Design Calculations
2024-06-20
Revision : 23-08-24
RESERVOIR_VESSEL_233L
1
Rev.
23-08-24
Date
Job Tag :
Job Name :
Vessel Tag :
Fatigue Calculation 7 Bar
Description
RESERVOIR_VESSEL_233L
RESERVOIR_VESSEL_233L
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
Aut.
Chk.
App.
QA
Description :
Drawing No :
1
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Design Calculations
RESERVOIR_VESSEL_233L
2024-06-20
Revision : 23-08-24
Table of Contents
Table of Contents ................................................................................................................................................................ 2
Codes, Guidelines and Standards Implemented. .............................................................................................................. 4
Design Conditions. .............................................................................................................................................................. 5
Allowable stresses and safety factors ................................................................................................................................. 6
Compartment 1 .................................................................................................................................................................. 6
Hydrostatic Test Pressure .................................................................................................................................................. 7
Hydrostatic Pressure........................................................................................................................................................... 9
Element(s) of geometry under internal pressure .............................................................................................................10
Kloepper Type Head (30.10) under internal pressure .....................................................................................................10
Kloepper Type Head (30.11) under internal pressure .....................................................................................................11
Cylindrical shell under internal pressure ........................................................................................................................12
Vessel under combination loading - Design case .............................................................................................................13
Model for analysis of stress due to support. .....................................................................................................................13
Lifted ................................................................................................................................................................................14
Compartment 1 .................................................................................................................................................................14
Erected .............................................................................................................................................................................15
Compartment 1 .................................................................................................................................................................15
Operating .........................................................................................................................................................................16
Compartment 1 .................................................................................................................................................................16
Shutdown ..........................................................................................................................................................................17
Compartment 1 .................................................................................................................................................................17
Test ...................................................................................................................................................................................18
Compartment 1 .................................................................................................................................................................18
Location of dominant stresses and worst cases. ...............................................................................................................19
Case 1 - Lifting P = 0. (New Inertias) (New Weight) .......................................................................................................20
Case 2 - Erected P = 0. (New Inertias) (New Weight) .....................................................................................................22
Case 3 - Operation (Corroded inertias) (New Weight) ....................................................................................................24
Case 4 - Shutdown P = 0. (Corroded inertias) (Corroded Weight) .................................................................................26
Case 5 - During test (Corroded inertias) (Corroded Weight) ..........................................................................................28
Case 6 - During test P = 0. (Corroded inertias) (Corroded Weight) ...............................................................................30
Maximum Allowable Working Pressure ..........................................................................................................................32
Maximum Allowable Pressure(Geometry). ......................................................................................................................32
Maximum Allowable Pressure (Nozzles). .........................................................................................................................32
Isolated Opening(s) ............................................................................................................................................................33
Opening N1 ......................................................................................................................................................................34
Opening N2 ......................................................................................................................................................................38
Opening N3 ......................................................................................................................................................................42
Opening N4 ......................................................................................................................................................................46
Opening N5 ......................................................................................................................................................................50
Saddles ................................................................................................................................................................................54
Saddle No. 1 .....................................................................................................................................................................55
Saddle No. 2 .....................................................................................................................................................................67
Circular stresses. ................................................................................................................................................................79
Nozzle Flexibility. ...............................................................................................................................................................80
Summary.............................................................................................................................................................................81
Summary of nozzles ..........................................................................................................................................................81
Summary of Geometry ......................................................................................................................................................83
Summary of Weights, Capacities and Painting Areas ......................................................................................................84
Summary of Foundation Loads ........................................................................................................................................85
Summary of Changes........................................................................................................................................................86
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Design Calculations
RESERVOIR_VESSEL_233L
2024-06-20
Revision : 23-08-24
Fatigue Analysis .................................................................................................................................................................87
List of customisable files. ...................................................................................................................................................89
Summary of Errors and Warnings. ..................................................................................................................................90
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Design Calculations
RESERVOIR_VESSEL_233L
2024-06-20
Revision : 23-08-24
Codes, Guidelines and Standards Implemented.
Pressure vessel design code:
EN 13445:2021 (2021-05)
Local load design method:
EN 13445:2021 (2021-05)
Standard of flange ratings:
EN 1092-1:2007
Standard for pipes:
EN 10220 / EN ISO 1127
Material standard(s) and update(s):
EN10028-7 April 2016
X5CrNi18-10
ASME II 2021
SA516GR60
Units:
SI
g = 9.80665 m/s2 [ Weight (N) = Mass (kg) × g ]
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
Plate
Plate
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Design Calculations
RESERVOIR_VESSEL_233L
2024-06-20
Revision : 23-08-24
Design Conditions.
Internal pressure :
Required MAWP :
Design Temperature :
Height of liquid :
Operating fluid spec. gravity :
Corrosion :
External pressure :
External temperature :
Test Pressure :
Test fluid spec. gravity :
Insulation Thickness :
Weight/density of insulation :
Construction Category :
Testing group :
Compartment 1
0.7 MPa
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
10 °C
480 mm
1
1
0 mm
35 kg/m3
/
3
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/
/
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/
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prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
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Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Allowable stresses and safety factors
EN 13445-3 §6
Nominal stress at design temperature.
f
minimum guaranteed tensile strength for the grade of material concerned at temperature (depending on the
Rm/T
load case).
Rm/20
Minimum guaranteed tensile strength at room temperature.
Rp0,2/T
Minimum guaranteed yield strength 0.2 % at temperature (depending on the load case).
Rp1,0/T
Minimum guaranteed yield strength 1 % at temperature (depending on the load case).
Average stress to cause rupture in 100,000 hours at design temperature.
R
Compartment 1
Excluding bolting
Testing group 3
Bolts
Nonaustenitic
steel
Austenitic
stainless steel
Copper
Nominal design stress f
Testing and exceptional load cases
Normal operating load cases fd
ftest
Creep
min( Rp0,2/T / 1.5 ; Rm/20 / 2.4 )
Rp0,2/T / 1.05
R / 1.5
max[ Rp1,0/T / 1.5 ; min( Rp1,0/T / 1.2 ; Rm/T / 3 ) ]
max( Rp1,0/T / 1.05 ; Rm/T / 2 )
R / 1.5
?
?
Aluminium
?
?
Nickel
?
?
Titanium
Cast Iron
Nonaustenitic
steel
Austenitic
stainless steel
?
min( Rp0,2/T / 1.9 ; Rm/20 / 3 )
?
Rp0,2/T / 1.33
R / ?
R / ?
R / ?
R / ?
R / 1.9
min( Rp0,2/T / 3 ; Rm/20 / 4 )
min( Rp0,2/T / 2 ; Rm/20 / 2.67 )
R / 1.5
Rm/T / 4
Rm/20 / 2.67
R / 1.5
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Design Calculations
RESERVOIR_VESSEL_233L
Hydrostatic Test Pressure
EN 13445-5 10.2.3.3
Ps = maximum allowable pressure
Pd = design pressure
fa = nominal design stress under normal operating conditions at test temperature.
fTd = nominal design stress under normal operating conditions at calculation temperature.
Phyd,ope = hydrostatic pressure in operation.
Phyd,test = hydrostatic pressure in test.
emin = minimum possible manufacturing thickness of the section in question
c = Corrosion
Testing group 1,2 or 3 : 10.2.3.3.1
Pt = MAX [ 1,43 Ps ; 1,25 Pd ( fa / fTd )min ]
For vessels where hydrostatic operating pressure > 3% of design pressure: Pt,mod = Pt + (Phyd,ope − Phyd,test ) with : Pt,mod ≥
Pt
Testing group 4 : 10.2.3.3.2
Material group 1.1 (c < 1 mm) : Pt = 2.2 Pd ( fa / fTd )min [ emin /( emin− c )]
Material group 1.1 (c ≥ 1 mm) : Pt = 2.0 Pd ( fa / fTd )min [ emin /( emin− c )]
Material group 8.1 : Pt = 1,85 Pd ( fa / fTd )min
For each component
fa
(MPa)
Pd(MPa)
Kloepper Type Head (01) 30.10
Shell (02) 31.05
Kloepper Type Head (03) 30.11
Neck
Nozzle
Pad
N1
Flange
Bolting
Neck
Nozzle
Pad
N2
Flange
Bolting
Neck
Nozzle
Pad
N3
Flange
Bolting
Neck
Nozzle
Pad
N4
Flange
Bolting
Neck
Nozzle
Pad
N5
Flange
Bolting
0.7
0.7
0.7
fTd
(MPa)
173.33
173.33
173.33
173.33
/
/
/
173.33
/
/
/
173.33
/
/
/
173.33
/
/
/
173.33
/
/
/
0.7
0.7
0.7
0.7
0.7
184.67
184.67
184.67
184.67
/
/
/
184.67
/
/
/
184.67
/
/
/
184.67
/
/
/
184.67
/
/
/
Compartment 1
0.7 MPa
1.001 MPa
Max. allowable pressure :
Ps =
test pressure :
max(Pt ,Pt,mod) =
emin
(mm)
c
(mm)
Pt
(MPa)
3.09
2.03
3.11
2
/
/
0
0
0
0
12
/
/
0
27
/
/
0
2
/
/
0
2
/
/
0
/
/
/
1.001
1.001
1.001
1.001
/
/
/
1.001
/
/
/
1.001
/
/
/
1.001
/
/
/
1.001
/
/
/
/
/
/
Use PED : Pt = MAX [ 1,43 Ps ; 1,25 Ps ( fa / ft )min ]
Ps = maximum allowable pressure
P = Design Pressure
fa = allowable stress at room temperature, normal operating conditions
ft = allowable stress under normal operating conditions
For each component
Kloepper Type Head (01) 30.10
Shell (02) 31.05
Kloepper Type Head (03) 30.11
P
(MPa)
fa
(MPa)
0.7
0.7
0.7
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
ft
(MPa)
173.33
173.33
173.33
7
184.67
184.67
184.67
e
(mm)
3.09
2.03
3.11
c
(mm)
Pt
(MPa)
0
0
0
1.001
1.001
1.001
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Design Calculations
RESERVOIR_VESSEL_233L
For each component
Nozzle
N1
Nozzle
N2
Nozzle
N3
Nozzle
N4
Nozzle
N5
Neck
Pad
Flange
Bolting
Neck
Pad
Flange
Bolting
Neck
Pad
Flange
Bolting
Neck
Pad
Flange
Bolting
Neck
Pad
Flange
Bolting
maximum allowable pressure :
Test Pressure at the Top :
P
(MPa)
fa
(MPa)
0.7
0.7
0.7
0.7
0.7
ft
(MPa)
173.33
/
/
/
173.33
/
/
/
173.33
/
/
/
173.33
/
/
/
173.33
/
/
/
184.67
/
/
/
184.67
/
/
/
184.67
/
/
/
184.67
/
/
/
184.67
/
/
/
Compartment 1
0.7 MPa
1.001 MPa
e
(mm)
c
(mm)
Pt
(MPa)
2
/
/
0
12
/
/
0
27
/
/
0
2
/
/
0
2
/
/
0
/
/
/
1.001
/
/
/
1.001
/
/
/
1.001
/
/
/
1.001
/
/
/
1.001
/
/
/
/
/
/
For vertical vessels with a test in horizontal position : P’t = Pt + Pt
Pt = additional hydrostatic pressure corresponding to the height of the vertical compartment.
Design Pressure P :
Test Pressure Pt :
Pt :
P’t :
Compartment 1
0.7 MPa
1.001 MPa
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Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Hydrostatic Pressure
Test
Operating
Type of
components
Horizontal
Specific
Gravity
liquid level
hydrostatic
height
Hydrostatic
pressure
(mm)
(mm)
(MPa)
Specific
Gravity
Vertical
liquid level
hydrostatic
height
Hydrostatic
pressure
(mm)
(mm)
(MPa)
liquid level
hydrostatic
height
Hydrostatic
pressure
(mm)
(mm)
(MPa)
Shell(s)
01 30.10
1
480.00
480.00
0.0047
1
494.00
494.00
0.0048
0.00
0.00
0.0000
02 31.05
1
480.00
480.00
0.0047
1
494.00
494.00
0.0048
0.00
0.00
0.0000
03 30.11
1
480.00
480.00
0.0047
1
494.00
494.00
0.0048
0.00
0.00
0.0000
Opening(s)
1
N1
1
/
0.00
0.0000
1
/
0.00
0.0000
/
0.00
0.0000
2
N2
1
/
0.00
0.0000
1
/
0.00
0.0000
/
0.00
0.0000
3
N3
1
/
233.00
0.0023
1
/
247.00
0.0024
/
0.00
0.0000
4
N4
1
/
480.00
0.0047
1
/
494.00
0.0048
/
0.00
0.0000
5
N5
1
/
480.00
0.0047
1
/
494.00
0.0048
/
0.00
0.0000
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Design Calculations
RESERVOIR_VESSEL_233L
Element(s) of geometry under internal pressure
Kloepper Type Head (30.10) under internal pressure
EN 13445:2021 (2021-05)
he
L.T
.
Di
De
hc
r
R
Conditions of applicability :
R  De
0.06Di  r  0.2Di
z = Weld joint efficiency
en = nominal thickness
f = Allowable stress
e = minimum required thickness
P = internal pressure
R = equivalent inside radius
r = inside knuckle radius = 50.018 mm
Di = Internal Diameter
he = outside height = 98.494 mm
en,min = (e+c)/Tol% shall be  en
r  2e
e  0.08 De
T = Temperature
 = circular stress
Pa = Max. allowable pressure
Ph = Hydrostatic pressure
De = External Diameter = 500.18 mm
c = corrosion + tolerance
Tol% = tolerance for pipes
ea = (enTol%)−c shall be  e
Analysis thickness ea  0.001De
es = PR/(2fz-0.5P)
  EN 13445-3 7.5.3.5
ey =  . k.P (0.75R+0.2Di) /f
 k  EN 13445-3 7.7
eb = (0.75R+0.2Di) [P/(111fb)(Di/r)0.825](1/1.5) ( fb = 1.6 Rp0,2/T / 1.5 at test conditions the value 1.5 shall be replaced by 1.05 )
required thickness : e = max[ es, ey, eb]
X5CrNi18-10
en = 3.090 mm
Seamless
Plate
Cold formed
Operation
Horizontal test
N
X
Operation
Horizontal test
N
X
Operation
Horizontal test
N
X
L.T
.
hc
e
 ec
Operation
Horizontal test
Tol% = /
Cor. = 0 mm
Schedule : /
DN : /
PWHT : No Radiography : Full
Tol. = 0 mm
P (MPa)
Ph (MPa)
T (°C)
f (MPa)
0.7047
1.0058
fb (MPa)
230.4
320
ea (mm)
3.090
3.090
0.0047
0.0048
10
20
184.67
260

1.005734
1.003646
 (MPa)
97.34
138.93
Rp0,2/T
(MPa)
216
210
R (mm)
Di (mm)
z
500.180
500.180
494.000
494.000
1
1
k
es (mm)
ey (mm)
eb (mm)
1
1
0.955
0.968
1.819
1.840
e (mm)
1.819
1.840
1.524
1.552
en,min (mm)
1.819
1.840
Pa (MPa)
1.34
1.88
EN 13445-3 7.5.3.4 Required thickness of the straight length
hc  lc,max : ec = max[ey, eb]
ea (mm)
184.67
3.090
260
3.090
hc = Straight flange = 17.5 mm
Di
lc,max (mm)
N
X
5.995
6.030
f (MPa)
MAWP ( 10 °C, Corroded) = 1.34 MPa
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
hc  lc,max : ec = PDi / (2fz−P)
emin (mm)
0.944
0.944
0.957
0.957
ec (mm)
MAWP ( 20 °C, new) = 1.25 MPa
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Design Calculations
RESERVOIR_VESSEL_233L
Kloepper Type Head (30.11) under internal pressure
EN 13445:2021 (2021-05)
he
L.T
.
Di
De
hc
r
R
Conditions of applicability :
R  De
0.06Di  r  0.2Di
z = Weld joint efficiency
en = nominal thickness
f = Allowable stress
e = minimum required thickness
P = internal pressure
R = equivalent inside radius
r = inside knuckle radius = 50.022 mm
Di = Internal Diameter
he = outside height = 98.512 mm
en,min = (e+c)/Tol% shall be  en
r  2e
e  0.08 De
T = Temperature
 = circular stress
Pa = Max. allowable pressure
Ph = Hydrostatic pressure
De = External Diameter = 500.22 mm
c = corrosion + tolerance
Tol% = tolerance for pipes
ea = (enTol%)−c shall be  e
Analysis thickness ea  0.001De
es = PR/(2fz-0.5P)
  EN 13445-3 7.5.3.5
ey =  . k.P (0.75R+0.2Di) /f
 k  EN 13445-3 7.7
eb = (0.75R+0.2Di) [P/(111fb)(Di/r)0.825](1/1.5) ( fb = Rp0,2/T / 1.5 at test conditions the value 1.5 shall be replaced by 1.05)
required thickness : e = max[ es, ey, eb]
X5CrNi18-10
en = 3.110 mm
Seamless
Plate
Tol% = /
Cor. = 0 mm
Operation
Horizontal test
N
X
Operation
Horizontal test
N
X
Operation
Horizontal test
N
X
L.T
.
hc
e
 ec
Operation
Horizontal test
Schedule : /
DN : /
PWHT : No Radiography : Full
Tol. = 0 mm
P (MPa)
Ph (MPa)
T (°C)
f (MPa)
0.7047
1.0058
fb (MPa)
144
200
ea (mm)
3.110
3.110
0.0047
0.0048
10
20
184.67
260

