API 650 Tank Design

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m

s Vw Vwm 3.6 Vw129.6 km

h Tank is outside the building.

Design temperature: Td 30 C

Snow load (kg/m2): Sn 100 kg

m2 Live Load on Roof (kg/m2): Lr 250 kg

m2 Seismic Zone :

(Turkis h Earthquake Code)

1

Corrosion allowance: CA 6 mm

Material: ST37-2

Height of courses (m): h0 1.5

Minimum Yield Strenght (MPa): Sy 235

Minimum Tensile Strenght (MPa): Sut 485

The Maximum Allowable Product Design Stress (MPa):

Sd1 2

3Sy

 Sd1156.667 MPa

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 Hliq10.5 m

Discharge pipe level (m): Hd 0 m

Tank usefull volume: V  Di

2



4 (HliqHd)

 V1.091 103 m3

Stored material: Su

Density of stored material:  1000 kg m3

Specific gravity: G 

1000

 G1

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1 Foot method can be used

Design shell thickness ( mm): td 4.9 Di (Hliq0.3)G

Sd  CA

 td9.669 mm

Hydrostatic test shell thickness ( mm): tt 4.9 Di (Hliq0.3) St

 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 6

 Variable Design Point Method can be used.

a) The bottom course thickness (t1) : Design shell thickness (mm):

t1d 1.06 0.0696 Di Hliq Hliq G Sd

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4.9 Hliq DiG Sd

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  CA  t1d9.929 mm

Hydrostatic test shell thickness (in):

t1t 1.06 0.0696 Di Hliq Hliq St

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4.9 Hliq Di St

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  t1t3.496 mm Sd2 2 5Sut  Sd2194 MPa Sd Sd1 Sd2

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 Sd min Sd( ) Sd156.667 Mpa

The Maximum Allowable Hydrostatic Test Stress (MPa): St1 3 4Sy  St1176.25 MPa St2 3 7Sut  St2207.857 MPa St St1 St2

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 St min St( ) St176.25 Mpa

Reference Standard: API Standard 650

12th Edition, 2013

B) SHELL DESIGN

1) 1 FOOT METHOD:

API 650 Section 5.6.3 Di11.5 m  60 m

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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 x x1 x2 x3

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 min x( )126.849 xe min x( ) t2d1 4.9 Di H2 xe 1000 

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 G Sd CA  t2d19.371 mm t2t1 4.9 Di H2 xe 1000 

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 St  t2t12.997 mm t t2d1 t2t1

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 max t( )9.371 t2a max t( ) t2a9.371 mm

t29.371

c) The third course thickness (t3):

Ratio for the lower course: ratio h0 1000 Ri 1000 t2 ( )  ratio6.462 Calculation of t3a: H3 H2h0 H38 m t t1d t1t

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 max t( )9.929 t1 max t( ) t19.929 mm

b) The second course thickness (t2):

Ratio for the bottom course: ratio h0 1000 Ri 1000 t1 

ratio6.278

Calculation of t2a: H1 H H2 H1h0

H29.5 m First trial for second course:

t2d 4.9 Di (Hliq0.3)G Sd  CA  t2d9.669 mm t2t 4.9 Di (Hliq0.3) St  t2t3.261 mm t t2d t2t

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 max t( )9.669 tu max t( ) tu9.669 mm

Thickness of lower course: tL t1 Ratio: K tL tu  K1.027 C K K( 1) 1 K1.5

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mm t3t1 4.9 Di H3 xe 1000 

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 St  t3t12.486 mm t t3d1 t3t1

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 max t( )8.797 t3a max t( ) t3a8.797 mm

t38.797 mm

d) The fourth course thickness (t4):

Ratio for the lower course: ratio h0 1000 Ri 1000 t3

( )

 ratio6.669

Calculation of t4a: H4 H3h0 H46.5 m

First trial for fourth course: t4d 4.9 Di (H40.3)G

Sd  CA  t4d8.23 mm t4t 4.9 Di (H40.3) St  t4t1.982 mm t t4d t4t

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 max t( )8.23 tu max t( ) tu8.23 mm

First trial for third course:

t3d 4.9 Di (H30.3)G Sd  CA  t3d8.77 mm t3t 4.9 Di (H30.3) St  t3t2.462 mm t t3d t3t

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 max t( )8.77 tu max t( ) tu8.77 mm

