IDM UID
7HL9UC
VERSION CREATED ON / VERSION / STATUS
30 Nov 2022 / 1.3 / Signed
EXTERNAL REFERENCE / VERSION
Report
EJMA Calculation Report for Cryostat DNB Port Duct
Bellows
EJMA Calculation Report for Cryostat DNB Port Duct Bellows in phase1# of IO supply
contract ITER/CT/21/4300002477
Author
Co-Authors
Reviewers
Approver
Read Access
Name
Du S.
Approval Process
Action
30 Nov 2022:signed
Affiliation
IO/DG/CNST/MCD/EVDA/ICCA
Pandey M. K.
Seropian C.
Vertongen P.
Xie H.
Gupta G. K.
IO/DG/CNST/MCD/EVDA/ICCA
IO/DG/SQD/NS
IO/DG/SQD/QMD
30 Nov 2022:recommended
IO/DG/CNST/MCD/EVDA/ICCA
IO/DG/CNST/MCD/EVDA/ICCA
Document Security: Internal Use
RO: Xie Han
LG: Bellows Task Force, LG: cryostat/building interface, LG: Cryostat IO team, AD: IO_Director-General,
AD: OBS - Configuration Management Division (CMD) - EXT, AD: OBS - Configuration Management
Division (CMD), AD: External Management Advisory Board, AD: OBS - VVPS Systems and Auxiliary
Functions S...
PDF generated on 30 Nov 2022
DISCLAIMER : UNCONTROLLED WHEN PRINTED – PLEASE CHECK THE STATUS OF THE DOCUMENT IN IDM
Change Log
EJMA Calculation Report for Cryostat DNB Port Duct Bellows (7HL9UC)
Version
Latest Status
Issue Date
v0.0
In Work
22 Mar 2022
v1.0
v1.1
v1.2
v1.3
Signed
Signed
Signed
Signed
29 Mar 2022
14 Nov 2022
30 Nov 2022
30 Nov 2022
Description of Change
First version
updated as per new version of load spec
Updated the calculation of the BK+CRICEII load case
One data for the BK+CRICEII has omitted to update, we have updated it.
PDF generated on 30 Nov 2022
DISCLAIMER : UNCONTROLLED WHEN PRINTED – PLEASE CHECK THE STATUS OF THE DOCUMENT IN IDM
Institute of Plasma Physics, Chinese Academy of Sciences
AEROSUN-TOLA Expansion Joint CO,.LTD
EJMA Calculation Report for Cryostat DNB Port
Duct Bellows
Submitted by ASIPP & Aerosun-tola
Abstract
This document is shown the EJMA calculation for cryostat DNB port duct bellow, which includes the codes,
parameter definition, calculation formula, evaluation criteria and calculation results.
File No.
Signatory
Contractor
AEROSUN-TOLA
ASIPP
REC-JS-01
Revision No.
V1.2
Prepared By
(Signature/Date)
Reviewed By
(Signature /Date)
Approved By
(Signature/Date)
2022.11.30
2022.11.30
2022.11.30
2022.11.30
2022.11.30
Page 1 of 23
Revision History:
Revision No.
Date
Descriptions
1.0
2022.3.22
The first version
2.0
2022.5.30
Update the conclusions
3.0
2022.11.8
Update the DNB port duct bellow design parameter and the
calculations
4.0
2022.11.30
Update the calculation of BK+Cr ICE II
Page 2 of 23
Table of Contents
1.
SCOPE........................................................................................................................................................4
2.
OVERVIEW OF LOADS .........................................................................................................................4
3.
ABBREVIATIONS ...................................................................................................................................5
4.
CODES AND REFERENCE....................................................................................................................7
5.
MATERIAL PROPERTIES & ALLOWABLE.....................................................................................8
6.
CALCULATION FORMULA .................................................................................................................8
7.
UNITS.......................................................................................................................................................11
8.
EVALUATION CRITERIA...................................................................................................................11
9.
DESIGN STATEMENT .........................................................................................................................11
10.
EXAMPLE ...........................................................................................................................................12
11.
CONCLUSIONS..................................................................................................................................13
12.
RECOMMENDATIONS ....................................................................................................................17
Page 3 of 23
1. Scope
This document shows the detailed calculation process of the DNB port duct bellow
according to EJMA 10th code.
2. Overview of loads
According to the load specification [2], the combination load cases are defined as following table.
Table 1 - Design conditions for cryostat DNB Port duct Bellows
Event
Cat.