1.005703
1.003615
 (MPa)
96.57
137.83
Rp0,2/T
(MPa)
216
210
R (mm)
Di (mm)
z
500.220
500.220
494.000
494.000
1
1
k
es (mm)
ey (mm)
eb (mm)
1
1
0.955
0.969
1.819
1.840
e (mm)
2.084
2.123
2.084
2.123
en,min (mm)
2.084
2.123
Pa (MPa)
1.35
1.9
EN 13445-3 7.5.3.4 Required thickness of the straight length
hc  lc,max : ec = max[ey, eb]
ea (mm)
f (MPa)
184.67
3.110
260
3.110
hc = Straight flange = 17.5 mm
Di
lc,max (mm)
N
X
6.418
6.476
MAWP ( 10 °C, Corroded) = 1.35 MPa
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
hc  lc,max : ec = PDi / (2fz−P)
emin (mm)
ec (mm)
0.944
0.944
0.957
0.957
MAWP ( 20 °C, new) = 1.26 MPa
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Design Calculations
RESERVOIR_VESSEL_233L
Cylindrical shell under internal pressure
EN 13445:2021 (2021-05) part 3 - 7.4.2
e = required thickness
en = nominal thickness
P = internal pressure
f = Nominal stress
De = External Diameter
c = corrosion + tolerance
Di = Internal Diameter
Tol% = tolerance for pipes
en,min = (e+c)/Tol% shall be  en
ea = (en Tol% ) −c shall be  e
7.4.1
e/De shall be  0.16
formula 7.4-1
formula 7.4-2
z = Weld joint efficiency
T = Temperature
 = circular stress
Pa = maximum allowable pressure
Ph = Hydrostatic pressure
e = P (Di+2c) / (2f.z−P)
e = P.De / (2f.z+P)
 = (P ((Di+2c) / ea + P) / (2 z)
 = (P.De / ea − P) / (2 z)
Shell (02) : 31.05 (Barrel)
X5CrNi18-10
en = 2.030 mm
Plate
Di = 494.00 mm
De = 498.06 mm
Tol% = /
Cor. = 0 mm
Tol. = 0 mm
P (MPa)
Ph (MPa)
T (°C)
f (MPa)
z
Operation
N 0.7047 0.0047
Horizontal test X 1.0058 0.0048
MAP (10 °C, corroded) = 1.28 MPa
10
20
184.67
260
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
Schedule : /
DN : /
PWHT : No Radiography : Spot
ea (mm)
 (MPa)
Pa (MPa)
0.85
2.030
101.29
1.28
1
2.030
122.89
2.13
MAP (20 °C, new) = 1.21 MPa
12
e (mm)
1.111
0.957
en,min
(mm)
1.111
0.957
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
Design Calculations
RESERVOIR_VESSEL_233L
2024-06-20
Revision : 23-08-24
Vessel under combination loading - Design case
Model for analysis of stress due to support.
Reactions per support, bending moment and shear loads are studied using a beam model on simple supported, with one
of the supports fixed either to the left or the right of the beam.
The beam is studied using the reduction process which is based on the Falk transmission matrices.
Support conditions allow for resolution of the moment and the rotation which are not subject to discontinuity when
crossing the support.
External single load and moment are applied at their acting point and are considered as a discontinuity similar to a
change in inertia or modulus of elasticity. Distributed loads do not constitute a discontinuity.
Reference axes are : beam x on the right, y up with positive loads down, moments > 0 from x to y.
Shell, liquid, and bundle own weight are considered as distributed loads while head weight, flange and cover, floating
head and nozzle are considered as concentrated loads.
Termination heads are removed and replaced as a concentrated load and an external moment. Hydrostatic height also
creates an external moment as a result of the hydrostatic pressure applied to its location
Each design case in analysed in the vertical and/or horizontal plane. The saddle reactions and bending moment used to
check shell stresses are the vector sum of the two planes. This also provides the new angle where the shell stress should
be checked
Thermal effects are considered by the friction factor to be an additional moment at the saddle location. A fixed saddle
balances all horizontal reactions. The horizontal longitudinal force due to friction is a function of the weight on the
sliding saddle multiplied by the coefficient of friction, the additional vertical loads due to the earthquake are not
considered. ( = 0.3)
Principal stresses are f1 = 0.5[σθ + σz + (σθ - σz)2 + 4 τ2] and f2 = 0.5[σθ + σz - (σθ - σz)2 + 4 τ2] and general primary
membrane stress intensity is σeq = max(|f1-f2|;|f1+0.5p|;|f2+0.5p|), with σθ: circumferential stress , σz: longitudinal stress
and τ: shear stress.
Saddle stresses are studied in the 3 axes.
For the purpose of wind and earthquake design, vibration periods are evaluated using the general modal equation [kω².m] Φ = 0 and solving the eigenvectors and eigenvalues.
The flexibility matrix 1/k is derived using the beam analysis method, using successive unit loads applied at the mass
location.
The resulting dynamic matrix is 1/g.1/k.m where g = acceleration due to gravity and m = mass matrix.
Eigenvectors correspond to the natural modes and eigenvalues to their frequencies.
Subtracting the mode under study from the starting vector allows for study of the higher mode
The Dunkerley method is used for stacked vessels. This enables the global circular frequency to be determined to
1/ω2 = 2/ω12 where ω1 is the circular frequency of one vessel. The final period is T = 2π/ω
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
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Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Lifted
Allowable stresses and safety factors – Lifted
EN 13445-3 §6
Nominal stress at design temperature.
f
minimum guaranteed tensile strength for the grade of material concerned at temperature (depending on the
Rm/T
load case).
Rm/20
Minimum guaranteed tensile strength at room temperature.
Rp0,2/T
Minimum guaranteed yield strength 0.2 % at temperature (depending on the load case).
Rp1,0/T
Minimum guaranteed yield strength 1 % at temperature (depending on the load case).
Average stress to cause rupture in 100,000 hours at design temperature.
R
Compartment 1
Excluding bolting
Testing group 3
Bolts
Nominal design stress f
Testing and exceptional load cases
Normal operating load cases fd
ftest
Creep
Nonaustenitic
steel
Austenitic
stainless steel
Copper
Aluminium
min( Rp0,2/T / 1.5 ; Rm/20 / 2.4 )
Rp0,2/T / 1.05
R / 1.5
max[ Rp1,0/T / 1.5 ; min( Rp1,0/T / 1.2 ; Rm/T / 3 ) ]
max( Rp1,0/T / 1.05 ; Rm/T / 2 )
R / 1.5
?
?
?
?
Nickel
?
?
Titanium
?
min( Rp0,2/T / 1.9 ; Rm/20 / 3 )
?
Rp0,2/T / 1.33
R / ?
R / ?
R / ?
R / ?
R / 1.9
min( Rp0,2/T / 3 ; Rm/20 / 4 )
min( Rp0,2/T / 2 ; Rm/20 / 2.67 )
R / 1.5
Rm/T / 4
Rm/20 / 2.67
R / 1.5
Cast Iron
Nonaustenitic
steel
Austenitic
stainless steel
Pressure / Temperature – Lifted
Design Pressure
Design Temperature
Compartment 1
0 MPa
20 °C
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
Compartment 2
0 MPa
20 °C
14
Compartment 3
0 MPa
20 °C
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Erected
Allowable stresses and safety factors – Erected
EN 13445-3 §6
Nominal stress at design temperature.
f
minimum guaranteed tensile strength for the grade of material concerned at temperature (depending on the
Rm/T
load case).
Rm/20
Minimum guaranteed tensile strength at room temperature.
Rp0,2/T
Minimum guaranteed yield strength 0.2 % at temperature (depending on the load case).
Rp1,0/T
Minimum guaranteed yield strength 1 % at temperature (depending on the load case).
Average stress to cause rupture in 100,000 hours at design temperature.
R
Compartment 1
Excluding bolting
Testing group 3
Bolts
Nominal design stress f
Testing and exceptional load cases
Normal operating load cases fd
ftest
Creep
Nonaustenitic
steel
Austenitic
stainless steel
Copper
Aluminium
min( Rp0,2/T / 1.5 ; Rm/20 / 2.4 )
Rp0,2/T / 1.05
R / 1.5
max[ Rp1,0/T / 1.5 ; min( Rp1,0/T / 1.2 ; Rm/T / 3 ) ]
max( Rp1,0/T / 1.05 ; Rm/T / 2 )
R / 1.5
?
?
?
?
Nickel
?
?
Titanium
?
min( Rp0,2/T / 1.9 ; Rm/20 / 3 )
?
Rp0,2/T / 1.33
R / ?
R / ?
R / ?
R / ?
R / 1.9
min( Rp0,2/T / 3 ; Rm/20 / 4 )
min( Rp0,2/T / 2 ; Rm/20 / 2.67 )
R / 1.5
Rm/T / 4
Rm/20 / 2.67
R / 1.5
Cast Iron
Nonaustenitic
steel
Austenitic
stainless steel
Pressure / Temperature – Erected
Design Pressure
Design Temperature
Compartment 1
0 MPa
20 °C
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
Compartment 2
0 MPa
20 °C
15
Compartment 3
0 MPa
20 °C
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2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Operating
Allowable stresses and safety factors – Operating
EN 13445-3 §6
Nominal stress at design temperature.
f
minimum guaranteed tensile strength for the grade of material concerned at temperature (depending on the
Rm/T
load case).
Rm/20
Minimum guaranteed tensile strength at room temperature.
Rp0,2/T
Minimum guaranteed yield strength 0.2 % at temperature (depending on the load case).
Rp1,0/T
Minimum guaranteed yield strength 1 % at temperature (depending on the load case).
Average stress to cause rupture in 100,000 hours at design temperature.
R
Compartment 1
Excluding bolting
Testing group 3
Bolts
Nominal design stress f
Testing and exceptional load cases
Normal operating load cases fd
ftest
Creep
Nonaustenitic
steel
Austenitic
stainless steel
Copper
Aluminium
min( Rp0,2/T / 1.5 ; Rm/20 / 2.4 )
Rp0,2/T / 1.05
R / 1.5
max[ Rp1,0/T / 1.5 ; min( Rp1,0/T / 1.2 ; Rm/T / 3 ) ]
max( Rp1,0/T / 1.05 ; Rm/T / 2 )
R / 1.5
?
?
?
?
Nickel
?
?
Titanium
?
min( Rp0,2/T / 1.9 ; Rm/20 / 3 )
?
Rp0,2/T / 1.33
R / ?
R / ?
R / ?
R / ?
R / 1.9
min( Rp0,2/T / 3 ; Rm/20 / 4 )
min( Rp0,2/T / 2 ; Rm/20 / 2.67 )
R / 1.5
Rm/T / 4
Rm/20 / 2.67
R / 1.5
Cast Iron
Nonaustenitic
steel
Austenitic
stainless steel
Pressure / Temperature – Operating
Design Pressure
Design Temperature
Compartment 1
0.7 MPa
10 °C
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
Compartment 2
0 MPa
0 °C
16
Compartment 3
0 MPa
0 °C
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2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Shutdown
Allowable stresses and safety factors – Shutdown
EN 13445-3 §6
Nominal stress at design temperature.
f
minimum guaranteed tensile strength for the grade of material concerned at temperature (depending on the
Rm/T
load case).
Rm/20
Minimum guaranteed tensile strength at room temperature.
Rp0,2/T
Minimum guaranteed yield strength 0.2 % at temperature (depending on the load case).
Rp1,0/T
Minimum guaranteed yield strength 1 % at temperature (depending on the load case).
Average stress to cause rupture in 100,000 hours at design temperature.
R
Compartment 1
Excluding bolting
Testing group 3
Bolts
Nominal design stress f
Testing and exceptional load cases
Normal operating load cases fd
ftest
Creep
Nonaustenitic
steel
Austenitic
stainless steel
Copper
Aluminium
min( Rp0,2/T / 1.5 ; Rm/20 / 2.4 )
Rp0,2/T / 1.05
R / 1.5
max[ Rp1,0/T / 1.5 ; min( Rp1,0/T / 1.2 ; Rm/T / 3 ) ]
max( Rp1,0/T / 1.05 ; Rm/T / 2 )
R / 1.5
?
?
?
?
Nickel
?
?
Titanium
?
min( Rp0,2/T / 1.9 ; Rm/20 / 3 )
?
Rp0,2/T / 1.33
R / ?
R / ?
R / ?
R / ?
R / 1.9
min( Rp0,2/T / 3 ; Rm/20 / 4 )
min( Rp0,2/T / 2 ; Rm/20 / 2.67 )
R / 1.5
Rm/T / 4
Rm/20 / 2.67
R / 1.5
Cast Iron
Nonaustenitic
steel
Austenitic
stainless steel
Pressure / Temperature – Shutdown
Design Pressure
Design Temperature
Compartment 1
0 MPa
10 °C
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
Compartment 2
0 MPa
0 °C
17
Compartment 3
0 MPa
0 °C
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Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Test
Allowable stresses and safety factors – Test
EN 13445-3 §6
Nominal stress at design temperature.
f
minimum guaranteed tensile strength for the grade of material concerned at temperature (depending on the
Rm/T
load case).
Rm/20
Minimum guaranteed tensile strength at room temperature.
Rp0,2/T
Minimum guaranteed yield strength 0.2 % at temperature (depending on the load case).
Rp1,0/T
Minimum guaranteed yield strength 1 % at temperature (depending on the load case).
Average stress to cause rupture in 100,000 hours at design temperature.
R
Nominal design stress f
Testing and exceptional load cases
Normal operating load cases fd
ftest
Compartment 1
Excluding bolting
Testing group 3
Bolts
Creep
Nonaustenitic
steel
Austenitic
stainless steel
Copper
Aluminium
min( Rp0,2/T / 1.5 ; Rm/20 / 2.4 )
Rp0,2/T / 1.05
R / 1.5
max[ Rp1,0/T / 1.5 ; min( Rp1,0/T / 1.2 ; Rm/T / 3 ) ]
max( Rp1,0/T / 1.05 ; Rm/T / 2 )
R / 1.5
?
?
?
?
Nickel
?
?
Titanium
?
min( Rp0,2/T / 1.9 ; Rm/20 / 3 )
?
Rp0,2/T / 1.33
R / ?
R / ?
R / ?
R / ?
R / 1.9
min( Rp0,2/T / 3 ; Rm/20 / 4 )
min( Rp0,2/T / 2 ; Rm/20 / 2.67 )
R / 1.5
Rm/T / 4
Rm/20 / 2.67
R / 1.5
Cast Iron
Nonaustenitic
steel
Austenitic
stainless steel
Pressure / Temperature – Test
Design Pressure
Design Temperature
Compartment 1
1.001 MPa
20 °C
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
Compartment 2
0 MPa
20 °C
18
Compartment 3
0 MPa
20 °C
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
Design Calculations
RESERVOIR_VESSEL_233L
2024-06-20
Revision : 23-08-24
Location of dominant stresses and worst cases.
Cases studied :
1
3
5
Lifting P = 0. (New Inertias) (New Weight)
Operation (Corroded inertias) (New Weight)
During test (Corroded inertias) (Corroded Weight)
(++) vertical downside and horizontal longitudinal to the right
(+−) vertical downside and horizontal longitudinal to the left
(+) vertical downside and horizontal cross
2
4
6
Erected P = 0. (New Inertias) (New Weight)
Shutdown P = 0. (Corroded inertias) (Corroded Weight)
During test P = 0. (Corroded inertias) (Corroded Weight)
(−+)
(−−)
(−)
vertical upside and horizontal longitudinal to the right
vertical upside and horizontal longitudinal to the left
vertical upside and horizontal cross
Verification of shell between the supports
3
6
3
4
5
02[01]
02[01]
02[01]
02[01]
02[01]
Primary membrane stress intensity (highest point)
Longitudinal compressive stress (highest point)
Primary membrane stress intensity (lowest point)
Longitudinal compressive stress (lowest point)
Stability
51.8 ≤ 184.7 MPa
0.9 ≤ 90.3 MPa
51 ≤ 184.7 MPa
0.6 ≤ 65.2 MPa
0.008 ≤ 1
(28%)
(1%)
(28%)
(1%)
(1%)
137.1 ≤ 7,298.5 daN
137.1 ≤ 11,858.7 daN
0.0106 ≤ 1
(2%)
(1%)
(1%)
2.5 ≤ 198.9 MPa
4.1 ≤ 198.9 MPa
0.9 ≤ 117.9 MPa
0.0286 ≤ 1
/
138 ≤ 998.1 daN
1 ≤ 100 MPa
(1%)
(2%)
(1%)
(3%)
Verification of shell in the plane of the supports
3
4
3
No. 1
No. 1
No. 2
Allowable load in longitudinal direction
Allowable load in circumferential direction
Stability
Support check
5
3
3
3
/
5
3
No. 1
No. 1
No. 1
No. 1
No. /
No. 1
No. 1
Stress at the low point of the saddle
Maximum bending stress
Compressive stress
Combined bending and compression
Tensile stress in the bolts
Stability (Number of ribs  2)
Shear stress in the bolts
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
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(14%)
(1%)
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Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Case 1 - Lifting P = 0. (New Inertias) (New Weight)
Moments and loads in plane of saddles.
Support
saddles
N Location
o.
(mm)
Stiffness
(daN/mm)
Vertical
Reactions
(daN)
Shear
Loads
(daN)
Horizontal
Bending
moments
(daN∙m)
Reactions
Shear
Loads
(daN)
Transverse
(daN)
Combined
Bending
moments
(daN∙m)
Reactions
Shear
Loads
(daN)
Reactions
(daN)
Longitudinal
(daN)
Bending
moments
(daN∙m)
1
50.0
22.8
-9.9
12.9
-0.9
0.0
0.0
0.0
0.0
22.8
-9.9
12.9
-0.9
2
1,050.0
20.1
-12.6
7.5
-0.6
0.0
0.0
0.0
0.0
20.1
-12.6
7.5
-0.6
Graph of bending moments and shear forces.
Vertical
Bending moments
Horizontal
1 daN∙m
1 daN∙m
1
Shear
2 forces
10 daN
1 daN
1
2
Wind/Earthquake Global Loads.
Wind Cross
/
Earthquake Cross
/
Earthquake Longitudinal
/
Earthquake Vertical
/
Vibration Periods and Center of Gravity.
Mode
Period
1
749.025×10-6 s
2
198.5081×10-6 s
3
96.98329×10-6 s
4
64.42242×10-6 s
5
48.47708×10-6 s
Center of Gravity
525 mm
Maximum Longitudinal Bending Stress Verification.
Circumferential stress :  = (P+P )R / t
P : Hydrostatic pressure
Pm : Pressure at the vessel equator
Longitudinal stress : z = Pm R / 2t  M K12 /  R2 t
General primary membrane stress intensity : eq = MAX( |  - z | ; | z – 0.5 P |)
Maximum allowable moment : Mmax =  R2 t fc
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
20
ft : allowable tensile stress
fc : allowable compressive stress
K12 : Coef. EN 13445-3 (16.8-11)
Pmax : allowable external pressure
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2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Component : 02[01] 31.05
P = 0 MPa
Maximum general primary membrane stress intensity : eq shall be  ft
Location (mm)
M (daN∙m)
R (mm)
K12
Pm (MPa)
 (MPa)
z (MPa)
573.3
2.4
248.0
1.4933
0.00
0.00
-0.09
573.3
+
2.4
248.0
1.4933
0.00
0.00
0.09
Maximum longitudinal compressive stress : z < 0  |z| shall be  MIN( ft ; fc )
Location (mm)
M (daN∙m)
R (mm)
K12
Pm (MPa)
z (MPa)
573.3
2.4
248.0
1.4933
0.00
-0.09
50.0
+
-0.9
248.0
1.4933
0.00
-0.04
Proof of stability : |P| / Pmax + |M| / Mmax shall be  1.0 (P > 0  P = 0)
Location = 573.3 mm fc = 90.34 MPa
M = 2.4 daN∙m
Mmax = 3,544 daN∙m
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
21
eq (MPa)
z
0.85
0.85
ft (MPa)
260.00
260.00
ft (MPa)
260.00
260.00
fc (MPa)
90.34
90.34
0.11
0.11
z
1
1
Pmax = +∞ MPa
Stab. = 0.0007
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
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Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Case 2 - Erected P = 0. (New Inertias) (New Weight)
Moments and loads in plane of saddles.
Support
saddles
N Location
o.
(mm)
Stiffness
(daN/mm)
Vertical
Reactions
(daN)
Shear
Loads
(daN)
Horizontal
Bending
moments
(daN∙m)
Reactions
Shear
Loads
(daN)
Transverse
(daN)
Combined
Bending
moments
(daN∙m)
Reactions
Shear
Loads
(daN)
Reactions
(daN)
Longitudinal
(daN)
Bending
moments
(daN∙m)
1
50.0
22.8
-9.9
12.9
-0.9
0.0
0.0
0.0
0.0
22.8
-9.9
12.9
-0.9
2
1,050.0
20.1
-12.6
7.5
-0.6
0.0
0.0
0.0
0.0
20.1
-12.6
7.5
-0.6
Graph of bending moments and shear forces.
Vertical
Bending moments
Horizontal
1 daN∙m
1 daN∙m
1
Shear
2 forces
10 daN
1 daN
1
2
Wind/Earthquake Global Loads.
Wind Cross
/
Earthquake Cross
/
Earthquake Longitudinal
/
Earthquake Vertical
/
Vibration Periods and Center of Gravity.
Mode
Period
1
749.025×10-6 s
2
198.5081×10-6 s
3
96.98329×10-6 s
4
64.42242×10-6 s
5
48.47708×10-6 s
Center of Gravity
525 mm
Maximum Longitudinal Bending Stress Verification.
Circumferential stress :  = (P+P )R / t
P : Hydrostatic pressure
Pm : Pressure at the vessel equator
Longitudinal stress : z = Pm R / 2t  M K12 /  R2 t
General primary membrane stress intensity : eq = MAX( |  - z | ; | z – 0.5 P |)
Maximum allowable moment : Mmax =  R2 t fc
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
22
ft : allowable tensile stress
fc : allowable compressive stress
K12 : Coef. EN 13445-3 (16.8-11)
Pmax : allowable external pressure
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Component : 02[01] 31.05
P = 0 MPa
Maximum general primary membrane stress intensity : eq shall be  ft
Location (mm)
M (daN∙m)
R (mm)
K12
Pm (MPa)
 (MPa)
z (MPa)
573.3
2.4
248.0
1.4933
0.00
0.00
-0.09
573.3
+
2.4
248.0
1.4933
0.00
0.00
0.09
Maximum longitudinal compressive stress : z < 0  |z| shall be  MIN( ft ; fc )
Location (mm)
M (daN∙m)
R (mm)
K12
Pm (MPa)
z (MPa)
573.3
2.4
248.0
1.4933
0.00
-0.09
50.0
+
-0.9
248.0
1.4933
0.00
-0.04
Proof of stability : |P| / Pmax + |M| / Mmax shall be  1.0 (P > 0  P = 0)
Location = 573.3 mm fc = 90.34 MPa
M = 2.4 daN∙m
Mmax = 3,544 daN∙m
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
23
eq (MPa)
z
0.85
0.85
ft (MPa)
260.00
260.00
ft (MPa)
260.00
260.00
fc (MPa)
90.34
90.34
0.11
0.11
z
1
1
Pmax = +∞ MPa
Stab. = 0.0007
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Case 3 - Operation (Corroded inertias) (New Weight)
Moments and loads in plane of saddles.
Support
saddles
N Location
o.
(mm)
Stiffness
(daN/mm)
Vertical
Reactions
(daN)
Shear
Loads
(daN)
Horizontal
Bending
moments
(daN∙m)
Shear
Loads
(daN)
Reactions
Transverse
(daN)
Combined
Bending
moments
(daN∙m)
Reactions
Shear
Loads
(daN)
Reactions
(daN)
Longitudinal
(daN)
Bending
moments
(daN∙m)
1
50.0
137.1
-28.0
109.1
0.9
-19.3
0.0
0.0
0.0
45.1
137.1
-28.0
109.1
0.9
-19.3
2
1,050.0
135.6
-109.0
26.6
-19.0
1.1
0.0
0.0
0.0
-45.1
135.6
-109.0
26.6
-19.0
1.1
Graph of bending moments and shear forces.
Vertical
Bending moments
10 daN∙m
Horizontal
1 daN∙m
1
Shear
2 forces
100 daN
1 daN
1
2
Wind/Earthquake Global Loads.
Wind Cross
/
Earthquake Cross
/
Earthquake Longitudinal
/
Earthquake Vertical
/
Vibration Periods and Center of Gravity.
Mode
Period
1
2.16365×10-3 s
2
549.9254×10-6 s
3
251.4758×10-6 s
4
148.7418×10-6 s
5
104.523×10-6 s
Center of Gravity
548 mm
Maximum Longitudinal Bending Stress Verification.
Circumferential stress :  = (P+P )R / t
P : Hydrostatic pressure
Pm : Pressure at the vessel equator
Longitudinal stress : z = Pm R / 2t  M K12 /  R2 t
General primary membrane stress intensity : eq = MAX( |  - z | ; | z – 0.5 P |)
Maximum allowable moment : Mmax =  R2 t fc
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
24
ft : allowable tensile stress
fc : allowable compressive stress
K12 : Coef. EN 13445-3 (16.8-11)
Pmax : allowable external pressure
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Component : 02[01] 31.05
P = 0.7 MPa
Maximum general primary membrane stress intensity : eq shall be  ft
Location (mm)
M (daN∙m)
R (mm)
K12
Pm (MPa)
 (MPa)
z (MPa)
50.0
-19.4
248.0
1.4933
0.70
85.52
43.64
50.0
+
-19.4
248.0
1.4933
0.70
85.52
42.16
Maximum longitudinal compressive stress : z < 0  |z| shall be  MIN( ft ; fc )
Location (mm)
M (daN∙m)
R (mm)
K12
Pm (MPa)
z (MPa)
552.0
8.0
248.0
1.4933
0.70
42.60
50.0
+
-19.4
248.0
1.4933
0.70
42.16
Proof of stability : |P| / Pmax + |M| / Mmax shall be  1.0 (P > 0  P = 0)
Location = 50 mm
fc = 65.2 MPa
M = -19.4 daN∙m
Mmax = 2,557.6 daN∙m
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
25
eq (MPa)
z
0.85
0.85
ft (MPa)
184.67
184.67
ft (MPa)
184.67
184.67
fc (MPa)
65.20
65.20
51.75
51.01
z
1
1
Pmax = +∞ MPa
Stab. = 0.0076
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Case 4 - Shutdown P = 0. (Corroded inertias) (Corroded Weight)
Moments and loads in plane of saddles.
Support
saddles
N Location
o.
(mm)
Stiffness
(daN/mm)
Vertical
Reactions
(daN)
Shear
Loads
(daN)
Horizontal
Bending
moments
(daN∙m)
Shear
Loads
(daN)
Reactions
Transverse
(daN)
Combined
Bending
moments
(daN∙m)
Reactions
Shear
Loads
(daN)
Reactions
(daN)
Longitudinal
(daN)
Bending
moments
(daN∙m)
1
50.0
137.1
-28.0
109.1
0.9
-19.3
0.0
0.0
0.0
45.1
137.1
-28.0
109.1
0.9
-19.3
2
1,050.0
135.6
-109.0
26.6
-19.0
1.1
0.0
0.0
0.0
-45.1
135.6
-109.0
26.6
-19.0
1.1
Graph of bending moments and shear forces.
Vertical
Bending moments
10 daN∙m
Horizontal
1 daN∙m
1
Shear
2 forces
100 daN
1 daN
1
2
Wind/Earthquake Global Loads.
Wind Cross
/
Earthquake Cross
/
Earthquake Longitudinal
/
Earthquake Vertical
/
Vibration Periods and Center of Gravity.
Mode
Period
1
2.16365×10-3 s
2
549.9254×10-6 s
3
251.4758×10-6 s
4
148.7418×10-6 s
5
104.523×10-6 s
Center of Gravity
548 mm
Maximum Longitudinal Bending Stress Verification.
Circumferential stress :  = (P+P )R / t
P : Hydrostatic pressure
Pm : Pressure at the vessel equator
Longitudinal stress : z = Pm R / 2t  M K12 /  R2 t
General primary membrane stress intensity : eq = MAX( |  - z | ; | z – 0.5 P |)
Maximum allowable moment : Mmax =  R2 t fc
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
26
ft : allowable tensile stress
fc : allowable compressive stress
K12 : Coef. EN 13445-3 (16.8-11)
Pmax : allowable external pressure
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Component : 02[01] 31.05
P = 0 MPa
Maximum general primary membrane stress intensity : eq shall be  ft
Location (mm)
M (daN∙m)
R (mm)
K12
Pm (MPa)
 (MPa)
z (MPa)
50.0
-19.4
248.0
1.4933
0.00
0.00
0.88
50.0
+
-19.4
248.0
1.4933
0.00
0.00
-0.60
Maximum longitudinal compressive stress : z < 0  |z| shall be  MIN( ft ; fc )
Location (mm)
M (daN∙m)
R (mm)
K12
Pm (MPa)
z (MPa)
552.0
8.0
248.0
1.4933
0.00
-0.16
50.0
+
-19.4
248.0
1.4933
0.00
-0.60
Proof of stability : |P| / Pmax + |M| / Mmax shall be  1.0 (P > 0  P = 0)
Location = 50 mm
fc = 65.2 MPa
M = -19.4 daN∙m
Mmax = 2,557.6 daN∙m
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
27
eq (MPa)
z
0.85
0.85
ft (MPa)
184.67
184.67
ft (MPa)
184.67
184.67
fc (MPa)
65.20
65.20
1.03
0.70
z
1
1
Pmax = +∞ MPa
Stab. = 0.0076
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Case 5 - During test (Corroded inertias) (Corroded Weight)
Moments and loads in plane of saddles.
Support
saddles
N Location
o.
(mm)
Stiffness
(daN/mm)
Vertical
Reactions
(daN)
Shear
Loads
(daN)
Horizontal
Bending
moments
(daN∙m)
Reactions
Shear
Loads
(daN)
Transverse
(daN)
Combined
Bending
moments
(daN∙m)
Reactions
Shear
Loads
(daN)
Reactions
(daN)
Longitudinal
(daN)
Bending
moments
(daN∙m)
1
50.0
138.0
-28.1
109.9
0.8
0.0
0.0
0.0
0.0
138.0
-28.1
109.9
0.8
2
1,050.0
136.5
-109.8
26.7
1.0
0.0
0.0
0.0
0.0
136.5
-109.8
26.7
1.0
Graph of bending moments and shear forces.
Vertical
Bending moments
Horizontal
1 daN∙m
10 daN∙m
1
Shear
2 forces
100 daN
1 daN
1
2
Wind/Earthquake Global Loads.
Wind Cross
/
Earthquake Cross
/
Earthquake Longitudinal
/
Earthquake Vertical
/
Vibration Periods and Center of Gravity.
Mode
Period
1
2.171308×10-3 s
2
551.821×10-6 s
3
252.3004×10-6 s
4
149.1802×10-6 s
5
104.774×10-6 s
Center of Gravity
548 mm
Maximum Longitudinal Bending Stress Verification.
Circumferential stress :  = (P+P )R / t
P : Hydrostatic pressure
Pm : Pressure at the vessel equator
Longitudinal stress : z = Pm R / 2t  M K12 /  R2 t
General primary membrane stress intensity : eq = MAX( |  - z | ; | z – 0.5 P |)
Maximum allowable moment : Mmax =  R2 t fc
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
28
ft : allowable tensile stress
fc : allowable compressive stress
K12 : Coef. EN 13445-3 (16.8-11)
Pmax : allowable external pressure
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Component : 02[01] 31.05
P = 1 MPa
Maximum general primary membrane stress intensity : eq shall be  ft
Location (mm)
M (daN∙m)
R (mm)
K12
Pm (MPa)
 (MPa)
z (MPa)
552.0
28.4
248.0
1.4933
1.00
122.30
60.22
552.0
+
28.4
248.0
1.4933
1.00
122.30
62.38
Maximum longitudinal compressive stress : z < 0  |z| shall be  MIN( ft ; fc )
Location (mm)
M (daN∙m)
R (mm)
K12
Pm (MPa)
z (MPa)
552.0
28.4
248.0
1.4933
1.00
60.22
50.0
+
0.8
248.0
1.4933
1.00
61.33
Proof of stability : |P| / Pmax + |M| / Mmax shall be  1.0 (P > 0  P = 0)
Location = 552 mm
fc = 90.34 MPa
M = 28.4 daN∙m
Mmax = 3,544 daN∙m
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
29
eq (MPa)
z
1
1
ft (MPa)
260.00
260.00
ft (MPa)
260.00
260.00
fc (MPa)
90.34
90.34
62.08
62.88
z
1
1
Pmax = +∞ MPa
Stab. = 0.008
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Case 6 - During test P = 0. (Corroded inertias) (Corroded Weight)
Moments and loads in plane of saddles.
Support
saddles
N Location
o.
(mm)
Stiffness
(daN/mm)
Vertical
Reactions
(daN)
Shear
Loads
(daN)
Horizontal
Bending
moments
(daN∙m)
Reactions
Shear
Loads
(daN)
Transverse
(daN)
Combined
Bending
moments
(daN∙m)
Reactions
Shear
Loads
(daN)
Reactions
(daN)
Longitudinal
(daN)
Bending
moments
(daN∙m)
1
50.0
138.0
-28.1
109.9
0.8
0.0
0.0
0.0
0.0
138.0
-28.1
109.9
0.8
2
1,050.0
136.5
-109.8
26.7
1.0
0.0
0.0
0.0
0.0
136.5
-109.8
26.7
1.0
Graph of bending moments and shear forces.
Vertical
Bending moments
Horizontal
1 daN∙m
10 daN∙m
1
Shear
2 forces
100 daN
1 daN
1
2
Wind/Earthquake Global Loads.
Wind Cross
/
Earthquake Cross
/
Earthquake Longitudinal
/
Earthquake Vertical
/
Vibration Periods and Center of Gravity.
Mode
Period
1
2.171308×10-3 s
2
551.821×10-6 s
3
252.3004×10-6 s
4
149.1802×10-6 s
5
104.774×10-6 s
Center of Gravity
548 mm
Maximum Longitudinal Bending Stress Verification.
Circumferential stress :  = (P+P )R / t
P : Hydrostatic pressure
Pm : Pressure at the vessel equator
Longitudinal stress : z = Pm R / 2t  M K12 /  R2 t
General primary membrane stress intensity : eq = MAX( |  - z | ; | z – 0.5 P |)
Maximum allowable moment : Mmax =  R2 t fc
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
30
ft : allowable tensile stress
fc : allowable compressive stress
K12 : Coef. EN 13445-3 (16.8-11)
Pmax : allowable external pressure
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Component : 02[01] 31.05
P = 0 MPa
Maximum general primary membrane stress intensity : eq shall be  ft
Location (mm)
M (daN∙m)
R (mm)
K12
Pm (MPa)
 (MPa)
z (MPa)
552.0
28.4
248.0
1.4933
0.00
0.00
-0.93
552.0
+
28.4
248.0
1.4933
0.00
0.00
1.23
Maximum longitudinal compressive stress : z < 0  |z| shall be  MIN( ft ; fc )
Location (mm)
M (daN∙m)
R (mm)
K12
Pm (MPa)
z (MPa)
552.0
28.4
248.0
1.4933
0.00
-0.93
50.0
+
0.8
248.0
1.4933
0.00
0.18
Proof of stability : |P| / Pmax + |M| / Mmax shall be  1.0 (P > 0  P = 0)
Location = 552 mm
fc = 90.34 MPa
M = 28.4 daN∙m
Mmax = 3,544 daN∙m
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
31
eq (MPa)
z
1
1
ft (MPa)
260.00
260.00
ft (MPa)
260.00
260.00
fc (MPa)
90.34
90.34
0.93
1.23
z
1
1
Pmax = +∞ MPa
Stab. = 0.008
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Maximum Allowable Working Pressure
Maximum Allowable Pressure(Geometry).
Type / Mark
Diameter
Thickness
30.10
31.05
30.11
(mm)
494.0
494.0
494.0
(mm)
3.1
2.0
3.1
01[04]
02[01]
03[04]
Max. allowable pressure
Operating
Test
(MPa)
(MPa)
1.3370
1.8824
1.2848
2.1281
1.3476
1.8974
Max. All. Ext. Pressure
Operating
Test
(MPa)
(MPa)
/
/
/
/
/
/
Hydrostatic pressure
Operating
Test
(MPa)
(MPa)
0.0047
0.0048
0.0047
0.0048
0.0047
0.0048
/
/
/
Maximum Allowable Pressure (Nozzles).
Tag
N1
N2
N3
N4
N5
Neck
Operating
(MPa)
9.2333
56.2270
66.2204
7.5647
7.5647
Flange
Test
(MPa)
15.2941
93.1343
109.6875
12.5301
12.5301
Operating
(MPa)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
Test
(MPa)
/
/
/
/
/
/
/
/
/
/
32
Operating
(MPa)
0.0000
0.0000
0.0023
0.0047
0.0047
Hydrostatic pressure
Test
(MPa)
0.0000
0.0000
0.0024
0.0048
0.0048
/
/
/
/
/
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Isolated Opening(s)
Shell (  = 0 ) or Cone (  > 0 ) : in the longitudinal section.
Figure 1
Figure 2
Afb
deb
de
lso
Afw
Afb
h
Afw
dib
Afp
hb

