B-2- Note de Calcul Mécanique Eau Brute 90GAD10BB001002 (GHN 90 M-------K11 DC 002 C)

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Note de Calcul Mécanique des Réservoirs Eau Brute 90GAD10BB001/002

POWER Centrales

CENTRALE A CYCLE COMBINE DE GHANNOUCH

Espace réservé aux tampons (Revue et validation du document - si nécessaire) :

Date d'Arrivée: Référence N° de ClassementSTEG:

Historique des RévisionsRev.

AB

Description de la Dernière RévisionC Mise à Jour

Remplace Echelle Numérotation ALSTOMGHN 90 M-------K11 DC 002 C

Responsable Dépt Auteur Vérifié Par: Approuvé par FormatIET BSW MS IET A4Origine du Document Type de Document Statut du Document

Note de Calcul FATit S Tit N é d'id tifi ti

Date Auteur Vérifié par Approuvé par Description / ModificationBSW MS IET Emis pour Approbation

1 x 400 MW

08/05/200919/06/2009 BSW MS IET Mise à Jour

Titre, Sous Titre Numéro d'identificationGHN 90 M-------K11 DC 002 CRev. Date Lang. PageC 13/09/2009 Fr./En. 1/ 36

Note de Calcul Mécanique des Réservoirs Eau Brute 90GAD10BB001/002

Réservoirs Eau Brute

GHN 90 M-------K11 DC 002 C Page 1 sur 36

Ref.: GHN 90 M-------K11 DC 002 C Page 2 / 36

1 PAGE DE GARDE (COVER PAGE)2 SOMMAIRE (SUMMARY)3 1- Objet (Subject)3 2- Documents de Référence & Standards (Reference Standards & Documents)3 3- Paramètres de Conception (Design Parameters)4 4- Vérification des Epaisseurs des Viroles (Shell Thickness Check)8 5- Vérification Epaisseur Fond (Bottom Thickness Check)9 6- Vérification Epaisseur Tôle Marginale (Annular Bottom Plate Thickness Check)11 7- Vérification Epaisseur Tôle Toit (Roof Plate Thickness Check)12 8- Vérification Non-Nécessité Poutre Intermédiaire (Intermediate Wind Girder Requirements Check)14 9- Vérification Event Central (Check of Central Vent) 15 10- Analyse Sismique (Seismic Analysis)21 11- Analyse de la Stabilité Sous l'Effet du Vent (Stability Check Under Wind Load)22 12- Vérification des Ancrages (Anchorage Check)27 13- Dimensionnement la Charpente du Toit (Check of Roof Structure)

SOCIETE TUNISIENNE DE L'ELECTRICITE ET DU GAZCENTRALE A CYCLE COMBINE DE GHANNOUCH 1 x 400 MW

Note de Calcul Mécanique des RéservoirsEau Brute 90GAD10BB001/002

SOMMAIRE (SUMMARY)

27 13- Dimensionnement la Charpente du Toit (Check of Roof Structure)



Ref.: GHN 90 M-------K11 DC 002 C Page 3 / 36

1- OBJET (SUBJECT)L'objectif de ce document est de vérifier les différents Eléments de deux réservoirs Eau Brute.L'analyse couvrira les différents éléments du réservoir: Robe, Tôle Toit, Tôle Bordure/Fond, Raidisseur, Ancrage & Charpente du Toit.The Objective of this documents is to check the different components of two Raw Water Tanks .The analysis covers the differents components of Tanks: Shell, Roof Plate, Bottom & Annular Bottom Plate,Wind Girder, Anchorage and Roof Structure .

2- DOCUMENTS DE REFERENCE & STANDARDS (REFERENCE STANDARDS & DOCUMENTS)2-1- DOCUMENTS DE REFERENCE (REFERENCE DOCUMENTS)

Datasheet des Réservoirs Eau Brute 90GAD10BB001/002 GHN/99/M/G02-------/DS/502/APlan guide réservoir d’eau brute GHN99MG02-------EA005APlan guide réservoir d’eau brute GHN99MG02-------EA006AListe des Codes et Norme GHN00M-------PMFNA131AEquipment Technical Dossier: Miscellaneous Storage Tanks GHN90M-------K11DL100BMiscellaneous Storage Tanks GHN90M-------K11ES001BEquipment General Technical Requirements GHN00M--------MEES500APiping Class Manual GHN00M GS140D

SOCIETE TUNISIENNE DE L'ELECTRICITE ET DU GAZCENTRALE A CYCLE COMBINE DE GHANNOUCH 1 x 400 MW

Note de Calcul Mécanique des RéservoirsEau Brute 90GAD10BB001/002

Piping Class Manual GHN00M--------GS140DSpécification Générale Peinture GHN00M----------GS120A

2-2- STANDARDS DE REFERENCE (REFERENCE STANDARDS)API650: Welded Steel Tanks for Oil StorageAPI RP2000: Venting Atmospheric and Low-Pressure Storage Tanks Nonrefrigerated and RefrigeratedAISI T-192: Steel Plate Engineering Data Series - Useful Information - Design of Plate Structures, Volume I & IIAISC 360-05: Specification for Structural Steel Buildings

3- PARAMETRES DE CONCEPTION (DESIGN PARAMETERS)

Température Maximale (Maximum Temperature) 50°CTempérature Minimale (Minimum Temperature) -5°CPression Interne (Internal Pressure) NAPression Externe (External Pressure) NACharge d'Exploitation sur Toit (Live Load on Roof) 200kg/m²Vitesse du Vent (Wind Velocity) 180km/hAccélération Sismique (Seismic Acceleration) 0.1gMatière Robe (Shell Material) A283 GR CMatière Fond (Bottom Material) A283 GR CMatière Tôle Toit (Roof Plate Material) A283 GR CMatière Charpente (Roof Structure Material) S235JR



4- Vérification des Epaisseurs des Viroles (Shell Thickness Check)

Design Condition Definition

Z1Z2

ZiZn

H1=

Hm

H2

Hi

Hn

Hm

ts2

tsi

tsn

ts1

14 <-D: Nominal Tank Diameter (m)13.5 <-H: Design Liquid Level (m)

1 <-G: Design Specific Gravity3 <-Cs: Shell Corrosion Allowance (mm)

50 <-Tmax: Maximum Operating Temperature (°C)-5 <-Tmin: Minimum Operating Temperature (°C)

2.5 <-P: Design Pressure (kPa)

Shell Courses Definition6 <-n: Number of Shell Courses

No.Corro AllowCsi

1 32 33 34 35 36 37 38 39101112

ASTM A283 GR C [Killled Or Semikilled]ASTM A283 GR C [Killled Or Semikilled]ASTM A283 GR C [Killled Or Semikilled]

Material Designation

ASTM A283 GR C [Killled Or Semikilled]ASTM A283 GR C [Killled Or Semikilled]ASTM A283 GR C [Killled Or Semikilled]ASTM A283 GR C [Killled Or Semikilled]ASTM A283 GR C [Killled Or Semikilled]

2.48 8

9

2.2 62.2 8

2.48 82.5 6

Shell Course HeightZi (m)

2.2 10

Nominal Shell Thickness

tsi (mm)

2.2 82.2

Z1Z2

ZiZn

H1=

Hm

H2

Hi

Hn

Hm

ts2

tsi

tsn

ts1



Check of 1-Foot Method Applicability

D ≤ 60m OK

Check of Maximum Design Pressure

P ≤ 18kPa OK

Allowable Stresses ComputationS d = Value From Table 3.2 [If T max <=90°C]Sd = 2/3 Y x m [If T max >90°C]

No.

123456789

Allowable Stress for the

Hydrostatic Test Condition St (MPa)

154154154154154154154154

Allowable Stress for the design

Condition Sd (MPa)

136.67136.67136.67136.67136.67136.67

NA 136.67205 NA

#N/A #N/A

205 NA

136.67#N/A #N/A

205 NA205

Yield Strength Reduction Factor

m

205 NA205 NA205 NA

205 NA

Minimum Specified yield

Strength Y (MPa)

9.8PHm HG

= +

1

i

i kk

H Hm Z=

= −∑

5 156 15 368 36 6010 60

ei

if D mif m D m

tif m D mif D m

<⎧⎪ ≤ <⎪= ⎨ ≤ <⎪⎪ ≥⎩

( )4.9 0.3idi si

di

D H Gt C

S−

= +

( )4.9 0.3iti

ti

D Ht

S−

=

9101112

Tmax ≤ 260°C OK

Minimum Shell Thickness Computation13.76 <-Hm: Modified Liquid Level (m)

No.

