   1.06 
0.0696  Di Hliq

 Hliq  G     4.9  Hliq  Di  G   CA     Sd  Sd    
t1d  9.929 mm
Hydrostatic test shell thickness (in):
 
t1t   1.06 
0.0696  Di Hliq

 Hliq     4.9  Hliq  Di      St  St    
t1t  3.496 mm
2
t 
 t1d     t1t 
max ( t)  9.929
t1  max ( t)
t1  9.929
mm
b) The second course thickness (t2): Ratio for the bottom course:
h0  1000
ratio 
ratio  6.278
Ri  1000  t1 Calculation of t2a:
H1  H
H2  H1  h0
H2  9.5 m
First trial for second course: t2d 
t2t 
t 
 t2d     t2t 
max ( t )  9.669
Thickness of lower course:
4.9  Di  ( Hliq  0.3)  G Sd
 CA
t2d  9.669 mm
4.9  Di  ( Hliq  0.3)
t2t  3.261 mm
St
tu  max ( t)
tu  9.669
Ratio:
tL  t1
tL
K 
K  1.027
tu
K  (K  1)
C 
mm
1  K1.5
C  0.013
Distance of the variable design point from the bottom of the course: (x) x1  0.61  ( Ri  1000  tu)  320  C  H2
x1  184.421
x2  1000  C  H2
x2  126.849
x3  1.22  ( Ri  1000  tu)
x3  287.66
 x1  x   x2  min ( x )  126.849 xe  min ( x )  x3   
 
4.9  Di   H2  t2d1 
Sd
 
4.9  Di   H2  t2t1 
t 
 t2d1     t2t1 
max ( t)  9.371
xe
 G  1000   CA t2d1  9.371 mm xe
 
1000 
St
t2a  max ( t)
t2t1  2.997
t2a  9.371 mm
t2  9.371
c) The third course thickness (t3): Ratio for the lower course:
ratio 
h0  1000
ratio  6.462
( Ri  1000  t2) Calculation of t3a:
H3  H2  h0
H3  8 m
3
mm
First trial for third course: t3d 
t3t 
t 
 t3d     t3t 
max ( t)  8.77
Thickness of lower course:
4.9  Di  ( H3  0.3)  G Sd
 CA
t3d  8.77
4.9  Di  ( H3  0.3)
t3t  2.462 mm
St
tu  max ( t)
tu  8.77
Ratio:
tL  t2
mm
K 
C 
mm
tL
K  1.069
tu K  (K  1)
C  0.034
1  K1.5
Distance of the variable design point from the bottom of the course: (x) x1  0.61  ( Ri  1000  tu)  320  C  H3
x1  223.265
x2  1000  C  H3
x2  269.644
x3  1.22  ( Ri  1000  tu)
x3  273.957
 x1  x   x2  min ( x )  223.265  x3   
xe  min ( x )
 
4.9  Di   H3  t3d1 
Sd
 
4.9  Di   H3  t3t1 
t 
 t3d1     t3t1 
t3  8.797
max ( t)  8.797
xe
 G  1000   CA
t3d1  8.797 mm
xe
  1000 
St
t3a  max ( t)
t3t1  2.486
mm
t3a  8.797
mm
mm
d) The fourth course thickness (t4): Ratio for the lower course:
ratio 
h0  1000
ratio  6.669
( Ri  1000  t3) Calculation of t4a:
H4  H3  h0
First trial for fourth course:
t4d 
t4t 
t 
 t4d     t4t 
max ( t)  8.23
H4  6.5
4.9  Di  ( H4  0.3)  G Sd 4.9  Di  ( H4  0.3) St
tu  max ( t)
 CA
t4d  8.23
mm
t4t  1.982 mm
tu  8.23
4
m
mm
Thickness of lower course:
Ratio:
tL  t3
tL
K 
K  1.069
tu K  (K  1)
C 
1  K1.5
C  0.034
Distance of the variable design point from the bottom of the course: (x) x1  0.61  ( Ri  1000  tu)  320  C  H4
x1  203.091
x2  1000  C  H4
x2  219.979
x3  1.22  ( Ri  1000  tu)
x3  265.396
 x1  x   x2  min ( x )  203.091  x3   
xe  min ( x ) xe
 
4.9  Di   H4  t4d1 
 
t4t1 
 t4d1     t4t1 
t4  8.265
max ( t)  8.265
 CA
Sd 4.9  Di   H4 
t 
 G 
1000 
xe
t4d1  8.265 mm
 
1000 
St
t4a  max ( t)
t4t1  2.013
mm
t4a  8.265
mm
mm
e) The fifth course thickness (t5): Ratio for the lower course:
ratio 
h0  1000
ratio  6.881
( Ri  1000  t4) Calculation of t5a:
H5  H4  h0
First trial for fourth course:
t5d 
t5t 
t 
 t5d     t5t 
max ( t)  7.691
Thickness of lower course:
tL  t4
H5  5
4.9  Di  ( H5  0.3)  G Sd
 CA
4.9  Di  ( H5  0.3)
t5d  7.691 mm
t5t  1.503 mm
St
tu  max ( t)
tu  7.691
Ratio:
K 
C 
Distance of the variable design point from the bottom of the course: (x)
5
m
tL
mm
K  1.075
tu K  (K  1)
1  K1.5
C  0.037
x1  0.61  ( Ri  1000  tu)  320  C  H5
x1  186.872
x2  1000  C  H5
x2  183.117
x3  1.22  ( Ri  1000  tu)
x3  256.549
 x1  x   x2  min ( x )  183.117  x3   
xe  min ( x )
 