Aps
eas/cos
eap
lp
ris
Apb
Afs
lbo
h
dib
Afp
Apb
Afs
deb
de
lso

Aps
hb
lbo
eas/cos
eap
lp
ris
lbi
a
eab
eab
a

eas
Ap

eas
Ap
De
De
Set-in nozzle
Set-on nozzle
Cylindrical or conical shell: in the lateral section
Domed head: in the plane that contains the axis of the nozzle and the center of the sphere.
Figure 3
Figure 4
deb
de
lso
Afp
h
Afp

Afs
Afs
eab
hb
Apb
lbo
hb
Apb
Ap
Afw
h
de
Afb

Afb
lso
lbo
Ap
Afw
lbi
lp
lp
a
a
dib
eap
Aps
ris
dib
eab
eap
deb
Aps
eas
Set-in nozzle
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
ris
eas
Set-on nozzle
33
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Opening N1
Isolated opening N1 [ in operation Int.P. ]
EN 13445-3 9.5
Nozzle without pad on Shell (No. 2)
P = 0.7 MPa
t = 10 °C
fs = 184.67 MPa
X5CrNi18-10
en,s = 2.03 mm
eas = 2.03 mm
cs = 0 mm
e,s = /
ris = 247 mm
(Process)
Set In
fb = 184.67 MPa
en,b = 2 mm
cb = 0 mm
fp = 184.67 MPa
de = 70 mm
deb = 70 mm
dib = 66 mm
eap = 0 mm
X5CrNi18-10
eab = 2 mm
e,b = /
X5CrNi18-10
[9.4.8] : if the distance between the bore and a shell weld is : lso, the distance between the weld and the center of the
opening should be: < dib/6 = 11 mm or > ln = min(0.5deb+2eas ; 0.5deb+40 mm) = 39.06 mm.
[9.5.2.3]: The angle θ between the nozzle weld and the shell generator should be < 45°.
Fig. 9.4-14 : eb/eas = 2
Fig. 9.4-15 : eab/eas = 3
[9.4.5.4]:dib/(2ris) ≤ 1
Required thickness of the nozzle neck under internal pressure : e = P∙de/(2fb∙z+P) = 0.156 mm ( z = 0.85 )
In the longitudinal section (  : Figure 1 )
De = 498.06 mm
 = 0 ° ≤ 60 °
rms= ris+eas /2 = 248.02 mm
 = 0.141
h = 0 mm
ls = 517 mm
hb = 37 mm
lp = 0 mm
wmin = 6.35 mm
lso =
wp = 31.73 mm
lbo =
c ,s
c ,s
= 31.73 mm
ec,s = 2.03 mm
eb = 2 mm
lb = min(lbo ; lb ) = 11.66 mm
lbi = min(0.5lbo; lbi ) = 0 mm
l p = min(l so; l p ; w ) = 0 mm
Fig. 9.4-14 : (eb/eas) ≤ 2
Pmax =
is
(deb − eb )eb = 11.66 mm
l s = min(l so; l s ) = 31.73 mm
w = 517 mm ≥ wmin
Afs = 64.4 mm2
Afp = 0 mm2
(2r + e )e
α=0°
a = 35 mm
lb = 37 mm
lbi = 0 mm
Afb = 27.4 mm2
Afw = 4 mm2
(Afs + Afw )  fs + Afb  fob + Af p  fop
Aps = 16,482.9 mm2
Ap = 0 mm2
(Ap + Ap + 0.5Ap ) + 0.5(Af + Af + Af + Af ) = 1.04 MPa ≥ P (67%)
s
b

s
w
b
p
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
34
Apb = 451.8 mm2
z=1
fob =min(fs;z fb)
fop = min(fs ;fp)
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Isolated opening N1 [ in test Int.P. ]
(Process)
EN 13445-3 9.5
Nozzle without pad on Shell (No. 2)
P = 1 MPa
t = 20 °C
fs = 260 MPa
X5CrNi18-10
en,s = 2.03 mm
eas = 2.03 mm
cs = 0 mm
e,s = /
ris = 247 mm
Set In
fb = 260 MPa
en,b = 2 mm
cb = 0 mm
fp = 260 MPa
de = 70 mm
deb = 70 mm
dib = 66 mm
eap = 0 mm
X5CrNi18-10
eab = 2 mm
e,b = /
X5CrNi18-10
[9.4.8] : if the distance between the bore and a shell weld is : lso, the distance between the weld and the center of the
opening should be: < dib/6 = 11 mm or > ln = min(0.5deb+2eas ; 0.5deb+40 mm) = 39.06 mm.
Fig. 9.4-14 : eb/eas = 2
Fig. 9.4-15 : eab/eas = 3
[9.4.5.4]:dib/(2ris) ≤ 1
Required thickness of the nozzle neck under internal pressure : e = P∙de/(2fb∙z+P) = 0.134 mm ( z = 1 )
In the longitudinal section (  : Figure 1 )
De = 498.06 mm
 = 0 ° ≤ 60 °
rms= ris+eas /2 = 248.02 mm
 = 0.141
h = 0 mm
ls = 517 mm
hb = 37 mm
lp = 0 mm
wmin = 6.35 mm
lso =
wp = 31.73 mm
lbo =
c ,s
c ,s
= 31.73 mm
ec,s = 2.03 mm
eb = 2 mm
lb = min(lbo ; lb ) = 11.66 mm
lbi = min(0.5lbo; lbi ) = 0 mm
l p = min(l so; l p ; w ) = 0 mm
Fig. 9.4-14 : (eb/eas) ≤ 2
Pmax =
is
(deb − eb )eb = 11.66 mm
l s = min(l so; l s ) = 31.73 mm
w = 517 mm ≥ wmin
Afs = 64.4 mm2
Afp = 0 mm2
(2r + e )e
α=0°
a = 35 mm
lb = 37 mm
lbi = 0 mm
Afb = 27.4 mm2
Afw = 4 mm2
(Afs + Afw )  fs + Afb  fob + Af p  fop
Aps = 16,482.9 mm2
Ap = 0 mm2
(Ap + Ap + 0.5Ap ) + 0.5(Af + Af + Af + Af ) = 1.47 MPa ≥ P (68%)
s
b

s
w
b
p
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
35
Apb = 451.8 mm2
z=1
fob =min(fs;z fb)
fop = min(fs ;fp)
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Local loads on nozzle N1 (Sustained).
FZ
FZ
MX
Afb
Afw11
MY
Afb
eb e
2
lp
Afp2 Afw22
Afs2
Afp1
r
ea
Aps2+Apb2+Ap2
R
Afs1
Aps1+Apb1+Ap1
EN 13445-3 16.5 - nozzle on cylindrical shell (P = 0.7 MPa)
f = 184.67 MPa
fb = 184.67 MPa
E = 200,000 MPa
f2 = /
eb = 2 mm
R = 248.02 mm
ea = 2.03 mm
r = 34 mm
lp = 0
e2 = 0
9.5.2 :
Afw1 = 4 mm2
Afw2 = 4 mm2
2
2
Aps1 = 8,222.1 mm
Afs1 = 64.4 mm
Afb1 = 27.4 mm2
2
2
Apb1 = 451.8 mm
Afp1 = 0 mm2
Ap1 = 0 mm
Aps2 = 16,482.9 mm2
Afs2 = 64.4 mm2
Afb2 = 27.4 mm2
Apb2 = 451.8 mm2
Afp2 = 0 mm2
Ap2 = 0 mm2
ea / 2R = 0.0041 the rules apply if : 0.001  ea / 2R  0.1
The nozzle thickness should be
deb = 11.66 mm
maintained over a distance of :
Distances to any other local load should
Dec =31.73 mm
be no less than :
External Diameter (nozzle)
d = 68 mm
D = 2R
d/D = 0.1371 shall be  0.5
ec = ea + e2  min( f2/f ; 1) = 2.03 mm
C4 = 1.1
(
c = d
Dec =2.1429
If c  10 the effects of a
twisting moment are
considerable
)
C2= 5.2042
C3 = 13.5068
C1 = 2.6507
eeq=ec.If plate with l P  D(ea + e2 ) , eeq = ea + min e2 l P
D(ea + e2 ) ; e2 min(f2 f ;1) ) : eeq=2.03 mm
Maximum permitted global loads (nozzle) (§16.14)
e = Rp1,0 / 1.3 / 1.25 =
c,all = e  = 184.67 MPa
160 MPa
K=0
=0
=0
Fmax =  d eb c,all
( w / l )max = 0
Mmax = /4 d2 eb c,all
Maximum allowable individual loads(§16.5.5)
𝑃max = [(𝐴𝑓s + 𝐴𝑓w ) ⋅ 𝑓s + 𝐴𝑓b ⋅ 𝑓ob + 𝐴𝑓p ⋅ 𝑓op ]⁄[(𝐴𝑝s + 𝐴𝑝b + 0.5𝐴𝑝ϕ ) + 0.5(𝐴𝑓s + 𝐴𝑓w + 𝐴𝑓b + 𝐴𝑓p )] (16.5-2)
𝑑
𝑑
𝐹Z,max = 𝑓𝑒𝑐2 max(𝐶1 ; 1.81)
𝑃max = min(𝑃max1 ; 𝑃max2 )
𝑀X,max = 𝑓𝑒𝑐2 max(𝐶2 ; 4.90) 𝑀Y,max = 𝑓𝑒𝑐2 max(𝐶3 ; 4.90)
4
4
2𝐹X
2𝐹Y
2𝑀Z
2
𝜏X =
𝜏Y =
𝜏Z = 2
𝜏 = √𝜏X + 𝜏Y2 + |𝜏Z |
𝜋𝑑𝑒c
𝜋𝑑𝑒c
𝜋𝑑 𝑒c
Pmax (MPa)
1.04 / X (daN)
0/-
Maximum allowable loads at the nozzle / pad outer diameter
FZ,max (daN)
MX,max (daN∙mm)
MY,max (daN∙mm)
201.7 / 6,733 / 0.1747×105 / Y (daN)
Z (daN)
 (daN)
0/0/0/-
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
36
Maximum allowable nozzle loads
Fmax (daN)
Mmax (daN∙mm)
7,890
0.1341×106
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
Design Calculations
RESERVOIR_VESSEL_233L
2024-06-20
Revision : 23-08-24
Allowable bounded area. ( = )
|MX| (daN∙mm)
|MY| (daN∙mm)
FZ,max
MY=0
FZ,max
MX,max(MY=0)
MY=MY,max
1,000
MX=0
MY,max(MX=0)
MX=MX,max
1,000
10
FZ (daN)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
10
37
FZ (daN)
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Opening N2
Isolated opening N2 [ in operation Int.P. ]
EN 13445-3 9.5
Nozzle without pad on Shell (No. 2)
P = 0.7 MPa
t = 10 °C
fs = 184.67 MPa
X5CrNi18-10
en,s = 2.03 mm
eas = 2.03 mm
cs = 0 mm
e,s = /
ris = 247 mm
(Process)
Set In
fb = 184.67 MPa
en,b = 12 mm
cb = 0 mm
fp = 184.67 MPa
de = 79 mm
deb = 79 mm
dib = 55 mm
eap = 0 mm
X5CrNi18-10
eab = 12 mm
e,b = /
X5CrNi18-10
[9.4.8] : if the distance between the bore and a shell weld is : lso, the distance between the weld and the center of the
opening should be: < dib/6 = 9.17 mm or > ln = min(0.5deb+2eas ; 0.5deb+40 mm) = 43.56 mm.
[9.5.2.3]: The angle θ between the nozzle weld and the shell generator should be < 45°.
Fig. 9.4-14 : eb/eas = 2
Fig. 9.4-15 : eab/eas = 3
[9.4.5.4]:dib/(2ris) ≤ 1
Required thickness of the nozzle neck under internal pressure : e = P∙de/(2fb∙z+P) = 0.176 mm ( z = 0.85 )
In the longitudinal section (  : Figure 1 )
De = 498.06 mm
 = 0 ° ≤ 60 °
rms= ris+eas /2 = 248.02 mm
 = 0.159
h = 0 mm
ls = 268.5 mm
hb = 36 mm
lp = 0 mm
α=0°
a = 39.5 mm
lb = 36 mm
lbi = 0 mm
wmin = 6.35 mm
lso =
(2r + e )e
wp = 31.73 mm
lbo =
(deb − eb )eb = 28.35 mm
Fig. 9.4-14 : (eb/eas) > 2
Pmax =
c ,s
c ,s
= 31.73 mm
l s = min(l so; l s ) = 31.73 mm
l p = min(l so; l p ; w ) = 0 mm
w = 268.5 mm ≥ wmin
Afs = 64.4 mm2
Afp = 0 mm2
is
Afb = 364.6 mm2
Afw = 4.1 mm2
(Afs + Afw )  fs + Afb  fob + Af p  fop
ec,s = 2.03 mm
eb = 12 mm
lb = min(lbo ; lb ) = 28.35 mm
lbi = min(0.5lbo; lbi ) = 0 mm
Aps = 17,594.4 mm2
Ap = 0 mm2
(Ap + Ap + 0.5Ap ) + 0.5(Af + Af + Af + Af ) = 4.29 MPa ≥ P (16%)
s
b

s
w
b
p
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
38
Apb = 835.6 mm2
z=1
fob =min(fs;z fb)
fop = min(fs ;fp)
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Isolated opening N2 [ in test Int.P. ]
(Process)
EN 13445-3 9.5
Nozzle without pad on Shell (No. 2)
P = 1 MPa
t = 20 °C
fs = 260 MPa
X5CrNi18-10
en,s = 2.03 mm
eas = 2.03 mm
cs = 0 mm
e,s = /
ris = 247 mm
Set In
fb = 260 MPa
en,b = 12 mm
cb = 0 mm
fp = 260 MPa
de = 79 mm
deb = 79 mm
dib = 55 mm
eap = 0 mm
X5CrNi18-10
eab = 12 mm
e,b = /
X5CrNi18-10
[9.4.8] : if the distance between the bore and a shell weld is : lso, the distance between the weld and the center of the
opening should be: < dib/6 = 9.17 mm or > ln = min(0.5deb+2eas ; 0.5deb+40 mm) = 43.56 mm.
Fig. 9.4-14 : eb/eas = 2
Fig. 9.4-15 : eab/eas = 3
[9.4.5.4]:dib/(2ris) ≤ 1
Required thickness of the nozzle neck under internal pressure : e = P∙de/(2fb∙z+P) = 0.152 mm ( z = 1 )
In the longitudinal section (  : Figure 1 )
De = 498.06 mm
 = 0 ° ≤ 60 °
rms= ris+eas /2 = 248.02 mm
 = 0.159
h = 0 mm
ls = 268.5 mm
hb = 36 mm
lp = 0 mm
wmin = 6.35 mm
lso =
wp = 31.73 mm
lbo =
c ,s
c ,s
= 31.73 mm
ec,s = 2.03 mm
eb = 12 mm
lb = min(lbo ; lb ) = 28.35 mm
lbi = min(0.5lbo; lbi ) = 0 mm
l p = min(l so; l p ; w ) = 0 mm
Fig. 9.4-14 : (eb/eas) > 2
Pmax =
is
(deb − eb )eb = 28.35 mm
l s = min(l so; l s ) = 31.73 mm
w = 268.5 mm ≥ wmin
Afs = 64.4 mm2
Afp = 0 mm2
(2r + e )e
α=0°
a = 39.5 mm
lb = 36 mm
lbi = 0 mm
Afb = 364.6 mm2
Afw = 4.1 mm2
(Afs + Afw )  fs + Afb  fob + Af p  fop
Aps = 17,594.4 mm2
Ap = 0 mm2
(Ap + Ap + 0.5Ap ) + 0.5(Af + Af + Af + Af ) = 6.04 MPa ≥ P (17%)
s
b

s
w
b
p
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
39
Apb = 835.6 mm2
z=1
fob =min(fs;z fb)
fop = min(fs ;fp)
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Local loads on nozzle N2 (Sustained).
FZ
FZ
MX
Afb
Afw11
MY
Afb
eb e
2
lp
Afp2 Afw22
Afs2
Afp1
r
ea
Aps2+Apb2+Ap2
R
Afs1
Aps1+Apb1+Ap1
EN 13445-3 16.5 - nozzle on cylindrical shell (P = 0.7 MPa)
f = 184.67 MPa
fb = 184.67 MPa
E = 200,000 MPa
f2 = /
eb = 12 mm
R = 248.02 mm
ea = 2.03 mm
r = 33.5 mm
lp = 0
e2 = 0
9.5.2 :
Afw1 = 4.1 mm2
Afw2 = 4.1 mm2
2
2
Aps1 = 8,782 mm
Afs1 = 64.4 mm
Afb1 = 364.6 mm2
2
2
Apb1 = 835.6 mm
Afp1 = 0 mm2
Ap1 = 0 mm
Aps2 = 17,594.4 mm2
Afs2 = 64.4 mm2
Afb2 = 364.6 mm2
Apb2 = 835.6 mm2
Afp2 = 0 mm2
Ap2 = 0 mm2
ea / 2R = 0.0041 the rules apply if : 0.001  ea / 2R  0.1
The nozzle thickness should be
deb = 28.35 mm
maintained over a distance of :
Distances to any other local load should
Dec =31.73 mm
be no less than :
External Diameter (nozzle)
d = 67 mm
D = 2R
d/D = 0.1351 shall be  0.5
ec = ea + e2  min( f2/f ; 1) = 2.03 mm
C4 = 1.1
(
c = d
Dec =2.1114
If c  10 the effects of a
twisting moment are
considerable
)
C2= 5.1888
C3 = 13.3536
C1 = 2.6206
eeq=ec.If plate with l P  D(ea + e2 ) , eeq = ea + min e2 l P
D(ea + e2 ) ; e2 min(f2 f ;1) ) : eeq=2.03 mm
Maximum permitted global loads (nozzle) (§16.14)
e = Rp1,0 / 1.3 / 1.25 =
c,all = e  = 184.67 MPa
160 MPa
K=0
=0
=0
Fmax =  d eb c,all
( w / l )max = 0
Mmax = /4 d2 eb c,all
Maximum allowable individual loads(§16.5.5)
𝑃max = [(𝐴𝑓s + 𝐴𝑓w ) ⋅ 𝑓s + 𝐴𝑓b ⋅ 𝑓ob + 𝐴𝑓p ⋅ 𝑓op ]⁄[(𝐴𝑝s + 𝐴𝑝b + 0.5𝐴𝑝ϕ ) + 0.5(𝐴𝑓s + 𝐴𝑓w + 𝐴𝑓b + 𝐴𝑓p )] (16.5-2)
𝑑
𝑑
𝐹Z,max = 𝑓𝑒𝑐2 max(𝐶1 ; 1.81)
𝑃max = min(𝑃max1 ; 𝑃max2 )
𝑀X,max = 𝑓𝑒𝑐2 max(𝐶2 ; 4.90) 𝑀Y,max = 𝑓𝑒𝑐2 max(𝐶3 ; 4.90)
4
4
2𝐹X
2𝐹Y
2𝑀Z
2
𝜏X =
𝜏Y =
𝜏Z = 2
𝜏 = √𝜏X + 𝜏Y2 + |𝜏Z |
𝜋𝑑𝑒c
𝜋𝑑𝑒c
𝜋𝑑 𝑒c
Pmax (MPa)
4.29 / X (daN)
0/-
Maximum allowable loads at the nozzle / pad outer diameter
FZ,max (daN)
MX,max (daN∙mm)
MY,max (daN∙mm)
199.4 / 6,614 / 0.1702×105 / Y (daN)
Z (daN)
 (daN)
0/0/0/-
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
40
Maximum allowable nozzle loads
Fmax (daN)
Mmax (daN∙mm)
46,643.9
0.7813×106
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
Design Calculations
RESERVOIR_VESSEL_233L
2024-06-20
Revision : 23-08-24
Allowable bounded area. ( = )
|MX| (daN∙mm)
|MY| (daN∙mm)
FZ,max
FZ,max
MY=0
MX=0
MX,max(MY=0)
MY=MY,max
MY,max(MX=0)
MX=MX,max
1,000
10
FZ (daN)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
1,000
10
41
FZ (daN)
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Opening N3
Isolated opening N3 [ in operation Int.P. ]
(Process)
EN 13445-3 9.5
Nozzle without pad on Kloepper Type Head (No. 1)
P = 0.7 MPa
t = 10 °C
fs = 184.67 MPa
X5CrNi18-10
fb = 184.67 MPa
en,s = 3.09 mm
eas = 3.09 mm
en,b = 27 mm
cs = 0 mm
cb = 0 mm
e,s = /
ris = 500.18 mm
fp = 184.67 MPa
Set In
de = 155 mm
deb = 155 mm
dib = 101 mm
eap = 0 mm
X5CrNi18-10
eab = 27 mm
e,b = /
X5CrNi18-10
[9.4.8] : if the distance between the bore and a shell weld is : lso, the distance between the weld and the center of the
opening should be: < dib/6 = 16.83 mm or > ln = min(0.5deb+2eas ; 0.5deb+40 mm) = 83.68 mm.
Fig. 9.4-14 : eb/eas = 2
Fig. 9.4-15 : eab/eas = 3
[9.4.5.3]:dib/De ≤ 0.6
Required thickness of the nozzle neck under internal pressure : e = P∙de/(2fb∙z+P) = 0.346 mm ( z = 0.85 )
In the plane that contains the axis of the nozzle and the radius of the sphere passing through the center of the
nozzle (  : Figure 3 )
De = 500.18 mm
 = 0 ° ≤ sin-1(1-δ) = 57.7 °
rms= ris+eas /2 = 501.72 mm
a = 77.81 mm
 = 0.154
h = 0 mm
ls = 128.02 mm
lb = 25.09 mm
hb = 21 mm
lp = 0 mm
lbi = 0 mm
wmin = 0 mm
lso =
wp = 55.68 mm
lbo =
w = 128.02 mm ≥ wmin
Fig. 9.4-14 : (eb/eas) > 2
(2r + e )e
is
c ,s
c ,s
= 55.68 mm
(deb − eb )eb = 58.79 mm
l s = min(l so; l s ) = 55.68 mm
l p = min(l so; l p ; w ) = 0 mm
ec,s = 3.09 mm
eb = 27 mm
lb = min(lbo ; lb ) = 25.09 mm
lbi = min(0.5lbo; lbi ) = 0 mm
Afs = 172.1 mm2
Afb = 760.8 mm2
Aps = 33,283 mm2
2
2
Afp = 0 mm
Afw = 9.5 mm
Ap = 0 mm2
(Afs + Afw )  fs + Afb  fob + Af p  fop
Pmax =
(Aps + Apb + 0.5Ap ) + 0.5(Afs + Afw + Af b+ Af p ) = 4.35 MPa ≥ P (16%)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
42
Apb = 1,422.9 mm2
z = 0.85
fob =min(fs;z fb)
fop = min(fs ;fp)
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Isolated opening N3 [ in test Int.P. ]
(Process)
EN 13445-3 9.5
Nozzle without pad on Kloepper Type Head (No. 1)
P = 1 MPa
t = 20 °C
fs = 260 MPa
X5CrNi18-10
fb = 260 MPa
en,s = 3.09 mm
eas = 3.09 mm
en,b = 27 mm
cs = 0 mm
cb = 0 mm
e,s = /
ris = 500.18 mm
fp = 260 MPa
Set In
de = 155 mm
deb = 155 mm
dib = 101 mm
eap = 0 mm
X5CrNi18-10
eab = 27 mm
e,b = /
X5CrNi18-10
[9.4.8] : if the distance between the bore and a shell weld is : lso, the distance between the weld and the center of the
opening should be: < dib/6 = 16.83 mm or > ln = min(0.5deb+2eas ; 0.5deb+40 mm) = 83.68 mm.
Fig. 9.4-14 : eb/eas = 2
Fig. 9.4-15 : eab/eas = 3
[9.4.5.3]:dib/De ≤ 0.6
Required thickness of the nozzle neck under internal pressure : e = P∙de/(2fb∙z+P) = 0.299 mm ( z = 1 )
In the plane that contains the axis of the nozzle and the radius of the sphere passing through the center of the
nozzle (  : Figure 3 )
De = 500.18 mm
 = 0 ° ≤ sin-1(1-δ) = 57.7 °
rms= ris+eas /2 = 501.72 mm
a = 77.81 mm
 = 0.154
h = 0 mm
ls = 128.02 mm
lb = 25.09 mm
hb = 21 mm
lp = 0 mm
lbi = 0 mm
wmin = 0 mm
lso =
wp = 55.68 mm
lbo =
w = 128.02 mm ≥ wmin
Fig. 9.4-14 : (eb/eas) > 2
(2r + e )e
is
c ,s
c ,s
= 55.68 mm
(deb − eb )eb = 58.79 mm
l s = min(l so; l s ) = 55.68 mm
l p = min(l so; l p ; w ) = 0 mm
ec,s = 3.09 mm
eb = 27 mm
lb = min(lbo ; lb ) = 25.09 mm
lbi = min(0.5lbo; lbi ) = 0 mm
Afs = 172.1 mm2
Afb = 760.8 mm2
Aps = 33,283 mm2
2
2
Afp = 0 mm
Afw = 9.5 mm
Ap = 0 mm2
(Afs + Afw )  fs + Afb  fob + Af p  fop
Pmax =
(Aps + Apb + 0.5Ap ) + 0.5(Afs + Afw + Af b+ Af p ) = 6.97 MPa ≥ P (14%)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
43
Apb = 1,422.9 mm2
z=1
fob =min(fs;z fb)
fop = min(fs ;fp)
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
Design Calculations
RESERVOIR_VESSEL_233L
2024-06-20
Revision : 23-08-24
Local loads on nozzle N3 (Sustained).
E = 200,000 MPa
fb = 184.67 MPa
f = 184.67 MPa
f2 = /
eb = 27 mm
R = 501.72 mm
ea = 3.09 mm
r = 64 mm
e2 = 0
lp = 0
§ 9.5.2 :
Aps = 33,283 mm2
Afs = 172.1 mm2
Apb = 1,422.9 mm2
Afb = 760.8 mm2
Afp = 0 mm2
Ap = 0 mm2
Afw = 9.5 mm2
ea/R = 0.0062 the rules apply if : 0.001  ea/R  0.1
The nozzle thickness should be
de b =58.79 mm
maintained over a distance of :
Distances to any other local load
Rec =39.37 mm
should be no less than :
EN 13445-3 16.4 nozzle on spherical shell (P = 0.7 MPa)
FZ
MB
Af
eb
Afw b
Af
lp
r
p
Afs
e2
ea
Aps+Apb+Ap
R
Nozzle outer diameter
d = 128 mm
D = 2R
C4 = 1.1
ec = ea + e2  min( f2/f ; 1 ) = 3.09 mm
eeq=ec. If plate with L 
 2fb eb
 f  ec