123456789101112

#N/A#N/A

5 0.00-4.70

0.00-4.70 5

#N/A #N/A

#N/A#N/A

#N/A#N/A

#N/A #N/A#N/A #N/A

#N/A #N/A

0.00 0.00

#N/A #N/A

-4.70

0.00 0.005 0.00

0.005

-4.70

0.00-2.22 5 0.00 0.00

5 0.000.26

2.072.76 5 4.23 1.09

5 5.344.96

4.037.16 5 6.44 3.05

5 7.559.36

5.9911.56 5 8.65 5.01

5 9.7513.76

Minimum Shell Thickness tsmi (mm)

Shell Course HeightHi (m)

Erection Shell Thicknesstei (mm)

Design Shell Thickness

tdi (mm)

Hydrostatic Shell Thickness

tti (mm)

8.657.556.44

0.000.000.000.00

5.345.000.000.00

9.75

9.8PHm HG

= +

1

i

i kk

H Hm Z=

= −∑

5 156 15 368 36 6010 60

ei

if D mif m D m

tif m D mif D m

<⎧⎪ ≤ <⎪= ⎨ ≤ <⎪⎪ ≥⎩

( )4.9 0.3idi si

di

D H Gt C

S−

= +

( )4.9 0.3iti

ti

D Ht

S−

=



tsi ≥ tsmi OK

Allowable Maximum Shell Thickness

No.

123456789101112

Impact Test Requirement

No

0.00#N/A #N/A


tsi (mm)

10.009.008.008.006.006.00

#N/A #N/A#N/A #N/A

0.000.00

25.00 OK8.0025.00 OK#N/A #N/A

8.000.00

25.00 OK25.00 OK25.00 OK

Maximum Allowable Shell

Thickness tmai (mm)

Status

25.00 OK25.00 OK25.00 OK

Status(No Impact TestMaterial Group

Minimum Allowable Temperature without Impact TestNo.

123456789101112

OKOK

(No Impact Test is required)

OKOKOKOKOK

#N/A#N/A #N/A

#N/A #N/A #N/A#N/A #N/A

OK#N/A#N/A

I -10.46

#N/A #N/AI -10.46

I -10.46I -10.46

I -12.00I -12.00

I -9.69

Material Group without Impact Test Tai (°C)

I -8.92



Shell Weight Computation

No.

123456789101112

36 321.46 <-Ws: Non Corroded Shell Weight (kg)22 338.39 <-Wsc: Corroded Shell Weight (kg)

0.00 0.00 0.00 0.000.00 0.00 0.00 0.00

0.00 0.00 0.00 0.000.00 0.00 0.00 0.00

0.00 0.00 0.00 0.000.00 0.00 0.00 0.00

2.20 6.00 4557.45 2278.722.50 6.00 5178.92 2589.46

2.20 8.00 6076.59 3797.872.20 8.00 6076.59 3797.87

2.20 10.00 7595.74 5317.022.20 9.00 6836.17 4557.45



tsi (mm)

Course WeightWi (kg)

Corroded Course Weight

Wci (kg)



5- Vérification Epaisseur Fond (Bottom Thickness Check)

Input ParametersASTM A283 GR C [Semikilled]

<-Bottom Plate Material Designation

Single-welded Full Fillet Lap Joint

<-Bottom Plate Joint

14 <-D: Nominal Tank Diameter (m)3 <-Cb: Bottom Plate Corrosion Allowance (mm)9 <-tb: Nominal Bottom Plate Thickness (mm)

-5 <-Tmin: Minimum Operating Temperature (°C)600 <-rab: Distance inside shell and any lap-welded joint in the bottom (mm)

Z tb

min(25;5*tb)

tb

tb


Z 5

50

5tb

Single-welded Butt Joint with Backing Strip

Square or V Grooves

tb

Single-welded Butt Joint

Square or V Grooves

Bottom Plate Thickness Check9 <-tbmin: Minimum Required Bottom Plate Thickness (mm)

t bmin =6mm+C b

tb ≥ tbmin OK

Impact Test RequirementI <-Material Group

-9.69 <-Ta: Minimum Allowable Temperature without Impact Test (°C)

Tmin ≥ Ta (No Impact Test is required) OK

Bottom Plate Weight Computation9 091.22 <-Wb: Non Corroded Bottom Plate Weight (kg)6 060.81 <-Wbc: Corroded Bottom Plate Weight (kg)

Z tb

min(25;5*tb)

tb

tb


Z 5

50

5tb

Single-welded Butt Joint with Backing Strip

Square or V Grooves

tb

Single-welded Butt Joint

Square or V Grooves



6- Vérification Epaisseur Tôle Marginale (Annular Bottom Plate Thickness Check)


<-Annular Bottom Plate Material Designation

ASTM A283 GR C [Semikilled]

<-Shell Plate Material Designation

10 <-ts1: First Shell Course Thickness (mm)14 <-D: Nominal Tank Diameter (m)

13.5 <-H: Design Liquid Level (m)1 <-G: Design Specific Gravity (m)

ts1

pab rab 50

( )1

4.9 0.3h

s

D Ht

σ−

=

( )min 0.5

215600 ; abab

tr Max mmHG

⎡ ⎤= ⎢ ⎥

⎢ ⎥⎣ ⎦

1 <-G: Design Specific Gravity (m)3 <-Cab: Annular Bottom Plate Corrosion Allowance (mm)9 <-tab: Nominal Annular Bottom Plate Thickness (mm)

600 <-rab: Distance inside shell and any lap-welded joint in the bottom (mm)60 <-pab: Outside projection outside the shell (mm)-5 <-Tmin: Minimum Operating Temperature (°C)

Check of Annular Bottom Plate Thickness90.55 <-σh: Hydrostatic Test Stress in the First Shell Course (MPa)

9 <-tabmin: Minimum Required Annular Bottom Plate Thickness (mm)

tab ≥ tabmin OK

Check of Annular Bottom Plate Inside Projection600.00 <-rabmin: Minimum Distance inside shell and any lap-welded joint in the bottom (mm)

50 <-pabmin: Minimum Outside projection outside the shell (mm)

rab ≥ rabmin OKpab ≥ pabmin OK

ts1

pab rab 50

( )1

4.9 0.3h

s

D Ht

σ−

=

( )min 0.5

215600 ; abab

tr Max mmHG

⎡ ⎤= ⎢ ⎥

⎢ ⎥⎣ ⎦



Impact Test RequirementI <-Material Group

-9.69 <-Ta: Minimum Allowable Temperature without Impact Test (°C)

Tmin ≥ Ta (No Impact Test is required) OK

Annular Bottom Plate Weight Computation2 144.60 <-Wab: Non Corroded Annular Bottom Plate Weight (kg)1 429.74 <-Wabc: Corroded Annular Bottom Plate Weight (kg)



7- Vérification Epaisseur Tôle Toit (Roof Plate Thickness Check)


<-Roof Plate Material Designation

14 <-D: Nominal Tank Diameter (m)9.46 <-θ: Angle of the cone elements to the horizontal (Deg)

5 <-tr: Nominal Roof Plate Thickness (mm)0 <-Cr: Roof Plate Corrosion Allowance (mm)

Roof Plate Thickness Check5 <-trmin: Minimum Required Roof Plate Thickness (mm)

t rmin =5mm+C r

tr ≥ trmin OK

Roof Plate Weight Computation6 125.41 <-Wr: Non Corroded Roof Plate Weight (kg)6 125.41 <-Wrc: Corroded Roof Plate Weight (kg)



8- Vérification Non-Nécessité Poutre Intermédiaire(Intermediate Wind Girder Requirements Check)

Design Condition DefinitionASTM A283 GR C [Semikilled]

<-Top Shell Course Material Designation

14 <-D: Nominal Tank Diameter (m)180 <-V: Wind Velocity (km/h)50 <-Tmax: Maximum Operating Temperature (°C)

Shell Courses Definition6 <-n: Number of Shell Courses

No.

12345

2.2 9


2.2 10


tsi (mm)

2.2 82.2 8

3

1 9.47 snsn

tH t kD

β⎛ ⎞= ⎜ ⎟⎝ ⎠

2160V

β ⎛ ⎞= ⎜ ⎟⎝ ⎠

56789101112

Maximum Design Temperature Factor Computation205 <-Y: Minimum Specified yield Strength (MPa)

NA <-m: Yield Strength Reduction Factor205 <-YT: Specified yield Strength at maximum Design Temperature (MPa)

1 <-k: Intermediate Wind Girder Reduction Factor at maximum Design Temperature

Maximum Height of unstiffened Shell Computation6 <-tsn: As ordered thickness of the top shell course (mm)

0.79 <-β: Wind Modification Factor

12.60 <-H1: Vertical Distance between intermediate wind girder and the top angle of the shellor the top wind girder of an open-top tank (m)

2.5 62.2 6

3

1 9.47 snsn

tH t kD

β⎛ ⎞= ⎜ ⎟⎝ ⎠

2160V

β ⎛ ⎞= ⎜ ⎟⎝ ⎠



Maximum Height of unstiffened Shell Computation

No.