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 C0.034

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 G Sd CA  t3d18.797

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mm

e) The fifth course thickness (t5):

( )

 ratio6.881

Calculation of t5a: H5 H4h0 H55 m

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 max t( )7.691 tu max t( ) tu7.691 mm

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 C0.037

Distance of the variable design point from the bottom of the course: (x) Thickness of lower course: tL t3 Ratio: K tL

tu  K1.069 C K K( 1) 1 K1.5

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 C0.034

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 St  t4t12.013 mm t t4d1 t4t1

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 max t( )8.265 t4a max t( ) t4a8.265 mm

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H63.5 m

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 max t( )7.151 tu max t( ) tu7.151 mm

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 C0.04

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 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 x x1 x2 x3

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 St  t5t11.54 mm t t5d1 t5t1

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 max t( )7.733 t5a max t( ) t5a7.733 mm

t57.733 mm

f) The sixth course thickness (t6):

( )

 ratio7.114

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t7t 4.9 Di (H70.3) St  t7t0.544 mm t t7d t7t

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 max t( )6.611 tu max t( ) tu6.611 mm

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 C0.044

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 G Sd CA  t7d16.688 mm x x1 x2 x3

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 St  t6t11.074 mm t t6d1 t6t1

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 max t( )7.209 t6a max t( ) t6a7.209 mm

t67.209 mm

g) The seventh course thickness (t7):

( )

 ratio7.368

Calculation of t7a: H7 H6h0 H72 m

Sd  CA

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mm

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 C0.049

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 St  t8t10.152 mm t t8d1 t8t1

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 max t( )6.171 t8a max t( ) t8a6.171 mm

t7t1 4.9 Di H7 xe 1000 

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 St  t7t10.611 mm t t7d1 t7t1

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 max t( )6.688 t7a max t( ) t7a6.688 mm

t76.688 mm

h) The eighth course thickness (t8):

( )

 ratio7.649

Calculation of t8a: H8 H7h0 H80.5 m

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 max t( )6.072 tu max t( ) tu6.072

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Mid Elevations (m) Mid Elevations of Shell Courses

Course No

Mid Elevations of Shell Courses:

h₈0.5 h₈ H8 th₈ 8 t86.171 8 h₇1.5 h₇ h0 th₇ 8 t76.688 7 h₆1.5 h₆ h0 th₆ 8 t67.209 6 h₅1.5 h₅ h0 th₅ 8 t57.733 hm₈10.75 hm₈ hm₇ h₇ 2  h₈ 2   8 hm₇9.75 hm₇ hm₆ h₆ 2  h₇ 2   7 hm₆8.25 hm₆ hm₅ h₅ 2  h₆ 2   6 hm₅6.75 hm₅ hm₄ h₄ 2  h₅ 2   5 hm₄5.25 hm₄ hm₃ h₃ 2  h₄ 2   4 hm₃3.75 hm₃ hm₂ h₂ 2  h₃ 2   3 hm₂2.25 hm₂ h₁ h₂ 2   2 hm₁0.75 hm₁ h₁ 2  1 Course No i 1nsh nsh 8

Number of Shell Courses:

Selected Thicness of Shell Courses:

mm tmin 5 m Di11.5 10 8 6 5 Plate Thickness (mm): t 60Di 36Di60 15Di36 Di15 Tank Diameter (m): Di

According to API 650 Section 5.6.1.1. minimum shell thickness can not be less than this values: Minimum shell thickness:

3) THICKNESSES OF ALL SHELL COURSES: mm t86.171 5 h₄1.5 h₄ h0 th₄ 10 t48.265 4 h₃1.5 h₃ h0 th₃ 10 t38.797 3 h₂1.5 h₂ h0 th₂ 12 t29.371 2 h₁1.5 h₁ h0 th₁ 12 t19.929 1 Course Height (m) Selected Thickness (mm) Thickness (mm)

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9 40t45 17 14 11 8 32t40 14 12 9 6 25t32 11 10 7 6 19t25

1) TOP WIND GIRDER:

D) TOP AND INTERMEDIATE WIND GIRDERS

mm w530.804 w 215 tbs Hliq G ( )  If annular plates are used, minimum radial width of annular plates:

mm tbs 8 Selected Bottom Plate Thickness:

mm tbs 12 Selected Annular Bottom Plate Thickness (including Corrosion Allowance):

mm tb6 19 16 13 HTS tt th₁St  Hydrostatic Test Stress (MPa):