Metal
DNB
temperature
Rad
Tor
Vert
[℃]
max min max min max min
Number
of cycles
NO
I
20
32
-
5
-
16
-
300
BK
I
20
63
-
8
-
34
-
500
NO + VDE II
II
20
42
22
16
-5
24
8
700
NO + Cr ICE II
BK + Cr ICE II
NO + SL-1
BK + SL-1
NO + VDE III
NO + Cr ICE III +
SMHV
BK + Cr ICE III +
SMHV
NO + SL-1 + VDE II
BK + HIG III +
SMHV
BK + LOCA NB III
NO + VDE IV
NO + Cr ICE IV
BK + Cr ICE IV
NO + Cr ICE III +
SL-2
BK + Cr ICE III +
SL-2
BK + HIG III + SL-2
NO+SL2
BK +SL2
II
II
II
II
III
III
20
20
20
20
20
20
42
73
33
64
51
42
30
62
13
37
6
9
7
10
25
6
4
7
-14
0
24
42
21
39
30
37
11
28
1
14
15
15
N/A
5×10
N/A
N/A
III
20
73
68
9
3
54
32
N/A
III
III
20
20
43
67
20
62
18
12
-7
6
29
46
3
23
N/A
N/A
III
IV
IV
IV
IV
20
20
20
20
20
63
51
39
71
43
13
36
8
25
3
6
7
-14
-1
34
30
25
43
41
1
10
N/A
N/A
N/A
N/A
N/A
IV
20
75
67
10
2
59
28
N/A
IV
IV
20
20
20
68
36
67
61
28
59
13
10
13
5
1
4
50
32
49
19
0
18
N/A
N/A
N/A
IV
Page 4 of 23
3. Abbreviations
x =Applied axial movement in compression or extension
y=Applied lateral deflection
Ac=Cross sectional metal area of one bellows convolution (Derived from the eighth or tenth
edition)

q


2

=  2 (rm )  2 [  2(rm )]2  [ w  2(rm )]2  nt p
(Dm)2
Ae = Effective Area = π 4
Cwb = Longitudinal weld joint efficiency factor of bellows from applicable code.
Cp = Factor used in specific design calculations to relate U-shaped bellows convolution segment
behavior to a simple strip beam
Cm = Material strength factor at temperatures below the creep range
= 1.5 for bellows in the annealed condition (without cold work)
= 1.5 (1.5 min., 3.0 max.) for bellows in the as-formed condition (with cold work)
Cd = Factor used in specific design calculations to relate U-shaped bellows convolution segment
behavior to a simple strip beam.
Cf = Factor used in specific design calculations to relate U-shaped bellows convolution segment
behavior to a simple strip beam.
Cθ = Column instability pressure reduction factor based on imposed angular rotation
= 1.0 for universal bellows
Db = Inside diameter of cylindrical tangent and bellows convolutions (mm)
Dm = Mean diameter of bellows convolutions, in (mm)
= Db+w + nt for "U" profile
Sab = Allowable material stress of bellows at design temperature
Sy = Yield strength at design temperature, unless otherwise determined, of the actual bellows
material after completion of bellows forming and any applicable heat treatment (MPa)
0.67CmSymSyh
=
Syc
Syc = Yield strength at room temperature of the bellows material in the annealed condition from the
Page 5 of 23
applicable code or standard reference (MPa)
Syh = Yield strength at design temperature of the bellows material in the annealed condition from
the applicable code or standard reference (MPa)
Sym = Yield strength at room temperature of the actual bellows material in the annealed condition
from the certified test report (MPa)
Eb =Modules of elasticity of bellows at room temperature
EC=Modules of elasticity of reinforcement collar at design temperature
Wb = Elevated temperature weld joint strength reduction factor of bellows from applicable design
code.