 = min
R(ea + e2 ) , eeq = ea + min  e2L

Maximum permitted global loads (nozzle) (§16.14)
e = Rp1,0 / 1.3 / 1.25 =
c,all = e  = 184.67 MPa
160 MPa
K=0
=0
eb 
;1 = 1
d 
s =
d
Rec
= 3.2509
R (ea + e2 ) ; e2  min (f2 f ;1) : eeq=3.09 mm

=0
Fmax =  d eb c,all
( w / l )max = 0
Mmax = /4 d2 eb c,all
Maximum allowable individual loads(§16.4.5)
𝑃max = [(𝐴𝑓s + 𝐴𝑓w ) ⋅ 𝑓s + 𝐴𝑓b ⋅ 𝑓ob + 𝐴𝑓p ⋅ 𝑓op ]⁄[(𝐴𝑝s + 𝐴𝑝b + 0.5𝐴𝑝ϕ ) + 0.5(𝐴𝑓s + 𝐴𝑓w + 𝐴𝑓b + 𝐴𝑓p )] (16.4-6)
𝑑
𝐹Z,max = 𝑓𝑒c2 {1.82 + 2.4(√1 + 𝜅)𝜆s + 0.91𝜅𝜆2s }
𝑀B,max = 𝑓𝑒c2 {4.9 + 2.0(√1 + 𝜅)𝜆s + 0.91𝜅𝜆2s }
4
2𝐹S
2𝑀Z
𝜏F =
𝜏Z = 2
𝜏 = |𝜏F | + |𝜏Z |
𝜋𝑑𝑒c
𝜋𝑑 𝑒c
Maximum allowable loads at the nozzle / pad outer diameter
Pmax (MPa)
FZ,max (daN)
MB,max (daN∙mm)
4.95 / 3,962.1 / 0.1338×106 / F (daN)
Z (daN)
 (daN)
0/0/0/-
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
44
Maximum allowable nozzle loads
Fmax (daN)
Mmax (daN∙mm)
200,499.3
0.6416×107
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
Design Calculations
RESERVOIR_VESSEL_233L
2024-06-20
Revision : 23-08-24
Allowable bounded area. ( = )
|MB| (daN∙mm)
FZ,max
MB,max
10,000
1,000
FZ (daN)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
45
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Opening N4
Isolated opening N4 [ in operation Int.P. ]
EN 13445-3 9.5
Nozzle without pad on Shell (No. 2)
P = 0.7 MPa
t = 10 °C
fs = 184.67 MPa
X5CrNi18-10
en,s = 2.03 mm
eas = 2.03 mm
cs = 0 mm
e,s = /
ris = 247 mm
(Process)
Set In
fb = 184.67 MPa
en,b = 2 mm
cb = 0 mm
fp = 184.67 MPa
de = 85 mm
deb = 85 mm
dib = 81 mm
eap = 0 mm
X5CrNi18-10
eab = 2 mm
e,b = /
X5CrNi18-10
[9.4.8] : if the distance between the bore and a shell weld is : lso, the distance between the weld and the center of the
opening should be: < dib/6 = 13.5 mm or > ln = min(0.5deb+2eas ; 0.5deb+40 mm) = 46.56 mm.
[9.5.2.3]: The angle θ between the nozzle weld and the shell generator should be < 45°.
Fig. 9.4-14 : eb/eas = 2
Fig. 9.4-15 : eab/eas = 3
[9.4.5.4]:dib/(2ris) ≤ 1
Required thickness of the nozzle neck under internal pressure : e = P∙de/(2fb∙z+P) = 0.19 mm ( z = 0.85 )
In the longitudinal section (  : Figure 1 )
De = 498.06 mm
 = 0 ° ≤ 60 °
rms= ris+eas /2 = 248.02 mm
 = 0.171
h = 0 mm
ls = 12.5 mm
hb = 15 mm
lp = 0 mm
wmin = 6.35 mm
lso =
wp = 31.73 mm
lbo =
c ,s
c ,s
= 31.73 mm
ec,s = 2.03 mm
eb = 2 mm
lb = min(lbo ; lb ) = 12.88 mm
lbi = min(0.5lbo; lbi ) = 0 mm
l p = min(l so; l p ; w ) = 0 mm
Fig. 9.4-14 : (eb/eas) ≤ 2
Pmax =
is
(deb − eb )eb = 12.88 mm
l s = min(l so; l s ) = 12.5 mm
w = 12.5 mm ≥ wmin
Afs = 25.4 mm2
Afp = 0 mm2
(2r + e )e
α=0°
a = 42.5 mm
lb = 15 mm
lbi = 0 mm
Afb = 29.8 mm2
Afw = 4 mm2
(Afs + Afw )  fs + Afb  fob + Af p  fop
Aps = 13,585 mm2
Ap = 0 mm2
(Ap + Ap + 0.5Ap ) + 0.5(Af + Af + Af + Af ) = 0.77 MPa ≥ P (92%)
s
b

s
w
b
p
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
46
Apb = 604 mm2
z=1
fob =min(fs;z fb)
fop = min(fs ;fp)
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Isolated opening N4 [ in test Int.P. ]
(Process)
EN 13445-3 9.5
Nozzle without pad on Shell (No. 2)
P = 1.01 MPa
t = 20 °C
fs = 260 MPa
X5CrNi18-10
en,s = 2.03 mm
eas = 2.03 mm
cs = 0 mm
e,s = /
ris = 247 mm
Set In
fb = 260 MPa
en,b = 2 mm
cb = 0 mm
fp = 260 MPa
de = 85 mm
deb = 85 mm
dib = 81 mm
eap = 0 mm
X5CrNi18-10
eab = 2 mm
e,b = /
X5CrNi18-10
[9.4.8] : if the distance between the bore and a shell weld is : lso, the distance between the weld and the center of the
opening should be: < dib/6 = 13.5 mm or > ln = min(0.5deb+2eas ; 0.5deb+40 mm) = 46.56 mm.
Fig. 9.4-14 : eb/eas = 2
Fig. 9.4-15 : eab/eas = 3
[9.4.5.4]:dib/(2ris) ≤ 1
Required thickness of the nozzle neck under internal pressure : e = P∙de/(2fb∙z+P) = 0.164 mm ( z = 1 )
In the longitudinal section (  : Figure 1 )
De = 498.06 mm
 = 0 ° ≤ 60 °
rms= ris+eas /2 = 248.02 mm
 = 0.171
h = 0 mm
ls = 12.5 mm
hb = 15 mm
lp = 0 mm
wmin = 6.35 mm
lso =
wp = 31.73 mm
lbo =
c ,s
c ,s
= 31.73 mm
ec,s = 2.03 mm
eb = 2 mm
lb = min(lbo ; lb ) = 12.88 mm
lbi = min(0.5lbo; lbi ) = 0 mm
l p = min(l so; l p ; w ) = 0 mm
Fig. 9.4-14 : (eb/eas) ≤ 2
Pmax =
is
(deb − eb )eb = 12.88 mm
l s = min(l so; l s ) = 12.5 mm
w = 12.5 mm ≥ wmin
Afs = 25.4 mm2
Afp = 0 mm2
(2r + e )e
α=0°
a = 42.5 mm
lb = 15 mm
lbi = 0 mm
Afb = 29.8 mm2
Afw = 4 mm2
(Afs + Afw )  fs + Afb  fob + Af p  fop
Aps = 13,585 mm2
Ap = 0 mm2
(Ap + Ap + 0.5Ap ) + 0.5(Af + Af + Af + Af ) = 1.08 MPa ≥ P (93%)
s
b

s
w
b
p
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
47
Apb = 604 mm2
z=1
fob =min(fs;z fb)
fop = min(fs ;fp)
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Local loads on nozzle N4 (Sustained).
FZ
FZ
MX
Afb
Afw11
MY
Afb
eb e
2
lp
Afp2 Afw22
Afs2
Afp1
r
ea
Aps2+Apb2+Ap2
R
Afs1
Aps1+Apb1+Ap1
EN 13445-3 16.5 - nozzle on cylindrical shell (P = 0.7 MPa)
f = 184.67 MPa
fb = 184.67 MPa
E = 200,000 MPa
f2 = /
eb = 2 mm
R = 248.02 mm
ea = 2.03 mm
r = 41.5 mm
lp = 0
e2 = 0
9.5.2 :
Afw1 = 4 mm2
Afw2 = 4 mm2
2
2
Aps1 = 9,156.1 mm
Afs1 = 64.4 mm
Afb1 = 29.8 mm2
2
2
Apb1 = 604 mm
Afp1 = 0 mm2
Ap1 = 0 mm
Aps2 = 13,585 mm2
Afs2 = 25.4 mm2
Afb2 = 29.8 mm2
Apb2 = 604 mm2
Afp2 = 0 mm2
Ap2 = 0 mm2
ea / 2R = 0.0041 the rules apply if : 0.001  ea / 2R  0.1
The nozzle thickness should be
deb = 12.88 mm
maintained over a distance of :
Distances to any other local load should
Dec =31.73 mm
be no less than :
External Diameter (nozzle)
d = 83 mm
D = 2R
d/D = 0.1673 shall be  0.5
c = d
ec = ea + e2  min( f2/f ; 1) = 2.03 mm
C4 = 1.1
(
C1 = 3.1011
)
Dec =2.6156
C2= 5.446
If c  10 the effects of a
twisting moment are
considerable
C3 = 15.799
eeq=ec.If plate with l P  D(ea + e2 ) , eeq = ea + min e2 l P
D(ea + e2 ) ; e2 min(f2 f ;1) ) : eeq=2.03 mm
Maximum permitted global loads (nozzle) (§16.14)
e = Rp1,0 / 1.3 / 1.25 =
c,all = e  = 184.67 MPa
160 MPa
K=0
=0
=0
Fmax =  d eb c,all
( w / l )max = 0
Mmax = /4 d2 eb c,all
Maximum allowable individual loads(§16.5.5)
𝑃max = [(𝐴𝑓s + 𝐴𝑓w ) ⋅ 𝑓s + 𝐴𝑓b ⋅ 𝑓ob + 𝐴𝑓p ⋅ 𝑓op ]⁄[(𝐴𝑝s + 𝐴𝑝b + 0.5𝐴𝑝ϕ ) + 0.5(𝐴𝑓s + 𝐴𝑓w + 𝐴𝑓b + 𝐴𝑓p )] (16.5-2)
𝑑
𝑑
𝐹Z,max = 𝑓𝑒𝑐2 max(𝐶1 ; 1.81)
𝑃max = min(𝑃max1 ; 𝑃max2 )
𝑀X,max = 𝑓𝑒𝑐2 max(𝐶2 ; 4.90) 𝑀Y,max = 𝑓𝑒𝑐2 max(𝐶3 ; 4.90)
4
4
2𝐹X
2𝐹Y
2𝑀Z
2
𝜏X =
𝜏Y =
𝜏Z = 2
𝜏 = √𝜏X + 𝜏Y2 + |𝜏Z |
𝜋𝑑𝑒c
𝜋𝑑𝑒c
𝜋𝑑 𝑒c
Pmax (MPa)
0.77 / X (daN)
0/-
Maximum allowable loads at the nozzle / pad outer diameter
FZ,max (daN)
MX,max (daN∙mm)
MY,max (daN∙mm)
236 / 8,600 / 0.2495×105 / Y (daN)
Z (daN)
 (daN)
0/0/0/-
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
48
Maximum allowable nozzle loads
Fmax (daN)
Mmax (daN∙mm)
9,630.5
0.1998×106
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
Design Calculations
RESERVOIR_VESSEL_233L
2024-06-20
Revision : 23-08-24
Allowable bounded area. ( = )
|MX| (daN∙mm)
|MY| (daN∙mm)
FZ,max
FZ,max
MX,max(MY=0)
MY=0
MY,max(MX=0)
MX=0
1,000
MY=MY,max
10
FZ (daN)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
1,000
MX=MX,max
49
10
FZ (daN)
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Opening N5
Isolated opening N5 [ in operation Int.P. ]
EN 13445-3 9.5
Nozzle without pad on Shell (No. 2)
P = 0.7 MPa
t = 10 °C
fs = 184.67 MPa
X5CrNi18-10
en,s = 2.03 mm
eas = 2.03 mm
cs = 0 mm
e,s = /
ris = 247 mm
(Process)
Set In
fb = 184.67 MPa
en,b = 2 mm
cb = 0 mm
fp = 184.67 MPa
de = 85 mm
deb = 85 mm
dib = 81 mm
eap = 0 mm
X5CrNi18-10
eab = 2 mm
e,b = /
X5CrNi18-10
[9.4.8] : if the distance between the bore and a shell weld is : lso, the distance between the weld and the center of the
opening should be: < dib/6 = 13.5 mm or > ln = min(0.5deb+2eas ; 0.5deb+40 mm) = 46.56 mm.
[9.5.2.3]: The angle θ between the nozzle weld and the shell generator should be < 45°.
Fig. 9.4-14 : eb/eas = 2
Fig. 9.4-15 : eab/eas = 3
[9.4.5.4]:dib/(2ris) ≤ 1
Required thickness of the nozzle neck under internal pressure : e = P∙de/(2fb∙z+P) = 0.19 mm ( z = 0.85 )
In the longitudinal section (  : Figure 1 )
De = 498.06 mm
 = 0 ° ≤ 60 °
rms= ris+eas /2 = 248.02 mm
 = 0.171
h = 0 mm
ls = 12.5 mm
hb = 15 mm
lp = 0 mm
wmin = 6.35 mm
lso =
wp = 31.73 mm
lbo =
c ,s
c ,s
= 31.73 mm
ec,s = 2.03 mm
eb = 2 mm
lb = min(lbo ; lb ) = 12.88 mm
lbi = min(0.5lbo; lbi ) = 0 mm
l p = min(l so; l p ; w ) = 0 mm
Fig. 9.4-14 : (eb/eas) ≤ 2
Pmax =
is
(deb − eb )eb = 12.88 mm
l s = min(l so; l s ) = 12.5 mm
w = 12.5 mm ≥ wmin
Afs = 25.4 mm2
Afp = 0 mm2
(2r + e )e
α=0°
a = 42.5 mm
lb = 15 mm
lbi = 0 mm
Afb = 29.8 mm2
Afw = 4 mm2
(Afs + Afw )  fs + Afb  fob + Af p  fop
Aps = 13,585 mm2
Ap = 0 mm2
(Ap + Ap + 0.5Ap ) + 0.5(Af + Af + Af + Af ) = 0.77 MPa ≥ P (92%)
s
b

s
w
b
p
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
50
Apb = 604 mm2
z=1
fob =min(fs;z fb)
fop = min(fs ;fp)
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Isolated opening N5 [ in test Int.P. ]
(Process)
EN 13445-3 9.5
Nozzle without pad on Shell (No. 2)
P = 1.01 MPa
t = 20 °C
fs = 260 MPa
X5CrNi18-10
en,s = 2.03 mm
eas = 2.03 mm
cs = 0 mm
e,s = /
ris = 247 mm
Set In
fb = 260 MPa
en,b = 2 mm
cb = 0 mm
fp = 260 MPa
de = 85 mm
deb = 85 mm
dib = 81 mm
eap = 0 mm
X5CrNi18-10
eab = 2 mm
e,b = /
X5CrNi18-10
[9.4.8] : if the distance between the bore and a shell weld is : lso, the distance between the weld and the center of the
opening should be: < dib/6 = 13.5 mm or > ln = min(0.5deb+2eas ; 0.5deb+40 mm) = 46.56 mm.
Fig. 9.4-14 : eb/eas = 2
Fig. 9.4-15 : eab/eas = 3
[9.4.5.4]:dib/(2ris) ≤ 1
Required thickness of the nozzle neck under internal pressure : e = P∙de/(2fb∙z+P) = 0.164 mm ( z = 1 )
In the longitudinal section (  : Figure 1 )
De = 498.06 mm
 = 0 ° ≤ 60 °
rms= ris+eas /2 = 248.02 mm
 = 0.171
h = 0 mm
ls = 12.5 mm
hb = 15 mm
lp = 0 mm
wmin = 6.35 mm
lso =
wp = 31.73 mm
lbo =
c ,s
c ,s
= 31.73 mm
ec,s = 2.03 mm
eb = 2 mm
lb = min(lbo ; lb ) = 12.88 mm
lbi = min(0.5lbo; lbi ) = 0 mm
l p = min(l so; l p ; w ) = 0 mm
Fig. 9.4-14 : (eb/eas) ≤ 2
Pmax =
is
(deb − eb )eb = 12.88 mm
l s = min(l so; l s ) = 12.5 mm
w = 12.5 mm ≥ wmin
Afs = 25.4 mm2
Afp = 0 mm2
(2r + e )e
α=0°
a = 42.5 mm
lb = 15 mm
lbi = 0 mm
Afb = 29.8 mm2
Afw = 4 mm2
(Afs + Afw )  fs + Afb  fob + Af p  fop
Aps = 13,585 mm2
Ap = 0 mm2
(Ap + Ap + 0.5Ap ) + 0.5(Af + Af + Af + Af ) = 1.08 MPa ≥ P (93%)
s
b

s
w
b
p
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
51
Apb = 604 mm2
z=1
fob =min(fs;z fb)
fop = min(fs ;fp)
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Local loads on nozzle N5 (Sustained).
FZ
FZ
MX
Afb
Afw11
MY
Afb
eb e
2
lp
Afp2 Afw22
Afs2
Afp1
r
ea
Aps2+Apb2+Ap2
R
Afs1
Aps1+Apb1+Ap1
EN 13445-3 16.5 - nozzle on cylindrical shell (P = 0.7 MPa)
f = 184.67 MPa
fb = 184.67 MPa
E = 200,000 MPa
f2 = /
eb = 2 mm
R = 248.02 mm
ea = 2.03 mm
r = 41.5 mm
lp = 0
e2 = 0
9.5.2 :
Afw1 = 4 mm2
Afw2 = 4 mm2
2
2
Aps1 = 9,156.1 mm
Afs1 = 64.4 mm
Afb1 = 29.8 mm2
2
2
Apb1 = 604 mm
Afp1 = 0 mm2
Ap1 = 0 mm
Aps2 = 13,585 mm2
Afs2 = 25.4 mm2
Afb2 = 29.8 mm2
Apb2 = 604 mm2
Afp2 = 0 mm2
Ap2 = 0 mm2
ea / 2R = 0.0041 the rules apply if : 0.001  ea / 2R  0.1
The nozzle thickness should be
deb = 12.88 mm
maintained over a distance of :
Distances to any other local load should
Dec =31.73 mm
be no less than :
External Diameter (nozzle)
d = 83 mm
D = 2R
d/D = 0.1673 shall be  0.5
c = d
ec = ea + e2  min( f2/f ; 1) = 2.03 mm
C4 = 1.1
(
C1 = 3.1011
)
Dec =2.6156
C2= 5.446
If c  10 the effects of a
twisting moment are
considerable
C3 = 15.799
eeq=ec.If plate with l P  D(ea + e2 ) , eeq = ea + min e2 l P
D(ea + e2 ) ; e2 min(f2 f ;1) ) : eeq=2.03 mm
Maximum permitted global loads (nozzle) (§16.14)
e = Rp1,0 / 1.3 / 1.25 =
c,all = e  = 184.67 MPa
160 MPa
K=0
=0
=0
Fmax =  d eb c,all
( w / l )max = 0
Mmax = /4 d2 eb c,all
Maximum allowable individual loads(§16.5.5)
𝑃max = [(𝐴𝑓s + 𝐴𝑓w ) ⋅ 𝑓s + 𝐴𝑓b ⋅ 𝑓ob + 𝐴𝑓p ⋅ 𝑓op ]⁄[(𝐴𝑝s + 𝐴𝑝b + 0.5𝐴𝑝ϕ ) + 0.5(𝐴𝑓s + 𝐴𝑓w + 𝐴𝑓b + 𝐴𝑓p )] (16.5-2)
𝑑
𝑑
𝐹Z,max = 𝑓𝑒𝑐2 max(𝐶1 ; 1.81)
𝑃max = min(𝑃max1 ; 𝑃max2 )
𝑀X,max = 𝑓𝑒𝑐2 max(𝐶2 ; 4.90) 𝑀Y,max = 𝑓𝑒𝑐2 max(𝐶3 ; 4.90)
4
4
2𝐹X
2𝐹Y
2𝑀Z
2
𝜏X =
𝜏Y =
𝜏Z = 2
𝜏 = √𝜏X + 𝜏Y2 + |𝜏Z |
𝜋𝑑𝑒c
𝜋𝑑𝑒c
𝜋𝑑 𝑒c
Pmax (MPa)
0.77 / X (daN)
0/-
Maximum allowable loads at the nozzle / pad outer diameter
FZ,max (daN)
MX,max (daN∙mm)
MY,max (daN∙mm)
236 / 8,600 / 0.2495×105 / Y (daN)
Z (daN)
 (daN)
0/0/0/-
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
52
Maximum allowable nozzle loads
Fmax (daN)
Mmax (daN∙mm)
9,630.5
0.1998×106
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
Design Calculations
RESERVOIR_VESSEL_233L
2024-06-20
Revision : 23-08-24
Allowable bounded area. ( = )
|MX| (daN∙mm)
|MY| (daN∙mm)
FZ,max
FZ,max
MX,max(MY=0)
MY=0
MY,max(MX=0)
MX=0
1,000
MY=MY,max
10
FZ (daN)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
1,000
MX=MX,max
53
10
FZ (daN)
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Saddles
M
EXA < 0
EXA > 0
EXA = 0
F
F
F
T
FB
EYV
a
a
K
H
a
EXF EXF
DB
D
EXF
EXF
EXA
G
EXA
G
EYV
C
EXV
L
B
E
E
E
Standard : /
G
Number of saddles = 2
Fixed support No. = 1
Saddle check, Equivalent section inertia (Detail)
Z-Z
K
G
CoG
E
X-X
EXA
D
K
Saddle No 1 (left)
Location = 50 mm
Stiffness = /
Diameter =498.06 mm
2 Bolts : Diameter = 20 mm ( Hole Diameter = 23 mm )
Base Plate
E
(mm)
160
B
(mm)
470
L
(mm)
4
C
(mm)
200
G
(mm)
100
EXV
(mm)
0
B
(mm)
470
L
(mm)
4
C
(mm)
200
G
(mm)
100
EXV
(mm)
0
H = 449 mm
T = 120 °
HT = /
Mass = 15 kg
2 Ribs
EYV
(mm)
/
Saddle No 2 (right)
Location = 1,050 mm
Stiffness = /
Diameter =498.06 mm
2 Bolts : Diameter = 20 mm ( Hole Diameter = 23 mm )
Base Plate
E
(mm)
160
a = Web thickness
CoG = Center of Gravity
D = Rib Spacing
E = Width
EXA = Offset
G = Bolt(s) Distance
K = Rib Thickness
K
(mm)
2
D
(mm)
300
H = 449 mm
T = 120 °
EYV
(mm)
/
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
Wear Plate
M
(mm)
2.03
D
(mm)
300
54
F
(mm)
200
FB
(mm)
55
HT = /
Mass = 15 kg
2 Ribs
K
(mm)
2
Welded
Web
EXF
(mm)
15
EXA
(mm)
-75
Welded
Wear Plate
M
(mm)
2.03
F
(mm)
200
a
(mm)
2
FB
(mm)
55
Web
EXF
(mm)
15
EXA
(mm)
-75
a
(mm)
2
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Saddle No. 1
Case 1 - Lifting P = 0. (New Inertias) (New Weight)
Calculation method : EN 13445-3 16.8
Material of saddle : SA516GR60
Pressure : P = 0 MPa
Horizontal (longitudinal) reaction : RaHL = 0 daN
Horizontal (cross) reaction : RaH = 0 daN
Maximum shear load : Qi = 12.9 daN
Distance a1 = 50 mm
Length L = 1,105 mm
Weight of saddle : Ws = 14.7 daN
Vertical Load : RaV = 22.8 daN
Reaction at support : Fi = 22.8 daN
Saddle
Pad
Shell
Yield Strength Leb
Width b1
Angle A
Allowable stress f2
Thickness e2
Width b2
Width a2
Angle 2A
Allowable stress f
All. Comp. Stress c,all
Modulus of elasticity E
Thickness ea
Mean radius R
Internal Diameter D
221 MPa
170 mm
120 °
 = A – 2.arctan (|RaH| / RaV) 120 °
b,all =K1K2f
1,2=
=
2.83a1
Di
−0.23K 6 K 8
K 5K 3
ea
Di
 PDi
2,2= 
 4ea
=
260 MPa
2 mm
200 mm
55 mm
145.31 °
2 = 2A – 2.arctan (|RaH| / RaV) 145.31 °
ea ≤ e2
a2 ≥ 0.1 D
0.91b1
4M i  1
Di2 ea  K 2 f
F2,max = 0.7 b,all ,2 Di ea  ea (K 3 K 5 )
1,3 =
−0.53K 4
K 7 K 9 K 10 sin(0.5 )
1 −  22
K1=
(1 3 + 1 2 ) + (1 3 + 1 2 )2 + (1 −  22 )12
Di ea
−
 2.718282−  sin 

; 0.25 
K3= max



K5=
2,3 =
PDi 1
2ea K 2 f
1.15 − 0.0025
sin(0.5 )
K6=
K2 = 1.25
K 4=
max(1.7 − 0.011667 ;0 )
sin(0.5 )


0 .8  + 6  

K8= min1.0 ;
0.017453 



K 7=
1
K10=
Feq = Fi  4 Di ea K 6 K 8

1.25
3
1.5
0.75  R ea E (ea R )
1.5 R L 1 + 42(R L ) (ea R )