MPa PS95.795 PS tdCA th₁CA

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Sd  Product Stress (MPa):

C) BOTTOM PLATES Hs4.991 Hs i h_ith_ihm_i

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i h_ith_i



 Center of Gravity of Shell Courses (m):

Weight of Shell Courses (kg): Wsh 3.006 10

4   Wsh Di  7.85 i h_ith_i



  mm tav9.636 tav i h_ith_i

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i h_i

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 Average Thickness of Tank Shell (mm):

9 7 6 6 t19  250  230  210  190

Stress in First Shell Course ,  (MPa) Plate Thickness of First

Shell Course, t (mm)

According to API 650 Table 5.1 Annular Bottom Plate Thickness (tb):

MPa  95.795

 max PS HTS(  ) Stress in First Shell Course (MPa):

MPa HTS47.898

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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 deg

Assume an angle for plate thickness calculation:  18 deg

Dead Load (with plate thickness assumption): DL 12 7.85( )0.01 DL0.942 kPa

Greater of load combinations:

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 Required minimum section modulus (cm3): Z Di

2 H  17 Vw 190

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2   Z39.815 cm3

Profile UNP100 can be selected with section Z = 41.2 cm3.

2) INTERMEDIATE WIND GIRDER:

The top shell course plate thickness: t 8 mm

The maximum height of the unstiffened shell : H1 9.47 t t Di

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3  190 Vw

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2   H194.477 m

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

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Wsh3.006 104 kg

Weight of Roof (with stiffeners): Wro (Di 0.5)

2

 

4 (tr1)(7.85)

 Wro1.154104 kg

Resisting weight: Wres Wsh Wro Wres4.16 104 kg

Overturning moment from wind load: Mw2.838 104 kg m  2 3 Wres Di 2

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 1.595 105 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

SUG 3 Seismic Use Group:

Effective Ground Acceleration Coefficient: (for Seismic Zone 1 according to TEC 2007)

A0 0.4 Seismic Zone 1 0.4 2 0.3 3 0.2 4 0.1

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Acceleration Coefficient T max T1 T2(  ) T3.542 kPa

Minimum roof plate thickness: trmin Di

4.8 sin   180

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 T 2.2   2  trmin11.838 mm

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

The wind load acting on tank: Fw fw Vw 190

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2  DiH 1000 9.81   Fw5.16 103 kg

Overturning moment from wind load: Mw Fw H 2 

 Mw2.838 104 kg m

Weight of tank:

Weight of Bottom Plates: Wb

Di0.001 th₁0.5

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2

4 tbs(7.85)

 Wb7.117 103 kg

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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 2

3Sms

 Sds1.2

For 1 second: Sd1 2

3Sm1

 Sd11.6

Design Response Spectrum (DRS): (According to ASCE 7-05 Section 11.4.5)

Characteristic Periods: T0 0.2 Sd1

Sds 

 T00.267 s

Importance Factor: (API 650 Table E-5)

I 1.5 Seismic Use Group 

1.0  1.25  1.5













Importance Factor

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)

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:

(14)

TsTTL Sa T( ) Sd1 T  When TLT Sa T( ) Sd1 TL T2 













 0 1 2 3 4 5 6 0.2 0.4 0.6 0.8 1 1.2 Period (s) Spe ct ral Res po ns e Ac c el era ti on Sa T( ) T

STRUCTURAL PERIOD OF VIBRATION Impulsive Natural Period

Density of Fluid:  1 103 kg

m3

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 Ts Sd1

Sds

 Ts1.333 s

Regional Dependent Transition Period for Longer Period Ground Motion:

TL 4 s (Regions outside the USA)

Natural Vibration Period (s): T 0.01 0.015 6

Design Responce Spectrum When TT0 Sa T( ) Sds 0.4 0.6 T

T0  



























 When T0TTs Sa T( ) Sds When

(15)

%g

Convective Spectral Acceleration Parameter

Coefficient to adjust the spectral acceleration from 5% - 0.5% damping: K 1.5

When TcTL Ac K Sd1 1 Tc













 I Ri













  When TcTL Ac K Sd1 TL Tc2













 I Rc













  Ac0.255 %g DESIGN LOADS

Effective Weight of Product

Diameter to Height Ratio: Di

Hliq 1.095

Total weight of tank contents (N): Wp  Di

2



4 Hliq9.81

 Wp1.07107 N

Equivalent Uniform Thickness of Tank Shell: (mm) (Average thickness)

tu tav tu9.636 mm

Impulsive Natural Period (s): (API 650 Eq. E.4.5.1)