123456789101112

8.26 <-Wtr: Height of the transformed shell (m)

0.00

0.000.000.000.00

0 0

Transposed width of Each Shell Course

Wtri (mm)0.610.801.071.072.202.500.00

0 00 0

0 00 0

2.5 60 0

2.2 82.2 6

2.2 92.2 8



tsi (mm)

2.2 10

5

sntri i

si

tW Zt

⎛ ⎞= ⎜ ⎟

⎝ ⎠

1

n

tr trii

W W=

= ∑12.60 <-H1: Vertical Distance between intermediate wind girder and the top angle of the shell

or the top wind girder of an open-top tank (m)

Wtr < H1 OK

5

sntri i

si

tW Zt

⎛ ⎞= ⎜ ⎟

⎝ ⎠

1

n

tr trii

W W=

= ∑



9- Vérification Event Central (Check of Central Vent)

InputFlash Point ≥ 37.8°C <-Flash Point

200 <-Qin: Liquid Inlet Flow Rate (m3/h)200 <-Qout: Liquid Outlet Flow Rate (m3/h)

2 000 <-V: Tank Capacity (m3)2.5 <-Pi: Maximum Inlet Pressure (kPa)

0.25 <-Pe: Maximum Vacuum Pressure (kPa)

2 2

;2 2

i e

i e

KQ KQA MaxP P

ρ ρ⎡ ⎤= ⎢ ⎥

⎢ ⎥⎣ ⎦

150

6

Z5Z6

di

SS316MESH 0.5MM

0.25 <-Pe: Maximum Vacuum Pressure (kPa)2.5 <-K: Head Loss Coefficient1.2 <-ρ: Air Density (kg/m3)

154.08 <-di: Vent Pipe Internal Diameter (mm)

In/Out Breathing Resulting from maximum Out/In flow of liquid from the tank188.000 <-Qain: Air Inbreath Flow Rate (m3/h)188.000 <-Qaout: Air Outbreath Flow Rate (m3/h)

In/Out Breathing Resulting From Thermal Effect337.000 <-Qainth: Air Inbreath Flow Rate (m3/h)202.000 <-Qaoutth: Air Outbreath Flow Rate (m3/h)

10 ≤ V ≤ 30 000m3 OK

Maximum Out/In flow of liquid from the tank525.000 <-Qe: Maximum Inbreath Flow Rate (m3/h)390.000 <-Qi: Maximum Outbreath Flow Rate (m3/h)

0.011 <-A: Minimum Venting Area (m²)

0.019 <-An: Nominal Venting Area (m²)

An ≥ A OK

2 2

;2 2

i e

i e

KQ KQA MaxP P

ρ ρ⎡ ⎤= ⎢ ⎥

⎢ ⎥⎣ ⎦

150

6

Z5Z6

di

SS316MESH 0.5MM



10- Analyse Sismique (Seismic Analysis)Mechanically Anchored Tank

Geometric Parameters14 <-D: Nominal Tank Diameter (m)

13.5 <-H: Maximum Design Product Level (m)7.66666667 <-tu: Equivalent Uniform Thickness of Tank Shell (mm)5.97705314 <-Xs: Height from Bottom of the Tank Shell to Shell Center of Gravity (m)14.0833333 <-Xr: Height from Bottom of the Tank Shell to Roof Center of Gravity (m)

6 <-ta: Corroded Thickness of the Annular Bottom Plate (mm)60 <-ra: Annular Bottom Plate Outside Projection (mm)0.7 <-Hfh: Net Free Height Between Maximum Liquid Level & Shell Top Angle (m)

Shell Plate Parameters6 <-n: Number of Shell Courses

No. Zk (mm)

tsk (mm)

Ck (mm)

Sk (MPa)

Ftyk (MPa)

1 2500 10 3 137 2052 2500 9 3 137 2053 2500 8 3 137 2054 2500 6 3 137 2055 2000 6 3 137 2055 2000 6 3 137 2056 1500 6 3 137 205789101112

<-Zk: Shell Course Height (mm)<-tsk: Nominal Shell Thickness (mm)<-Csk: Shell Course Corrosion Allowance (mm)<-Sk: Allowable Stress for the design Condition (MPa)<-Ftyk: Mnimum Specified Yield Strength of Shell Course (MPa)

Seismic Parameters

Self-Anchored <-Type of Anchorage (Self-Anchored;Mechanically-Anchored)0.1 <-SP: Design Level Peak Ground Acceleration (%g)

1.25 <-I: Seismic Importance Factor (Table E-5)Class E <-Site Class (Class A/B/C/D/E)

Weight & Material Propperties Definition110 223 <-Wf: Weight of Tank Bottom (N)

21 141 850 <-Wp: Total Weight of Tank Content (N)73 605 <-Wr: Total Weight of Tank Roof (Plate, Structure, Roof Nozzle & Handrail) (N)

377 425 <-Ws: Total Weight of Tank Shell & Appurtenances (Shell, Ladder, Shell Nozzle & Platform) (N)2.5 <‐P: Internal Design Pressure (kPa)

1 <‐G: Design Specific Gravity1 000 <-ρ: Density of Fluid (kg/m3)

200 000 <-E: Elastic Modulus of Tank Material (MPa)205 <-Fy: Minimum Specified Yield Strength of Annular Bottom Plate (MPa)



Impulsive Natural Period Computation0.96 <-H/D: Maximum Design Liquid Level To Nominal Tank Diameter Ratio6.15 <-Ci: Coefficient for Determining Impulsive Period of Tank System (Fig. E-1)

0.223 <-Ti: Natural Period of Vibration for Impulsive mode of Behavior (s)

Convective Period Computation0.58 <-Ks: Sloshing Period Coefficient

3.90 <-Tc: Natural Period of the Convective (Sloshing) Mode of Behaviour of the Liquid (s)

Impulsive Spectral Acceleration Coefficients Computation0.25 <-SS: Mapped Earthquake Spectral Response Acceleration Parameter at 0.2s (%g)

2.5 <-Fa: Acceleration-based Site Coefficient (at 0.2s Period) (Table E-1)3.5 <-Rwi: Force Reduction Coefficient for the Impulsive Mode (Table E-4)

12000

Ei

iu

C HTtD

ρ

=

0.5783.68tanh

sKH

D

=⎛ ⎞⎜ ⎟⎝ ⎠

1.8c sT K D=

1 1.25 PS S=

2.5S PS S=

10.007;2.5 0.5i a Pwi wi

I IA Max QF S S If Class ER R

⎛ ⎞= ≥⎜ ⎟

⎝ ⎠

2

2.5

2.5

Sa P c L

c wcc i

S La P c L

c wc

T IKQF S if T TT R

A AT T IKQF S if T TT R

⎧ ≤⎪⎪= ≤⎨⎪ >⎪⎩

1vS

a S

F STF S

=

3.5 Rwi: Force Reduction Coefficient for the Impulsive Mode (Table E 4)0.67 <-Q: Scaling Factor0.15 <-Ai: Impulsive Design Response Spectrum Acceleration Coefficient (%g)

Convective Spectral Acceleration Coefficients Computation0.125 <-S1: Mapped Earthquake Spectral Response Acceleration Parameter at 1s (%g)

3.425 <-Fv: Velocity-based Site Coefficient (at 1s Period) (Table E-2)2 <-Rwc: Force Reduction Coefficient for the Convective Mode (Table E-4)4 <-TL: Regional-dependent Transition Period for longer period Ground Motion (s)

0.685 <-TS: Time Coefficient

1.5 <-K: Coefficient to Adjust the Spectral Acceleration for 5% to 0.5%0.07 <-Ac: Convective Design Response Spectrum Acceleration Coefficient (%g)

12000

Ei

iu

C HTtD

ρ

=

0.5783.68tanh

sKH

D

=⎛ ⎞⎜ ⎟⎝ ⎠

1.8c sT K D=

1 1.25 PS S=

2.5S PS S=

10.007;2.5 0.5i a Pwi wi

I IA Max QF S S If Class ER R

⎛ ⎞= ≥⎜ ⎟

⎝ ⎠

2

2.5

2.5

Sa P c L

c wcc i

S La P c L

c wc

T IKQF S if T TT R

A AT T IKQF S if T TT R

⎧ ≤⎪⎪= ≤⎨⎪ >⎪⎩

1vS

a S

F STF S

=



Design Loads Computation16 362 226 <-Wi: Effective Impulsive Portion of the Liquid Weight (N)

5 034 222 <-Wc: Effective Convective (Sloshing) Portion of the Liquid Weight (N)

2 518 375 <-Vi: Design Base Shear due to Impulsive Component (N)

345 748 <-Vc: Design Base Shear due to Convective Component (N)

2 541 998 <-V: Total Design Base Shear (N)