4.9  Di   H5  t5d1 
 
t5t1 
 t5d1     t5t1 
t5  7.733
max ( t)  7.733
 G 
Sd 4.9  Di   H5 
t 
xe
1000 
 CA
t5d1  7.733 mm
xe
  1000 
St
t5a  max ( t)
t5t1  1.54
mm
t5a  7.733
mm
mm
f) The sixth course thickness (t6): Ratio for the lower course:
ratio 
h0  1000
ratio  7.114
( Ri  1000  t5) Calculation of t6a:
H6  H5  h0
First trial for fourth course:
t6d 
t6t 
t 
 t6d     t6t 
max ( t)  7.151
Thickness of lower course:
tL  t5
H6  3.5
4.9  Di  ( H6  0.3)  G Sd
 CA
4.9  Di  ( H6  0.3)
t6d  7.151 mm
t6t  1.023 mm
St
tu  max ( t)
tu  7.151
Ratio:
K 
C 
tL
mm
K  1.081
tu
K  (K  1)
1  K1.5
Distance of the variable design point from the bottom of the course: (x) x1  0.61  ( Ri  1000  tu)  320  C  H6
x1  168.278
x2  1000  C  H6
x2  139.326
x3  1.22  ( Ri  1000  tu)
x3  247.387
6
m
C  0.04
 x1  x   x2  min ( x )  139.326  x3   
xe  min ( x )
 
4.9  Di   H6  t6d1 
Sd
 
4.9  Di   H6  t6t1  t 
 t6d1     t6t1 
t6  7.209
max ( t)  7.209
xe
 G  1000   CA t6d1  7.209 mm xe
 
1000 
St
t6a  max ( t)
t6t1  1.074
mm
t6a  7.209
mm
mm
g) The seventh course thickness (t7): Ratio for the lower course:
h0  1000
ratio 
ratio  7.368
( Ri  1000  t6) Calculation of t7a:
H7  H6  h0
First trial for fourth course:
t7d 
t7t 
t 
 t7d     t7t 
max ( t)  6.611
Thickness of lower course:
H7  2
4.9  Di  ( H7  0.3)  G Sd
 CA
t7d  6.611 mm
4.9  Di  ( H7  0.3)
t7t  0.544 mm
St
tu  max ( t)
tL  t6
tu  6.611
Ratio:
m
K 
tL
K  1.09
tu
C 
mm
K  (K  1)
1  K  1.5
C  0.044
Distance of the variable design point from the bottom of the course: (x) x1  0.61  ( Ri  1000  tu)  320  C  H7
x1  147.168
x2  1000  C  H7
x2  88.227
x3  1.22  ( Ri  1000  tu)
x3  237.871
 x1  x   x2  min ( x )  88.227  x3   
xe  min ( x )
 
4.9  Di   H7  t7d1 
Sd
7
xe
 G  1000   CA t7d1  6.688 mm
 
4.9  Di   H7  t7t1  t 
 t7d1     t7t1 
t7  6.688
max ( t)  6.688
xe
  1000 
St
t7a  max ( t)
t7t1  0.611
mm
t7a  6.688
mm
mm
h) The eighth course thickness (t8): Ratio for the lower course:
h0  1000
ratio 
ratio  7.649
( Ri  1000  t7) Calculation of t8a:
H8  H7  h0
First trial for fourth course:
t8d 
t8t 
t 
 t8d     t8t 
max ( t)  6.072
Thickness of lower course:
H8  0.5
4.9  Di  ( H8  0.3)  G Sd
 CA
t8d  6.072 mm
4.9  Di  ( H8  0.3)
t8t  0.064 mm
St
tu  max ( t)
tu  6.072
Ratio:
tL  t7
m
K 
tL
K  1.101
tu
C 
mm
K  (K  1)
1  K1.5
C  0.049
Distance of the variable design point from the bottom of the course: (x) x1  0.61  ( Ri  1000  tu)  320  C  H8
x1  121.877
x2  1000  C  H8
x2  24.68
x3  1.22  ( Ri  1000  tu)
x3  227.959
 x1  x   x2  min ( x )  24.68  x3   
xe  min ( x )
 
4.9  Di   H8  t8d1 
 
t8t1 
 t8d1     t8t1 
max ( t)  6.171
 G 
1000 
Sd 4.9  Di   H8 
t 
xe
St
t8a  max ( t)
8
xe
 CA
t8d1  6.171 mm
 
1000 
t8t1  0.152
mm
t8a  6.171
mm
t8  6.171
mm
3) THICKNESSES OF ALL SHELL COURSES: Minimum shell thickness: According to API 650 Section 5.6.1.1. minimum shell thickness can not be less than this values: Tank Diameter (m): Di
Di  15
15  Di  36
36  Di  60
5
6
8
Plate Thickness (mm): t Di  11.5
60  Di 10
m
tmin  5
Selected Thicness of Shell Courses: Number of Shell Courses:
nsh  8
i  1  nsh
Course No
Thickness (mm)
Selected Thickness (mm)
Course Height (m)
1
t1  9.929
th1  12
h1  h0
h1  1.5
2
t2  9.371
th2  12
h2  h0
h2  1.5
3
t3  8.797
th3  10
h3  h0
h3  1.5
4
t4  8.265
th4  10
h4  h0
h4  1.5
5
t5  7.733
th5  8
h5  h0
h5  1.5
6
t6  7.209
th6  8
h6  h0
h6  1.5
7
t7  6.688
th7  8
h7  h0
h7  1.5
8
t8  6.171
th8  8
h8  H8
h8  0.5
Mid Elevations of Shell Courses: Course No
Mid Elevations of Shell Courses h1
1
hm1 
2
hm2  h1 
3
hm3  hm2 
4
hm4  hm3 
5
hm5  hm4 
6
hm6  hm5 
7
hm7  hm6 
8
hm8  hm7 
Mid Elevations (m) hm1  0.75
2 h2
hm2  2.25
2 h2 2 h3 2 h4 2 h5 2 h6 2 h7 2






h3
hm3  3.75
2 h4
hm4  5.25
2 h5
hm5  6.75
2 h6
hm6  8.25
2 h7
hm7  9.75
2 h8
hm8  10.75
2
9
mm
 hi thi Average Thickness of Tank Shell (mm):
i
tav 
tav  9.636