Ti 1 2000 Ci Hliq tu Di   E   Ti0.127 s

Convective (Sloshing) Period

Sloshing Period Coefficient: Ks 0.578

tanh 3.68 Hliq Di













 Ks0.579

The First Mode Sloshing Wave Period (s ): (API 650 Eq. E.4.5.2)

Tc 1.8 Ks  Di Tc3.532 s

DESIGN SPECTRAL RESPONSE ACCELERATIONS

Impulsive Spectral Acceleration P arameter

Ai Sds I Ri













  Ai0.45

(16)

Di Hliq 1.333 Xi 0.375 Hliq When Di Hliq 1.333 Xi 0.5 0.094 Di Hliq  













Hliq  Xi4.169 m

Height of the Lateral Seismic Force: Applied to Wc (m)

(API 650 Eq. E.6.1.2.1)

Xc 1.0 cosh 3.67 Hliq Di













1 3.67 Hliq Di













sinh 3.67 Hliq Di













 













Hliq   Xc7.579 m Center of Action for S lab 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)

Selection of Height Equation:

When Di Hliq 1.333 Xis 0.375 1.0 1.333 0.866 Di Hliq  tanh 0.866 Di Hliq 













1.0 













 













 Hliq  Effective Impulsive Weight (N):

(API 650 Eq. E.6.1.1)

Selection of Effective Impulsive Weight Equation:

When Di Hliq 1.333 Wi tanh 0.866 Di Hliq 













0.866 Di Hliq  Wp   When Di Hliq 1.333 Wi 1.0 0.218 Di Hliq  













Wp  Wi8.144106 N

Effective Convective Weight (N):

(API 650 Eq. E.6.1.1) Wc 0.230

Di Hliq  tanh 3.67 Hliq Di













 Wp  Wc2.689 106 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:

(17)

Xr H 1 3 Di 2 tan   180 



























   Xr11.623 m

Ringwall Overturning Moment (Nm): (API 650 Eq. E.6.1.5)

for global evaluations

Mrw [Ai Wi Xi(  Ws Xs Wr Xr )]2 [Ac Wc Xc(  )]2

Mrw1.733107 Nm

Slab Overturning Moment (Nm): (API 650 Eq. E.6.1.5)

Ms [Ai Wi Xis(  Ws Xs Wr Xr )]2 [Ac Wc Xcs(  )]2

Ms2.363 107 Nm

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.

Vertical Seismic Acceleration Coeff. (%g): Av 0.2 Sds 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 Y10.5 m When Di Hliq 1.333 Xis 0.5 0.06 Di Hliq  













Hliq  Xis5.94 m

Height of the Lateral Seismic Force: Applied to Wc (m)

(API 650 Eq. E.6.1.2.2)

Xcs 1.0 cosh 3.67 Hliq Di













1.937 3.67 Hliq Di













sinh 3.67 Hliq Di













 













Hliq   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.

Total weight of tank shell (N): Ws Wsh 9.81 Ws2.949 105 N

Height of Shell's Center of Gravity (m) Xs Hs Xs4.991 m

Weight of Roof (N): Wr Wro 9.81 Wr1.132 105 N

(18)

ts6 mm

Total Combined Hoop Stress (MPa): t Nh Ni

2 Nc2   (Av Nh )2  ts  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: all 1.33 Sd all208.367 MPa

Comparison: t133.74 MPa  all208.367 MPa

Hoop Stress Ratio: SRhs t

all

 SRhs0.642 OK

Calculation for the 2.nd shell course:

Distance from liquid surface to analysis point (m): Y Hliqh0 Y9 m Impulsive Hoop Membrane Force in Tank Shell (N/mm):

(API 650 Eq. E.6.1.4)

Selection of Force Equation:

When Di Hliq 1.333 Ni 8.48 Ai GDiHliq Y Hliq 0.5 Y Hliq













2  













 tanh 0.866 Di Hliq 













  When Di Hliq 1.333 and Y0.75 Di Ni 5.22 Ai GDi 2  Y 0.75 Di 0.5 Y 0.75 Di













2  













  When Di Hliq 1.333 and Y0.75 Di Ni 2.6 Ai G Di 2   Ni154.732 N mm Convective Hoop Membrane Force in Tank Shell (N/mm):