Qmax = 
0.25  R ea E (ea R )1.5 1.5


Fc,max = Dea c,all
1 + 0.010472 

1.45 − 0.007505
sin(0.5 )
K11 =
3
Di ea b1 Di

Verification of load-carrying capacity with reinforcing plate [b2  K11Di+1.5b1 (K11= 0.0637) ]
Optimized Design 1 (b2 et 2 shall be replaced by b1 et  )
K3 = 0.25
K4 = 0.1735
 = 0.0184
 = 5.7472
K6 = 0.0049
K7 = 0.3766
K8 = 0.0862
K9 = 0.5873
K1,2 = 1.5
1,2 = -0.0005
2,2 = 0.0001
b,all,2 = 487.5 MPa
K1,3 = 0.4048
1,3 = -2.111
2,3 = 0
b,all,3 = 131.552 MPa
Fi shall be  min( F2,max ; F3,max ) = 10,646.4 daN
Optimized Design 2 (ec shall be replaced by ea ) ( ec =
1 − 2.718282−  cos 
K 9= 1 −
F3,max = 0.9 b,all ,3 Di ea  ea (K 7 K 9 K10 )
Mmax =  4 D 2 ea c,all
260 MPa
90.3 MPa
200,000 MPa
2 mm
248 mm
494 mm

0.65
1 + (6 )
2
60

5
0.10472 3 Di ea
  L R  8.7 R e 
a


 L R  8.7 R ea 


K5 = 0.8242
K10 = 0.2063
F2,max = 10,646.4 daN
F3,max = 16,676.4 daN

ea2 + e22 min 1; (f2 f ) = 2.9 mm )
 = 0.0218
K3 = 0.25
 = 4.1079
K6 = 0.3464
K7 = 0.6344
K8 = 0.119
K1,2 = 1.495
1,2 = -0.0386
2,2 = 0.0001
K1,3 = 0.5425
1,3 = -1.4726
2,3 = 0
Fi shall be  min( F2,max ; F3,max ) = 14,985.7 daN
2
K4 = 0.2457
K9 = 0.5481
b,all,2 = 485.876 MPa
b,all,3 = 176.329 MPa
Proof of stability
Feq = 10.1 daN
Pmax = +∞ MPa
Mmax = 3,543.99 daN∙m
Fc,max = 28,578.8 daN
|P|/Pmax + |Mi|/Mmax + Feq/Fc,max + (Qi/Qmax)2 = 0.0006 shall be  1.0 (for P > 0  P = 0)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
55
K5 = 0.9815
K10 = 0.2937
F2,max = 14,985.7 daN
F3,max = 16,801.8 daN
Qmax = 18,451.5 daN
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Saddle check
Stress due to horizontal reaction on the saddle
K = (1+ cos  – 0.5 sin² ) / ( –  + sin  cos ) =0.2035
 = 2.0944 rad
H = K Q = 46 N
Ab = 165.3 mm2
Sb = H / (2/3 Ab) = 0.42 MPa ≤ (90% Leb) (198.9 MPa)
Bending and compression stresses (See detail)
Hb = 449 mm
LEFF = 200 mm
Mzz = RaH . Hb
Mxx = RaHL . LEFF
| Mzz | = 0 daN∙m
| Mxx | = 0 daN∙m
Izz = 29.45401×106 mm4
Ixx = 2,429,753 mm4
Szz = Izz/v = 125,336.2 mm3
Sxx = Ixx/v = 21,888.34 mm3
Sbz = | Mzz | / Szz
Sbx = | Mxx | / Sxx
Sbz = 0 MPa ≤ (90% Leb) (198.9 MPa)
Sbx = 0 MPa ≤ (90% Leb) (198.9 MPa)
A = 1,480 mm2 fb = 210.48 MPa Sbc = RaV / A
Sbc = 0.15 MPa ≤ (0.8 fb ) (168.38 MPa)
max(Sbz ; Sbx ) / (90% Leb) + Sbc / (0.8 fb ) ≤ 1
Stability of web plate [CODAP C9.3.2.7] [AD S3/2 6.1.1]
hb2 = 324.5 mm
lb = 431.3 mm
eba = 2 mm
Eb = 202,350 MPa fb = 90% Leb = 198.9 MPa
x = hb2 / lb
Kb = 2.261
 b = fb 103 / Eb
 = 0.058
Qmax = lb eba fb  = 998.1 daN
Base Plate. Thickness check under compression (Dennis Moss, Fourth Edition)
K
EXW
R
Ww
l2
L
l1
ꙍ
E
Width
E = 160 mm
Length
B = 470 mm
Web thickness
K = 2 mm
Offset (Length)
EXV = 0 mm
Offset (Width)
EXW = 23 mm
Q+ = MAX( 0 ; Q+Ws) = 37.5 daN
Lw = B − 2∙EXV = 470 mm
Lr = n∙R = 270 mm
fu = Q+ / (Lw + Lr) = 0.05 daN/mm
Ww = 0.7∙min(K, L) = 1.4 mm
l1= EXW+K+Ww +Lmin = 27.09 mm
l2= E − l1 = 132.91 mm
ꙍ = fu / (l1 + 0.5 l2) = 0.0005 daN/mm2
Number of ribs
n= 2
Rib's length
R = 135 mm
Allowable Stress (90%Leb)
fb = 198.9 MPa
ꙍ∙l2 2
Lmin = √
fb
=0.69 mm ≤L=4 mm
Stresses in the bolts ( nb = 2 ; Sb = 225.2 mm2 ; xb = 200 mm )
Max. Tensile : bT = max{ 0 ; [ |Mzz| / (xb. nb/2) – (RaV + WS) /nb ] / Sb } = 0 MPa ≤ fbolt = 170 MPa
2
Max. Shear : bL = [√𝑅𝑎𝐻2 + 𝑅𝑎𝐻𝐿
]⁄(𝑆𝑏 ∙ 𝑛𝑏 ) = 0 MPa ≤ fbolt,shear = 170 MPa
fbolt,shear = fbolt / 1
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
56
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Case 2 - Erected P = 0. (New Inertias) (New Weight)
Calculation method : EN 13445-3 16.8
Material of saddle : SA516GR60
Pressure : P = 0 MPa
Horizontal (longitudinal) reaction : RaHL = 0 daN
Horizontal (cross) reaction : RaH = 0 daN
Maximum shear load : Qi = 12.9 daN
Distance a1 = 50 mm
Length L = 1,105 mm
Weight of saddle : Ws = 14.7 daN
Vertical Load : RaV = 22.8 daN
Reaction at support : Fi = 22.8 daN
Saddle
Pad
Shell
Yield Strength Leb
Width b1
Angle A
Allowable stress f2
Thickness e2
Width b2
Width a2
Angle 2A
Allowable stress f
All. Comp. Stress c,all
Modulus of elasticity E
Thickness ea
Mean radius R
Internal Diameter D
221 MPa
170 mm
120 °
 = A – 2.arctan (|RaH| / RaV) 120 °
b,all =K1K2f
1,2=
=
2.83a1
Di
−0.23K 6 K 8
K 5K 3
ea
Di
 PDi
2,2= 
 4ea
=
260 MPa
2 mm
200 mm
55 mm
145.31 °
2 = 2A – 2.arctan (|RaH| / RaV) 145.31 °
ea ≤ e2
a2 ≥ 0.1 D
0.91b1
Di ea
−
4M i  1
Di2 ea  K 2 f
F2,max = 0.7 b,all ,2 Di ea  ea (K 3 K 5 )
1,3 =
−0.53K 4
K 7 K 9 K 10 sin(0.5 )
K1=
2,3 =
PDi 1
2ea K 2 f
1 −  22
(1 3 + 1 2 ) + (1 3 + 1 2 )2 + (1 −  22 )12
K2 = 1.25
 2.718282−  sin 

; 0.25 
K3= max



K 4=
1.15 − 0.0025
K5=
sin(0.5 )
1.45 − 0.007505
K 7=
sin(0.5 )
max(1.7 − 0.011667 ;0 )
K6=
sin(0.5 )


0 .8  + 6  

K8= min1.0 ;
0.017453 



1
K10=
Feq = Fi  4 Di ea K 6 K 8

1.25
3
1.5
0.75  R ea E (ea R )
1.5 R L 1 + 42(R L ) (ea R )


Qmax = 
0.25  R ea E (ea R )1.5 1.5


Mmax =  4 D ea c,all
Fc,max = Dea c,all
K11 =
1 + 0.010472  3 Di ea b1 Di

Verification of load-carrying capacity with reinforcing plate [b2  K11Di+1.5b1 (K11= 0.0637) ]
Optimized Design 1 (b2 et 2 shall be replaced by b1 et  )
K3 = 0.25
K4 = 0.1735
 = 0.0184
 = 5.7472
K6 = 0.0049
K7 = 0.3766
K8 = 0.0862
K9 = 0.5873
K1,2 = 1.5
1,2 = -0.0005
2,2 = 0.0001
b,all,2 = 487.5 MPa
K1,3 = 0.4048
1,3 = -2.111
2,3 = 0
b,all,3 = 131.552 MPa
Fi shall be  min( F2,max ; F3,max ) = 10,646.4 daN
Optimized Design 2 (ec shall be replaced by ea ) ( ec =

1 − 2.718282−  cos 

K 9= 1 −
F3,max = 0.9 b,all ,3 Di ea  ea (K 7 K 9 K10 )
2
260 MPa
90.3 MPa
200,000 MPa
2 mm
248 mm
494 mm
0.65
1 + (6 )
2
60

5
0.10472 3 Di ea
  L R  8.7 R e 
a


 L R  8.7 R ea 


K5 = 0.8242
K10 = 0.2063
F2,max = 10,646.4 daN
F3,max = 16,676.4 daN

ea2 + e22 min 1; (f2 f ) = 2.9 mm )
 = 0.0218
K3 = 0.25
 = 4.1079
K6 = 0.3464
K7 = 0.6344
K8 = 0.119
K1,2 = 1.495
1,2 = -0.0386
2,2 = 0.0001
K1,3 = 0.5425
1,3 = -1.4726
2,3 = 0
Fi shall be  min( F2,max ; F3,max ) = 14,985.7 daN
2
K4 = 0.2457
K9 = 0.5481
b,all,2 = 485.876 MPa
b,all,3 = 176.329 MPa
Proof of stability
Feq = 10.1 daN
Pmax = +∞ MPa
Mmax = 3,543.99 daN∙m
Fc,max = 28,578.8 daN
|P|/Pmax + |Mi|/Mmax + Feq/Fc,max + (Qi/Qmax)2 = 0.0006 shall be  1.0 (for P > 0  P = 0)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
57
K5 = 0.9815
K10 = 0.2937
F2,max = 14,985.7 daN
F3,max = 16,801.8 daN
Qmax = 18,451.5 daN
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Saddle check
Stress due to horizontal reaction on the saddle
K = (1+ cos  – 0.5 sin² ) / ( –  + sin  cos ) =0.2035
 = 2.0944 rad
H = K Q = 46 N
Ab = 165.3 mm2
Sb = H / (2/3 Ab) = 0.42 MPa ≤ (90% Leb) (198.9 MPa)
Bending and compression stresses (See detail)
Hb = 449 mm
LEFF = 200 mm
Mzz = RaH . Hb
Mxx = RaHL . LEFF
| Mzz | = 0 daN∙m
| Mxx | = 0 daN∙m
Izz = 29.45401×106 mm4
Ixx = 2,429,753 mm4
Szz = Izz/v = 125,336.2 mm3
Sxx = Ixx/v = 21,888.34 mm3
Sbz = | Mzz | / Szz
Sbx = | Mxx | / Sxx
Sbz = 0 MPa ≤ (90% Leb) (198.9 MPa)
Sbx = 0 MPa ≤ (90% Leb) (198.9 MPa)
A = 1,480 mm2 fb = 210.48 MPa Sbc = RaV / A
Sbc = 0.15 MPa ≤ (0.8 fb ) (168.38 MPa)
max(Sbz ; Sbx ) / (90% Leb) + Sbc / (0.8 fb ) ≤ 1
Stability of web plate [CODAP C9.3.2.7] [AD S3/2 6.1.1]
hb2 = 324.5 mm
lb = 431.3 mm
eba = 2 mm
Eb = 202,350 MPa fb = 90% Leb = 198.9 MPa
x = hb2 / lb
Kb = 2.261
 b = fb 103 / Eb
 = 0.058
Qmax = lb eba fb  = 998.1 daN
Base Plate. Thickness check under compression (Dennis Moss, Fourth Edition)
K
EXW
R
Ww
l2
L
l1
ꙍ
E
Width
E = 160 mm
Length
B = 470 mm
Web thickness
K = 2 mm
Offset (Length)
EXV = 0 mm
Offset (Width)
EXW = 23 mm
Q+ = MAX( 0 ; Q+Ws) = 37.5 daN
Lw = B − 2∙EXV = 470 mm
Lr = n∙R = 270 mm
fu = Q+ / (Lw + Lr) = 0.05 daN/mm
Ww = 0.7∙min(K, L) = 1.4 mm
l1= EXW+K+Ww +Lmin = 27.09 mm
l2= E − l1 = 132.91 mm
ꙍ = fu / (l1 + 0.5 l2) = 0.0005 daN/mm2
Number of ribs
n= 2
Rib's length
R = 135 mm
Allowable Stress (90%Leb)
fb = 198.9 MPa
ꙍ∙l2 2
Lmin = √
fb
=0.69 mm ≤L=4 mm
Stresses in the bolts ( nb = 2 ; Sb = 225.2 mm2 ; xb = 200 mm )
Max. Tensile : bT = max{ 0 ; [ |Mzz| / (xb. nb/2) – (RaV + WS) /nb ] / Sb } = 0 MPa ≤ fbolt = 170 MPa
2
Max. Shear : bL = [√𝑅𝑎𝐻2 + 𝑅𝑎𝐻𝐿
]⁄(𝑆𝑏 ∙ 𝑛𝑏 ) = 0 MPa ≤ fbolt,shear = 170 MPa
fbolt,shear = fbolt / 1
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
58
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Case 3 - Operation (Corroded inertias) (New Weight)
Calculation method : EN 13445-3 16.8
Material of saddle : SA516GR60
Pressure : P = 0.702 MPa
Horizontal (longitudinal) reaction : RaHL = 45.1 daN
Horizontal (cross) reaction : RaH = 0 daN
Maximum shear load : Qi = 109.1 daN
Distance a1 = 50 mm
Length L = 1,105 mm
Weight of saddle : Ws = 14.7 daN
Vertical Load : RaV = 137.1 daN
Reaction at support : Fi = 137.1 daN
Saddle
Pad
Shell
Yield Strength Leb
Width b1
Angle A
Allowable stress f2
Thickness e2
Width b2
Width a2
Angle 2A
Allowable stress f
All. Comp. Stress c,all
Modulus of elasticity E
Thickness ea
Mean radius R
Internal Diameter D
221 MPa
170 mm
120 °
 = A – 2.arctan (|RaH| / RaV) 120 °
b,all =K1K2f
1,2=
=
2.83a1
Di
−0.23K 6 K 8
K 5K 3
ea
Di
 PDi
2,2= 
 4ea
=
184.7 MPa
2 mm
200 mm
55 mm
145.31 °
2 = 2A – 2.arctan (|RaH| / RaV) 145.31 °
ea ≤ e2
a2 ≥ 0.1 D
0.91b1
Di ea
−
4M i  1
Di2 ea  K 2 f
F2,max = 0.7 b,all ,2 Di ea  ea (K 3 K 5 )
1,3 =
−0.53K 4
K 7 K 9 K 10 sin(0.5 )
K1=
2,3 =
PDi 1
2ea K 2 f
1 −  22
(1 3 + 1 2 ) + (1 3 + 1 2 )2 + (1 −  22 )12
K2 = 1.25
 2.718282−  sin 

; 0.25 
K3= max



K 4=
1.15 − 0.0025
K5=
sin(0.5 )
1.45 − 0.007505
K 7=
sin(0.5 )
max(1.7 − 0.011667 ;0 )
K6=
sin(0.5 )


0 .8  + 6  

K8= min1.0 ;
0.017453 



1
K10=
Feq = Fi  4 Di ea K 6 K 8

1.25
3
1.5
0.75  R ea E (ea R )
1.5 R L 1 + 42(R L ) (ea R )


Qmax = 
0.25  R ea E (ea R )1.5 1.5


Mmax =  4 D ea c,all
Fc,max = Dea c,all
K11 =
1 + 0.010472  3 Di ea b1 Di

Verification of load-carrying capacity with reinforcing plate [b2  K11Di+1.5b1 (K11= 0.0637) ]
Optimized Design 1 (b2 et 2 shall be replaced by b1 et  )
K3 = 0.25
K4 = 0.1735
 = 0.0184
 = 5.7472
K6 = 0.0049
K7 = 0.3766
K8 = 0.0862
K9 = 0.5873
K1,2 = 1.4478
1,2 = -0.0005
2,2 = 0.1872
b,all,2 = 334.2 MPa
K1,3 = 0.552
1,3 = -2.111
2,3 = 0.3702
b,all,3 = 127.41 MPa
Fi shall be  min( F2,max ; F3,max ) = 7,298.5 daN
Optimized Design 2 (ec shall be replaced by ea ) ( ec =

1 − 2.718282−  cos 

K 9= 1 −
F3,max = 0.9 b,all ,3 Di ea  ea (K 7 K 9 K10 )
2
184.7 MPa
65.2 MPa
200,000 MPa
2 mm
248 mm
494 mm
0.65
1 + (6 )
2
60

5
0.10472 3 Di ea
  L R  8.7 R e 
a


 L R  8.7 R ea 


K5 = 0.8242
K10 = 0.2063
F2,max = 7,298.5 daN
F3,max = 16,151.3 daN

ea2 + e22 min 1; (f2 f ) = 2.9 mm )
 = 0.0218
K3 = 0.25
 = 4.1079
K6 = 0.3464
K7 = 0.6344
K8 = 0.119
K1,2 = 1.4916
1,2 = -0.0386
2,2 = 0.1324
K1,3 = 0.6799
1,3 = -1.4726
2,3 = 0.2618
Fi shall be  min( F2,max ; F3,max ) = 10,619.5 daN
2
K4 = 0.2457
K9 = 0.5481
b,all,2 = 344.315 MPa
b,all,3 = 156.941 MPa
Proof of stability
Feq = 60.7 daN
Pmax = +∞ MPa
Mmax = 2,557.58 daN∙m
Fc,max = 20,624.4 daN
|P|/Pmax + |Mi|/Mmax + Feq/Fc,max + (Qi/Qmax)2 = 0.0105 shall be  1.0 (for P > 0  P = 0)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
59
K5 = 0.9815
K10 = 0.2937
F2,max = 10,619.5 daN
F3,max = 14,954.4 daN
Qmax = 18,451.5 daN
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Saddle check
Stress due to horizontal reaction on the saddle
K = (1+ cos  – 0.5 sin² ) / ( –  + sin  cos ) =0.2035
 = 2.0944 rad
H = K Q = 279 N
Ab = 165.3 mm2
Sb = H / (2/3 Ab) = 2.53 MPa ≤ (90% Leb) (198.9 MPa)
Bending and compression stresses (See detail)
Hb = 449 mm
LEFF = 200 mm
Mzz = RaH . Hb
Mxx = RaHL . LEFF
| Mzz | = 0 daN∙m
| Mxx | = 9.02 daN∙m
Izz = 29.45401×106 mm4
Ixx = 2,429,753 mm4
Szz = Izz/v = 125,336.2 mm3
Sxx = Ixx/v = 21,888.34 mm3
Sbz = | Mzz | / Szz
Sbx = | Mxx | / Sxx
Sbz = 0 MPa ≤ (90% Leb) (198.9 MPa)
Sbx = 4.12 MPa ≤ (90% Leb) (198.9 MPa)
A = 1,480 mm2 fb = 147.33 MPa Sbc = RaV / A
Sbc = 0.93 MPa ≤ (0.8 fb ) (117.87 MPa)
max(Sbz ; Sbx ) / (90% Leb) + Sbc / (0.8 fb ) ≤ 1
Stability of web plate [CODAP C9.3.2.7] [AD S3/2 6.1.1]
hb2 = 324.5 mm
lb = 431.3 mm
eba = 2 mm
Eb = 203,050 MPa fb = 90% Leb = 198.9 MPa
x = hb2 / lb
Kb = 2.261
 b = fb 103 / Eb
 = 0.058
Qmax = lb eba fb  = 1,001.5 daN
Base Plate. Thickness check under compression (Dennis Moss, Fourth Edition)
K
EXW
R
Ww
l2
L
l1
ꙍ
E
Width
E = 160 mm
Length
B = 470 mm
Web thickness
K = 2 mm
Offset (Length)
EXV = 0 mm
Offset (Width)
EXW = 23 mm
Q+ = MAX( 0 ; Q+Ws) = 151.8 daN
Lw = B − 2∙EXV = 470 mm
Lr = n∙R = 270 mm
fu = Q+ / (Lw + Lr) = 0.21 daN/mm
Ww = 0.7∙min(K, L) = 1.4 mm
l1= EXW+K+Ww +Lmin = 27.79 mm
l2= E − l1 = 132.21 mm
ꙍ = fu / (l1 + 0.5 l2) = 0.0022 daN/mm2
Number of ribs
n= 2
Rib's length
R = 135 mm
Allowable Stress (90%Leb)
fb = 198.9 MPa
ꙍ∙l2 2
Lmin = √
fb
=1.39 mm ≤L=4 mm
Stresses in the bolts ( nb = 2 ; Sb = 225.2 mm2 ; xb = 200 mm )
Max. Tensile : bT = max{ 0 ; [ |Mzz| / (xb. nb/2) – (RaV + WS) /nb ] / Sb } = 0 MPa ≤ fbolt = 100 MPa
2
Max. Shear : bL = [√𝑅𝑎𝐻2 + 𝑅𝑎𝐻𝐿
]⁄(𝑆𝑏 ∙ 𝑛𝑏 ) = 1 MPa ≤ fbolt,shear = 100 MPa
fbolt,shear = fbolt / 1
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
60
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Case 4 - Shutdown P = 0. (Corroded inertias) (Corroded Weight)
Calculation method : EN 13445-3 16.8
Material of saddle : SA516GR60
Pressure : P = 0.002 MPa
Horizontal (longitudinal) reaction : RaHL = 45.1 daN
Horizontal (cross) reaction : RaH = 0 daN
Maximum shear load : Qi = 109.1 daN
Distance a1 = 50 mm
Length L = 1,105 mm
Weight of saddle : Ws = 14.7 daN
Vertical Load : RaV = 137.1 daN
Reaction at support : Fi = 137.1 daN
Saddle
Pad
Shell
Yield Strength Leb
Width b1
Angle A
Allowable stress f2
Thickness e2
Width b2
Width a2
Angle 2A
Allowable stress f
All. Comp. Stress c,all
Modulus of elasticity E
Thickness ea
Mean radius R
Internal Diameter D
221 MPa
170 mm
120 °
 = A – 2.arctan (|RaH| / RaV) 120 °
b,all =K1K2f
1,2=
=
2.83a1
Di
−0.23K 6 K 8
K 5K 3
ea
Di
 PDi
2,2= 
 4ea
=
184.7 MPa
2 mm
200 mm
55 mm
145.31 °
2 = 2A – 2.arctan (|RaH| / RaV) 145.31 °
ea ≤ e2
a2 ≥ 0.1 D
0.91b1
K1=
Di ea
−
4M i  1
Di2 ea  K 2 f
F2,max = 0.7 b,all ,2 Di ea  ea (K 3 K 5 )
1,3 =
−0.53K 4
K 7 K 9 K 10 sin(0.5 )
2,3 =
1 −  22
(1 3 + 1 2 ) + (1 3 + 1 2 )2 + (1 −  22 )12
K2 = 1.25
 2.718282−  sin 

; 0.25 
K3= max



K 4=
1.15 − 0.0025
K5=
sin(0.5 )
1.45 − 0.007505
K 7=
sin(0.5 )
max(1.7 − 0.011667 ;0 )
K6=
sin(0.5 )


0 .8  + 6  

K8= min1.0 ;
0.017453 



PDi 1
2ea K 2 f
1
K10=
Feq = Fi  4 Di ea K 6 K 8

1.25
3
1.5
0.75  R ea E (ea R )
1.5 R L 1 + 42(R L ) (ea R )


Qmax = 
0.25  R ea E (ea R )1.5 1.5


Mmax =  4 D ea c,all
Fc,max = Dea c,all
K11 =
1 + 0.010472  3 Di ea b1 Di

Verification of load-carrying capacity with reinforcing plate [b2  K11Di+1.5b1 (K11= 0.0637) ]
Optimized Design 1 (b2 et 2 shall be replaced by b1 et  )
K3 = 0.25
K4 = 0.1735
 = 0.0184
 = 5.7472
K6 = 0.0049
K7 = 0.3766
K8 = 0.0862
K9 = 0.5873
K1,2 = 1.5
1,2 = -0.0005
2,2 = 0.0027
b,all,2 = 346.249 MPa
K1,3 = 0.4053
1,3 = -2.111
2,3 = 0.0012
b,all,3 = 93.547 MPa
Fi shall be  min( F2,max ; F3,max ) = 7,561.6 daN
Optimized Design 2 (ec shall be replaced by ea ) ( ec =
 = 0.0218
 = 4.1079
K6 = 0.3464
K7 = 0.6344
1,2 = -0.0386
2,2 = 0.0004
1,3 = -1.4726
2,3 = 0.0009
Fi shall be  min( F2,max ; F3,max ) = 10,644 daN

1 − 2.718282−  cos 

K 9= 1 −
F3,max = 0.9 b,all ,3 Di ea  ea (K 7 K 9 K10 )
2
184.7 MPa
65.2 MPa
200,000 MPa
2 mm
248 mm
494 mm
0.65
1 + (6 )
2
60