Center of Action Computation (For Ring Wall Overturning Moment)5.434 <-Xi: Height From Bottom of Tank Shell to the Center of Action of Lateral Impulsive Force (m)

tanh 0.8661.333

0.866

1 0.218 1.333

p

i

p

DDH W ifD HW

HD DW ifH H

⎧ ⎛ ⎞⎜ ⎟⎪ ⎝ ⎠⎪ ≥

⎪= ⎨⎪⎪⎛ ⎞− <⎜ ⎟⎪⎝ ⎠⎩

3.670.230 tanhc pD HW WH D

⎛ ⎞= ⎜ ⎟⎝ ⎠

( )i i s r f iV A W W W W= + + +

c c cV AW=

2 2i cV A A= +

0.375 1.333

0.5 0.094 1.333i

DH ifHXD DH ifH H

⎧ ≥⎪⎪= ⎨⎛ ⎞⎪ − <⎜ ⎟⎪⎝ ⎠⎩

3.67cosh 11

3.67 3.67sinhc

HDX H

H HD D

⎡ ⎤⎛ ⎞ −⎜ ⎟⎢ ⎥⎝ ⎠⎢ ⎥= −⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

0.8660.375 1 1.333 1 1.333

tanh 0.866

0.5 0.06 1.333

is

DDH H if

D HX H

D DH ifH H

⎧ ⎡ ⎤⎛ ⎞⎪ ⎢ ⎥⎜ ⎟⎪ ⎢ ⎥⎜ ⎟+ − ≥⎪ ⎛ ⎞⎢ ⎥⎜ ⎟= ⎜ ⎟⎨ ⎜ ⎟⎢ ⎥⎝ ⎠⎝ ⎠⎣ ⎦⎪⎪⎡ ⎤+ <⎪⎢ ⎥⎣ ⎦⎩

3.67cosh 1.9371

3.67 3.67sinhcs

HDX H

H HD D

⎡ ⎤⎛ ⎞ −⎜ ⎟⎢ ⎥⎝ ⎠⎢ ⎥= −⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

9.901 <-Xc: Height From Bottom of Tank Shell to the Center of Action of Lateral Convective Force (m)

Center of Action Computation (For Slab Overturning Moment)7.590 <-Xis: Height From Bottom of Tank Shell to the Center of Action of Lateral Impulsive Force (m)

10.108 <-Xcs: Height From Bottom of Tank Shell to the Center of Action of Lateral Convective Force (m)

tanh 0.8661.333

0.866

1 0.218 1.333

p

i

p

DDH W ifD HW

HD DW ifH H

⎧ ⎛ ⎞⎜ ⎟⎪ ⎝ ⎠⎪ ≥

⎪= ⎨⎪⎪⎛ ⎞− <⎜ ⎟⎪⎝ ⎠⎩

3.670.230 tanhc pD HW WH D

⎛ ⎞= ⎜ ⎟⎝ ⎠

( )i i s r f iV A W W W W= + + +

c c cV AW=

2 2i cV A A= +

0.375 1.333

0.5 0.094 1.333i

DH ifHXD DH ifH H

⎧ ≥⎪⎪= ⎨⎛ ⎞⎪ − <⎜ ⎟⎪⎝ ⎠⎩

3.67cosh 11

3.67 3.67sinhc

HDX H

H HD D

⎡ ⎤⎛ ⎞ −⎜ ⎟⎢ ⎥⎝ ⎠⎢ ⎥= −⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

0.8660.375 1 1.333 1 1.333

tanh 0.866

0.5 0.06 1.333

is

DDH H if

D HX H

D DH ifH H

⎧ ⎡ ⎤⎛ ⎞⎪ ⎢ ⎥⎜ ⎟⎪ ⎢ ⎥⎜ ⎟+ − ≥⎪ ⎛ ⎞⎢ ⎥⎜ ⎟= ⎜ ⎟⎨ ⎜ ⎟⎢ ⎥⎝ ⎠⎝ ⎠⎣ ⎦⎪⎪⎡ ⎤+ <⎪⎢ ⎥⎣ ⎦⎩

3.67cosh 1.9371

3.67 3.67sinhcs

HDX H

H HD D

⎡ ⎤⎛ ⎞ −⎜ ⎟⎢ ⎥⎝ ⎠⎢ ⎥= −⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦



Overturning Moment Computation14 141 514 <-Mrw: Ringwall Moment (Nm)

19 289 761 <-Ms: Slab Moment (Nm)

Vertical Seismic Acceleration Computation0.058 <-Av: Vertical Seismic Acceleration Coefficient (%g)

10 524 <-Fv: Vertical Seismic Up/Down Load (N)

Dynamic Liquid Hoop Stresses Computation

( ) ( )2 2rw i i i s s r r c c cM A W X W X W X A W X⎡ ⎤ ⎡ ⎤= + + +⎣ ⎦ ⎣ ⎦

( ) ( )2 2s i i is s s r r c c csM A W X W X W X A W X⎡ ⎤ ⎡ ⎤= + + +⎣ ⎦ ⎣ ⎦

0.35v a PA QF S=

1

1

k

k jj

Y H Z−

=

= −∑

k sk kt t C= −

2

22

2

8.48 0.5 tanh 0.866 1.333

5.22 0.5 1.33 & 0.750.75 0.75

2.6 1.33 & 0.75

k ki

k kik i k

i k

Y Y D DAGDH ifH H H H

Y Y DN AGD if Y DD D H

DAGD if Y DH

⎧ ⎡ ⎤⎛ ⎞ ⎛ ⎞− ≥⎪ ⎢ ⎥ ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠⎪ ⎢ ⎥⎣ ⎦

⎪⎡ ⎤⎪ ⎛ ⎞ ⎡ ⎤= − < <⎢ ⎥⎨ ⎜ ⎟ ⎢ ⎥⎣ ⎦⎝ ⎠⎢ ⎥⎪ ⎣ ⎦

⎪ ⎡ ⎤⎪ < ≥⎢ ⎥⎪ ⎣ ⎦⎩

4.9hk kN GY D=

( )2 3.681.85 cosh

3.68cosh

kc

ck

H YA GD

DN

HD

⎡ ⎤−⎢ ⎥⎣ ⎦=

⎡ ⎤⎢ ⎥⎣ ⎦

( )22 2hk ik ck v hk

Tkk

N N N A Nt

σ+ + +

=

1.33Tk kS S=

( )0.4v v s rF A W W= +

No.Yk (m)

tk (mm)

Nik (N/mm)

Nck (N/mm)

Nhk (N/mm)

σTk (MPa)

STk (MPa)

CheckσTk≤STk

1 13.5 7 75.83 1.43 926.10 145.60 182.21 OK2 11 6 75.83 1.75 754.60 140.38 182.21 OK3 8.5 5 73.36 2.86 583.10 132.80 182.21 OK4 6 3 62.14 5.24 411.60 159.48 182.21 OK5 3.5 3 42.29 9.97 240.10 95.25 182.21 OK6 1.5 3 20.20 16.81 102.90 43.28 182.21 OK789101112

<-Yk: Distance From Liquid Surface to Shell Course Bottom (m)<-tk: Corroded Shell Thickness (mm)<-Nik: Impulsive Hoop Membrane Force in Tank Shell (N/mm)<-Nck: Convective Hoop Membrane Force in Tank Shell (N/mm)<-Nhk: Product Hydrostatic Membrane Force (N/mm)<-σTk: Total Combined Hoop Stress in the Shell (MPa)< S : Allowable Tensile Stress For Seismic Load Case (MPa)

( ) ( )2 2rw i i i s s r r c c cM A W X W X W X A W X⎡ ⎤ ⎡ ⎤= + + +⎣ ⎦ ⎣ ⎦

( ) ( )2 2s i i is s s r r c c csM A W X W X W X A W X⎡ ⎤ ⎡ ⎤= + + +⎣ ⎦ ⎣ ⎦

0.35v a PA QF S=

1

1

k

k jj

Y H Z−

=

= −∑

k sk kt t C= −

2

22

2

8.48 0.5 tanh 0.866 1.333

5.22 0.5 1.33 & 0.750.75 0.75

2.6 1.33 & 0.75

k ki

k kik i k

i k

Y Y D DAGDH ifH H H H

Y Y DN AGD if Y DD D H

DAGD if Y DH

⎧ ⎡ ⎤⎛ ⎞ ⎛ ⎞− ≥⎪ ⎢ ⎥ ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠⎪ ⎢ ⎥⎣ ⎦