(API 650 Eq. E.6.1.4)

Nc 1.85 Ac GDi2cosh 3.68 (HliqY) Di 













 cosh 3.68 Hliq Di













 Nc4.325 N mm

Liquid Hydrostatic Membrane Force in Tank Shell (N/mm):

Nh Y G Di 2 9.81

 Nh592.279 N

mm Thickness of the shell ring under consideration (mm): ts th₁CA

(19)

ts6 mm

2 Nc2   (Av Nh )2  ts  t117.445 MPa

all

 SRhs0.564 OK

Calculation for the 3.rd shell course:

Distance from liquid surface to analysis point (m): Y Hliq2 h0 Y7.5 m Impulsive Hoop Membrane Force in Tank Shell (N/mm):

(API 650 Eq. E.6.1.4)













2  





































2  













(API 650 Eq. E.6.1.4)

























 Nc4.833 N mm

Nh Y G Di 2 9.81

 Nh507.668 N

mm Thickness of the shell ring under consideration (mm): ts th₂CA

(20)

ts4 mm

2 Nc2   (Av Nh )2  ts  t151.633 MPa

all

 SRhs0.728 OK

FOUNDATION LOADS

Dead Load per Unit Length (N/m): (Shell and Roof)

DL WsWr Di 

 DL1.13 104 N

m Impulsive Hoop Membrane Force in Tank Shell (N/mm):

(API 650 Eq. E.6.1.4)













2  





































2  













(API 650 Eq. E.6.1.4)

























 Nc6.476 N mm

Nh Y G Di 2 9.81

 Nh423.056 N

mm Thickness of the shell ring under consideration (mm): ts th3CA

(21)

VSF2.711 103 N m

Total Vertical Seismic Force (N): (Shell, Roof and Liquid)

Fvst Av Wt Fvst2.666 106 N

Total Vertical Load (N):

(Total Vertical Seismic and Total Dead W.)

Fvt Fvst Wt Fvt1.377 107 N

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 Wr Di 

 wr3.134103 N

m Distributed Compression Force due to Shell (N/m): ws Ws

Di 

 ws8.163103 N

m Total Distributed Compression Force (N/m): wt wr ws wt1.13104 N m

Vertical Seismic Acceleration (g's): Av0.24

Minimum Anchorage Resistance (N/m): (API 650 Eq. E.6.2.1.2)

wab 1.273 Mrw Di2 wt 1( 0.4 Av ) 









 wab1.566105 N m Live Load per Unit Length (N/m):

(Live Load on Roof)

LL Lr 9.81 (Di0.5) 2   4  Di   LL7.677103 N m Total Dead Weight (N):

(Shell, Roof and Liquid)

Wt WsWrWp Wt1.111 107 N

Total Load per Unit Area during Operation (N/m2): (Shell, Roof and Liquid)

Wo Wt Di2 4













 Wo1.069 105 N m2 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 [Ai Wi( Ws Wr)]2 (Ac Wc )2

Seq3.909106 N

Ringwall Overturning Moment due to Seismic Load (Nm): Mrw1.733107 Nm

Slab Overturning Moment due to Seismic Load (Nm): Ms2.363 107 Nm

Vertical Seismic Force (N): (Shell and Roof)

Fvs Av Ws(  Wr) Fvs9.795104 N

Vertical Seismic Force per Unit Length (N/m): (Shel and Roof)

VSF Fvs

Di 

( )

(22)

Anchor Bolt Characteristics Cast in headed stud anchor

Nominal Diameter of Anchor (mm): db 48 mm

Threaded Area of Bolt (mm2): Ath 0.75 db

2

  4

 Ath1.357 103 mm2

Anchor bolt material: S275JR (St44-2) or equivalent

Ultimate Tensile Strenght (MPa): Sub 430

Yield S trenght (MP a): 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

Bolt Spacing to Diameter ratio Bsp 1000

db 31.929 Max traction on single bolt (kN) Tb wab Bsp

1000

 Tb240 kN

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 mm

Bolt Circle Diameter (m): Db Di 2

Dbs th₁ 1000  

 Db11.708 m

Bolt Spacing Angle:  360

nb

  15 degrees

Bolt Spacing (m): Bsp Db 

nb

 Bsp1.533 m

(23)