mm
hi
i 4
 hi thi
Wsh  Di    7.85 
Weight of Shell Courses (kg):
Wsh  3.006  10
i
 hi thi hmi Center of Gravity of Shell Courses (m):
i
Hs 
Hs  4.991

hi  thi
i
C) BOTTOM PLATES td  CA
Product Stress (MPa):
PS 
Hydrostatic Test Stress (MPa):
HTS 
Stress in First Shell Course (MPa):
th1  CA tt th1
 Sd
PS  95.795
 St
MPa
HTS  47.898 MPa
  max ( PS  HTS)
  95.795
MPa
According to API 650 Table 5.1 Annular Bottom Plate Thickness (tb): Plate Thickness of First Shell Course, t (mm)
tb  6
Stress in First Shell Course,  (MPa)   190
  210
  230
  250
t  19
6
6
7
19  t  25
6
7
10
11
25  t  32
6
9
12
14
32  t  40
8
11
14
17
40  t  45
9
13
16
19
9
mm Selected Annular Bottom Plate Thickness (including Corrosion Allowance):
tbs  12 mm
Selected Bottom Plate Thickness:
tbs  8
If annular plates are used, minimum radial width of annular plates:
w 
215  tbs ( Hliq  G)
D) TOP AND INTERMEDIATE WIND GIRDERS 1) TOP WIND GIRDER:
10
mm
w  530.804 mm
2
Required minimum section modulus (cm3):
Z 
Di  H 17
 Vw    190 
2

3
Z  39.815
cm
H1  94.477
m
Profile UNP100 can be selected with section Z = 41.2 cm3.
2) INTERMEDIATE WIND GIRDER: The top shell course plate thickness:
t  8
The maximum height of the unstiffened shell :
H1  9.47  t 
mm
 t    Di 
3
 190    Vw 
2

Vertical distance between the intermediate wind girder and top wind girder H1:
H1  94.477
m
If the height of the transformed shell, Wtr, is greater than the maximum height H1, an intermediate wind girder is required.
H1  94.477
m

 Wtr  8.806
m
The intermediate wind girder is not required.
E) ROOF PLATES Loads Dead Load (the weight of the roof):
DL = t x (7.85) x 0.01
kPa
Design External Pressure:
Pe  0.25
kPa
Roof Live Load:
LR  Lr  0.01
LR  2.5
kPa
Snow Load:
S  Sn  0.01
S1
kPa
Self supporting cone roof Self supporting cone roofs should conform to the following requirements: Angle of the cone roof elements to the horizontal (degree):
9.5    37
Assume an angle for plate thickness calculation:
  18
Dead Load (with plate thickness assumption):
DL  12  ( 7.85)  0.01
DL  0.942
kPa
1) DL + (Lr or S) + 0.4Pe
T1  DL  LR  0.4  Pe
T1  3.542
kPa
2) DL + Pe + 0.4(Lr or S)
T2  DL  Pe  0.4  LR
T2  2.192
kPa
deg
deg
Greater of load combinations:
11
T  max ( T1  T2)
Minimum roof plate thickness:
trmin 
T  3.542
Di
    4.8  sin    180 

T 2.2
kPa
trmin  11.838 mm
2
Calculated minimum roof plate thickness should not be greater than 13 mm according to API 650. Therefore supported cone roof will not be considered. Selected plate thickness of the supported cone roof:
tr  12
mm
F) OVERTURNING STABILITY UNDER WINDLOAD The wind pressure on projected areas of cylindrical surfaces for 100 miles/h wind velocity: fw  0.86
kPa 2
 Vw   Di  H  1000  9.81  190 
The wind load acting on tank:
Fw  fw  
Overturning moment from wind load:
Mw  Fw 
3
Fw  5.16  10
H
kg 4
kg  m
3
kg
Mw  2.838  10
2
Weight of tank: Weight of Bottom Plates:
Wb 
 Di  0.001 th1  0.52   4
 tbs  ( 7.85) Wb  7.117  10
4
Weight of Shell Courses:
Wsh  3.006  10
kg
2
( Di  0.5)  
Weight of Roof (with stiffeners):
Wro 
Resisting weight:
Wres  Wsh  Wro
Overturning moment from wind load:
Mw  2.838  10
4
4
4
 ( tr  1)  ( 7.85)
kg  m
Wro  1.154  10
kg
4
Wres  4.16  10

 Wres  Di   1.595  105  3  2  2

kg
kg  m
There is no overturning due to wind load. Therefore anchor bolts are not required.
G) SEISMIC DESIGN OF TANK (for MCE - Maximum Considered Earthquake) Reference Standard:
API Standard 650, ASCE 7
SEISMIC DESIGN FACTORS Seismic Use Group: Effective Ground Acceleration Coefficient: (for Seismic Zone 1 according to TEC 2007)
SUG  3 Seismic Zone
A0  0.4
Acceleration Coefficient
12
1 2 3 4     0.4 0.3 0.2 0.1 
Importance Factor: (API 650 Table E-5)
I  1.5
Response Modification Factor - impulsive: (API 650 Table E-4)
Ri  4
(mechanically anchored)
Response Modification Factor - convective: (API 650 Table E-4)
Rc  2
(mechanically anchored)
        1.0 1.25 1.5 
Seismic Use Group Importance Factor
SITE GROUND MOTION Acceleration Parameters For sites not addressed by ASCE methods, the peak ground acceleration method shall be used. The peak ground acceleration parameter will be calculated by using the effective ground acceleration coefficient in TE C 2007. With a conservative approach, the effective ground acceleration coefficient in TEC 2007 will be multiplied by two. Peak Ground Acceleration Parameter:
Sp  A0  2
Sp  0.8
Mapped MCE, 5% damped, spectral response acceleration parameter at short periods (0.2 sec), %g
Ss  2.5  Sp
Ss  2
Mapped MCE, 5 percent damped, spectral response acceleration parameter at a period of 1 sec, %g
S1  1.25  Sp
S1  1
Modifications for Site Soil Conditions Site Class based on the Site Soil Properties:
E
Acceleration Based Site Coefficient - at 0.2 sec period: (API 650 Table E-1)
Fa  0.9
Velocity Based Site Coefficient - at 1.0 sec period: (API 650 Table E-1
Fv  2.4
Adjusted Maximum Considered Earthquake (MCE) Spectral Response Acceleration Parameters: (According to ASCE 7-05 Section 11.4.3) For short periods:
Sms  Ss  Fa
Sms  1.8
For 1 second:
Sm1  S1  Fv
Sm1  2.4
Design Spectral Response Acceleration Parameters: (According to ASCE 7-05 Section 11.4.4) For short periods:
Sds 
For 1 second:
Sd1 
2 3 2 3
 Sms
Sds  1.2
 Sm1
Sd1  1.6
Design Response Spectrum (DRS): (According to ASCE 7-05 Section 11.4.5) Characteristic Periods:
T0  0.2 
Sd1 Sds
13
T0  0.267 s
Sd1
Ts 
Ts  1.333 s
Sds
Regional Dependent Transition Period for Longer Period Ground Motion: TL  4
(Regions outside the USA)
s
Natural Vibration Period (s):
T  0.01  0.015  6
Design Responce Spectrum
When
T  T0
Sa ( T)  Sds   0.4  0.6 
When
T0  T  Ts
Sa ( T)  Sds
When
Ts  T  TL
Sa ( T) 
TL  T
Sa ( T)   Sd1 
When
 