⎪⎡ ⎤⎪ ⎛ ⎞ ⎡ ⎤= − < <⎢ ⎥⎨ ⎜ ⎟ ⎢ ⎥⎣ ⎦⎝ ⎠⎢ ⎥⎪ ⎣ ⎦

⎪ ⎡ ⎤⎪ < ≥⎢ ⎥⎪ ⎣ ⎦⎩

4.9hk kN GY D=

( )2 3.681.85 cosh

3.68cosh

kc

ck

H YA GD

DN

HD

⎡ ⎤−⎢ ⎥⎣ ⎦=

⎡ ⎤⎢ ⎥⎣ ⎦

( )22 2hk ik ck v hk

Tkk

N N N A Nt

σ+ + +

=

1.33Tk kS S=

( )0.4v v s rF A W W= +



Anchorage Requirement Check0.977 <-Ge: Effective Specific Gravity Including Vertical Seismic Effects

30 882 <-wa: Force Resisting Uplift in Annular Region (N/m)

1 674 <-wrs: Roof Loading Acting on Shell (N/m)

10 255 <-wt: Shell & Roof Weight Acting at Base of Shell (N/m)

8 750 <-wint: Design uplift Load due to Product Pressure (N/m)

1.93 <-J: Anchorage Ratio

J > 1.54 OK

( )1 0.4e vG G A= −

( )99 ;201.1a a y e ew Min t F HG HDG=

rrs

WwDπ

=

st rs

Ww WDπ

= +

( )( )2int1 0.4 0.4

rw

t v a

MJD w A w w

=− + −

int 4PDw =

( )2

1.273 1 0.4rwAB t v

Mw w AD

⎛ ⎞= − −⎜ ⎟⎝ ⎠

S ABU Dwπ=

( )1

1.273 11 0.4² 1000

rwc t v

Mw AD t

σ ⎛ ⎞= + +⎜ ⎟⎝ ⎠

21

21

21

1 21

83 44

83 7.5 ;0.5 442.5

c

ty

t GHDifD t

Ft GHDMin GH F if

D t

⎧≥⎪

⎪= ⎨⎛ ⎞⎪ + <⎜ ⎟⎪ ⎝ ⎠⎩

Anchor Load Computation81 832 <-wAB: Design uplift Load On Anchors per Unit Circumferential Length (N/m)

3 599 166 <-US: Seismic Uplift Load (N)

Shell Compression Stresses Computation15 <-σc: Maximum Longitudinal Shell Compression Stress (MPa)

42 <-Fc: Allowable Longitudinal Shell-Membrane Compression Stress (MPa)

σc ≤ Fc OK

( )1 0.4e vG G A= −

( )99 ;201.1a a y e ew Min t F HG HDG=

rrs

WwDπ

=

st rs

Ww WDπ

= +

( )( )2int1 0.4 0.4

rw

t v a

MJD w A w w

=− + −

int 4PDw =

( )2

1.273 1 0.4rwAB t v

Mw w AD

⎛ ⎞= − −⎜ ⎟⎝ ⎠

S ABU Dwπ=

( )1

1.273 11 0.4² 1000

rwc t v

Mw AD t

σ ⎛ ⎞= + +⎜ ⎟⎝ ⎠

21

21

21

1 21

83 44

83 7.5 ;0.5 442.5

c

ty

t GHDifD t

Ft GHDMin GH F if

D t

⎧≥⎪

⎪= ⎨⎛ ⎞⎪ + <⎜ ⎟⎪ ⎝ ⎠⎩



Tank Freeboard Check0.137 <-Af: Acceleration Coefficient for Sloshing Wave Height Calculation (%g)

0.962 <-δs: Height of Sloshing Wave Above the Product (m)

0.673 <-Hf: Minimum Free Height (m)

Hf ≤ Hfh OK

Seismic Loading Computation0.15 <-Ai: Impulsive Design Response Spectrum Acceleration Coefficient (%g)

0.058 <-Av: Vertical Seismic Acceleration Coefficient (%g)10 524 <-Fv: Vertical Seismic Up/Down Load (N)

2 541 998 <-V: Total Design Base Shear (N)14 141 514 <-Mrw: Ringwall Moment (Nm)

146 <-σT1: First Shell Course Hoop Stress due To Seismic Loading & Product Weight (MPa)

2

2.5 4

42.5 4

sa P c

cf

sa P c

c

TKQF S I if TT

ATKQF S I if T

T

⎧ ⎛ ⎞≤⎪ ⎜ ⎟

⎪ ⎝ ⎠= ⎨⎛ ⎞⎪ >⎜ ⎟⎪ ⎝ ⎠⎩

0.5s fDAδ =

0.7f sH δ=

146 <-σT1: First Shell Course Hoop Stress due To Seismic Loading & Product Weight (MPa)3 599 166 <-US: Ring Wall Uplift Load due to Seismic & Dead Load (N)

2

2.5 4

42.5 4

sa P c

cf

sa P c

c

TKQF S I if TT

ATKQF S I if T

T

⎧ ⎛ ⎞≤⎪ ⎜ ⎟

⎪ ⎝ ⎠= ⎨⎛ ⎞⎪ >⎜ ⎟⎪ ⎝ ⎠⎩

0.5s fDAδ =

0.7f sH δ=



11- Analyse de la Stabilité Sous l'Effet du Vent (Stability Check Under Wind Load)Anchored Tank

Geometric Parameters14 <-D: Nominal Tank Diameter (m)

13.5 <-H: Maximum Design Product Level (m)6 <-ta: Corroded Thickness of the Annular Bottom Plate (mm)7 <-t1: Corroded Thickness of First Shell Course (mm)

Weight & Material Propperties Definition73 605 <-Wr: Total Weight of Tank Roof (Plate, Structure, Roof Nozzle & Handrail) (N)

377 425 <-Ws: Total Weight of Tank Shell & Appurtenances (Shell, Ladder, Shell Nozzle & Platform) (N)577 882 <-WT: Total Weight of Tank (N)

1 <‐G: Design Specific Gravity180 <-V: Design Wind Speed (m/s)

Wind Overturning Moment Computation0.77 <-PC: Wind Pressure on Vertical Projected Areas of Cylindrical Surface (kPa)

1.29 <-PU: Wind Pressure Uplift on Roof Surface (kPa)

2

0.86190CVP ⎛ ⎞= ⎜ ⎟

⎝ ⎠

2

1.44190UVP ⎛ ⎞= ⎜ ⎟

⎝ ⎠

2 3

2 8C U

wHD P D PM π

= +

1 021 165 <-Mw: Wind Overturning Moment About Shell-to-Bottom Joint (Nm)

Wind Loading on Foundation1.29 <-PU: Wind Pressure Uplift on Roof Surface (kPa)

1 021 165 <-Mw: Wind Overturning Moment About Shell-to-Bottom Joint (Nm)795 804 <-Fvw: Wind Upward Vertical Loading (N)145 881 <-Vw: Wind Horizontal Loading (N)

2

0.86190CVP ⎛ ⎞= ⎜ ⎟

⎝ ⎠

2

1.44190UVP ⎛ ⎞= ⎜ ⎟

⎝ ⎠

2 3

2 8C U

wHD P D PM π

= +



12- Vérification des Ancrages (Anchorage Check)Mechanically Anchored Tank

Anchorage ParametersS275JR <-Anchor Bolt Material

265 <-Sya: Anchor Bolt Material Yield Strength (MPa)

ra

c

ta

h

t1e

f

k

w

dh

db

b

j

ag

265 < Sya: Anchor Bolt Material Yield Strength (MPa)206 <-Sy: First Shell Course Material Yield Strength (MPa)1.5 <-Ca: Anchor Chair Corrosion Allowance (MPa)

13.5 <‐H: Design Liquid Level (m)14 <-D: Nominal Tank Diameter (m)

M30 <-Anchor Bolt Diameter36 <-nA: Number of Equally-Spaced Anchors Around Tank Circumference

220 <-a: Top Plate Width (mm)150 <-b: Top Plate Length (mm)30 <-c: Top Plate Thickness (mm)80 <-e: Anchor Bolt Eccentricity (mm)

120 <-g: Distance Between Vertical Plate (mm)500 <-h: Chair Height (mm)25 <-j: Vertical Plate Thickness (mm)10 <-w: Weld Size (Leg Dimension) (mm)6 <-ta: Corroded Thickness of the Annular Bottom Plate (mm)

60 <-ra: Annular Bottom Plate Outside Projection (mm)7 <-t1: First Shell Course Corroded Thickness (mm)5 <-th: Roof Plate Thickness (mm)

42 <-dh: Bolt Hole Diameter (mm)

Seismic Load Parameters10 524 <-Fv: Vertical Seismic Up/Down Load (N)

2 541 998 <-V: Total Design Base Shear (N)14 141 514 <-Mrw: Ringwall Moment (Nm)

146 <-σT1: First Shell Course Hoop Stress due To Seismic Loading & Product Weight (MPa)3 599 166 <-US: Ring Wall Uplift Load due to Seismic & Dead Load (N)