Kr = Circumferential stress factor
= The greater of the following but not less than 1.0
2(q + ex) + Kθeθ + ey
2q
2(q ‒ ex) + Kθeθ + ey
2q
Where ex and ey are based on axial extension concurrent with pressure P
Where ex and eyare based on axial compression concurrent with pressure P
Kθ= Angular rotation internal pressure effect factor
eθ + eyp
=
eθ
for single bellows
= 1.0 for universal bellows
e = Total equivalent axial movement per convolution (mm)
eθ = Axial movement per convolution resulting from imposed angular rotation (mm)
ey = Axial movement per convolution resulting from imposed lateral deflection y (mm)
eyp = Axial movement per convolution resulting from internal pressure on a single bellows with
imposed angular rotation (mm)
Lt = Bellows tangent length
Lc = Bellows tangent collar length (mm)
w =Convolution height of bellows
q =Convolution pitch of bellows
rm =Mean radius of bellows convolution
t =Nominal material thickness of one ply
Page 6 of 23
tc = Bellows tangent reinforcing collar material thickness (mm)
tp = Bellows material thickness for one ply, corrected for thinning during forming
(mm)
Db
= t Dm for bellows formed from tubes with inside diameter equal to Db
n =No. of bellows material plies
N =Number of convolutions
Lb =Bellows convoluted length (mm)
=Nq
Lu =Distance between outermost ends of the convolutions in a universal Expansion Joint (mm)
L ∗ = Lu - Lb
Ku = Factor establishing relationship between equivalent axial displacement per convolution due to
lateral deflection and the ratio Lu/ (2Lb)
Ca=2.0 when tangent is fully supported against the pressure
=1.5when tangent is not fully supported against the pressure
fi = Bellows theoretical axial elastic spring rate
rm= Mean radius ofbellows convolution
ric + rir + nt
=
2
ric = The crest convolution inside radius
rir= The root convolution inside radius
P = Pressure (MPa)
Psc = Limiting internal design pressure based on column instability (MPa)
Psi = Limiting design pressure based on in-plane instability and local plasticity (MPa)
α = Inplane instability stress interaction factor
0.5
= 1 + 2δ2 + (1 ‒ 2δ2 + 4δ4)
k = A factor which considers the stiffening effect of the attachment weld and the end convolution
on the pressure capacity of the bellows tangent
=
Lt
1.5 Dbt
If k≥1, use k = 1
4. Codes and reference
The following codes, standards and specifications will be followed:
Page 7 of 23
[1]
[2]
[3]
[4]
Technical Specification of Cryostat NB Port Duct&Cell Bellows, ITER_D_3PA3BW v1_3
HNB_DNB_Bellows_System_Load_Specification, ITER_D_PJ27GU v13
IO-DR-01 Correction of thermal displacement, ITER_D_83JSKX v1.1
EJMA 10th Edition
5. Material properties & allowable
Type：Tied universal expansion joint
Convolution shape： “U” shape
Material：SS 304L
 Design Pressure：Design pressure should refer to load specification [2], see Table 4 and
Table 5 for details.
 Design Temperature：Design Temperature should refer to load specification [2], see Table
24 for details.
Allowable material stress of bellows at design temperature(20℃)： Sabt =115 MPa
Modules of elasticity of bellows at room temperature：
Eb = 172000 MPa
Modules of elasticity of bellows at design temperature(20℃)：
Ebt = 172000 MPa
Convolution height of bellows：
w = 65 mm
Convolution pitch of bellows：
q = 60 mm
Mean radius of bellows convolution：
rm = 4 =15 mm
Nominal material thickness of one ply：
t = 1.0 mm
No. of bellows material plies：
n=2
Number of convolutions：
N=5
q
6. Calculation formula
Expansion Joints may be subjected to axial movement, angular movement, lateral deflection or
any combination of these.
Axial movement for a dual bellows Expansion Joint
ex 
x
2N
Equivalent axial movement per convolution resulting from imposed lateral deflection
Page 8 of 23
L∗
3Dm
ey = 2NLb
1+ L
L∗
b
∗ 2
x
∗
L
1 + 3( L ) (L ± 2)
y (For universal Expansion Joints)
b
The positive sign is valid for axial extension and the negative one for axial compression.
Combining movements：
The effects of combined movement may be calculated as follows:
ey + eθ + |ex|
ec = MAX e K + |e |
θ θ
x
{
}
e + e ‒ |e |
e = MAX{ e K ‒ |e | }
y
e
θ
θ θ
x
x
e=Max (ec,ee)
The equivalent axial movement range per convolution, (e), results from the movement of an expansion
Joint from its initial position in the piping system to the operating position under consideration. When
an Expansion Joint is installed without lateral or angular cold spring, e is the greater of ec or ee as
calculated from the initial to the operating position under consideration. When cold springing is
involved the ec and ec due to the cold spring must be added algebraically to the ec and ee due to
movement from the neutral to the operating position in order to obtain the maximum movement range,
e.