Np3.747103 Comparison:

kN Np3.747103 Np p s Npn

Design pull out strength (kN):

kN Npn6.661103 Npn Np cp

Nominal pull out strength (kN):

kN Np4.758103 Np 8 Abrg flc103

Pull out strength in tension of an headed bolt (kN):

Levhali ankrajin beton içi levha boyutlari mm2 Abrg2.379 104 Abrg 1602 db 2   4













  Nm Ms1.698 107 Ms [Ai 0.7 (Wi Xis  Ws Xs  Wr Xr )]2[Ac Wc Xcs(  )]2

Slab Overturning Moment (Nm):

As Ms is used for a verification based on ASD criterion a new evaluation can be made as follows: U 4 Ms

Di

 W2 1( 0.4 Av ) 

Seismic uplift loads (N):

N W21.679 105 W2 Wsh tavCA tav













 Wro trCA tr













 













9.81 

Dead load of shell minus any corrosion allowance and any dead load including roof plate acting on the shell minus any corrosion allowance (N):

According to Table 3.21 of API 650 Bolt adequacy for uplift loads

OK kN

Nsa328.265 

kN Bolt tension demand (kN)

kN Nsa328.265 Nsa s t Nsa

Bolt tension capacity (kN)

kN Nsa583.582 Nsa Ath min futa 860 (  )103

Nominal bolt strength in tension (kN)

MPa futa430 futa min Sub 860(  1.9 Syb )

Design tensile strength (ACI 318 D.5.1.2) (MPa)

s 0.75 Additional seismic strength reduction factor

t 0.75 Reduction Factor (according to clause D.4.4.a)

Bolts tension capacity (according to clause D.5)

Bearing area at head of anchor bolt (mm2):

p 0.75 Reduction Factor:

cp 1.4 Modification Factor:

Pullout strength in tension (according to clause D.5.3)

OK FUt0.731

FUt Nua

Nsa  Bolt usage ratio:

kN Nua240  kN Nsa328.265 Comparison: kN Nua240 Nua Tb

(24)

nsk 24

Material: S275 JRG2

Plate minimum yield stress (MPa) ysk 275

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.

Total Base Shear due to seismic load (N): 0.7 Seq 2.736 106 N

Shear for each shear key (N): Ssk 0.7 Seq nsk

 Ssk1.14105

Concrete compression (MPa): fc Ssk

wsk dp

 fc11.402 MPa

Concrete allowable compression (MPa): fcall 0.65 0.85 flc fcall13.813 MPa

Concrete compression ratio SRck fc

fcall

 SRck0.825 OK

Global verification

Shear area (mm2): Assk tsk wsk Assk2103 mm2

Seismic uplift loads (N): Uasd 4 Ms

Di

 W2 1( 0.4 Av )

 Uasd5.753106 Nm

Uplift load per anchor (N): tb Uasd

nb

 tb2.397 105 N

Allowable Ancher Bolt Stress (MPa): according to Table 3.21 of API 650

al 0.8 Syb al220 MPa

Average induced stress (MPa): ub tb

Ath

 ub176.627 MPa

Uplift stress ratio SRu ub

al

 SRu0.803 OK

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 mm

(25)