 
Sd1 T

TL 

T
2

Spectral Response Acceleration
1.2
1
0.8
Sa ( T) 0.6
0.4
0.2
0
1
2
3
4
T Period (s)
STRUCTURAL PERIOD OF VIBRATION Impulsive Natural Period Density of Fluid:
  1  10
3
kg m
Height to Diameter Ratio:
Hliq Di
 0.913
Coefficient Ci: (API 650 Figure E-1)
Ci  7.2
Elastic Modulus of Tank Material (MPa):
E  2.1  10
5
14
3
5
6
T
  T0 
Equivalent Uniform Thickness of Tank Shell: (mm) (Average thickness)
tu  tav
Impulsive Natural Period (s): (API 650 Eq. E.4.5.1)
Ti 
1

Ci  Hliq
2000

tu

tu  9.636
mm
Ti  0.127
s
E
Di
Convective (Sloshing) Period Sloshing Period Coefficient:
0.578
Ks 
Ks  0.579
 3.68  Hliq 
tanh 

The First Mode Sloshing Wave Period (s ): (API 650 Eq. E.4.5.2)
Di
 
Tc  1.8  Ks  Di
Tc  3.532
s
DESIGN SPECTRAL RESPONSE ACCELERATIONS Impulsive Spectral Acceleration Parameter
 I   Ri 
Ai  Sds  
Ai  0.45
%g
Convective Spectral Acceleration Parameter Coefficient to adjust the spectral acceleration from 5% - 0.5% damping:
K  1.5
 1   I     Tc   Ri 
When
Tc  TL
Ac  K  Sd1  
When
Tc  TL
Ac  K  Sd1  
 TL    I    2  Rc  Tc    Ac  0.255
%g
DESIGN LOADS Effective Weight of Product Diameter to Height Ratio:
Di Hliq
 1.095 2
Total weight of tank contents (N):
Wp 
  Di 4
 Hliq    9.81
15
Wp  1.07  10
7
N
Effective Impulsive Weight (N): (API 650 Eq. E.6.1.1)
Selection of Effective Impulsive Weight Equation:
When
Di Hliq
When
 
tanh  0.866 
Di Hliq
Wi 
 1.333
0.866 
  Hliq   Wp
Di
Hliq
 
 1.333
Di
Wi   1.0  0.218 
Di
  Wp 
Hliq 
6
N
Wi  8.144  10
Effective Convective Weight (N): (API 650 Eq. E.6.1.1)
Wc  0.230 
Di Hliq
 3.67  Hliq   Wp   Di 
 tanh 
6
Wc  2.689  10
N
Center of Action for Ringwall Overturning Moment The ringwall overturning moment is the portion of the total overturning moment that acts at the base of the tank shell perimeter. This moment is used to determine loads on a ringwall foundation, the tank anchorage forces, and to check the longitudinal shell compression.
Height of the Lateral Seismic Force: Applied to Wi (m) (API 650 Eq. E.6.1.2.1)
Selection of Height Equation:
When
Di Hliq
When
Di Hliq
 1.333
 1.333
Xi  0.375  Hliq
 
Xi   0.5  0.094 
Di
  Hliq  Hliq  m
Xi  4.169
  3.67  Hliq   1  cosh    Di    Hliq Xc   1.0    3.67  Hliq   sinh  3.67  Hliq         Di   Di  
Height of the Lateral Seismic Force: Applied to Wc (m) (API 650 Eq. E.6.1.2.1)
Xc  7.579
m
Center of Action for Slab Overturning Moment The slab overturning moment is the total overturning moment acting across the entire tank base cross section. This overturning moment is used to design slab and pile cap foundation (if any). Height of the Lateral Seismic Force: Applied to Wi (m) (API 650 Eq. E.6.1.2.2) When
Selection of Height Equation:
Di Hliq
 1.333
  0.866  Di   Hliq Xis  0.375   1.0  1.333    1.0   Hliq    Di     tanh  0.866  Hliq    16
When
Di Hliq
 