When the bellows is pre-compressed:
E = Max (ec (pre-compressed/extension)+ee (Working condition),ee (pre-compressed/
extension)+ec (Working condition))
Bellows Tangent Circumferential Membrane Stress Due to Pressure
P  Db  nt  Lt Eb k
2  ntEb Lt  Db  nt   tc kEc Lc Dc 
2
S1 
(long side)
Bellows Circumferential Membrane Stress Due to Pressure
S2 
PDm K r q
2 Ac
Bellows Meridional Membrane Stress Due to Pressure:
Page 9 of 23
S3 
Pw
2nt p
Bellows Meridional Bending Stress Due to Pressure:
S4 
Pw  w 

2
 Cp
2n  t p 
Note: The above stresses should be evaluated for pressure capacity as follows:
S1&S2 ≤CwbWbSab
S3+ S4≤ CmSab (Below the Creep Range)
S3+ (S4/1.25)≤Sab (In the Creep Range)
Bellows Meridional Membrane Stress Due to Deflection
S5 
Eb t p 2 e
2 w3c f
Bellows Meridional Bending Stress Due to Deflection
S6 
5 Eb t p e
3w2 cd
Notes: Modulus of elasticity, Eb, in Equations S5 and S6 is at room temperature.
Fatigue life:




c


Nc 
 145St  b 
 f

 c

3.4
(Unit: MPa)
For Austenitic stainless steels, C=1.86×106, b=54000, unless otherwise indicated by specification, a
traditional value, fc =1, is used when providing EJMA calculations.
St  0.7  S3  S 4    S5  S6 
Limiting Internal Design Pressure Based on Column Instability for universal expansion joints (both
ends rigidly supported)
Page 10 of 23
Psc 
0.34 C fiu
4N 2q
Limiting Design Pressure Based on In-plane Instability and Local Plasticity at Temperatures Below
the Creep Range
Psi 
1.3 Ac S y
K r Dm q a
Bellows Theoretical Axial Elastic Spring Rate per Convolution
fiu  1.7
Dm Eb t p 3 n
w3c f
7. Units
The units used in this analysis are listed in Table 2.
Item
Unit name
Length
Millimeter
Temperature
Degrees Centigrade
Pressure
Mega Pa
Area
Square millimeter
Moment of inertia
Moment
Axial/Lateral stiffness
Angular stiffness
Force
Newton
Unit symbol
mm
℃
MPa
mm2
mm4
N.m
N/mm
N.m/deg
N
8. Evaluation criteria
For class I and II conditions, the design of every Expansion Joint must be such that the total
displacement per convolution from all sources does not exceed the rated values:
ec (calculated) ≦ ec (max)= q/2-nt
ee (calculated) ≦ ee (max)=q/2
9. Design Statement
Design parameters of DNB Duct Bellows are listed below:
Height of wave: 65mm;
Pitch of wave: 60mm;
Number of wave: 5*2;
Number of layer: 2*1.0mm;
Shape of flange: Straight
Page 11 of 23
10.Example
This is an example for how-to calculate the ee and ec in colding & operating status.
Use BK condition as example:
X=57mm, y=-46mm, z=34mm
Notice: in EJMA, there is no negative or position value in lateral direction.
1. Colding status: x=0mm, y=24mm, z=-20mm
Axial movement for universal bellows Expansion Joints：
𝑒𝑥 =
𝑥
0
=
=0
2𝑁 2 × 5
Equivalent axial movement per convolution resulting from imposed lateral deflection
L∗
1+ L
694
3(3280 + 60 + 2) 1 + 250 694
y
=
ey = 2NLb
x
2
694 2(694)
2 × 5 × 250
∗
L∗
1 + 3 250
1 + 3( L ) (L ± 2)
3Dm
b
L∗
2
( )
b
=19.62
242 + 20
Combining movements：
The effects of combined movement may be calculated as follows:
ey + eθ + |ex|
19.62 + 0 + |0|
=19.62
ec = MAX e K + |e | = MAX
0 + |0|
θ θ
x
}
{
} {
e + e ‒ |e |
19.62 + 0 ‒ |0|
e = MAX{ e K ‒ |e | } = MAX{
}=19.62
0 ‒ |0|
y
e
θ
θ θ
x
x
2. Operating Status: x=57mm, y=-22mm, z=14mm
Axial movement for universal bellows Expansion Joints：
𝑒𝑥 =
𝑥
57
=
= 5.7
2𝑁 2 × 5
Equivalent axial movement per convolution resulting from imposed lateral deflection
L∗
1+ L
694
694
3(3280 + 60 + 2) 1 + 250
y
=
ey = 2NLb
57
x
2
2
∗
694
2
×
5
×
250
∗
L
1 + 3 250 694 + 2
1 + 3( L ) (L ± 2)
3Dm
b
L∗
( )(
b
)
2
222 + 14
=15.73
Combining movements：
The effects of combined movement may be calculated as follows:
ey + eθ ‒ |ex|
15.73 + 0 ‒ |5.7|
=10.03
ec = MAX e K ‒ |e | = MAX
0 ‒ |5.7|
θ θ
x
{
}
{
}
Page 12 of 23
ey + eθ + |ex|
15.73 + 0 + |5.7|
=21.43
ee = MAX e K + |e | = MAX
0 + |5.7|
θ θ
x
{
}
{
}
so, ec = 19.62, ee = 21.43
11.Conclusions
The calculation summary results are listed in table 4.