5
0.10472 3 Di ea
  L R  8.7 R e 
a


 L R  8.7 R ea 


K5 = 0.8242
K10 = 0.2063
F2,max = 7,561.6 daN
F3,max = 11,858.7 daN

ea2 + e22 min 1; (f2 f ) = 2.9 mm )
K3 = 0.25
K8 = 0.119
K1,2 = 1.4951
K1,3 = 0.543
2
K4 = 0.2457
K9 = 0.5481
b,all,2 = 345.11 MPa
b,all,3 = 125.343 MPa
Proof of stability
Feq = 60.7 daN
Pmax = +∞ MPa
Mmax = 2,557.58 daN∙m
Fc,max = 20,624.4 daN
|P|/Pmax + |Mi|/Mmax + Feq/Fc,max + (Qi/Qmax)2 = 0.0105 shall be  1.0 (for P > 0  P = 0)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
61
K5 = 0.9815
K10 = 0.2937
F2,max = 10,644 daN
F3,max = 11,943.5 daN
Qmax = 18,451.5 daN
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Saddle check
Stress due to horizontal reaction on the saddle
K = (1+ cos  – 0.5 sin² ) / ( –  + sin  cos ) =0.2035
 = 2.0944 rad
H = K Q = 279 N
Ab = 165.3 mm2
Sb = H / (2/3 Ab) = 2.53 MPa ≤ (90% Leb) (198.9 MPa)
Bending and compression stresses (See detail)
Hb = 449 mm
LEFF = 200 mm
Mzz = RaH . Hb
Mxx = RaHL . LEFF
| Mzz | = 0 daN∙m
| Mxx | = 9.02 daN∙m
Izz = 29.45401×106 mm4
Ixx = 2,429,753 mm4
Szz = Izz/v = 125,336.2 mm3
Sxx = Ixx/v = 21,888.34 mm3
Sbz = | Mzz | / Szz
Sbx = | Mxx | / Sxx
Sbz = 0 MPa ≤ (90% Leb) (198.9 MPa)
Sbx = 4.12 MPa ≤ (90% Leb) (198.9 MPa)
A = 1,480 mm2 fb = 147.33 MPa Sbc = RaV / A
Sbc = 0.93 MPa ≤ (0.8 fb ) (117.87 MPa)
max(Sbz ; Sbx ) / (90% Leb) + Sbc / (0.8 fb ) ≤ 1
Stability of web plate [CODAP C9.3.2.7] [AD S3/2 6.1.1]
hb2 = 324.5 mm
lb = 431.3 mm
eba = 2 mm
Eb = 203,050 MPa fb = 90% Leb = 198.9 MPa
x = hb2 / lb
Kb = 2.261
 b = fb 103 / Eb
 = 0.058
Qmax = lb eba fb  = 1,001.5 daN
Base Plate. Thickness check under compression (Dennis Moss, Fourth Edition)
K
EXW
R
Ww
l2
L
l1
ꙍ
E
Width
E = 160 mm
Length
B = 470 mm
Web thickness
K = 2 mm
Offset (Length)
EXV = 0 mm
Offset (Width)
EXW = 23 mm
Q+ = MAX( 0 ; Q+Ws) = 151.8 daN
Lw = B − 2∙EXV = 470 mm
Lr = n∙R = 270 mm
fu = Q+ / (Lw + Lr) = 0.21 daN/mm
Ww = 0.7∙min(K, L) = 1.4 mm
l1= EXW+K+Ww +Lmin = 27.79 mm
l2= E − l1 = 132.21 mm
ꙍ = fu / (l1 + 0.5 l2) = 0.0022 daN/mm2
Number of ribs
n= 2
Rib's length
R = 135 mm
Allowable Stress (90%Leb)
fb = 198.9 MPa
ꙍ∙l2 2
Lmin = √
fb
=1.39 mm ≤L=4 mm
Stresses in the bolts ( nb = 2 ; Sb = 225.2 mm2 ; xb = 200 mm )
Max. Tensile : bT = max{ 0 ; [ |Mzz| / (xb. nb/2) – (RaV + WS) /nb ] / Sb } = 0 MPa ≤ fbolt = 100 MPa
2
Max. Shear : bL = [√𝑅𝑎𝐻2 + 𝑅𝑎𝐻𝐿
]⁄(𝑆𝑏 ∙ 𝑛𝑏 ) = 1 MPa ≤ fbolt,shear = 100 MPa
fbolt,shear = fbolt / 1
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
62
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Case 5 - During test (Corroded inertias) (Corroded Weight)
Calculation method : EN 13445-3 16.8
Material of saddle : SA516GR60
Pressure : P = 1.003 MPa
Horizontal (longitudinal) reaction : RaHL = 0 daN
Horizontal (cross) reaction : RaH = 0 daN
Maximum shear load : Qi = 109.9 daN
Distance a1 = 50 mm
Length L = 1,105 mm
Weight of saddle : Ws = 14.7 daN
Vertical Load : RaV = 138 daN
Reaction at support : Fi = 138 daN
Saddle
Pad
Shell
Yield Strength Leb
Width b1
Angle A
Allowable stress f2
Thickness e2
Width b2
Width a2
Angle 2A
Allowable stress f
All. Comp. Stress c,all
Modulus of elasticity E
Thickness ea
Mean radius R
Internal Diameter D
221 MPa
170 mm
120 °
 = A – 2.arctan (|RaH| / RaV) 120 °
b,all =K1K2f
1,2=
=
2.83a1
Di
−0.23K 6 K 8
K 5K 3
ea
Di
 PDi
2,2= 
 4ea
=
260 MPa
2 mm
200 mm
55 mm
145.31 °
2 = 2A – 2.arctan (|RaH| / RaV) 145.31 °
ea ≤ e2
a2 ≥ 0.1 D
0.91b1
Di ea
−
4M i  1
Di2 ea  K 2 f
F2,max = 0.7 b,all ,2 Di ea  ea (K 3 K 5 )
1,3 =
−0.53K 4
K 7 K 9 K 10 sin(0.5 )
K1=
2,3 =
PDi 1
2ea K 2 f
1 −  22
(1 3 + 1 2 ) + (1 3 + 1 2 )2 + (1 −  22 )12
K2 = 1.05
 2.718282−  sin 

; 0.25 
K3= max



K 4=
1.15 − 0.0025
K5=
sin(0.5 )
1.45 − 0.007505
K 7=
sin(0.5 )
max(1.7 − 0.011667 ;0 )
K6=
sin(0.5 )


0 .8  + 6  

K8= min1.0 ;
0.017453 



1
K10=
Feq = Fi  4 Di ea K 6 K 8

1.25
3
1.5
0.75  R ea E (ea R )
1.5 R L 1 + 42(R L ) (ea R )


Qmax = 
0.25  R ea E (ea R )1.5 1.5


Mmax =  4 D ea c,all
Fc,max = Dea c,all
K11 =
1 + 0.010472  3 Di ea b1 Di

Verification of load-carrying capacity with reinforcing plate [b2  K11Di+1.5b1 (K11= 0.0637) ]
Optimized Design 1 (b2 et 2 shall be replaced by b1 et  )
K3 = 0.25
K4 = 0.1735
 = 0.0184
 = 5.7472
K6 = 0.0049
K7 = 0.3766
K8 = 0.0862
K9 = 0.5873
K1,2 = 1.4255
1,2 = -0.0005
2,2 = 0.2235
b,all,2 = 389.161 MPa
K1,3 = 0.5824
1,3 = -2.111
2,3 = 0.4472
b,all,3 = 158.984 MPa
Fi shall be  min( F2,max ; F3,max ) = 8,498.8 daN
Optimized Design 2 (ec shall be replaced by ea ) ( ec =

1 − 2.718282−  cos 

K 9= 1 −
F3,max = 0.9 b,all ,3 Di ea  ea (K 7 K 9 K10 )
2
260 MPa
90.3 MPa
200,000 MPa
2 mm
248 mm
494 mm
0.65
1 + (6 )
2
60

5
0.10472 3 Di ea
  L R  8.7 R e 
a


 L R  8.7 R ea 


K5 = 0.8242
K10 = 0.2063
F2,max = 8,498.8 daN
F3,max = 20,153.9 daN

ea2 + e22 min 1; (f2 f ) = 2.9 mm )
 = 0.0218
K3 = 0.25
 = 4.1079
K6 = 0.3464
K7 = 0.6344
K8 = 0.119
K1,2 = 1.4848
1,2 = -0.0386
2,2 = 0.1581
K1,3 = 0.7082
1,3 = -1.4726
2,3 = 0.3162
Fi shall be  min( F2,max ; F3,max ) = 12,501.9 daN
2
K4 = 0.2457
K9 = 0.5481
b,all,2 = 405.348 MPa
b,all,3 = 193.326 MPa
Proof of stability
Feq = 61.1 daN
Pmax = +∞ MPa
Mmax = 3,543.99 daN∙m
Fc,max = 28,578.8 daN
|P|/Pmax + |Mi|/Mmax + Feq/Fc,max + (Qi/Qmax)2 = 0.0024 shall be  1.0 (for P > 0  P = 0)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
63
K5 = 0.9815
K10 = 0.2937
F2,max = 12,501.9 daN
F3,max = 18,421.4 daN
Qmax = 18,451.5 daN
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Saddle check
Stress due to horizontal reaction on the saddle
K = (1+ cos  – 0.5 sin² ) / ( –  + sin  cos ) =0.2035
 = 2.0944 rad
H = K Q = 281 N
Ab = 165.3 mm2
Sb = H / (2/3 Ab) = 2.55 MPa ≤ (90% Leb) (198.9 MPa)
Bending and compression stresses (See detail)
Hb = 449 mm
LEFF = 200 mm
Mzz = RaH . Hb
Mxx = RaHL . LEFF
| Mzz | = 0 daN∙m
| Mxx | = 0 daN∙m
Izz = 29.45401×106 mm4
Ixx = 2,429,753 mm4
Szz = Izz/v = 125,336.2 mm3
Sxx = Ixx/v = 21,888.34 mm3
Sbz = | Mzz | / Szz
Sbx = | Mxx | / Sxx
Sbz = 0 MPa ≤ (90% Leb) (198.9 MPa)
Sbx = 0 MPa ≤ (90% Leb) (198.9 MPa)
A = 1,480 mm2 fb = 210.48 MPa Sbc = RaV / A
Sbc = 0.93 MPa ≤ (0.8 fb ) (168.38 MPa)
max(Sbz ; Sbx ) / (90% Leb) + Sbc / (0.8 fb ) ≤ 1
Stability of web plate [CODAP C9.3.2.7] [AD S3/2 6.1.1]
hb2 = 324.5 mm
lb = 431.3 mm
eba = 2 mm
Eb = 202,350 MPa fb = 90% Leb = 198.9 MPa
x = hb2 / lb
Kb = 2.261
 b = fb 103 / Eb
 = 0.058
Qmax = lb eba fb  = 998.1 daN
Base Plate. Thickness check under compression (Dennis Moss, Fourth Edition)
K
EXW
R
Ww
l2
L
l1
ꙍ
E
Width
E = 160 mm
Length
B = 470 mm
Web thickness
K = 2 mm
Offset (Length)
EXV = 0 mm
Offset (Width)
EXW = 23 mm
Q+ = MAX( 0 ; Q+Ws) = 152.7 daN
Lw = B − 2∙EXV = 470 mm
Lr = n∙R = 270 mm
fu = Q+ / (Lw + Lr) = 0.21 daN/mm
Ww = 0.7∙min(K, L) = 1.4 mm
l1= EXW+K+Ww +Lmin = 27.79 mm
l2= E − l1 = 132.21 mm
ꙍ = fu / (l1 + 0.5 l2) = 0.0022 daN/mm2
Number of ribs
n= 2
Rib's length
R = 135 mm
Allowable Stress (90%Leb)
fb = 198.9 MPa
ꙍ∙l2 2
Lmin = √
fb
=1.39 mm ≤L=4 mm
Stresses in the bolts ( nb = 2 ; Sb = 225.2 mm2 ; xb = 200 mm )
Max. Tensile : bT = max{ 0 ; [ |Mzz| / (xb. nb/2) – (RaV + WS) /nb ] / Sb } = 0 MPa ≤ fbolt = 170 MPa
2
Max. Shear : bL = [√𝑅𝑎𝐻2 + 𝑅𝑎𝐻𝐿
]⁄(𝑆𝑏 ∙ 𝑛𝑏 ) = 0 MPa ≤ fbolt,shear = 170 MPa
fbolt,shear = fbolt / 1
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
64
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Case 6 - During test P = 0. (Corroded inertias) (Corroded Weight)
Calculation method : EN 13445-3 16.8
Material of saddle : SA516GR60
Pressure : P = 0.002 MPa
Horizontal (longitudinal) reaction : RaHL = 0 daN
Horizontal (cross) reaction : RaH = 0 daN
Maximum shear load : Qi = 109.9 daN
Distance a1 = 50 mm
Length L = 1,105 mm
Weight of saddle : Ws = 14.7 daN
Vertical Load : RaV = 138 daN
Reaction at support : Fi = 138 daN
Saddle
Pad
Shell
Yield Strength Leb
Width b1
Angle A
Allowable stress f2
Thickness e2
Width b2
Width a2
Angle 2A
Allowable stress f
All. Comp. Stress c,all
Modulus of elasticity E
Thickness ea
Mean radius R
Internal Diameter D
221 MPa
170 mm
120 °
 = A – 2.arctan (|RaH| / RaV) 120 °
b,all =K1K2f
1,2=
=
2.83a1
Di
−0.23K 6 K 8
K 5K 3
ea
Di
 PDi
2,2= 
 4ea
=
260 MPa
2 mm
200 mm
55 mm
145.31 °
2 = 2A – 2.arctan (|RaH| / RaV) 145.31 °
ea ≤ e2
a2 ≥ 0.1 D
0.91b1
Di ea
−
4M i  1
Di2 ea  K 2 f
F2,max = 0.7 b,all ,2 Di ea  ea (K 3 K 5 )
1,3 =
−0.53K 4
K 7 K 9 K 10 sin(0.5 )
K1=
2,3 =
PDi 1
2ea K 2 f
1 −  22
(1 3 + 1 2 ) + (1 3 + 1 2 )2 + (1 −  22 )12
K2 = 1.05
 2.718282−  sin 

; 0.25 
K3= max



K 4=
1.15 − 0.0025
K5=
sin(0.5 )
1.45 − 0.007505
K 7=
sin(0.5 )
max(1.7 − 0.011667 ;0 )
K6=
sin(0.5 )


0 .8  + 6  

K8= min1.0 ;
0.017453 



1
K10=
Feq = Fi  4 Di ea K 6 K 8

1.25
3
1.5
0.75  R ea E (ea R )
1.5 R L 1 + 42(R L ) (ea R )


Qmax = 
0.25  R ea E (ea R )1.5 1.5


Mmax =  4 D ea c,all
Fc,max = Dea c,all
K11 =
1 + 0.010472  3 Di ea b1 Di

Verification of load-carrying capacity with reinforcing plate [b2  K11Di+1.5b1 (K11= 0.0637) ]
Optimized Design 1 (b2 et 2 shall be replaced by b1 et  )
K3 = 0.25
K4 = 0.1735
 = 0.0184
 = 5.7472
K6 = 0.0049
K7 = 0.3766
K8 = 0.0862
K9 = 0.5873
K1,2 = 1.5
1,2 = -0.0005
2,2 = 0.0005
b,all,2 = 409.5 MPa
K1,3 = 0.4052
1,3 = -2.111
2,3 = 0.0011
b,all,3 = 110.621 MPa
Fi shall be  min( F2,max ; F3,max ) = 8,942.9 daN
Optimized Design 2 (ec shall be replaced by ea ) ( ec =

1 − 2.718282−  cos 

K 9= 1 −
F3,max = 0.9 b,all ,3 Di ea  ea (K 7 K 9 K10 )
2
260 MPa
90.3 MPa
200,000 MPa
2 mm
248 mm
494 mm
0.65
1 + (6 )
2
60

5
0.10472 3 Di ea
  L R  8.7 R e 
a


 L R  8.7 R ea 


K5 = 0.8242
K10 = 0.2063
F2,max = 8,942.9 daN
F3,max = 14,023.1 daN

ea2 + e22 min 1; (f2 f ) = 2.9 mm )
 = 0.0218
K3 = 0.25
 = 4.1079
K6 = 0.3464
K7 = 0.6344
K8 = 0.119
K1,2 = 1.4951
1,2 = -0.0386
2,2 = 0.0003
K1,3 = 0.543
1,3 = -1.4726
2,3 = 0.0008
Fi shall be  min( F2,max ; F3,max ) = 12,588.3 daN
2
K4 = 0.2457
K9 = 0.5481
b,all,2 = 408.149 MPa
b,all,3 = 148.226 MPa
Proof of stability
Feq = 61.1 daN
Pmax = +∞ MPa
Mmax = 3,543.99 daN∙m
Fc,max = 28,578.8 daN
|P|/Pmax + |Mi|/Mmax + Feq/Fc,max + (Qi/Qmax)2 = 0.0024 shall be  1.0 (for P > 0  P = 0)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
65
K5 = 0.9815
K10 = 0.2937
F2,max = 12,588.3 daN
F3,max = 14,124 daN
Qmax = 18,451.5 daN
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Saddle check
Stress due to horizontal reaction on the saddle
K = (1+ cos  – 0.5 sin² ) / ( –  + sin  cos ) =0.2035
 = 2.0944 rad
H = K Q = 281 N
Ab = 165.3 mm2
Sb = H / (2/3 Ab) = 2.55 MPa ≤ (90% Leb) (198.9 MPa)
Bending and compression stresses (See detail)
Hb = 449 mm
LEFF = 200 mm
Mzz = RaH . Hb
Mxx = RaHL . LEFF
| Mzz | = 0 daN∙m
| Mxx | = 0 daN∙m
Izz = 29.45401×106 mm4
Ixx = 2,429,753 mm4
Szz = Izz/v = 125,336.2 mm3
Sxx = Ixx/v = 21,888.34 mm3
Sbz = | Mzz | / Szz
Sbx = | Mxx | / Sxx
Sbz = 0 MPa ≤ (90% Leb) (198.9 MPa)
Sbx = 0 MPa ≤ (90% Leb) (198.9 MPa)
A = 1,480 mm2 fb = 210.48 MPa Sbc = RaV / A
Sbc = 0.93 MPa ≤ (0.8 fb ) (168.38 MPa)
max(Sbz ; Sbx ) / (90% Leb) + Sbc / (0.8 fb ) ≤ 1
Stability of web plate [CODAP C9.3.2.7] [AD S3/2 6.1.1]
hb2 = 324.5 mm
lb = 431.3 mm
eba = 2 mm
Eb = 202,350 MPa fb = 90% Leb = 198.9 MPa
x = hb2 / lb
Kb = 2.261
 b = fb 103 / Eb
 = 0.058
Qmax = lb eba fb  = 998.1 daN
Base Plate. Thickness check under compression (Dennis Moss, Fourth Edition)
K
EXW
R
Ww
l2
L
l1
ꙍ
E
Width
E = 160 mm
Length
B = 470 mm
Web thickness
K = 2 mm
Offset (Length)
EXV = 0 mm
Offset (Width)
EXW = 23 mm
Q+ = MAX( 0 ; Q+Ws) = 152.7 daN
Lw = B − 2∙EXV = 470 mm
Lr = n∙R = 270 mm
fu = Q+ / (Lw + Lr) = 0.21 daN/mm
Ww = 0.7∙min(K, L) = 1.4 mm
l1= EXW+K+Ww +Lmin = 27.79 mm
l2= E − l1 = 132.21 mm
ꙍ = fu / (l1 + 0.5 l2) = 0.0022 daN/mm2
Number of ribs
n= 2
Rib's length
R = 135 mm
Allowable Stress (90%Leb)
fb = 198.9 MPa
ꙍ∙l2 2
Lmin = √
fb
=1.39 mm ≤L=4 mm
Stresses in the bolts ( nb = 2 ; Sb = 225.2 mm2 ; xb = 200 mm )
Max. Tensile : bT = max{ 0 ; [ |Mzz| / (xb. nb/2) – (RaV + WS) /nb ] / Sb } = 0 MPa ≤ fbolt = 170 MPa
2
Max. Shear : bL = [√𝑅𝑎𝐻2 + 𝑅𝑎𝐻𝐿
]⁄(𝑆𝑏 ∙ 𝑛𝑏 ) = 0 MPa ≤ fbolt,shear = 170 MPa
fbolt,shear = fbolt / 1
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
66
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Saddle No. 2
Case 1 - Lifting P = 0. (New Inertias) (New Weight)
Calculation method : EN 13445-3 16.8
Material of saddle : SA516GR60
Pressure : P = 0 MPa
Horizontal (longitudinal) reaction : RaHL = 0 daN
Horizontal (cross) reaction : RaH = 0 daN
Maximum shear load : Qi = 12.6 daN
Distance a1 = 55 mm
Length L = 1,105 mm
Weight of saddle : Ws = 14.7 daN
Vertical Load : RaV = 20.1 daN
Reaction at support : Fi = 20.1 daN
Saddle
Pad
Shell
Yield Strength Leb
Width b1
Angle A
Allowable stress f2
Thickness e2
Width b2
Width a2
Angle 2A
Allowable stress f
All. Comp. Stress c,all
Modulus of elasticity E
Thickness ea
Mean radius R
Internal Diameter D
221 MPa
170 mm
120 °
 = A – 2.arctan (|RaH| / RaV) 120 °
b,all =K1K2f
1,2=
=
2.83a1
Di
−0.23K 6 K 8
K 5K 3
ea
Di
 PDi
2,2= 
 4ea
=
260 MPa
2 mm
200 mm
55 mm
145.31 °
2 = 2A – 2.arctan (|RaH| / RaV) 145.31 °
ea ≤ e2
a2 ≥ 0.1 D
0.91b1
4M i  1
Di2 ea  K 2 f
F2,max = 0.7 b,all ,2 Di ea  ea (K 3 K 5 )
1,3 =
−0.53K 4
K 7 K 9 K 10 sin(0.5 )
1 −  22
K1=
(1 3 + 1 2 ) + (1 3 + 1 2 )2 + (1 −  22 )12
Di ea
−
 2.718282−  sin 

; 0.25 
K3= max



K5=
2,3 =
PDi 1
2ea K 2 f
1.15 − 0.0025
sin(0.5 )
K6=
K2 = 1.25
K 4=
max(1.7 − 0.011667 ;0 )
sin(0.5 )


0 .8  + 6  

K8= min1.0 ;
0.017453 



K 7=
1
K10=
Feq = Fi  4 Di ea K 6 K 8

1.25
3
1.5
0.75  R ea E (ea R )
1.5 R L 1 + 42(R L ) (ea R )


Qmax = 
0.25  R ea E (ea R )1.5 1.5


Fc,max = Dea c,all
1 + 0.010472 

1.45 − 0.007505
sin(0.5 )
K11 =
3
Di ea b1 Di

Verification of load-carrying capacity with reinforcing plate [b2  K11Di+1.5b1 (K11= 0.0637) ]
Optimized Design 1 (b2 et 2 shall be replaced by b1 et  )
K3 = 0.25
K4 = 0.1735
 = 0.0202
 = 5.7472
K6 = 0.0049
K7 = 0.3766
K8 = 0.0926
K9 = 0.5884
K1,2 = 1.5
1,2 = -0.0005
2,2 = 0
b,all,2 = 487.5 MPa
K1,3 = 0.4054
1,3 = -2.1073
2,3 = 0
b,all,3 = 131.748 MPa
Fi shall be  min( F2,max ; F3,max ) = 10,646.4 daN
Optimized Design 2 (ec shall be replaced by ea ) ( ec =
1 − 2.718282−  cos 
K 9= 1 −
F3,max = 0.9 b,all ,3 Di ea  ea (K 7 K 9 K10 )
Mmax =  4 D 2 ea c,all
260 MPa
90.3 MPa
200,000 MPa
2 mm
248 mm
494 mm

0.65
1 + (6 )
2
60

5
0.10472 3 Di ea
  L R  8.7 R e 
a


 L R  8.7 R ea 


K5 = 0.8242
K10 = 0.2063
F2,max = 10,646.4 daN
F3,max = 16,671.8 daN

ea2 + e22 min 1; (f2 f ) = 2.9 mm )
 = 0.024
K3 = 0.25
 = 4.1079
K6 = 0.3464
K7 = 0.6344
K8 = 0.128
K1,2 = 1.4942
1,2 = -0.0416
2,2 = 0
K1,3 = 0.5438
1,3 = -1.4683
2,3 = 0
Fi shall be  min( F2,max ; F3,max ) = 14,977.8 daN
2
K4 = 0.2457
K9 = 0.5497
b,all,2 = 485.622 MPa
b,all,3 = 176.728 MPa
Proof of stability
Feq = 9.6 daN
Pmax = +∞ MPa
Mmax = 3,543.99 daN∙m
Fc,max = 28,578.8 daN
|P|/Pmax + |Mi|/Mmax + Feq/Fc,max + (Qi/Qmax)2 = 0.0005 shall be  1.0 (for P > 0  P = 0)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
67
K5 = 0.9815
K10 = 0.2937
F2,max = 14,977.8 daN
F3,max = 16,791 daN
Qmax = 18,451.5 daN
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Saddle check
Stress due to horizontal reaction on the saddle
K = (1+ cos  – 0.5 sin² ) / ( –  + sin  cos ) =0.2035
 = 2.0944 rad
H = K Q = 41 N
Ab = 165.3 mm2
Sb = H / (2/3 Ab) = 0.37 MPa ≤ (90% Leb) (198.9 MPa)
Bending and compression stresses (See detail)
Hb = 449 mm
LEFF = 200 mm
Mzz = RaH . Hb
Mxx = RaHL . LEFF
| Mzz | = 0 daN∙m
| Mxx | = 0 daN∙m
Izz = 29.45401×106 mm4
Ixx = 2,429,753 mm4
Szz = Izz/v = 125,336.2 mm3
Sxx = Ixx/v = 21,888.34 mm3
Sbz = | Mzz | / Szz
Sbx = | Mxx | / Sxx
Sbz = 0 MPa ≤ (90% Leb) (198.9 MPa)
Sbx = 0 MPa ≤ (90% Leb) (198.9 MPa)
A = 1,480 mm2 fb = 210.48 MPa Sbc = RaV / A
Sbc = 0.14 MPa ≤ (0.8 fb ) (168.38 MPa)
max(Sbz ; Sbx ) / (90% Leb) + Sbc / (0.8 fb ) ≤ 1
Stability of web plate [CODAP C9.3.2.7] [AD S3/2 6.1.1]
hb2 = 324.5 mm
lb = 431.3 mm
eba = 2 mm
Eb = 202,350 MPa fb = 90% Leb = 198.9 MPa
x = hb2 / lb
Kb = 2.261
 b = fb 103 / Eb
 = 0.058
Qmax = lb eba fb  = 998.1 daN
Base Plate. Thickness check under compression (Dennis Moss, Fourth Edition)
K
EXW
R
Ww
l2
L
l1
ꙍ
E
Width
E = 160 mm
Length
B = 470 mm
Web thickness
K = 2 mm
Offset (Length)
EXV = 0 mm
Offset (Width)
EXW = 23 mm
Q+ = MAX( 0 ; Q+Ws) = 34.9 daN
Lw = B − 2∙EXV = 470 mm
Lr = n∙R = 270 mm
fu = Q+ / (Lw + Lr) = 0.05 daN/mm
Ww = 0.7∙min(K, L) = 1.4 mm
l1= EXW+K+Ww +Lmin = 27.07 mm
l2= E − l1 = 132.93 mm
ꙍ = fu / (l1 + 0.5 l2) = 0.0005 daN/mm2
Number of ribs
n= 2
Rib's length
R = 135 mm
Allowable Stress (90%Leb)
fb = 198.9 MPa
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
68
ꙍ∙l2 2
Lmin = √
fb
=0.67 mm ≤L=4 mm
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Case 2 - Erected P = 0. (New Inertias) (New Weight)
Calculation method : EN 13445-3 16.8
Material of saddle : SA516GR60
Pressure : P = 0 MPa
Horizontal (longitudinal) reaction : RaHL = 0 daN
Horizontal (cross) reaction : RaH = 0 daN
Maximum shear load : Qi = 12.6 daN
Distance a1 = 55 mm
Length L = 1,105 mm
Weight of saddle : Ws = 14.7 daN
Vertical Load : RaV = 20.1 daN
Reaction at support : Fi = 20.1 daN
Saddle
Pad
Shell
Yield Strength Leb
Width b1
Angle A
Allowable stress f2
Thickness e2
Width b2
Width a2
Angle 2A
Allowable stress f
All. Comp. Stress c,all
Modulus of elasticity E
Thickness ea
Mean radius R
Internal Diameter D
221 MPa
170 mm
120 °
 = A – 2.arctan (|RaH| / RaV) 120 °
b,all =K1K2f
1,2=
=
2.83a1
Di
−0.23K 6 K 8
K 5K 3
ea
Di
 PDi
2,2= 
 4ea
=
260 MPa
2 mm
200 mm
55 mm
145.31 °
2 = 2A – 2.arctan (|RaH| / RaV) 145.31 °
ea ≤ e2
a2 ≥ 0.1 D
0.91b1
Di ea
−
4M i  1
Di2 ea  K 2 f
F2,max = 0.7 b,all ,2 Di ea  ea (K 3 K 5 )
1,3 =
−0.53K 4
K 7 K 9 K 10 sin(0.5 )
K1=
2,3 =
PDi 1
2ea K 2 f
1 −  22
(1 3 + 1 2 ) + (1 3 + 1 2 )2 + (1 −  22 )12
K2 = 1.25
 2.718282−  sin 