 1.333
Xis   0.5  0.06 
Di
  Hliq  Hliq  m
Xis  5.94
Height of the Lateral Seismic Force: Applied to Wc (m) (API 650 Eq. E.6.1.2.2)
 Xcs   1.0   
 3.67  Hliq   1.937    Di    Hliq 3.67  Hliq 3.67  Hliq    sinh        Di   Di   cosh 
Xcs  7.785
m
Overturning Moment The seismic overturning moment at the base of the tank is evaluated as the SRSS summation of the impulsive and convective components multiplied by the respective moment arms to the center of action of these forces. 5
Total weight of tank shell (N):
Ws  Wsh  9.81
Ws  2.949  10
Height of Shell's Center of Gravity (m)
Xs  Hs
Xs  4.991
Weight of Roof (N):
Wr  Wro  9.81
Wr  1.132  10
Height of Roof's Center of Gravity (m)
Xr  H 
Ringwall Overturning Moment (Nm): (API 650 Eq. E.6.1.5) for global evaluations
Mrw 
Slab Overturning Moment (Nm): (API 650 Eq. E.6.1.5)
Ms 
m 5
 Di  tan         3 2  180   1

Xr  11.623
2
[ Ai  ( Wi  Xi  Ws  Xs  Wr  Xr) ]  [ Ac  ( Wc  Xc) ]
2
7
2
[ Ai  ( Wi  Xis  Ws  Xs  Wr  Xr) ]  [ Ac  ( Wc  Xcs ) ] 7
Vertical Seismic Effects The vertical seismic acceleration parameter Av is defined as 0.14*Sds in API 650 and as 0.2*Sds in ASCE 7 method. Conservatively 0.2*Sds is choosen in calculations. Av  0.24
Dynamic Liquid Hoop Forces Dynamic hoop tensile stress due to seismic motion of the liquid is calculated by the following formulas. Calculation for the 1.st shell course: Distance from liquid surface to analysis point (m):
Y  Hliq
17
Y  10.5 m
Nm
2
Ms  2.363  10
Av  0.2  Sds
N
m
Mrw  1.733  10
Vertical Seismic Acceleration Coeff. (%g):
N
Nm
Impulsive Hoop Membrane Force in Tank Shell (N/mm): (API 650 Eq. E.6.1.4)
When
Di Hliq
When
Di Hliq
When
Di Hliq
Selection of Force Equation:
2  Y  Y    tanh  0.866  Di   0.5      Hliq   Hliq  Hliq   
Ni  8.48  Ai  G  Di  Hliq  
 1.333
 1.333
and
Y  0.75  Di
2  Y Y     Ni  5.22  Ai  G  Di   0.5      0.75  Di  0.75  Di  
 1.333
and
Y  0.75  Di
Ni  2.6  Ai  G  Di
2
2
N
Ni  154.732
mm
Convective Hoop Membrane Force in Tank Shell (N/mm): (API 650 Eq. E.6.1.4)
 
2
1.85  Ac  G  Di  cosh  3.68  Nc 
( Hliq  Y)  Di
 3.68  Hliq    Di 
 
N
Nc  4.325
mm
cosh 
Liquid Hydrostatic Membrane Force in Tank Shell (N/mm): Y  G  Di
Nh 
2
Thickness of the shell ring under consideration (mm):
Total Combined Hoop Stress (MPa):
t 
ts  th1  CA 2
Nh 
N
Nh  592.279
 9.81
ts  6
2
Ni  Nc  ( Av  Nh) ts
mm
mm
2
t  133.74
MPa
The maximum allowable hoop tension membrane stress for the combination of hydrostatic and dynamic membrane hoop effects should be less than allowable design stress of the shell increased by 33%. Allowable Stress for MCE seismic design:
Comparison:
t  133.74
Hoop Stress Ratio:
all  1.33  Sd
MPa

all  208.367
SRhs 
t all
all  208.367
MPa
SRhs  0.642
OK
MPa
Calculation for the 2.nd shell course: Distance from liquid surface to analysis point (m):
Y  Hliq  h0
18
Y9
m
Impulsive Hoop Membrane Force in Tank Shell (N/mm): (API 650 Eq. E.6.1.4)
When
Di Hliq
When
Di Hliq
When
Di Hliq
Selection of Force Equation:
2  Y  Y    tanh  0.866  Di   0.5      Hliq   Hliq  Hliq   
Ni  8.48  Ai  G  Di  Hliq  
 1.333
 1.333
and
 1.333
and
2

Y  0.75  Di
Ni  5.22  Ai  G  Di  
Y  0.75  Di
Ni  2.6  Ai  G  Di
Y
 0.75  Di
2  Y     0.75  Di  
 0.5  
2
N
Ni  154.732
mm
Convective Hoop Membrane Force in Tank Shell (N/mm): (API 650 Eq. E.6.1.4)
 
2
1.85  Ac  G  Di  cosh  3.68  Nc 
( Hliq  Y)  Di
 3.68  Hliq    Di 
 
N
Nc  4.833
mm
cosh 
Liquid Hydrostatic Membrane Force in Tank Shell (N/mm): Y  G  Di
Nh 
2
Thickness of the shell ring under consideration (mm):
Total Combined Hoop Stress (MPa):
t 
ts  th2  CA 2
Nh 
N
Nh  507.668
 9.81
ts  6
2
Ni  Nc  ( Av  Nh) ts
mm
mm
2
t  117.445
MPa
The maximum allowable hoop tension membrane stress for the combination of hydrostatic and dynamic membrane hoop effects should be less than allowable design stress of the shell increased by 33%. Allowable Stress for MCE seismic design:
Comparison:
t  117.445
Hoop Stress Ratio:
all  1.33  Sd
MPa

all  208.367
SRhs 
t all
all  208.367
MPa
SRhs  0.564
OK
MPa
Calculation for the 3.rd shell course: Distance from liquid surface to analysis point (m):
Y  Hliq  2  h0
19
Y  7.5
m
Impulsive Hoop Membrane Force in Tank Shell (N/mm): (API 650 Eq. E.6.1.4)
When
Di Hliq
When
Di Hliq
When
Di Hliq
Selection of Force Equation:
2  Y Y   Di    Ni  8.48  Ai  G  Di  Hliq    0.5      tanh  0.866   Hliq   Hliq  Hliq   
 1.333
 1.333
and
 1.333
and
2