Wind Load Parameters1 021 165 <-Mw: Wind Overturning Moment About Shell-to-Bottom Joint (Nm)

ra

c

ta

h

t1e

f

k

w

dh

db

b

j

ag

1 021 165 Mw: Wind Overturning Moment About Shell to Bottom Joint (Nm)795 804 <-Fvw: Wind Upward Vertical Loading (N)145 881 <-Vw: Wind Horizontal Loading (N)

ra

c

ta

h

t1e

f

k

w

dh

db

b

j

ag



Design Parameters1.5 <‐P: Internal Design Pressure (kPa)

1 <‐G: Design Specific GravityNo <‐Frangible Joint Design (Yes/No)

0 <‐Pf: Failure Pressure (0 if None Frangible Joint Design) (kPa)0 <‐Pt: Internal Test Pressure (kPa)

252 589 <-W1: Corroded Dead Load of Shell & Roof Excluding Roof Plate Weight (N)313 857 <-W2: Corroded Dead Load of Shell & Roof (N)389 763 <-W3: Dead Load of Shell & Roof Excluding Roof Plate Weight (N)

Bolt Parameters Computation30 <-db: Nominal Bolt Diameter (mm)

519 <-As: Bolt Nominal Stress Area (mm²)

db ≥ 25mm OK

πD/nA ≤ 3m OK

Anchor Bolt Check

No.Ui (N)

PABi (N)

PAi (N)

σABi (MPa)

Formula ValueCheckσABi≤

SABi

1 0 0 0 0 105 105 OK

SABi (MPa)

Load Case Net Uplift FormulaU (N)

(P-0.08th)D²-W1Dead Weight & Internal Design

P

iABi

A

UPn

= AiABi

s

PA

σ =( );1.5Ai ya s ABiP Min S A P=

1 0 0 0 0 105 105 OK

2 0 0 0 0 140 140 OK

3 0 0 0 0 Sya 265 OK

4 0 0 0 0 Sya 265 OK

5 0 0 0 0 0.8 Sya 212 OK

6 3 726 576 103 516 137 535 199 0.8 Sya 212 OK

7 193 505 5 375 8 063 10 140 140 OK

8 3 942 176 109 505 137 535 211 0.8 Sya 212 OK

<-Ui: Net Uplift (0 if Negative Value) (N)<-PABi: Anchor Design Load (N)<-PAi: Anchorage Attachment Design Load (N)<-σABi: Anchor Bolt Tensile Stress (MPa)<-σABi: Anchor Bolt Tensile Stress (MPa)<-SABi: Allowable Anchor Bolt Stress (MPa)

(3Pf-0.08th)D²-W3

4Mw/D-W2

Frangible Pressure

Dead Weight & Wind Load

Dead Weight & Seismic Load

Design Pressure, Dead Weight & Wind Load

Design Pressure, Dead Weight & Seismic Load

4Mrw/D-W2

(P-0.08th)D²+4Mw/D-W1

(P-0.08th)D²+4Mrw/D-W1

(P-0.08th)D -W1

(Pt-0.08th)D²-W1

(1.5Pf-0.08th)D²-W3

Pressure

Dead Weight & Test Pressure

Failure Pressure

iABi

A

UPn

= AiABi

s

PA

σ =( );1.5Ai ya s ABiP Min S A P=iABi

A

UPn

= AiABi

s

PA

σ =( );1.5Ai ya s ABiP Min S A P=



Anchor Chair Parameters Computation28.5 <-cc: Corroded Thickness of Anchor Chair Top Plate (mm)

23.5 <-jc: Vertical Plate Corroded Thickness (mm)

49 <-f: Distance from Outside of Top Plate to Edge of Hole (mm)

105 <-k: Average Vertical Plate width (mm)

7000 <-R: Shell Internal Radius (mm)

0.970 <-Z: Reduction Factor

Anchor Chair Top Plate Check

c ac c C= −

c aj j C= −

2hdf b e= − −

2ab rk +

=

( )2 0.375 0.22Aitbi b

c

PS g dfc

= −

2

11

1

0.177 125.4

a a

Zat t

tRt

=⎛ ⎞

+⎜ ⎟⎝ ⎠

2DR =

No.Stbi

(MPa)Formula Value

Check Stbi≤

Ssi

1 0 140 140 OK

2 0 170 170 OK

3 0 Sy 206 OK

4 0 Sy 206 OK

5 0 170 170 OK

6 133 170 170 OK

7 8 170 170 OK

8 133 170 170 OK

<-Stbi: Anchor Chair Top Plate Bending Stress (MPa)<-SSi: Allowable Anchor Chair & Shell Stress (MPa)

4Mrw/D-W2

Design Pressure, Dead Weight & Wind Load

(P-0.08th)D²+4Mw/D-W1

Design Pressure, Dead Weight & Seismic Load

(P-0.08th)D²+4Mrw/D-W1

(3Pf-0.08th)D²-W3

Dead Weight & Test Pressure (Pt-0.08th)D²-W1

Failure Pressure (1.5Pf-0.08th)D²-W3

Frangible Pressure

SSi (MPa)

Load Case Net Uplift FormulaU (N)

Dead Weight & Internal Design Pressure

(P-0.08th)D²-W1

Dead Weight & Wind Load 4Mw/D-W2

Dead Weight & Seismic Load

c ac c C= −

c aj j C= −

2hdf b e= − −

2ab rk +

=

( )2 0.375 0.22Aitbi b

c

PS g dfc

= −

2

11

1

0.177 125.4

a a

Zat t

tRt

=⎛ ⎞

+⎜ ⎟⎝ ⎠

2DR =

c ac c C= −

c aj j C= −

2hdf b e= − −

2ab rk +

=

( )2 0.375 0.22Aitbi b

c

PS g dfc

= −

2

11

1

0.177 125.4

a a

Zat t

tRt

=⎛ ⎞

+⎜ ⎟⎝ ⎠

2DR =



Shell Stresses Check

No.Sbi

(MPa)σhi

(MPa)τi

(MPa)S1i

(MPa)S2i

(MPa)Si

(MPa)Smaxi (MPa)

SSi (MPa)

Check Smaxi≤

Ssi

1 0 135 0.00 135 0 135 135 140 OK

2 0 132 0.00 132 0 132 132 170 OK

3 0 132 0.00 132 0 132 132 206 OK

4 0 132 0.00 132 0 132 132 206 OK

5 0 132 0.00 132 0 132 132 170 OK

6 162 146 7.97 165 142 23 165 170 OKσT1

1.5PfD/t1+4.9GHD/t1

3PfD/t1+4.9GHD/t1

4.9GHD/t1

Hoop Stress Formulaσh (MPa)

PD/t1+4.9GHD/t1

PtD/t1+4.9HD/t1

( )2 0.3331 1

1

1.32 0.0311.43 ² 4 ²

Aibi

P e ZS aht RtahRt

⎡ ⎤⎢ ⎥⎢ ⎥= +⎢ ⎥+⎢ ⎥⎣ ⎦ ( ){ }2 2

11 42i bi hi bi hi iS σ σ σ σ τ= + + − +

( ){ }2 22

1 42i bi hi bi hi iS σ σ σ σ τ= + − − +

1 2i i iS S S= −

( )2 2Ai

iP

w a hτ =

+( )max 1 2; ;i i i iS Max S S S=

[ ]min1 ;12.7 ;0.04

170Ami

aPj Max mm h c C

k MPa⎛ ⎞= − +⎜ ⎟⎝ ⎠

7 9 135 0.47 135 9 126 135 170 OK

8 162 149 7.97 165 145 21 165 170 OK

<-Sbi: Shell Bending Stress at Anchor Chair Junction (MPa)<-Shi: Hoop Stress at Anchor Chair Junction (MPa)<-τi: Shear Stress at Anchor Chair Junction (MPa)<-S1i: First Principal Stress at Anchor Chair Junction (MPa)<-S2i: Second Principal Stress at Anchor Chair Junction (MPa)<-Si: Tresca Combined Stress at Anchor Chair Junction (MPa)<-Smaxi: Tresca Combined Stress at Anchor Chair Junction (MPa)<-SSi: Allowable Anchor Chair & Shell Stress (MPa)

Vertical Side Plate Check137 535 <-PAmi: Anchorage Attachment Maximum Design Load (N)