; 0.25 
K3= max



K 4=
1.15 − 0.0025
K5=
sin(0.5 )
1.45 − 0.007505
K 7=
sin(0.5 )
max(1.7 − 0.011667 ;0 )
K6=
sin(0.5 )


0 .8  + 6  

K8= min1.0 ;
0.017453 



1
K10=
Feq = Fi  4 Di ea K 6 K 8

1.25
3
1.5
0.75  R ea E (ea R )
1.5 R L 1 + 42(R L ) (ea R )


Qmax = 
0.25  R ea E (ea R )1.5 1.5


Mmax =  4 D ea c,all
Fc,max = Dea c,all
K11 =
1 + 0.010472  3 Di ea b1 Di

Verification of load-carrying capacity with reinforcing plate [b2  K11Di+1.5b1 (K11= 0.0637) ]
Optimized Design 1 (b2 et 2 shall be replaced by b1 et  )
K3 = 0.25
K4 = 0.1735
 = 0.0202
 = 5.7472
K6 = 0.0049
K7 = 0.3766
K8 = 0.0926
K9 = 0.5884
K1,2 = 1.5
1,2 = -0.0005
2,2 = 0
b,all,2 = 487.5 MPa
K1,3 = 0.4054
1,3 = -2.1073
2,3 = 0
b,all,3 = 131.748 MPa
Fi shall be  min( F2,max ; F3,max ) = 10,646.4 daN
Optimized Design 2 (ec shall be replaced by ea ) ( ec =

1 − 2.718282−  cos 

K 9= 1 −
F3,max = 0.9 b,all ,3 Di ea  ea (K 7 K 9 K10 )
2
260 MPa
90.3 MPa
200,000 MPa
2 mm
248 mm
494 mm
0.65
1 + (6 )
2
60

5
0.10472 3 Di ea
  L R  8.7 R e 
a


 L R  8.7 R ea 


K5 = 0.8242
K10 = 0.2063
F2,max = 10,646.4 daN
F3,max = 16,671.8 daN

ea2 + e22 min 1; (f2 f ) = 2.9 mm )
 = 0.024
K3 = 0.25
 = 4.1079
K6 = 0.3464
K7 = 0.6344
K8 = 0.128
K1,2 = 1.4942
1,2 = -0.0416
2,2 = 0
K1,3 = 0.5438
1,3 = -1.4683
2,3 = 0
Fi shall be  min( F2,max ; F3,max ) = 14,977.8 daN
2
K4 = 0.2457
K9 = 0.5497
b,all,2 = 485.622 MPa
b,all,3 = 176.728 MPa
Proof of stability
Feq = 9.6 daN
Pmax = +∞ MPa
Mmax = 3,543.99 daN∙m
Fc,max = 28,578.8 daN
|P|/Pmax + |Mi|/Mmax + Feq/Fc,max + (Qi/Qmax)2 = 0.0005 shall be  1.0 (for P > 0  P = 0)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
69
K5 = 0.9815
K10 = 0.2937
F2,max = 14,977.8 daN
F3,max = 16,791 daN
Qmax = 18,451.5 daN
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Saddle check
Stress due to horizontal reaction on the saddle
K = (1+ cos  – 0.5 sin² ) / ( –  + sin  cos ) =0.2035
 = 2.0944 rad
H = K Q = 41 N
Ab = 165.3 mm2
Sb = H / (2/3 Ab) = 0.37 MPa ≤ (90% Leb) (198.9 MPa)
Bending and compression stresses (See detail)
Hb = 449 mm
LEFF = 200 mm
Mzz = RaH . Hb
Mxx = RaHL . LEFF
| Mzz | = 0 daN∙m
| Mxx | = 0 daN∙m
Izz = 29.45401×106 mm4
Ixx = 2,429,753 mm4
Szz = Izz/v = 125,336.2 mm3
Sxx = Ixx/v = 21,888.34 mm3
Sbz = | Mzz | / Szz
Sbx = | Mxx | / Sxx
Sbz = 0 MPa ≤ (90% Leb) (198.9 MPa)
Sbx = 0 MPa ≤ (90% Leb) (198.9 MPa)
A = 1,480 mm2 fb = 210.48 MPa Sbc = RaV / A
Sbc = 0.14 MPa ≤ (0.8 fb ) (168.38 MPa)
max(Sbz ; Sbx ) / (90% Leb) + Sbc / (0.8 fb ) ≤ 1
Stability of web plate [CODAP C9.3.2.7] [AD S3/2 6.1.1]
hb2 = 324.5 mm
lb = 431.3 mm
eba = 2 mm
Eb = 202,350 MPa fb = 90% Leb = 198.9 MPa
x = hb2 / lb
Kb = 2.261
 b = fb 103 / Eb
 = 0.058
Qmax = lb eba fb  = 998.1 daN
Base Plate. Thickness check under compression (Dennis Moss, Fourth Edition)
K
EXW
R
Ww
l2
L
l1
ꙍ
E
Width
E = 160 mm
Length
B = 470 mm
Web thickness
K = 2 mm
Offset (Length)
EXV = 0 mm
Offset (Width)
EXW = 23 mm
Q+ = MAX( 0 ; Q+Ws) = 34.9 daN
Lw = B − 2∙EXV = 470 mm
Lr = n∙R = 270 mm
fu = Q+ / (Lw + Lr) = 0.05 daN/mm
Ww = 0.7∙min(K, L) = 1.4 mm
l1= EXW+K+Ww +Lmin = 27.07 mm
l2= E − l1 = 132.93 mm
ꙍ = fu / (l1 + 0.5 l2) = 0.0005 daN/mm2
Number of ribs
n= 2
Rib's length
R = 135 mm
Allowable Stress (90%Leb)
fb = 198.9 MPa
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
70
ꙍ∙l2 2
Lmin = √
fb
=0.67 mm ≤L=4 mm
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Case 3 - Operation (Corroded inertias) (New Weight)
Calculation method : EN 13445-3 16.8
Material of saddle : SA516GR60
Pressure : P = 0.702 MPa
Horizontal (longitudinal) reaction : RaHL = -45.1 daN
Horizontal (cross) reaction : RaH = 0 daN
Maximum shear load : Qi = 109 daN
Distance a1 = 55 mm
Length L = 1,105 mm
Weight of saddle : Ws = 14.7 daN
Vertical Load : RaV = 135.6 daN
Reaction at support : Fi = 135.6 daN
Saddle
Pad
Shell
Yield Strength Leb
Width b1
Angle A
Allowable stress f2
Thickness e2
Width b2
Width a2
Angle 2A
Allowable stress f
All. Comp. Stress c,all
Modulus of elasticity E
Thickness ea
Mean radius R
Internal Diameter D
221 MPa
170 mm
120 °
 = A – 2.arctan (|RaH| / RaV) 120 °
b,all =K1K2f
1,2=
=
2.83a1
Di
−0.23K 6 K 8
K 5K 3
ea
Di
 PDi
2,2= 
 4ea
=
184.7 MPa
2 mm
200 mm
55 mm
145.31 °
2 = 2A – 2.arctan (|RaH| / RaV) 145.31 °
ea ≤ e2
a2 ≥ 0.1 D
0.91b1
Di ea
−
4M i  1
Di2 ea  K 2 f
F2,max = 0.7 b,all ,2 Di ea  ea (K 3 K 5 )
1,3 =
−0.53K 4
K 7 K 9 K 10 sin(0.5 )
K1=
2,3 =
PDi 1
2ea K 2 f
1 −  22
(1 3 + 1 2 ) + (1 3 + 1 2 )2 + (1 −  22 )12
K2 = 1.25
 2.718282−  sin 

; 0.25 
K3= max



K 4=
1.15 − 0.0025
K5=
sin(0.5 )
1.45 − 0.007505
K 7=
sin(0.5 )
max(1.7 − 0.011667 ;0 )
K6=
sin(0.5 )


0 .8  + 6  

K8= min1.0 ;
0.017453 



1
K10=
Feq = Fi  4 Di ea K 6 K 8

1.25
3
1.5
0.75  R ea E (ea R )
1.5 R L 1 + 42(R L ) (ea R )


Qmax = 
0.25  R ea E (ea R )1.5 1.5


Mmax =  4 D ea c,all
Fc,max = Dea c,all
K11 =
1 + 0.010472  3 Di ea b1 Di

Verification of load-carrying capacity with reinforcing plate [b2  K11Di+1.5b1 (K11= 0.0637) ]
Optimized Design 1 (b2 et 2 shall be replaced by b1 et  )
K3 = 0.25
K4 = 0.1735
 = 0.0202
 = 5.7472
K6 = 0.0049
K7 = 0.3766
K8 = 0.0926
K9 = 0.5884
K1,2 = 1.4478
1,2 = -0.0005
2,2 = 0.1872
b,all,2 = 334.21 MPa
K1,3 = 0.5528
1,3 = -2.1073
2,3 = 0.3702
b,all,3 = 127.597 MPa
Fi shall be  min( F2,max ; F3,max ) = 7,298.7 daN
Optimized Design 2 (ec shall be replaced by ea ) ( ec =

1 − 2.718282−  cos 

K 9= 1 −
F3,max = 0.9 b,all ,3 Di ea  ea (K 7 K 9 K10 )
2
184.7 MPa
65.2 MPa
200,000 MPa
2 mm
248 mm
494 mm
0.65
1 + (6 )
2
60

5
0.10472 3 Di ea
  L R  8.7 R e 
a


 L R  8.7 R ea 


K5 = 0.8242
K10 = 0.2063
F2,max = 7,298.7 daN
F3,max = 16,146.6 daN

ea2 + e22 min 1; (f2 f ) = 2.9 mm )
 = 0.024
K3 = 0.25
 = 4.1079
K6 = 0.3464
K7 = 0.6344
K8 = 0.128
K1,2 = 1.4926
1,2 = -0.0416
2,2 = 0.1324
K1,3 = 0.6814
1,3 = -1.4683
2,3 = 0.2618
Fi shall be  min( F2,max ; F3,max ) = 10,626.4 daN
2
K4 = 0.2457
K9 = 0.5497
b,all,2 = 344.537 MPa
b,all,3 = 157.291 MPa
Proof of stability
Feq = 64.5 daN
Pmax = +∞ MPa
Mmax = 2,557.58 daN∙m
Fc,max = 20,624.4 daN
|P|/Pmax + |Mi|/Mmax + Feq/Fc,max + (Qi/Qmax)2 = 0.0106 shall be  1.0 (for P > 0  P = 0)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
71
K5 = 0.9815
K10 = 0.2937
F2,max = 10,626.4 daN
F3,max = 14,944.2 daN
Qmax = 18,451.5 daN
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Saddle check
Stress due to horizontal reaction on the saddle
K = (1+ cos  – 0.5 sin² ) / ( –  + sin  cos ) =0.2035
 = 2.0944 rad
H = K Q = 276 N
Ab = 165.3 mm2
Sb = H / (2/3 Ab) = 2.5 MPa ≤ (90% Leb) (198.9 MPa)
Bending and compression stresses (See detail)
Hb = 449 mm
LEFF = 200 mm
Mzz = RaH . Hb
Mxx = RaHL . LEFF
| Mzz | = 0 daN∙m
| Mxx | = 9.02 daN∙m
Izz = 29.45401×106 mm4
Ixx = 2,429,753 mm4
Szz = Izz/v = 125,336.2 mm3
Sxx = Ixx/v = 21,888.34 mm3
Sbz = | Mzz | / Szz
Sbx = | Mxx | / Sxx
Sbz = 0 MPa ≤ (90% Leb) (198.9 MPa)
Sbx = 4.12 MPa ≤ (90% Leb) (198.9 MPa)
A = 1,480 mm2 fb = 147.33 MPa Sbc = RaV / A
Sbc = 0.92 MPa ≤ (0.8 fb ) (117.87 MPa)
max(Sbz ; Sbx ) / (90% Leb) + Sbc / (0.8 fb ) ≤ 1
Stability of web plate [CODAP C9.3.2.7] [AD S3/2 6.1.1]
hb2 = 324.5 mm
lb = 431.3 mm
eba = 2 mm
Eb = 203,050 MPa fb = 90% Leb = 198.9 MPa
x = hb2 / lb
Kb = 2.261
 b = fb 103 / Eb
 = 0.058
Qmax = lb eba fb  = 1,001.5 daN
Base Plate. Thickness check under compression (Dennis Moss, Fourth Edition)
K
EXW
R
Ww
l2
L
l1
ꙍ
E
Width
E = 160 mm
Length
B = 470 mm
Web thickness
K = 2 mm
Offset (Length)
EXV = 0 mm
Offset (Width)
EXW = 23 mm
Q+ = MAX( 0 ; Q+Ws) = 150.3 daN
Lw = B − 2∙EXV = 470 mm
Lr = n∙R = 270 mm
fu = Q+ / (Lw + Lr) = 0.2 daN/mm
Ww = 0.7∙min(K, L) = 1.4 mm
l1= EXW+K+Ww +Lmin = 27.78 mm
l2= E − l1 = 132.22 mm
ꙍ = fu / (l1 + 0.5 l2) = 0.0022 daN/mm2
Number of ribs
n= 2
Rib's length
R = 135 mm
Allowable Stress (90%Leb)
fb = 198.9 MPa
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
72
ꙍ∙l2 2
Lmin = √
fb
=1.38 mm ≤L=4 mm
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Case 4 - Shutdown P = 0. (Corroded inertias) (Corroded Weight)
Calculation method : EN 13445-3 16.8
Material of saddle : SA516GR60
Pressure : P = 0.002 MPa
Horizontal (longitudinal) reaction : RaHL = -45.1 daN
Horizontal (cross) reaction : RaH = 0 daN
Maximum shear load : Qi = 109 daN
Distance a1 = 55 mm
Length L = 1,105 mm
Weight of saddle : Ws = 14.7 daN
Vertical Load : RaV = 135.6 daN
Reaction at support : Fi = 135.6 daN
Saddle
Pad
Shell
Yield Strength Leb
Width b1
Angle A
Allowable stress f2
Thickness e2
Width b2
Width a2
Angle 2A
Allowable stress f
All. Comp. Stress c,all
Modulus of elasticity E
Thickness ea
Mean radius R
Internal Diameter D
221 MPa
170 mm
120 °
 = A – 2.arctan (|RaH| / RaV) 120 °
b,all =K1K2f
1,2=
=
2.83a1
Di
−0.23K 6 K 8
K 5K 3
ea
Di
 PDi
2,2= 
 4ea
=
184.7 MPa
2 mm
200 mm
55 mm
145.31 °
2 = 2A – 2.arctan (|RaH| / RaV) 145.31 °
ea ≤ e2
a2 ≥ 0.1 D
0.91b1
Di ea
−
4M i  1
Di2 ea  K 2 f
F2,max = 0.7 b,all ,2 Di ea  ea (K 3 K 5 )
1,3 =
−0.53K 4
K 7 K 9 K 10 sin(0.5 )
K1=
2,3 =
PDi 1
2ea K 2 f
1 −  22
(1 3 + 1 2 ) + (1 3 + 1 2 )2 + (1 −  22 )12
K2 = 1.25
 2.718282−  sin 

; 0.25 
K3= max



K 4=
1.15 − 0.0025
K5=
sin(0.5 )
1.45 − 0.007505
K 7=
sin(0.5 )
max(1.7 − 0.011667 ;0 )
K6=
sin(0.5 )


0 .8  + 6  

K8= min1.0 ;
0.017453 



1
K10=
Feq = Fi  4 Di ea K 6 K 8

1.25
3
1.5
0.75  R ea E (ea R )
1.5 R L 1 + 42(R L ) (ea R )


Qmax = 
0.25  R ea E (ea R )1.5 1.5


Mmax =  4 D ea c,all
Fc,max = Dea c,all
K11 =
1 + 0.010472  3 Di ea b1 Di

Verification of load-carrying capacity with reinforcing plate [b2  K11Di+1.5b1 (K11= 0.0637) ]
Optimized Design 1 (b2 et 2 shall be replaced by b1 et  )
K3 = 0.25
K4 = 0.1735
 = 0.0202
 = 5.7472
K6 = 0.0049
K7 = 0.3766
K8 = 0.0926
K9 = 0.5884
K1,2 = 1.5
1,2 = -0.0005
2,2 = 0.0027
b,all,2 = 346.249 MPa
K1,3 = 0.4059
1,3 = -2.1073
2,3 = 0.0012
b,all,3 = 93.686 MPa
Fi shall be  min( F2,max ; F3,max ) = 7,561.6 daN
Optimized Design 2 (ec shall be replaced by ea ) ( ec =

1 − 2.718282−  cos 

K 9= 1 −
F3,max = 0.9 b,all ,3 Di ea  ea (K 7 K 9 K10 )
2
184.7 MPa
65.2 MPa
200,000 MPa
2 mm
248 mm
494 mm
0.65
1 + (6 )
2
60

5
0.10472 3 Di ea
  L R  8.7 R e 
a


 L R  8.7 R ea 


K5 = 0.8242
K10 = 0.2063
F2,max = 7,561.6 daN
F3,max = 11,855.4 daN

ea2 + e22 min 1; (f2 f ) = 2.9 mm )
 = 0.024
K3 = 0.25
 = 4.1079
K6 = 0.3464
K7 = 0.6344
K8 = 0.128
K1,2 = 1.4943
1,2 = -0.0416
2,2 = 0.0003
K1,3 = 0.5442
1,3 = -1.4683
2,3 = 0.0009
Fi shall be  min( F2,max ; F3,max ) = 10,638.5 daN
2
K4 = 0.2457
K9 = 0.5497
b,all,2 = 344.93 MPa
b,all,3 = 125.627 MPa
Proof of stability
Feq = 64.5 daN
Pmax = +∞ MPa
Mmax = 2,557.58 daN∙m
Fc,max = 20,624.4 daN
|P|/Pmax + |Mi|/Mmax + Feq/Fc,max + (Qi/Qmax)2 = 0.0106 shall be  1.0 (for P > 0  P = 0)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
73
K5 = 0.9815
K10 = 0.2937
F2,max = 10,638.5 daN
F3,max = 11,935.8 daN
Qmax = 18,451.5 daN
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Saddle check
Stress due to horizontal reaction on the saddle
K = (1+ cos  – 0.5 sin² ) / ( –  + sin  cos ) =0.2035
 = 2.0944 rad
H = K Q = 276 N
Ab = 165.3 mm2
Sb = H / (2/3 Ab) = 2.5 MPa ≤ (90% Leb) (198.9 MPa)
Bending and compression stresses (See detail)
Hb = 449 mm
LEFF = 200 mm
Mzz = RaH . Hb
Mxx = RaHL . LEFF
| Mzz | = 0 daN∙m
| Mxx | = 9.02 daN∙m
Izz = 29.45401×106 mm4
Ixx = 2,429,753 mm4
Szz = Izz/v = 125,336.2 mm3
Sxx = Ixx/v = 21,888.34 mm3
Sbz = | Mzz | / Szz
Sbx = | Mxx | / Sxx
Sbz = 0 MPa ≤ (90% Leb) (198.9 MPa)
Sbx = 4.12 MPa ≤ (90% Leb) (198.9 MPa)
A = 1,480 mm2 fb = 147.33 MPa Sbc = RaV / A
Sbc = 0.92 MPa ≤ (0.8 fb ) (117.87 MPa)
max(Sbz ; Sbx ) / (90% Leb) + Sbc / (0.8 fb ) ≤ 1
Stability of web plate [CODAP C9.3.2.7] [AD S3/2 6.1.1]
hb2 = 324.5 mm
lb = 431.3 mm
eba = 2 mm
Eb = 203,050 MPa fb = 90% Leb = 198.9 MPa
x = hb2 / lb
Kb = 2.261
 b = fb 103 / Eb
 = 0.058
Qmax = lb eba fb  = 1,001.5 daN
Base Plate. Thickness check under compression (Dennis Moss, Fourth Edition)
K
EXW
R
Ww
l2
L
l1
ꙍ
E
Width
E = 160 mm
Length
B = 470 mm
Web thickness
K = 2 mm
Offset (Length)
EXV = 0 mm
Offset (Width)
EXW = 23 mm
Q+ = MAX( 0 ; Q+Ws) = 150.3 daN
Lw = B − 2∙EXV = 470 mm
Lr = n∙R = 270 mm
fu = Q+ / (Lw + Lr) = 0.2 daN/mm
Ww = 0.7∙min(K, L) = 1.4 mm
l1= EXW+K+Ww +Lmin = 27.78 mm
l2= E − l1 = 132.22 mm
ꙍ = fu / (l1 + 0.5 l2) = 0.0022 daN/mm2
Number of ribs
n= 2
Rib's length
R = 135 mm
Allowable Stress (90%Leb)
fb = 198.9 MPa
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
74
ꙍ∙l2 2
Lmin = √
fb
=1.38 mm ≤L=4 mm
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Case 5 - During test (Corroded inertias) (Corroded Weight)
Calculation method : EN 13445-3 16.8
Material of saddle : SA516GR60
Pressure : P = 1.003 MPa
Horizontal (longitudinal) reaction : RaHL = 0 daN
Horizontal (cross) reaction : RaH = 0 daN
Maximum shear load : Qi = 109.8 daN
Distance a1 = 55 mm
Length L = 1,105 mm
Weight of saddle : Ws = 14.7 daN
Vertical Load : RaV = 136.5 daN
Reaction at support : Fi = 136.5 daN
Saddle
Pad
Shell
Yield Strength Leb
Width b1
Angle A
Allowable stress f2
Thickness e2
Width b2
Width a2
Angle 2A
Allowable stress f
All. Comp. Stress c,all
Modulus of elasticity E
Thickness ea
Mean radius R
Internal Diameter D
221 MPa
170 mm
120 °
 = A – 2.arctan (|RaH| / RaV) 120 °
b,all =K1K2f
1,2=
=
2.83a1
Di
−0.23K 6 K 8
K 5K 3
ea
Di
 PDi
2,2= 
 4ea
=
260 MPa
2 mm
200 mm
55 mm
145.31 °
2 = 2A – 2.arctan (|RaH| / RaV) 145.31 °
ea ≤ e2
a2 ≥ 0.1 D
0.91b1
Di ea
−
4M i  1
Di2 ea  K 2 f
F2,max = 0.7 b,all ,2 Di ea  ea (K 3 K 5 )
1,3 =
−0.53K 4
K 7 K 9 K 10 sin(0.5 )
K1=
2,3 =
PDi 1
2ea K 2 f
1 −  22
(1 3 + 1 2 ) + (1 3 + 1 2 )2 + (1 −  22 )12
K2 = 1.05
 2.718282−  sin 

; 0.25 
K3= max



K 4=
1.15 − 0.0025
K5=
sin(0.5 )
1.45 − 0.007505
K 7=
sin(0.5 )
max(1.7 − 0.011667 ;0 )
K6=
sin(0.5 )


0 .8  + 6  

K8= min1.0 ;
0.017453 



1
K10=
Feq = Fi  4 Di ea K 6 K 8

1.25
3
1.5
0.75  R ea E (ea R )
1.5 R L 1 + 42(R L ) (ea R )


Qmax = 
0.25  R ea E (ea R )1.5 1.5


Mmax =  4 D ea c,all
Fc,max = Dea c,all
K11 =
1 + 0.010472  3 Di ea b1 Di

Verification of load-carrying capacity with reinforcing plate [b2  K11Di+1.5b1 (K11= 0.0637) ]
Optimized Design 1 (b2 et 2 shall be replaced by b1 et  )
K3 = 0.25
K4 = 0.1735
 = 0.0202
 = 5.7472
K6 = 0.0049
K7 = 0.3766
K8 = 0.0926
K9 = 0.5884
K1,2 = 1.4255
1,2 = -0.0005
2,2 = 0.2235
b,all,2 = 389.175 MPa
K1,3 = 0.5832
1,3 = -2.1073
2,3 = 0.4472
b,all,3 = 159.218 MPa
Fi shall be  min( F2,max ; F3,max ) = 8,499.1 daN
Optimized Design 2 (ec shall be replaced by ea ) ( ec =

1 − 2.718282−  cos 

K 9= 1 −
F3,max = 0.9 b,all ,3 Di ea  ea (K 7 K 9 K10 )
2
260 MPa
90.3 MPa
200,000 MPa
2 mm
248 mm
494 mm
0.65
1 + (6 )
2
60