Y  0.75  Di
Ni  5.22  Ai  G  Di  
Y  0.75  Di
Ni  2.6  Ai  G  Di
Y
 0.75  Di
2  Y     0.75  Di  
 0.5  
2
N
Ni  152.685
mm
Convective Hoop Membrane Force in Tank Shell (N/mm): (API 650 Eq. E.6.1.4)
 
2
1.85  Ac  G  Di  cosh  3.68  Nc 
( Hliq  Y)  Di
 3.68  Hliq    Di 
 
N
Nc  6.476
mm
cosh 
Liquid Hydrostatic Membrane Force in Tank Shell (N/mm): Y  G  Di
Nh 
2
Thickness of the shell ring under consideration (mm):
Total Combined Hoop Stress (MPa):
t 
ts  th3  CA 2
Nh 
N
Nh  423.056
 9.81
ts  4
2
Ni  Nc  ( Av  Nh) ts
mm
mm
2
MPa
t  151.633
The maximum allowable hoop tension membrane stress for the combination of hydrostatic and dynamic membrane hoop effects should be less than allowable design stress of the shell increased by 33%. Allowable Stress for MCE seismic design:
Comparison:
t  151.633
Hoop Stress Ratio:
MPa
all  1.33  Sd

all  208.367
SRhs 
t all
all  208.367
MPa
SRhs  0.728
OK
MPa
FOUNDATION LOADS Dead Load per Unit Length (N/m): (Shell and Roof)
DL 
Ws  Wr
20
Di  
DL  1.13  10
4
N m
2
Lr  9.81 
( Di  0.5)   4
Live Load per Unit Length (N/m): (Live Load on Roof)
LL 
Total Dead Weight (N): (Shell, Roof and Liquid)
Wt  Ws  Wr  Wp
Total Load per Unit Area during Operation (N/m2): (Shell, Roof and Liquid)
Wo 
LL  7.677  10
Di  
N
3
m 7
Wt  1.111  10
Wt
N N
5
Wo  1.069  10
 Di2       4 
m
2
Seismic loads: The equivalent lateral seismic forces are calculated by considering the effective mass and dynamic liquid pressures. The seismic base shear is evaluated as the SRSS summation of the impulsive and convective components.
Base Shear due to Seismic Load (N):
Seq 
2
[ Ai  ( Wi  Ws  Wr) ]  ( Ac  Wc )
2 6
N
7
Seq  3.909  10 Ringwall Overturning Moment due to Seismic Load (Nm):
Mrw  1.733  10
Nm
Slab Overturning Moment due to Seismic Load (Nm):
Ms  2.363  10
7
Nm
4
Vertical Seismic Force (N): (Shell and Roof)
Fvs  Av  ( Ws  Wr)
Vertical Seismic Force per Unit Length (N/m): (Shel and Roof)
VSF 
Total Vertical Seismic Force (N): (Shell, Roof and Liquid)
Fvst  Av  Wt
Fvst  2.666  10
N
Total Vertical Load (N): (Total Vertical Seismic and Total Dead W.)
Fvt  Fvst  Wt
Fvt  1.377  10
7
N
Fvs ( Di   )
Fvs  9.795  10
3
VSF  2.711  10
6
N
N m
ANCHORAGE LOADS Resistance to the overturning (ringwall) moment at the base of the shell is provided by mechanical anchorage devices (anchor bolts). The resisting weight of the liquid is neglected in the calculation of the uplift load on the anchors. The anchors are sized to provide at least the minimum anchorage resistance calculated as follows: Distributed Compression Force due to Roof (N/m): wr 
Distributed Compression Force due to Shell (N/m): ws  Total Distributed Compression Force (N/m):
Wr Di   Ws Di  
wt  wr  ws
Vertical Seismic Acceleration (g's):
Minimum Anchorage Resistance (N/m): (API 650 Eq. E.6.2.1.2)
3
wr  3.134  10
N m
3
ws  8.163  10 4
wt  1.13  10
N m N m
Av  0.24
wab 
 1.273  Mrw  wt  ( 1  0.4  Av)  wab  1.566  105   2  Di  21
N m
ANCHOR BOLT VERIFICATION (LRFD CRITERION) Due to the adoption of shear keys, anchor bolts are subjected to traction loads only. Max applied tractions are evaluated from above calculated anchorage loads and anchor bolt capacity is determined according to ACI 318-05 Appendix D Requirements according to API 650 E.7.1.2:
- Minimum 6 anchors should be provided. - The spacing between anchors should be less than 3 m. - Anchors should have a minimum diameter of 25 mm.
Number of Equally Spaced Anchors Around the Tank Circumference:
nb  24
Distance from bolt center to shell (mm):
Dbs  92
Bolt Circle Diameter (m):
Db  Di  2 
Bolt Spacing Angle:
 
Bolt Spacing (m):
Dbs  th1 1000
360
Db  11.708
Db  
m
degrees
  15
nb
Bsp 
mm
Bsp  1.533
nb
Concrete strength (MPa):
flc  25
m
MPa
Anchor Bolt Characteristics Cast in headed stud anchor Nominal Diameter of Anchor (mm):
db  48
Threaded Area of Bolt (mm2):
Ath 
mm 2
0.75  db   4
3
Ath  1.357  10
Anchor bolt material: S275JR (St44-2) or equivalent Ultimate Tensile Strenght (MPa):
Sub  430
Yield Strenght (MPa):
Syb  275
Maximum traction As LRFD design method is used for anchor bolt verification, following load combination will be adopted U = 0.9 x D + E Bsp  1000
Bolt Spacing to Diameter ratio
db Max traction on single bolt (kN)
Tb 
wab  Bsp 1000
22
Tb  240
 31.929
kN
2
mm
Bolts tension capacity (according to clause D.5) Reduction Factor (according to clause D.4.4.a)
t  0.75
Additional seismic strength reduction factor
s  0.75
Design tensile strength (ACI 318 D.5.1.2) (MPa)
futa  min ( Sub  860  1.9  Syb)
Nominal bolt strength in tension (kN)
Nsa  Ath  min ( futa  860)  10
Nsa  583.582
Bolt tension capacity (kN)
Nsa  s  t  Nsa
Nsa  328.265 kN
Bolt tension demand (kN)
Nua  Tb
Nua  240
Comparison:
futa  430
3
Nsa  328.265 kN
Nua  240