20 <-jmin: Minimum Vertical Plate Thickness (mm)

j ≥ jmin OK

PD/t1+4.9GHD/t1

PD/t1+σT1

( )2 0.3331 1

1

1.32 0.0311.43 ² 4 ²

Aibi

P e ZS aht RtahRt

⎡ ⎤⎢ ⎥⎢ ⎥= +⎢ ⎥+⎢ ⎥⎣ ⎦ ( ){ }2 2


( ){ }2 22


1 2i i iS S S= −

( )2 2Ai

iP

w a hτ =


[ ]min1 ;12.7 ;0.04

170Ami

aPj Max mm h c C

k MPa⎛ ⎞= − +⎜ ⎟⎝ ⎠

( )2 0.3331 1

1

1.32 0.0311.43 ² 4 ²

Aibi

P e ZS aht RtahRt

⎡ ⎤⎢ ⎥⎢ ⎥= +⎢ ⎥+⎢ ⎥⎣ ⎦ ( ){ }2 2


( ){ }2 22


1 2i i iS S S= −

( )2 2Ai

iP

w a hτ =


[ ]min1 ;12.7 ;0.04

170Ami

aPj Max mm h c C

k MPa⎛ ⎞= − +⎜ ⎟⎝ ⎠



Weld Check

No.τvi

(MPa)τhi

(MPa)τTi

(MPa)SSi

(MPa)

Check Smaxi≤

Ssi

1 0.00 0.00 0.00 140 OK

2 0.00 0.00 0.00 170 OK

3 0.00 0.00 0.00 206 OK

4 0.00 0.00 0.00 206 OK

5 0.00 0.00 0.00 170 OK

6 7.97 2.81 8.45 170 OK

7 0.47 0.16 0.50 170 OK

8 7.97 2.81 8.45 170 OK

( )2 2Ai

viP

w a hτ =

+ ( )2 0.667 ²Ai

hiP e

w ah hτ =

+2 2

Ti vi hiτ τ τ= +

<-τvi: Weld Vertical Stress (MPa)<-τhi: Weld Horizontal Stress (MPa)<-τi: Weld Total Stress (MPa)<-SSi: Allowable Anchor Chair & Shell Stress (MPa)

( )2 2Ai

viP

w a hτ =

+ ( )2 0.667 ²Ai

hiP e

w ah hτ =

+2 2

Ti vi hiτ τ τ= +



13- Dimensionnement la Charpente du Toit (Check of Roof Structure)

Main Geometric Parameters14000 <-D: Nominal Tank Diameter (mm)

9.46 <-α: Slope Angle (Deg)Compression Ring Parameters

1400 <-Dc: Compression Ring Outside Diameter (mm)10 <-tcr: Compression Ring Box Plate Thickness (mm)

140 <-a: Compression Ring Box Width (mm)S235JR <-Compression Ring Material Designation

200 000 <-Ecr: Compression Ring Material Young Modulus (MPa)235 <-Ycr: Compression Ring Minimum Yield Strength (MPa)

Dc

Dα

b=D

r/cos

(α)

Dr

a

tcr

tcr

tcr



Shell Compression Ring Definition5 <-tr: Nominal Roof Plate Thickness (mm)0 <-Cr: Roof Plate Corrosion Allowance (mm)6 <-ts: Nominal Shell Plate Thickness (mm)3 <-Cs: Shell Plate Corrosion Allowance (mm)

20 <-r: Roof Plate Position (mm)L130x12 <-Shell Compression Ring Section

S275JR <-Shell Compression Ring Material Designation 200 000 <-Eco: ShellCompression Ring Material Young Modulus (MPa)

235 <-Yco: Shell Compression Ring Minimum Yield Strength (MPa)Loadings Definition

45 <-DLs: Self Weight of Roof Structure (kg/m²)45 <-DL: Roof Plate Roof Accessories Weight (kg/m²)

200 <-LL: Live Load on Roof (kg/m²)1.292 <-PU: Wind Pressure Uplift on Roof Surface (kPa)0.058 <-Av: Vertical Seismic Acceleration Coefficient (%g)

2.5 <-Pi: Design Internal Pressure (kPa)0.25 <-Pe: Design External Pressure (kPa)

0 <-Pt: Hydrostatic Test Pressure (kPa)Rafter Definition

IPE180 <-Rafter Section28 <-N: Total Number of Roof Rafter

S235JR <-Rafter Material Designation 200 000 <-E: Rafter Material Young Modulus (MPa)

235 <-Y: Rafter Minimum Yield Strength (MPa)Main Rafter Characteristics

2 395 <-A: Rafter Section Area (mm²)180 <-Dr: Rafter Section Height (mm)91 <-h: Rafter Section Width (mm)

8.00 <-tf : Rafter Flange Thickness (mm)5.30 <-tw: Rafter Web Thickness (mm)

13 169 590 <-Ix: Rafter Moment of Inertia along x-axis (mm4)1 008 504 <-Iy: Rafter Moment of Inertia along y-axis (mm4)

146 329 <-Zx: Rafter Modulus About x-axis (mm3)22 165 <-Zy: Rafter Modulus About y-axis (mm3)

74 <-rx: Rafter Moment radius of Gyration along x-axis (mm)21 <-ry: Rafter Moment radius of Gyration along y-axis (mm)19 <-Wl: Rafter Unit Weight (kg/m)

Rafter Parameters Computation5 <-E: Vertical Seismic Down Load (kg/m²)

6 387 <-L: Rafter Length (mm)

141 <-σa: Allowable Rafter Bending Stress (MPa)( )2cos

cD DLα

−=

1.67aYσ =

( )v sE A DL DL= +

tf

Dr

y

x

h

r

tw

wh

wc

r

ts

trα



Rafter Loading Computation

No. Formula Valueq2i

(N/mm)q1i

(N/mm)q2ni

(N/mm)q1ni

(N/mm)q2ti

(N/mm)q1ti

(N/mm)

1 DL+DLs-Pi -1 617.10 -2.54 -0.25 -2.51 -0.25 -0.42 -0.04

2DL+DLs-

Pt882.90 1.39 0.14 1.37 0.14 0.23 0.02

3DL+DLs-PU-0.4Pi

-1 409.51 -2.21 -0.22 -2.18 -0.22 -0.36 -0.04

4DL+DLs-PU+0.4Pi

-309.51 -0.49 -0.05 -0.48 -0.05 -0.08 -0.01

5DL+DLs+LL+0.4Pe

2 944.90 4.63 0.46 4.56 0.46 0.76 0.08

6DL+DLs+Pe+0.4LL 1 917.70 3.01 0.30 2.97 0.30 0.50 0.05

7DL+DLs-E-0.4Pi

-168.60 -0.26 -0.03 -0.26 -0.03 -0.04 0.00

<-pi: Design Load (N/m²)<-q2i: Maximum Linear Load Applied on Rafter (N/mm)<-q1i: Minimum Linear Load Applied on Rafter (N/mm)<-q2ni: Maximum Normal Linear Load Applied on Rafter (N/mm)<-q1ni: Minimum Normal Linear Load Applied on Rafter (N/mm)<-q2ti: Maximum Compression/Tension linear load applied on Rafter (N/mm)<-q1ti: Minimum Compression/Tension Linear Load Applied on Rafter (N/mm)

Load Case Designation

pi (N/m²)

(e-2) Gravity Loads

(a) Fluid and Internal Pressure

(b) Hydrostatic Pressure

(c) Wind & Internal Pressure

(d) Wind & External Pressure

(e-1) Gravity Loads

(f) Seismic

2i

iDpqN

π= 1

c ii

D pqN

π= ( )2 2 cosni iq q α=

( )1 1 cosni iq q α=

( )2 2 sinti iq q α=

( )1 1 sinti iq q α=



Rafter Stresses Check

No.x0i

(mm)Mbi

(Nmm)σbi

(MPa)σci

(MPa)σi

(MPa)Checkσ1i ≤ σa

1 5 026.32 -5 449 680 37.24 0.89 38.13 OK

2 3 607.01 3 905 383 26.69 0.49 27.18 OK

3 5 026.32 -4 750 095 32.46 0.78 33.24 OK

4 5 026.32 -1 043 059 7.13 0.17 7.30 OK

5 3 607.01 13 026 349 89.02 1.62 90.64 OK

6 3 607.01 8 482 675 57.97 1.06 59.03 OK

7 5 026.32 -568 196 3.88 0.09 3.98 OK

<-x0i: Abscisse of Maximum Moment (mm)<-Mbi: Maximum Moment due to Normal Loading on Rafter (Nmm)<-σbi: Rafter Bending Stress (MPa)<-σc: Rafter Compression/Tension Stress (MPa)<-σi: Rafter due to combined bending & Compression/Tension Stress (MPa)






(e-1) Gravity Loads

(e-2) Gravity Loads

(f) Seismic

2 21 1 2 2

0 12 13

ni ni ni nii ni

ni ni

q q q q Lx qq q

⎡ ⎤+ += −⎢ ⎥

−⎢ ⎥⎣ ⎦

( ) ( )322 1 0 1 2 01 0 2

2 6 6ni ni i ni ni ini i

bi

q q x q q Lxq xML

− += − − +

bibi

x

MZ

σ =

( )2 1

2ti ti

ci

q q LA

σ+

=

i bi ciσ σ σ= +



Rafter Reaction Computation & Displacement Check

No.Rvi (N)

Rhi (N)

fi (mm)