5
0.10472 3 Di ea
  L R  8.7 R e 
a


 L R  8.7 R ea 


K5 = 0.8242
K10 = 0.2063
F2,max = 8,499.1 daN
F3,max = 20,147.9 daN

ea2 + e22 min 1; (f2 f ) = 2.9 mm )
 = 0.024
K3 = 0.25
 = 4.1079
K6 = 0.3464
K7 = 0.6344
K8 = 0.128
K1,2 = 1.4861
1,2 = -0.0416
2,2 = 0.158
K1,3 = 0.7097
1,3 = -1.4683
2,3 = 0.3162
Fi shall be  min( F2,max ; F3,max ) = 12,512.9 daN
2
K4 = 0.2457
K9 = 0.5497
b,all,2 = 405.704 MPa
b,all,3 = 193.755 MPa
Proof of stability
Feq = 65 daN
Pmax = +∞ MPa
Mmax = 3,543.99 daN∙m
Fc,max = 28,578.8 daN
|P|/Pmax + |Mi|/Mmax + Feq/Fc,max + (Qi/Qmax)2 = 0.0026 shall be  1.0 (for P > 0  P = 0)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
75
K5 = 0.9815
K10 = 0.2937
F2,max = 12,512.9 daN
F3,max = 18,408.6 daN
Qmax = 18,451.5 daN
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Saddle check
Stress due to horizontal reaction on the saddle
K = (1+ cos  – 0.5 sin² ) / ( –  + sin  cos ) =0.2035
 = 2.0944 rad
H = K Q = 278 N
Ab = 165.3 mm2
Sb = H / (2/3 Ab) = 2.52 MPa ≤ (90% Leb) (198.9 MPa)
Bending and compression stresses (See detail)
Hb = 449 mm
LEFF = 200 mm
Mzz = RaH . Hb
Mxx = RaHL . LEFF
| Mzz | = 0 daN∙m
| Mxx | = 0 daN∙m
Izz = 29.45401×106 mm4
Ixx = 2,429,753 mm4
Szz = Izz/v = 125,336.2 mm3
Sxx = Ixx/v = 21,888.34 mm3
Sbz = | Mzz | / Szz
Sbx = | Mxx | / Sxx
Sbz = 0 MPa ≤ (90% Leb) (198.9 MPa)
Sbx = 0 MPa ≤ (90% Leb) (198.9 MPa)
A = 1,480 mm2 fb = 210.48 MPa Sbc = RaV / A
Sbc = 0.92 MPa ≤ (0.8 fb ) (168.38 MPa)
max(Sbz ; Sbx ) / (90% Leb) + Sbc / (0.8 fb ) ≤ 1
Stability of web plate [CODAP C9.3.2.7] [AD S3/2 6.1.1]
hb2 = 324.5 mm
lb = 431.3 mm
eba = 2 mm
Eb = 202,350 MPa fb = 90% Leb = 198.9 MPa
x = hb2 / lb
Kb = 2.261
 b = fb 103 / Eb
 = 0.058
Qmax = lb eba fb  = 998.1 daN
Base Plate. Thickness check under compression (Dennis Moss, Fourth Edition)
K
EXW
R
Ww
l2
L
l1
ꙍ
E
Width
E = 160 mm
Length
B = 470 mm
Web thickness
K = 2 mm
Offset (Length)
EXV = 0 mm
Offset (Width)
EXW = 23 mm
Q+ = MAX( 0 ; Q+Ws) = 151.2 daN
Lw = B − 2∙EXV = 470 mm
Lr = n∙R = 270 mm
fu = Q+ / (Lw + Lr) = 0.2 daN/mm
Ww = 0.7∙min(K, L) = 1.4 mm
l1= EXW+K+Ww +Lmin = 27.78 mm
l2= E − l1 = 132.22 mm
ꙍ = fu / (l1 + 0.5 l2) = 0.0022 daN/mm2
Number of ribs
n= 2
Rib's length
R = 135 mm
Allowable Stress (90%Leb)
fb = 198.9 MPa
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
76
ꙍ∙l2 2
Lmin = √
fb
=1.38 mm ≤L=4 mm
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Case 6 - During test P = 0. (Corroded inertias) (Corroded Weight)
Calculation method : EN 13445-3 16.8
Material of saddle : SA516GR60
Pressure : P = 0.002 MPa
Horizontal (longitudinal) reaction : RaHL = 0 daN
Horizontal (cross) reaction : RaH = 0 daN
Maximum shear load : Qi = 109.8 daN
Distance a1 = 55 mm
Length L = 1,105 mm
Weight of saddle : Ws = 14.7 daN
Vertical Load : RaV = 136.5 daN
Reaction at support : Fi = 136.5 daN
Saddle
Pad
Shell
Yield Strength Leb
Width b1
Angle A
Allowable stress f2
Thickness e2
Width b2
Width a2
Angle 2A
Allowable stress f
All. Comp. Stress c,all
Modulus of elasticity E
Thickness ea
Mean radius R
Internal Diameter D
221 MPa
170 mm
120 °
 = A – 2.arctan (|RaH| / RaV) 120 °
b,all =K1K2f
1,2=
=
2.83a1
Di
−0.23K 6 K 8
K 5K 3
ea
Di
 PDi
2,2= 
 4ea
=
260 MPa
2 mm
200 mm
55 mm
145.31 °
2 = 2A – 2.arctan (|RaH| / RaV) 145.31 °
ea ≤ e2
a2 ≥ 0.1 D
0.91b1
Di ea
−
4M i  1
Di2 ea  K 2 f
F2,max = 0.7 b,all ,2 Di ea  ea (K 3 K 5 )
1,3 =
−0.53K 4
K 7 K 9 K 10 sin(0.5 )
K1=
2,3 =
PDi 1
2ea K 2 f
1 −  22
(1 3 + 1 2 ) + (1 3 + 1 2 )2 + (1 −  22 )12
K2 = 1.05
 2.718282−  sin 

; 0.25 
K3= max



K 4=
1.15 − 0.0025
K5=
sin(0.5 )
1.45 − 0.007505
K 7=
sin(0.5 )
max(1.7 − 0.011667 ;0 )
K6=
sin(0.5 )


0 .8  + 6  

K8= min1.0 ;
0.017453 



1
K10=
Feq = Fi  4 Di ea K 6 K 8

1.25
3
1.5
0.75  R ea E (ea R )
1.5 R L 1 + 42(R L ) (ea R )


Qmax = 
0.25  R ea E (ea R )1.5 1.5


Mmax =  4 D ea c,all
Fc,max = Dea c,all
K11 =
1 + 0.010472  3 Di ea b1 Di

Verification of load-carrying capacity with reinforcing plate [b2  K11Di+1.5b1 (K11= 0.0637) ]
Optimized Design 1 (b2 et 2 shall be replaced by b1 et  )
K3 = 0.25
K4 = 0.1735
 = 0.0202
 = 5.7472
K6 = 0.0049
K7 = 0.3766
K8 = 0.0926
K9 = 0.5884
K1,2 = 1.5
1,2 = -0.0005
2,2 = 0.0004
b,all,2 = 409.5 MPa
K1,3 = 0.4058
1,3 = -2.1073
2,3 = 0.0011
b,all,3 = 110.786 MPa
Fi shall be  min( F2,max ; F3,max ) = 8,942.9 daN
Optimized Design 2 (ec shall be replaced by ea ) ( ec =

1 − 2.718282−  cos 

K 9= 1 −
F3,max = 0.9 b,all ,3 Di ea  ea (K 7 K 9 K10 )
2
260 MPa
90.3 MPa
200,000 MPa
2 mm
248 mm
494 mm
0.65
1 + (6 )
2
60

5
0.10472 3 Di ea
  L R  8.7 R e 
a


 L R  8.7 R ea 


K5 = 0.8242
K10 = 0.2063
F2,max = 8,942.9 daN
F3,max = 14,019.3 daN

ea2 + e22 min 1; (f2 f ) = 2.9 mm )
 = 0.024
K3 = 0.25
 = 4.1079
K6 = 0.3464
K7 = 0.6344
K8 = 0.128
K1,2 = 1.4943
1,2 = -0.0416
2,2 = 0.0003
K1,3 = 0.5442
1,3 = -1.4683
2,3 = 0.0008
Fi shall be  min( F2,max ; F3,max ) = 12,581.8 daN
2
K4 = 0.2457
K9 = 0.5497
b,all,2 = 407.936 MPa
b,all,3 = 148.562 MPa
Proof of stability
Feq = 65 daN
Pmax = +∞ MPa
Mmax = 3,543.99 daN∙m
Fc,max = 28,578.8 daN
|P|/Pmax + |Mi|/Mmax + Feq/Fc,max + (Qi/Qmax)2 = 0.0026 shall be  1.0 (for P > 0  P = 0)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
77
K5 = 0.9815
K10 = 0.2937
F2,max = 12,581.8 daN
F3,max = 14,114.9 daN
Qmax = 18,451.5 daN
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Saddle check
Stress due to horizontal reaction on the saddle
K = (1+ cos  – 0.5 sin² ) / ( –  + sin  cos ) =0.2035
 = 2.0944 rad
H = K Q = 278 N
Ab = 165.3 mm2
Sb = H / (2/3 Ab) = 2.52 MPa ≤ (90% Leb) (198.9 MPa)
Bending and compression stresses (See detail)
Hb = 449 mm
LEFF = 200 mm
Mzz = RaH . Hb
Mxx = RaHL . LEFF
| Mzz | = 0 daN∙m
| Mxx | = 0 daN∙m
Izz = 29.45401×106 mm4
Ixx = 2,429,753 mm4
Szz = Izz/v = 125,336.2 mm3
Sxx = Ixx/v = 21,888.34 mm3
Sbz = | Mzz | / Szz
Sbx = | Mxx | / Sxx
Sbz = 0 MPa ≤ (90% Leb) (198.9 MPa)
Sbx = 0 MPa ≤ (90% Leb) (198.9 MPa)
A = 1,480 mm2 fb = 210.48 MPa Sbc = RaV / A
Sbc = 0.92 MPa ≤ (0.8 fb ) (168.38 MPa)
max(Sbz ; Sbx ) / (90% Leb) + Sbc / (0.8 fb ) ≤ 1
Stability of web plate [CODAP C9.3.2.7] [AD S3/2 6.1.1]
hb2 = 324.5 mm
lb = 431.3 mm
eba = 2 mm
Eb = 202,350 MPa fb = 90% Leb = 198.9 MPa
x = hb2 / lb
Kb = 2.261
 b = fb 103 / Eb
 = 0.058
Qmax = lb eba fb  = 998.1 daN
Base Plate. Thickness check under compression (Dennis Moss, Fourth Edition)
K
EXW
R
Ww
l2
L
l1
ꙍ
E
Width
E = 160 mm
Length
B = 470 mm
Web thickness
K = 2 mm
Offset (Length)
EXV = 0 mm
Offset (Width)
EXW = 23 mm
Q+ = MAX( 0 ; Q+Ws) = 151.2 daN
Lw = B − 2∙EXV = 470 mm
Lr = n∙R = 270 mm
fu = Q+ / (Lw + Lr) = 0.2 daN/mm
Ww = 0.7∙min(K, L) = 1.4 mm
l1= EXW+K+Ww +Lmin = 27.78 mm
l2= E − l1 = 132.22 mm
ꙍ = fu / (l1 + 0.5 l2) = 0.0022 daN/mm2
Number of ribs
n= 2
Rib's length
R = 135 mm
Allowable Stress (90%Leb)
fb = 198.9 MPa
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
78
ꙍ∙l2 2
Lmin = √
fb
=1.38 mm ≤L=4 mm
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Circular stresses.
Type
Tag
01[04]
30.10
02[01]
31.05
03[04]
30.11
Diameter
Internal
(mm)
494.0
494.0
494.0
Length
(mm)
116.0
1,070.0
116.0
Thickness
(mm)
3.090
2.030
3.110
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
Operating
(MPa)
97.34
101.29
96.57
79
Horizontal test
Vertical test
(MPa)
(MPa)
138.93
122.89
137.83
/
/
/
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
Design Calculations
RESERVOIR_VESSEL_233L
2024-06-20
Revision : 23-08-24
Nozzle Flexibility.
The following flexibilities, computed per BS/PD 5500 Annex G, should be used in "beam-type" analysis of piping and
should be inserted at the surface of the branch/header or nozzle-vessel junction..
Nozzle
Tag
N1
N2
N3
N4
N5
Location
(mm)
552.0
797.0
-100.0
55.0
1,050.0
Level of stiffening line (*)
Axial Translational
low
top
(mm)
(mm)
(mm/daN)
0.0
1,105.0
7.924×10-3
0.0
1,105.0
7.045×10-3
/
/
23.282×10-6
0.0
1,105.0
6.357×10-3
0.0
1,105.0
6.357×10-3
Rotation
(longitudinal)
(rad/daN∙m)
8.121643×10-3
5.389634×10-3
7.853512×10-6
4.004641×10-3
4.004641×10-3
Rotation
(circular)
(rad/daN∙m)
8.791344×10-3
5.94606×10-3
7.853512×10-6
4.516085×10-3
4.516085×10-3
(*) the stiffening line may be a tangent line (head or skirt or cone) , a stiffener, a flange or the nearest Tubesheet.
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
80
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Summary
[01]
[04]
Shell
Kloepper Type Head
Summary of nozzles
Tag
Summary of nozzles [ Location and Dimensions ].
Location
Ori.
Inc.
(°)
(°)
Loc.
(mm)
Exc.
(mm)
Dimensions (mm)
Neck
Reinforcement
DN
Thk.
Sch.
Type
(a)
(b)
Diam.
Flange
Projectio
DN
n
Rating Typ.
37.00
36.00
21.00
15.00
15.00
/
/
/
/
/
N1
552.0
0.00
0.00
0.00
70.00
2.000
/
/
/
/
N2
797.0
0.00
0.00
0.00
79.00
12.000
/
/
/
/
N3
-100.0
0.00
0.00
0.00
155.00
27.000
/
/
/
/
N4
55.0 180.00
0.00
0.00
85.00
2.000
/
/
/
/
N5
1,050.0 180.00
0.00
0.00
85.00
2.000
/
/
/
/
(a),(b) : Pad (ring) = thickness, Width ; Self Reinforcing = Height, over thickness ; Internal Plate = thickness, Height
NB :
/
/
/
/
/
/
/
/
/
/
The external projection and the overthickness height of a self are measured along the axis of the nozzle.
Operati
ng
N1
N2
N3
N4
N5
Set-in (+)
Set-on(-)
Tag
Summary of nozzles [ Adjacent Openings, Goose and Material ].
(+)
(+)
(+)
(+)
(+)
A
A
A
A
A
Nozzle Type
Goose
Adjacent openings
Material
hydrostatic height
Radius
Loc.
Operating
Test
(mm)
(mm)
(mm)
(mm)
Neck
Pad
Flange
None
/
/
0.00
0.0
X5CrNi18-10
/
None
/
/
0.00
0.0
X5CrNi18-10
/
None
/
/
233.00
247.0
X5CrNi18-10
/
None
/
/
480.00
494.0
X5CrNi18-10
/
None
/
/
480.00
494.0
X5CrNi18-10
/
A = Process, H = manhole, E = With Blind Flange, L = Instrument, AP = Boot, XT = transition by head,
CA = Shell Inlet, CS = Shell Outlet, TA = Tube side inlet, TS = Tube side Outlet.
/
/
/
/
/
Summary of nozzles [ Type, Weight and Local Loads ].
Shell
Operating
Tag
Loc.
No.
Mass
Piping
Nozzle
+
Flange
(kg)
Thk.
+
Ext. Dia. Loads
(mm)
Local Loads
N1 02[01]
A
0.1
0.0
/
/
N2 02[01]
A
0.8
0.0
/
/
N3 01[04]
A
2.6
0.0
/
/
N4 02[01]
A
0.1
0.0
/
/
N5 02[01]
A
0.1
0.0
/
/
S
T
O
S
T
O
S
T
O
S
T
O
S
T
O
Longitudinal Circumferential
Shear Load
Shear Load
(daN)
(daN)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
Longitudinal
Bending
Moment
(daN∙m)
Radial Load
(daN)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
81
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Circular
Bending
Moment
(daN∙m)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Torsional
moment
(daN∙m)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Shell
No.
Nozzle Type
Flange Weight
Loads
Operating
Tag
Loc.
Mass
Piping
Nozzle
+
Flange
(kg)
Thk.
+
Ext. Dia. Loads
(mm)
Local Loads
Longitudinal Circumferential
Shear Load
Shear Load
(daN)
(daN)
Radial Load
(daN)
Longitudinal
Bending
Moment
(daN∙m)
Circular
Bending
Moment
(daN∙m)
Torsional
moment
(daN∙m)
A = Process, H = manhole, E = With Blind Flange, L = Instrument, AP = Boot, XT = transition by head,
CA = Shell Inlet, CS = Shell Outlet, TA = Tube side inlet, TS = Tube side Outlet.
With blind flange if present.
S = Sustained, T = Thermal, O = Occasional
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Design Calculations
RESERVOIR_VESSEL_233L
Summary of Geometry
Type
Tag
Diameter
Internal
(mm)
Length
(mm)
Cumulative
Thickness Angle
height
(mm)
(mm)
(°)
Mass
(kg)
Flanges
ratings
Specifi
c
Gravity
Material
01[04]
30.10
494.0
116.0
17.5
3.090
0
6.7
7.90
X5CrNi18-10
02[01]
31.05
494.0
1,070.0
1,087.5
2.030
0
26.7
7.90
X5CrNi18-10
03[04]
30.11
494.0
116.0
1,087.5
3.110
0
6.7
7.90
X5CrNi18-10
Angle : half angle at apex for a concentric cone ; maximum angle between cone and cylinder for an eccentric cone.
Material: (N) = normalized
NB: Italic line indicates an element for which the calculation under pressure has not been done.
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Design Calculations
RESERVOIR_VESSEL_233L
Summary of Weights, Capacities and Painting Areas
Lifted
Shells
Heads
Support saddles
Nozzles
Mass (kg)
27
13
30
4
Total mass
N.B. : New weight
74 kg
Erected
Shells
Heads
Support saddles
Nozzles
Mass (kg)
27
13
30
4
Total mass
N.B. : New weight
74 kg
Operating
Shells
Heads
Support saddles
Nozzles
Liquid (Compartment 1)
Mass (kg)
27
13
30
4
234
Total mass
N.B. : New weight
308 kg
Shutdown
Shells
Heads
Support saddles
Nozzles
Liquid (Compartment 1)
Mass (kg)
27
13
30
4
234
Total mass
N.B. : New weight
308 kg
Test
Shells
Heads
Support saddles
Nozzles
Liquid (Compartment 1)
Mass (kg)
27
13
30
4
236
Total mass (Compartment 1)
N.B. : New weight
310 kg
Capacity (m3)
Compartment 1
0.236
Area (m2)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
Vessel = 2.2
84
/
/
/
/
Support = 1.2
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2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Summary of Foundation Loads
RaV :
RaHT :
RaHL :
AmT :
AmL :
Vertical reaction in daN
Horizontal (cross) reaction in daN
Horizontal (longitudinal) reaction in daN (*)
Circumferential bending moment in daN∙m
Longitudinal bending moment in daN∙m
Stacked vessels: loads for the combined stack.
(++)
(+−)
(−+)
(−−)
(+)
(−)
seismic load
vertical downside and horizontal longitudinal to the right
vertical downside and horizontal longitudinal to the left
vertical upside and horizontal longitudinal to the right
vertical upside and horizontal longitudinal to the left
vertical downside and horizontal cross
vertical upside and horizontal cross
(*) The horizontal longitudinal force due to friction is a function of the weight on the sliding saddle multiplied by the coefficient of friction, the
additional vertical loads due to the earthquake are not considered.
Design case
1 - Lifting P = 0. (New Inertias) (New Weight)
2 - Erected P = 0. (New Inertias) (New Weight)
3 - Operation (Corroded inertias) (New Weight)
4 - Shutdown P = 0. (Corroded inertias) (Corroded Weight)
5 - During test (Corroded inertias) (Corroded Weight)
6 - During test P = 0. (Corroded inertias) (Corroded Weight)
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
Support
No.
1
2
1
2
1
2
1
2
1
2
1
2
85
RaV
(daN)
38
35
38
35
152
150
152
150
153
151
153
151
RaHT
(daN)
0
0
0
0
0
0
0
0
0
0
0
0
RaHL
(daN)
0
0
0
0
45
-45
45
-45
0
0
0
0
AmT
(daN∙m)
0
0
0
0
0
0
0
0
0
0
0
0
AmL
(daN∙m)
0
0
0
0
0
0
0
0
0
0
0
0
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
2024-06-20
Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Summary of Changes
Item Tag
1
2
Description
Saddle
Saddle
Component Properties
Wear Plate - Thickness
Wear Plate - Thickness
Input(*)
10 mm
10 mm
Output
2.03 mm
2.03 mm
(*) Default initial value or input value specified by user.
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Design Calculations
RESERVOIR_VESSEL_233L
Fatigue Analysis
EN 13445:2021 (2021-05) – 17 – Fatigue Analysis
Compartment : 1
Life duration : 20 year(s)
Type of cycle
1
List of elementary cycles grouped by type
No. of cycles
characteristic of cycles
By period
Total
Pmax (MPa)
Pmin (MPa)
P (MPa)
1
7300
0.5
0.5
0
Tag
Compartment
Shell type
W8
1
02 [01] 31.05
W1
1
01 [04] 30.10
02 [01] 31.05
W2
1
03 [04] 30.11
02 [01] 31.05
W3
1
N1
02 [01] 31.05
W4
1
N2
02 [01] 31.05
W5
1
N3
01 [04] 30.10
W6
1
N4
02 [01] 31.05
W7
1
N5
02 [01] 31.05
(*) The assembly is verified by considering the height of the throat to be ≥ 0.8es.
Figure : 1.1
W8
Type
1
W1
Type
1
f = 184.67 MPa
Pmax = 1.28 MPa


1
2
3
4
0
/
Ce
1
/
0
0.5
/
1.275
0
Ct
1
 (MPa)
91.63
 (MPa)
91.63
D (MPa)
52.3
cut (MPa)
28.7
0
N
9.3041×105
u
0.015
n i / Ni
0.0078
 ni/Ni = 0.0078
Figure : 1.2
Class : 80
De = 0 mm
z = 0.85
en = 2.03 mm
z = 0.85
eu = 2.03 mm
(*)
(*)
(*)
(*)
(*)
4 (mm)
en = 2.03 mm
eu = 2.03 mm
f = 184.67 MPa
Pmax = 1.34 MPa
u
/
n i / Ni
0.0027
 ni/Ni = 0.0027
 (mm)
4 (mm)


1
2
3
4
0.53
/
Ct
1
/
Ce
1
0.1
0.1305
 (MPa)
72.24
/
/
D (MPa)
58.9
cut (MPa)
32.4
/
N
2.7168×106

1.046
Figure : 1.2
W2
De = 498.06 mm
Assembly type
butt welded - shells
butt welded - shells
butt welded - shells
opening
opening
opening
opening
opening
 (mm)

Class : 71
Fig.
1.1
1.2
1.2
3
3
3
3
3
tmoy (°C)
17.5
f = 184.67 MPa
Pmax = 1.35 MPa
 (mm)
4 (mm)


1
2
3
4
0.54
/
Ct
1
/
Ce
1
0.1
0.133
/
/
 (MPa)
71.81
 (MPa)
71.81
D (MPa)
58.9
cut (MPa)
32.4
/
N
2.7655×106
u
/
n i / Ni
0.0026
 ni/Ni = 0.0026
Class : 63
De = 498.06 mm

Class : 80
 (MPa)
72.24
De = 0 mm
z = 0.85
en = 2.03 mm
eu = 2.03 mm
Type
1
1.0481
f = 184.67 MPa
Pmax = 1.04 MPa
W3
 (mm)
4 (mm)


1
2
3
4
/
/
Ct
1
/
Ce
1
/
/
/
/
 (MPa)
265.91
 (MPa)
265.91
D (MPa)
46.4
cut (MPa)
25.5
/
N
26,599
u
/
n i / Ni
0.2744
 ni/Ni = 0.2744
Class : 63
De = 498.06 mm
Figure : 3
z = 0.85
en = 2 mm
eu = 2 mm
Type
1

f = 184.67 MPa
Pmax = 4.29 MPa
W4
 (mm)
4 (mm)


1
2
3
4
/
/
Ct
1
/
Ce
1
/
/
/
/
 (MPa)
64.57
 (MPa)
64.57
D (MPa)
46.4
cut (MPa)
25.5
/
N
1.8574×106
u
/
n i / Ni
0.0039
 ni/Ni = 0.0039
3
Figure : 3
Type
1

3
z = 0.85
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
en = 2.03 mm
87
eu = 2.03 mm
prodia2 43.01.01.011 2023-01-19 Bentley Systems, Inc.
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Revision : 23-08-24
Design Calculations
RESERVOIR_VESSEL_233L
Figure : 3
W5
f = 184.67 MPa
Pmax = 4.35 MPa
 (mm)
4 (mm)
Class : 63
De = 500.18 mm


z = 0.85
1
en = 3.09 mm
2
eu = 3.09 mm
3
4
/
/
Ct
1
/
Ce
1
/
/
/
/
 (MPa)
63.71
 (MPa)
63.71
D (MPa)
46.4
cut (MPa)
25.5
/
N
1.9341×106
u
/
n i / Ni
0.0038
 ni/Ni = 0.0038
Class : 63
De = 498.06 mm
Type
1

f = 184.67 MPa
Pmax = 0.77 MPa
W6
 (mm)
4 (mm)


1
2
3
4
/
/
Ct
1
/
Ce
1
/
/
/
/
 (MPa)
360.25
 (MPa)
360.25
D (MPa)
46.4
cut (MPa)
25.5
/
N
10,696
u
/
n i / Ni
0.6825
 ni/Ni = 0.6825
Class : 63
De = 498.06 mm
3
Figure : 3
z = 0.85
en = 2 mm
eu = 2 mm
Type
1

f = 184.67 MPa
Pmax = 0.77 MPa
W7
 (mm)
4 (mm)


1
2
3
4
/
/
Ct
1
/
Ce
1
/
/
/
/
 (MPa)
360.25
 (MPa)
360.25
D (MPa)
46.4
cut (MPa)
25.5
/
N
10,696
u
/
n i / Ni
0.6825
 ni/Ni = 0.6825
3
Figure : 3
Type
1

3
z = 0.85
AutoPipeVessel CONNECT Edition procal 43.01.01.011 2023-01-19
en = 2 mm
88
eu = 2 mm
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Design Calculations
RESERVOIR_VESSEL_233L
2024-06-20
Revision : 23-08-24
List of customisable files.
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Design Calculations
RESERVOIR_VESSEL_233L
2024-06-20
Revision : 23-08-24
Summary of Errors and Warnings.
No.
Explanation
( the number is used for technical support)
Error (s) :
/
Warning (s) :
1011
Allowable compressive stress [EN 13445-3 16.14.8] : Using fabrication tolerance quality class C and taking
factor ψ = 0.75 is a conservative assumption for vessels that satisfy the manufacturing tolerance requirements of
EN 13445-4, Clause 6.
Total: 0 error(s) and 1 warning(s).
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