Bolt usage ratio:
kN
kN
kN
Nua
FUt 
MPa
OK
FUt  0.731
Nsa
Pullout strength in tension (according to clause D.5.3) Modification Factor:
cp  1.4
Reduction Factor:
p  0.75
Bearing area at head of anchor bolt (mm2):
 db2     Abrg  160    4 
Pull out strength in tension of an headed bolt (kN):
Np  8  Abrg  flc  10
Nominal pull out strength (kN):
Npn  Np  cp
Npn  6.661  10 kN
Design pull out strength (kN):
Np  p  s  Npn
Np  3.747  10 kN
Comparison:
3
Np  3.747  10 kN
2

Nsa  328.265
2
4
Abrg  2.379  10 mm
3
3
Np  4.758  kN 10
3
3
OK
kN
Bolt adequacy for uplift loads According to Table 3.21 of API 650 Dead load of shell minus any corrosion allowance and any dead load including roof plate acting on the shell minus any corrosion allowance (N):
 
 tav  CA   Wro  tr  CA    9.81     tav   tr  
W2   Wsh  
Seismic uplift loads (N):
U  4 
Ms Di
5
N
7
Nm
W2  1.679  10
 W2  ( 1  0.4  Av)
As Ms is used for a verification based on ASD criterion a new evaluation can be made as follows: Slab Overturning Moment (Nm): Ms 
2
[ Ai  0.7  ( Wi  Xis  Ws  Xs  Wr  Xr) ]  [ Ac  ( Wc  Xcs ) ]
23
2
Ms  1.698  10
Levhali
Seismic uplift loads (N):
Uplift load per anchor (N):
Uasd  4 
tb 
Ms Di
Uasd
al  0.8  Syb
Average induced stress (MPa):
ub 
5
6
Nm
N
MPa
al  220
tb
ub  176.627 MPa
Ath ub
SRu 
Uasd  5.753  10
tb  2.397  10
nb
Allowable Ancher Bolt Stress (MPa): according to Table 3.21 of API 650
Uplift stress ratio
 W2  ( 1  0.4  Av)
OK
SRu  0.803
al
SHEAR KEY VERIFICATION (ASD CRITERION) Shear keys characteristics
Depth of shear key (mm):
dp  100 mm
Width of shear key (mm):
wsk  100 mm
Thickness of shear key (mm):
tsk  20
Number:
nsk  24
Material:
S275 JRG2
Plate minimum yield stress (MPa)
ysk  275
mm
Verification procedure The shear keys are verified for the bending moment and shear stresses in the plates produced by the concrete bearing reaction in the contact area, assumed as uniformly distributed. Two verifications are performed: A global verification at the shear key connection to the annular plate A local verification at the connection of the two vertical plates forming the shear key. 6
Total Base Shear due to seismic load (N):
0.7  Seq  2.736  10
Shear for each shear key (N):
Ssk 
Concrete compression (MPa):
fc 
0.7  Seq nsk Ssk
wsk  dp
Concrete allowable compression (MPa):
fcall  0.65  0.85  flc
Concrete compression ratio
SRck 
fc fcall
N 5
Ssk  1.14  10
fc  11.402 MPa
fcall  13.813
MPa OK
SRck  0.825
Global verification Shear area (mm2):
Assk  tsk  wsk
24
Assk  2  10
3
2
mm
Shear stress (MPa):
 
Ssk
Shear key allowable bending stress (MPa):
allsk 
Shear key allowable shear stress (MPa):
allsk 
MPa
  57.009
Assk 2 3
allsk  183.333 MPa
 ysk
allsk
MPa
allsk  129.636
2 Shear stress ratio:

SR 
dp
Arm of the global concrete reaction (mm):
afc 
Global bending moment (Nmm):
Mgk  Ssk  afc
Global inertia moment (mm4):
Igk 
afc  50
2
1
mm 6
Mgk  5.701  10
3
12
OK
SR  0.44
allsk
  ( wsk)  tsk  ( wsk  tsk)  tsk
3
 4
6
Igk  1.72  10 Global section modulus (mm3):
Shear key global bending stress (MPa):
Shear key global bending stress ratio.
Igk
Wgk 
gk 
wsk
mm
3
4
Wgk  3.44  10
2
Mgk
mm
gk  165.723 MPa
Wgk
SRgk 
Nmm
gk
OK
SRgk  0.904
allsk
Local verification Conservatively we consider a simple cantilever beam of unit width
Shear key overhang (mm):
esk 
wsk  tsk
Bending moment due to concrete reaction (Nmm/mm): Mlk  fc  esk  1
Shear key section modulus per unit depth (mm3/mm): Wlk 
Shear key bending stress (MPa):
Shear key local bending stress ratio:
esk  40
2
lk 
6
2
Mlk Wlk
SRlk 
25
 tsk
esk
lk allsk
2
mm 3 N  mm
Mlk  9.121  10
mm 3
Wlk  66.667
lk  136.821
SRlk  0.746
mm
mm MPa
OK
MAXIMUM LONGITUDILAN SHELL MEMBRANE COMPRESSION STRESS Shell Compression in Mechanically Anchored Tanks The maximum longitudinal shell compression stress at the bottom of the shell for mechanically anchored tanks is evaluated according to API 650 E.6.2.2.2 Thickness of Bottom Shell Course less CA (mm): tsb  th1  CA