mm3

Shear key global bending stress (MPa): gk Mgk Wgk

 gk165.723 MPa

Shear key global bending stress ratio. SRgk gk allsk

 SRgk0.904 OK

Local verification

Conservatively we consider a simple cantilever beam of unit width

Shear key overhang (mm): esk wsktsk

2

 esk40 mm

Bending moment due to concrete reaction (Nmm/mm): Mlk fc esk esk 2 

 Mlk9.121 103 N mm

mm Shear key section modulus per unit depth (mm3/mm): Wlk 1

6 tsk 2   Wlk66.667 mm 3 mm

Shear key bending stress (MPa): lk Mlk

Wlk

 lk136.821 MPa

Shear key local bending stress ratio: SRlk lk allsk

 SRlk0.746 OK

Shear stress (MPa):  Ssk

Assk

  57.009 MPa

Shear key allowable bending stress (MPa): allsk 2 3ysk

 allsk183.333 MPa

Shear key allowable shear stress (MPa): allsk allsk 2

 allsk129.636 MPa

Shear stress ratio: SR 

allsk

 SR0.44 OK

Arm of the global concrete reaction (mm): afc dp 2

 afc50 mm

Global bending moment (Nmm): Mgk Ssk afc Mgk5.701106 Nmm

Global inertia moment (mm4): Igk 1

12 (wsk) 3 tsk   (wsktsk) tsk 3





  Igk1.72 106 mm4

Global section modulus (mm3): Wgk Igk

wsk2

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c29.865 MPa  Fc41.625 MPa

Compression Stress Ratio: Rcs c Fc

 Rcs0.717 OK

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 MPa

Plate allowable stress (MPa): ball Sd ball156.667 MPa

Bolt eccentricity (mm): a Dbs a92 mm

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 tsb6 mm

c wt 1(  0.4 Av ) 1.273 Mrw Di2 













1 1000 tsb   c29.865 MPa

Allowable Longitudinal Shell Membrane Compression Stress

The seismic allowable stress Fc is evaluated according to API 650 E.6.2.2.3

The Parameter: Para G Hliq Di

2

 tsb2

 Para38.573

The Allowable Compression Stress (MPa): (API 650 Eq. E.6.2.2.3)

Selection of Stress Equation:

When G Hliq Di 2  tsb2 44  Fc 83 tsb Di  When G Hliq Di 2  tsb2 44  Fc 83 tsb 2.5 Di 7.5 (G Hliq ) 0.5 Sy  Fc41.625 MPa Comparison:

(27)

Bolt pitch (mm): bp Bsp 1000 bp1.533103 mm

Base plate span between chairs (mm): bs bp(b2 tg ) bs1.383103 mm

Number of gussets per chair: ng 2

Shell reinforcement plate thickness (mm:) rpt 20 mm Shell reinforcement plate halfwidth (mm): rpw 200mm 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 Db2 wt 1( 0.4 Av 0.7) 













bp 1000   Tbc2.305105 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105 N

Maximum compression per unit length (N/m): C wt 1( 0.4 Av 0.7) 1.273 Mrw Di2  

C1.789 105 N m Height from top of annular plate (mm): h 250 mm

Distance between gussets (mm): b 100 mm

Thickness of bottom shell (mm): ts th₁ ts12 mm

Bolt diameter (mm): db48 mm

Bolt hole in the top plate (mm) dbh db 24 dbh72

mm tg 25 Thickness of gussets (mm): mm e49 e c dbh 2   Top plate width ouside bolt hole (mm):

mm c 85 Top plate edge distance from bolt axis (mm):

mm A 400 Top plate width (mm):

mm tc 30 Top plate thickness (mm):

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tg25 mm

Shell reinforcement plate thickness (mm): rpt20 mm

Shell reinforcement plate halfwidth (mm): rpw200 mm

Section total area (mm2): Ag bg tg rpt rpw Ag6.4 103 mm2

Neutral axis distance from midsurface of reinforcement plate (mm): na tg bg bg 2 rpt 2 













Ag   na21.75 mm

Longitudinal inertia moment (mm4):

Il tg bg 3  12 tg bg bg 2 rpt 2  na













2   rpw rpt 3  12   rpt rpw (na)2  Il7.023106 mm4

Transv ersal inertia moment (mm4): It 1

12 bg tg 3  rpt rpw 3





  It1.346107 mm4 Inertia radius (mm): rl Il Ag  rl33.125 mm rt It Ag  rt45.857 mm

Annular bottom plate characteristics

Selected bottom plate thickness (mm): tb tbs tb8 mm

Annular plate width (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): tp Tbc e tc 2

0.375 b 0.22db

( )



 tp140.808 MPa

Top plate bending stress ratio SRtp tp

ball

 SRtp0.899 OK

Gusset verification

Gusset maximum axial compression force (N): Cg Tbc ng

 Cg1.152105 N

Gusset width at bottom edge (mm): wo 15 mm

Gusset mean width (mm): bg (a c)wo

2

 bg96 mm

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OK SRcg0.133

SRcg cg

cgall  Compression stress ratio

MPa cg18.008 cg Cg

Ag  Max compression stress (MPa)

MPa cgall135.608 cgall 1 IF h rmin 













2 2 rmin 2 













5 3 3 IF h 8 Cc rmin 













 IF h rmin 













3 1 8 Cc 3  













y  

Allowable compression stress (MPa):

Cc132.813 Cc 2  2 E y   Cc factor: MPa y235 Yield s tress (MPa):

MPa E 210000 Young's modulus (MPa):

IF 1 Instability Factor:

mm rmin33.125 rmin min rl rt(  )