L/fiCheck

L/fi ≥ 200

1 -8 923 -19 737 7.97 801 OK

2 4 872 10 776 -6.98 915 OK

3 -7 778 -17 203 6.95 919 OK

4 -1 708 -3 778 1.53 4 186 OK

5 16 250 35 943 -23.28 274 OK

6 10 582 23 406 -15.16 421 OK

7 -930 -2 058 0.83 7 683 OK

<-Rvi: Vertical Shell Reaction (N)<-Rhi: Radial Load on Compression Ring & Shell Stiffener (N)<-fi: Maximum Rafter Displacement (mm)






(e-1) Gravity Loads

(e-2) Gravity Loads

(f) Seismic

( ) ( ) ( )5 3 342 1 0 1 2 0 1 2 01 0 2 7 8

24 120 36 360ni ni i ni ni i ni ni ini i

ix x x x

q q x q q Lx q q L xq xfEI EI L EI EI

− + += − − + −

1 2

2i i

viq qR L+

= ( )1 2

3 6 sini i

hiq q LR

α⎛ ⎞= +⎜ ⎟⎝ ⎠



Compression Ring Parameters Computation182 <-b: Compression Ring Box Height (mm)

6 050 <-Acr: Compression Ring Box Cross Section Area (mm²)

18 330 217 <-Icry: Compression Ring Box Section Moment of Inertia Along y-Axis (mm4)

309 228 <-Zcry: Compression Ring Box Section Modulus Along y-Axis (mm3)

13 <-θ: Angle Between Rafters (Deg)

630 <-Rc: Compression Ring Mean Radius (mm)

0.992 <-k2: Compression Ring Hoop Stress Deformation Factor

141 <-σcra: Allowable Stresses for Compression Ring (MPa)

( )cosrDbα

=

( )2 2 2cr cr cr crA at b t t= + −

( )( )22 2 24cr cr

cry

ba b t a tZ

− − −=

2c

cD aR −

=

360N

θ =

( ) ( )33 2 212

cr crcry

ba b t a tI

− − −=

2 21 ycr

cr c

Ik

A R= −

1.67cr

craY

σ =



Compression Ring Stresses Check

No.Npi (N)

Mpi (Nmm)

Nmi (N)

Mmi (Nmm)

σpi (MPa)

σmi (MPa)

σcri (MPa)

Checkσcri≤σcra

1 -19 924 255 101 -20 050 -445 398 4 5 5 OK

2 10 878 -139 280 10 947 243 177 2 3 3 OK

3 -17 366 222 354 -17 476 -388 222 4 4 4 OK

4 -3 813 48 826 -3 837 -85 248 1 1 1 OK

5 36 283 -464 565 36 513 811 115 7 9 9 OK

6 23 627 -302 522 23 777 528 193 5 6 6 OK

7 -2 077 26 597 -2 090 -46 438 0 0 0 OK

<-Npi: Axial Effort Applied to Compression Ring at Point Load (N)<-Mpi: Bending Moment Applied to Compression Ring at Point Load (Nmm)<-Nmi: Axial Effort Applied to Compression Ring at Mid Point (N)<-Mmi: Bending Moment Applied to Compression Ring at Mid Point (Nmm)<-σpi: Compression Ring Bending & Axial Stress at Point Load (MPa)<-σmi: Compression Ring Bending & Axial Stress at Mid Point (MPa)<-σcri: Compression Ring Maximum Bending & Axial Stress (MPa)






(e-1) Gravity Loads

(e-2) Gravity Loads

(f) Seismic

4sin2

hipi

RNθ

=⎛ ⎞⎜ ⎟⎝ ⎠

( )2sinhi

miRN

θ=

( )2 1

2 tanhi c

piR R kM

θ θ⎛ ⎞

= − −⎜ ⎟⎜ ⎟⎝ ⎠

( )21

2 sinhi c

miR R kM

θ θ⎛ ⎞

= −⎜ ⎟⎜ ⎟⎝ ⎠

pi pipi

cry cr

M NZ A

σ = +

mi mimi

cry cr

M NZ A

σ = +

( );cri pi miMaxσ σ σ=



Shell Compression Ring Parameters

42 579 <-R2: Length of the Normal to the Roof Measured from the Verical Centerline (mm)

138 <-wh: Maximum Width of Participating Roof (mm)

87 <-wc: Maximum Width of Participating Shell (mm)

130 <-aS: L Shape Height (mm)4 720 000 <-IyS: L Shape Neutral Axis Moment of Inertia Along y-Axis (mm4)

3 000 <-AS: L Shape Section Area (mm²)94 <-XS: L Shape Neutral Position (mm)

1 075 282 <-IyRP: Roof Plate Neutral Axis Moment of Inertia Along y-Axis (mm4)

692 <-ARP: Roof Plate Section Area (mm²)

178 <-XRP: Roof Plate Neutral Position (mm)

196 <-IySP: Shell Plate Neutral Axis Moment of Inertia Along y-Axis (mm4)

( )2 2sinDRα

=

( )( )2300;0.3h r rw Min R t C= −

( )0.62c s sDw t C= −

( ) ( ) ( ) ( )33

cos ² sin ²12 12

r r h h r ryRP

t C w w t CI α α

− −= +

( )RP r r hA t C w= −

( )cos2

hRP S

wX a r

α= − +

( )3

12c s s

ySP

w t CI

−=

α

wh

wc

r

tsctrc

XRP

XSP



261 <-ASP: Shell Plate Section Area (mm²)

132 <-XSP: Shell Plate Neutral Position (mm)

3 953 <-Aco: Shell Compression Ring Cross Section Area (mm²)

111 <-Xco: Compression Ring Plate Neutral Position (mm)

9 945 277 <-Iyco: Shell Compression Ring Moment of Inertia Along y-axis (mm4)

73 336 <-Zyco: Shell Compression Ring Section Modulus Along y-Axis (mm3)

7 000 <-R: Shell Compression Ring Mean Radius (mm)

1.000 <-k2o: Shell Compression Ring Hoop Stress Deformation Factor

141 <-σcoa: Allowable Stresses for Shell Compression Ring (MPa)

co s RP SPA A A A= + +

2DR =

1.67co

coaY

σ =

2 21 ycoo

co

Ik

A R= −

( )SP s s cA t C w= −

( )2

s sSP S

t CX a

−= +

RP RP SP SP S Sco

co

X A X A X AXA

+ +=

( ) ( ) ( )2 2 2yco yRP RP co RP ySP SP co SP yS S co SI I A X X I A X X I A X X= + − + + − + + −

( );

cosyco yco

ycoco S h co

I IZ Min

X a r w Xα⎛ ⎞

= ⎜ ⎟⎜ ⎟− + −⎝ ⎠



Shell Compression Ring Stresses Check

No.Npoi (N)

Mpoi (Nmm)

Nmoi (N)

Mmoi (Nmm)

σpoi (MPa)

σmoi (MPa)

σcoi (MPa)

Checkσcri≤σcra

1 -19 924 2 834 460 -20 050 -4 948 870 44 73 73 OK

2 10 878 -1 547 551 10 947 2 701 971 24 40 40 OK

3 -17 366 2 470 595 -17 476 -4 313 575 38 63 63 OK

4 -3 813 542 510 -3 837 -947 205 8 14 14 OK

5 36 283 -5 161 834 36 513 9 012 385 80 132 132 OK

6 23 627 -3 361 353 23 777 5 868 807 52 86 86 OK

7 -2 077 295 527 -2 090 -515 980 5 8 8 OK

<-Npoi: Axial Effort Applied to Outside Compression Ring at Point Load (N)<-Mpoi: Bending Moment Applied to Outside Compression Ring at Point Load (Nmm)<-Nmoi: Axial Effort Applied to Outside Compression Ring at Mid Point (N)<-Mmoi: Bending Moment Applied to Outside Compression Ring at Mid Point (Nmm)<-σpoi: Outside Compression Ring Bending & Axial Stress at Point Load (MPa)<-σmoi: Outside Compression Ring Bending & Axial Stress at Mid Point (MPa)<-σcoi: Outside Compression Ring Maximum Bending & Axial Stress (MPa)




(e-1) Gravity Loads

(e-2) Gravity Loads

(f) Seismic



4sin2

hipoi

RNθ

=⎛ ⎞⎜ ⎟⎝ ⎠

( )2sinhi

moiRN

θ=

( )2 1

2 tanhi

poiR R kM

θ θ⎛ ⎞

= − −⎜ ⎟⎜ ⎟⎝ ⎠

( )21

2 sinhi

moiR R kM

θ θ⎛ ⎞

= −⎜ ⎟⎜ ⎟⎝ ⎠

poi poipoi

coy co

M NZ A

σ = +

moi moimoi

coy co

M NZ A

σ = +

( );coi poi moiMaxσ σ σ=