c  wt  ( 1  0.4  Av) 
1.273  Mrw
1
  1000  tsb 
2
Di

tsb  6
mm
MPa
c  29.865
Allowable Longitudinal Shell Membrane Compression Stress The seismic allowable stress Fc is evaluated according to API 650 E.6.2.2.3 2
The Parameter:
Para 
G  Hliq  Di
Para  38.573
2
tsb The Allowable Compression Stress (MPa): (API 650 Eq. E.6.2.2.3)
Selection of Stress Equation: 2
G  Hliq  Di
When
 44
2
Fc 
tsb
83  tsb Di
2
G  Hliq  Di
When
2
 44
tsb
Fc 
83  tsb 2.5  Di
 7.5  ( G  Hliq)  0.5  Sy Fc  41.625
Comparison:
c  29.865
Compression Stress Ratio:
Rcs 
MPa

c
Fc  41.625
MPa
MPa
OK
Rcs  0.717
Fc
ANCHOR CHAIR VERIFICATION (ASD CRITERION) The tank is anchored to the foundation by mean of anchor bolts and chairs. The verification of various components of the chair (top plate and gussets) is performed according to procedure 3-14 'Design of base details for vertical vessels' of Pressure Vessel Design Manual by D. Moss. Used symbols are shown in next figure. Input data Material S235 JRG2 Plate minimum yield stress (MPa):
y  Sy
y  235
Plate allowable stress (MPa):
ball  Sd
ball  156.667 MPa
Bolt eccentricity (mm):
a  Dbs
a  92
26
MPa
mm
Height from top of annular plate (mm):
h  250 mm
Distance between gussets (mm):
b  100 mm
Thickness of bottom shell (mm):
ts  th1
Bolt diameter (mm):
ts  12
mm
db  48
mm
Bolt hole in the top plate (mm)
dbh  db  24
Top plate thickness (mm):
tc  30
Top plate width (mm):
A  400 mm
Top plate edge distance from bolt axis (mm):
c  85
Top plate width ouside bolt hole (mm):
e  c 
Thickness of gussets (mm):
tg  25 mm
Bolt pitch (mm):
bp  Bsp  1000
bp  1.533  10
3
mm
Base plate span between chairs (mm):
bs  bp  ( b  2  tg)
bs  1.383  10
3
mm
Number of gussets per chair:
ng  2
Shell reinforcement plate thickness (mm:)
rpt  20 mm
Shell reinforcement plate halfwidth (mm):
rpw  200 mm
dbh  72
mm
mm
mm
dbh
e  49 mm
2
Design loads Bolt traction As ASD design method is used for anchor chair verification, a new evaluation of max bolt traction is done as follows:
Maximum traction on single bolt (N):
Tbc 
 1.273  Mrw  wt  ( 1  0.4  Av  0.7)   bp   1000 2  Db  Tbc  2.305  10
5
N
For additional conservatism we consider the max between the computed traction and the ASD bolt capacity Maximum load considered for the chair verification (N): Tbc max Tbc0.7Nsa1000 Tbc  2.305  10
Maximum compression per unit length (N/m):
C  wt  ( 1  0.4  Av  0.7) 
5
N
1.273  Mrw 2
Di
5
C  1.789  10
27
N m
Annular bottom plate characteristics Selected bottom plate thickness (mm):
tb  tbs
tb  8
Annular plate width (mm):
mm
w  530.804
mm
Top plate verification The top plate is assumed as a beam, with dimensions e x A, with partially fixed ends, and a portion (1/3) of the total anchor bolt force Tbc, distributed along part of the span.
Maximum induced bending stress (MPa):
Tbc
tp 
2
 ( 0.375  b  0.22db)
tp  140.808 MPa
e  tc
Top plate bending stress ratio
SRtp 
tp
OK
SRtp  0.899
ball
Gusset verification Gusset maximum axial compression force (N):
Tbc
Cg 
5
Cg  1.152  10
ng
Gusset width at bottom edge (mm):
wo  15 mm
Gusset mean width (mm):
bg 
( a  c )  wo
bg  96
2
mm
Gusset thickness (mm):
tg  25
Shell reinforcement plate thickness (mm):
rpt  20 mm
Shell reinforcement plate halfwidth (mm):
rpw  200
Section total area (mm2):
Neutral axis distance from midsurface of reinforcement plate (mm):
N
mm
mm 2
3
Ag  bg  tg  rpt  rpw
Ag  6.4  10
 bg  rpt    2  2 na  tg  bg 
na  21.75
Ag
mm
mm
Longitudinal inertia moment (mm4): 3
Il 
tg  bg 12
2
3
 bg  rpt  na  rpw  rpt  rpt  rpw  ( na) 2  2 12 2 
6
 tg  bg  
Transv ersal inertia moment (mm4):
It 
Inertia radius (mm):
rl 
 12 1
Ag
28
3
 bg  tg  rpt  rpw
Il
rt 
Il  7.023  10
It Ag

3
7
It  1.346  10
rl  33.125
mm
rt  45.857
mm
4
mm
4
mm
rmin  min ( rl  rt) Instability Factor:
IF  1
Young's modulus (MPa):
E  210000 MPa
Yield s tress (MPa):
rmin  33.125 mm
y  235
Cc factor:
2 E
Cc 
2  
y
MPa
Cc  132.813
Allowable compression stress (MPa):
cgall 
2   IF  h        rmin   1  2  2  rmin   3 5  h    IF  h   1     3  IF     3 3  8  Cc  rmin   rmin  8  Cc  
Max compression stress (MPa)
Compression stress ratio
cg 
Cg Ag
SRcg 
29
 y
cg cgall
cgall  135.608 MPa
cg  18.008
SRcg  0.133
MPa
OK

Dear All,
We are working on a project where there is are requirements to carry out preliminary design. I need some suggestion regarding wall thickness. As per the API 650, 5.6.1.1, the minimum plate thickness required for 36m diameter tank is 8mm. Now my question is does this 8mm includes corrosion allowance or I have to consider like 8+3 corrosion allowance = 11mm. Please advise. The tank dimensions are 36m dia x 15m height with 3mm corrosion allowance.
Regards