Page 13 of 23
Table 3 The evaluation criteria
Event
Cat.
Metal temperature
[℃]
Stress evaluation
Life assessment
criteria
NO
BK
NO + VDE II
NO + Cr ICE II
BK + Cr ICE II
NO + SL-1
BK + SL-1
NO + VDE III
NO + Cr ICE III +
SMHV
BK + Cr ICE III +
SMHV
NO + SL-1 + VDE II
BK + HIG III + SMHV
BK + LOCA NB III
NO + VDE IV
NO + Cr ICE IV
BK + Cr ICE IV
NO + Cr ICE III + SL-2
BK + Cr ICE III + SL-2
BK + HIG III + SL-2
NO+SL-2
BK +SL-2
I
I
II
II
II
II
II
III
III
20
20
20
20
20
20
20
20
20
S1≤CwbSab=115
S2≤CwbSab=115
S3+S4≤CmSab=251.9
Cw=1
Cm=2.19
FEA
FEA
≦q/2 –nt=28
≦q/2 –nt=28
≦q/2 –nt=28
≦q/2 –nt=28
≦q/2 –nt=28
N/A
≦q/2 –nt=28
N/A
N/A
III
20
FEA
N/A
III
III
III
IV
IV
IV
IV
IV
IV
IV
IV
20
20
20
20
20
20
20
20
20
20
20
FEA
FEA
FEA
FEA
FEA
FEA
FEA
FEA
FEA
FEA
FEA
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
300
500
700
15
15
5×10
Page 14 of 23
Evaluation criteria
ec
ee
≤q/2 =30
≤q/2 =30
≤q/2 =30
≤q/2=30
≤q/2=30
≤q/2 =30
Table 4 Calculation results and evaluation results
Event
NO
BK
NO + VDE II
NO + Cr ICE II
BK + Cr ICE II
NO + SL-1
BK + SL-1
Cat.
I
I
II
II
II
II
II
S1
Stress(MPa)
S2
S3+S4
Axial spring
rate
(Kx)
21.38≤CwbSab=115
21.38≤CwbSab=115
21.38≤CwbSab=115
21.38≤CwbSab=115
21.38≤CwbSab=115
21.38≤CwbSab=115
21.38≤CwbSab=115
26.73≤CwbSab=115
27.66≤CwbSab=115
27.81≤CwbSab=115
27.37≤CwbSab=115
28.16≤CwbSab=115
27.31≤CwbSab=115
28.20≤CwbSab=115
74.41≤CmSab=251.9
74.41≤CmSab=251.9
74.41≤CmSab=251.9
74.41≤CmSab=251.9
74.41≤CmSab=251.9
74.41≤CmSab=251.9
74.41≤CmSab=251.9
261.11
261.11
261.11
261.11
261.11
261.11
261.11
Lateral
rate
(Ky)
spring
Life assessment
criteria
1823.52
1909.3
1840.83
1840.83
1943.26
1823.52
1912.65
Page 15 of 23
75926
1240
4453
8598
500
17961
736
Equivalent displacement
ec
ee
8.69
21.1
15.56
13.42
26.51
11.47
24.03
8.69
15.8
14.46
12.32
19.2
11.47
18.53
Result of
evaluation
qualified
qualified
qualified
qualified
qualified
qualified
qualified
12.Recommendations
According to the result of EJMA calculation:
 All the design conditions in Technical Specifications were qualified except the displacement
in Cat.III&IV which will be verified in following by FEA.
Page 16 of 23
Appendix 1-NO
Page 17 of 23
Appendix 2-BK
Page 18 of 23
Appendix 3-NO + VDE II
Page 19 of 23
Appendix 4- NO + Cr ICE II
Page 20 of 23
Appendix 5- BK+CRICEII
Page 21 of 23
Appendix 6-NO + SL-1
Page 22 of 23
Appendix 7- BK + SL-1
Page 23 of 23